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<div><h2 class="title">
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<a name="special_function_error_rates_rep"></a>Special Function Error Rates Report</h2></div>
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<a name="special_function_error_rates_rep.legal"></a><p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<div class="toc">
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<p><b>Table of Contents</b></p>
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<dl>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta">beta</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta_incomplete_">beta
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(incomplete)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_betac">betac</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_binomial_coefficient">binomial_coefficient</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_boost_math_powm1">boost::math::powm1</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cbrt">cbrt</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cos_pi">cos_pi</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i">cyl_bessel_i</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_">cyl_bessel_i
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(integer orders)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime">cyl_bessel_i_prime</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_">cyl_bessel_i_prime
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(integer orders)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j">cyl_bessel_j</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_">cyl_bessel_j
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(integer orders)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime">cyl_bessel_j_prime</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_">cyl_bessel_j_prime
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(integer orders)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k">cyl_bessel_k</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_">cyl_bessel_k
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(integer orders)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime">cyl_bessel_k_prime</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_">cyl_bessel_k_prime
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(integer orders)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann">cyl_neumann</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_">cyl_neumann
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(integer orders)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime">cyl_neumann_prime</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_">cyl_neumann_prime
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(integer orders)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_digamma">digamma</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1">ellint_1</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1_complete_">ellint_1
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(complete)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2">ellint_2</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2_complete_">ellint_2
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(complete)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3">ellint_3</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3_complete_">ellint_3
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(complete)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d">ellint_d</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d_complete_">ellint_d
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(complete)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rc">ellint_rc</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rd">ellint_rd</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rf">ellint_rf</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rg">ellint_rg</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rj">ellint_rj</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf">erf</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf_inv">erf_inv</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc">erfc</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc_inv">erfc_inv</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_Ei_">expint
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(Ei)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_En_">expint
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(En)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expm1">expm1</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p">gamma_p</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inv">gamma_p_inv</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inva">gamma_p_inva</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q">gamma_q</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inv">gamma_q_inv</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inva">gamma_q_inva</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_hermite">hermite</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_heuman_lambda">heuman_lambda</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta">ibeta</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inv">ibeta_inv</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inva">ibeta_inva</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_invb">ibeta_invb</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac">ibetac</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inv">ibetac_inv</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inva">ibetac_inva</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_invb">ibetac_invb</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_cn">jacobi_cn</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_dn">jacobi_dn</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_sn">jacobi_sn</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_zeta">jacobi_zeta</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_">laguerre(n,
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m, x)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_x_">laguerre(n,
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x)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p">legendre_p</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p_associated_">legendre_p
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(associated)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_q">legendre_q</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_lgamma">lgamma</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_log1p">log1p</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF">non
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central beta CDF</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement">non
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central beta CDF complement</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF">non
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central chi squared CDF</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement">non
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central chi squared CDF complement</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF">non
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central t CDF</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement">non
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central t CDF complement</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_owens_t">owens_t</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_polygamma">polygamma</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_powm1">powm1</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sin_pi">sin_pi</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel">sph_bessel</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel_prime">sph_bessel_prime</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann">sph_neumann</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann_prime">sph_neumann_prime</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i">spherical_harmonic_i</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r">spherical_harmonic_r</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sqrt1pm1">sqrt1pm1</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma">tgamma</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma1pm1">tgamma1pm1</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio">tgamma_delta_ratio</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_">tgamma
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(incomplete)</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_lower">tgamma_lower</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_ratio">tgamma_ratio</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_trigamma">trigamma</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_zeta">zeta</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.error_logs">Error Logs</a></span></dt>
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<dt><span class="section"><a href="index.html#special_function_error_rates_rep.all_the_tables">Tables</a></span></dt>
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</dl>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="special_function_error_rates_rep.section_beta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta" title="beta">beta</a>
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</h2></div></div></div>
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<div class="table">
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<a name="special_function_error_rates_rep.section_beta.table_beta"></a><p class="title"><b>Table 1. Error rates for beta</b></p>
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<div class="table-contents"><table class="table" summary="Error rates for beta">
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<colgroup>
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<col>
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<col>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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</th>
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<th>
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<p>
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GNU C++ version 7.1.0<br> linux<br> double
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</p>
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</th>
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<th>
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<p>
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GNU C++ version 7.1.0<br> linux<br> long double
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</p>
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</th>
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<th>
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<p>
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Sun compiler version 0x5150<br> Sun Solaris<br> long double
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</p>
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</th>
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<th>
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<p>
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Microsoft Visual C++ version 14.1<br> Win32<br> double
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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Beta Function: Small Values
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
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2.1:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And
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other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
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Max = 1.14ε (Mean = 0.574ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 2.86ε (Mean = 1.22ε)</span><br> <br>
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(<span class="emphasis"><em><cmath>:</em></span> Max = 364ε (Mean = 76.2ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 2.86ε (Mean = 1.22ε)</span>
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 2.23ε (Mean = 1.14ε)</span>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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Beta Function: Medium Values
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 0.978ε (Mean = 0.0595ε)</span><br> <br>
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(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br>
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(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03ε (Mean = 265ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 61.4ε (Mean = 19.4ε)</span><br> <br>
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(<span class="emphasis"><em><cmath>:</em></span> Max = 1.07e+03ε (Mean = 264ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 107ε (Mean = 24.5ε)</span>
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 96.5ε (Mean = 22.4ε)</span>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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Beta Function: Divergent Values
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 176ε (Mean = 28ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.99ε (Mean = 2.44ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 128ε (Mean = 23.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.8ε (Mean = 2.71ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.4ε (Mean = 2.19ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_beta_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta_incomplete_" title="beta (incomplete)">beta
|
|
(incomplete)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_beta_incomplete_.table_beta_incomplete_"></a><p class="title"><b>Table 2. Error rates for beta (incomplete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.1ε (Mean = 2.32ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.7ε (Mean = 3.19ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.94ε (Mean = 2.17ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.568ε (Mean = 0.0254ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 69.2ε (Mean = 13.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 174ε (Mean = 25ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 90ε (Mean = 12.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.0325ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 633ε (Mean = 29.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.0323ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.6ε (Mean = 3.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 51.8ε (Mean = 11ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26ε (Mean = 6.28ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_betac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_betac" title="betac">betac</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_betac.table_betac"></a><p class="title"><b>Table 3. Error rates for betac</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for betac">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.92ε (Mean = 2.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.2ε (Mean = 2.94ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.94ε (Mean = 2.06ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.949ε (Mean = 0.098ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 63.5ε (Mean = 13.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 97.6ε (Mean = 24.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 90.6ε (Mean = 14.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.72e+03ε (Mean = 113ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.1ε (Mean = 3.65ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 103ε (Mean = 17.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26.2ε (Mean = 6.36ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_binomial_coefficient"></a><a class="link" href="index.html#special_function_error_rates_rep.section_binomial_coefficient" title="binomial_coefficient">binomial_coefficient</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_binomial_coefficient.table_binomial_coefficient"></a><p class="title"><b>Table 4. Error rates for binomial_coefficient</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Binomials: small arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.369ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.369ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Binomials: large arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.939ε (Mean = 0.314ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26.6ε (Mean = 6.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 53.2ε (Mean = 10.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 37.2ε (Mean = 7.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_boost_math_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_boost_math_powm1" title="boost::math::powm1">boost::math::powm1</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_boost_math_powm1.table_boost_math_powm1"></a><p class="title"><b>Table 5. Error rates for boost::math::powm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
powm1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.04ε (Mean = 0.493ε))<br>
|
|
<br> <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.04ε (Mean = 0.493ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06ε (Mean = 0.425ε))<br>
|
|
<br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06ε (Mean = 0.425ε))<br>
|
|
<br> <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.88ε (Mean = 0.49ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.88ε (Mean = 0.49ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.486ε))<br>
|
|
<br> <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cbrt"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cbrt" title="cbrt">cbrt</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cbrt.table_cbrt"></a><p class="title"><b>Table 6. Error rates for cbrt</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cbrt">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
cbrt Function
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε))
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cos_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cos_pi" title="cos_pi">cos_pi</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cos_pi.table_cos_pi"></a><p class="title"><b>Table 7. Error rates for cos_pi</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cos_pi">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.284ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi near integers and half integers
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.298ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i" title="cyl_bessel_i">cyl_bessel_i</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_i.table_cyl_bessel_i"></a><p class="title"><b>Table 8. Error rates for cyl_bessel_i</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.661ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.762ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.64ε (Mean = 0.202ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.767ε (Mean = 0.398ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel In: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 140ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Iv: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 3.53ε (Mean = 1.39ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 616ε (Mean = 221ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.12ε (Mean = 1.95ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.97ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel In: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 7.37ε (Mean = 2.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.62ε (Mean = 1.06ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 645ε (Mean = 132ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 176ε (Mean = 39.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.67ε (Mean = 1.88ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Iv: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.35ε (Mean = 1.62ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.05e+03ε (Mean = 224ε)
|
|
<a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 283ε (Mean = 88.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.46ε (Mean = 1.71ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Iv: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 6.66ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 118ε (Mean = 57.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 6.59ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.67ε (Mean = 1.64ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_" title="cyl_bessel_i (integer orders)">cyl_bessel_i
|
|
(integer orders)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 9. Error rates for cyl_bessel_i (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.661ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.762ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.64ε (Mean = 0.202ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.767ε (Mean = 0.398ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel In: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 140ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime" title="cyl_bessel_i_prime">cyl_bessel_i_prime</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 10. Error rates for cyl_bessel_i_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.354ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.36ε (Mean = 0.782ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'n: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 701ε (Mean = 212ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'v: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.512ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.76e+03ε (Mean = 1.19e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'n: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.95ε (Mean = 1.06ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 195ε (Mean = 37.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.85ε (Mean = 1.82ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'v: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.1ε (Mean = 2.93ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 336ε (Mean = 68.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14ε (Mean = 2.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'v: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.5ε (Mean = 26.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_" title="cyl_bessel_i_prime (integer orders)">cyl_bessel_i_prime
|
|
(integer orders)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 11. Error rates for cyl_bessel_i_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.354ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.36ε (Mean = 0.782ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'n: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 701ε (Mean = 212ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_j"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j" title="cyl_bessel_j">cyl_bessel_j</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_j.table_cyl_bessel_j"></a><p class="title"><b>Table 12. Error rates for cyl_bessel_j</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.52ε (Mean = 1.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data (Tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean =
|
|
1.96e+08ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.73ε (Mean = 0.976ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data (tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean =
|
|
1.58e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean
|
|
= 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 112ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 5.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 4.11ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 3.49e+05ε (Mean = 8.09e+04ε)
|
|
<a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10ε (Mean = 2.24ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.39e+05ε (Mean = 5.37e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 4.22ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.9ε (Mean = 3.89ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 34.9ε (Mean = 17.4ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 5.9ε (Mean = 3.76ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 607ε (Mean = 305ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.31ε (Mean = 5.52ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50.8ε (Mean = 3.69ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.12e+03ε (Mean = 88.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 3.93ε (Mean = 1.22ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 99.6ε (Mean = 22ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 17.5ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.4ε (Mean = 1.68ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 501ε (Mean = 52.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 6.74ε (Mean = 1.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 260ε (Mean = 34ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.24ε (Mean = 1.17ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Random Data (Tricky large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 5.01e+17ε (Mean
|
|
= 6.23e+16ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 71.6ε (Mean = 11.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 785ε (Mean = 97.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.2ε (Mean = 8.67ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_" title="cyl_bessel_j (integer orders)">cyl_bessel_j
|
|
(integer orders)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 13. Error rates for cyl_bessel_j (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean =
|
|
1.96e+08ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span><br>
|
|
<br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max
|
|
= 2.54e+08ε (Mean = 1.04e+08ε))</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data (tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean =
|
|
1.58e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+07ε (Mean
|
|
= 6.5e+06ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean
|
|
= 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 112ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime" title="cyl_bessel_j_prime">cyl_bessel_j_prime</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 14. Error rates for cyl_bessel_j_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.82ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data (Tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.34ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data (tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 287ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 288ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14ε (Mean = 6.13ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21.5ε (Mean = 4.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 9.31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 9.32ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.7ε (Mean = 8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 989ε (Mean = 495ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 989ε (Mean = 495ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.9ε (Mean = 1.61ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.3ε (Mean = 1.85ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 79.4ε (Mean = 16.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.34ε (Mean = 0.999ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.885ε (Mean = 0.033ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 139ε (Mean = 6.47ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 279ε (Mean = 27.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 176ε (Mean = 9.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Random Data (Tricky large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 474ε (Mean = 62.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 474ε (Mean = 64.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 379ε (Mean = 45.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_" title="cyl_bessel_j_prime (integer orders)">cyl_bessel_j_prime
|
|
(integer orders)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 15. Error rates for cyl_bessel_j_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.82ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.34ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data (tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 287ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 288ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN': Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14ε (Mean = 6.13ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_k"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k" title="cyl_bessel_k">cyl_bessel_k</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_k.table_cyl_bessel_k"></a><p class="title"><b>Table 16. Error rates for cyl_bessel_k</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.833ε (Mean = 0.601ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.436ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.552ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.894ε (Mean = 0.516ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kn: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 8.48ε (Mean = 2.98ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.6ε (Mean = 1.21ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kv: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.58ε (Mean = 2.39ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 13ε (Mean = 4.81ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 3.15ε (Mean = 1.35ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.21ε (Mean = 2.53ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.78ε (Mean = 2.19ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kv: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 42.3ε (Mean = 19.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 84.6ε (Mean = 37.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.3ε (Mean = 21ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.8ε (Mean = 26.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kn: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.55ε (Mean = 1.12ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71ε (Mean = 1.76ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 7.47ε (Mean = 1.34ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.55ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.34ε (Mean = 1.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kv: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71ε (Mean = 1.47ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 7.37ε (Mean = 1.49ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.88ε (Mean = 1.47ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.33ε (Mean = 1.62ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_" title="cyl_bessel_k (integer orders)">cyl_bessel_k
|
|
(integer orders)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 17. Error rates for cyl_bessel_k (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.833ε (Mean = 0.601ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.436ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.552ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kn: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 8.48ε (Mean = 2.98ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.6ε (Mean = 1.21ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime" title="cyl_bessel_k_prime">cyl_bessel_k_prime</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 18. Error rates for cyl_bessel_k_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.761ε (Mean = 0.444ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'n: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.17ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'v: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.94ε (Mean = 2.44ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.94ε (Mean = 2.34ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.94ε (Mean = 1.47ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'v: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.2ε (Mean = 42.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 58.7ε (Mean = 42.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.6ε (Mean = 11.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'n: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.45ε (Mean = 1.19ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.45ε (Mean = 1.19ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.67ε (Mean = 1.73ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'v: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.95ε (Mean = 1.53ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.95ε (Mean = 1.52ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.32ε (Mean = 1.65ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_" title="cyl_bessel_k_prime (integer orders)">cyl_bessel_k_prime
|
|
(integer orders)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 19. Error rates for cyl_bessel_k_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.761ε (Mean = 0.444ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'n: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.17ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann" title="cyl_neumann">cyl_neumann</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_neumann.table_cyl_neumann"></a><p class="title"><b>Table 20. Error rates for cyl_neumann</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 167ε (Mean = 56.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.61ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 193ε (Mean = 64.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.72ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yn: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean
|
|
= 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.24e+04ε (Mean = 4e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 35ε (Mean = 11.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yv: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.7ε (Mean = 4.93ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.49e+15ε (Mean
|
|
= 1.05e+15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 243ε (Mean = 73.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.7ε (Mean = 5.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.89ε (Mean = 3.27ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yv: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.682ε (Mean = 0.335ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 1.33ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.682ε (Mean = 0.423ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y0 and Y1: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.8ε (Mean = 3.04ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.59e+03ε (Mean = 500ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 83ε (Mean = 14.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.8ε (Mean = 3.04ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.17ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yn: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 338ε (Mean = 27.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 4.01e+03ε (Mean = 348ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 691ε (Mean = 67.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 338ε (Mean = 27.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 117ε (Mean = 10.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yv: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.23e+03ε (Mean = 69.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_" title="cyl_neumann (integer orders)">cyl_neumann
|
|
(integer orders)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 21. Error rates for cyl_neumann (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 167ε (Mean = 56.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+03ε (Mean = 1.81e+03ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 193ε (Mean = 64.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+04ε (Mean = 6.2e+03ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yn: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean
|
|
= 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 35ε (Mean = 11.9ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 2.49e+05ε (Mean = 8.14e+04ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime" title="cyl_neumann_prime">cyl_neumann_prime</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_neumann_prime.table_cyl_neumann_prime"></a><p class="title"><b>Table 22. Error rates for cyl_neumann_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 37.1ε (Mean = 12.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34ε (Mean = 11.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'n: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 18.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 21.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 563ε (Mean = 178ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'v: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21.5ε (Mean = 6.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 13.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 13.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.7ε (Mean = 10.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'v: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.627ε (Mean = 0.237ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'0 and Y'1: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.95ε (Mean = 1.36ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'n: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 621ε (Mean = 36ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'v: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56.8ε (Mean = 2.59ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.23e+04ε (Mean = 1.13e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_" title="cyl_neumann_prime (integer orders)">cyl_neumann_prime
|
|
(integer orders)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 23. Error rates for cyl_neumann_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 37.1ε (Mean = 12.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34ε (Mean = 11.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'n: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 18.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 21.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 563ε (Mean = 178ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_digamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_digamma" title="digamma">digamma</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_digamma.table_digamma"></a><p class="title"><b>Table 24. Error rates for digamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for digamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.18ε (Mean = 0.331ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.98ε (Mean = 0.369ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Near the Positive Root
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135ε (Mean = 11.9ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 2.02e+03ε (Mean = 256ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.37ε (Mean = 0.477ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.471ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.997ε (Mean = 0.527ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Near Zero
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.17ε (Mean = 0.564ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.953ε (Mean = 0.337ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Negative Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 180ε (Mean = 13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 180ε (Mean = 13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 214ε (Mean = 16.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Values near 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.592ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.592ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Integer arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 4.33ε (Mean = 0.982ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.452ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Half integer arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 46.2ε (Mean = 7.24ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.78ε (Mean = 0.314ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1" title="ellint_1">ellint_1</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_1.table_ellint_1"></a><p class="title"><b>Table 25. Error rates for ellint_1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral F: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.919ε (Mean = 0.544ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.94ε (Mean = 0.509ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.919ε (Mean = 0.542ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral F: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.99ε (Mean = 0.797ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.561ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.26ε (Mean = 0.631ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_1_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1_complete_" title="ellint_1 (complete)">ellint_1
|
|
(complete)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_1_complete_.table_ellint_1_complete_"></a><p class="title"><b>Table 26. Error rates for ellint_1 (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral K: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.623ε (Mean = 0.393ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.887ε (Mean = 0.296ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.915ε (Mean = 0.547ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral K: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32ε (Mean = 0.688ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.473ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.958ε (Mean = 0.408ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_2"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2" title="ellint_2">ellint_2</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_2.table_ellint_2"></a><p class="title"><b>Table 27. Error rates for ellint_2</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_2">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.63ε (Mean = 0.325ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.656ε (Mean = 0.317ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.727ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.4ε (Mean = 1.16ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 3.08e+04ε (Mean = 3.84e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.632ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.23ε (Mean = 0.639ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Small Angles
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.5ε (Mean = 0.118ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.283ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 2ε (Mean = 0.333ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.283ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.421ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_2_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2_complete_" title="ellint_2 (complete)">ellint_2
|
|
(complete)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_2_complete_.table_ellint_2_complete_"></a><p class="title"><b>Table 28. Error rates for ellint_2 (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 170ε (Mean = 55.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.469ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.615ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.34ε (Mean = 1.18ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.49e+04ε (Mean = 3.39e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.629ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.71ε (Mean = 0.553ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_3"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3" title="ellint_3">ellint_3</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_3.table_ellint_3"></a><p class="title"><b>Table 29. Error rates for ellint_3</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_3">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral PI: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 475ε (Mean = 86.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 565ε (Mean = 102ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral PI: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.37e+20ε (Mean
|
|
= 3.47e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 633ε (Mean = 50.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.49ε (Mean = 0.885ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.33ε (Mean = 0.971ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral PI: Large Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.52e+18ε (Mean
|
|
= 4.83e+17ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1ε (Mean = 7.77ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.7ε (Mean = 0.892ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.86ε (Mean = 0.944ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_3_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3_complete_" title="ellint_3 (complete)">ellint_3
|
|
(complete)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_3_complete_.table_ellint_3_complete_"></a><p class="title"><b>Table 30. Error rates for ellint_3 (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Complete Elliptic Integral PI: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 6.31e+20ε (Mean
|
|
= 1.53e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.4ε (Mean = 0.575ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.971ε (Mean = 0.464ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Complete Elliptic Integral PI: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 8.78e+20ε (Mean
|
|
= 1.02e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 24ε (Mean = 2.99ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.4ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.46ε (Mean = 0.657ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_d"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d" title="ellint_d">ellint_d</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_d.table_ellint_d"></a><p class="title"><b>Table 31. Error rates for ellint_d</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_d">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.862ε (Mean = 0.568ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.862ε (Mean = 0.457ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral D: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.01ε (Mean = 0.928ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.87ε (Mean = 0.805ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_d_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d_complete_" title="ellint_d (complete)">ellint_d
|
|
(complete)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_d_complete_.table_ellint_d_complete_"></a><p class="title"><b>Table 32. Error rates for ellint_d (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral D: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.355ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_rc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rc" title="ellint_rc">ellint_rc</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_rc.table_ellint_rc"></a><p class="title"><b>Table 33. Error rates for ellint_rc</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
RC: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.4ε (Mean = 0.624ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.433ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.962ε (Mean = 0.407ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_rd"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rd" title="ellint_rd">ellint_rd</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_rd.table_ellint_rd"></a><p class="title"><b>Table 34. Error rates for ellint_rd</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.59ε (Mean = 0.878ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.73ε (Mean = 0.831ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 0.803ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88ε (Mean = 0.839ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.65ε (Mean = 0.82ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 16.5ε (Mean = 0.843ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = y
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74ε (Mean = 0.84ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.85ε (Mean = 0.865ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.51ε (Mean = 0.816ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = 0, y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2ε (Mean = 0.656ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.19ε (Mean = 0.522ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.16ε (Mean = 0.497ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.03ε (Mean = 0.418ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.85ε (Mean = 0.781ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.79ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.64ε (Mean = 0.894ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_rf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rf" title="ellint_rf">ellint_rf</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_rf.table_ellint_rf"></a><p class="title"><b>Table 35. Error rates for ellint_rf</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.73ε (Mean = 0.804ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.54ε (Mean = 0.674ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.02ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: x = y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.999ε (Mean = 0.34ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.345ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.34ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: x = y or y = z or x = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89ε (Mean = 0.749ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.21ε (Mean = 0.394ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: x = 0, y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.29ε (Mean = 0.527ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.894ε (Mean = 0.338ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.407ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: z = 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.54ε (Mean = 0.781ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.539ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.587ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_rg"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rg" title="ellint_rg">ellint_rg</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_rg.table_ellint_rg"></a><p class="title"><b>Table 36. Error rates for ellint_rg</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983ε (Mean = 0.0172ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.95ε (Mean = 0.951ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.65ε (Mean = 0.929ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: two values 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: All values the same or zero
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.288ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.06ε (Mean = 0.348ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: two values the same
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594ε (Mean = 0.0103ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.51ε (Mean = 0.404ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.374ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: one value zero
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.14ε (Mean = 0.722ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.674ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ellint_rj"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rj" title="ellint_rj">ellint_rj</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ellint_rj.table_ellint_rj"></a><p class="title"><b>Table 37. Error rates for ellint_rj</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 186ε (Mean = 6.67ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 215ε (Mean = 7.66ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: 4 Equal Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.03ε (Mean = 0.418ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: 3 Equal Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.96ε (Mean = 1.06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 20.8ε (Mean = 0.986ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 39.9ε (Mean = 1.17ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: 2 Equal Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57ε (Mean = 0.754ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 220ε (Mean = 6.64ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 214ε (Mean = 5.28ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: Equal z and p
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62ε (Mean = 0.699ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 17.2ε (Mean = 1.16ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 16.1ε (Mean = 1.14ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_erf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf" title="erf">erf</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_erf.table_erf"></a><p class="title"><b>Table 38. Error rates for erf</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erf">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06ε (Mean = 0.319ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.31ε (Mean = 0.368ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.197ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.171ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 1.19ε (Mean = 0.244ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max
|
|
= 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_erf_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf_inv" title="erf_inv">erf_inv</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_erf_inv.table_erf_inv"></a><p class="title"><b>Table 39. Error rates for erf_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erf_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse Erf Function
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.08ε (Mean = 0.395ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.09ε (Mean = 0.502ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_erfc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc" title="erfc">erfc</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_erfc.table_erfc"></a><p class="title"><b>Table 40. Error rates for erfc</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erfc">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max
|
|
= 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01ε (Mean = 0.485ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64ε (Mean = 0.662ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.76ε (Mean = 0.38ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9ε (Mean = 0.472ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_erfc_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc_inv" title="erfc_inv">erfc_inv</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_erfc_inv.table_erfc_inv"></a><p class="title"><b>Table 41. Error rates for erfc_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Inverse Erfc Function
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.397ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.08ε (Mean = 0.403ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.491ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Inverse Erfc Function: extreme values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_expint_Ei_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_Ei_" title="expint (Ei)">expint
|
|
(Ei)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_expint_Ei_.table_expint_Ei_"></a><p class="title"><b>Table 42. Error rates for expint (Ei)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral Ei
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96ε (Mean = 0.703ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.05ε (Mean = 0.835ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.43ε (Mean = 0.54ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral Ei: double exponent range
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.612ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.72ε (Mean = 0.607ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.66ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral Ei: long exponent range
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.98ε (Mean = 0.575ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_expint_En_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_En_" title="expint (En)">expint
|
|
(En)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_expint_En_.table_expint_En_"></a><p class="title"><b>Table 43. Error rates for expint (En)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for expint (En)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral En
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5ε (Mean = 17.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.16ε (Mean = 1.85ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral En: small z values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 115ε (Mean = 23.6ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.62ε (Mean = 0.531ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral E1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988ε (Mean = 0.469ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.965ε (Mean = 0.414ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.965ε (Mean = 0.408ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.988ε (Mean = 0.486ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_expm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expm1" title="expm1">expm1</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_expm1.table_expm1"></a><p class="title"><b>Table 44. Error rates for expm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for expm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Random test data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.992ε (Mean = 0.402ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.992ε (Mean = 0.402ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793ε (Mean = 0.126ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.428ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.496ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε))
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_gamma_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p" title="gamma_p">gamma_p</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_gamma_p.table_gamma_p"></a><p class="title"><b>Table 45. Error rates for gamma_p</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_p">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 389ε (Mean = 44ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 41.6ε (Mean = 8.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 239ε (Mean = 30.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 35.1ε (Mean = 6.98ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.01ε (Mean = 0.306ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.464ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.461ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.54ε (Mean = 0.439ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.11e+03ε (Mean = 67.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 243ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 66.2ε (Mean = 12.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.8ε (Mean = 2.66ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 71.6ε (Mean = 9.47ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 13ε (Mean = 2.97ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_gamma_p_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inv" title="gamma_p_inv">gamma_p_inv</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_gamma_p_inv.table_gamma_p_inv"></a><p class="title"><b>Table 46. Error rates for gamma_p_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88ε (Mean = 0.868ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 0.406ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.466ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.71ε (Mean = 0.34ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 0.816ε (Mean = 0.0874ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.924ε (Mean = 0.108ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547ε (Mean = 61.6ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.17e+03ε (Mean = 1.45e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.09e+04ε (Mean = 1.3e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.1e+03ε (Mean = 131ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_gamma_p_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inva" title="gamma_p_inva">gamma_p_inva</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_gamma_p_inva.table_gamma_p_inva"></a><p class="title"><b>Table 47. Error rates for gamma_p_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Incomplete gamma inverses.
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.87ε (Mean = 1.15ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.08ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.92ε (Mean = 1.03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_gamma_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q" title="gamma_q">gamma_q</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_gamma_q.table_gamma_q"></a><p class="title"><b>Table 48. Error rates for gamma_q</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_q">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 131ε (Mean = 12.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 32.3ε (Mean = 6.61ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 199ε (Mean = 26.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.7ε (Mean = 4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6ε (Mean = 11ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45ε (Mean = 0.885ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45ε (Mean = 0.819ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.26ε (Mean = 0.74ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.02e+03ε (Mean = 62.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 469ε (Mean = 31.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 138ε (Mean = 16.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.1ε (Mean = 2.07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 54.7ε (Mean = 6.16ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.72ε (Mean = 1.48ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_gamma_q_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inv" title="gamma_q_inv">gamma_q_inv</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_gamma_q_inv.table_gamma_q_inv"></a><p class="title"><b>Table 49. Error rates for gamma_q_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66ε (Mean = 0.792ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.2ε (Mean = 0.627ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.2ε (Mean = 0.683ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.88ε (Mean = 0.469ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894ε (Mean = 0.106ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415ε (Mean = 48.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.28e+03ε (Mean = 1.09e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 451ε (Mean = 64.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_gamma_q_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inva" title="gamma_q_inva">gamma_q_inva</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_gamma_q_inva.table_gamma_q_inva"></a><p class="title"><b>Table 50. Error rates for gamma_q_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Incomplete gamma inverses.
