344 lines
14 KiB
C++
344 lines
14 KiB
C++
// Copyright Matthew Pulver 2018 - 2019.
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// Distributed under the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt or copy at
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// https://www.boost.org/LICENSE_1_0.txt)
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#include "test_autodiff.hpp"
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#include <boost/utility/identity_type.hpp>
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BOOST_AUTO_TEST_SUITE(test_autodiff_3)
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BOOST_AUTO_TEST_CASE_TEMPLATE(atanh_test, T, all_float_types) {
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const T eps = 3000 * test_constants_t<T>::pct_epsilon(); // percent
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constexpr unsigned m = 5;
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const T cx = 0.5;
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auto x = make_fvar<T, m>(cx);
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auto y = atanh(x);
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// BOOST_CHECK_EQUAL(y.derivative(0) , atanh(cx)); // fails due to overload
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BOOST_CHECK_CLOSE(y.derivative(0u), atanh(static_cast<T>(x)), eps);
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BOOST_CHECK_CLOSE(y.derivative(1u), static_cast<T>(4) / 3, eps);
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BOOST_CHECK_CLOSE(y.derivative(2u), static_cast<T>(16) / 9, eps);
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BOOST_CHECK_CLOSE(y.derivative(3u), static_cast<T>(224) / 27, eps);
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BOOST_CHECK_CLOSE(y.derivative(4u), static_cast<T>(1280) / 27, eps);
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BOOST_CHECK_CLOSE(y.derivative(5u), static_cast<T>(31232) / 81, eps);
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(atan_test, T, all_float_types) {
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BOOST_MATH_STD_USING
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using namespace boost;
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const T cx = 1.0;
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constexpr unsigned m = 5;
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const auto x = make_fvar<T, m>(cx);
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auto y = atan(x);
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const auto eps = boost::math::tools::epsilon<T>();
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BOOST_CHECK_CLOSE(y.derivative(0u), boost::math::constants::pi<T>() / 4, eps);
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BOOST_CHECK_CLOSE(y.derivative(1u), T(0.5), eps);
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BOOST_CHECK_CLOSE(y.derivative(2u), T(-0.5), eps);
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BOOST_CHECK_CLOSE(y.derivative(3u), T(0.5), eps);
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BOOST_CHECK_CLOSE(y.derivative(4u), T(0), eps);
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BOOST_CHECK_CLOSE(y.derivative(5u), T(-3), eps);
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(erf_test, T, all_float_types) {
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BOOST_MATH_STD_USING
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using namespace boost;
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const T eps = 300 * 100 * boost::math::tools::epsilon<T>(); // percent
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const T cx = 1.0;
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constexpr unsigned m = 5;
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const auto x = make_fvar<T, m>(cx);
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auto y = erf(x);
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BOOST_CHECK_CLOSE(y.derivative(0u), erf(static_cast<T>(x)), eps);
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BOOST_CHECK_CLOSE(
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y.derivative(1u),
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T(2) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
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BOOST_CHECK_CLOSE(
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y.derivative(2u),
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T(-4) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
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BOOST_CHECK_CLOSE(
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y.derivative(3u),
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T(4) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
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BOOST_CHECK_CLOSE(
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y.derivative(4u),
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T(8) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
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BOOST_CHECK_CLOSE(
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y.derivative(5u),
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T(-40) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(sinc_test, T, bin_float_types) {
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BOOST_MATH_STD_USING
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const T eps = 20000 * boost::math::tools::epsilon<T>(); // percent
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const T cx = 1;
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constexpr unsigned m = 5;
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auto x = make_fvar<T, m>(cx);
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auto y = sinc(x);
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BOOST_CHECK_CLOSE(y.derivative(0u), sin(cx), eps);
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BOOST_CHECK_CLOSE(y.derivative(1u), cos(cx) - sin(cx), eps);
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BOOST_CHECK_CLOSE(y.derivative(2u), sin(cx) - 2 * cos(cx), eps);
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BOOST_CHECK_CLOSE(y.derivative(3u), T(5) * cos(cx) - T(3) * sin(cx), eps);
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BOOST_CHECK_CLOSE(y.derivative(4u), T(13) * sin(cx) - T(20) * cos(cx), eps);
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BOOST_CHECK_CLOSE(y.derivative(5u), T(101) * cos(cx) - T(65) * sin(cx), eps);
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// Test at x = 0
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auto y2 = sinc(make_fvar<T, 10>(0));
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BOOST_CHECK_CLOSE(y2.derivative(0u), T(1), eps);
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BOOST_CHECK_CLOSE(y2.derivative(1u), T(0), eps);
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BOOST_CHECK_CLOSE(y2.derivative(2u), -cx / T(3), eps);
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BOOST_CHECK_CLOSE(y2.derivative(3u), T(0), eps);
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BOOST_CHECK_CLOSE(y2.derivative(4u), cx / T(5), eps);
