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Diffstat (limited to 'src/third_party/boost-1.56.0/boost/math/special_functions/erf.hpp')
| -rw-r--r-- | src/third_party/boost-1.56.0/boost/math/special_functions/erf.hpp | 1155 |
1 files changed, 0 insertions, 1155 deletions
diff --git a/src/third_party/boost-1.56.0/boost/math/special_functions/erf.hpp b/src/third_party/boost-1.56.0/boost/math/special_functions/erf.hpp deleted file mode 100644 index f7f75b0bc7a..00000000000 --- a/src/third_party/boost-1.56.0/boost/math/special_functions/erf.hpp +++ /dev/null @@ -1,1155 +0,0 @@ -// (C) Copyright John Maddock 2006. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_SPECIAL_ERF_HPP -#define BOOST_MATH_SPECIAL_ERF_HPP - -#ifdef _MSC_VER -#pragma once -#endif - -#include <boost/math/special_functions/math_fwd.hpp> -#include <boost/math/tools/config.hpp> -#include <boost/math/special_functions/gamma.hpp> -#include <boost/math/tools/roots.hpp> -#include <boost/math/policies/error_handling.hpp> -#include <boost/math/tools/big_constant.hpp> - -namespace boost{ namespace math{ - -namespace detail -{ - -// -// Asymptotic series for large z: -// -template <class T> -struct erf_asympt_series_t -{ - erf_asympt_series_t(T z) : xx(2 * -z * z), tk(1) - { - BOOST_MATH_STD_USING - result = -exp(-z * z) / sqrt(boost::math::constants::pi<T>()); - result /= z; - } - - typedef T result_type; - - T operator()() - { - BOOST_MATH_STD_USING - T r = result; - result *= tk / xx; - tk += 2; - if( fabs(r) < fabs(result)) - result = 0; - return r; - } -private: - T result; - T xx; - int tk; -}; -// -// How large z has to be in order to ensure that the series converges: -// -template <class T> -inline float erf_asymptotic_limit_N(const T&) -{ - return (std::numeric_limits<float>::max)(); -} -inline float erf_asymptotic_limit_N(const mpl::int_<24>&) -{ - return 2.8F; -} -inline float erf_asymptotic_limit_N(const mpl::int_<53>&) -{ - return 4.3F; -} -inline float erf_asymptotic_limit_N(const mpl::int_<64>&) -{ - return 4.8F; -} -inline float erf_asymptotic_limit_N(const mpl::int_<106>&) -{ - return 6.5F; -} -inline float erf_asymptotic_limit_N(const mpl::int_<113>&) -{ - return 6.8F; -} - -template <class T, class Policy> -inline T erf_asymptotic_limit() -{ - typedef typename policies::precision<T, Policy>::type precision_type; - typedef typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<24> >, - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<0> >, - mpl::int_<0>, - mpl::int_<24> - >::type, - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<53> >, - mpl::int_<53>, - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<64> >, - mpl::int_<64>, - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<106> >, - mpl::int_<106>, - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<113> >, - mpl::int_<113>, - mpl::int_<0> - >::type - >::type - >::type - >::type - >::type tag_type; - return erf_asymptotic_limit_N(tag_type()); -} - -template <class T, class Policy, class Tag> -T erf_imp(T z, bool invert, const Policy& pol, const Tag& t) -{ - BOOST_MATH_STD_USING - - BOOST_MATH_INSTRUMENT_CODE("Generic erf_imp called"); - - if(z < 0) - { - if(!invert) - return -erf_imp(T(-z), invert, pol, t); - else - return 1 + erf_imp(T(-z), false, pol, t); - } - - T result; - - if(!invert && (z > detail::erf_asymptotic_limit<T, Policy>())) - { - detail::erf_asympt_series_t<T> s(z); - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, 1); - policies::check_series_iterations<T>("boost::math::erf<%1%>(%1%, %1%)", max_iter, pol); - } - else - { - T x = z * z; - if(x < 0.6) - { - // Compute P: - result = z * exp(-x); - result /= sqrt(boost::math::constants::pi<T>()); - if(result != 0) - result *= 2 * detail::lower_gamma_series(T(0.5f), x, pol); - } - else if(x < 1.1f) - { - // Compute Q: - invert = !invert; - result = tgamma_small_upper_part(T(0.5f), x, pol); - result /= sqrt(boost::math::constants::pi<T>()); - } - else - { - // Compute Q: - invert = !invert; - result = z * exp(-x); - result /= sqrt(boost::math::constants::pi<T>()); - result *= upper_gamma_fraction(T(0.5f), x, policies::get_epsilon<T, Policy>()); - } - } - if(invert) - result = 1 - result; - return result; -} - -template <class T, class Policy> -T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<53>& t) -{ - BOOST_MATH_STD_USING - - BOOST_MATH_INSTRUMENT_CODE("53-bit precision erf_imp called"); - - if(z < 0) - { - if(!invert) - return -erf_imp(T(-z), invert, pol, t); - else if(z < -0.5) - return 2 - erf_imp(T(-z), invert, pol, t); - else - return 1 + erf_imp(T(-z), false, pol, t); - } - - T result; - - // - // Big bunch of selection statements now to pick - // which implementation to use, - // try to put most likely options first: - // - if(z < 0.5) - { - // - // We're going to calculate erf: - // - if(z < 1e-10) - { - if(z == 0) - { - result = T(0); - } - else - { - static const T c = BOOST_MATH_BIG_CONSTANT(T, 53, 0.003379167095512573896158903121545171688); - result = static_cast<T>(z * 1.125f + z * c); - } - } - else - { - // Maximum Deviation Found: 1.561e-17 - // Expected Error Term: 1.561e-17 - // Maximum Relative Change in Control Points: 1.155e-04 - // Max Error found at double precision = 2.961182e-17 - - static const T Y = 1.044948577880859375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0834305892146531832907), - BOOST_MATH_BIG_CONSTANT(T, 53, -0.338165134459360935041), - BOOST_MATH_BIG_CONSTANT(T, 53, -0.0509990735146777432841), - BOOST_MATH_BIG_CONSTANT(T, 53, -0.00772758345802133288487), - BOOST_MATH_BIG_CONSTANT(T, 