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.42ε (Mean = 1.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.86ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.05ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_hermite"></a><a class="link" href="index.html#special_function_error_rates_rep.section_hermite" title="hermite">hermite</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_hermite.table_hermite"></a><p class="title"><b>Table 51. Error rates for hermite</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for hermite">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Hermite Polynomials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.46ε (Mean = 1.41ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_heuman_lambda"></a><a class="link" href="index.html#special_function_error_rates_rep.section_heuman_lambda" title="heuman_lambda">heuman_lambda</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_heuman_lambda.table_heuman_lambda"></a><p class="title"><b>Table 52. Error rates for heuman_lambda</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.08ε (Mean = 0.734ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Heuman Lambda: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.82ε (Mean = 0.609ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.82ε (Mean = 0.608ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.12ε (Mean = 0.588ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ibeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta" title="ibeta">ibeta</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ibeta.table_ibeta"></a><p class="title"><b>Table 53. Error rates for ibeta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 22.9ε (Mean = 3.35ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.97ε (Mean = 2.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21.3ε (Mean = 2.75ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.4ε (Mean = 1.93ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 232ε (Mean = 27.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50ε (Mean = 12.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 124ε (Mean = 18.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 106ε (Mean = 16.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 574ε (Mean = 49.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.32e+03ε (Mean = 68.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 62.2ε (Mean = 8.95ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.45ε (Mean = 0.814ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 44.5ε (Mean = 10.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.85ε (Mean = 0.791ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ibeta_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inv" title="ibeta_inv">ibeta_inv</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ibeta_inv.table_ibeta_inv"></a><p class="title"><b>Table 54. Error rates for ibeta_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11ε (Mean = 0.345ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121ε (Mean
|
|
= 3.28e+119ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.8e+04ε (Mean = 2.66e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.07e+04ε (Mean = 2.86e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.59e+03ε (Mean = 277ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ibeta_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inva" title="ibeta_inva">ibeta_inva</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ibeta_inva.table_ibeta_inva"></a><p class="title"><b>Table 55. Error rates for ibeta_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 377ε (Mean = 24.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 438ε (Mean = 31.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 242ε (Mean = 22.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ibeta_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_invb" title="ibeta_invb">ibeta_invb</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ibeta_invb.table_ibeta_invb"></a><p class="title"><b>Table 56. Error rates for ibeta_invb</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.765ε (Mean = 0.0422ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 407ε (Mean = 27.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 407ε (Mean = 24.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 409ε (Mean = 19.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ibetac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac" title="ibetac">ibetac</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ibetac.table_ibetac"></a><p class="title"><b>Table 57. Error rates for ibetac</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 22.4ε (Mean = 3.67ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.6ε (Mean = 2.22ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 13.8ε (Mean = 2.68ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.94ε (Mean = 1.71ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 204ε (Mean = 25.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 73.9ε (Mean = 11.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 132ε (Mean = 19.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56.7ε (Mean = 14.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.981ε (Mean = 0.0573ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889ε (Mean = 68.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.31e+04ε (Mean = 2.04e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.88e+03ε (Mean = 82.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 84.6ε (Mean = 18ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.34ε (Mean = 1.11ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 107ε (Mean = 17.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.37ε (Mean = 1.03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ibetac_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inv" title="ibetac_inv">ibetac_inv</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ibetac_inv.table_ibetac_inv"></a><p class="title"><b>Table 58. Error rates for ibetac_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.977ε (Mean = 0.0976ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132ε (Mean
|
|
= 8.65e+130ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.88e+04ε (Mean = 3.16e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.05e+04ε (Mean = 3.33e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.93e+03ε (Mean = 198ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ibetac_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inva" title="ibetac_inva">ibetac_inva</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ibetac_inva.table_ibetac_inva"></a><p class="title"><b>Table 59. Error rates for ibetac_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.683ε (Mean = 0.0314ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 382ε (Mean = 22.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 315ε (Mean = 23.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 408ε (Mean = 26.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_ibetac_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_invb" title="ibetac_invb">ibetac_invb</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_ibetac_invb.table_ibetac_invb"></a><p class="title"><b>Table 60. Error rates for ibetac_invb</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 317ε (Mean = 19.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 369ε (Mean = 22.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 271ε (Mean = 16.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_jacobi_cn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_cn" title="jacobi_cn">jacobi_cn</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_jacobi_cn.table_jacobi_cn"></a><p class="title"><b>Table 61. Error rates for jacobi_cn</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 71.6ε (Mean = 19.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 71.6ε (Mean = 19.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 45.8ε (Mean = 11.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43ε (Mean = 0.803ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.68ε (Mean = 0.443ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.68ε (Mean = 0.454ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.83ε (Mean = 0.455ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.4ε (Mean = 0.594ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.4ε (Mean = 0.602ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26.2ε (Mean = 1.17ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Modulus near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 675ε (Mean = 87.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 675ε (Mean = 86.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 513ε (Mean = 126ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Large Phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03ε (Mean = 477ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.27e+04ε (Mean = 1.93e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_jacobi_dn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_dn" title="jacobi_dn">jacobi_dn</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_jacobi_dn.table_jacobi_dn"></a><p class="title"><b>Table 62. Error rates for jacobi_dn</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 49ε (Mean = 14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 49ε (Mean = 14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34.3ε (Mean = 8.71ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3ε (Mean = 0.61ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.473ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.481ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.52ε (Mean = 0.466ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 22.4ε (Mean = 0.777ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 22.4ε (Mean = 0.763ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 16.1ε (Mean = 0.685ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Modulus near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.24e+03ε (Mean = 482ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Large Phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 22ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.67e+04ε (Mean = 1e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_jacobi_sn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_sn" title="jacobi_sn">jacobi_sn</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_jacobi_sn.table_jacobi_sn"></a><p class="title"><b>Table 63. Error rates for jacobi_sn</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 341ε (Mean = 80.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 341ε (Mean = 80.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 481ε (Mean = 113ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.02ε (Mean = 1.07ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.01ε (Mean = 0.584ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.01ε (Mean = 0.593ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.92ε (Mean = 0.567ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.11ε (Mean = 0.385ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Modulus near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 109ε (Mean = 7.35ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 109ε (Mean = 7.38ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.2ε (Mean = 1.85ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Large Phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.36e+04ε (Mean = 2.54e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_jacobi_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_zeta" title="jacobi_zeta">jacobi_zeta</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_jacobi_zeta.table_jacobi_zeta"></a><p class="title"><b>Table 64. Error rates for jacobi_zeta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.52ε (Mean = 0.357ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.99ε (Mean = 0.824ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.96ε (Mean = 1.06ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.89ε (Mean = 0.824ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Large Phi Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.92ε (Mean = 0.951ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.05ε (Mean = 1.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.52ε (Mean = 0.977ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_laguerre_n_m_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_" title="laguerre(n, m, x)">laguerre(n,
|
|
m, x)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_laguerre_n_m_x_.table_laguerre_n_m_x_"></a><p class="title"><b>Table 65. Error rates for laguerre(n, m, x)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Associated Laguerre Polynomials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434ε (Mean = 10.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 206ε (Mean = 6.86ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 6.38ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 434ε (Mean = 11.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_laguerre_n_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_x_" title="laguerre(n, x)">laguerre(n,
|
|
x)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_laguerre_n_x_.table_laguerre_n_x_"></a><p class="title"><b>Table 66. Error rates for laguerre(n, x)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Laguerre Polynomials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03ε (Mean = 185ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 4.2e+03ε (Mean = 251ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.1e+03ε (Mean = 185ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_legendre_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p" title="legendre_p">legendre_p</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_legendre_p.table_legendre_p"></a><p class="title"><b>Table 67. Error rates for legendre_p</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for legendre_p">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211ε (Mean = 20.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 124ε (Mean = 13.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 69.2ε (Mean = 9.58ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 211ε (Mean = 20.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300ε (Mean = 33.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 343ε (Mean = 32.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 699ε (Mean = 59.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 300ε (Mean = 33.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_legendre_p_associated_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p_associated_" title="legendre_p (associated)">legendre_p
|
|
(associated)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_legendre_p_associated_.table_legendre_p_associated_"></a><p class="title"><b>Table 68. Error rates for legendre_p (associated)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Associated Legendre Polynomials: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 175ε (Mean = 9.36ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 77.7ε (Mean = 5.59ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 121ε (Mean = 7.14ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_legendre_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_q" title="legendre_q">legendre_q</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_legendre_q.table_legendre_q"></a><p class="title"><b>Table 69. Error rates for legendre_q</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for legendre_q">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4ε (Mean = 7.46ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50.9ε (Mean = 9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50.9ε (Mean = 8.98ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 46.4ε (Mean = 7.32ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03ε (Mean = 366ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.6e+03ε (Mean = 366ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_lgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_lgamma" title="lgamma">lgamma</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_lgamma.table_lgamma"></a><p class="title"><b>Table 70. Error rates for lgamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for lgamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
factorials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.55ε (Mean = 0.592ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.308ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.914ε (Mean = 0.175ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 7.99e+04ε (Mean = 1.68e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 2
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -10
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 4.22ε (Mean = 1.26ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.997ε (Mean = 0.412ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.412ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -55
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 250ε (Mean = 60.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_log1p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_log1p" title="log1p">log1p</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_log1p.table_log1p"></a><p class="title"><b>Table 71. Error rates for log1p</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for log1p">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Random test data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846ε (Mean = 0.153ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.3ε (Mean = 0.66ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε))
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_non_central_beta_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF" title="non central beta CDF">non
|
|
central beta CDF</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_non_central_beta_CDF.table_non_central_beta_CDF"></a><p class="title"><b>Table 72. Error rates for non central beta CDF</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.0649ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26ε (Mean
|
|
= 3.5e+24ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 824ε (Mean = 27.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 832ε (Mean = 38.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 242ε (Mean = 31ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36ε (Mean
|
|
= 1.19e+35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.57e+04ε (Mean = 4.45e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.66e+03ε (Mean = 500ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement" title="non central beta CDF complement">non
|
|
central beta CDF complement</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 73. Error rates for non central beta CDF complement</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.0936ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97ε (Mean
|
|
= 1.37e+96ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 396ε (Mean = 50.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 554ε (Mean = 57.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 624ε (Mean = 62.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.56e+03ε (Mean = 707ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.25e+04ε (Mean = 1.49e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF" title="non central chi squared CDF">non
|
|
central chi squared CDF</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 74. Error rates for non central chi squared CDF</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.99ε (Mean = 0.0544ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727ε (Mean = 121ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 46.5ε (Mean = 10.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 115ε (Mean = 13.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 48.9ε (Mean = 10ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08ε (Mean
|
|
= 2.23e+07ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.79e+03ε (Mean = 723ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement" title="non central chi squared CDF complement">non
|
|
central chi squared CDF complement</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 75. Error rates for non central chi squared CDF complement</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 107ε (Mean = 17.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 171ε (Mean = 22.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 98.6ε (Mean = 15.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.43e+03ε (Mean = 705ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_non_central_t_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF" title="non central t CDF">non
|
|
central t CDF</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_non_central_t_CDF.table_non_central_t_CDF"></a><p class="title"><b>Table 76. Error rates for non central t CDF</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15ε (Mean
|
|
= 8.49e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 139ε (Mean = 31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 145ε (Mean = 30.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 135ε (Mean = 32.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (small non-centrality)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 2.09e+03ε (Mean = 244ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.86ε (Mean = 1.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.15ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.17ε (Mean = 1.45ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (large parameters)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46ε (Mean = 0.657ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 286ε (Mean = 62.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_non_central_t_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement" title="non central t CDF complement">non
|
|
central t CDF complement</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_non_central_t_CDF_complement.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 77. Error rates for non central t CDF complement</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15ε (Mean
|
|
= 6.72e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 201ε (Mean = 31.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 340ε (Mean = 43.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 154ε (Mean = 32.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (small non-centrality)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.87e+03ε (Mean = 263ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.5ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.5ε (Mean = 2.39ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.6ε (Mean = 1.63ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (large parameters)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24ε (Mean = 0.945ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 227ε (Mean = 50.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_owens_t"></a><a class="link" href="index.html#special_function_error_rates_rep.section_owens_t" title="owens_t">owens_t</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_owens_t.table_owens_t"></a><p class="title"><b>Table 78. Error rates for owens_t</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for owens_t">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Owens T (medium small values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.34ε (Mean = 0.944ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.34ε (Mean = 0.911ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.37ε (Mean = 0.98ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Owens T (large and diverse values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 49ε (Mean = 2.16ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 24.5ε (Mean = 1.39ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.78ε (Mean = 0.621ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_polygamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_polygamma" title="polygamma">polygamma</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_polygamma.table_polygamma"></a><p class="title"><b>Table 79. Error rates for polygamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for polygamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9ε (Mean = 12.8ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 108ε (Mean = 15.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.38ε (Mean = 1.84ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34.3ε (Mean = 7.65ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.32ε (Mean = 1.95ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - large arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244ε (Mean = 32.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.23ε (Mean = 0.323ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.1ε (Mean = 0.848ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 150ε (Mean = 13.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - negative arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6ε (Mean = 3.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 269ε (Mean = 87.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 269ε (Mean = 88.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 497ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - large negative arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.79ε (Mean = 0.197ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 155ε (Mean = 96.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 155ε (Mean = 96.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 162ε (Mean = 101ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - small arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 15.2ε (Mean = 5.03ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 106ε (Mean = 20ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3ε (Mean = 0.496ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - Large orders and other bug cases
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 151ε (Mean = 39.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 54.5ε (Mean = 13.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 145ε (Mean = 55.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 200ε (Mean = 57.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_powm1" title="powm1">powm1</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_powm1.table_powm1"></a><p class="title"><b>Table 80. Error rates for powm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for powm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
powm1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.04ε (Mean = 0.493ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.88ε (Mean = 0.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_sin_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sin_pi" title="sin_pi">sin_pi</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_sin_pi.table_sin_pi"></a><p class="title"><b>Table 81. Error rates for sin_pi</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sin_pi">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.335ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.336ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.99ε (Mean = 0.328ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi near integers and half integers
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.343ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_sph_bessel"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel" title="sph_bessel">sph_bessel</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_sph_bessel.table_sph_bessel"></a><p class="title"><b>Table 82. Error rates for sph_bessel</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Bessel j: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.91e+06ε (Mean = 1.09e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.978ε (Mean = 0.0445ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03ε (Mean = 107ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 243ε (Mean = 33.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 245ε (Mean = 16.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_sph_bessel_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel_prime" title="sph_bessel_prime">sph_bessel_prime</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_sph_bessel_prime.table_sph_bessel_prime"></a><p class="title"><b>Table 83. Error rates for sph_bessel_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Bessel j': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 33.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 307ε (Mean = 25.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_sph_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann" title="sph_neumann">sph_neumann</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_sph_neumann.table_sph_neumann"></a><p class="title"><b>Table 84. Error rates for sph_neumann</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
y: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 234ε (Mean = 19.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 281ε (Mean = 31.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_sph_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann_prime" title="sph_neumann_prime">sph_neumann_prime</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_sph_neumann_prime.table_sph_neumann_prime"></a><p class="title"><b>Table 85. Error rates for sph_neumann_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
y': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.988ε (Mean = 0.0869ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 158ε (Mean = 18.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 158ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 296ε (Mean = 25.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_spherical_harmonic_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i" title="spherical_harmonic_i">spherical_harmonic_i</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_spherical_harmonic_i.table_spherical_harmonic_i"></a><p class="title"><b>Table 86. Error rates for spherical_harmonic_i</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Spherical Harmonics
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_spherical_harmonic_r"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r" title="spherical_harmonic_r">spherical_harmonic_r</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_spherical_harmonic_r.table_spherical_harmonic_r"></a><p class="title"><b>Table 87. Error rates for spherical_harmonic_r</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Spherical Harmonics
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_sqrt1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sqrt1pm1" title="sqrt1pm1">sqrt1pm1</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_sqrt1pm1.table_sqrt1pm1"></a><p class="title"><b>Table 88. Error rates for sqrt1pm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
sqrt1pm1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.404ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.33ε (Mean = 0.404ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.54ε (Mean = 0.563ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.35ε (Mean = 0.497ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_tgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma" title="tgamma">tgamma</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_tgamma.table_tgamma"></a><p class="title"><b>Table 89. Error rates for tgamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
factorials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 314ε (Mean = 93.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.67ε (Mean = 0.617ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.85ε (Mean = 0.566ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1ε (Mean = 0.335ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.608ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 1ε (Mean = 0.376ε))<br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 1ε (Mean = 0.376ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0.5ε (Mean = 0.0791ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.635ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1ε (Mean = 0.32ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.51ε (Mean = 1.02ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.1ε (Mean = 0.59ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 2
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1ε (Mean = 0.191ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.1ε (Mean = 1.55ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.733ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -10
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 34.9ε (Mean = 9.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.75ε (Mean = 0.895ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.86ε (Mean = 0.881ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -55
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 3.89e+04ε (Mean = 9.52e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.69ε (Mean = 1.09ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.7ε (Mean = 1.35ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+04ε (Mean = 6.71e+03ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_tgamma1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma1pm1" title="tgamma1pm1">tgamma1pm1</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_tgamma1pm1.table_tgamma1pm1"></a><p class="title"><b>Table 90. Error rates for tgamma1pm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
tgamma1pm1(dz)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.12ε (Mean = 0.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.61ε (Mean = 0.84ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.31ε (Mean = 0.517ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_tgamma_delta_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio" title="tgamma_delta_ratio">tgamma_delta_ratio</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_tgamma_delta_ratio.table_tgamma_delta_ratio"></a><p class="title"><b>Table 91. Error rates for tgamma_delta_ratio</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small delta ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.83ε (Mean = 1.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 15.4ε (Mean = 2.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.56ε (Mean = 1.31ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small delta ratios (negative delta)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.94ε (Mean = 1.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.3ε (Mean = 2.03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.43ε (Mean = 1.42ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small integer ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.74ε (Mean = 0.736ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small integer ratios (negative delta)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.15ε (Mean = 0.685ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
integer tgamma ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.968ε (Mean = 0.386ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
integer tgamma ratios (negative delta)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.974ε (Mean = 0.175ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_tgamma_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_" title="tgamma (incomplete)">tgamma
|
|
(incomplete)</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_tgamma_incomplete_.table_tgamma_incomplete_"></a><p class="title"><b>Table 92. Error rates for tgamma (incomplete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 200ε (Mean = 13.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.47ε (Mean = 1.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 412ε (Mean = 95.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.14ε (Mean = 1.76ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean
|
|
= 1.05e+09ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.31ε (Mean = 0.775ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.13ε (Mean = 0.717ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.53ε (Mean = 0.66ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 117ε (Mean = 12.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.52ε (Mean = 1.48ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 79.6ε (Mean = 20.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.16ε (Mean = 1.33ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_tgamma_lower"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_lower" title="tgamma_lower">tgamma_lower</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_tgamma_lower.table_tgamma_lower"></a><p class="title"><b>Table 93. Error rates for tgamma_lower</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833ε (Mean = 0.0315ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.79ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 363ε (Mean = 63.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.62ε (Mean = 1.49ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.555ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.558ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.525ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.83ε (Mean = 1.15ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 84.7ε (Mean = 17.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.69ε (Mean = 0.849ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_tgamma_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_ratio" title="tgamma_ratio">tgamma_ratio</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_tgamma_ratio.table_tgamma_ratio"></a><p class="title"><b>Table 94. Error rates for tgamma_ratio</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
tgamma ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.694ε (Mean = 0.0347ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.99ε (Mean = 1.15ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 174ε (Mean = 61.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.28ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_trigamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_trigamma" title="trigamma">trigamma</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_trigamma.table_trigamma"></a><p class="title"><b>Table 95. Error rates for trigamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for trigamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.382ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.section_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_zeta" title="zeta">zeta</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.section_zeta.table_zeta"></a><p class="title"><b>Table 96. Error rates for zeta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for zeta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Random values greater than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5.45ε (Mean = 1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 8.69ε (Mean = 1.03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.093ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Random values less than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.03ε (Mean = 2.93ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 538ε (Mean = 59.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 137ε (Mean = 13.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 70.1ε (Mean = 17.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.84ε (Mean = 3.12ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Values close to and greater than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 7.73ε (Mean = 4.07ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.994ε (Mean = 0.421ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Values close to and less than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.53e+06ε (Mean = 1.87e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.991ε (Mean = 0.28ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.508ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.375ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Integer arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 70.3ε (Mean = 17.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.75ε (Mean = 1.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 28ε (Mean = 5.62ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9ε (Mean = 3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.error_logs"></a><a class="link" href="index.html#special_function_error_rates_rep.error_logs" title="Error Logs">Error Logs</a>
|
|
</h2></div></div></div>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h0"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in">Error
|
|
Output For cyl_bessel_j (integer orders) with compiler Microsoft Visual C++
|
|
version 14.1 and library <math.h> and test data Bessel JN: Mathworld
|
|
Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_"></a>CAUTION:
|
|
Found non-finite result, when a finite value was expected at entry 16<br>
|
|
Found: -nan(ind) Expected 0 Error: 1.79769e+308<br> 10, 1e-100, 0<br> CAUTION:
|
|
Gross error found at entry 16.<br> Found: -nan(ind) Expected 0 Error: 1.79769e+308<br>
|
|
10, 1e-100, 0<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h1"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso">Error
|
|
Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and
|
|
library GSL 2.1 and test data Associated Legendre Polynomials: Small Values</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values"></a>domain
|
|
error<br> 3.75573, -3, 0.264719, 0.0186823<br> domain error<br> 3.75573,
|
|
-3, 0.670017, 0.0085227<br> domain error<br> 3.75573, -3, 0.915014, 0.00136786<br>
|
|
domain error<br> 3.75573, -3, 0.93539, 0.000921218<br> domain error<br>
|
|
3.75573, -2, -0.804919, -0.035427<br> domain error<br> 3.75573, -2, -0.623236,
|
|
-0.0476446<br> domain error<br> 3.75573, -2, 0.629447, 0.0475072<br>
|
|
domain error<br> 3.75573, -2, 0.929777, 0.0157498<br> domain error<br>
|
|
3.75573, -2, 0.985763, 0.0034837<br> domain error<br> 3.75573, -1, 0.093763,
|
|