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BOOST_CHECK_CLOSE(y2.derivative(5u), T(0), eps);
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BOOST_CHECK_CLOSE(y2.derivative(6u), -cx / T(7), eps);
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BOOST_CHECK_CLOSE(y2.derivative(7u), T(0), eps);
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BOOST_CHECK_CLOSE(y2.derivative(8u), cx / T(9), eps);
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BOOST_CHECK_CLOSE(y2.derivative(9u), T(0), eps);
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BOOST_CHECK_CLOSE(y2.derivative(10u), -cx / T(11), eps);
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(sinh_and_cosh, T, bin_float_types) {
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BOOST_MATH_STD_USING
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const T eps = 300 * boost::math::tools::epsilon<T>(); // percent
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const T cx = 1;
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constexpr unsigned m = 5;
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auto x = make_fvar<T, m>(cx);
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auto s = sinh(x);
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auto c = cosh(x);
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BOOST_CHECK_CLOSE(s.derivative(0u), sinh(static_cast<T>(x)), eps);
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BOOST_CHECK_CLOSE(c.derivative(0u), cosh(static_cast<T>(x)), eps);
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for (auto i : boost::irange(m + 1)) {
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BOOST_CHECK_CLOSE(s.derivative(i), static_cast<T>(i % 2 == 1 ? c : s), eps);
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BOOST_CHECK_CLOSE(c.derivative(i), static_cast<T>(i % 2 == 1 ? s : c), eps);
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}
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}
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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BOOST_AUTO_TEST_CASE_TEMPLATE(tanh_test, T, all_float_types) {
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using bmp::fabs;
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using bmp::tanh;
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using detail::fabs;
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using detail::tanh;
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using std::fabs;
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using std::tanh;
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constexpr std::array<const char *, 6> tanh_derivatives{
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{"0."
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"76159415595576488811945828260479359041276859725793655159681050012195324"
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"457663848345894752167367671442190275970155",
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"0."
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"41997434161402606939449673904170144491718672823077095471331144024458989"
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"95240483056156940088623187260",
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"-0."
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"63970000844922450018849176930384395321921136306079914494299856318702069"
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"34885434644440069533372017992",
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"0."
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"62162668077129626310653042872222339967572411755445418563968706335816206"
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"22188951465548376863495698762",
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"0."
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"66509104475050167773507148092106234992757132833203125448814929383096463"
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"47626843278089998045994094537",
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"-5."
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"55689355847371979760458290231697200987383372116293456019531342394708989"
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"7942786231796317250984197038"}};
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const T cx = 1;
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constexpr std::size_t m = 5;
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auto x = make_fvar<T, m>(cx);
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auto t = tanh(x);
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for (auto i : boost::irange(tanh_derivatives.size())) {
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BOOST_TEST_WARN(isNearZero(t.derivative(i) -
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boost::lexical_cast<T>(tanh_derivatives[i])));
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}
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}
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#endif
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BOOST_AUTO_TEST_CASE_TEMPLATE(tan_test, T, bin_float_types) {
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BOOST_MATH_STD_USING
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const T eps = 800 * boost::math::tools::epsilon<T>(); // percent
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const T cx = boost::math::constants::third_pi<T>();
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const T root_three = boost::math::constants::root_three<T>();
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constexpr unsigned m = 5;
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const auto x = make_fvar<T, m>(cx);
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auto y = tan(x);
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BOOST_CHECK_CLOSE(y.derivative(0u), root_three, eps);
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BOOST_CHECK_CLOSE(y.derivative(1u), T(4), eps);
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BOOST_CHECK_CLOSE(y.derivative(2u), T(8) * root_three, eps);
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BOOST_CHECK_CLOSE(y.derivative(3u), T(80), eps);
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BOOST_CHECK_CLOSE(y.derivative(4u), T(352) * root_three, eps);
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BOOST_CHECK_CLOSE(y.derivative(5u), T(5824), eps);
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(fmod_test, T, bin_float_types) {
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BOOST_MATH_STD_USING
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constexpr unsigned m = 3;
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const T cx = 3.25;
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const T cy = 0.5;
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auto x = make_fvar<T, m>(cx);
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auto y = fmod(x, autodiff_fvar<T, m>(cy));
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BOOST_CHECK_EQUAL(y.derivative(0u), T(0.25));