53, -0.000322780120964605683831), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.455004033050794024546), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0875222600142252549554), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.00858571925074406212772), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.000370900071787748000569), - }; - T zz = z * z; - result = z * (Y + tools::evaluate_polynomial(P, zz) / tools::evaluate_polynomial(Q, zz)); - } - } - else if(invert ? (z < 28) : (z < 5.8f)) - { - // - // We'll be calculating erfc: - // - invert = !invert; - if(z < 1.5f) - { - // Maximum Deviation Found: 3.702e-17 - // Expected Error Term: 3.702e-17 - // Maximum Relative Change in Control Points: 2.845e-04 - // Max Error found at double precision = 4.841816e-17 - static const T Y = 0.405935764312744140625f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, -0.098090592216281240205), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.178114665841120341155), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.191003695796775433986), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0888900368967884466578), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0195049001251218801359), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.00180424538297014223957), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 53, 1.84759070983002217845), - BOOST_MATH_BIG_CONSTANT(T, 53, 1.42628004845511324508), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.578052804889902404909), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.12385097467900864233), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0113385233577001411017), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.337511472483094676155e-5), - }; - BOOST_MATH_INSTRUMENT_VARIABLE(Y); - BOOST_MATH_INSTRUMENT_VARIABLE(P[0]); - BOOST_MATH_INSTRUMENT_VARIABLE(Q[0]); - BOOST_MATH_INSTRUMENT_VARIABLE(z); - result = Y + tools::evaluate_polynomial(P, T(z - 0.5)) / tools::evaluate_polynomial(Q, T(z - 0.5)); - BOOST_MATH_INSTRUMENT_VARIABLE(result); - result *= exp(-z * z) / z; - BOOST_MATH_INSTRUMENT_VARIABLE(result); - } - else if(z < 2.5f) - { - // Max Error found at double precision = 6.599585e-18 - // Maximum Deviation Found: 3.909e-18 - // Expected Error Term: 3.909e-18 - // Maximum Relative Change in Control Points: 9.886e-05 - static const T Y = 0.50672817230224609375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, -0.0243500476207698441272), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0386540375035707201728), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.04394818964209516296), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0175679436311802092299), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.00323962406290842133584), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.000235839115596880717416), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 53, 1.53991494948552447182), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.982403709157920235114), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.325732924782444448493), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0563921837420478160373), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.00410369723978904575884), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 1.5)) / tools::evaluate_polynomial(Q, T(z - 1.5)); - result *= exp(-z * z) / z; - } - else if(z < 4.5f) - { - // Maximum Deviation Found: 1.512e-17 - // Expected Error Term: 1.512e-17 - // Maximum Relative Change in Control Points: 2.222e-04 - // Max Error found at double precision = 2.062515e-17 - static const T Y = 0.5405750274658203125f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, 0.00295276716530971662634), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0137384425896355332126), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.00840807615555585383007), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.00212825620914618649141), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.000250269961544794627958), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.113212406648847561139e-4), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 53, 1.04217814166938418171), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.442597659481563127003), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0958492726301061423444), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0105982906484876531489), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.000479411269521714493907), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 3.5)) / tools::evaluate_polynomial(Q, T(z - 3.5)); - result *= exp(-z * z) / z; - } - else - { - // Max Error found at double precision = 2.997958e-17 - // Maximum Deviation Found: 2.860e-17 - // Expected Error Term: 2.859e-17 - // Maximum Relative Change in Control Points: 1.357e-05 - static const T Y = 0.5579090118408203125f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, 0.00628057170626964891937), - BOOST_MATH_BIG_CONSTANT(T, 53, 0.0175389834052493308818), - BOOST_MATH_BIG_CONSTANT(T, 53, -0.212652252872804219852), - BOOST_MATH_BIG_CONSTANT(T, 53, -0.687717681153649930619), - BOOST_MATH_BIG_CONSTANT(T, 53, -2.5518551727311523996), - BOOST_MATH_BIG_CONSTANT(T, 53, -3.22729451764143718517), - BOOST_MATH_BIG_CONSTANT(T, 53, -2.8175401114513378771), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 53, 2.79257750980575282228), - BOOST_MATH_BIG_CONSTANT(T, 53, 11.0567237927800161565), - BOOST_MATH_BIG_CONSTANT(T, 53, 15.930646027911794143), - BOOST_MATH_BIG_CONSTANT(T, 53, 22.9367376522880577224), - BOOST_MATH_BIG_CONSTANT(T, 