-0.118979<br> domain error<br> 4.28576, -4, 0.0944412, 0.00255792<br>
|
|
domain error<br> 4.28576, -4, 0.670017, 0.000790849<br> domain error<br>
|
|
4.28576, -3, -0.746026, -0.00458957<br> domain error<br> 4.28576, -2, -0.623236,
|
|
0.0219016<br> domain error<br> 4.28576, -2, 0.629447, 0.0223081<br> domain
|
|
error<br> 4.28576, -2, 0.93539, 0.0133504<br> domain error<br> 4.28576,
|
|
-1, 0.915014, 0.132001<br> domain error<br> 4.28576, -1, 0.985763, 0.0787743<br>
|
|
domain error<br> 4.43859, -4, 0.093763, 0.00255858<br> domain error<br>
|
|
4.43859, -4, 0.811584, 0.000303404<br> domain error<br> 4.43859, -4, 0.826752,
|
|
0.000260835<br> domain error<br> 4.43859, -4, 0.929777, 4.78235e-05<br>
|
|
domain error<br> 4.43859, -3, -0.804919, -0.00350364<br> domain error<br>
|
|
4.43859, -3, -0.729046, -0.00487043<br> domain error<br> 4.43859, -3, -0.623236,
|
|
-0.00620995<br> domain error<br> 4.43859, -3, 0.93539, 0.000861698<br>
|
|
domain error<br> 4.43859, -2, -0.557932, 0.0169167<br> domain error<br>
|
|
4.43859, -2, -0.443004, 0.0062586<br> domain error<br> 4.43859, -2, 0.915014,
|
|
0.016481<br> domain error<br> 4.43859, -1, 0.629447, -0.0138523<br> domain
|
|
error<br> 5.39088, -5, 0.0944412, 0.000254649<br> domain error<br> 5.39088,
|
|
-5, 0.264719, 0.000217164<br> domain error<br> 5.39088, -5, 0.670017, 5.87083e-05<br>
|
|
domain error<br> 5.39088, -5, 0.915014, 2.78273e-06<br> domain error<br>
|
|
5.39088, -3, 0.929777, 0.000880849<br> domain error<br> 5.39088, -2, 0.629447,
|
|
0.00448021<br> domain error<br> 5.39088, -2, 0.826752, 0.01718<br> domain
|
|
error<br> 5.39088, -2, 0.937736, 0.011583<br> domain error<br> 5.39088,
|
|
-1, -0.804919, 0.0276144<br> domain error<br> 5.39088, -1, -0.746026, -0.0119425<br>
|
|
domain error<br> 5.39088, -1, -0.443004, -0.0525987<br> domain error<br>
|
|
5.39088, -1, 0.811584, 0.032475<br> domain error<br> 5.39088, -1, 0.985763,
|
|
0.0759289<br> domain error<br> 5.97861, -5, -0.729046, 3.91223e-05<br>
|
|
domain error<br> 5.97861, -5, -0.383666, 0.000174899<br> domain error<br>
|
|
5.97861, -5, 0.93539, 1.43993e-06<br> domain error<br> 5.97861, -4, -0.623236,
|
|
-0.000607048<br> domain error<br> 5.97861, -4, 0.264719, 0.00059614<br>
|
|
domain error<br> 5.97861, -3, 0.629447, 0.00313497<br> domain error<br>
|
|
5.97861, -3, 0.670017, 0.00323895<br> domain error<br> 5.97861, -2, 0.915014,
|
|
0.0140705<br> domain error<br> 5.97861, -2, 0.992923, 0.00171356<br>
|
|
domain error<br> 5.97861, -1, -0.746026, -0.0119425<br> domain error<br>
|
|
5.97861, -1, 0.937736, 0.106972<br> domain error<br> 7.01297, -6, -0.443004,
|
|
-4.99177e-06<br> domain error<br> 7.01297, -6, 0.629447, 3.00689e-06<br>
|
|
domain error<br> 7.01297, -6, 0.811584, 7.00407e-07<br> domain error<br>
|
|
7.01297, -6, 0.985763, 4.83431e-10<br> domain error<br> 7.01297, -3, 0.670017,
|
|
0.000233323<br> domain error<br> 7.01297, -2, -0.804919, -0.0027739<br>
|
|
domain error<br> 7.01297, -1, -0.383666, 0.0397866<br> domain error<br>
|
|
7.01297, -1, 0.929777, 0.0544549<br> domain error<br> 7.54701, -7, 0.929777,
|
|
1.42008e-09<br> domain error<br> 7.54701, -6, 0.992923, 6.04622e-11<br>
|
|
domain error<br> 7.54701, -5, -0.804919, 1.18502e-05<br> domain error<br>
|
|
7.54701, -5, -0.623236, 2.57049e-05<br> domain error<br> 7.54701, -5, -0.557932,
|
|
2.60266e-05<br> domain error<br> 7.54701, -5, 0.826752, 9.64276e-06<br>
|
|
domain error<br> 7.54701, -4, -0.746026, -0.0001618<br> domain error<br>
|
|
7.54701, -3, 0.0944412, 0.000622493<br> domain error<br> 7.54701, -3, 0.985763,
|
|
9.14782e-05<br> domain error<br> 7.54701, -1, 0.811584, -0.0376184<br>
|
|
domain error<br> 11.8439, -10, -0.557932, -2.32652e-11<br> domain error<br>
|
|
11.8439, -10, 0.811584, 1.01194e-12<br> domain error<br> 11.8439, -8, -0.746026,
|
|
-1.34891e-09<br> domain error<br> 11.8439, -8, -0.729046, -1.5428e-09<br>
|
|
domain error<br> 11.8439, -8, 0.985763, 5.90035e-14<br> domain error<br>
|
|
11.8439, -4, 0.629447, -1.44723e-05<br> domain error<br> 11.8439, -4, 0.929777,
|
|
1.98812e-05<br> domain error<br> 11.8439, -3, 0.670017, -4.58296e-05<br>
|
|
domain error<br> 11.8439, -2, 0.826752, -0.00244759<br> domain error<br>
|
|
11.8439, -2, 0.992923, 0.00151458<br> domain error<br> 11.8439, -1, -0.383666,
|
|
0.00419108<br> domain error<br> 11.85, -11, 0.093763, 1.16526e-11<br>
|
|
domain error<br> 11.85, -11, 0.929777, 2.05797e-16<br> domain error<br>
|
|
11.85, -11, 0.93539, 1.32249e-16<br> domain error<br> *** FURTHER CONTENT
|
|
HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h2"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0">Error
|
|
Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and
|
|
library <cmath> and test data Associated Legendre Polynomials: Small
|
|
Values</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values"></a>order
|
|
parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.264719, 0.0186823<br>
|
|
order parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.670017,
|
|
0.0085227<br> order parameters less than 0 not supported in TR1<br> 3.75573,
|
|
-3, 0.915014, 0.00136786<br> order parameters less than 0 not supported in
|
|
TR1<br> 3.75573, -3, 0.93539, 0.000921218<br> order parameters less than
|
|
0 not supported in TR1<br> 3.75573, -2, -0.804919, -0.035427<br> order
|
|
parameters less than 0 not supported in TR1<br> 3.75573, -2, -0.623236, -0.0476446<br>
|
|
order parameters less than 0 not supported in TR1<br> 3.75573, -2, 0.629447,
|
|
0.0475072<br> order parameters less than 0 not supported in TR1<br> 3.75573,
|
|
-2, 0.929777, 0.0157498<br> order parameters less than 0 not supported in
|
|
TR1<br> 3.75573, -2, 0.985763, 0.0034837<br> order parameters less than
|
|
0 not supported in TR1<br> 3.75573, -1, 0.093763, -0.118979<br> order parameters
|
|
less than 0 not supported in TR1<br> 4.28576, -4, 0.0944412, 0.00255792<br>
|
|
order parameters less than 0 not supported in TR1<br> 4.28576, -4, 0.670017,
|
|
0.000790849<br> order parameters less than 0 not supported in TR1<br> 4.28576,
|
|
-3, -0.746026, -0.00458957<br> order parameters less than 0 not supported
|
|
in TR1<br> 4.28576, -2, -0.623236, 0.0219016<br> order parameters less
|
|
than 0 not supported in TR1<br> 4.28576, -2, 0.629447, 0.0223081<br> order
|
|
parameters less than 0 not supported in TR1<br> 4.28576, -2, 0.93539, 0.0133504<br>
|
|
order parameters less than 0 not supported in TR1<br> 4.28576, -1, 0.915014,
|
|
0.132001<br> order parameters less than 0 not supported in TR1<br> 4.28576,
|
|
-1, 0.985763, 0.0787743<br> order parameters less than 0 not supported in
|
|
TR1<br> 4.43859, -4, 0.093763, 0.00255858<br> order parameters less than
|
|
0 not supported in TR1<br> 4.43859, -4, 0.811584, 0.000303404<br> order
|
|
parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.826752, 0.000260835<br>
|
|
order parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.929777,
|
|
4.78235e-05<br> order parameters less than 0 not supported in TR1<br> 4.43859,
|
|
-3, -0.804919, -0.00350364<br> order parameters less than 0 not supported
|
|
in TR1<br> 4.43859, -3, -0.729046, -0.00487043<br> order parameters less
|
|
than 0 not supported in TR1<br> 4.43859, -3, -0.623236, -0.00620995<br>
|
|
order parameters less than 0 not supported in TR1<br> 4.43859, -3, 0.93539,
|
|
0.000861698<br> order parameters less than 0 not supported in TR1<br> 4.43859,
|
|
-2, -0.557932, 0.0169167<br> order parameters less than 0 not supported in
|
|
TR1<br> 4.43859, -2, -0.443004, 0.0062586<br> order parameters less than
|
|
0 not supported in TR1<br> 4.43859, -2, 0.915014, 0.016481<br> order parameters
|
|
less than 0 not supported in TR1<br> 4.43859, -1, 0.629447, -0.0138523<br>
|
|
order parameters less than 0 not supported in TR1<br> 5.39088, -5, 0.0944412,
|
|
0.000254649<br> order parameters less than 0 not supported in TR1<br> 5.39088,
|
|
-5, 0.264719, 0.000217164<br> order parameters less than 0 not supported
|
|
in TR1<br> 5.39088, -5, 0.670017, 5.87083e-05<br> order parameters less
|
|
than 0 not supported in TR1<br> 5.39088, -5, 0.915014, 2.78273e-06<br>
|
|
order parameters less than 0 not supported in TR1<br> 5.39088, -3, 0.929777,
|
|
0.000880849<br> order parameters less than 0 not supported in TR1<br> 5.39088,
|
|
-2, 0.629447, 0.00448021<br> order parameters less than 0 not supported in
|
|
TR1<br> 5.39088, -2, 0.826752, 0.01718<br> order parameters less than 0
|
|
not supported in TR1<br> 5.39088, -2, 0.937736, 0.011583<br> order parameters
|
|
less than 0 not supported in TR1<br> 5.39088, -1, -0.804919, 0.0276144<br>
|
|
order parameters less than 0 not supported in TR1<br> 5.39088, -1, -0.746026,
|
|
-0.0119425<br> order parameters less than 0 not supported in TR1<br> 5.39088,
|
|
-1, -0.443004, -0.0525987<br> order parameters less than 0 not supported
|
|
in TR1<br> 5.39088, -1, 0.811584, 0.032475<br> order parameters less than
|
|
0 not supported in TR1<br> 5.39088, -1, 0.985763, 0.0759289<br> order parameters
|
|
less than 0 not supported in TR1<br> 5.97861, -5, -0.729046, 3.91223e-05<br>
|
|
order parameters less than 0 not supported in TR1<br> 5.97861, -5, -0.383666,
|
|
0.000174899<br> order parameters less than 0 not supported in TR1<br> 5.97861,
|
|
-5, 0.93539, 1.43993e-06<br> order parameters less than 0 not supported in
|
|
TR1<br> 5.97861, -4, -0.623236, -0.000607048<br> order parameters less
|
|
than 0 not supported in TR1<br> 5.97861, -4, 0.264719, 0.00059614<br> order
|
|
parameters less than 0 not supported in TR1<br> 5.97861, -3, 0.629447, 0.00313497<br>
|
|
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h3"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Bessel Iv: Mathworld Data (large values)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_"></a>CAUTION:
|
|
Gross error found at entry 0.<br> Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br>
|
|
-1, 3.72917e-155, 1.86459e-155<br> CAUTION: Gross error found at entry 1.<br>
|
|
Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br> 1, 3.72917e-155, 1.86459e-155<br>
|
|
CAUTION: Gross error found at entry 3.<br> Found: 0 Expected 8.02269e-175
|
|
Error: 3.60559e+133<br> 1.125, 3.72917e-155, 8.02269e-175<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h4"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in">Error
|
|
Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library Rmath 3.2.3 and test data Bessel In: Mathworld Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_"></a>Unsupported
|
|
domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br>
|
|
Unsupported domain<br> -100, -200, 4.35275e+74<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h5"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0">Error
|
|
Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library Rmath 3.2.3 and test data Bessel I1: Mathworld Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_"></a>Unsupported
|
|
domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br>
|
|
Unsupported domain<br> 1, -10, -2670.99<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h6"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1">Error
|
|
Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library Rmath 3.2.3 and test data Bessel I0: Mathworld Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_"></a>Unsupported
|
|
domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br>
|
|
Unsupported domain<br> 0, -1, 1.26607<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h7"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Bessel In: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data"></a>Unsupported
|
|
domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br>
|
|
Unsupported domain<br> -100, -200, 4.35275e+74<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h8"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Bessel I1: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data"></a>Unsupported
|
|
domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br>
|
|
Unsupported domain<br> 1, -10, -2670.99<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h9"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Bessel I0: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data"></a>Unsupported
|
|
domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br>
|
|
Unsupported domain<br> 0, -1, 1.26607<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h10"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Bessel J: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data"></a>CAUTION:
|
|
Gross error found at entry 6.<br> Found: 0 Expected -0.000747424 Error: 3.3591e+304<br>
|
|
5.5, 1e+06, -0.000747424<br> CAUTION: Gross error found at entry 7.<br>
|
|
Found: 0 Expected -0.0007766 Error: 3.49022e+304<br> 5.125, 1e+06, -0.0007766<br>
|
|
CAUTION: Gross error found at entry 8.<br> Found: 0 Expected -0.000466323
|
|
Error: 2.09576e+304<br> 5.875, 1e+06, -0.000466323<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h11"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0">Error
|
|
Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library Rmath 3.2.3 and test data Bessel JN: Mathworld Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_"></a>Unsupported
|
|
domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br>
|
|
Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br>
|
|
CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964
|
|
Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br>
|
|
-5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br>
|
|
Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found
|
|
at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br>
|
|
-10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br>
|
|
Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h12"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1">Error
|
|
Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library Rmath 3.2.3 and test data Bessel J1: Mathworld Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_"></a>Unsupported
|
|
domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br>
|
|
Unsupported domain<br> 1, -10, -0.0434727<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h13"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2">Error
|
|
Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library Rmath 3.2.3 and test data Bessel J0: Mathworld Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_"></a>Unsupported
|
|
domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br>
|
|
Unsupported domain<br> 0, -10, -0.245936<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h14"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Bessel JN: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data"></a>Unsupported
|
|
domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br>
|
|
Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br>
|
|
CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964
|
|
Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br>
|
|
-5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br>
|
|
Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found
|
|
at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br>
|
|
-10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br>
|
|
Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h15"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Bessel J1: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data"></a>Unsupported
|
|
domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br>
|
|
Unsupported domain<br> 1, -10, -0.0434727<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h16"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Bessel J0: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data"></a>Unsupported
|
|
domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br>
|
|
Unsupported domain<br> 0, -10, -0.245936<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h17"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with">Error
|
|
Output For ibetac_inv with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Inverse incomplete beta</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION:
|
|
Gross error found at entry 7.<br> Found: 3.8247e-302 Expected 0 Error: 1.71891e+06<br>
|
|
1.38853e-05, 0.0497627, 0.632396, 0, 0<br> CAUTION: Gross error found at
|
|
entry 71.<br> Found: 1.38362e-204 Expected 0 Error: 6.21832e+103<br> 3.77931e-05,
|
|
0.0150073, 0.835025, 0, 0<br> CAUTION: Gross error found at entry 90.<br>
|
|
Found: 1.09275e-303 Expected 0 Error: 49109.6<br> 4.29383e-05, 0.0428761,
|
|
0.814742, 0, 0<br> CAUTION: Gross error found at entry 102.<br> Found:
|
|
3.8625e-304 Expected 0 Error: 17358<br> 4.80089e-05, 0.0296236, 0.913384,
|
|
0, 0<br> CAUTION: Gross error found at entry 115.<br> Found: 1.51774e-303
|
|
Expected 0 Error: 68209.8<br> 0.000130387, 0.0404969, 0.814742, 0, 0<br>
|
|
CAUTION: Gross error found at entry 123.<br> Found: 1.28036e-303 Expected
|
|
0 Error: 57541.4<br> 0.000149328, 0.0201182, 0.905801, 5.70765e-267, 0<br>
|
|
CAUTION: Gross error found at entry 133.<br> Found: 1.96732e-302 Expected
|
|
0 Error: 884160<br> 0.000173563, 0.0301908, 0.913384, 4.21662e-213, 0<br>
|
|
CAUTION: Gross error found at entry 159.<br> Found: 1.48697e-191 Expected
|
|
0 Error: 6.68279e+116<br> 0.000260723, 0.0252933, 0.632396, 0, 0<br> CAUTION:
|
|
Gross error found at entry 256.<br> Found: 9.24166e-245 Expected 0 Error:
|
|
4.15342e+63<br> 0.00246975, 0.016063, 0.913384, 1, 0<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h18"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_">Error
|
|
Output For ibeta_inv with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Inverse incomplete beta</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION:
|
|
Gross error found at entry 1.<br> Found: 1.90197e-247 Expected 0 Error: 8.54789e+60<br>
|
|
1.12733e-05, 0.022662, 0.135563, 0, 0<br> CAUTION: Gross error found at entry
|
|
30.<br> Found: 1.36217e-301 Expected 0 Error: 6.12191e+06<br> 2.10769e-05,
|
|
0.0448972, 0.221112, 0, 0<br> CAUTION: Gross error found at entry 152.<br>
|
|
Found: 2.92621e-285 Expected 0 Error: 1.31511e+23<br> 0.000240381, 0.017982,
|
|
0.221112, 0, 0<br> CAUTION: Gross error found at entry 184.<br> Found:
|
|
5.63355e-203 Expected 0 Error: 2.53185e+105<br> 0.000348822, 0.0275467, 0.135563,
|
|
0, 1.88165e-166<br> CAUTION: Gross error found at entry 205.<br> Found:
|
|
5.52731e-303 Expected 0 Error: 248409<br> 0.000441212, 0.0313573, 0.127074,
|
|
0, 9.07221e-121<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h19"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_bet"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_bet">Error
|
|
Output For non central beta CDF complement with compiler GNU C++ version 7.1.0
|
|
and library Rmath 3.2.3 and test data Non Central Beta, large parameters</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION:
|
|
Gross error found at entry 10.<br> Found: 9.76918e-10 Expected 1.61248e-15
|
|
Error: 605846<br> 290.682, 72.6705, 20005.4, 0.997663, 1, 1.61248e-15<br>
|
|
CAUTION: Gross error found at entry 11.<br> Found: 9.94184e-10 Expected 3.0108e-42
|
|
Error: 3.30205e+32<br> 290.682, 145.341, 53489.1, 0.998663, 1, 3.0108e-42<br>
|
|
CAUTION: Gross error found at entry 16.<br> Found: 8.45406e-10 Expected 4.46652e-22
|
|
Error: 1.89276e+12<br> 290.682, 1162.73, 2308.07, 0.656921, 1, 4.46652e-22<br>
|
|
CAUTION: Gross error found at entry 17.<br> Found: 9.41971e-10 Expected 1.7241e-50
|
|
Error: 5.46356e+40<br> 290.682, 1453.41, 8064.48, 0.832237, 1, 1.7241e-50<br>
|
|
CAUTION: Gross error found at entry 18.<br> Found: 9.30663e-10 Expected 2.09803e-305
|
|
Error: 4.43589e+295<br> 975.766, 731.824, 232.285, 0.919742, 1, 2.09803e-305<br>
|
|
CAUTION: Gross error found at entry 27.<br> Found: 9.76918e-10 Expected 9.3474e-18
|
|
Error: 1.04512e+08<br> 1879.05, 187.905, 20005.4, 0.992215, 1, 9.3474e-18<br>
|
|
CAUTION: Gross error found at entry 28.<br> Found: 9.94184e-10 Expected 1.8122e-90
|
|
Error: 5.48607e+80<br> 1879.05, 469.762, 53489.1, 0.994618, 1, 1.8122e-90<br>
|
|
CAUTION: Gross error found at entry 32.<br> Found: 9.27224e-10 Expected 3.18255e-15
|
|
Error: 291345<br> 1879.05, 3758.1, 1879.05, 0.480508, 1, 3.18255e-15<br>
|
|
CAUTION: Gross error found at entry 33.<br> Found: 8.45406e-10 Expected 1.10218e-77
|
|
Error: 7.67029e+67<br> 1879.05, 5637.15, 2308.07, 0.458181, 1, 1.10218e-77<br>
|
|
CAUTION: Gross error found at entry 34.<br> Found: 9.30663e-10 Expected 0
|
|
Error: 4.18262e+298<br> 2308.07, 1154.03, 232.285, 0.919371, 1, 0<br> CAUTION:
|
|
Gross error found at entry 35.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br>
|
|
2308.07, 1731.05, 290.682, 0.917262, 1, 0<br> CAUTION: Gross error found
|
|
at entry 43.<br> Found: 9.94184e-10 Expected 3.57283e-70 Error: 2.78262e+60<br>
|
|
8064.48, 806.448, 53489.1, 0.988678, 1, 3.57283e-70<br> CAUTION: Gross error
|
|
found at entry 48.<br> Found: 8.45406e-10 Expected 8.78057e-74 Error: 9.62814e+63<br>
|
|
8064.48, 16129, 2308.07, 0.421531, 1, 8.78057e-74<br> CAUTION: Gross error
|
|
found at entry 49.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br>
|
|
15674.4, 3918.59, 232.285, 0.933726, 1, 0<br> CAUTION: Gross error found
|
|
at entry 50.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br>
|
|
15674.4, 7837.19, 290.682, 0.917179, 1, 0<br> CAUTION: Gross error found
|
|
at entry 51.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 15674.4,
|
|
11755.8, 975.766, 0.915784, 1, 0<br> CAUTION: Gross error found at entry
|
|
63.<br> Found: 9.41971e-10 Expected 2.31296e-171 Error: 4.07258e+161<br>
|
|
20005.4, 40010.8, 8064.48, 0.432094, 1, 2.31296e-171<br> CAUTION: Gross error
|
|
found at entry 64.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br>
|
|
53489.1, 5348.92, 232.285, 0.954635, 1, 0<br> CAUTION: Gross error found
|
|
at entry 65.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br>
|
|
53489.1, 13372.3, 290.682, 0.933478, 1, 0<br> CAUTION: Gross error found
|
|
at entry 66.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 53489.1,
|
|
26744.6, 975.766, 0.91717, 1, 0<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h20"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be0">Error
|
|
Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library
|
|
Rmath 3.2.3 and test data Non Central Beta, large parameters</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION:
|
|
Gross error found at entry 0.<br> Found: 9.1136e-209 Expected 5.82279e-200
|
|
Error: 6.38913e+08<br> 232.285, 209.056, 232.285, 0.062486, 5.82279e-200,
|
|
1<br> CAUTION: Gross error found at entry 1.<br> Found: 4.08108e-115 Expected
|
|
2.37643e-112 Error: 581.304<br> 232.285, 229.962, 290.682, 0.155342, 2.37643e-112,
|
|
1<br> CAUTION: Gross error found at entry 2.<br> Found: 1.07549e-93 Expected
|
|
9.53431e-89 Error: 88650<br> 232.285, 232.052, 975.766, 0.378086, 9.53431e-89,
|
|
1<br> CAUTION: Gross error found at entry 3.<br> Found: 2.58402e-54 Expected
|
|
8.27353e-53 Error: 31.0181<br> 232.285, 232.285, 1879.05, 0.625865, 8.27353e-53,
|
|
1<br> CAUTION: Gross error found at entry 4.<br> Found: 1.93718e-19 Expected
|
|
6.64275e-16 Error: 3428.08<br> 232.285, 232.308, 2308.07, 0.770774, 6.64275e-16,
|
|
1<br> CAUTION: Gross error found at entry 21.<br> Found: 8.12962e-240 Expected
|
|
1.82294e-219 Error: 2.24234e+20<br> 975.766, 974.79, 1879.05, 0.331337, 1.82294e-219,
|
|
1<br> CAUTION: Gross error found at entry 22.<br> Found: 3.47274e-69 Expected
|
|
1.42183e-67 Error: 39.9426<br> 975.766, 975.766, 2308.07, 0.514323, 1.42183e-67,
|
|
1<br> CAUTION: Gross error found at entry 23.<br> Found: 5.86885e-50 Expected
|
|
1.27896e-47 Error: 216.923<br> 975.766, 975.863, 8064.48, 0.753209, 1.27896e-47,
|
|
1<br> CAUTION: Gross error found at entry 39.<br> Found: 4.82785e-230 Expected
|
|
1.25446e-213 Error: 2.59838e+16<br> 2308.07, 2308.07, 8064.48, 0.54983, 1.25446e-213,
|
|
1<br> CAUTION: Gross error found at entry 40.<br> Found: 1.22971e-87 Expected
|
|
1.82618e-85 Error: 147.505<br> 2308.07, 2308.3, 15674.4, 0.733174, 1.82618e-85,
|
|
1<br> CAUTION: Gross error found at entry 56.<br> Found: 2.97337e-127 Expected
|
|
2.56068e-124 Error: 860.205<br> 15674.4, 15675.9, 20005.4, 0.55883, 2.56068e-124,
|
|
1<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h21"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be1">Error
|
|
Output For non central beta CDF complement with compiler GNU C++ version 7.1.0
|
|
and library Rmath 3.2.3 and test data Non Central Beta, medium parameters</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION:
|
|
Gross error found at entry 296.<br> Found: 9.44166e-10 Expected 6.22975e-10
|
|
Error: 0.515577<br> 22.9367, 114.683, 19.5081, 0.480981, 1, 6.22975e-10<br>
|
|
CAUTION: Gross error found at entry 369.<br> Found: 2.52234e-10 Expected
|
|
1.40246e-10 Error: 0.79851<br> 27.5277, 20.6457, 0.956697, 0.915111, 1, 1.40246e-10<br>
|
|
CAUTION: Gross error found at entry 429.<br> Found: 1.18105e-09 Expected
|
|
7.45745e-10 Error: 0.58372<br> 28.8063, 21.6047, 60.3826, 0.946143, 1, 7.45745e-10<br>
|
|
CAUTION: Gross error found at entry 430.<br> Found: 2.44435e-09 Expected
|
|
1.60695e-09 Error: 0.521115<br> 28.8063, 21.6047, 148.129, 0.965121, 1, 1.60695e-09<br>
|
|
CAUTION: Gross error found at entry 477.<br> Found: 7.57435e-10 Expected
|
|
7.14133e-11 Error: 9.60635<br> 28.8063, 144.032, 42.3849, 0.504845, 1, 7.14133e-11<br>
|
|
CAUTION: Gross error found at entry 489.<br> Found: 4.8561e-10 Expected 5.62991e-11
|
|
Error: 7.62553<br> 31.9438, 23.9579, 44.2068, 0.93835, 1, 5.62991e-11<br>
|
|
CAUTION: Gross error found at entry 490.<br> Found: 8.35187e-10 Expected
|
|
1.87483e-10 Error: 3.45473<br> 31.9438, 23.9579, 135.747, 0.961117, 1, 1.87483e-10<br>
|
|
CAUTION: Gross error found at entry 491.<br> Found: 1.00174e-09 Expected
|
|
2.38491e-10 Error: 3.20032<br> 31.9438, 23.9579, 191.501, 0.968273, 1, 2.38491e-10<br>
|
|
CAUTION: Gross error found at entry 537.<br> Found: 7.29746e-10 Expected
|
|
1.31223e-12 Error: 555.111<br> 31.9438, 159.719, 34.2373, 0.489796, 1, 1.31223e-12<br>
|
|
CAUTION: Gross error found at entry 538.<br> Found: 2.49663e-09 Expected
|
|
1.54239e-09 Error: 0.618681<br> 31.9438, 159.719, 126.472, 0.581861, 1, 1.54239e-09<br>
|
|
CAUTION: Gross error found at entry 549.<br> Found: 4.16125e-10 Expected
|
|
4.8536e-13 Error: 856.353<br> 38.0822, 28.5617, 34.773, 0.931853, 1, 4.8536e-13<br>
|
|
CAUTION: Gross error found at entry 550.<br> Found: 9.69907e-10 Expected
|
|
2.87054e-12 Error: 336.883<br> 38.0822, 28.5617, 127.953, 0.956104, 1, 2.87054e-12<br>
|
|
CAUTION: Gross error found at entry 551.<br> Found: 5.90132e-10 Expected
|
|
4.08361e-12 Error: 143.512<br> 38.0822, 28.5617, 183.147, 0.963764, 1, 4.08361e-12<br>
|
|
CAUTION: Gross error found at entry 597.<br> Found: 4.67033e-10 Expected
|
|
9.82939e-16 Error: 475139<br> 38.0822, 190.411, 27.0954, 0.475419, 1, 9.82939e-16<br>
|
|
CAUTION: Gross error found at entry 598.<br> Found: 9.33207e-10 Expected
|
|
4.03465e-12 Error: 230.298<br> 38.0822, 190.411, 100.733, 0.544491, 1, 4.03465e-12<br>
|
|
CAUTION: Gross error found at entry 599.<br> Found: 7.4092e-10 Expected 9.53942e-11
|
|
Error: 6.76693<br> 38.0822, 190.411, 169.826, 0.594614, 1, 9.53942e-11<br>
|
|
CAUTION: Gross error found at entry 609.<br> Found: 5.71813e-10 Expected
|
|
1.17207e-14 Error: 48785.7<br> 42.7789, 32.0842, 28.3773, 0.927814, 1, 1.17207e-14<br>
|
|
CAUTION: Gross error found at entry 610.<br> Found: 5.16834e-10 Expected
|
|
9.62679e-14 Error: 5367.71<br> 42.7789, 32.0842, 109.376, 0.950307, 1, 9.62679e-14<br>
|
|
CAUTION: Gross error found at entry 611.<br> Found: 6.08012e-10 Expected
|
|
1.7454e-13 Error: 3482.51<br> 42.7789, 32.0842, 175.686, 0.960431, 1, 1.7454e-13<br>
|
|
CAUTION: Gross error found at entry 657.<br> Found: 5.59489e-10 Expected
|
|
2.86344e-18 Error: 1.95391e+08<br> 42.7789, 213.895, 21.9724, 0.467166, 1,
|
|
2.86344e-18<br> CAUTION: Gross error found at entry 658.<br> Found: 5.14798e-10
|
|
Expected 2.50972e-14 Error: 20511.2<br> 42.7789, 213.895, 84.4175, 0.522676,
|
|
1, 2.50972e-14<br> CAUTION: Gross error found at entry 659.<br> Found:
|
|
8.49991e-10 Expected 2.38005e-12 Error: 356.131<br> 42.7789, 213.895, 160.056,
|
|
0.576191, 1, 2.38005e-12<br> CAUTION: Gross error found at entry 671.<br>
|
|
Found: 3.03281e-10 Expected 2.22036e-15 Error: 136590<br> 44.5963, 33.4472,
|
|
22.4929, 0.924976, 1, 2.22036e-15<br> CAUTION: Gross error found at entry
|
|
672.<br> Found: 8.40636e-10 Expected 2.22384e-14 Error: 37800.1<br> 44.5963,
|
|
33.4472, 94.9517, 0.946545, 1, 2.22384e-14<br> CAUTION: Gross error found
|
|
at entry 673.<br> Found: 8.15021e-10 Expected 4.75974e-14 Error: 17122.2<br>
|
|
44.5963, 33.4472, 162.945, 0.95793, 1, 4.75974e-14<br> CAUTION: Gross error
|
|
found at entry 716.<br> Found: 1.11988e-10 Expected 2.84965e-22 Error: 3.92989e+11<br>
|
|
44.5963, 222.981, 0.956697, 0.445432, 1, 2.84965e-22<br> CAUTION: Gross error
|
|
found at entry 717.<br> Found: 7.99524e-10 Expected 3.04552e-15 Error: 262523<br>
|
|
44.5963, 222.981, 78.4454, 0.515267, 1, 3.04552e-15<br> CAUTION: Gross error
|
|
found at entry 718.<br> Found: 8.0958e-10 Expected 5.89458e-13 Error: 1372.43<br>
|
|
44.5963, 222.981, 158.441, 0.57107, 1, 5.89458e-13<br> *** FURTHER CONTENT
|
|
HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h22"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be2">Error
|
|
Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library
|
|
Rmath 3.2.3 and test data Non Central Beta, medium parameters</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION:
|
|
Gross error found at entry 14.<br> Found: 4.64669e-35 Expected 7.14875e-33
|
|
Error: 152.846<br> 1.45431, 1.30887, 158.441, 0.0983847, 7.14875e-33, 1<br>
|
|
CAUTION: Gross error found at entry 15.<br> Found: 4.66674e-46 Expected 3.13332e-40
|
|
Error: 671416<br> 1.45431, 1.30887, 196.222, 0.09869, 3.13332e-40, 1<br>
|
|
CAUTION: Gross error found at entry 18.<br> Found: 5.84342e-28 Expected 3.61559e-27
|
|
Error: 5.18745<br> 1.45431, 1.43976, 159.586, 0.245596, 3.61559e-27, 1<br>
|
|
CAUTION: Gross error found at entry 19.<br> Found: 1.72833e-34 Expected 1.76943e-33
|
|
Error: 9.2378<br> 1.45431, 1.43976, 198.576, 0.246444, 1.76943e-33, 1<br>
|
|
CAUTION: Gross error found at entry 22.<br> Found: 1.76915e-19 Expected 3.69506e-18
|
|
Error: 19.8861<br> 1.45431, 1.45285, 159.621, 0.491116, 3.69506e-18, 1<br>
|
|
CAUTION: Gross error found at entry 23.<br> Found: 2.52007e-25 Expected 2.00482e-22
|
|
Error: 794.544<br> 1.45431, 1.45285, 199.292, 0.492849, 2.00482e-22, 1<br>
|
|
CAUTION: Gross error found at entry 73.<br> Found: 2.04477e-34 Expected 2.45287e-33
|
|
Error: 10.9958<br> 7.62448, 6.86203, 148.129, 0.0921776, 2.45287e-33, 1<br>
|
|
CAUTION: Gross error found at entry 74.<br> Found: 2.36587e-46 Expected 7.32638e-42
|
|
Error: 30966<br> 7.62448, 6.86203, 193.539, 0.093784, 7.32638e-42, 1<br>
|
|
CAUTION: Gross error found at entry 76.<br> Found: 3.29122e-26 Expected 7.418e-25
|
|
Error: 21.5387<br> 7.62448, 7.54824, 148.626, 0.228717, 7.418e-25, 1<br>
|
|
CAUTION: Gross error found at entry 77.<br> Found: 1.70126e-32 Expected 1.07666e-31
|
|
Error: 5.32864<br> 7.62448, 7.54824, 193.774, 0.23303, 1.07666e-31, 1<br>
|
|
CAUTION: Gross error found at entry 79.<br> Found: 1.3478e-15 Expected 4.21836e-15
|
|
Error: 2.12982<br> 7.62448, 7.61686, 151.548, 0.457773, 4.21836e-15, 1<br>
|
|
CAUTION: Gross error found at entry 80.<br> Found: 8.78487e-21 Expected 3.41238e-19
|
|
Error: 37.8438<br> 7.62448, 7.61686, 194.119, 0.465826, 3.41238e-19, 1<br>
|
|
CAUTION: Gross error found at entry 132.<br> Found: 3.85783e-23 Expected
|
|
1.54142e-22 Error: 2.99555<br> 19.9593, 17.9634, 44.2068, 0.0698905, 1.54142e-22,
|
|
1<br> CAUTION: Gross error found at entry 133.<br> Found: 8.6122e-39 Expected
|
|
3.94361e-38 Error: 3.5791<br> 19.9593, 17.9634, 135.747, 0.0829178, 3.94361e-38,
|
|
1<br> CAUTION: Gross error found at entry 134.<br> Found: 3.61781e-52 Expected
|
|
3.98669e-48 Error: 11018.6<br> 19.9593, 17.9634, 191.501, 0.0864897, 3.98669e-48,
|
|
1<br> CAUTION: Gross error found at entry 135.<br> Found: 2.07122e-15 Expected
|
|
7.08614e-15 Error: 2.42124<br> 19.9593, 19.7597, 55.6996, 0.176444, 7.08614e-15,
|
|
1<br> CAUTION: Gross error found at entry 136.<br> Found: 2.28223e-27 Expected
|
|
2.16759e-25 Error: 93.977<br> 19.9593, 19.7597, 136.272, 0.20393, 2.16759e-25,
|
|
1<br> CAUTION: Gross error found at entry 137.<br> Found: 6.4251e-34 Expected
|
|
4.0064e-33 Error: 5.23554<br> 19.9593, 19.7597, 191.898, 0.213398, 4.0064e-33,
|
|
1<br> CAUTION: Gross error found at entry 139.<br> Found: 2.1734e-14 Expected
|
|
4.65637e-14 Error: 1.14243<br> 19.9593, 19.9394, 145.168, 0.410858, 4.65637e-14,
|
|
1<br> CAUTION: Gross error found at entry 140.<br> Found: 2.18388e-19 Expected
|
|
5.1677e-18 Error: 22.663<br> 19.9593, 19.9394, 192.978, 0.426523, 5.1677e-18,
|
|
1<br> CAUTION: Gross error found at entry 192.<br> Found: 3.29537e-23 Expected
|
|
8.29996e-23 Error: 1.51867<br> 22.4174, 20.1757, 34.773, 0.0661999, 8.29996e-23,
|
|
1<br> CAUTION: Gross error found at entry 193.<br> Found: 7.86091e-39 Expected
|
|
2.77686e-38 Error: 2.5325<br> 22.4174, 20.1757, 127.953, 0.0809614, 2.77686e-38,
|
|
1<br> CAUTION: Gross error found at entry 194.<br> Found: 3.0161e-51 Expected
|
|
4.5396e-48 Error: 1504.12<br> 22.4174, 20.1757, 183.147, 0.0848857, 4.5396e-48,
|
|
1<br> CAUTION: Gross error found at entry 195.<br> Found: 3.08022e-14 Expected
|
|
1.42713e-13 Error: 3.6332<br> 22.4174, 22.1932, 37.6764, 0.162145, 1.42713e-13,
|
|
1<br> CAUTION: Gross error found at entry 196.<br> Found: 8.89935e-28 Expected
|
|
2.56187e-25 Error: 286.871<br> 22.4174, 22.1932, 131.096, 0.199361, 2.56187e-25,
|
|
1<br> CAUTION: Gross error found at entry 197.<br> Found: 9.34392e-34 Expected
|
|
6.14831e-33 Error: 5.58001<br> 22.4174, 22.1932, 186.799, 0.209601, 6.14831e-33,
|
|
1<br> CAUTION: Gross error found at entry 199.<br> Found: 2.79341e-13 Expected
|
|
4.79277e-13 Error: 0.71574<br> 22.4174, 22.395, 131.148, 0.398015, 4.79277e-13,
|
|
1<br> CAUTION: Gross error found at entry 200.<br> Found: 3.13989e-19 Expected
|
|
7.01608e-18 Error: 21.345<br> 22.4174, 22.395, 191.433, 0.419933, 7.01608e-18,
|
|
1<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h23"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_chi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_chi">Error
|
|
Output For non central chi squared CDF complement with compiler GNU C++ version
|
|
7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, large
|
|
parameters</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters"></a>CAUTION:
|
|
Gross error found at entry 12.<br> Found: 0 Expected 1.17655e-12 Error: 5.28771e+295<br>
|
|
101.815, 5236.73, 6406.25, 1, 1.17655e-12<br> CAUTION: Gross error found
|
|
at entry 13.<br> Found: 0 Expected 1.79374e-44 Error: 8.06149e+263<br>
|
|
101.815, 9735.22, 12788.2, 1, 1.79374e-44<br> CAUTION: Gross error found
|
|
at entry 35.<br> Found: 2.58682e-14 Expected 1.84404e-61 Error: 1.4028e+47<br>
|
|
107.623, 122.456, 920.317, 1, 1.84404e-61<br> CAUTION: Gross error found
|
|
at entry 36.<br> Found: 0 Expected 2.30757e-102 Error: 1.03707e+206<br>
|
|
107.623, 156.292, 1319.58, 1, 2.30757e-102<br> CAUTION: Gross error found
|
|
at entry 52.<br> Found: 0 Expected 6.40952e-24 Error: 2.88059e+284<br>
|
|
114.68, 417.884, 1065.13, 1, 6.40952e-24<br> CAUTION: Gross error found at
|
|
entry 53.<br> Found: 0 Expected 1.02366e-98 Error: 4.60058e+209<br> 114.68,
|
|
669.781, 2353.38, 1, 1.02366e-98<br> CAUTION: Gross error found at entry
|
|
69.<br> Found: 0 Expected 6.55726e-39 Error: 2.94699e+269<br> 118.032,
|
|
3168.71, 4930.11, 1, 6.55726e-39<br> CAUTION: Gross error found at entry
|
|
85.<br> Found: 0 Expected 7.30688e-22 Error: 3.28388e+286<br> 163.004,
|
|
9735.22, 11877.9, 1, 7.30688e-22<br> CAUTION: Gross error found at entry
|
|
86.<br> Found: 0 Expected 1.17171e-111 Error: 5.26596e+196<br> 163.004,
|
|
25344.1, 33159.2, 1, 1.17171e-111<br> CAUTION: Gross error found at entry
|
|
108.<br> Found: 1.12355e-13 Expected 2.67349e-61 Error: 4.20255e+47<br>
|
|
256.292, 122.456, 1136.25, 1, 2.67349e-61<br> CAUTION: Gross error found
|
|
at entry 109.<br> Found: 1.16462e-13 Expected 8.30595e-116 Error: 1.40216e+102<br>
|
|
256.292, 156.292, 1650.34, 1, 8.30595e-116<br> CAUTION: Gross error found
|
|
at entry 124.<br> Found: 1.05804e-13 Expected 1.01672e-15 Error: 103.064<br>
|
|
517.884, 417.884, 1403.65, 1, 1.01672e-15<br> CAUTION: Gross error found
|
|
at entry 125.<br> Found: 2.00728e-13 Expected 3.50192e-56 Error: 5.73194e+42<br>
|
|
517.884, 669.781, 2375.33, 1, 3.50192e-56<br> CAUTION: Gross error found
|
|
at entry 141.<br> Found: 0 Expected 1.36924e-20 Error: 6.15368e+287<br>
|
|
769.781, 3168.71, 5120.04, 1, 1.36924e-20<br> CAUTION: Gross error found
|
|
at entry 142.<br> Found: 0 Expected 3.19215e-72 Error: 1.43463e+236<br>
|
|
769.781, 5236.73, 9009.76, 1, 3.19215e-72<br> CAUTION: Gross error found
|
|
at entry 157.<br> Found: 0 Expected 7.26231e-08 Error: 3.26385e+300<br>
|
|
1223.88, 9735.22, 12055, 1, 7.26231e-08<br> CAUTION: Gross error found at
|
|
entry 158.<br> Found: 0 Expected 4.5906e-56 Error: 2.06312e+252<br> 1223.88,
|
|
25344.1, 31881.6, 1, 4.5906e-56<br> CAUTION: Gross error found at entry 194.<br>
|
|
Found: 0 Expected 5.34714e-12 Error: 2.40313e+296<br> 9835.22, 122.456, 10953.4,
|
|
1, 5.34714e-12<br> CAUTION: Gross error found at entry 195.<br> Found:
|
|
0 Expected 4.84412e-40 Error: 2.17706e+268<br> 9835.22, 156.292, 11989.8,
|
|
1, 4.84412e-40<br> CAUTION: Gross error found at entry 196.<br> Found:
|
|
0 Expected 5.50199e-83 Error: 2.47272e+225<br> 9835.22, 417.884, 13329, 1,
|
|
5.50199e-83<br> CAUTION: Gross error found at entry 197.<br> Found: 0 Expected
|
|
1.28192e-205 Error: 5.76124e+102<br> 9835.22, 669.781, 15757.5, 1, 1.28192e-205<br>
|
|
CAUTION: Gross error found at entry 211.<br> Found: 0 Expected 3.83272e-28
|
|
Error: 1.72251e+280<br> 25444.1, 1123.88, 29224.8, 1, 3.83272e-28<br> CAUTION:
|
|
Gross error found at entry 212.<br> Found: 0 Expected 1.69815e-101 Error:
|
|
7.63188e+206<br> 25444.1, 3168.71, 34335.4, 1, 1.69815e-101<br> CAUTION:
|
|
Gross error found at entry 213.<br> Found: 0 Expected 1.09245e-217 Error:
|
|
4.90974e+90<br> 25444.1, 5236.73, 39885.1, 1, 1.09245e-217<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h24"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0">Error
|
|
Output For non central chi squared CDF complement with compiler GNU C++ version
|
|
7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, medium
|
|
parameters</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters"></a>CAUTION:
|
|
Gross error found at entry 36.<br> Found: 1.11022e-14 Expected 1.30043e-26
|
|
Error: 8.53738e+11<br> 1.95191, 109.376, 445.313, 1, 1.30043e-26<br> CAUTION:
|
|
Gross error found at entry 37.<br> Found: 0 Expected 1.45478e-39 Error: 6.53812e+268<br>
|
|
1.95191, 109.444, 556.98, 1, 1.45478e-39<br> CAUTION: Gross error found at
|
|
entry 54.<br> Found: 2.91989e-14 Expected 4.25949e-21 Error: 6.85501e+06<br>
|
|
1.95191, 159.586, 484.613, 1, 4.25949e-21<br> CAUTION: Gross error found
|
|
at entry 55.<br> Found: 0 Expected 1.33424e-37 Error: 5.99639e+270<br>
|
|
1.95191, 159.621, 646.292, 1, 1.33424e-37<br> CAUTION: Gross error found
|
|
at entry 56.<br> Found: 1.25455e-14 Expected 1.95903e-56 Error: 6.40393e+41<br>
|
|
1.95191, 160.056, 810.04, 1, 1.95903e-56<br> CAUTION: Gross error found at
|
|
entry 73.<br> Found: 0 Expected 4.34735e-25 Error: 1.9538e+283<br> 1.95191,
|
|
193.539, 586.473, 1, 4.34735e-25<br> CAUTION: Gross error found at entry
|
|
74.<br> Found: 0 Expected 4.66119e-45 Error: 2.09485e+263<br> 1.95191,
|
|
193.774, 782.902, 1, 4.66119e-45<br> CAUTION: Gross error found at entry
|
|
75.<br> Found: 4.77396e-15 Expected 8.92248e-68 Error: 5.35048e+52<br>
|
|
1.95191, 194.119, 980.352, 1, 8.92248e-68<br> CAUTION: Gross error found
|
|
at entry 111.<br> Found: 0 Expected 3.1064e-15 Error: 1.39609e+293<br>
|
|
20.4105, 84.4175, 314.484, 1, 3.1064e-15<br> CAUTION: Gross error found at
|
|
entry 112.<br> Found: 0 Expected 7.50903e-29 Error: 3.37473e+279<br> 20.4105,
|
|
94.9517, 461.449, 1, 7.50903e-29<br> CAUTION: Gross error found at entry
|
|
113.<br> Found: 3.77476e-15 Expected 1.74225e-43 Error: 2.1666e+28<br>
|
|
20.4105, 97.0751, 587.428, 1, 1.74225e-43<br> CAUTION: Gross error found
|
|
at entry 130.<br> Found: 8.88178e-16 Expected 4.13277e-23 Error: 2.14911e+07<br>
|
|
20.4105, 151.548, 515.876, 1, 4.13277e-23<br> CAUTION: Gross error found
|
|
at entry 131.<br> Found: 1.75415e-14 Expected 1.92146e-41 Error: 9.12928e+26<br>
|
|
20.4105, 152.75, 692.642, 1, 1.92146e-41<br> CAUTION: Gross error found at
|
|
entry 132.<br> Found: 1.38778e-14 Expected 7.09864e-64 Error: 1.95499e+49<br>
|
|
20.4105, 158.441, 894.26, 1, 7.09864e-64<br> CAUTION: Gross error found at
|
|
entry 149.<br> Found: 2.22045e-16 Expected 8.74501e-28 Error: 2.5391e+11<br>
|
|
20.4105, 191.433, 635.532, 1, 8.74501e-28<br> CAUTION: Gross error found
|
|
at entry 150.<br> Found: 0 Expected 6.94227e-50 Error: 3.12002e+258<br>
|
|
20.4105, 191.501, 847.648, 1, 6.94227e-50<br> CAUTION: Gross error found
|
|
at entry 151.<br> Found: 3.40838e-14 Expected 5.3889e-75 Error: 6.32482e+60<br>
|
|
20.4105, 191.898, 1061.55, 1, 5.3889e-75<br> CAUTION: Gross error found at
|
|
entry 206.<br> Found: 5.88418e-15 Expected 2.69136e-22 Error: 2.18632e+07<br>
|
|
22.8625, 141.209, 492.215, 1, 2.69136e-22<br> CAUTION: Gross error found
|
|
at entry 207.<br> Found: 3.60822e-14 Expected 1.64941e-40 Error: 2.18759e+26<br>
|
|
22.8625, 145.168, 672.121, 1, 1.64941e-40<br> CAUTION: Gross error found
|
|
at entry 208.<br> Found: 3.73035e-14 Expected 1.6094e-61 Error: 2.31784e+47<br>
|
|
22.8625, 148.129, 854.96, 1, 1.6094e-61<br> CAUTION: Gross error found at
|
|
entry 225.<br> Found: 0 Expected 3.73672e-27 Error: 1.67937e+281<br> 22.8625,
|
|
182.675, 616.613, 1, 3.73672e-27<br> CAUTION: Gross error found at entry
|
|
226.<br> Found: 0 Expected 8.85688e-49 Error: 3.98049e+259<br> 22.8625,
|
|
183.147, 824.038, 1, 8.85688e-49<br> CAUTION: Gross error found at entry
|
|
227.<br> Found: 0 Expected 2.29176e-74 Error: 1.02997e+234<br> 22.8625,
|
|
186.799, 1048.31, 1, 2.29176e-74<br> CAUTION: Gross error found at entry
|
|
282.<br> Found: 0 Expected 2.18831e-21 Error: 9.8348e+286<br> 23.3804,
