219 lines
6.1 KiB
C++
219 lines
6.1 KiB
C++
// (C) Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <boost/math/special_functions/gamma.hpp>
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#include <boost/math/special_functions/erf.hpp> // for inverses
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#include <boost/math/constants/constants.hpp>
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#include <fstream>
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#include <boost/math/tools/test_data.hpp>
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#include "mp_t.hpp"
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using namespace boost::math::tools;
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using namespace std;
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float external_f;
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float force_truncate(const float* f)
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{
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external_f = *f;
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return external_f;
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}
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float truncate_to_float(mp_t r)
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{
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float f = boost::math::tools::real_cast<float>(r);
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return force_truncate(&f);
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}
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struct erf_data_generator
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{
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boost::math::tuple<mp_t, mp_t> operator()(mp_t z)
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{
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// very naively calculate spots using the gamma function at high precision:
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int sign = 1;
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if(z < 0)
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{
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sign = -1;
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z = -z;
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}
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mp_t g1, g2;
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g1 = boost::math::tgamma_lower(mp_t(0.5), z * z);
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g1 /= sqrt(boost::math::constants::pi<mp_t>());
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g1 *= sign;
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if(z < 0.5)
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{
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g2 = 1 - (sign * g1);
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}
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else
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{
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g2 = boost::math::tgamma(mp_t(0.5), z * z);
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g2 /= sqrt(boost::math::constants::pi<mp_t>());
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}
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if(sign < 1)
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g2 = 2 - g2;
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return boost::math::make_tuple(g1, g2);
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}
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};
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double double_factorial(int N)
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{
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double result = 1;
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while(N > 2)
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{
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N -= 2;
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result *= N;
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}
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return result;
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}
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void asymptotic_limit(int Bits)
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{
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//
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// The following block of code estimates how large z has
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// to be before we can use the asymptotic expansion for
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// erf/erfc and still get convergence: the series becomes
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// divergent eventually so we have to be careful!
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//
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double result = (std::numeric_limits<double>::max)();
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int terms = 0;
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for(int n = 1; n < 15; ++n)
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{
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double lim = (Bits-n) * log(2.0) - log(sqrt(3.14)) + log(double_factorial(2*n+1));
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double x = 1;
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while(x*x + (2*n+1)*log(x) <= lim)
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x += 0.1;
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if(x < result)
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{
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result = x;
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terms = n;
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}
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}
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std::cout << "Erf asymptotic limit for "
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<< Bits << " bit numbers is "
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<< result << " after approximately "
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<< terms << " terms." << std::endl;
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result = (std::numeric_limits<double>::max)();
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terms = 0;
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for(int n = 1; n < 30; ++n)
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{
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double x = pow(double_factorial(2*n+1)/pow(2.0, n-Bits), 1 / (2.0*n));
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if(x < result)
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{
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result = x;
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terms = n;
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}
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}
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std::cout << "Erfc asymptotic limit for "
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<< Bits << " bit numbers is "
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<< result << " after approximately "
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<< terms << " terms." << std::endl;
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}
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boost::math::tuple<mp_t, mp_t> erfc_inv(mp_t r)
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{
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mp_t x = exp(-r * r);
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x = x.convert_to<double>();
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std::cout << x << " ";
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mp_t result = boost::math::erfc_inv(x);
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std::cout << result << std::endl;
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return boost::math::make_tuple(x, result);
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}
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int main(int argc, char*argv [])
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{
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parameter_info<mp_t> arg1;
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test_data<mp_t> data;
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bool cont;
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std::string line;
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if(argc >= 2)
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{
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if(strcmp(argv[1], "--limits") == 0)
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{
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asymptotic_limit(24);
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asymptotic_limit(53);
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asymptotic_limit(64);
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asymptotic_limit(106);
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asymptotic_limit(113);
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return 0;
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}
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else if(strcmp(argv[1], "--erf_inv") == 0)
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{
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mp_t (*f)(mp_t);
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f = boost::math::erf_inv;
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std::cout << "Welcome.\n"
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"This program will generate spot tests for the inverse erf function:\n";
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std::cout << "Enter the number of data points: ";
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int points;
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std::cin >> points;
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data.insert(f, make_random_param(mp_t(-1), mp_t(1), points));
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}
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else if(strcmp(argv[1], "--erfc_inv") == 0)
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{
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boost::math::tuple<mp_t, mp_t> (*f)(mp_t);
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f = erfc_inv;
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std::cout << "Welcome.\n"
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"This program will generate spot tests for the inverse erfc function:\n";
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std::cout << "Enter the maximum *result* expected from erfc_inv: ";
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double max_val;
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std::cin >> max_val;
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std::cout << "Enter the number of data points: ";
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int points;
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std::cin >> points;
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parameter_info<mp_t> arg = make_random_param(mp_t(0), mp_t(max_val), points);
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arg.type |= dummy_param;
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data.insert(f, arg);
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}
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}
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else
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{
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std::cout << "Welcome.\n"
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"This program will generate spot tests for the erf and erfc functions:\n"
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" erf(z) and erfc(z)\n\n";
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do{
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if(0 == get_user_parameter_info(arg1, "a"))
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return 1;
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data.insert(erf_data_generator(), arg1);
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std::cout << "Any more data [y/n]?";
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std::getline(std::cin, line);
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boost::algorithm::trim(line);
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cont = (line == "y");
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}while(cont);
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}
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std::cout << "Enter name of test data file [default=erf_data.ipp]";
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std::getline(std::cin, line);
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boost::algorithm::trim(line);
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if(line == "")
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line = "erf_data.ipp";
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std::ofstream ofs(line.c_str());
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ofs << std::scientific << std::setprecision(40);
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write_code(ofs, data, "erf_data");
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return 0;
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}
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/* Output for asymptotic limits:
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Erf asymptotic limit for 24 bit numbers is 2.8 after approximately 6 terms.
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Erfc asymptotic limit for 24 bit numbers is 4.12064 after approximately 17 terms.
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Erf asymptotic limit for 53 bit numbers is 4.3 after approximately 11 terms.
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Erfc asymptotic limit for 53 bit numbers is 6.19035 after approximately 29 terms.
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Erf asymptotic limit for 64 bit numbers is 4.8 after approximately 12 terms.
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Erfc asymptotic limit for 64 bit numbers is 7.06004 after approximately 29 terms.
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Erf asymptotic limit for 106 bit numbers is 6.5 after approximately 14 terms.
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Erfc asymptotic limit for 106 bit numbers is 11.6626 after approximately 29 terms.
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Erf asymptotic limit for 113 bit numbers is 6.8 after approximately 14 terms.
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Erfc asymptotic limit for 113 bit numbers is 12.6802 after approximately 29 terms.
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*/
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