53, 13.5064170191802889145), - BOOST_MATH_BIG_CONSTANT(T, 53, 5.48409182238641741584), - }; - result = Y + tools::evaluate_polynomial(P, T(1 / z)) / tools::evaluate_polynomial(Q, T(1 / z)); - result *= exp(-z * z) / z; - } - } - else - { - // - // Any value of z larger than 28 will underflow to zero: - // - result = 0; - invert = !invert; - } - - if(invert) - { - result = 1 - result; - } - - return result; -} // template <class T, class Lanczos>T erf_imp(T z, bool invert, const Lanczos& l, const mpl::int_<53>& t) - - -template <class T, class Policy> -T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<64>& t) -{ - BOOST_MATH_STD_USING - - BOOST_MATH_INSTRUMENT_CODE("64-bit precision erf_imp called"); - - if(z < 0) - { - if(!invert) - return -erf_imp(T(-z), invert, pol, t); - else if(z < -0.5) - return 2 - erf_imp(T(-z), invert, pol, t); - else - return 1 + erf_imp(T(-z), false, pol, t); - } - - T result; - - // - // Big bunch of selection statements now to pick which - // implementation to use, try to put most likely options - // first: - // - if(z < 0.5) - { - // - // We're going to calculate erf: - // - if(z == 0) - { - result = 0; - } - else if(z < 1e-10) - { - static const T c = BOOST_MATH_BIG_CONSTANT(T, 64, 0.003379167095512573896158903121545171688); - result = z * 1.125 + z * c; - } - else - { - // Max Error found at long double precision = 1.623299e-20 - // Maximum Deviation Found: 4.326e-22 - // Expected Error Term: -4.326e-22 - // Maximum Relative Change in Control Points: 1.474e-04 - static const T Y = 1.044948577880859375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0834305892146531988966), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.338097283075565413695), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.0509602734406067204596), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.00904906346158537794396), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.000489468651464798669181), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.200305626366151877759e-4), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.455817300515875172439), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0916537354356241792007), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0102722652675910031202), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000650511752687851548735), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.189532519105655496778e-4), - }; - result = z * (Y + tools::evaluate_polynomial(P, T(z * z)) / tools::evaluate_polynomial(Q, T(z * z))); - } - } - else if(invert ? (z < 110) : (z < 6.4f)) - { - // - // We'll be calculating erfc: - // - invert = !invert; - if(z < 1.5) - { - // Max Error found at long double precision = 3.239590e-20 - // Maximum Deviation Found: 2.241e-20 - // Expected Error Term: -2.241e-20 - // Maximum Relative Change in Control Points: 5.110e-03 - static const T Y = 0.405935764312744140625f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, -0.0980905922162812031672), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.159989089922969141329), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.222359821619935712378), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.127303921703577362312), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0384057530342762400273), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00628431160851156719325), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000441266654514391746428), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.266689068336295642561e-7), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 2.03237474985469469291), - BOOST_MATH_BIG_CONSTANT(T, 64, 1.78355454954969405222), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.867940326293760578231), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.248025606990021698392), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0396649631833002269861), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00279220237309449026796), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 0.5f)) / tools::evaluate_polynomial(Q, T(z - 0.5f)); - result *= exp(-z * z) / z; - } - else if(z < 2.5) - { - // Max Error found at long double precision = 3.686211e-21 - // Maximum Deviation Found: 1.495e-21 - // Expected Error Term: -1.494e-21 - // Maximum Relative Change in Control Points: 1.793e-04 - static const T Y = 0.50672817230224609375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, -0.024350047620769840217), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0343522687935671451309), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0505420824305544949541), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0257479325917757388209), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00669349844190354356118), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00090807914416099524444), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.515917266698050027934e-4), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 1.71657861671930336344), - BOOST_MATH_BIG_CONSTANT(T, 64, 1.26409634824280366218), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.512371437838969015941), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.120902623051120950935), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0158027197831887485261), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000897871370778031611439), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 1.5f)) / tools::evaluate_polynomial(Q, T(z - 1.5f)); - result *= exp(-z * z) / z; - } - else if(z < 4.5) - { - // Maximum Deviation Found: 1.107e-20 - // Expected