|
|
132.721, 468.305, 1, 2.18831e-21<br> CAUTION: Gross error found at entry
|
|
283.<br> Found: 0 Expected 1.3071e-38 Error: 5.87439e+269<br> 23.3804,
|
|
135.747, 636.51, 1, 1.3071e-38<br> CAUTION: Gross error found at entry 284.<br>
|
|
Found: 1.84297e-14 Expected 8.27843e-58 Error: 2.22623e+43<br> 23.3804, 136.272,
|
|
798.262, 1, 8.27843e-58<br> CAUTION: Gross error found at entry 301.<br>
|
|
Found: 0 Expected 9.85282e-26 Error: 4.42808e+282<br> 23.3804, 169.826, 579.619,
|
|
1, 9.85282e-26<br> CAUTION: Gross error found at entry 302.<br> Found:
|
|
0 Expected 4.8094e-47 Error: 2.16145e+261<br> 23.3804, 174.486, 791.465,
|
|
1, 4.8094e-47<br> CAUTION: Gross error found at entry 303.<br> Found: 1.11022e-16
|
|
Expected 6.70476e-71 Error: 1.65587e+54<br> 23.3804, 175.686, 995.333, 1,
|
|
6.70476e-71<br> CAUTION: Gross error found at entry 358.<br> Found: 0 Expected
|
|
3.9702e-21 Error: 1.7843e+287<br> 26.2704, 126.472, 458.227, 1, 3.9702e-21<br>
|
|
CAUTION: Gross error found at entry 359.<br> *** FURTHER CONTENT HAS BEEN
|
|
TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h25"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c">Error
|
|
Output For non central t CDF complement with compiler GNU C++ version 7.1.0
|
|
and library Rmath 3.2.3 and test data Non Central T</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T"></a>CAUTION:
|
|
Gross error found at entry 56.<br> Found: 0.000186411 Expected 7.85192e-05
|
|
Error: 1.37408<br> 61.6335, 46.2251, 68.8608, 0.999921, 7.85192e-05<br>
|
|
CAUTION: Gross error found at entry 75.<br> Found: 0.00011439 Expected 5.05344e-05
|
|
Error: 1.26361<br> 80.8418, 60.6313, 86.1278, 0.999949, 5.05344e-05<br>
|
|
CAUTION: Gross error found at entry 93.<br> Found: 0.000655162 Expected 0.000423927
|
|
Error: 0.545458<br> 100.733, 50.3663, 65.7619, 0.999576, 0.000423927<br>
|
|
CAUTION: Gross error found at entry 112.<br> Found: 0.000518249 Expected
|
|
0.00034473 Error: 0.503348<br> 127.953, 63.9764, 81.0824, 0.999655, 0.00034473<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h26"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0">Error
|
|
Output For non central t CDF with compiler GNU C++ version 7.1.0 and library
|
|
Rmath 3.2.3 and test data Non Central T</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T"></a>CAUTION:
|
|
Gross error found at entry 74.<br> Found: 0.000830062 Expected 0.000522858
|
|
Error: 0.587549<br> 79.7478, -39.8739, -53.8066, 0.000522858, 0.999477<br>
|
|
CAUTION: Gross error found at entry 94.<br> Found: 7.69292e-05 Expected 3.54024e-05
|
|
Error: 1.17299<br> 101.191, -75.8936, -104.104, 3.54024e-05, 0.999965<br>
|
|
CAUTION: Gross error found at entry 113.<br> Found: 5.07713e-05 Expected
|
|
2.4439e-05 Error: 1.07747<br> 128.792, -96.5942, -128.112, 2.4439e-05, 0.999976<br>
|
|
CAUTION: Gross error found at entry 132.<br> Found: 4.08612e-05 Expected
|
|
2.01542e-05 Error: 1.02743<br> 146.56, -109.92, -143.392, 2.01542e-05, 0.99998<br>
|
|
CAUTION: Gross error found at entry 151.<br> Found: 3.55146e-05 Expected
|
|
1.7803e-05 Error: 0.994869<br> 159.586, -119.689, -154.522, 1.7803e-05, 0.999982<br>
|
|
CAUTION: Gross error found at entry 170.<br> Found: 3.03671e-05 Expected
|
|
1.55023e-05 Error: 0.958873<br> 175.686, -131.765, -168.211, 1.55023e-05,
|
|
0.999984<br> CAUTION: Gross error found at entry 189.<br> Found: 2.61339e-05
|
|
Expected 1.3581e-05 Error: 0.924298<br> 192.978, -144.733, -182.834, 1.3581e-05,
|
|
0.999986<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h27"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_">Error
|
|
Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Mathematica Data - Large orders and other bug cases</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases"></a>CAUTION:
|
|
Found non-finite result, when a finite value was expected at entry 0<br>
|
|
Found: -nan Expected 2.07309e+257 Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br>
|
|
CAUTION: Gross error found at entry 0.<br> Found: -nan Expected 2.07309e+257
|
|
Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br> CAUTION: Found non-finite
|
|
result, when a finite value was expected at entry 1<br> Found: -nan Expected
|
|
7.42912e+188 Error: 1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION:
|
|
Gross error found at entry 1.<br> Found: -nan Expected 7.42912e+188 Error:
|
|
1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION: Found non-finite result,
|
|
when a finite value was expected at entry 2<br> Found: -nan Expected -4.81295e+247
|
|
Error: 1.79769e+308<br> 166, 2, -4.81295e+247<br> CAUTION: Gross error
|
|
found at entry 2.<br> Found: -nan Expected -4.81295e+247 Error: 1.79769e+308<br>
|
|
166, 2, -4.81295e+247<br> CAUTION: Found non-finite result, when a finite
|
|
value was expected at entry 3<br> Found: -nan Expected -1.88439e+218 Error:
|
|
1.79769e+308<br> 166, 3, -1.88439e+218<br> CAUTION: Gross error found at
|
|
entry 3.<br> Found: -nan Expected -1.88439e+218 Error: 1.79769e+308<br>
|
|
166, 3, -1.88439e+218<br> CAUTION: Found non-finite result, when a finite
|
|
value was expected at entry 4<br> Found: -nan Expected 7.53144e+74 Error:
|
|
1.79769e+308<br> 171, 23, 7.53144e+74<br> CAUTION: Gross error found at
|
|
entry 4.<br> Found: -nan Expected 7.53144e+74 Error: 1.79769e+308<br> 171,
|
|
23, 7.53144e+74<br> CAUTION: Found non-finite result, when a finite value
|
|
was expected at entry 5<br> Found: -nan Expected -6.52661e-66 Error: 1.79769e+308<br>
|
|
168, 150, -6.52661e-66<br> CAUTION: Gross error found at entry 5.<br> Found:
|
|
-nan Expected -6.52661e-66 Error: 1.79769e+308<br> 168, 150, -6.52661e-66<br>
|
|
CAUTION: Found non-finite result, when a finite value was expected at entry
|
|
6<br> Found: -nan Expected 9.2734e-88 Error: 1.79769e+308<br> 169, 202,
|
|
9.2734e-88<br> CAUTION: Gross error found at entry 6.<br> Found: -nan Expected
|
|
9.2734e-88 Error: 1.79769e+308<br> 169, 202, 9.2734e-88<br> Outside supported
|
|
domain<br> 20, -9.5, -0.00103076<br> Outside supported domain<br> 21,
|
|
-9.5, 4.28582e+26<br> Outside supported domain<br> 22, -9.5, -0.00419144<br>
|
|
Outside supported domain<br> 23, -9.5, 8.6745e+29<br> Outside supported
|
|
domain<br> 24, -9.5, -0.0204825<br> Outside supported domain<br> 25,
|
|
-9.5, 2.08188e+33<br> Outside supported domain<br> 26, -9.5, -0.118403<br>
|
|
Outside supported domain<br> 27, -9.5, 5.84592e+36<br> Outside supported
|
|
domain<br> 28, -9.5, -0.798969<br> Outside supported domain<br> 29, -9.5,
|
|
1.89875e+40<br> Outside supported domain<br> 30, -9.5, -6.22245<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h28"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0">Error
|
|
Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Mathematica Data - large negative arguments</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments"></a>Outside
|
|
supported domain<br> 124, -1.5, 7.63705e+240<br> Outside supported domain<br>
|
|
124, -2.5, 7.63705e+240<br> Outside supported domain<br> 124, -3.5, 7.63705e+240<br>
|
|
Outside supported domain<br> 124, -4.5, 7.63705e+240<br> Outside supported
|
|
domain<br> 124, -5.5, 7.63705e+240<br> Outside supported domain<br> 124,
|
|
-6.5, 7.63705e+240<br> Outside supported domain<br> 124, -7.5, 7.63705e+240<br>
|
|
Outside supported domain<br> 124, -8.5, 7.63705e+240<br> Outside supported
|
|
domain<br> 124, -9.5, 7.63705e+240<br> Outside supported domain<br> 124,
|
|
-10.5, 7.63705e+240<br> Outside supported domain<br> 124, -11.5, 7.63705e+240<br>
|
|
Outside supported domain<br> 124, -12.5, 7.63705e+240<br> Outside supported
|
|
domain<br> 124, -13.5, 7.63705e+240<br> Outside supported domain<br>
|
|
124, -14.5, 7.63705e+240<br> Outside supported domain<br> 124, -15.5, 7.63705e+240<br>
|
|
Outside supported domain<br> 124, -16.5, 7.63705e+240<br> Outside supported
|
|
domain<br> 124, -17.5, 7.63705e+240<br> Outside supported domain<br>
|
|
124, -18.5, 7.63705e+240<br> Outside supported domain<br> 124, -19.5, 7.63705e+240<br>
|
|
Outside supported domain<br> 124, -20.5, 7.63705e+240<br> Outside supported
|
|
domain<br> 124, -1.5, -7.63705e+240<br> Outside supported domain<br>
|
|
124, -2.5, -7.63705e+240<br> Outside supported domain<br> 124, -3.5, -7.63705e+240<br>
|
|
Outside supported domain<br> 124, -4.5, -7.63705e+240<br> Outside supported
|
|
domain<br> 124, -5.5, -7.63705e+240<br> Outside supported domain<br>
|
|
124, -6.5, -7.63705e+240<br> Outside supported domain<br> 124, -7.5, -7.63705e+240<br>
|
|
Outside supported domain<br> 124, -8.5, -7.63705e+240<br> Outside supported
|
|
domain<br> 124, -9.5, -7.63705e+240<br> Outside supported domain<br>
|
|
124, -10.5, -7.63705e+240<br> Outside supported domain<br> 124, -11.5,
|
|
-7.63705e+240<br> Outside supported domain<br> 124, -12.5, -7.63705e+240<br>
|
|
Outside supported domain<br> 124, -13.5, -7.63705e+240<br> Outside supported
|
|
domain<br> 124, -14.5, -7.63705e+240<br> Outside supported domain<br>
|
|
124, -15.5, -7.63705e+240<br> Outside supported domain<br> 124, -16.5,
|
|
-7.63705e+240<br> Outside supported domain<br> 124, -17.5, -7.63705e+240<br>
|
|
Outside supported domain<br> 124, -18.5, -7.63705e+240<br> Outside supported
|
|
domain<br> 124, -19.5, -7.63705e+240<br> Outside supported domain<br>
|
|
124, -20.5, -7.63705e+240<br> Outside supported domain<br> 1, -0.5, 8.9348<br>
|
|
Outside supported domain<br> 2, -0.5, -0.828797<br> Outside supported domain<br>
|
|
3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47425<br>
|
|
Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br>
|
|
6, -0.5, -43.4579<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br>
|
|
Outside supported domain<br> 8, -0.5, -1059.96<br> Outside supported domain<br>
|
|
9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -42108.9<br>
|
|
Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported
|
|
domain<br> 12, -0.5, -2.46448e+06<br> Outside supported domain<br> 13,
|
|
-0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -1.9918e+08<br>
|
|
Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported
|
|
domain<br> 16, -0.5, -2.12394e+10<br> Outside supported domain<br> 17,
|
|
-0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -2.88824e+12<br>
|
|
Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported
|
|
domain<br> 20, -0.5, -4.87773e+14<br> Outside supported domain<br> 21,
|
|
-0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br>
|
|
Outside supported domain<br> 2, -0.5, -0.828843<br> Outside supported domain<br>
|
|
3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47791<br>
|
|
Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br>
|
|
6, -0.5, -44.0732<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br>
|
|
Outside supported domain<br> 8, -0.5, -1237.15<br> Outside supported domain<br>
|
|
9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -120071<br>
|
|
Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported
|
|
domain<br> 12, -0.5, -5.11131e+07<br> Outside supported domain<br> 13,
|
|
-0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -4.1064e+10<br>
|
|
Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported
|
|
domain<br> 16, -0.5, -4.44822e+13<br> Outside supported domain<br> 17,
|
|
-0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -6.08254e+16<br>
|
|
Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported
|
|
domain<br> 20, -0.5, -1.02182e+20<br> Outside supported domain<br> 21,
|
|
-0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br>
|
|
Outside supported domain<br> 2, -0.5, -0.828751<br> Outside supported domain<br>
|
|
3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47059<br>
|
|
Outside supported domain<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY
|
|
***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h29"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1">Error
|
|
Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Mathematica Data - negative arguments</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments"></a>Outside
|
|
supported domain<br> 1, -12.75, 19.6638<br> Outside supported domain<br>
|
|
1, -12.25, 19.6608<br> Outside supported domain<br> 1, -11.75, 19.6576<br>
|
|
Outside supported domain<br> 1, -11.25, 19.6542<br> Outside supported domain<br>
|
|
1, -10.75, 19.6504<br> Outside supported domain<br> 1, -10.25, 19.6463<br>
|
|
Outside supported domain<br> 1, -9.75, 19.6417<br> Outside supported domain<br>
|
|
1, -9.25, 19.6367<br> Outside supported domain<br> 1, -8.75, 19.6312<br>
|
|
Outside supported domain<br> 1, -8.25, 19.625<br> Outside supported domain<br>
|
|
1, -7.75, 19.6181<br> Outside supported domain<br> 1, -7.25, 19.6104<br>
|
|
Outside supported domain<br> 1, -6.75, 19.6015<br> Outside supported domain<br>
|
|
1, -6.25, 19.5913<br> Outside supported domain<br> 1, -5.75, 19.5795<br>
|
|
Outside supported domain<br> 1, -5.25, 19.5657<br> Outside supported domain<br>
|
|
1, -4.75, 19.5493<br> Outside supported domain<br> 1, -4.25, 19.5294<br>
|
|
Outside supported domain<br> 1, -3.75, 19.505<br> Outside supported domain<br>
|
|
1, -3.25, 19.4741<br> Outside supported domain<br> 1, -2.75, 19.4339<br>
|
|
Outside supported domain<br> 1, -2.25, 19.3794<br> Outside supported domain<br>
|
|
1, -1.75, 19.3016<br> Outside supported domain<br> 1, -1.25, 19.1819<br>
|
|
Outside supported domain<br> 1, -0.75, 18.9751<br> Outside supported domain<br>
|
|
1, -0.25, 18.5419<br> Outside supported domain<br> 2, -12.75, -124.031<br>
|
|
Outside supported domain<br> 2, -12.25, 124.019<br> Outside supported domain<br>
|
|
2, -11.75, -124.032<br> Outside supported domain<br> 2, -11.25, 124.018<br>
|
|
Outside supported domain<br> 2, -10.75, -124.033<br> Outside supported
|
|
domain<br> 2, -10.25, 124.016<br> Outside supported domain<br> 2, -9.75,
|
|
-124.035<br> Outside supported domain<br> 2, -9.25, 124.015<br> Outside
|
|
supported domain<br> 2, -8.75, -124.037<br> Outside supported domain<br>
|
|
2, -8.25, 124.012<br> Outside supported domain<br> 2, -7.75, -124.04<br>
|
|
Outside supported domain<br> 2, -7.25, 124.009<br> Outside supported domain<br>
|
|
2, -6.75, -124.044<br> Outside supported domain<br> 2, -6.25, 124.003<br>
|
|
Outside supported domain<br> 2, -5.75, -124.051<br> Outside supported domain<br>
|
|
2, -5.25, 123.995<br> Outside supported domain<br> 2, -4.75, -124.061<br>
|
|
Outside supported domain<br> 2, -4.25, 123.981<br> Outside supported domain<br>
|
|
2, -3.75, -124.08<br> Outside supported domain<br> 2, -3.25, 123.955<br>
|
|
Outside supported domain<br> 2, -2.75, -124.118<br> Outside supported domain<br>
|
|
2, -2.25, 123.897<br> Outside supported domain<br> 2, -1.75, -124.214<br>
|
|
Outside supported domain<br> 2, -1.25, 123.721<br> Outside supported domain<br>
|
|
2, -0.75, -124.587<br> Outside supported domain<br> 2, -0.25, 122.697<br>
|
|
Outside supported domain<br> 3, -12.75, 1558.54<br> Outside supported domain<br>
|
|
3, -12.25, 1558.54<br> Outside supported domain<br> 3, -11.75, 1558.54<br>
|
|
Outside supported domain<br> 3, -11.25, 1558.54<br> Outside supported domain<br>
|
|
3, -10.75, 1558.54<br> Outside supported domain<br> 3, -10.25, 1558.54<br>
|
|
Outside supported domain<br> 3, -9.75, 1558.54<br> Outside supported domain<br>
|
|
3, -9.25, 1558.54<br> Outside supported domain<br> 3, -8.75, 1558.54<br>
|
|
Outside supported domain<br> 3, -8.25, 1558.54<br> Outside supported domain<br>
|
|
3, -7.75, 1558.54<br> Outside supported domain<br> 3, -7.25, 1558.54<br>
|
|
Outside supported domain<br> 3, -6.75, 1558.54<br> Outside supported domain<br>
|
|
3, -6.25, 1558.54<br> Outside supported domain<br> 3, -5.75, 1558.54<br>
|
|
Outside supported domain<br> 3, -5.25, 1558.54<br> Outside supported domain<br>
|
|
3, -4.75, 1558.53<br> Outside supported domain<br> 3, -4.25, 1558.53<br>
|
|
Outside supported domain<br> 3, -3.75, 1558.52<br> Outside supported domain<br>
|
|
3, -3.25, 1558.51<br> Outside supported domain<br> 3, -2.75, 1558.49<br>
|
|
Outside supported domain<br> 3, -2.25, 1558.46<br> Outside supported domain<br>
|
|
3, -1.75, 1558.38<br> Outside supported domain<br> 3, -1.25, 1558.22<br>
|
|
Outside supported domain<br> 3, -0.75, 1557.75<br> Outside supported domain<br>
|
|
3, -0.25, 1555.76<br> Outside supported domain<br> 4, -12.75, -24481.6<br>
|
|
Outside supported domain<br> 4, -12.25, 24481.6<br> Outside supported domain<br>
|
|
4, -11.75, -24481.6<br> Outside supported domain<br> 4, -11.25, 24481.6<br>
|
|
Outside supported domain<br> 4, -10.75, -24481.6<br> Outside supported
|
|
domain<br> 4, -10.25, 24481.6<br> Outside supported domain<br> 4, -9.75,
|
|
-24481.6<br> Outside supported domain<br> 4, -9.25, 24481.6<br> Outside
|
|
supported domain<br> 4, -8.75, -24481.6<br> Outside supported domain<br>
|
|
4, -8.25, 24481.6<br> Outside supported domain<br> 4, -7.75, -24481.6<br>
|
|
Outside supported domain<br> 4, -7.25, 24481.6<br> Outside supported domain<br>
|
|
4, -6.75, -24481.6<br> Outside supported domain<br> 4, -6.25, 24481.6<br>
|
|
Outside supported domain<br> 4, -5.75, -24481.6<br> Outside supported domain<br>
|
|
4, -5.25, 24481.6<br> Outside supported domain<br> *** FURTHER CONTENT
|
|
HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h30"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2">Error
|
|
Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
|
|
3.2.3 and test data Mathematica Data - large arguments</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments"></a>CAUTION:
|
|
Gross error found at entry 211.<br> Found: -0 Expected -8.44974e-268 Error:
|
|
3.79751e+40<br> 30, 8.58993e+09, -8.44974e-268<br> CAUTION: Gross error
|
|
found at entry 212.<br> Found: -0 Expected -7.86943e-277 Error: 3.5367e+31<br>
|
|
30, 1.71799e+10, -7.86943e-277<br> CAUTION: Gross error found at entry 213.<br>
|
|
Found: -0 Expected -7.32898e-286 Error: 3.29381e+22<br> 30, 3.43597e+10,
|
|
-7.32898e-286<br> CAUTION: Gross error found at entry 214.<br> Found: -0
|
|
Expected -6.82564e-295 Error: 3.0676e+13<br> 30, 6.87195e+10, -6.82564e-295<br>
|
|
CAUTION: Gross error found at entry 215.<br> Found: -0 Expected -6.35687e-304
|
|
Error: 28568.3<br> 30, 1.37439e+11, -6.35687e-304<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h31"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel Iv: Mathworld Data (large values)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_"></a>domain
|
|
error<br> -1, 3.72917e-155, 1.86459e-155<br> domain error<br> -1.125,
|
|
3.72917e-155, -1.34964e+173<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h32"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel Iv: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data"></a>domain
|
|
error<br> -80.4919, 24.7501, 4.18698e+28<br> domain error<br> -80.4919,
|
|
63.7722, 2.03248e+06<br> domain error<br> -74.6026, 24.7501, 7.20977e+23<br>
|
|
domain error<br> -74.6026, 63.7722, 8.7549e+08<br> domain error<br> -72.9046,
|
|
24.7501, 1.04535e+22<br> domain error<br> -72.9046, 63.7722, 4.7162e+09<br>
|
|
domain error<br> -62.3236, 24.7501, 3.65147e+14<br> domain error<br>
|
|
-62.3236, 63.7722, 8.56683e+13<br> domain error<br> -55.7932, 24.7501,
|
|
-7.70364e+09<br> domain error<br> -55.7932, 63.7722, 1.95969e+16<br>
|
|
domain error<br> -44.3004, 9.50706, 2.93478e+22<br> domain error<br>
|
|
-44.3004, 24.7501, 640.568<br> domain error<br> -44.3004, 63.7722, 8.05557e+19<br>
|
|
domain error<br> -38.3666, 5.11399, 2.89105e+27<br> domain error<br>
|
|
-38.3666, 9.50706, 8.80632e+16<br> domain error<br> -38.3666, 24.7501,
|
|
0.389004<br> domain error<br> -38.3666, 63.7722, 3.06303e+21<br> underflow<br>
|
|
81.1584, 0.00177219, 0<br> underflow<br> 81.1584, 0.00221773, 0<br> underflow<br>
|
|
81.1584, 0.0074445, 6.08857e-319<br> underflow<br> 82.6752, 0.00177219,
|
|
0<br> underflow<br> 82.6752, 0.00221773, 0<br> underflow<br> 82.6752,
|
|
0.0074445, 0<br> underflow<br> 91.5014, 0.00177219, 0<br> underflow<br>
|
|
91.5014, 0.00221773, 0<br> underflow<br> 91.5014, 0.0074445, 0<br> underflow<br>
|
|
91.5014, 0.014336, 0<br> underflow<br> 91.5014, 0.0176092, 0<br> underflow<br>
|
|
92.9777, 0.00177219, 0<br> underflow<br> 92.9777, 0.00221773, 0<br> underflow<br>
|
|
92.9777, 0.0074445, 0<br> underflow<br> 92.9777, 0.014336, 0<br> underflow<br>
|
|
92.9777, 0.0176092, 0<br> underflow<br> 93.539, 0.00177219, 0<br> underflow<br>
|
|
93.539, 0.00221773, 0<br> underflow<br> 93.539, 0.0074445, 0<br> underflow<br>
|
|
93.539, 0.014336, 0<br> underflow<br> 93.539, 0.0176092, 0<br> underflow<br>
|
|
93.7736, 0.00177219, 0<br> underflow<br> 93.7736, 0.00221773, 0<br> underflow<br>
|
|
93.7736, 0.0074445, 0<br> underflow<br> 93.7736, 0.014336, 0<br> underflow<br>
|
|
93.7736, 0.0176092, 0<br> underflow<br> 98.5763, 0.00177219, 0<br> underflow<br>
|
|
98.5763, 0.00221773, 0<br> underflow<br> 98.5763, 0.0074445, 0<br> underflow<br>
|
|
98.5763, 0.014336, 0<br> underflow<br> 98.5763, 0.0176092, 0<br> underflow<br>
|
|
99.2923, 0.00177219, 0<br> underflow<br> 99.2923, 0.00221773, 0<br> underflow<br>
|
|
99.2923, 0.0074445, 0<br> underflow<br> 99.2923, 0.014336, 0<br> underflow<br>
|
|
99.2923, 0.0176092, 0<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h33"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel In: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data"></a>underflow<br>
|
|
70, 0.00177219, 1.75887e-314<br> underflow<br> 73, 0.00177219, 0<br>
|
|
underflow<br> 73, 0.00221773, 4.24896e-322<br> underflow<br> 76, 0.00177219,
|
|
0<br> underflow<br> 76, 0.00221773, 0<br> underflow<br> 79, 0.00177219,
|
|
0<br> underflow<br> 79, 0.00221773, 0<br> underflow<br> 79, 0.0074445,
|
|
1.38676e-309<br> underflow<br> 82, 0.00177219, 0<br> underflow<br>
|
|
82, 0.00221773, 0<br> underflow<br> 82, 0.0074445, 1.33398e-322<br> underflow<br>
|
|
85, 0.00177219, 0<br> underflow<br> 85, 0.00221773, 0<br> underflow<br>
|
|
85, 0.0074445, 0<br> underflow<br> 85, 0.014336, 1.81568e-311<br> underflow<br>
|
|
88, 0.00177219, 0<br> underflow<br> 88, 0.00221773, 0<br> underflow<br>
|
|
88, 0.0074445, 0<br> underflow<br> 88, 0.014336, 9.88131e-324<br> underflow<br>
|
|
88, 0.0176092, 7.34647e-316<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h34"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel Iv: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data"></a>domain
|
|
error<br> -4.99902, 2.125, 0.0267921<br> domain error<br> -5.5, 10, 597.578<br>
|
|
domain error<br> -5.5, 100, 9.22363e+41<br> domain error<br> -10.0003,
|
|
0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 50, 1.07153e+20<br>
|
|
domain error<br> -141.4, 100, 2066.28<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h35"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2">Error
|
|
Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library GSL 2.1 and test data Bessel In: Mathworld Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_"></a>underflow<br>
|
|
10, 1e-100, 0<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h36"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel In: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data"></a>domain
|
|
error<br> -2, 0, 0<br> domain error<br> -5, 100, 9.47009e+41<br> domain
|
|
error<br> -5, -1, -0.000271463<br> domain error<br> 10, -5, 0.00458004<br>
|
|
domain error<br> -100, -200, 4.35275e+74<br> underflow<br> 10, 1e-100,
|
|
0<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h37"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel I1: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data"></a>domain
|
|
error<br> 1, -2, -1.59064<br> domain error<br> 1, -8, -399.873<br>
|
|
domain error<br> 1, -10, -2670.99<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h38"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel I0: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data"></a>domain
|
|
error<br> 0, -2, 2.27959<br> domain error<br> 0, -7, 168.594<br> domain
|
|
error<br> 0, -1, 1.26607<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h39"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel Iv: Mathworld Data (large values)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_"></a>Bad
|
|
argument in __cyl_bessel_i.<br> -1, 3.72917e-155, 1.86459e-155<br> Bad
|
|
argument in __cyl_bessel_i.<br> -1.125, 3.72917e-155, -1.34964e+173<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h40"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel Iv: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data"></a>Bad
|
|
argument in __cyl_bessel_i.<br> -80.4919, 24.7501, 4.18698e+28<br> Bad
|
|
argument in __cyl_bessel_i.<br> -80.4919, 63.7722, 2.03248e+06<br> Bad
|
|
argument in __cyl_bessel_i.<br> -74.6026, 24.7501, 7.20977e+23<br> Bad
|
|
argument in __cyl_bessel_i.<br> -74.6026, 63.7722, 8.7549e+08<br> Bad argument
|
|
in __cyl_bessel_i.<br> -72.9046, 24.7501, 1.04535e+22<br> Bad argument
|
|
in __cyl_bessel_i.<br> -72.9046, 63.7722, 4.7162e+09<br> Bad argument in
|
|
__cyl_bessel_i.<br> -62.3236, 24.7501, 3.65147e+14<br> Bad argument in
|
|
__cyl_bessel_i.<br> -62.3236, 63.7722, 8.56683e+13<br> Bad argument in
|
|
__cyl_bessel_i.<br> -55.7932, 24.7501, -7.70364e+09<br> Bad argument in
|
|
__cyl_bessel_i.<br> -55.7932, 63.7722, 1.95969e+16<br> Bad argument in
|
|
__cyl_bessel_i.<br> -44.3004, 9.50706, 2.93478e+22<br> Bad argument in
|
|
__cyl_bessel_i.<br> -44.3004, 24.7501, 640.568<br> Bad argument in __cyl_bessel_i.<br>
|
|
-44.3004, 63.7722, 8.05557e+19<br> Bad argument in __cyl_bessel_i.<br>
|
|
-38.3666, 5.11399, 2.89105e+27<br> Bad argument in __cyl_bessel_i.<br>
|
|
-38.3666, 9.50706, 8.80632e+16<br> Bad argument in __cyl_bessel_i.<br>
|
|
-38.3666, 24.7501, 0.389004<br> Bad argument in __cyl_bessel_i.<br> -38.3666,
|
|
63.7722, 3.06303e+21<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h41"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel Iv: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_i.<br> -4.99902, 2.125, 0.0267921<br> Bad argument
|
|
in __cyl_bessel_i.<br> -5.5, 10, 597.578<br> Bad argument in __cyl_bessel_i.<br>
|
|
-5.5, 100, 9.22363e+41<br> Bad argument in __cyl_bessel_i.<br> -10.0003,
|
|
0.000976562, 1.41474e+35<br> Bad argument in __cyl_bessel_i.<br> -10.0003,
|
|
50, 1.07153e+20<br> Bad argument in __cyl_bessel_i.<br> -141.4, 100, 2066.28<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h42"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3">Error
|
|
Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library <cmath> and test data Bessel In: Mathworld Data (Integer
|
|
Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_"></a>Bad
|
|
argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br>
|
|
-5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br>
|
|
Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument
|
|
in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h43"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4">Error
|
|
Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library <cmath> and test data Bessel I1: Mathworld Data (Integer
|
|
Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_"></a>Bad
|
|
argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br>
|
|
1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h44"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5">Error
|
|
Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library <cmath> and test data Bessel I0: Mathworld Data (Integer
|
|
Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_"></a>Bad
|
|
argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br>
|
|
0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h45"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel In: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br>
|
|
-5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br>
|
|
Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument
|
|
in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h46"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel I1: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br>
|
|
1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h47"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5">Error
|
|
Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel I0: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br>
|
|
0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h48"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel J: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data"></a>underflow<br>
|
|
63.8868, 5.5381e-05, 0<br> underflow<br> 63.8868, 6.9304e-05, 0<br> underflow<br>
|
|
63.8868, 0.000232641, 0<br> underflow<br> 63.8868, 0.000448, 8.39912e-323<br>
|
|
underflow<br> 63.8868, 0.000550287, 4.32897e-317<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h49"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel J: Mathworld Data (large values)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_"></a>domain
|
|
error<br> -0.5, 1.2459e-206, 7.14823e+102<br> domain error<br> -256,
|
|
8, 0<br> domain error<br> -2.5, 4, -0.0145679<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h50"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel J: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data"></a>domain
|
|
error<br> -5.5, 3.1416, -2.5582<br> domain error<br> -5.5, 10000, 0.00244984<br>
|
|
domain error<br> -5.5, 10000, 0.00244984<br> domain error<br> -5.5, 1e+06,
|
|
0.000279243<br> domain error<br> -0.5, 101, 0.0708185<br> domain error<br>
|
|
-10.0003, 0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 15, -0.0902239<br>
|
|
domain error<br> -10.0003, 100, -0.0547614<br> domain error<br> -10.0003,
|
|
20000, -0.00556869<br> domain error<br> -8.5, 12.5664, -0.257087<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h51"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3">Error
|
|
Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library GSL 2.1 and test data Bessel JN: Mathworld Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_"></a>underflow<br>
|
|
10, 1e-100, 0<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h52"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel JN: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data"></a>domain
|
|
error<br> -1, 1.25, -0.510623<br> domain error<br> -2, 0, 0<br> domain
|
|
error<br> 5, -10, 0.234062<br> domain error<br> -5, 1e+06, 0.000725964<br>
|
|
domain error<br> -5, -1, 0.000249758<br> domain error<br> 10, -10, 0.207486<br>
|
|
domain error<br> 10, -5, 0.0014678<br> domain error<br> -10, 1e+06, -0.000331079<br>
|
|
underflow<br> 10, 1e-100, 0<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h53"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel J1: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data"></a>domain
|
|
error<br> 1, -2, -0.576725<br> domain error<br> 1, -8, -0.234636<br>
|
|
domain error<br> 1, -10, -0.0434727<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h54"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel J0: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data"></a>domain
|
|
error<br> 0, -2, 0.223891<br> domain error<br> 0, -8, 0.171651<br>
|
|
domain error<br> 0, -10, -0.245936<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h55"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel J: Mathworld Data (large values)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_"></a>Bad
|
|
argument in __cyl_bessel_j.<br> -0.5, 1.2459e-206, 7.14823e+102<br> Bad
|
|
argument in __cyl_bessel_j.<br> -256, 8, 1.46866e-353<br> Bad argument
|
|
in __cyl_bessel_j.<br> -2.5, 4, -0.0145679<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h56"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel J: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_j.<br> -5.5, 3.1416, -2.5582<br> Bad argument
|
|
in __cyl_bessel_j.<br> -5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br>
|
|
-5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br> -5.5, 1e+06,
|
|
0.000279243<br> Bad argument in __cyl_bessel_j.<br> -0.5, 101, 0.0708185<br>
|
|
Bad argument in __cyl_bessel_j.<br> -10.0003, 0.000976562, 1.41474e+35<br>
|
|
Bad argument in __cyl_bessel_j.<br> -10.0003, 15, -0.0902239<br> Bad argument
|
|
in __cyl_bessel_j.<br> -10.0003, 100, -0.0547614<br> Bad argument in __cyl_bessel_j.<br>
|
|
-10.0003, 20000, -0.00556869<br> Bad argument in __cyl_bessel_j.<br> -8.5,
|
|
12.5664, -0.257087<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h57"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4">Error
|
|
Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library <cmath> and test data Bessel JN: Mathworld Data (Integer
|
|
Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_"></a>Bad
|
|
argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in
|
|
__cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br>
|
|
5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br>
|
|
Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument
|
|
in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br>
|
|
10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br>
|
|
CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318
|
|
Error: 2.305<br> 1000, 100000, 0.00128318<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h58"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5">Error
|
|
Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library <cmath> and test data Bessel J1: Mathworld Data (Integer
|
|
Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_"></a>Bad
|
|
argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br>
|
|
1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h59"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6">Error
|
|
Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library <cmath> and test data Bessel J0: Mathworld Data (Integer
|
|
Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_"></a>Bad
|
|
argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br>
|
|
0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h60"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel JN: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in
|
|
__cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br>
|
|
5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br>
|
|
Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument
|
|
in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br>
|
|
10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br>
|
|
CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318
|
|
Error: 2.305<br> 1000, 100000, 0.00128318<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h61"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel J1: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br>
|
|
1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h62"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3">Error
|
|
Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel J0: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br>
|
|
0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h63"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi">Error
|
|
Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel Kv: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data"></a>domain
|
|
error<br> -80.4919, 24.7501, 6.57902e+28<br> domain error<br> -80.4919,
|
|
63.7722, 2.39552e-09<br> domain error<br> -80.4919, 125.28, 3.06904e-45<br>
|
|
domain error<br> -80.4919, 255.547, 2.30343e-107<br> domain error<br>
|
|
-80.4919, 503.011, 1.20315e-217<br> domain error<br> -80.4919, 1007.46,
|
|
0<br> domain error<br> -80.4919, 1185.4, 0<br> domain error<br> -80.4919,
|
|
3534.52, 0<br> domain error<br> -80.4919, 8071.55, 0<br> domain error<br>
|
|
-80.4919, 16229.2, 0<br> domain error<br> -80.4919, 32066.2, 0<br> domain
|
|
error<br> -80.4919, 36367.9, 0<br> domain error<br> -74.6026, 24.7501,
|
|
1.19405e+24<br> domain error<br> -74.6026, 63.7722, 5.81897e-12<br> domain
|
|
error<br> -74.6026, 125.28, 9.89214e-47<br> domain error<br> -74.6026,
|
|
255.547, 3.9726e-108<br> domain error<br> -74.6026, 503.011, 4.87462e-218<br>
|
|
domain error<br> -74.6026, 1007.46, 0<br> domain error<br> -74.6026,
|
|
1185.4, 0<br> domain error<br> -74.6026, 3534.52, 0<br> domain error<br>
|
|
-74.6026, 8071.55, 0<br> domain error<br> -74.6026, 16229.2, 0<br> domain
|
|
error<br> -74.6026, 32066.2, 0<br> domain error<br> -74.6026, 36367.9,
|
|
0<br> domain error<br> -72.9046, 24.7501, 5.5618e+22<br> domain error<br>
|
|
-72.9046, 63.7722, 1.09452e-12<br> domain error<br> -72.9046, 125.28, 3.8393e-47<br>
|
|
domain error<br> -72.9046, 255.547, 2.45173e-108<br> domain error<br>
|
|
-72.9046, 503.011, 3.80454e-218<br> domain error<br> -72.9046, 1007.46,
|
|
0<br> domain error<br> -72.9046, 1185.4, 0<br> domain error<br> -72.9046,
|
|
3534.52, 0<br> domain error<br> -72.9046, 8071.55, 0<br> domain error<br>
|
|
-72.9046, 16229.2, 0<br> domain error<br> -72.9046, 32066.2, 0<br> domain
|
|
error<br> -72.9046, 36367.9, 0<br> domain error<br> -62.3236, 24.7501,
|
|
6.74518e+14<br> domain error<br> -62.3236, 63.7722, 6.54531e-17<br> domain
|
|
error<br> -62.3236, 125.28, 1.65653e-49<br> domain error<br> -62.3236,
|
|
255.547, 1.54767e-109<br> domain error<br> -62.3236, 503.011, 9.22721e-219<br>
|
|
domain error<br> -62.3236, 1007.46, 0<br> domain error<br> -62.3236,
|
|
1185.4, 0<br> domain error<br> -62.3236, 3534.52, 0<br> domain error<br>
|
|
-62.3236, 8071.55, 0<br> domain error<br> -62.3236, 16229.2, 0<br> domain
|
|
error<br> -62.3236, 32066.2, 0<br> domain error<br> -62.3236, 36367.9,
|
|
0<br> domain error<br> -55.7932, 24.7501, 2.00028e+10<br> domain error<br>
|
|
-55.7932, 63.7722, 3.01107e-19<br> domain error<br> -55.7932, 125.28, 8.54693e-51<br>
|
|
domain error<br> -55.7932, 255.547, 3.47666e-110<br> domain error<br>
|
|
-55.7932, 503.011, 4.29705e-219<br> domain error<br> -55.7932, 1007.46,
|
|
0<br> domain error<br> -55.7932, 1185.4, 0<br> domain error<br> -55.7932,
|
|
3534.52, 0<br> domain error<br> -55.7932, 8071.55, 0<br> domain error<br>
|
|
-55.7932, 16229.2, 0<br> domain error<br> -55.7932, 32066.2, 0<br> domain
|
|
error<br> -55.7932, 36367.9, 0<br> domain error<br> -44.3004, 9.50706,
|
|
5.6936e+22<br> domain error<br> -44.3004, 24.7501, 1242.73<br> domain
|
|
error<br> -44.3004, 63.7722, 7.99341e-23<br> domain error<br> -44.3004,
|
|
125.28, 9.88149e-53<br> domain error<br> -44.3004, 255.547, 3.73007e-111<br>
|
|
domain error<br> -44.3004, 503.011, 1.37367e-219<br> domain error<br>
|
|
-44.3004, 1007.46, 0<br> domain error<br> -44.3004, 1185.4, 0<br> domain
|
|
error<br> -44.3004, 3534.52, 0<br> domain error<br> -44.3004, 8071.55,
|
|
0<br> domain error<br> -44.3004, 16229.2, 0<br> domain error<br> -44.3004,
|
|
32066.2, 0<br> domain error<br> -44.3004, 36367.9, 0<br> domain error<br>
|
|
-38.3666, 5.11399, 4.97154e+27<br> domain error<br> -38.3666, 9.50706,
|
|
1.51436e+17<br> domain error<br> -38.3666, 24.7501, 0.639495<br> domain
|
|
error<br> -38.3666, 63.7722, 2.19334e-24<br> domain error<br> -38.3666,
|
|
125.28, 1.45351e-53<br> domain error<br> -38.3666, 255.547, 1.43713e-111<br>
|
|
domain error<br> -38.3666, 503.011, 8.44445e-220<br> domain error<br>
|
|
-38.3666, 1007.46, 0<br> domain error<br> -38.3666, 1185.4, 0<br> domain
|
|
error<br> -38.3666, 3534.52, 0<br> domain error<br> -38.3666, 8071.55,
|
|
0<br> domain error<br> -38.3666, 16229.2, 0<br> domain error<br> -38.3666,
|
|
32066.2, 0<br> domain error<br> -38.3666, 36367.9, 0<br> underflow<br>
|
|
9.3763, 1007.46, 0<br> underflow<br> 9.3763, 1185.4, 0<br> underflow<br>
|
|
9.3763, 3534.52, 0<br> underflow<br> 9.3763, 8071.55, 0<br> underflow<br>
|
|
9.3763, 16229.2, 0<br> underflow<br> 9.3763, 32066.2, 0<br> underflow<br>
|
|
9.3763, 36367.9, 0<br> underflow<br> 9.44412, 1007.46, 0<br> underflow<br>
|
|
9.44412, 1185.4, 0<br> underflow<br> 9.44412, 3534.52, 0<br> underflow<br>
|
|
9.44412, 8071.55, 0<br> underflow<br> 9.44412, 16229.2, 0<br> underflow<br>
|
|
9.44412, 32066.2, 0<br> underflow<br> 9.44412, 36367.9, 0<br> underflow<br>
|
|
26.4719, 1007.46, 0<br> underflow<br> 26.4719, 1185.4, 0<br> underflow<br>
|
|
26.4719, 3534.52, 0<br> underflow<br> 26.4719, 8071.55, 0<br> underflow<br>
|
|
26.4719, 16229.2, 0<br> underflow<br> 26.4719, 32066.2, 0<br> underflow<br>
|
|
26.4719, 36367.9, 0<br> underflow<br> 62.9447, 1007.46, 0<br> underflow<br>
|
|
62.9447, 1185.4, 0<br> underflow<br> 62.9447, 3534.52, 0<br> underflow<br>
|
|
62.9447, 8071.55, 0<br> underflow<br> 62.9447, 16229.2, 0<br> underflow<br>
|
|
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h64"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0">Error
|
|
Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel Kn: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data"></a>underflow<br>
|
|
0, 1007.46, 0<br> underflow<br> 0, 1185.4, 0<br> underflow<br> 0, 3534.52,
|
|
0<br> underflow<br> 0, 8071.55, 0<br> underflow<br> 0, 16229.2, 0<br>
|
|
underflow<br> 0, 32066.2, 0<br> underflow<br> 0, 36367.9, 0<br> underflow<br>
|
|
1, 1007.46, 0<br> underflow<br> 1, 1185.4, 0<br> underflow<br> 1, 3534.52,
|
|
0<br> underflow<br> 1, 8071.55, 0<br> underflow<br> 1, 16229.2, 0<br>
|
|
underflow<br> 1, 32066.2, 0<br> underflow<br> 1, 36367.9, 0<br> underflow<br>
|
|
4, 1007.46, 0<br> underflow<br> 4, 1185.4, 0<br> underflow<br> 4, 3534.52,
|
|
0<br> underflow<br> 4, 8071.55, 0<br> underflow<br> 4, 16229.2, 0<br>
|
|
underflow<br> 4, 32066.2, 0<br> underflow<br> 4, 36367.9, 0<br> underflow<br>
|
|
7, 1007.46, 0<br> underflow<br> 7, 1185.4, 0<br> underflow<br> 7, 3534.52,
|
|
0<br> underflow<br> 7, 8071.55, 0<br> underflow<br> 7, 16229.2, 0<br>
|
|
underflow<br> 7, 32066.2, 0<br> underflow<br> 7, 36367.9, 0<br> underflow<br>
|
|
10, 1007.46, 0<br> underflow<br> 10, 1185.4, 0<br> underflow<br> 10,
|
|
3534.52, 0<br> underflow<br> 10, 8071.55, 0<br> underflow<br> 10, 16229.2,
|
|
0<br> underflow<br> 10, 32066.2, 0<br> underflow<br> 10, 36367.9, 0<br>
|
|
underflow<br> 13, 1007.46, 0<br> underflow<br> 13, 1185.4, 0<br> underflow<br>
|
|
13, 3534.52, 0<br> underflow<br> 13, 8071.55, 0<br> underflow<br> 13,
|
|
16229.2, 0<br> underflow<br> 13, 32066.2, 0<br> underflow<br> 13, 36367.9,
|
|
0<br> underflow<br> 16, 1007.46, 0<br> underflow<br> 16, 1185.4, 0<br>
|
|
underflow<br> 16, 3534.52, 0<br> underflow<br> 16, 8071.55, 0<br> underflow<br>
|
|
16, 16229.2, 0<br> underflow<br> 16, 32066.2, 0<br> underflow<br> 16,
|
|
36367.9, 0<br> underflow<br> 19, 1007.46, 0<br> underflow<br> 19, 1185.4,
|
|