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BOOST_CHECK_EQUAL(y.derivative(1u), T(1));
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BOOST_CHECK_EQUAL(y.derivative(2u), T(0));
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BOOST_CHECK_EQUAL(y.derivative(3u), T(0));
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(round_and_trunc, T, all_float_types) {
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BOOST_MATH_STD_USING
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constexpr unsigned m = 3;
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const T cx = 3.25;
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auto x = make_fvar<T, m>(cx);
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auto y = round(x);
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BOOST_CHECK_EQUAL(y.derivative(0u), round(cx));
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BOOST_CHECK_EQUAL(y.derivative(1u), T(0));
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BOOST_CHECK_EQUAL(y.derivative(2u), T(0));
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BOOST_CHECK_EQUAL(y.derivative(3u), T(0));
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y = trunc(x);
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BOOST_CHECK_EQUAL(y.derivative(0u), trunc(cx));
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BOOST_CHECK_EQUAL(y.derivative(1u), T(0));
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BOOST_CHECK_EQUAL(y.derivative(2u), T(0));
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BOOST_CHECK_EQUAL(y.derivative(3u), T(0));
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(iround_and_itrunc, T, all_float_types) {
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BOOST_MATH_STD_USING
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using namespace boost::math;
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constexpr unsigned m = 3;
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const T cx = 3.25;
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auto x = make_fvar<T, m>(cx);
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int y = iround(x);
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BOOST_CHECK_EQUAL(y, iround(cx));
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y = itrunc(x);
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BOOST_CHECK_EQUAL(y, itrunc(cx));
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(lambert_w0_test, T, all_float_types) {
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const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
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constexpr unsigned m = 10;
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const T cx = 3;
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// Mathematica: N[Table[D[ProductLog[x], {x, n}], {n, 0, 10}] /. x -> 3, 52]
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constexpr std::array<const char *, m + 1> answers{
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{"1.049908894964039959988697070552897904589466943706341",
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"0.1707244807388472968312949774415522047470762509741737",
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"-0.04336545501146252734105411312976167858858970875797718",
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"0.02321456264324789334313200360870492961288748451791104",
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"-0.01909049778427783072663170526188353869136655225133878",
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"0.02122935002563637629500975949987796094687564718834156",
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"-0.02979093848448877259041971538394953658978044986784643",
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"0.05051290266216717699803334605370337985567016837482099",
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"-0.1004503154972645060971099914384090562800544486549660",
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"0.2292464437392250211967939182075930820454464472006425",
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"-0.5905839053125614593682763387470654123192290838719517"}};
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auto x = make_fvar<T, m>(cx);
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auto y = lambert_w0(x);
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for (auto i : boost::irange(m + 1)) {
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const T answer = boost::lexical_cast<T>(answers[i]);
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BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
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}
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// const T cx0 = -1 / boost::math::constants::e<T>();
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// auto edge = lambert_w0(make_fvar<T,m>(cx0));
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// std::cout << "edge = " << edge << std::endl;
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// edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
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// edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
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// edge =
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// depth(1)(-1,3.68935e+19,-9.23687e+57,4.62519e+96,-2.89497e+135,2.02945e+174,-1.52431e+213,1.19943e+252,-9.75959e+290,8.14489e+329,-6.93329e+368)
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(digamma_test, T, all_float_types) {
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const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
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constexpr unsigned m = 10;
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const T cx = 3;
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// Mathematica: N[Table[PolyGamma[n, 3], {n, 0, 10}], 52]
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constexpr std::array<const char *, m + 1> answers{
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{"0.9227843350984671393934879099175975689578406640600764"
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,"0.3949340668482264364724151666460251892189499012067984"
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,"-0.1541138063191885707994763230228999815299725846809978"
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,"0.1189394022668291490960221792470074166485057115123614"
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,"-0.1362661234408782319527716749688200333699420680459075"
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,"0.2061674381338967657421515749104633482180988039424274"
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,"-0.3864797149844353246542358918536669119017636069718686"
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,"0.8623752376394704685736020836084249051623848752441025"
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,"-2.228398747634885327823655450854278779627928241914664"
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,"6.536422382626807143525565747764891144367614117601463"
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,"-21.4366066287129906188428320541054572790340793874298"}};