Error Term: -1.106e-20 - // Maximum Relative Change in Control Points: 1.709e-04 - // Max Error found at long double precision = 1.446908e-20 - static const T Y = 0.5405750274658203125f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0029527671653097284033), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0141853245895495604051), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0104959584626432293901), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00343963795976100077626), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00059065441194877637899), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.523435380636174008685e-4), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.189896043050331257262e-5), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 1.19352160185285642574), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.603256964363454392857), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.165411142458540585835), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0259729870946203166468), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00221657568292893699158), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.804149464190309799804e-4), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 3.5f)) / tools::evaluate_polynomial(Q, T(z - 3.5f)); - result *= exp(-z * z) / z; - } - else - { - // Max Error found at long double precision = 7.961166e-21 - // Maximum Deviation Found: 6.677e-21 - // Expected Error Term: 6.676e-21 - // Maximum Relative Change in Control Points: 2.319e-05 - static const T Y = 0.55825519561767578125f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00593438793008050214106), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0280666231009089713937), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.141597835204583050043), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.978088201154300548842), - BOOST_MATH_BIG_CONSTANT(T, 64, -5.47351527796012049443), - BOOST_MATH_BIG_CONSTANT(T, 64, -13.8677304660245326627), - BOOST_MATH_BIG_CONSTANT(T, 64, -27.1274948720539821722), - BOOST_MATH_BIG_CONSTANT(T, 64, -29.2545152747009461519), - BOOST_MATH_BIG_CONSTANT(T, 64, -16.8865774499799676937), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 4.72948911186645394541), - BOOST_MATH_BIG_CONSTANT(T, 64, 23.6750543147695749212), - BOOST_MATH_BIG_CONSTANT(T, 64, 60.0021517335693186785), - BOOST_MATH_BIG_CONSTANT(T, 64, 131.766251645149522868), - BOOST_MATH_BIG_CONSTANT(T, 64, 178.167924971283482513), - BOOST_MATH_BIG_CONSTANT(T, 64, 182.499390505915222699), - BOOST_MATH_BIG_CONSTANT(T, 64, 104.365251479578577989), - BOOST_MATH_BIG_CONSTANT(T, 64, 30.8365511891224291717), - }; - result = Y + tools::evaluate_polynomial(P, T(1 / z)) / tools::evaluate_polynomial(Q, T(1 / z)); - result *= exp(-z * z) / z; - } - } - else - { - // - // Any value of z larger than 110 will underflow to zero: - // - result = 0; - invert = !invert; - } - - if(invert) - { - result = 1 - result; - } - - return result; -} // template <class T, class Lanczos>T erf_imp(T z, bool invert, const Lanczos& l, const mpl::int_<64>& t) - - -template <class T, class Policy> -T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<113>& t) -{ - BOOST_MATH_STD_USING - - BOOST_MATH_INSTRUMENT_CODE("113-bit precision erf_imp called"); - - if(z < 0) - { - if(!invert) - return -erf_imp(T(-z), invert, pol, t); - else if(z < -0.5) - return 2 - erf_imp(T(-z), invert, pol, t); - else - return 1 + erf_imp(T(-z), false, pol, t); - } - - T result; - - // - // Big bunch of selection statements now to pick which - // implementation to use, try to put most likely options - // first: - // - if(z < 0.5) - { - // - // We're going to calculate erf: - // - if(z == 0) - { - result = 0; - } - else if(z < 1e-20) - { - static const T c = BOOST_MATH_BIG_CONSTANT(T, 113, 0.003379167095512573896158903121545171688); - result = z * 1.125 + z * c; - } - else - { - // Max Error found at long double precision = 2.342380e-35 - // Maximum Deviation Found: 6.124e-36 - // Expected Error Term: -6.124e-36 - // Maximum Relative Change in Control Points: 3.492e-10 - static const T Y = 1.0841522216796875f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0442269454158250738961589031215451778), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.35549265736002144875335323556961233), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0582179564566667896225454670863270393), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0112694696904802304229950538453123925), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.000805730648981801146251825329609079099), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.566304966591936566229702842075966273e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.169655010425186987820201021510002265e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.344448249920445916714548295433198544e-7), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.466542092785657604666906909196052522), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.100005087012526447295176964142107611), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0128341535890117646540050072234142603), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00107150448466867929159660677016658186), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.586168368028999183607733369248338474e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.196230608502104324965623171516808796e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.313388521582925207734229967907890146e-7), - }; - result = z * (Y + tools::evaluate_polynomial(P, T(z * z)) / tools::evaluate_polynomial(Q, T(z * z))); - } - } - else if(invert ? (z < 110) : (z < 8.65f)) - { - // - // We'll be calculating erfc: - // - invert = !invert; - if(z < 1) - { - // Max Error found at long double precision = 3.246278e-35 - // Maximum Deviation Found: 1.388e-35 - // Expected Error Term: 1.387e-35 - // Maximum Relative Change in Control Points: 6.127e-05 - static const T Y = 0.371877193450927734375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0640320213544647969396032886581290455), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.200769874440155895637857443946706731), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.378447199873537170666487408805779826), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.30521399466465939450398642044975127), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.146890026406815277906781824723458196), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0464837937749539978247589252732769567), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00987895759019540115099100165904822903), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00137507575429025512038051025154301132), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0001144764551085935580772512359680516), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.436544865032836914773944382339900079e-5), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 2.47651182872457465043733800302427977), - BOOST_MATH_BIG_CONSTANT(T, 113, 2.78706486002517996428836400245547955), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.87295924621659627926365005293130693), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.829375825174365625428280908787261065), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.251334771307848291593780143950311514), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0522110268876176186719436765734722473), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00718332151250963182233267040106902368), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000595279058621482041084986219276392459), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.226988669466501655990637599399326874e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.270666232259029102353426738909226413e-10), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 0.5f)) / tools::evaluate_polynomial(Q, T(z - 0.5f)); - result *= exp(-z * z) / z; - } - else if(z < 1.5) - { - // Max Error found at long double precision = 2.215785e-35 - // Maximum Deviation Found: 1.539e-35 - // Expected Error Term: 1.538e-35 - // Maximum Relative Change in Control Points: 6.104e-05 - static const T Y = 0.45658016204833984375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0289965858925328393392496555094848345), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0868181194868601184627743162571779226), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.169373435121178901746317404936356745), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.13350446515949251201104889028133486), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0617447837290183627136837688446313313), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0185618495228251406703152962489700468), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00371949406491883508764162050169531013), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000485121708792921297742105775823900772), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.376494706741453489892108068231400061e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.133166058052466262415271732172490045e-5), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 2.32970330146503867261275580968135126), - BOOST_MATH_BIG_CONSTANT(T, 113, 2.46325715420422771961250513514928746), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.55307882560757679068505047390857842), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.644274289865972449441174485441409076), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.182609091063258208068606847453955649), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0354171651271241474946129665801606795), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00454060370165285246451879969534083997), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000349871943711566546821198612518656486), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.123749319840299552925421880481085392e-4), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 1.0f)) / tools::evaluate_polynomial(Q, T(z - 1.0f)); - result *= exp(-z * z) / z; - } - else if(z < 2.25) - { - // Maximum Deviation Found: 1.418e-35 - // Expected Error Term: 1.418e-35 - // Maximum Relative Change in Control Points: 1.316e-04 - // Max Error found at long double precision = 1.998462e-35 - static const T Y = 0.50250148773193359375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0201233630504573402185161184151016606), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0331864357574860196516686996302305002), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0716562720864787193337475444413405461), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0545835322082103985114927569724880658), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0236692635189696678976549720784989593), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00656970902163248872837262539337601845), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00120282643299089441390490459256235021), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000142123229065182650020762792081622986), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.991531438367015135346716277792989347e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.312857043762117596999398067153076051e-6), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 