0<br> underflow<br> 19, 3534.52, 0<br> underflow<br> 19, 8071.55, 0<br>
|
|
underflow<br> 19, 16229.2, 0<br> underflow<br> 19, 32066.2, 0<br> underflow<br>
|
|
19, 36367.9, 0<br> underflow<br> 22, 1007.46, 0<br> underflow<br> 22,
|
|
1185.4, 0<br> underflow<br> 22, 3534.52, 0<br> underflow<br> 22, 8071.55,
|
|
0<br> underflow<br> 22, 16229.2, 0<br> underflow<br> 22, 32066.2, 0<br>
|
|
underflow<br> 22, 36367.9, 0<br> underflow<br> 25, 1007.46, 0<br> underflow<br>
|
|
25, 1185.4, 0<br> underflow<br> 25, 3534.52, 0<br> underflow<br> 25,
|
|
8071.55, 0<br> underflow<br> 25, 16229.2, 0<br> underflow<br> 25, 32066.2,
|
|
0<br> underflow<br> 25, 36367.9, 0<br> underflow<br> 28, 1007.46, 0<br>
|
|
underflow<br> 28, 1185.4, 0<br> underflow<br> 28, 3534.52, 0<br> underflow<br>
|
|
28, 8071.55, 0<br> underflow<br> 28, 16229.2, 0<br> underflow<br> 28,
|
|
32066.2, 0<br> underflow<br> 28, 36367.9, 0<br> underflow<br> 31, 1007.46,
|
|
0<br> underflow<br> 31, 1185.4, 0<br> underflow<br> 31, 3534.52, 0<br>
|
|
underflow<br> 31, 8071.55, 0<br> underflow<br> 31, 16229.2, 0<br> underflow<br>
|
|
31, 32066.2, 0<br> underflow<br> 31, 36367.9, 0<br> underflow<br> 34,
|
|
1007.46, 0<br> underflow<br> 34, 1185.4, 0<br> underflow<br> 34, 3534.52,
|
|
0<br> underflow<br> 34, 8071.55, 0<br> underflow<br> 34, 16229.2, 0<br>
|
|
underflow<br> 34, 32066.2, 0<br> underflow<br> 34, 36367.9, 0<br> underflow<br>
|
|
37, 1007.46, 0<br> underflow<br> 37, 1185.4, 0<br> underflow<br> 37,
|
|
3534.52, 0<br> underflow<br> 37, 8071.55, 0<br> underflow<br> 37, 16229.2,
|
|
0<br> underflow<br> 37, 32066.2, 0<br> underflow<br> 37, 36367.9, 0<br>
|
|
underflow<br> 40, 1007.46, 0<br> underflow<br> 40, 1185.4, 0<br> underflow<br>
|
|
40, 3534.52, 0<br> underflow<br> 40, 8071.55, 0<br> underflow<br> 40,
|
|
16229.2, 0<br> underflow<br> 40, 32066.2, 0<br> underflow<br> 40, 36367.9,
|
|
0<br> underflow<br> 43, 1007.46, 0<br> underflow<br> 43, 1185.4, 0<br>
|
|
underflow<br> 43, 3534.52, 0<br> underflow<br> 43, 8071.55, 0<br> underflow<br>
|
|
43, 16229.2, 0<br> underflow<br> 43, 32066.2, 0<br> underflow<br> 43,
|
|
36367.9, 0<br> underflow<br> 46, 1007.46, 0<br> underflow<br> 46, 1185.4,
|
|
0<br> underflow<br> 46, 3534.52, 0<br> underflow<br> 46, 8071.55, 0<br>
|
|
underflow<br> 46, 16229.2, 0<br> underflow<br> 46, 32066.2, 0<br> underflow<br>
|
|
46, 36367.9, 0<br> underflow<br> 49, 1007.46, 0<br> underflow<br> 49,
|
|
1185.4, 0<br> underflow<br> 49, 3534.52, 0<br> underflow<br> 49, 8071.55,
|
|
0<br> underflow<br> 49, 16229.2, 0<br> underflow<br> 49, 32066.2, 0<br>
|
|
underflow<br> 49, 36367.9, 0<br> underflow<br> 52, 1007.46, 0<br> underflow<br>
|
|
52, 1185.4, 0<br> underflow<br> 52, 3534.52, 0<br> underflow<br> 52,
|
|
8071.55, 0<br> underflow<br> 52, 16229.2, 0<br> underflow<br> 52, 32066.2,
|
|
0<br> underflow<br> 52, 36367.9, 0<br> underflow<br> 55, 1007.46, 0<br>
|
|
underflow<br> 55, 1185.4, 0<br> underflow<br> 55, 3534.52, 0<br> underflow<br>
|
|
55, 8071.55, 0<br> underflow<br> 55, 16229.2, 0<br> underflow<br> 55,
|
|
32066.2, 0<br> underflow<br> 55, 36367.9, 0<br> underflow<br> 58, 1007.46,
|
|
0<br> underflow<br> 58, 1185.4, 0<br> underflow<br> 58, 3534.52, 0<br>
|
|
underflow<br> 58, 8071.55, 0<br> underflow<br> 58, 16229.2, 0<br> underflow<br>
|
|
58, 32066.2, 0<br> underflow<br> 58, 36367.9, 0<br> underflow<br> 61,
|
|
1007.46, 0<br> underflow<br> 61, 1185.4, 0<br> underflow<br> 61, 3534.52,
|
|
0<br> underflow<br> 61, 8071.55, 0<br> underflow<br> 61, 16229.2, 0<br>
|
|
underflow<br> 61, 32066.2, 0<br> underflow<br> 61, 36367.9, 0<br> underflow<br>
|
|
64, 1007.46, 0<br> underflow<br> 64, 1185.4, 0<br> underflow<br> 64,
|
|
3534.52, 0<br> underflow<br> 64, 8071.55, 0<br> underflow<br> 64, 16229.2,
|
|
0<br> underflow<br> 64, 32066.2, 0<br> underflow<br> 64, 36367.9, 0<br>
|
|
underflow<br> 67, 1007.46, 0<br> underflow<br> 67, 1185.4, 0<br> underflow<br>
|
|
67, 3534.52, 0<br> underflow<br> 67, 8071.55, 0<br> underflow<br> 67,
|
|
16229.2, 0<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h65"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1">Error
|
|
Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel Kv: Mathworld Data (large values)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_"></a>domain
|
|
error<br> -1, 3.72917e-155, 2.68156e+154<br> domain error<br> -1.125,
|
|
3.72917e-155, 5.53984e+173<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h66"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2">Error
|
|
Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel Kv: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data"></a>domain
|
|
error<br> -5.5, 10, 7.33045e-05<br> domain error<br> -5.5, 100, 5.41275e-45<br>
|
|
domain error<br> -141.399, 50, 1.30185e+42<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h67"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3">Error
|
|
Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Bessel Kn: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data"></a>domain
|
|
error<br> -5, 100, 5.27326e-45<br> domain error<br> -10, 1, 1.80713e+08<br>
|
|
domain error<br> -1000, 700, 6.51562e-31<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h68"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4">Error
|
|
Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel Kv: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data"></a>Bad
|
|
argument in __cyl_bessel_k.<br> -80.4919, 24.7501, 6.57902e+28<br> Bad
|
|
argument in __cyl_bessel_k.<br> -80.4919, 63.7722, 2.39552e-09<br> Bad
|
|
argument in __cyl_bessel_k.<br> -80.4919, 125.28, 3.06904e-45<br> Bad argument
|
|
in __cyl_bessel_k.<br> -80.4919, 255.547, 2.30343e-107<br> Bad argument
|
|
in __cyl_bessel_k.<br> -80.4919, 503.011, 1.20315e-217<br> Bad argument
|
|
in __cyl_bessel_k.<br> -80.4919, 1007.46, 2.86537e-438<br> Bad argument
|
|
in __cyl_bessel_k.<br> -80.4919, 1185.4, 8.63263e-516<br> Bad argument
|
|
in __cyl_bessel_k.<br> -80.4919, 3534.52, 5.01367e-1537<br> Bad argument
|
|
in __cyl_bessel_k.<br> -80.4919, 8071.55, 7.76555e-3508<br> Bad argument
|
|
in __cyl_bessel_k.<br> -80.4919, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br>
|
|
-80.4919, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -80.4919,
|
|
36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -74.6026, 24.7501, 1.19405e+24<br>
|
|
Bad argument in __cyl_bessel_k.<br> -74.6026, 63.7722, 5.81897e-12<br>
|
|
Bad argument in __cyl_bessel_k.<br> -74.6026, 125.28, 9.89214e-47<br> Bad
|
|
argument in __cyl_bessel_k.<br> -74.6026, 255.547, 3.9726e-108<br> Bad
|
|
argument in __cyl_bessel_k.<br> -74.6026, 503.011, 4.87462e-218<br> Bad
|
|
argument in __cyl_bessel_k.<br> -74.6026, 1007.46, 1.82221e-438<br> Bad
|
|
argument in __cyl_bessel_k.<br> -74.6026, 1185.4, 5.87506e-516<br> Bad
|
|
argument in __cyl_bessel_k.<br> -74.6026, 3534.52, 4.40608e-1537<br> Bad
|
|
argument in __cyl_bessel_k.<br> -74.6026, 8071.55, 7.3384e-3508<br> Bad
|
|
argument in __cyl_bessel_k.<br> -74.6026, 16229.2, 0<br> Bad argument in
|
|
__cyl_bessel_k.<br> -74.6026, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br>
|
|
-74.6026, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -72.9046,
|
|
24.7501, 5.5618e+22<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 63.7722,
|
|
1.09452e-12<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 125.28, 3.8393e-47<br>
|
|
Bad argument in __cyl_bessel_k.<br> -72.9046, 255.547, 2.45173e-108<br>
|
|
Bad argument in __cyl_bessel_k.<br> -72.9046, 503.011, 3.80454e-218<br>
|
|
Bad argument in __cyl_bessel_k.<br> -72.9046, 1007.46, 1.60949e-438<br>
|
|
Bad argument in __cyl_bessel_k.<br> -72.9046, 1185.4, 5.28662e-516<br>
|
|
Bad argument in __cyl_bessel_k.<br> -72.9046, 3534.52, 4.25273e-1537<br>
|
|
Bad argument in __cyl_bessel_k.<br> -72.9046, 8071.55, 7.22542e-3508<br>
|
|
Bad argument in __cyl_bessel_k.<br> -72.9046, 16229.2, 0<br> Bad argument
|
|
in __cyl_bessel_k.<br> -72.9046, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br>
|
|
-72.9046, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -62.3236,
|
|
24.7501, 6.74518e+14<br> Bad argument in __cyl_bessel_k.<br> -62.3236,
|
|
63.7722, 6.54531e-17<br> Bad argument in __cyl_bessel_k.<br> -62.3236,
|
|
125.28, 1.65653e-49<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 255.547,
|
|
1.54767e-109<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 503.011,
|
|
9.22721e-219<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1007.46,
|
|
7.91894e-439<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1185.4,
|
|
2.89281e-516<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 3534.52,
|
|
3.4736e-1537<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 8071.55,
|
|
6.6126e-3508<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 16229.2,
|
|
0<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 32066.2, 0<br> Bad
|
|
argument in __cyl_bessel_k.<br> -62.3236, 36367.9, 0<br> Bad argument in
|
|
__cyl_bessel_k.<br> -55.7932, 24.7501, 2.00028e+10<br> Bad argument in
|
|
__cyl_bessel_k.<br> -55.7932, 63.7722, 3.01107e-19<br> Bad argument in
|
|
__cyl_bessel_k.<br> -55.7932, 125.28, 8.54693e-51<br> Bad argument in __cyl_bessel_k.<br>
|
|
-55.7932, 255.547, 3.47666e-110<br> Bad argument in __cyl_bessel_k.<br>
|
|
-55.7932, 503.011, 4.29705e-219<br> Bad argument in __cyl_bessel_k.<br>
|
|
-55.7932, 1007.46, 5.40242e-439<br> Bad argument in __cyl_bessel_k.<br>
|
|
-55.7932, 1185.4, 2.08996e-516<br> Bad argument in __cyl_bessel_k.<br>
|
|
-55.7932, 3534.52, 3.11458e-1537<br> Bad argument in __cyl_bessel_k.<br>
|
|
-55.7932, 8071.55, 6.30409e-3508<br> Bad argument in __cyl_bessel_k.<br>
|
|
-55.7932, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932,
|
|
32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932, 36367.9, 0<br>
|
|
Bad argument in __cyl_bessel_k.<br> -44.3004, 9.50706, 5.6936e+22<br> Bad
|
|
argument in __cyl_bessel_k.<br> -44.3004, 24.7501, 1242.73<br> Bad argument
|
|
in __cyl_bessel_k.<br> -44.3004, 63.7722, 7.99341e-23<br> Bad argument
|
|
in __cyl_bessel_k.<br> -44.3004, 125.28, 9.88149e-53<br> Bad argument in
|
|
__cyl_bessel_k.<br> -44.3004, 255.547, 3.73007e-111<br> Bad argument in
|
|
__cyl_bessel_k.<br> -44.3004, 503.011, 1.37367e-219<br> Bad argument in
|
|
__cyl_bessel_k.<br> -44.3004, 1007.46, 3.05398e-439<br> Bad argument in
|
|
__cyl_bessel_k.<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h69"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5">Error
|
|
Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel Kv: Mathworld Data (large values)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_"></a>Bad
|
|
argument in __cyl_bessel_k.<br> -1, 3.72917e-155, 2.68156e+154<br> Bad
|
|
argument in __cyl_bessel_k.<br> -1.125, 3.72917e-155, 5.53984e+173<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h70"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6">Error
|
|
Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel Kv: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_k.<br> -5.5, 10, 7.33045e-05<br> Bad argument
|
|
in __cyl_bessel_k.<br> -5.5, 100, 5.41275e-45<br> Bad argument in __cyl_bessel_k.<br>
|
|
-141.399, 50, 1.30185e+42<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h71"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in">Error
|
|
Output For cyl_bessel_k (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library <cmath> and test data Bessel Kn: Mathworld Data (Integer
|
|
Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_"></a>Bad
|
|
argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in
|
|
__cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br>
|
|
-1000, 700, 6.51562e-31<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h72"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7">Error
|
|
Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Bessel Kn: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data"></a>Bad
|
|
argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in
|
|
__cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br>
|
|
-1000, 700, 6.51562e-31<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h73"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit">Error
|
|
Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Yv: Mathworld Data (large values)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_"></a>domain
|
|
error<br> -0.5, 1.2459e-206, 8.90598e-104<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h74"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0">Error
|
|
Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Yv: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data"></a>domain
|
|
error<br> -5.5, 3.125, -0.0274994<br> domain error<br> -5.5, 10000, -0.00759344<br>
|
|
domain error<br> -10.0003, 0.000976562, -1.50382e+38<br> domain error<br>
|
|
-10.0003, 100, 0.0583042<br> domain error<br> -141.75, 100, -3.8101e+09<br>
|
|
domain error<br> -8.5, 12.5664, 0.0436808<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h75"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1">Error
|
|
Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL
|
|
2.1 and test data Yn: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data"></a>domain
|
|
error<br> -5, 1e+06, 0.000331052<br> domain error<br> -10, 1e+06, 0.000725952<br>
|
|
domain error<br> -1000, 700, -1.88753e+77<br> domain error<br> -25, 8,
|
|
3.45114e+08<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h76"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2">Error
|
|
Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Yv: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data"></a>CAUTION:
|
|
Gross error found at entry 394.<br> Found: -3.29903 Expected 0.0192842 Error:
|
|
1.18973e+4932<br> 125.28, 1007.46, 0.0192842<br> CAUTION: Gross error found
|
|
at entry 395.<br> Found: 1.13543 Expected 0.0230358 Error: 48.2897<br>
|
|
125.28, 1185.4, 0.0230358<br> CAUTION: Gross error found at entry 396.<br>
|
|
Found: 0.00119445 Expected 0.00460223 Error: 2.85302<br> 125.28, 3534.52,
|
|
0.00460223<br> CAUTION: Gross error found at entry 403.<br> Found: 1068
|
|
Expected -0.00270959 Error: 1.18973e+4932<br> 255.547, 1007.46, -0.00270959<br>
|
|
CAUTION: Gross error found at entry 404.<br> Found: -395.006 Expected 0.00738845
|
|
Error: 1.18973e+4932<br> 255.547, 1185.4, 0.00738845<br> CAUTION: Gross
|
|
error found at entry 405.<br> Found: 1.08701 Expected -0.000407036 Error:
|
|
1.18973e+4932<br> 255.547, 3534.52, -0.000407036<br> CAUTION: Gross error
|
|
found at entry 406.<br> Found: 0.0232211 Expected 0.00886946 Error: 1.61809<br>
|
|
255.547, 8071.55, 0.00886946<br> CAUTION: Gross error found at entry 411.<br>
|
|
Found: 65895.7 Expected -0.0158467 Error: 1.18973e+4932<br> 503.011, 1007.46,
|
|
-0.0158467<br> CAUTION: Gross error found at entry 412.<br> Found: -123316
|
|
Expected 0.00594357 Error: 1.18973e+4932<br> 503.011, 1185.4, 0.00594357<br>
|
|
CAUTION: Gross error found at entry 413.<br> Found: -706.209 Expected 0.010151
|
|
Error: 1.18973e+4932<br> 503.011, 3534.52, 0.010151<br> CAUTION: Gross
|
|
error found at entry 414.<br> Found: -21.2081 Expected 0.00888375 Error:
|
|
1.18973e+4932<br> 503.011, 8071.55, 0.00888375<br> CAUTION: Gross error
|
|
found at entry 415.<br> Found: 0.0272835 Expected 0.00552287 Error: 3.94008<br>
|
|
503.011, 16229.2, 0.00552287<br> CAUTION: Gross error found at entry 416.<br>
|
|
Found: 0.0103324 Expected 0.00445559 Error: 1.31898<br> 503.011, 32066.2,
|
|
0.00445559<br> CAUTION: Gross error found at entry 417.<br> Found: 0.00540788
|
|
Expected -0.00384344 Error: 1.18973e+4932<br> 503.011, 36367.9, -0.00384344<br>
|
|
CAUTION: Gross error found at entry 418.<br> Found: 5.43091e+07 Expected
|
|
-0.0772843 Error: 1.18973e+4932<br> 1007.46, 1007.46, -0.0772843<br> CAUTION:
|
|
Gross error found at entry 419.<br> Found: -2.84383e+07 Expected 0.0304312
|
|
Error: 1.18973e+4932<br> 1007.46, 1185.4, 0.0304312<br> CAUTION: Gross
|
|
error found at entry 420.<br> Found: -61440.2 Expected -0.00474217 Error:
|
|
1.29562e+07<br> 1007.46, 3534.52, -0.00474217<br> CAUTION: Gross error
|
|
found at entry 421.<br> Found: -4126.89 Expected -0.0074205 Error: 556146<br>
|
|
1007.46, 8071.55, -0.0074205<br> CAUTION: Gross error found at entry 422.<br>
|
|
Found: -69.2831 Expected -0.00179572 Error: 38581.4<br> 1007.46, 16229.2,
|
|
-0.00179572<br> CAUTION: Gross error found at entry 423.<br> Found: 2.32048
|
|
Expected 0.000750053 Error: 3092.76<br> 1007.46, 32066.2, 0.000750053<br>
|
|
CAUTION: Gross error found at entry 424.<br> Found: 3.90724 Expected 0.00305125
|
|
Error: 1279.54<br> 1007.46, 36367.9, 0.00305125<br> CAUTION: Gross error
|
|
found at entry 425.<br> Found: -1.83374e+08 Expected -7.25176e+28 Error:
|
|
3.95463e+20<br> 1185.4, 1007.46, -7.25176e+28<br> CAUTION: Gross error
|
|
found at entry 426.<br> Found: 1.09822e+08 Expected -0.0732059 Error: 1.18973e+4932<br>
|
|
1185.4, 1185.4, -0.0732059<br> CAUTION: Gross error found at entry 427.<br>
|
|
Found: 315632 Expected 0.000479585 Error: 6.58136e+08<br> 1185.4, 3534.52,
|
|
0.000479585<br> CAUTION: Gross error found at entry 428.<br> Found: 16815.6
|
|
Expected 0.00174909 Error: 9.61391e+06<br> 1185.4, 8071.55, 0.00174909<br>
|
|
CAUTION: Gross error found at entry 429.<br> Found: 133.356 Expected 0.00416288
|
|
Error: 32033.6<br> 1185.4, 16229.2, 0.00416288<br> CAUTION: Gross error
|
|
found at entry 430.<br> Found: -1.38401 Expected -0.000320056 Error: 4323.27<br>
|
|
1185.4, 32066.2, -0.000320056<br> CAUTION: Gross error found at entry 431.<br>
|
|
Found: -17.7085 Expected -0.00417656 Error: 4238.96<br> 1185.4, 36367.9,
|
|
-0.00417656<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h77"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3">Error
|
|
Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Yv: Mathworld Data (large values)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_"></a>Bad
|
|
argument in __cyl_neumann_n.<br> -0.5, 1.2459e-206, 8.90598e-104<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h78"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4">Error
|
|
Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Yv: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data"></a>Bad
|
|
argument in __cyl_neumann_n.<br> -5.5, 3.125, -0.0274994<br> Bad argument
|
|
in __cyl_neumann_n.<br> -5.5, 10000, -0.00759344<br> Bad argument in __cyl_neumann_n.<br>
|
|
-10.0003, 0.000976562, -1.50382e+38<br> Bad argument in __cyl_neumann_n.<br>
|
|
-10.0003, 100, 0.0583042<br> Bad argument in __cyl_neumann_n.<br> -141.75,
|
|
100, -3.8101e+09<br> Bad argument in __cyl_neumann_n.<br> -8.5, 12.5664,
|
|
0.0436808<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h79"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int">Error
|
|
Output For cyl_neumann (integer orders) with compiler GNU C++ version 7.1.0
|
|
and library <cmath> and test data Yn: Mathworld Data (Integer Version)</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_"></a>Bad
|
|
argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument
|
|
in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error
|
|
found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br>
|
|
1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000,
|
|
700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h80"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5">Error
|
|
Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Yn: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data"></a>Bad
|
|
argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument
|
|
in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error
|
|
found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br>
|
|
1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000,
|
|
700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h81"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi">Error
|
|
Output For beta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and
|
|
test data Beta Function: Small Values</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values"></a>CAUTION:
|
|
Found non-finite result, when a finite value was expected at entry 22<br>
|
|
Found: inf Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155,
|
|
5.69832e+154<br> CAUTION: Gross error found at entry 22.<br> Found: inf
|
|
Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155,
|
|
5.69832e+154<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h82"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_">Error
|
|
Output For ellint_rj with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data RJ: Random data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data"></a>domain
|
|
error<br> 1.77787e-31, 1.40657e+18, 10.046, -4.8298e-10, -2.51795e-10<br>
|
|
domain error<br> 3.37448e-31, 4.65772e+22, 0.469831, -4.33756e-09, -2.95865e-11<br>
|
|
domain error<br> 5.25297e-31, 5.85483e+25, 2.02482e-15, -1.87347e-28, 3.36445e+07<br>
|
|
domain error<br> 6.22216e-31, 3.43401e+23, 0.673005, -2.7626e-13, -7.58898e-12<br>
|
|
domain error<br> 6.26875e-31, 2.62568e-13, 1.06394e+24, -1.36451e+14, -6.70372e-25<br>
|
|
domain error<br> 6.84599e-31, 3.57666e-29, 1.82191e+11, -3.63292e+08, -8.35235e-13<br>
|
|
domain error<br> 8.90482e-31, 1.97093e-28, 1.14939e-31, -1.26424e-12, -6.39454e+26<br>
|
|
domain error<br> 1.07374e-30, 1.70005e-12, 1.88773e-25, -1.16558e-29, 4.31668e+32<br>
|
|
domain error<br> 1.17141e-30, 24.2523, 3.67522e+21, -4.79065e-22, 2.2702e-05<br>
|
|
domain error<br> 1.64143e-30, 2.01978e-22, 2.58942e+12, -8.52649e-12, -2.82629e+06<br>
|
|
domain error<br> 1.85141e-30, 0.0386712, 2.37846e-13, -1.57357e+15, -1.38574e-13<br>
|
|
domain error<br> 2.70034e-30, 4.43896e-24, 7.54576e+16, -1.1436e-14, -1.10082e+07<br>
|
|
domain error<br> 4.01162e-30, 2.73343e+23, 1.32333e+13, -1.86032e-07, -4.16626e-25<br>
|
|
domain error<br> 4.13665e-30, 1.08034e-30, 3.13547e-16, -5.58099e-08, -5.14643e+16<br>
|
|
domain error<br> 4.3728e-30, 7.79812e+12, 8.58894e+21, -4.58312e-24, 5.28901e-09<br>
|
|
domain error<br> 5.6397e-30, 1.64768e+23, 9.64423e-15, -1.82207e+20, -1.62886e-30<br>
|
|
domain error<br> 9.89841e-30, 9.69731e+10, 1.03263e+21, -0.00343967, -9.62714e-22<br>
|
|
domain error<br> 1.3797e-29, 6.03357e+08, 5.62497e-15, -5.87235e+16, -5.80287e-20<br>
|
|
domain error<br> 1.96963e-29, 3.22384e-25, 2.92187e+23, -3.80643e+27, -8.2513e-38<br>
|
|
domain error<br> 2.00927e-29, 5.6976e-05, 1.16219e+25, -1.64129e-22, 0.00318397<br>
|
|
domain error<br> 7.29506e-29, 5904.94, 9.93922e+10, -19.528, -1.60795e-09<br>
|
|
domain error<br> 1.19698e-28, 1.66816e-22, 28472, -1.21137e-19, -5.84699e+17<br>
|
|
domain error<br> 1.64095e-28, 2.13421e-21, 7.8914e-15, -1.77584e-07, -1.70156e+15<br>
|
|
domain error<br> 2.03475e-28, 4.40987e+15, 28739.1, -9624.5, -1.29418e-12<br>
|
|
domain error<br> 2.73113e-28, 1.08457e+19, 4.00674e+08, -5.70043e-11, 1.092e-17<br>
|
|
domain error<br> 5.52633e-28, 1.45707e-17, 1.29411e-27, -1.67255e-15, -5.84881e+24<br>
|
|
domain error<br> 5.61278e-28, 9.22881e-12, 8.64222e-13, -5.6282e+23, -4.57782e-18<br>
|
|
domain error<br> 6.08465e-28, 1.32249e+26, 1.25536e-30, -1.89097e-14, -223.246<br>
|
|
domain error<br> 9.50943e-28, 2.49682e-18, 0.000904584, -3.1419e-12, -2.44954e+14<br>
|
|
domain error<br> 1.20779e-27, 35383.2, 1.35533e-15, -4.67834e-24, 3.20581e+15<br>
|
|
domain error<br> 2.29822e-27, 3.35258e-16, 2.60689e+08, -9.99161e-20, -5.4924e+11<br>
|
|
domain error<br> 3.0926e-27, 3.11839e-13, 3.37883e-23, -1.94349e+26, -3.55191e-19<br>
|
|
domain error<br> 3.12803e-27, 1.15118e+16, 1.52495e+10, -4.2399e+13, -3.07515e-21<br>
|
|
domain error<br> 4.49747e-27, 716.685, 1.69018e-23, -1.32558e-14, -9.2291e+13<br>
|
|
domain error<br> 4.84575e-27, 3.44028e-27, 3.42665e+09, -812.399, -2.12767e-06<br>
|
|
domain error<br> 5.81424e-27, 3.70845e-15, 3.69338e+11, -4.15794e+06, -2.95944e-11<br>
|
|
domain error<br> 6.08654e-27, 1.23742e+08, 1.09124e-26, -2.19946e+16, -4.90896e-19<br>
|
|
domain error<br> 7.71967e-27, 9.46115e-26, 1.24324e+25, -522800, -5.83203e-17<br>
|
|
domain error<br> 9.20037e-27, 207550, 2.45782e-17, -6.06901e+29, -2.88945e-31<br>
|
|
domain error<br> 1.75502e-26, 5.81507e+16, 8.83063e+21, -1.11214e-21, 1.57697e-11<br>
|
|
domain error<br> 2.29965e-26, 2.9716e-21, 1.81059e-25, -5.23972e-08, -6.23302e+18<br>
|
|
domain error<br> 2.32628e-26, 0.0655133, 1.62901e-21, -7.15441e-17, -9.88586e+17<br>
|
|
domain error<br> 3.49194e-26, 2.53343e+14, 756.217, -1.3359e+10, -1.275e-16<br>
|
|
domain error<br> 1.009e-25, 0.0694304, 1.20267e-14, -1.55746e-22, 2.10701e+17<br>
|
|
domain error<br> 3.54771e-25, 1.67999e-27, 2.3917e+24, -9.98754e+25, -1.11704e-36<br>
|
|
domain error<br> 6.31714e-25, 3.4594e-28, 6.37951e-24, -1.25529e-24, -9.56292e+35<br>
|
|
domain error<br> 6.74086e-25, 2.47169e+12, 1.32962e+23, -6.78845e+06, -3.32861e-24<br>
|
|
domain error<br> 1.8099e-24, 4.5215e-06, 8.66937e-11, -3.70795e-08, -1.41893e+11<br>
|
|
domain error<br> 2.29798e-24, 9.30454e-30, 6.56584e-17, -9890.38, -373149<br>
|
|
domain error<br> 2.88161e-24, 8.82377e-05, 1.57747e+21, -4.25068e-24, 2260.61<br>
|
|
domain error<br> 3.25991e-24, 1.92923e+29, 3.09752e-05, -1.00986e+11, -1.25485e-24<br>
|
|
domain error<br> 6.36705e-24, 2.8074e+22, 1.75569e-13, -1.53152e+24, -4.89823e-34<br>
|
|
domain error<br> 7.90772e-24, 2.11611e-30, 1.42682e-07, -0.00296297, -5.38814e+07<br>
|
|
domain error<br> 1.05302e-23, 4.83473e+26, 4.43149e-30, -1.56818e+13, -3.6836e-25<br>
|
|
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h83"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c">Error
|
|
Output For ellint_1 with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Elliptic Integral F: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data"></a>CAUTION:
|
|
Gross error found at entry 9.<br> Found: -7.02862e+09 Expected 1.04181e+20
|
|
Error: 1.18973e+4932<br> 1e+20, 0.390625, 1.04181e+20<br> CAUTION: Gross
|
|
error found at entry 10.<br> Found: -9.3866e+09 Expected 1.39133e+50 Error:
|
|
1.18973e+4932<br> 1e+50, 0.875, 1.39133e+50<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h84"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple">Error
|
|
Output For ellint_2 (complete) with compiler GNU C++ version 7.1.0 and library
|
|
GSL 2.1 and test data Elliptic Integral E: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data"></a>domain
|
|
error<br> -1, 1<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h85"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c">Error
|
|
Output For ellint_2 with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Elliptic Integral E: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data"></a>CAUTION:
|
|
Gross error found at entry 7.<br> Found: -6.3027e+09 Expected 9.34215e+09
|
|
Error: 1.18973e+4932<br> 1e+10, -0.5, 9.34215e+09<br> CAUTION: Gross error
|
|
found at entry 8.<br> Found: -6.48129e+09 Expected 7.08861e+19 Error: 1.18973e+4932<br>
|
|
7.3787e+19, 0.390625, 7.08861e+19<br> CAUTION: Gross error found at entry
|
|
9.<br> Found: -5.13973e+09 Expected 7.1259e+49 Error: 1.18973e+4932<br>
|
|
9.35361e+49, 0.878906, 7.1259e+49<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h86"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple">Error
|
|
Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library
|
|
GSL 2.1 and test data Complete Elliptic Integral PI: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data"></a>domain
|
|
error<br> -4.14952e+180, 0.5, 7.71119e-91<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h87"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c">Error
|
|
Output For ellint_3 with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Elliptic Integral PI: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data"></a>domain
|
|
error<br> 1.125, 10, 0.25, 0.662468<br> domain error<br> 1.125, 3, 0.25,
|
|
-0.142697<br> domain error<br> 1.00391, 21.5, 0.125, -0.535406<br> domain
|
|
error<br> 1, 2, 0.5, -2.87535<br> domain error<br> 1, -2, 0.5, 2.87535<br>
|
|
domain error<br> 1, 2, 6.22302e-61, -2.18504<br> domain error<br> 1,
|
|
-2, 6.22302e-61, 2.18504<br> domain error<br> 20, 3.14257, 0.5, 0.000975941<br>
|
|
domain error<br> 20, -3.14257, 0.5, -0.000975941<br> domain error<br>
|
|
1.01562, 1.6958, 0.5, -27.1647<br> domain error<br> 1.01562, -1.6958, 0.5,
|
|
27.1647<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h88"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0">Error
|
|
Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library
|
|
<cmath> and test data Complete Elliptic Integral PI: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data"></a>Argument
|
|
too small in __ellint_rj<br> -87.1743, 0.126987, 0.167413<br> Argument
|
|
too small in __ellint_rj<br> -87.1743, 0.135477, 0.167431<br> Argument
|
|
too small in __ellint_rj<br> -87.1743, 0.221034, 0.167683<br> Argument
|
|
too small in __ellint_rj<br> -87.1743, 0.308167, 0.168078<br> Argument
|
|
too small in __ellint_rj<br> -87.1743, 0.632359, 0.17122<br> Argument too
|
|
small in __ellint_rj<br> -87.1743, 0.814724, 0.175341<br> Argument too
|
|
small in __ellint_rj<br> -87.1743, 0.835009, 0.176056<br> Argument too
|
|
small in __ellint_rj<br> -87.1743, 0.905792, 0.179501<br> Argument too
|
|
small in __ellint_rj<br> -87.1743, 0.913376, 0.180014<br> Argument too
|
|
small in __ellint_rj<br> -87.1743, 0.968868, 0.186162<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.126987, 0.168233<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.135477, 0.168252<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.221034, 0.168506<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.308167, 0.168905<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.632359, 0.172077<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.814724, 0.176237<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.835009, 0.176958<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.905792, 0.180437<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.913376, 0.180955<br> Argument too
|
|
small in __ellint_rj<br> -86.3168, 0.968868, 0.187163<br> Argument too
|
|
small in __ellint_rj<br> -77.6756, 0.126987, 0.177238<br> Argument too
|
|
small in __ellint_rj<br> -77.6756, 0.135477, 0.177258<br> Argument too
|
|
small in __ellint_rj<br> -77.6756, 0.221034, 0.17754<br> Argument too small
|
|
in __ellint_rj<br> -77.6756, 0.308167, 0.17798<br> Argument too small in
|
|
__ellint_rj<br> -77.6756, 0.632359, 0.181485<br> Argument too small in
|
|
__ellint_rj<br> -77.6756, 0.814724, 0.186089<br> Argument too small in
|
|
__ellint_rj<br> -77.6756, 0.835009, 0.186888<br> Argument too small in
|
|
__ellint_rj<br> -77.6756, 0.905792, 0.190742<br> Argument too small in
|
|
__ellint_rj<br> -77.6756, 0.913376, 0.191315<br> Argument too small in
|
|
__ellint_rj<br> -77.6756, 0.968868, 0.1982<br> Argument too small in __ellint_rj<br>
|
|
-68.8751, 0.126987, 0.188077<br> Argument too small in __ellint_rj<br>
|
|
-68.8751, 0.135477, 0.188099<br> Argument too small in __ellint_rj<br>
|
|
-68.8751, 0.221034, 0.188414<br> Argument too small in __ellint_rj<br>
|
|
-68.8751, 0.308167, 0.188907<br> Argument too small in __ellint_rj<br>
|
|
-68.8751, 0.632359, 0.192834<br> Argument too small in __ellint_rj<br>
|
|
-68.8751, 0.814724, 0.198<br> Argument too small in __ellint_rj<br> -68.8751,
|
|
0.835009, 0.198896<br> Argument too small in __ellint_rj<br> -68.8751,
|
|
0.905792, 0.203226<br> Argument too small in __ellint_rj<br> -68.8751,
|
|
0.913376, 0.203871<br> Argument too small in __ellint_rj<br> -68.8751,
|
|
0.968868, 0.211615<br> Argument too small in __ellint_rj<br> -36.1317,
|
|
0.126987, 0.258074<br> Argument too small in __ellint_rj<br> -36.1317,
|
|
0.135477, 0.258115<br> Argument too small in __ellint_rj<br> -36.1317,
|
|
0.221034, 0.258686<br> Argument too small in __ellint_rj<br> -36.1317,
|
|
0.308167, 0.259579<br> Argument too small in __ellint_rj<br> -36.1317,
|
|
0.632359, 0.266738<br> Argument too small in __ellint_rj<br> -36.1317,
|
|
0.814724, 0.276242<br> Argument too small in __ellint_rj<br> -36.1317,
|
|
0.835009, 0.2779<br> Argument too small in __ellint_rj<br> -36.1317, 0.905792,
|
|
0.285938<br> Argument too small in __ellint_rj<br> -36.1317, 0.913376,
|
|
0.287139<br> Argument too small in __ellint_rj<br> -36.1317, 0.968868,
|
|
0.301608<br> Argument too small in __ellint_rj<br> -17.7129, 0.126987,
|
|
0.363673<br> Argument too small in __ellint_rj<br> -17.7129, 0.135477,
|
|
0.36375<br> Argument too small in __ellint_rj<br> -17.7129, 0.221034, 0.364822<br>
|
|
Argument too small in __ellint_rj<br> -17.7129, 0.308167, 0.366503<br>
|
|
Argument too small in __ellint_rj<br> -17.7129, 0.632359, 0.380066<br>
|
|
Argument too small in __ellint_rj<br> -17.7129, 0.814724, 0.398311<br>
|
|
Argument too small in __ellint_rj<br> -17.7129, 0.835009, 0.401518<br>
|
|
Argument too small in __ellint_rj<br> -17.7129, 0.905792, 0.417145<br>
|
|
Argument too small in __ellint_rj<br> -17.7129, 0.913376, 0.41949<br> Argument
|
|
too small in __ellint_rj<br> -17.7129, 0.968868, 0.447893<br> Argument
|
|
too small in __ellint_rj<br> -15.6641, 0.126987, 0.385409<br> Argument
|
|
too small in __ellint_rj<br> -15.6641, 0.135477, 0.385495<br> Argument
|
|
too small in __ellint_rj<br> -15.6641, 0.221034, 0.386686<br> Argument
|
|
too small in __ellint_rj<br> -15.6641, 0.308167, 0.388553<br> Argument
|
|
too small in __ellint_rj<br> -15.6641, 0.632359, 0.403643<br> Argument
|
|
too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY
|
|
***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h89"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1">Error
|
|
Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library
|
|
<cmath> and test data Complete Elliptic Integral PI: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION:
|
|
Gross error found at entry 3.<br> Found: 1.28255 Expected 2.22144 Error:
|
|
0.732051<br> 0.5, 0, 2.22144<br> Argument too small in __ellint_rj<br>
|
|
-4, 0.3, 0.712709<br> Argument too small in __ellint_rj<br> -100000, -0.5,
|
|
0.00496945<br> Argument too small in __ellint_rj<br> -1e+10, -0.75, 1.5708e-05<br>
|
|
CAUTION: Gross error found at entry 8.<br> Found: 1.45615 Expected 101.045
|
|
Error: 68.3919<br> 0.999023, -0.875, 101.045<br> Argument too small in
|
|
__ellint_rj<br> -4.14952e+180, 0.5, 7.71119e-91<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h90"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0">Error
|
|
Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Elliptic Integral PI: Large Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data"></a>Argument
|
|
too small in __ellint_rj<br> -88.2952, -8.04919, 0.814724, -0.874724<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, -7.46026, 0.135477, -0.827189<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, -7.29046, 0.905792, -0.877476<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, -6.23236, 0.835009, -0.652152<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, -5.57932, 0.126987, -0.512276<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, -4.43004, 0.968868, -0.543324<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, -3.83666, 0.913376, -0.513389<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 0.93763, 0.221034, 0.158243<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 0.944412, 0.632359, 0.160101<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 2.64719, 0.308167, 0.188127<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 6.29447, 0.0975404, 0.676465<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 6.70017, 0.547221, 0.817785<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 8.11584, 0.278498, 0.837452<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 8.26752, 0.188382, 0.837571<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 9.15014, 0.546881, 0.885365<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 9.29777, 0.992881, 1.06701<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 9.3539, 0.957507, 1.03573<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 9.37736, 0.996461, 1.13933<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 9.85763, 0.964889, 1.24906<br>
|
|
Argument too small in __ellint_rj<br> -88.2952, 9.92923, 0.967695, 1.25621<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, -8.04919, 0.157613, -0.841405<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, -7.46026, 0.725839, -0.859877<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, -7.29046, 0.970593, -0.914439<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, -6.23236, 0.98111, -0.710627<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, -5.57932, 0.957167, -0.58106<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, -4.43004, 0.109862, -0.499839<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, -3.83666, 0.485376, -0.494286<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 0.93763, 0.798106, 0.162644<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 0.944412, 0.80028, 0.16282<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 2.64719, 0.297029, 0.18978<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 6.29447, 0.141886, 0.682392<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 6.70017, 0.00478348, 0.812885<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 8.11584, 0.421761, 0.849249<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 8.26752, 0.112465, 0.843648<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 9.15014, 0.915736, 0.953733<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 9.29777, 0.639763, 0.936743<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 9.3539, 0.792207, 0.987359<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 9.37736, 0.878431, 1.02525<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 9.85763, 0.959492, 1.25508<br>
|
|
Argument too small in __ellint_rj<br> -86.8166, 9.92923, 0.503663, 1.16735<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, -8.04919, 0.655741, -0.873305<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, -7.46026, 0.797929, -0.879044<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, -7.29046, 0.0357117, -0.840785<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, -6.23236, 0.361294, -0.635502<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, -5.57932, 0.849129, -0.558231<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, -4.43004, 0.211924, -0.506533<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, -3.83666, 0.933993, -0.527681<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, 0.93763, 0.68136, 0.163458<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, 0.944412, 0.678735, 0.163582<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, 2.64719, 0.398739, 0.193458<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, 6.29447, 0.75774, 0.716086<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, 6.70017, 0.740647, 0.847849<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, 8.11584, 0.743132, 0.883827<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, 8.26752, 0.474759, 0.864181<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, 9.15014, 0.392227, 0.895646<br>
|
|
Argument too small in __ellint_rj<br> -84.7616, 9.29777, 0.422088, 0.933423<br>
|
|
Argument too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED
|
|
FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h91"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1">Error
|
|
Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Elliptic Integral PI: Random Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data"></a>CAUTION:
|
|
Gross error found at entry 150.<br> Found: 1.09748 Expected 1.76311 Error:
|
|
0.606506<br> 0.546881, 1.27977, 0.349984, 1.76311<br> CAUTION: Gross error
|
|
found at entry 151.<br> Found: 1.39529 Expected 2.4686 Error: 0.769232<br>
|
|
0.546881, 1.31163, 0.907365, 2.4686<br> CAUTION: Gross error found at entry
|
|
152.<br> Found: 1.17627 Expected 2.03097 Error: 0.726615<br> 0.546881,
|
|
1.42281, 0.196595, 2.03097<br> CAUTION: Gross error found at entry 153.<br>
|
|
Found: 1.47192 Expected 2.76894 Error: 0.881179<br> 0.546881, 1.43473, 0.848468,
|
|
2.76894<br> CAUTION: Gross error found at entry 154.<br> Found: 1.23674
|
|
Expected 2.22733 Error: 0.800966<br> 0.546881, 1.50405, 0.251084, 2.22733<br>
|
|
CAUTION: Gross error found at entry 155.<br> Found: 1.87704 Expected 3.98415
|
|
Error: 1.12257<br> 0.546881, 1.51564, 0.955018, 3.98415<br> CAUTION: Gross
|
|
error found at entry 156.<br> Found: 1.35817 Expected 2.53989 Error: 0.870091<br>
|
|
0.546881, 1.52005, 0.616045, 2.53989<br> CAUTION: Gross error found at entry
|
|
157.<br> Found: 1.48427 Expected 2.87082 Error: 0.934166<br> 0.546881,
|
|
1.52189, 0.778898, 2.87082<br> CAUTION: Gross error found at entry 158.<br>
|
|
Found: 1.32687 Expected 2.48679 Error: 0.874176<br> 0.546881, 1.55961, 0.473289,
|
|
2.48679<br> CAUTION: Gross error found at entry 159.<br> Found: 2.37485
|
|
Expected 5.58805 Error: 1.35301<br> 0.546881, 1.56524, 0.98746, 5.58805<br>
|
|
CAUTION: Gross error found at entry 170.<br> Found: 1.08889 Expected 1.74565
|
|
Error: 0.603142<br> 0.547221, 1.27977, 0.285839, 1.74565<br> CAUTION: Gross
|
|
error found at entry 171.<br> Found: 1.21346 Expected 2.03956 Error: 0.680778<br>
|
|
0.547221, 1.31163, 0.67982, 2.03956<br> CAUTION: Gross error found at entry
|
|
172.<br> Found: 1.36407 Expected 2.48392 Error: 0.820965<br> 0.547221,
|
|
1.42281, 0.7572, 2.48392<br> CAUTION: Gross error found at entry 173.<br>
|
|
Found: 1.21442 Expected 2.12881 Error: 0.752947<br> 0.547221, 1.43473, 0.39232,
|
|
2.12881<br> CAUTION: Gross error found at entry 174.<br> Found: 1.4409
|
|
Expected 2.74399 Error: 0.904352<br> 0.547221, 1.50405, 0.753729, 2.74399<br>
|
|
CAUTION: Gross error found at entry 175.<br> Found: 1.32796 Expected 2.46156
|
|
Error: 0.853642<br> 0.547221, 1.51564, 0.561557, 2.46156<br> CAUTION: Gross
|
|
error found at entry 176.<br> Found: 1.27163 Expected 2.32413 Error: 0.82767<br>
|
|
0.547221, 1.52005, 0.380446, 2.32413<br> CAUTION: Gross error found at entry
|
|
177.<br> Found: 1.24298 Expected 2.25511 Error: 0.814274<br> 0.547221,
|
|
1.52189, 0.208068, 2.25511<br> CAUTION: Gross error found at entry 178.<br>
|
|
Found: 1.36528 Expected 2.58635 Error: 0.894379<br> 0.547221, 1.55961, 0.567822,
|
|
2.58635<br> CAUTION: Gross error found at entry 179.<br> Found: 1.35151
|
|
Expected 2.55463 Error: 0.890206<br> 0.547221, 1.56524, 0.527371, 2.55463<br>