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auto x = make_fvar<T, m>(cx);
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auto y = digamma(x);
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for (auto i : boost::irange(m + 1)) {
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const T answer = boost::lexical_cast<T>(answers[i]);
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BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
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}
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(lgamma_test, T, all_float_types) {
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const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
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constexpr unsigned m = 10;
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const T cx = 3;
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// Mathematica: N[Table[D[LogGamma[x],{x,n}] /. x->3, {n, 0, 10}], 52]
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constexpr std::array<const char *, m + 1> answers{
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{"0.6931471805599453094172321214581765680755001343602553"
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,"0.9227843350984671393934879099175975689578406640600764"
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,"0.3949340668482264364724151666460251892189499012067984"
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,"-0.1541138063191885707994763230228999815299725846809978"
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,"0.1189394022668291490960221792470074166485057115123614"
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,"-0.1362661234408782319527716749688200333699420680459075"
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,"0.2061674381338967657421515749104633482180988039424274"
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,"-0.3864797149844353246542358918536669119017636069718686"
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,"0.8623752376394704685736020836084249051623848752441025"
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,"-2.228398747634885327823655450854278779627928241914664"
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,"6.536422382626807143525565747764891144367614117601463"}};
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auto x = make_fvar<T, m>(cx);
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auto y = lgamma(x);
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for (auto i : boost::irange(m + 1)) {
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const T answer = boost::lexical_cast<T>(answers[i]);
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BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
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}
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(tgamma_test, T, all_float_types) {
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const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
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constexpr unsigned m = 10;
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const T cx = 3;
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// Mathematica: N[Table[D[Gamma[x],{x,n}] /. x->3, {n, 0, 10}], 52]
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constexpr std::array<const char *, m + 1> answers{
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{"2.0"
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,"1.845568670196934278786975819835195137915681328120153"
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,"2.492929991902693057942510065508124245503778067273315"
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,"3.449965013523673365279327178241708777509009968597547"
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,"5.521798578098737512443417699412265532987916790978887"
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,"8.845805593922864253981346455183370214190789096412155"
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,"15.86959874461221647760760269963155031595848150772695"
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,"27.46172054213435946038727460195592342721862288816812"
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,"54.64250508485402729556251663145824730270508661240771"
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,"96.08542140594972502872131946513104238293824803599579"
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,"222.0936743583156040996433943128676567542497584689499"}};
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auto x = make_fvar<T, m>(cx);
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auto y = tgamma(x);
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for (auto i : boost::irange(m + 1)) {
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const T answer = boost::lexical_cast<T>(answers[i]);
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BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
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}
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(tgamma2_test, T, all_float_types) {
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//const T eps = 5000 * boost::math::tools::epsilon<T>(); // ok for non-multiprecision
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const T eps = 500000 * boost::math::tools::epsilon<T>(); // percent
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constexpr unsigned m = 10;
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const T cx = -1.5;
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// Mathematica: N[Table[D[Gamma[x],{x,n}] /. x->-3/2, {n, 0, 10}], 52]
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constexpr std::array<const char *, m + 1> answers{
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{"2.363271801207354703064223311121526910396732608163183"
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,"1.661750260668596505586468565464938761014714509096807"
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,"23.33417984355457252918927856618603412638766668207679"
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,"47.02130025080143055642555842335081335790754507072526"
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,"1148.336052788822231948472800239024335856568111484074"
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,"3831.214710988836934569706027888431190714054814541186"
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,"138190.9008816865362698874238213771413807566436072179"
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,"644956.0066517306036921195893233874126907491308967028"
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,"3.096453684470713902448094810299787572782887316764214e7"
|
|
,"1.857893143852025058151037296906468662709947415219451e8"
|
|
,"1.114762466163487983067783853825224537320312784955935e10"}};
|
|
auto x = make_fvar<T, m>(cx);
|
|
auto y = tgamma(x);
|
|
for (auto i : boost::irange(m + 1)) {
|
|
const T answer = boost::lexical_cast<T>(answers[i]);
|
|
BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
|
|
}
|
|
}
|
|
|
|
BOOST_AUTO_TEST_SUITE_END()
|