2.13506082409097783827103424943508554), - BOOST_MATH_BIG_CONSTANT(T, 113, 2.06399257267556230937723190496806215), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.18678481279932541314830499880691109), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.447733186643051752513538142316799562), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.11505680005657879437196953047542148), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.020163993632192726170219663831914034), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00232708971840141388847728782209730585), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000160733201627963528519726484608224112), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.507158721790721802724402992033269266e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.18647774409821470950544212696270639e-12), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 1.5f)) / tools::evaluate_polynomial(Q, T(z - 1.5f)); - result *= exp(-z * z) / z; - } - else if (z < 3) - { - // Maximum Deviation Found: 3.575e-36 - // Expected Error Term: 3.575e-36 - // Maximum Relative Change in Control Points: 7.103e-05 - // Max Error found at long double precision = 5.794737e-36 - static const T Y = 0.52896785736083984375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -0.00902152521745813634562524098263360074), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0145207142776691539346923710537580927), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0301681239582193983824211995978678571), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0215548540823305814379020678660434461), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00864683476267958365678294164340749949), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00219693096885585491739823283511049902), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000364961639163319762492184502159894371), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.388174251026723752769264051548703059e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.241918026931789436000532513553594321e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.676586625472423508158937481943649258e-7), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.93669171363907292305550231764920001), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.69468476144051356810672506101377494), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.880023580986436640372794392579985511), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.299099106711315090710836273697708402), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0690593962363545715997445583603382337), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0108427016361318921960863149875360222), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00111747247208044534520499324234317695), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.686843205749767250666787987163701209e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.192093541425429248675532015101904262e-5), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 2.25f)) / tools::evaluate_polynomial(Q, T(z - 2.25f)); - result *= exp(-z * z) / z; - } - else if(z < 3.5) - { - // Maximum Deviation Found: 8.126e-37 - // Expected Error Term: -8.126e-37 - // Maximum Relative Change in Control Points: 1.363e-04 - // Max Error found at long double precision = 1.747062e-36 - static const T Y = 0.54037380218505859375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0033703486408887424921155540591370375), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0104948043110005245215286678898115811), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0148530118504000311502310457390417795), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00816693029245443090102738825536188916), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00249716579989140882491939681805594585), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0004655591010047353023978045800916647), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.531129557920045295895085236636025323e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.343526765122727069515775194111741049e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.971120407556888763695313774578711839e-7), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.59911256167540354915906501335919317), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.136006830764025173864831382946934), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.468565867990030871678574840738423023), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.122821824954470343413956476900662236), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0209670914950115943338996513330141633), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00227845718243186165620199012883547257), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000144243326443913171313947613547085553), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.407763415954267700941230249989140046e-5), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 3.0f)) / tools::evaluate_polynomial(Q, T(z - 3.0f)); - result *= exp(-z * z) / z; - } - else if(z < 5.5) - { - // Maximum Deviation Found: 5.804e-36 - // Expected Error Term: -5.803e-36 - // Maximum Relative Change in Control Points: 2.475e-05 - // Max Error found at long double precision = 1.349545e-35 - static const T Y = 