|
|
CAUTION: Gross error found at entry 189.<br> Found: 1.01047 Expected 1.52344
|
|
Error: 0.507658<br> 0.632359, 0.993308, 0.964966, 1.52344<br> CAUTION:
|
|
Gross error found at entry 190.<br> Found: 1.05231 Expected 1.84135 Error:
|
|
0.749817<br> 0.632359, 1.27977, 0.129906, 1.84135<br> CAUTION: Gross error
|
|
found at entry 191.<br> Found: 1.07393 Expected 1.92224 Error: 0.789918<br>
|
|
0.632359, 1.31163, 0.154438, 1.92224<br> CAUTION: Gross error found at entry
|
|
192.<br> Found: 1.22616 Expected 2.43657 Error: 0.987156<br> 0.632359,
|
|
1.42281, 0.568824, 2.43657<br> CAUTION: Gross error found at entry 193.<br>
|
|
Found: 1.18462 Expected 2.33142 Error: 0.968083<br> 0.632359, 1.43473, 0.394908,
|
|
2.33142<br> CAUTION: Gross error found at entry 194.<br> Found: 1.25094
|
|
Expected 2.59169 Error: 1.0718<br> 0.632359, 1.50405, 0.469391, 2.59169<br>
|
|
CAUTION: Gross error found at entry 195.<br> Found: 1.23693 Expected 2.56158
|
|
Error: 1.07091<br> 0.632359, 1.51564, 0.387296, 2.56158<br> CAUTION: Gross
|
|
error found at entry 196.<br> Found: 1.19839 Expected 2.45293 Error: 1.04685<br>
|
|
0.632359, 1.52005, 0.0119021, 2.45293<br> CAUTION: Gross error found at entry
|
|
197.<br> Found: 1.39415 Expected 3.05228 Error: 1.18935<br> 0.632359, 1.52189,
|
|
0.726955, 3.05228<br> CAUTION: Gross error found at entry 198.<br> Found:
|
|
1.25489 Expected 2.6569 Error: 1.11723<br> 0.632359, 1.55961, 0.337123, 2.6569<br>
|
|
CAUTION: Gross error found at entry 199.<br> Found: 1.27021 Expected 2.70857
|
|
Error: 1.13237<br> 0.632359, 1.56524, 0.38857, 2.70857<br> CAUTION: Gross
|
|
error found at entry 209.<br> Found: 0.83304 Expected 1.35947 Error: 0.631944<br>
|
|
0.814724, 0.993308, 0.119547, 1.35947<br> CAUTION: Gross error found at entry
|
|
210.<br> Found: 1.07764 Expected 2.50291 Error: 1.32258<br> *** FURTHER
|
|
CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h92"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2">Error
|
|
Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Elliptic Integral PI: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION:
|
|
Gross error found at entry 0.<br> Found: -0.809353 Expected -1.55741 Error:
|
|
0.924263<br> 1, -1, 0, -1.55741<br> CAUTION: Gross error found at entry
|
|
11.<br> Found: 1.07555 Expected 13.2822 Error: 11.3492<br> 0.999023, 1.5,
|
|
0, 13.2822<br> CAUTION: Gross error found at entry 13.<br> Found: -5.86896e+09
|
|
Expected 1.53659e+10 Error: 1.18973e+4932<br> 0.5, 1e+10, 0.5, 1.53659e+10<br>
|
|
Argument too small in __ellint_rj<br> -100000, 10, 0.75, 0.0347926<br>
|
|
Argument too small in __ellint_rj<br> -1e+10, 10, 0.875, 0.000109956<br>
|
|
Argument too small in __ellint_rj<br> -1e+10, 1e+20, 0.875, 1.00001e+15<br>
|
|
Argument too small in __ellint_rj<br> -1e+10, 1.57031, 0.875, 1.57081e-05<br>
|
|
CAUTION: Gross error found at entry 18.<br> Found: -6.25413e+09 Expected
|
|
6.43274e+21 Error: 1.18973e+4932<br> 0.999023, 1e+20, 0.875, 6.43274e+21<br>
|
|
CAUTION: Gross error found at entry 19.<br> Found: 0.102424 Expected 0.196321
|
|
Error: 0.916748<br> 50, 0.125, 0.25, 0.196321<br> CAUTION: Gross error
|
|
found at entry 20.<br> Found: 0.798807 Expected 1.773 Error: 1.21956<br>
|
|
1.125, 1, 0.25, 1.773<br> CAUTION: Gross error found at entry 21.<br> Found:
|
|
7.07138 Expected 0.662468 Error: 9.6743<br> 1.125, 10, 0.25, 0.662468<br>
|
|
CAUTION: Gross error found at entry 22.<br> Found: 2.04288 Expected -0.142697
|
|
Error: 1.18973e+4932<br> 1.125, 3, 0.25, -0.142697<br> CAUTION: Gross error
|
|
found at entry 23.<br> Found: 1.07762 Expected 22.2699 Error: 19.6659<br>
|
|
1.00391, 1.5, 0.125, 22.2699<br> CAUTION: Gross error found at entry 24.<br>
|
|
Found: 15.1275 Expected -0.535406 Error: 1.18973e+4932<br> 1.00391, 21.5,
|
|
0.125, -0.535406<br> CAUTION: Gross error found at entry 41.<br> Found:
|
|
1.57454 Expected 3.0338 Error: 0.926787<br> 0.5, 2, 0, 3.0338<br> CAUTION:
|
|
Gross error found at entry 42.<br> Found: 3.0338 Expected 1.57454 Error:
|
|
0.926787<br> -0.5, 2, 0, 1.57454<br> CAUTION: Gross error found at entry
|
|
43.<br> Found: -1.57454 Expected -3.0338 Error: 0.926787<br> 0.5, -2, 0,
|
|
-3.0338<br> CAUTION: Gross error found at entry 44.<br> Found: -3.0338
|
|
Expected -1.57454 Error: 0.926787<br> -0.5, -2, 0, -1.57454<br> CAUTION:
|
|
Found non-finite result, when a finite value was expected at entry 51<br>
|
|
Found: inf Expected -2.87535 Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br>
|
|
CAUTION: Gross error found at entry 51.<br> Found: inf Expected -2.87535
|
|
Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br> CAUTION: Found non-finite
|
|
result, when a finite value was expected at entry 52<br> Found: -inf Expected
|
|
2.87535 Error: 1.18973e+4932<br> 1, -2, 0.5, 2.87535<br> CAUTION: Gross
|
|
error found at entry 52.<br> Found: -inf Expected 2.87535 Error: 1.18973e+4932<br>
|
|
1, -2, 0.5, 2.87535<br> CAUTION: Found non-finite result, when a finite value
|
|
was expected at entry 53<br> Found: inf Expected -2.18504 Error: 1.18973e+4932<br>
|
|
1, 2, 6.22302e-61, -2.18504<br> CAUTION: Gross error found at entry 53.<br>
|
|
Found: inf Expected -2.18504 Error: 1.18973e+4932<br> 1, 2, 6.22302e-61,
|
|
-2.18504<br> CAUTION: Found non-finite result, when a finite value was expected
|
|
at entry 54<br> Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1,
|
|
-2, 6.22302e-61, 2.18504<br> CAUTION: Gross error found at entry 54.<br>
|
|
Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1, -2, 6.22302e-61,
|
|
2.18504<br> CAUTION: Gross error found at entry 57.<br> Found: 0.703907
|
|
Expected 0.000975941 Error: 720.259<br> 20, 3.14257, 0.5, 0.000975941<br>
|
|
CAUTION: Gross error found at entry 58.<br> Found: -0.703907 Expected -0.000975941
|
|
Error: 720.259<br> 20, -3.14257, 0.5, -0.000975941<br> CAUTION: Gross error
|
|
found at entry 59.<br> Found: 1.24445 Expected -27.1647 Error: 1.18973e+4932<br>
|
|
1.01562, 1.6958, 0.5, -27.1647<br> CAUTION: Gross error found at entry 60.<br>
|
|
Found: -1.24445 Expected 27.1647 Error: 1.18973e+4932<br> 1.01562, -1.6958,
|
|
0.5, 27.1647<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h93"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_">Error
|
|
Output For expint (Ei) with compiler GNU C++ version 7.1.0 and library <cmath>
|
|
and test data Exponential Integral Ei</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei"></a>Continued
|
|
fraction failed in __expint_En_cont_frac.<br> -1.30539, -0.134326<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h94"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp">Error
|
|
Output For ibeta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and
|
|
test data Incomplete Beta Function: Large and Diverse Values</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values"></a>underflow<br>
|
|
1.04761e-05, 39078.2, 0.913384, 95444.4, 0, 1, 0<br> underflow<br> 1.2158e-05,
|
|
24110.5, 0.135563, 82239.7, 0, 1, 0<br> underflow<br> 1.30342e-05, 26168.3,
|
|
0.127074, 76710.7, 0, 1, 0<br> underflow<br> 1.51962e-05, 16177.5, 0.814742,
|
|
65795.4, 0, 1, 0<br> underflow<br> 1.64873e-05, 470997, 0.127074, 60639.1,
|
|
0, 1, 0<br> underflow<br> 1.66259e-05, 147819, 0.632396, 60134.5, 0, 1,
|
|
0<br> underflow<br> 1.78638e-05, 439.387, 0.835025, 55972.4, 0, 1, 0<br>
|
|
underflow<br> 2.00434e-05, 482.007, 0.905801, 49885.1, 0, 1, 0<br> underflow<br>
|
|
2.05189e-05, 236088, 0.835025, 48722.7, 0, 1, 0<br> underflow<br> 2.14336e-05,
|
|
3719.28, 0.814742, 46647, 0, 1, 0<br> underflow<br> 2.24486e-05, 445071,
|
|
0.221112, 44532.6, 0, 1, 0<br> underflow<br> 2.34849e-05, 25542.8, 0.968871,
|
|
42569.8, 0, 1, 0<br> underflow<br> 2.39993e-05, 462.946, 0.814742, 41661.1,
|
|
0, 1, 0<br> underflow<br> 2.52178e-05, 1832.27, 0.913384, 39646.4, 0, 1,
|
|
0<br> underflow<br> 2.87756e-05, 25491.8, 0.905801, 34740.9, 0, 1, 0<br>
|
|
underflow<br> 2.89316e-05, 494.984, 0.968871, 34557.6, 0, 1, 0<br> underflow<br>
|
|
3.11413e-05, 348144, 0.308236, 32098.3, 0, 1, 0<br> underflow<br> 3.12319e-05,
|
|
33713, 0.221112, 32007.5, 0, 1, 0<br> underflow<br> 3.19889e-05, 3931.19,
|
|
0.308236, 31251.9, 0, 1, 0<br> underflow<br> 3.27129e-05, 3109.49, 0.968871,
|
|
30560.4, 0, 1, 0<br> underflow<br> 3.27529e-05, 25796.3, 0.835025, 30520.9,
|
|
0, 1, 0<br> underflow<br> 3.34106e-05, 3378.01, 0.221112, 29922, 0, 1,
|
|
0<br> underflow<br> 3.40793e-05, 288783, 0.814742, 29330.2, 0, 1, 0<br>
|
|
underflow<br> 3.46418e-05, 411.559, 0.913384, 28860.3, 0, 1, 0<br> underflow<br>
|
|
3.61632e-05, 311937, 0.905801, 27639.2, 0, 1, 0<br> underflow<br> 3.75686e-05,
|
|
386440, 0.913384, 26604.5, 0, 1, 0<br> underflow<br> 3.99261e-05, 495352,
|
|
0.968871, 25032.6, 0, 1, 0<br> underflow<br> 4.01492e-05, 3246.23, 0.905801,
|
|
24898.5, 0, 1, 0<br> underflow<br> 4.0288e-05, 2569.28, 0.835025, 24812.9,
|
|
0, 1, 0<br> underflow<br> 4.11667e-05, 24253.8, 0.308236, 24280.8, 0, 1,
|
|
0<br> underflow<br> 4.17714e-05, 274447, 0.135563, 23926.7, 0, 1, 0<br>
|
|
underflow<br> 4.66877e-05, 3780.93, 0.632396, 21410.1, 0, 1, 0<br> underflow<br>
|
|
4.73604e-05, 48598.7, 0.632396, 21103.3, 0, 1, 0<br> underflow<br> 0.00013245,
|
|
251.768, 0.968871, 7543.9, 0, 1, 0<br> underflow<br> 0.000168283, 195801,
|
|
0.905801, 5929.61, 0, 1, 0<br> underflow<br> 0.000177906, 276489, 0.814742,
|
|
5607.86, 0, 1, 0<br> underflow<br> 0.000183097, 316055, 0.127074, 5448.36,
|
|
0, 1, 0<br> underflow<br> 0.000190369, 159132, 0.835025, 5240.42, 0, 1,
|
|
0<br> underflow<br> 0.000191066, 419861, 0.913384, 5220.29, 0, 1, 0<br>
|
|
underflow<br> 0.000192195, 177798, 0.308236, 5190.39, 0, 1, 0<br> underflow<br>
|
|
0.000220499, 107380, 0.135563, 4523.03, 0, 1, 0<br> underflow<br> 0.00022254,
|
|
1432.25, 0.814742, 4485.74, 0, 1, 0<br> underflow<br> 0.000240291, 49604.4,
|
|
0.632396, 4150.25, 0, 1, 0<br> underflow<br> 0.000251444, 15605.8, 0.135563,
|
|
3966.81, 0, 1, 0<br> underflow<br> 0.000274279, 289206, 0.968871, 3632.79,
|
|
0, 1, 0<br> underflow<br> 0.000274343, 2954.47, 0.308236, 3636.51, 0, 1,
|
|
0<br> underflow<br> 0.000278714, 4023.16, 0.632396, 3579.05, 0, 1, 0<br>
|
|
underflow<br> 0.000288369, 460073, 0.221112, 3454.19, 0, 1, 0<br> underflow<br>
|
|
0.000294717, 4642.26, 0.221112, 3384.08, 0, 1, 0<br> underflow<br> 0.000303403,
|
|
2574.36, 0.835025, 3287.52, 0, 1, 0<br> underflow<br> 0.000304309, 4480.75,
|
|
0.905801, 3277.17, 0, 1, 0<br> underflow<br> 0.00031313, 47957, 0.308236,
|
|
3182.22, 0, 1, 0<br> underflow<br> 0.000320063, 25544.6, 0.905801, 3113.68,
|
|
0, 1, 0<br> underflow<br> 0.000334818, 29065.5, 0.968871, 2975.86, 0, 1,
|
|
0<br> underflow<br> 0.00034899, 41187.6, 0.913384, 2854.23, 0, 1, 0<br>
|
|
underflow<br> 0.000350247, 426.308, 0.905801, 2848.5, 0, 1, 0<br> underflow<br>
|
|
0.000357727, 31752.2, 0.127074, 2784.5, 0, 1, 0<br> underflow<br> 0.000412091,
|
|
367.714, 0.913384, 2420.17, 0, 1, 0<br> underflow<br> 0.000417933, 4668.47,
|
|
0.968871, 2383.72, 0, 1, 0<br> underflow<br> 0.000424632, 17994.9, 0.221112,
|
|
2344.63, 0, 1, 0<br> underflow<br> 0.000427051, 2443.44, 0.913384, 2333.28,
|
|
0, 1, 0<br> underflow<br> 0.000437724, 454399, 0.632396, 2270.98, 0, 1,
|
|
0<br> underflow<br> 0.000450377, 10660.8, 0.835025, 2210.53, 0, 1, 0<br>
|
|
underflow<br> 0.000475601, 19603, 0.814742, 2092.17, 0, 1, 0<br> underflow<br>
|
|
0.00116972, 4487.22, 0.221112, 845.964, 0, 1, 0<br> underflow<br> 0.00124188,
|
|
211066, 0.632396, 792.493, 0, 1, 0<br> underflow<br> 0.00128578, 4738.41,
|
|
0.308236, 768.75, 0, 1, 0<br> underflow<br> 0.00133388, 46277.8, 0.913384,
|
|
738.46, 0, 1, 0<br> underflow<br> 0.00138692, 2158.76, 0.814742, 712.816,
|
|
0, 1, 0<br> underflow<br> 0.00153268, 13060.2, 0.968871, 642.474, 0, 1,
|
|
0<br> underflow<br> 0.00159946, 1780.43, 0.968871, 617.202, 0, 1, 0<br>
|
|
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h95"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_">Error
|
|
Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Jacobi Elliptic: Modulus near 1</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m|
|
|
> 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br>
|
|
-4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246,
|
|
1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359,
|
|
0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354,
|
|
0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347,
|
|
0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343,
|
|
0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157,
|
|
0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br>
|
|
|m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br>
|
|
|m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m|
|
|
> 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m|
|
|
> 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| >
|
|
1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br>
|
|
-4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246,
|
|
1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239,
|
|
-0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849,
|
|
0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665,
|
|
0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br>
|
|
|m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| >
|
|
1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| >
|
|
1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| >
|
|
1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| >
|
|
1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br>
|
|
-3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br>
|
|
-3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br>
|
|
-3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br>
|
|
-3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br>
|
|
-3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br>
|
|
-3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br>
|
|
-3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br>
|
|
-3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br>
|
|
-3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br>
|
|
-3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523,
|
|
1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635,
|
|
0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358,
|
|
0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br>
|
|
|m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br>
|
|
|m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br>
|
|
|m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br>
|
|
|m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br>
|
|
|m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br>
|
|
|m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br>
|
|
|m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br>
|
|
|m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br>
|
|
|m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br>
|
|
|m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br>
|
|
|m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br>
|
|
|m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br>
|
|
|m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| >
|
|
1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br>
|
|
-3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618,
|
|
1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001,
|
|
-0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003,
|
|
-0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004,
|
|
-0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603,
|
|
0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523,
|
|
0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445,
|
|
0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612,
|
|
0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126,
|
|
0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193,
|
|
0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667,
|
|
0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451,
|
|
-0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253,
|
|
-0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681,
|
|
-0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br>
|
|
|m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER
|
|
CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h96"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_">Error
|
|
Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Jacobi Elliptic: Modulus near 1</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m|
|
|
> 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br>
|
|
-4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246,
|
|
1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359,
|
|
0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354,
|
|
0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347,
|
|
0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343,
|
|
0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157,
|
|
0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br>
|
|
|m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br>
|
|
|m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m|
|
|
> 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m|
|
|
> 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| >
|
|
1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br>
|
|
-4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246,
|
|
1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239,
|
|
-0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849,
|
|
0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665,
|
|
0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br>
|
|
|m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| >
|
|
1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| >
|
|
1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| >
|
|
1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| >
|
|
1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br>
|
|
-3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br>
|
|
-3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br>
|
|
-3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br>
|
|
-3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br>
|
|
-3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br>
|
|
-3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br>
|
|
-3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br>
|
|
-3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br>
|
|
-3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br>
|
|
-3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523,
|
|
1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635,
|
|
0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358,
|
|
0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br>
|
|
|m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br>
|
|
|m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br>
|
|
|m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br>
|
|
|m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br>
|
|
|m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br>
|
|
|m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br>
|
|
|m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br>
|
|
|m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br>
|
|
|m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br>
|
|
|m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br>
|
|
|m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br>
|
|
|m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br>
|
|
|m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| >
|
|
1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br>
|
|
-3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618,
|
|
1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001,
|
|
-0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003,
|
|
-0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004,
|
|
-0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603,
|
|
0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523,
|
|
0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445,
|
|
0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612,
|
|
0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126,
|
|
0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193,
|
|
0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667,
|
|
0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451,
|
|
-0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253,
|
|
-0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681,
|
|
-0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br>
|
|
|m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER
|
|
CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h97"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_">Error
|
|
Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Jacobi Elliptic: Modulus near 1</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m|
|
|
> 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br>
|
|
-4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246,
|
|
1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359,
|
|
0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354,
|
|
0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347,
|
|
0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343,
|
|
0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157,
|
|
0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br>
|
|
|m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br>
|
|
|m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m|
|
|
> 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m|
|
|
> 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| >
|
|
1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br>
|
|
-4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246,
|
|
1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239,
|
|
-0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849,
|
|
0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665,
|
|
0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br>
|
|
|m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| >
|
|
1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| >
|
|
1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| >
|
|
1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| >
|
|
1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br>
|
|
-3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br>
|
|
-3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br>
|
|
-3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br>
|
|
-3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br>
|
|
-3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br>
|
|
-3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br>
|
|
-3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br>
|
|
-3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br>
|
|
-3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br>
|
|
-3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523,
|
|
1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635,
|
|
0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358,
|
|
0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br>
|
|
|m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br>
|
|
|m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br>
|
|
|m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br>
|
|
|m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br>
|
|
|m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br>
|
|
|m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br>
|
|
|m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br>
|
|
|m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br>
|
|
|m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br>
|
|
|m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br>
|
|
|m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br>
|
|
|m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br>
|
|
|m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| >
|
|
1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br>
|
|
-3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618,
|
|
1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001,
|
|
-0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003,
|
|
-0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004,
|
|
-0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603,
|
|
0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523,
|
|
0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445,
|
|
0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612,
|
|
0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126,
|
|
0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193,
|
|
0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667,
|
|
0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451,
|
|
-0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253,
|
|
-0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681,
|
|
-0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br>
|
|
|m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER
|
|
CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h98"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0">Error
|
|
Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Jacobi Elliptic: Random Small Values</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m|
|
|
> 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br>
|
|
2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12,
|
|
1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11,
|
|
1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br>
|
|
|m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br>
|
|
1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10,
|
|
1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10,
|
|
1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br>
|
|
|m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br>
|
|
2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09,
|
|
1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09,
|
|
1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br>
|
|
|m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br>
|
|
1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07,
|
|
1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07,
|
|
1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m|
|
|
> 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br>
|
|
3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06,
|
|
1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05,
|
|
1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m|
|
|
> 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br>
|
|
9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495,
|
|
1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521,
|
|
1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br>
|
|
|m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br>
|
|
|m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br>
|
|
|m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br>
|
|
|m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br>
|
|
|m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br>
|
|
|m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br>
|
|
|m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m|
|
|
> 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| >
|
|
1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br>
|
|
0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574,
|
|
1.65574, 0.408154, 0.912913, -0.737088<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h99"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0">Error
|
|
Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Jacobi Elliptic: Random Small Values</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m|
|
|
> 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br>
|
|
2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12,
|
|
1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11,
|
|
1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br>
|
|
|m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br>
|
|
1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10,
|
|
1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10,
|
|
1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br>
|
|
|m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br>
|
|
2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09,
|
|
1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09,
|
|
1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br>
|
|
|m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br>
|
|
1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07,
|
|
1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07,
|
|
1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m|
|
|
> 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br>
|
|
3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06,
|
|
1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05,
|
|
1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m|
|
|
> 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br>
|
|
9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495,
|
|
1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521,
|
|
1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br>
|
|
|m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br>
|
|
|m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br>
|
|
|m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br>
|
|
|m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br>
|
|
|m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br>
|
|
|m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br>
|
|
|m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m|
|
|
> 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| >
|
|
1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br>
|
|
0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574,
|
|
1.65574, 0.408154, 0.912913, -0.737088<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h100"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0">Error
|
|
Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Jacobi Elliptic: Random Small Values</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m|
|
|
> 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br>
|
|
2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12,
|
|
1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11,
|
|
1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br>
|
|
|m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br>
|
|
1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10,
|
|
1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10,
|
|
1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br>
|
|
|m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br>
|
|
2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09,
|
|
1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09,
|
|
1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br>
|
|
|m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br>
|
|
1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07,
|
|
1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07,
|
|
1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m|
|
|
> 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br>
|
|
3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06,
|
|
1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05,
|
|
1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m|
|
|
> 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br>
|
|
9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495,
|
|
1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521,
|
|
1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br>
|
|
|m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br>
|
|
|m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br>
|
|
|m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br>
|
|
|m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br>
|
|
|m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br>
|
|
|m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br>
|
|
|m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m|
|
|
> 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| >
|
|
1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br>
|
|
0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574,
|
|
1.65574, 0.408154, 0.912913, -0.737088<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h101"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1">Error
|
|
Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Jacobi Elliptic: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m|
|
|
> 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br>
|
|
-2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183,
|
|
0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319,
|
|
0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br>
|
|
|m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| >
|
|
1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25,
|
|
1.5, -0.618665, 0.785655, 0.372585<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h102"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1">Error
|
|
Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Jacobi Elliptic: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m|
|
|
> 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br>
|
|
-2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183,
|
|
0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319,
|
|
0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br>
|
|
|m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| >
|
|
1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25,
|
|
1.5, -0.618665, 0.785655, 0.372585<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h103"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1">Error
|
|
Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Jacobi Elliptic: Mathworld Data</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m|
|
|
> 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br>
|
|
-2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183,
|
|
0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319,
|
|
0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br>
|
|
|m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| >
|
|
1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25,
|
|
1.5, -0.618665, 0.785655, 0.372585<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h104"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3">Error
|
|
Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Mathematica Data - Large orders and other bug cases</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases"></a>underflow<br>
|
|
168, 150, -6.52661e-66<br> underflow<br> 169, 202, 9.2734e-88<br> domain
|
|
error<br> 20, -9.5, -0.00103076<br> domain error<br> 21, -9.5, 4.28582e+26<br>
|
|
domain error<br> 22, -9.5, -0.00419144<br> domain error<br> 23, -9.5,
|
|
8.6745e+29<br> domain error<br> 24, -9.5, -0.0204825<br> domain error<br>
|
|
25, -9.5, 2.08188e+33<br> domain error<br> 26, -9.5, -0.118403<br> domain
|
|
error<br> 27, -9.5, 5.84592e+36<br> domain error<br> 28, -9.5, -0.798969<br>
|
|
domain error<br> 29, -9.5, 1.89875e+40<br> domain error<br> 30, -9.5,
|
|
-6.22245<br> underflow<br> 10, 1.32923e+36, -0<br> underflow<br> 15,
|
|
1.32923e+36, 0<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h105"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4">Error
|
|
Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Mathematica Data - large negative arguments</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments"></a>domain
|
|
error<br> 124, -1.5, 7.63705e+240<br> domain error<br> 124, -2.5, 7.63705e+240<br>
|
|
domain error<br> 124, -3.5, 7.63705e+240<br> domain error<br> 124, -4.5,
|
|
7.63705e+240<br> domain error<br> 124, -5.5, 7.63705e+240<br> domain
|
|
error<br> 124, -6.5, 7.63705e+240<br> domain error<br> 124, -7.5, 7.63705e+240<br>
|
|
domain error<br> 124, -8.5, 7.63705e+240<br> domain error<br> 124, -9.5,
|
|
7.63705e+240<br> domain error<br> 124, -10.5, 7.63705e+240<br> domain
|
|
error<br> 124, -11.5, 7.63705e+240<br> domain error<br> 124, -12.5, 7.63705e+240<br>
|
|
domain error<br> 124, -13.5, 7.63705e+240<br> domain error<br> 124, -14.5,
|
|
7.63705e+240<br> domain error<br> 124, -15.5, 7.63705e+240<br> domain
|
|
error<br> 124, -16.5, 7.63705e+240<br> domain error<br> 124, -17.5, 7.63705e+240<br>
|
|
domain error<br> 124, -18.5, 7.63705e+240<br> domain error<br> 124, -19.5,
|
|
7.63705e+240<br> domain error<br> 124, -20.5, 7.63705e+240<br> domain
|
|
error<br> 124, -1.5, -7.63705e+240<br> domain error<br> 124, -2.5, -7.63705e+240<br>
|
|
domain error<br> 124, -3.5, -7.63705e+240<br> domain error<br> 124, -4.5,
|
|
-7.63705e+240<br> domain error<br> 124, -5.5, -7.63705e+240<br> domain
|
|
error<br> 124, -6.5, -7.63705e+240<br> domain error<br> 124, -7.5, -7.63705e+240<br>
|
|
domain error<br> 124, -8.5, -7.63705e+240<br> domain error<br> 124, -9.5,
|
|
-7.63705e+240<br> domain error<br> 124, -10.5, -7.63705e+240<br> domain
|
|
error<br> 124, -11.5, -7.63705e+240<br> domain error<br> 124, -12.5,
|
|
-7.63705e+240<br> domain error<br> 124, -13.5, -7.63705e+240<br> domain
|
|
error<br> 124, -14.5, -7.63705e+240<br> domain error<br> 124, -15.5,
|
|
-7.63705e+240<br> domain error<br> 124, -16.5, -7.63705e+240<br> domain
|
|
error<br> 124, -17.5, -7.63705e+240<br> domain error<br> 124, -18.5,
|
|
-7.63705e+240<br> domain error<br> 124, -19.5, -7.63705e+240<br> domain
|
|
error<br> 124, -20.5, -7.63705e+240<br> domain error<br> 2, -0.5, -0.828797<br>
|
|
domain error<br> 3, -0.5, 193.409<br> domain error<br> 4, -0.5, -3.47425<br>
|
|
domain error<br> 5, -0.5, 15371.1<br> domain error<br> 6, -0.5, -43.4579<br>
|
|
domain error<br> 7, -0.5, 2.58068e+06<br> domain error<br> 8, -0.5, -1059.96<br>
|
|
domain error<br> 9, -0.5, 7.43185e+08<br> domain error<br> 10, -0.5,
|
|
-42108.9<br> domain error<br> 11, -0.5, 3.26999e+11<br> domain error<br>
|
|
12, -0.5, -2.46448e+06<br> domain error<br> 13, -0.5, 2.04047e+14<br>
|
|
domain error<br> 14, -0.5, -1.9918e+08<br> domain error<br> 15, -0.5,
|
|
1.71399e+17<br> domain error<br> 16, -0.5, -2.12394e+10<br> domain error<br>
|
|
17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5, -2.88824e+12<br>
|
|
domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br> 20, -0.5,
|
|
-4.87773e+14<br> domain error<br> 21, -0.5, 4.28582e+26<br> domain error<br>
|
|
2, -0.5, -0.828843<br> domain error<br> 3, -0.5, 193.409<br> domain error<br>
|
|
4, -0.5, -3.47791<br> domain error<br> 5, -0.5, 15371.1<br> domain error<br>
|
|
6, -0.5, -44.0732<br> domain error<br> 7, -0.5, 2.58068e+06<br> domain
|
|
error<br> 8, -0.5, -1237.15<br> domain error<br> 9, -0.5, 7.43185e+08<br>
|
|
domain error<br> 10, -0.5, -120071<br> domain error<br> 11, -0.5, 3.26999e+11<br>
|
|
domain error<br> 12, -0.5, -5.11131e+07<br> domain error<br> 13, -0.5,
|
|
2.04047e+14<br> domain error<br> 14, -0.5, -4.1064e+10<br> domain error<br>
|
|
15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, -4.44822e+13<br>
|
|
domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5,
|
|
-6.08254e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br>
|
|
20, -0.5, -1.02182e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br>
|
|
domain error<br> 2, -0.5, -0.828751<br> domain error<br> 3, -0.5, 193.409<br>
|
|
domain error<br> 4, -0.5, -3.47059<br> domain error<br> 5, -0.5, 15371.1<br>
|
|
domain error<br> 6, -0.5, -42.8426<br> domain error<br> 7, -0.5, 2.58068e+06<br>
|
|
domain error<br> 8, -0.5, -882.773<br> domain error<br> 9, -0.5, 7.43185e+08<br>
|
|
domain error<br> 10, -0.5, 35853.7<br> domain error<br> 11, -0.5, 3.26999e+11<br>
|
|
domain error<br> 12, -0.5, 4.61841e+07<br> domain error<br> 13, -0.5,
|
|
2.04047e+14<br> domain error<br> 14, -0.5, 4.06656e+10<br> domain error<br>
|
|
15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, 4.44397e+13<br>
|
|
domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5,
|
|
6.08197e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br>
|
|
20, -0.5, 1.02181e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h106"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5">Error
|
|
Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Mathematica Data - negative arguments</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments"></a>domain
|
|
error<br> 2, -12.75, -124.031<br> domain error<br> 2, -12.25, 124.019<br>
|
|
domain error<br> 2, -11.75, -124.032<br> domain error<br> 2, -11.25,
|
|
124.018<br> domain error<br> 2, -10.75, -124.033<br> domain error<br>
|
|
2, -10.25, 124.016<br> domain error<br> 2, -9.75, -124.035<br> domain
|
|
error<br> 2, -9.25, 124.015<br> domain error<br> 2, -8.75, -124.037<br>
|
|
domain error<br> 2, -8.25, 124.012<br> domain error<br> 2, -7.75, -124.04<br>
|
|
domain error<br> 2, -7.25, 124.009<br> domain error<br> 2, -6.75, -124.044<br>
|
|
domain error<br> 2, -6.25, 124.003<br> domain error<br> 2, -5.75, -124.051<br>
|
|
domain error<br> 2, -5.25, 123.995<br> domain error<br> 2, -4.75, -124.061<br>
|
|
domain error<br> 2, -4.25, 123.981<br> domain error<br> 2, -3.75, -124.08<br>
|
|
domain error<br> 2, -3.25, 123.955<br> domain error<br> 2, -2.75, -124.118<br>
|
|
domain error<br> 2, -2.25, 123.897<br> domain error<br> 2, -1.75, -124.214<br>
|
|
domain error<br> 2, -1.25, 123.721<br> domain error<br> 2, -0.75, -124.587<br>
|
|
domain error<br> 2, -0.25, 122.697<br> domain error<br> 3, -12.75, 1558.54<br>
|
|
domain error<br> 3, -12.25, 1558.54<br> domain error<br> 3, -11.75, 1558.54<br>
|
|
domain error<br> 3, -11.25, 1558.54<br> domain error<br> 3, -10.75, 1558.54<br>
|
|
domain error<br> 3, -10.25, 1558.54<br> domain error<br> 3, -9.75, 1558.54<br>
|
|
domain error<br> 3, -9.25, 1558.54<br> domain error<br> 3, -8.75, 1558.54<br>
|
|
domain error<br> 3, -8.25, 1558.54<br> domain error<br> 3, -7.75, 1558.54<br>
|
|
domain error<br> 3, -7.25, 1558.54<br> domain error<br> 3, -6.75, 1558.54<br>
|
|
domain error<br> 3, -6.25, 1558.54<br> domain error<br> 3, -5.75, 1558.54<br>
|
|
domain error<br> 3, -5.25, 1558.54<br> domain error<br> 3, -4.75, 1558.53<br>
|
|
domain error<br> 3, -4.25, 1558.53<br> domain error<br> 3, -3.75, 1558.52<br>
|
|
domain error<br> 3, -3.25, 1558.51<br> domain error<br> 3, -2.75, 1558.49<br>
|
|
domain error<br> 3, -2.25, 1558.46<br> domain error<br> 3, -1.75, 1558.38<br>
|
|
domain error<br> 3, -1.25, 1558.22<br> domain error<br> 3, -0.75, 1557.75<br>
|
|
domain error<br> 3, -0.25, 1555.76<br> domain error<br> 4, -12.75, -24481.6<br>
|
|
domain error<br> 4, -12.25, 24481.6<br> domain error<br> 4, -11.75, -24481.6<br>
|
|
domain error<br> 4, -11.25, 24481.6<br> domain error<br> 4, -10.75, -24481.6<br>
|
|
domain error<br> 4, -10.25, 24481.6<br> domain error<br> 4, -9.75, -24481.6<br>
|
|
domain error<br> 4, -9.25, 24481.6<br> domain error<br> 4, -8.75, -24481.6<br>
|
|
domain error<br> 4, -8.25, 24481.6<br> domain error<br> 4, -7.75, -24481.6<br>
|
|
domain error<br> 4, -7.25, 24481.6<br> domain error<br> 4, -6.75, -24481.6<br>
|
|
domain error<br> 4, -6.25, 24481.6<br> domain error<br> 4, -5.75, -24481.6<br>
|
|
domain error<br> 4, -5.25, 24481.6<br> domain error<br> 4, -4.75, -24481.6<br>
|
|
domain error<br> 4, -4.25, 24481.6<br> domain error<br> 4, -3.75, -24481.6<br>
|
|
domain error<br> 4, -3.25, 24481.5<br> domain error<br> 4, -2.75, -24481.6<br>
|
|
domain error<br> 4, -2.25, 24481.5<br> domain error<br> 4, -1.75, -24481.8<br>
|
|
domain error<br> 4, -1.25, 24481.1<br> domain error<br> 4, -0.75, -24483.2<br>
|
|
domain error<br> 4, -0.25, 24473.2<br> domain error<br> 5, -12.75, 492231<br>
|
|
domain error<br> 5, -12.25, 492231<br> domain error<br> 5, -11.75, 492231<br>
|
|
domain error<br> 5, -11.25, 492231<br> domain error<br> 5, -10.75, 492231<br>
|
|
domain error<br> 5, -10.25, 492231<br> domain error<br> 5, -9.75, 492231<br>
|
|
domain error<br> 5, -9.25, 492231<br> domain error<br> 5, -8.75, 492231<br>
|
|
domain error<br> 5, -8.25, 492231<br> domain error<br> 5, -7.75, 492231<br>
|
|
domain error<br> 5, -7.25, 492231<br> domain error<br> 5, -6.75, 492231<br>
|
|
domain error<br> 5, -6.25, 492231<br> domain error<br> 5, -5.75, 492231<br>
|
|
domain error<br> 5, -5.25, 492231<br> domain error<br> 5, -4.75, 492231<br>
|
|
domain error<br> 5, -4.25, 492231<br> domain error<br> 5, -3.75, 492231<br>
|
|
domain error<br> 5, -3.25, 492231<br> domain error<br> 5, -2.75, 492231<br>
|
|
domain error<br> 5, -2.25, 492231<br> domain error<br> 5, -1.75, 492231<br>
|
|
domain error<br> 5, -1.25, 492230<br> domain error<br> 5, -0.75, 492227<br>
|
|
domain error<br> 5, -0.25, 492199<br> domain error<br> 6, -12.75, -1.17912e+07<br>
|
|
domain error<br> 6, -12.25, 1.17912e+07<br> domain error<br> 6, -11.75,
|
|
-1.17912e+07<br> domain error<br> 6, -11.25, 1.17912e+07<br> domain error<br>
|
|
6, -10.75, -1.17912e+07<br> domain error<br> 6, -10.25, 1.17912e+07<br>
|
|
domain error<br> 6, -9.75, -1.17912e+07<br> domain error<br> 6, -9.25,
|
|
1.17912e+07<br> domain error<br> 6, -8.75, -1.17912e+07<br> domain error<br>
|
|
6, -8.25, 1.17912e+07<br> domain error<br> 6, -7.75, -1.17912e+07<br>
|
|
domain error<br> 6, -7.25, 1.17912e+07<br> domain error<br> 6, -6.75,
|
|
-1.17912e+07<br> domain error<br> 6, -6.25, 1.17912e+07<br> domain error<br>
|
|
6, -5.75, -1.17912e+07<br> domain error<br> 6, -5.25, 1.17912e+07<br>
|
|
domain error<br> 6, -4.75, -1.17912e+07<br> domain error<br> 6, -4.25,
|
|
1.17912e+07<br> domain error<br> 6, -3.75, -1.17912e+07<br> domain error<br>
|
|
6, -3.25, 1.17912e+07<br> domain error<br> 6, -2.75, -1.17912e+07<br>
|
|
domain error<br> 6, -2.25, 1.17912e+07<br> domain error<br> 6, -1.75,
|
|
-1.17912e+07<br> domain error<br> 6, -1.25, 1.17912e+07<br> *** FURTHER
|
|
CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
|
|
</p>
|
|
<h5>
|
|
<a name="special_function_error_rates_rep.error_logs.h107"></a>
|
|
<span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6">Error
|
|
Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
|
|
and test data Mathematica Data - large arguments</a>
|
|
</h5>
|
|
<p>
|
|
<a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments"></a>underflow<br>
|
|
30, 8.58993e+09, -8.44974e-268<br> underflow<br> 30, 1.71799e+10, -7.86943e-277<br>
|
|
underflow<br> 30, 3.43597e+10, -7.32898e-286<br> underflow<br> 30, 6.87195e+10,
|
|
-6.82564e-295<br> underflow<br> 30, 1.37439e+11, -6.35687e-304<br> underflow<br>
|
|
30, 2.74878e+11, -5.9203e-313<br> underflow<br> 30, 5.49756e+11, -5.53354e-322<br>
|
|
underflow<br> 30, 1.09951e+12, -0<br> underflow<br> 30, 2.19902e+12,
|
|
-0<br> underflow<br> 30, 4.39805e+12, -0<br> underflow<br> 30, 8.79609e+12,
|
|
-0<br> underflow<br> 30, 1.75922e+13, -0<br> underflow<br> 30, 3.51844e+13,
|
|
-0<br> underflow<br> 30, 7.03687e+13, -0<br> underflow<br> 30, 1.40737e+14,
|
|
-0<br> underflow<br> 30, 2.81475e+14, -0<br> underflow<br> 30, 5.6295e+14,
|
|
-0<br> underflow<br> 30, 1.1259e+15, -0<br> underflow<br> 30, 2.2518e+15,
|
|
-0<br> underflow<br> 30, 4.5036e+15, -0<br> underflow<br> 30, 9.0072e+15,
|
|
-0<br> underflow<br> 30, 1.80144e+16, -0<br> underflow<br> 30, 3.60288e+16,
|
|
-0<br> underflow<br> 30, 7.20576e+16, -0<br> underflow<br> 30, 1.44115e+17,
|
|
-0<br> underflow<br> 30, 2.8823e+17, -0<br> underflow<br> 30, 5.76461e+17,
|
|
-0<br> underflow<br> 30, 1.15292e+18, -0<br> underflow<br> 30, 2.30584e+18,
|
|
-0<br> underflow<br> 30, 4.61169e+18, -0<br> underflow<br> 30, 9.22337e+18,
|
|
-0<br> underflow<br> 30, 1.84467e+19, -0<br> underflow<br> 30, 3.68935e+19,
|
|
-0<br> underflow<br> 30, 7.3787e+19, -0<br> underflow<br> 30, 1.47574e+20,
|
|
-0<br> underflow<br> 30, 2.95148e+20, -0<br> underflow<br> 30, 5.90296e+20,
|
|
-0<br> underflow<br> 30, 1.18059e+21, -0<br> underflow<br> 30, 2.36118e+21,
|
|
-0<br> underflow<br> 30, 4.72237e+21, -0<br> underflow<br> 30, 9.44473e+21,
|
|
-0<br> underflow<br> 30, 1.88895e+22, -0<br> underflow<br> 30, 3.77789e+22,
|
|
-0<br> underflow<br> 30, 7.55579e+22, -0<br> underflow<br> 30, 1.51116e+23,
|
|
-0<br> underflow<br> 30, 3.02231e+23, -0<br> underflow<br> 30, 6.04463e+23,
|
|
-0<br> underflow<br> 30, 1.20893e+24, -0<br> underflow<br> 30, 2.41785e+24,
|
|
-0<br> underflow<br> 30, 4.8357e+24, -0<br> underflow<br> 30, 9.67141e+24,
|
|
-0<br> underflow<br> 30, 1.93428e+25, -0<br> underflow<br> 30, 3.86856e+25,
|
|
-0<br> underflow<br> 30, 7.73713e+25, -0<br> underflow<br> 30, 1.54743e+26,
|
|
-0<br> underflow<br> 30, 3.09485e+26, -0<br> underflow<br> 30, 6.1897e+26,
|
|
-0<br> underflow<br> 30, 1.23794e+27, -0<br> underflow<br> 30, 2.47588e+27,
|
|
-0<br> underflow<br> 30, 4.95176e+27, -0<br> underflow<br> 30, 9.90352e+27,
|
|
-0<br> underflow<br> 30, 1.9807e+28, -0<br> underflow<br> 30, 3.96141e+28,
|
|
-0<br> underflow<br> 30, 7.92282e+28, -0<br> underflow<br> 30, 1.58456e+29,
|
|
-0<br> underflow<br> 30, 3.16913e+29, -0<br> underflow<br> 30, 6.33825e+29,
|
|
-0<br> underflow<br> 30, 1.26765e+30, -0<br>
|
|
</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
|
<a name="special_function_error_rates_rep.all_the_tables"></a><a class="link" href="index.html#special_function_error_rates_rep.all_the_tables" title="Tables">Tables</a>
|
|
</h2></div></div></div>
|
|
<div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_beta"></a><p class="title"><b>Table 97. Error rates for beta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for beta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.14ε (Mean = 0.574ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.86ε (Mean = 1.22ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 364ε (Mean = 76.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.86ε (Mean = 1.22ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.23ε (Mean = 1.14ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.978ε (Mean = 0.0595ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03ε (Mean = 265ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 61.4ε (Mean = 19.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.07e+03ε (Mean = 264ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 107ε (Mean = 24.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 96.5ε (Mean = 22.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Beta Function: Divergent Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 176ε (Mean = 28ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.99ε (Mean = 2.44ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 128ε (Mean = 23.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.8ε (Mean = 2.71ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.4ε (Mean = 2.19ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_beta_incomplete_"></a><p class="title"><b>Table 98. Error rates for beta (incomplete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.1ε (Mean = 2.32ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.7ε (Mean = 3.19ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.94ε (Mean = 2.17ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.568ε (Mean = 0.0254ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 69.2ε (Mean = 13.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 174ε (Mean = 25ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 90ε (Mean = 12.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.0325ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 633ε (Mean = 29.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.0323ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.6ε (Mean = 3.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 51.8ε (Mean = 11ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26ε (Mean = 6.28ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_betac"></a><p class="title"><b>Table 99. Error rates for betac</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for betac">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.92ε (Mean = 2.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.2ε (Mean = 2.94ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.94ε (Mean = 2.06ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.949ε (Mean = 0.098ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 63.5ε (Mean = 13.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 97.6ε (Mean = 24.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 90.6ε (Mean = 14.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.72e+03ε (Mean = 113ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.1ε (Mean = 3.65ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 103ε (Mean = 17.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26.2ε (Mean = 6.36ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_binomial_coefficient"></a><p class="title"><b>Table 100. Error rates for binomial_coefficient</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Binomials: small arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.369ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.369ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Binomials: large arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.939ε (Mean = 0.314ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26.6ε (Mean = 6.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 53.2ε (Mean = 10.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 37.2ε (Mean = 7.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_boost_math_powm1"></a><p class="title"><b>Table 101. Error rates for boost::math::powm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
powm1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.04ε (Mean = 0.493ε))<br>
|
|
<br> <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.04ε (Mean = 0.493ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06ε (Mean = 0.425ε))<br>
|
|
<br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06ε (Mean = 0.425ε))<br>
|
|
<br> <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.88ε (Mean = 0.49ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.88ε (Mean = 0.49ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.486ε))<br>
|
|
<br> <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cbrt"></a><p class="title"><b>Table 102. Error rates for cbrt</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cbrt">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
cbrt Function
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε))
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cos_pi"></a><p class="title"><b>Table 103. Error rates for cos_pi</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cos_pi">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.284ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi near integers and half integers
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.298ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i"></a><p class="title"><b>Table 104. Error rates for cyl_bessel_i</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.661ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.762ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.64ε (Mean = 0.202ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.767ε (Mean = 0.398ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel In: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 140ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Iv: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 3.53ε (Mean = 1.39ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 616ε (Mean = 221ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.12ε (Mean = 1.95ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.97ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel In: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 7.37ε (Mean = 2.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.62ε (Mean = 1.06ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 645ε (Mean = 132ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 176ε (Mean = 39.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.67ε (Mean = 1.88ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Iv: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.35ε (Mean = 1.62ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.05e+03ε (Mean = 224ε)
|
|
<a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 283ε (Mean = 88.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.46ε (Mean = 1.71ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Iv: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 6.66ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 118ε (Mean = 57.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 6.59ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.67ε (Mean = 1.64ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 105. Error rates for cyl_bessel_i (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.661ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.762ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.64ε (Mean = 0.202ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.767ε (Mean = 0.398ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel In: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 140ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 106. Error rates for cyl_bessel_i_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.354ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.36ε (Mean = 0.782ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'n: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 701ε (Mean = 212ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'v: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.512ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.76e+03ε (Mean = 1.19e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'n: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.95ε (Mean = 1.06ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 195ε (Mean = 37.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.85ε (Mean = 1.82ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'v: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.1ε (Mean = 2.93ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 336ε (Mean = 68.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14ε (Mean = 2.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'v: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.5ε (Mean = 26.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 107. Error rates for cyl_bessel_i_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.82ε (Mean = 0.354ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.36ε (Mean = 0.782ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'n: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 701ε (Mean = 212ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j"></a><p class="title"><b>Table 108. Error rates for cyl_bessel_j</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.52ε (Mean = 1.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data (Tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean =
|
|
1.96e+08ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.73ε (Mean = 0.976ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data (tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean =
|
|
1.58e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean
|
|
= 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 112ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 5.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 4.11ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 3.49e+05ε (Mean = 8.09e+04ε)
|
|
<a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10ε (Mean = 2.24ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.39e+05ε (Mean = 5.37e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 4.22ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.9ε (Mean = 3.89ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 34.9ε (Mean = 17.4ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 5.9ε (Mean = 3.76ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 607ε (Mean = 305ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.31ε (Mean = 5.52ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50.8ε (Mean = 3.69ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.12e+03ε (Mean = 88.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 3.93ε (Mean = 1.22ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 99.6ε (Mean = 22ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 17.5ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.4ε (Mean = 1.68ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 501ε (Mean = 52.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 6.74ε (Mean = 1.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 260ε (Mean = 34ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.24ε (Mean = 1.17ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Random Data (Tricky large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 5.01e+17ε (Mean
|
|
= 6.23e+16ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 71.6ε (Mean = 11.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 785ε (Mean = 97.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.2ε (Mean = 8.67ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 109. Error rates for cyl_bessel_j (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean =
|
|
1.96e+08ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span><br>
|
|
<br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max
|
|
= 2.54e+08ε (Mean = 1.04e+08ε))</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data (tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean =
|
|
1.58e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+07ε (Mean
|
|
= 6.5e+06ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean
|
|
= 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 112ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 110. Error rates for cyl_bessel_j_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.82ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data (Tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.34ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data (tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 287ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 288ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14ε (Mean = 6.13ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21.5ε (Mean = 4.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 9.31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 9.32ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.7ε (Mean = 8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 989ε (Mean = 495ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 989ε (Mean = 495ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.9ε (Mean = 1.61ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.3ε (Mean = 1.85ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 79.4ε (Mean = 16.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.34ε (Mean = 0.999ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.885ε (Mean = 0.033ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 139ε (Mean = 6.47ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 279ε (Mean = 27.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 176ε (Mean = 9.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Random Data (Tricky large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 474ε (Mean = 62.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 474ε (Mean = 64.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 379ε (Mean = 45.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 111. Error rates for cyl_bessel_j_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.82ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.34ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data (tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 287ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 288ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN': Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14ε (Mean = 6.13ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k"></a><p class="title"><b>Table 112. Error rates for cyl_bessel_k</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.833ε (Mean = 0.601ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.436ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.552ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.894ε (Mean = 0.516ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kn: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 8.48ε (Mean = 2.98ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.6ε (Mean = 1.21ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kv: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.58ε (Mean = 2.39ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 13ε (Mean = 4.81ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 3.15ε (Mean = 1.35ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.21ε (Mean = 2.53ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.78ε (Mean = 2.19ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kv: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 42.3ε (Mean = 19.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 84.6ε (Mean = 37.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.3ε (Mean = 21ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.8ε (Mean = 26.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kn: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.55ε (Mean = 1.12ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71ε (Mean = 1.76ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 7.47ε (Mean = 1.34ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.55ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.34ε (Mean = 1.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kv: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71ε (Mean = 1.47ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 7.37ε (Mean = 1.49ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.88ε (Mean = 1.47ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.33ε (Mean = 1.62ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 113. Error rates for cyl_bessel_k (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.833ε (Mean = 0.601ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.436ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.552ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kn: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 8.48ε (Mean = 2.98ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.6ε (Mean = 1.21ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 114. Error rates for cyl_bessel_k_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.761ε (Mean = 0.444ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'n: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.17ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'v: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.94ε (Mean = 2.44ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.94ε (Mean = 2.34ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.94ε (Mean = 1.47ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'v: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.2ε (Mean = 42.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 58.7ε (Mean = 42.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.6ε (Mean = 11.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'n: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.45ε (Mean = 1.19ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.45ε (Mean = 1.19ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.67ε (Mean = 1.73ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'v: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.95ε (Mean = 1.53ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.95ε (Mean = 1.52ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.32ε (Mean = 1.65ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 115. Error rates for cyl_bessel_k_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.761ε (Mean = 0.444ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'n: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.17ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann"></a><p class="title"><b>Table 116. Error rates for cyl_neumann</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 167ε (Mean = 56.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.61ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 193ε (Mean = 64.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.72ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yn: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean
|
|
= 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.24e+04ε (Mean = 4e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 35ε (Mean = 11.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yv: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.7ε (Mean = 4.93ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.49e+15ε (Mean
|
|
= 1.05e+15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 243ε (Mean = 73.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.7ε (Mean = 5.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.89ε (Mean = 3.27ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yv: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0.682ε (Mean = 0.335ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 1.33ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.682ε (Mean = 0.423ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y0 and Y1: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.8ε (Mean = 3.04ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.59e+03ε (Mean = 500ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 83ε (Mean = 14.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.8ε (Mean = 3.04ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.17ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yn: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 338ε (Mean = 27.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 4.01e+03ε (Mean = 348ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 691ε (Mean = 67.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 338ε (Mean = 27.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 117ε (Mean = 10.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yv: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.23e+03ε (Mean = 69.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 117. Error rates for cyl_neumann (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 167ε (Mean = 56.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+03ε (Mean = 1.81e+03ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 193ε (Mean = 64.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+04ε (Mean = 6.2e+03ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yn: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean
|
|
= 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 35ε (Mean = 11.9ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 2.49e+05ε (Mean = 8.14e+04ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime"></a><p class="title"><b>Table 118. Error rates for cyl_neumann_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 37.1ε (Mean = 12.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34ε (Mean = 11.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'n: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 18.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 21.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 563ε (Mean = 178ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'v: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21.5ε (Mean = 6.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 13.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 13.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.7ε (Mean = 10.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'v: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.627ε (Mean = 0.237ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'0 and Y'1: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.95ε (Mean = 1.36ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'n: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 621ε (Mean = 36ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'v: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56.8ε (Mean = 2.59ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.23e+04ε (Mean = 1.13e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 119. Error rates for cyl_neumann_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 37.1ε (Mean = 12.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34ε (Mean = 11.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'n: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 18.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 21.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 563ε (Mean = 178ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_digamma"></a><p class="title"><b>Table 120. Error rates for digamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for digamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.18ε (Mean = 0.331ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.98ε (Mean = 0.369ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Near the Positive Root
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135ε (Mean = 11.9ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 2.02e+03ε (Mean = 256ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.37ε (Mean = 0.477ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.471ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.997ε (Mean = 0.527ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Near Zero
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.17ε (Mean = 0.564ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.953ε (Mean = 0.337ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Negative Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 180ε (Mean = 13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 180ε (Mean = 13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 214ε (Mean = 16.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Values near 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.592ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.592ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Integer arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 4.33ε (Mean = 0.982ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.452ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Half integer arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 46.2ε (Mean = 7.24ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.78ε (Mean = 0.314ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_1"></a><p class="title"><b>Table 121. Error rates for ellint_1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral F: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.919ε (Mean = 0.544ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.94ε (Mean = 0.509ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.919ε (Mean = 0.542ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral F: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.99ε (Mean = 0.797ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.561ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.26ε (Mean = 0.631ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_1_complete_"></a><p class="title"><b>Table 122. Error rates for ellint_1 (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral K: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.623ε (Mean = 0.393ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.887ε (Mean = 0.296ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.915ε (Mean = 0.547ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral K: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32ε (Mean = 0.688ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.473ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.958ε (Mean = 0.408ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_2"></a><p class="title"><b>Table 123. Error rates for ellint_2</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_2">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.63ε (Mean = 0.325ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.656ε (Mean = 0.317ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.727ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.4ε (Mean = 1.16ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 3.08e+04ε (Mean = 3.84e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.632ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.23ε (Mean = 0.639ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Small Angles
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.5ε (Mean = 0.118ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.283ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 2ε (Mean = 0.333ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.283ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.421ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_2_complete_"></a><p class="title"><b>Table 124. Error rates for ellint_2 (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 170ε (Mean = 55.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.469ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.615ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.34ε (Mean = 1.18ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.49e+04ε (Mean = 3.39e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.629ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.71ε (Mean = 0.553ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_3"></a><p class="title"><b>Table 125. Error rates for ellint_3</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_3">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral PI: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 475ε (Mean = 86.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 565ε (Mean = 102ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral PI: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.37e+20ε (Mean
|
|
= 3.47e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 633ε (Mean = 50.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.49ε (Mean = 0.885ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.33ε (Mean = 0.971ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral PI: Large Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.52e+18ε (Mean
|
|
= 4.83e+17ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1ε (Mean = 7.77ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.7ε (Mean = 0.892ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.86ε (Mean = 0.944ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_3_complete_"></a><p class="title"><b>Table 126. Error rates for ellint_3 (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Complete Elliptic Integral PI: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 6.31e+20ε (Mean
|
|
= 1.53e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.4ε (Mean = 0.575ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.971ε (Mean = 0.464ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Complete Elliptic Integral PI: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 8.78e+20ε (Mean
|
|
= 1.02e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 24ε (Mean = 2.99ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.4ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.46ε (Mean = 0.657ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_d"></a><p class="title"><b>Table 127. Error rates for ellint_d</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_d">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.862ε (Mean = 0.568ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.862ε (Mean = 0.457ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral D: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.01ε (Mean = 0.928ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.87ε (Mean = 0.805ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_d_complete_"></a><p class="title"><b>Table 128. Error rates for ellint_d (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral D: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.355ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rc"></a><p class="title"><b>Table 129. Error rates for ellint_rc</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
RC: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.4ε (Mean = 0.624ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.433ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.962ε (Mean = 0.407ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rd"></a><p class="title"><b>Table 130. Error rates for ellint_rd</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.59ε (Mean = 0.878ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.73ε (Mean = 0.831ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 0.803ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88ε (Mean = 0.839ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.65ε (Mean = 0.82ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 16.5ε (Mean = 0.843ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = y
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74ε (Mean = 0.84ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.85ε (Mean = 0.865ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.51ε (Mean = 0.816ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = 0, y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2ε (Mean = 0.656ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.19ε (Mean = 0.522ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.16ε (Mean = 0.497ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.03ε (Mean = 0.418ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.85ε (Mean = 0.781ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.79ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.64ε (Mean = 0.894ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rf"></a><p class="title"><b>Table 131. Error rates for ellint_rf</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.73ε (Mean = 0.804ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.54ε (Mean = 0.674ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.02ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: x = y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.999ε (Mean = 0.34ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.345ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.34ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: x = y or y = z or x = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89ε (Mean = 0.749ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.21ε (Mean = 0.394ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: x = 0, y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.29ε (Mean = 0.527ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.894ε (Mean = 0.338ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.407ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: z = 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.54ε (Mean = 0.781ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.539ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.587ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rg"></a><p class="title"><b>Table 132. Error rates for ellint_rg</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983ε (Mean = 0.0172ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.95ε (Mean = 0.951ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.65ε (Mean = 0.929ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: two values 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: All values the same or zero
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.288ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.06ε (Mean = 0.348ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: two values the same
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594ε (Mean = 0.0103ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.51ε (Mean = 0.404ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.374ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: one value zero
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.14ε (Mean = 0.722ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.674ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ellint_rj"></a><p class="title"><b>Table 133. Error rates for ellint_rj</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 186ε (Mean = 6.67ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 215ε (Mean = 7.66ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: 4 Equal Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.03ε (Mean = 0.418ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: 3 Equal Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.96ε (Mean = 1.06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 20.8ε (Mean = 0.986ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 39.9ε (Mean = 1.17ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: 2 Equal Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57ε (Mean = 0.754ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 220ε (Mean = 6.64ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 214ε (Mean = 5.28ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: Equal z and p
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62ε (Mean = 0.699ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 17.2ε (Mean = 1.16ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 16.1ε (Mean = 1.14ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_erf"></a><p class="title"><b>Table 134. Error rates for erf</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erf">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06ε (Mean = 0.319ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.31ε (Mean = 0.368ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.197ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.171ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 1.19ε (Mean = 0.244ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max
|
|
= 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_erf_inv"></a><p class="title"><b>Table 135. Error rates for erf_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erf_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse Erf Function
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.08ε (Mean = 0.395ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.09ε (Mean = 0.502ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_erfc"></a><p class="title"><b>Table 136. Error rates for erfc</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erfc">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max
|
|
= 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01ε (Mean = 0.485ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64ε (Mean = 0.662ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.76ε (Mean = 0.38ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9ε (Mean = 0.472ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_erfc_inv"></a><p class="title"><b>Table 137. Error rates for erfc_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Inverse Erfc Function
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.397ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.08ε (Mean = 0.403ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.491ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Inverse Erfc Function: extreme values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_expint_Ei_"></a><p class="title"><b>Table 138. Error rates for expint (Ei)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral Ei
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96ε (Mean = 0.703ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.05ε (Mean = 0.835ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.43ε (Mean = 0.54ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral Ei: double exponent range
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.612ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.72ε (Mean = 0.607ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.66ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral Ei: long exponent range
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.98ε (Mean = 0.575ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_expint_En_"></a><p class="title"><b>Table 139. Error rates for expint (En)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for expint (En)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral En
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5ε (Mean = 17.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.16ε (Mean = 1.85ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral En: small z values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 115ε (Mean = 23.6ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.62ε (Mean = 0.531ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral E1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988ε (Mean = 0.469ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.965ε (Mean = 0.414ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.965ε (Mean = 0.408ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.988ε (Mean = 0.486ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_expm1"></a><p class="title"><b>Table 140. Error rates for expm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for expm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Random test data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.992ε (Mean = 0.402ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.992ε (Mean = 0.402ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793ε (Mean = 0.126ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.428ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.496ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε))
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_gamma_p"></a><p class="title"><b>Table 141. Error rates for gamma_p</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_p">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 389ε (Mean = 44ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 41.6ε (Mean = 8.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 239ε (Mean = 30.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 35.1ε (Mean = 6.98ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.01ε (Mean = 0.306ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.464ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.461ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.54ε (Mean = 0.439ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.11e+03ε (Mean = 67.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 243ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 66.2ε (Mean = 12.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.8ε (Mean = 2.66ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 71.6ε (Mean = 9.47ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 13ε (Mean = 2.97ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inv"></a><p class="title"><b>Table 142. Error rates for gamma_p_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88ε (Mean = 0.868ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 0.406ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.466ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.71ε (Mean = 0.34ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 0.816ε (Mean = 0.0874ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.924ε (Mean = 0.108ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547ε (Mean = 61.6ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.17e+03ε (Mean = 1.45e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.09e+04ε (Mean = 1.3e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.1e+03ε (Mean = 131ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inva"></a><p class="title"><b>Table 143. Error rates for gamma_p_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Incomplete gamma inverses.
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.87ε (Mean = 1.15ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.08ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.92ε (Mean = 1.03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_gamma_q"></a><p class="title"><b>Table 144. Error rates for gamma_q</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_q">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 131ε (Mean = 12.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 32.3ε (Mean = 6.61ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 199ε (Mean = 26.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.7ε (Mean = 4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6ε (Mean = 11ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45ε (Mean = 0.885ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45ε (Mean = 0.819ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.26ε (Mean = 0.74ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.02e+03ε (Mean = 62.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 469ε (Mean = 31.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 138ε (Mean = 16.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.1ε (Mean = 2.07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 54.7ε (Mean = 6.16ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.72ε (Mean = 1.48ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inv"></a><p class="title"><b>Table 145. Error rates for gamma_q_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66ε (Mean = 0.792ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.2ε (Mean = 0.627ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.2ε (Mean = 0.683ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.88ε (Mean = 0.469ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894ε (Mean = 0.106ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415ε (Mean = 48.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.28e+03ε (Mean = 1.09e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 451ε (Mean = 64.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inva"></a><p class="title"><b>Table 146. Error rates for gamma_q_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Incomplete gamma inverses.
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.42ε (Mean = 1.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.86ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.05ε (Mean = 1.08ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_hermite"></a><p class="title"><b>Table 147. Error rates for hermite</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for hermite">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Hermite Polynomials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.46ε (Mean = 1.41ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_heuman_lambda"></a><p class="title"><b>Table 148. Error rates for heuman_lambda</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.08ε (Mean = 0.734ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Heuman Lambda: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.82ε (Mean = 0.609ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.82ε (Mean = 0.608ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.12ε (Mean = 0.588ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ibeta"></a><p class="title"><b>Table 149. Error rates for ibeta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 22.9ε (Mean = 3.35ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.97ε (Mean = 2.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21.3ε (Mean = 2.75ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.4ε (Mean = 1.93ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 232ε (Mean = 27.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50ε (Mean = 12.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 124ε (Mean = 18.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 106ε (Mean = 16.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 574ε (Mean = 49.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.32e+03ε (Mean = 68.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 62.2ε (Mean = 8.95ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.45ε (Mean = 0.814ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 44.5ε (Mean = 10.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.85ε (Mean = 0.791ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inv"></a><p class="title"><b>Table 150. Error rates for ibeta_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11ε (Mean = 0.345ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121ε (Mean
|
|
= 3.28e+119ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.8e+04ε (Mean = 2.66e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.07e+04ε (Mean = 2.86e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.59e+03ε (Mean = 277ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inva"></a><p class="title"><b>Table 151. Error rates for ibeta_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 377ε (Mean = 24.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 438ε (Mean = 31.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 242ε (Mean = 22.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ibeta_invb"></a><p class="title"><b>Table 152. Error rates for ibeta_invb</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.765ε (Mean = 0.0422ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 407ε (Mean = 27.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 407ε (Mean = 24.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 409ε (Mean = 19.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ibetac"></a><p class="title"><b>Table 153. Error rates for ibetac</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 22.4ε (Mean = 3.67ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.6ε (Mean = 2.22ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 13.8ε (Mean = 2.68ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.94ε (Mean = 1.71ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 204ε (Mean = 25.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 73.9ε (Mean = 11.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 132ε (Mean = 19.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56.7ε (Mean = 14.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.981ε (Mean = 0.0573ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889ε (Mean = 68.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.31e+04ε (Mean = 2.04e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.88e+03ε (Mean = 82.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 84.6ε (Mean = 18ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.34ε (Mean = 1.11ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 107ε (Mean = 17.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.37ε (Mean = 1.03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inv"></a><p class="title"><b>Table 154. Error rates for ibetac_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.977ε (Mean = 0.0976ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132ε (Mean
|
|
= 8.65e+130ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.88e+04ε (Mean = 3.16e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.05e+04ε (Mean = 3.33e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.93e+03ε (Mean = 198ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inva"></a><p class="title"><b>Table 155. Error rates for ibetac_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.683ε (Mean = 0.0314ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 382ε (Mean = 22.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 315ε (Mean = 23.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 408ε (Mean = 26.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_ibetac_invb"></a><p class="title"><b>Table 156. Error rates for ibetac_invb</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 317ε (Mean = 19.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 369ε (Mean = 22.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 271ε (Mean = 16.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_cn"></a><p class="title"><b>Table 157. Error rates for jacobi_cn</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 71.6ε (Mean = 19.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 71.6ε (Mean = 19.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 45.8ε (Mean = 11.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43ε (Mean = 0.803ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.68ε (Mean = 0.443ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.68ε (Mean = 0.454ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.83ε (Mean = 0.455ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.4ε (Mean = 0.594ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.4ε (Mean = 0.602ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26.2ε (Mean = 1.17ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Modulus near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 675ε (Mean = 87.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 675ε (Mean = 86.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 513ε (Mean = 126ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Large Phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03ε (Mean = 477ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.27e+04ε (Mean = 1.93e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_dn"></a><p class="title"><b>Table 158. Error rates for jacobi_dn</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 49ε (Mean = 14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 49ε (Mean = 14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34.3ε (Mean = 8.71ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3ε (Mean = 0.61ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.473ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.481ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.52ε (Mean = 0.466ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 22.4ε (Mean = 0.777ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 22.4ε (Mean = 0.763ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 16.1ε (Mean = 0.685ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Modulus near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.24e+03ε (Mean = 482ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Large Phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 22ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.67e+04ε (Mean = 1e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_sn"></a><p class="title"><b>Table 159. Error rates for jacobi_sn</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 341ε (Mean = 80.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 341ε (Mean = 80.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 481ε (Mean = 113ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.02ε (Mean = 1.07ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.01ε (Mean = 0.584ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.01ε (Mean = 0.593ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.92ε (Mean = 0.567ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.11ε (Mean = 0.385ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Modulus near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 109ε (Mean = 7.35ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 109ε (Mean = 7.38ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.2ε (Mean = 1.85ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Large Phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.36e+04ε (Mean = 2.54e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_jacobi_zeta"></a><p class="title"><b>Table 160. Error rates for jacobi_zeta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.52ε (Mean = 0.357ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.99ε (Mean = 0.824ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.96ε (Mean = 1.06ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.89ε (Mean = 0.824ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Large Phi Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.92ε (Mean = 0.951ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.05ε (Mean = 1.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.52ε (Mean = 0.977ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_m_x_"></a><p class="title"><b>Table 161. Error rates for laguerre(n, m, x)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Associated Laguerre Polynomials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434ε (Mean = 10.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 206ε (Mean = 6.86ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 6.38ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 434ε (Mean = 11.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_x_"></a><p class="title"><b>Table 162. Error rates for laguerre(n, x)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Laguerre Polynomials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03ε (Mean = 185ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 4.2e+03ε (Mean = 251ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.1e+03ε (Mean = 185ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_legendre_p"></a><p class="title"><b>Table 163. Error rates for legendre_p</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for legendre_p">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211ε (Mean = 20.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 124ε (Mean = 13.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 69.2ε (Mean = 9.58ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 211ε (Mean = 20.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300ε (Mean = 33.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 343ε (Mean = 32.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 699ε (Mean = 59.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 300ε (Mean = 33.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_legendre_p_associated_"></a><p class="title"><b>Table 164. Error rates for legendre_p (associated)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Associated Legendre Polynomials: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 175ε (Mean = 9.36ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 77.7ε (Mean = 5.59ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 121ε (Mean = 7.14ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_legendre_q"></a><p class="title"><b>Table 165. Error rates for legendre_q</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for legendre_q">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4ε (Mean = 7.46ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50.9ε (Mean = 9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50.9ε (Mean = 8.98ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 46.4ε (Mean = 7.32ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03ε (Mean = 366ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.6e+03ε (Mean = 366ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_lgamma"></a><p class="title"><b>Table 166. Error rates for lgamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for lgamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
factorials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1.55ε (Mean = 0.592ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.308ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.914ε (Mean = 0.175ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 7.99e+04ε (Mean = 1.68e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 2
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -10
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 4.22ε (Mean = 1.26ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.997ε (Mean = 0.412ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.412ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -55
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 250ε (Mean = 60.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_log1p"></a><p class="title"><b>Table 167. Error rates for log1p</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for log1p">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Random test data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846ε (Mean = 0.153ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.3ε (Mean = 0.66ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε))
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF"></a><p class="title"><b>Table 168. Error rates for non central beta CDF</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.0649ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26ε (Mean
|
|
= 3.5e+24ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 824ε (Mean = 27.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 832ε (Mean = 38.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 242ε (Mean = 31ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36ε (Mean
|
|
= 1.19e+35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.57e+04ε (Mean = 4.45e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.66e+03ε (Mean = 500ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 169. Error rates for non central beta CDF complement</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.0936ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97ε (Mean
|
|
= 1.37e+96ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 396ε (Mean = 50.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 554ε (Mean = 57.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 624ε (Mean = 62.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.56e+03ε (Mean = 707ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.25e+04ε (Mean = 1.49e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 170. Error rates for non central chi squared CDF</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.99ε (Mean = 0.0544ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727ε (Mean = 121ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 46.5ε (Mean = 10.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 115ε (Mean = 13.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 48.9ε (Mean = 10ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08ε (Mean
|
|
= 2.23e+07ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.79e+03ε (Mean = 723ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 171. Error rates for non central chi squared CDF complement</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 107ε (Mean = 17.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 171ε (Mean = 22.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 98.6ε (Mean = 15.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.43e+03ε (Mean = 705ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF"></a><p class="title"><b>Table 172. Error rates for non central t CDF</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15ε (Mean
|
|
= 8.49e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 139ε (Mean = 31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 145ε (Mean = 30.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 135ε (Mean = 32.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (small non-centrality)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 2.09e+03ε (Mean = 244ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.86ε (Mean = 1.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.15ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.17ε (Mean = 1.45ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (large parameters)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46ε (Mean = 0.657ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 286ε (Mean = 62.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 173. Error rates for non central t CDF complement</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15ε (Mean
|
|
= 6.72e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 201ε (Mean = 31.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 340ε (Mean = 43.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 154ε (Mean = 32.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (small non-centrality)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 1.87e+03ε (Mean = 263ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.5ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.5ε (Mean = 2.39ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.6ε (Mean = 1.63ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (large parameters)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24ε (Mean = 0.945ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 227ε (Mean = 50.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_owens_t"></a><p class="title"><b>Table 174. Error rates for owens_t</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for owens_t">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Owens T (medium small values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.34ε (Mean = 0.944ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.34ε (Mean = 0.911ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.37ε (Mean = 0.98ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Owens T (large and diverse values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 49ε (Mean = 2.16ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 24.5ε (Mean = 1.39ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.78ε (Mean = 0.621ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_polygamma"></a><p class="title"><b>Table 175. Error rates for polygamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for polygamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9ε (Mean = 12.8ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 108ε (Mean = 15.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.38ε (Mean = 1.84ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34.3ε (Mean = 7.65ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.32ε (Mean = 1.95ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - large arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244ε (Mean = 32.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.23ε (Mean = 0.323ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.1ε (Mean = 0.848ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 150ε (Mean = 13.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - negative arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6ε (Mean = 3.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 269ε (Mean = 87.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 269ε (Mean = 88.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 497ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - large negative arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.79ε (Mean = 0.197ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 155ε (Mean = 96.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 155ε (Mean = 96.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 162ε (Mean = 101ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - small arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 15.2ε (Mean = 5.03ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 106ε (Mean = 20ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3ε (Mean = 0.496ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - Large orders and other bug cases
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 151ε (Mean = 39.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 54.5ε (Mean = 13.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 145ε (Mean = 55.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 200ε (Mean = 57.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_powm1"></a><p class="title"><b>Table 176. Error rates for powm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for powm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
powm1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.04ε (Mean = 0.493ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.88ε (Mean = 0.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_sin_pi"></a><p class="title"><b>Table 177. Error rates for sin_pi</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sin_pi">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.335ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.336ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.99ε (Mean = 0.328ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi near integers and half integers
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.343ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel"></a><p class="title"><b>Table 178. Error rates for sph_bessel</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Bessel j: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.91e+06ε (Mean = 1.09e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.978ε (Mean = 0.0445ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03ε (Mean = 107ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 243ε (Mean = 33.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 245ε (Mean = 16.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel_prime"></a><p class="title"><b>Table 179. Error rates for sph_bessel_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Bessel j': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 33.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 307ε (Mean = 25.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann"></a><p class="title"><b>Table 180. Error rates for sph_neumann</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
y: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 234ε (Mean = 19.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 281ε (Mean = 31.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann_prime"></a><p class="title"><b>Table 181. Error rates for sph_neumann_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
y': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.988ε (Mean = 0.0869ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 158ε (Mean = 18.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 158ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 296ε (Mean = 25.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_i"></a><p class="title"><b>Table 182. Error rates for spherical_harmonic_i</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Spherical Harmonics
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_r"></a><p class="title"><b>Table 183. Error rates for spherical_harmonic_r</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Spherical Harmonics
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_sqrt1pm1"></a><p class="title"><b>Table 184. Error rates for sqrt1pm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
sqrt1pm1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.404ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.33ε (Mean = 0.404ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.54ε (Mean = 0.563ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.35ε (Mean = 0.497ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_tgamma"></a><p class="title"><b>Table 185. Error rates for tgamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
factorials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.2.3:</em></span> Max = 314ε (Mean = 93.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.67ε (Mean = 0.617ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.85ε (Mean = 0.566ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1ε (Mean = 0.335ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.608ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 1ε (Mean = 0.376ε))<br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 1ε (Mean = 0.376ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0.5ε (Mean = 0.0791ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.635ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1ε (Mean = 0.32ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.51ε (Mean = 1.02ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.1ε (Mean = 0.59ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 2
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 1ε (Mean = 0.191ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.1ε (Mean = 1.55ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.733ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -10
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 34.9ε (Mean = 9.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.75ε (Mean = 0.895ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.86ε (Mean = 0.881ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -55
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
|
|
Max = 3.89e+04ε (Mean = 9.52e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.69ε (Mean = 1.09ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.7ε (Mean = 1.35ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+04ε (Mean = 6.71e+03ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_tgamma1pm1"></a><p class="title"><b>Table 186. Error rates for tgamma1pm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
tgamma1pm1(dz)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.12ε (Mean = 0.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.61ε (Mean = 0.84ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.31ε (Mean = 0.517ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_delta_ratio"></a><p class="title"><b>Table 187. Error rates for tgamma_delta_ratio</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small delta ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.83ε (Mean = 1.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 15.4ε (Mean = 2.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.56ε (Mean = 1.31ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small delta ratios (negative delta)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.94ε (Mean = 1.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.3ε (Mean = 2.03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.43ε (Mean = 1.42ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small integer ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.74ε (Mean = 0.736ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small integer ratios (negative delta)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.15ε (Mean = 0.685ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
integer tgamma ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.968ε (Mean = 0.386ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
integer tgamma ratios (negative delta)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.974ε (Mean = 0.175ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_incomplete_"></a><p class="title"><b>Table 188. Error rates for tgamma (incomplete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 200ε (Mean = 13.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.47ε (Mean = 1.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 412ε (Mean = 95.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.14ε (Mean = 1.76ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean
|
|
= 1.05e+09ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.31ε (Mean = 0.775ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.13ε (Mean = 0.717ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.53ε (Mean = 0.66ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 117ε (Mean = 12.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.52ε (Mean = 1.48ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 79.6ε (Mean = 20.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.16ε (Mean = 1.33ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_lower"></a><p class="title"><b>Table 189. Error rates for tgamma_lower</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833ε (Mean = 0.0315ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.79ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 363ε (Mean = 63.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.62ε (Mean = 1.49ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.555ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.558ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.525ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.83ε (Mean = 1.15ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 84.7ε (Mean = 17.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.69ε (Mean = 0.849ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_tgamma_ratio"></a><p class="title"><b>Table 190. Error rates for tgamma_ratio</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
tgamma ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.694ε (Mean = 0.0347ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.99ε (Mean = 1.15ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 174ε (Mean = 61.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.28ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_trigamma"></a><p class="title"><b>Table 191. Error rates for trigamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for trigamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.382ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="special_function_error_rates_rep.all_the_tables.table_zeta"></a><p class="title"><b>Table 192. Error rates for zeta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for zeta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Random values greater than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 5.45ε (Mean = 1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 8.69ε (Mean = 1.03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.093ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Random values less than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.03ε (Mean = 2.93ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 538ε (Mean = 59.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 137ε (Mean = 13.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 70.1ε (Mean = 17.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.84ε (Mean = 3.12ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Values close to and greater than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 7.73ε (Mean = 4.07ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.994ε (Mean = 0.421ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Values close to and less than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br>
|
|
(<span class="emphasis"><em><cmath>:</em></span> Max = 8.53e+06ε (Mean = 1.87e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 0.991ε (Mean = 0.28ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.508ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.375ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Integer arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
|
|
Max = 70.3ε (Mean = 17.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
2.1:</em></span> Max = 3.75ε (Mean = 1.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 28ε (Mean = 5.62ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9ε (Mean = 3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
</div>
|
|
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
|
<td align="left"><p><small>Last revised: March 09, 2018 at 13:43:44 GMT</small></p></td>
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<td align="right"><div class="copyright-footer"></div></td>
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