0.55000019073486328125f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00118142849742309772151454518093813615), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0072201822885703318172366893469382745), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0078782276276860110721875733778481505), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00418229166204362376187593976656261146), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00134198400587769200074194304298642705), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000283210387078004063264777611497435572), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.405687064094911866569295610914844928e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.39348283801568113807887364414008292e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.248798540917787001526976889284624449e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.929502490223452372919607105387474751e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.156161469668275442569286723236274457e-9), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.52955245103668419479878456656709381), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.06263944820093830054635017117417064), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.441684612681607364321013134378316463), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.121665258426166960049773715928906382), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0232134512374747691424978642874321434), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00310778180686296328582860464875562636), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000288361770756174705123674838640161693), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.177529187194133944622193191942300132e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.655068544833064069223029299070876623e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.11005507545746069573608988651927452e-7), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 4.5f)) / tools::evaluate_polynomial(Q, T(z - 4.5f)); - result *= exp(-z * z) / z; - } - else if(z < 7.5) - { - // Maximum Deviation Found: 1.007e-36 - // Expected Error Term: 1.007e-36 - // Maximum Relative Change in Control Points: 1.027e-03 - // Max Error found at long double precision = 2.646420e-36 - static const T Y = 0.5574436187744140625f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000293236907400849056269309713064107674), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00225110719535060642692275221961480162), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00190984458121502831421717207849429799), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000747757733460111743833929141001680706), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000170663175280949889583158597373928096), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.246441188958013822253071608197514058e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.229818000860544644974205957895688106e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.134886977703388748488480980637704864e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.454764611880548962757125070106650958e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.673002744115866600294723141176820155e-10), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.12843690320861239631195353379313367), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.569900657061622955362493442186537259), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.169094404206844928112348730277514273), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0324887449084220415058158657252147063), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00419252877436825753042680842608219552), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00036344133176118603523976748563178578), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.204123895931375107397698245752850347e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.674128352521481412232785122943508729e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.997637501418963696542159244436245077e-8), - }; - result = Y + tools::evaluate_polynomial(P, T(z - 6.5f)) / tools::evaluate_polynomial(Q, T(z - 6.5f)); - result *= exp(-z * z) / z; - } - else if(z < 11.5) - { - // Maximum Deviation Found: 8.380e-36 - // Expected Error Term: 8.380e-36 - // Maximum Relative Change in Control Points: 2.632e-06 - // Max Error found at long double precision = 9.849522e-36 - static const T Y = 0.56083202362060546875f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000282420728751494363613829834891390121), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00175387065018002823433704079355125161), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0021344978564889819420775336322920375), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00124151356560137532655039683963075661), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000423600733566948018555157026862139644), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.914030340865175237133613697319509698e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.126999927156823363353809747017945494e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.110610959842869849776179749369376402e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.55075079477173482096725348704634529e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.119735694018906705225870691331543806e-8), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.69889613396167354566098060039549882), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.28824647372749624464956031163282674), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.572297795434934493541628008224078717), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.164157697425571712377043857240773164), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0315311145224594430281219516531649562), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00405588922155632380812945849777127458), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000336929033691445666232029762868642417), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.164033049810404773469413526427932109e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.356615210500531410114914617294694857e-6), - }; - result = Y + tools::evaluate_polynomial(P, T(z / 2 - 4.75f)) / tools::evaluate_polynomial(Q, T(z / 2 - 4.75f)); - result *= exp(-z * z) / z; - } - else - { - // Maximum Deviation Found: 1.132e-35 - // Expected Error Term: -1.132e-35 - // Maximum Relative Change in Control Points: 4.674e-04 - // Max Error found at long double precision = 1.162590e-35 - static const T Y = 0.5632686614990234375f; - static const T P[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000920922048732849448079451574171836943), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00321439044532288750501700028748922439), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.250455263029390118657884864261823431), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.906807635364090342031792404764598142), - BOOST_MATH_BIG_CONSTANT(T, 113, -8.92233572835991735876688745989985565), - BOOST_MATH_BIG_CONSTANT(T, 113, -21.7797433494422564811782116907878495), - BOOST_MATH_BIG_CONSTANT(T, 113, -91.1451915251976354349734589601171659), - BOOST_MATH_BIG_CONSTANT(T, 113, -144.1279109655993927069052125017673), - BOOST_MATH_BIG_CONSTANT(T, 113, -313.845076581796338665519022313775589), - BOOST_MATH_BIG_CONSTANT(T, 113, -273.11378811923343424081101235736475), - BOOST_MATH_BIG_CONSTANT(T, 113, -271.651566205951067025696102600443452), - BOOST_MATH_BIG_CONSTANT(T, 113, -60.0530577077238079968843307523245547), - }; - static const T Q[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 3.49040448075464744191022350947892036), - BOOST_MATH_BIG_CONSTANT(T, 113, 34.3563592467165971295915749548313227), - BOOST_MATH_BIG_CONSTANT(T, 113, 84.4993232033879023178285731843850461), - BOOST_MATH_BIG_CONSTANT(T, 113, 376.005865281206894120659401340373818), - BOOST_MATH_BIG_CONSTANT(T, 113, 629.95369438888946233003926191755125), - BOOST_MATH_BIG_CONSTANT(T, 113, 1568.35771983533158591604513304269098), - BOOST_MATH_BIG_CONSTANT(T, 113, 1646.02452040831961063640827116581021), - BOOST_MATH_BIG_CONSTANT(T, 113, 2299.96860633240298708910425594484895), - BOOST_MATH_BIG_CONSTANT(T, 113, 1222.73204392037452750381340219906374), - BOOST_MATH_BIG_CONSTANT(T, 113, 799.359797306084372350264298361110448), - BOOST_MATH_BIG_CONSTANT(T, 113, 72.7415265778588087243442792401576737), - }; - result = Y + tools::evaluate_polynomial(P, T(1 / z)) / tools::evaluate_polynomial(Q, T(1 / z)); - result *= exp(-z * z) / z; - } - } - else - { - // - // Any value of z larger than 110 will underflow to zero: - // - result = 0; - invert = !invert; - } - - if(invert) - { - result = 1 - result; - } - - return result; -} // template <class T, class Lanczos>T erf_imp(T z, bool invert, const Lanczos& l, const mpl::int_<113>& t) - -template <class T, class Policy, class tag> -struct erf_initializer -{ - struct init - { - init() - { - do_init(tag()); - } - static void do_init(const mpl::int_<0>&){} - static void do_init(const mpl::int_<53>&) - { - boost::math::erf(static_cast<T>(1e-12), Policy()); - boost::math::erf(static_cast<T>(0.25), Policy()); - boost::math::erf(static_cast<T>(1.25), Policy()); - boost::math::erf(static_cast<T>(2.25), Policy()); - boost::math::erf(static_cast<T>(4.25), Policy()); - boost::math::erf(static_cast<T>(5.25), Policy()); - } - static void do_init(const mpl::int_<64>&) - { - boost::math::erf(static_cast<T>(1e-12), Policy()); - boost::math::erf(static_cast<T>(0.25), Policy()); - boost::math::erf(static_cast<T>(1.25), Policy()); - boost::math::erf(static_cast<T>(2.25), Policy()); - boost::math::erf(static_cast<T>(4.25), Policy()); - boost::math::erf(static_cast<T>(5.25), Policy()); - } - static void do_init(const mpl::int_<113>&) - { - boost::math::erf(static_cast<T>(1e-22), Policy()); - boost::math::erf(static_cast<T>(0.25), Policy()); - boost::math::erf(static_cast<T>(1.25), Policy()); - boost::math::erf(static_cast<T>(2.125), Policy()); - boost::math::erf(static_cast<T>(2.75), Policy()); - boost::math::erf(static_cast<T>(3.25), Policy()); - boost::math::erf(static_cast<T>(5.25), Policy()); - boost::math::erf(static_cast<T>(7.25), Policy()); - boost::math::erf(static_cast<T>(11.25), Policy()); - boost::math::erf(static_cast<T>(12.5), Policy()); - } - void force_instantiate()const{} - }; - static const init initializer; - static void force_instantiate() - { - initializer.force_instantiate(); - } -}; - -template <class T, class Policy, class tag> -const typename erf_initializer<T, Policy, tag>::init erf_initializer<T, Policy, tag>::initializer; - -} // namespace detail - -template <class T, class Policy> -inline typename tools::promote_args<T>::type erf(T z, const Policy& /* pol */) -{ - typedef typename tools::promote_args<T>::type result_type; - typedef typename policies::evaluation<result_type, Policy>::type value_type; - typedef typename policies::precision<result_type, Policy>::type precision_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - BOOST_MATH_INSTRUMENT_CODE("result_type = " << typeid(result_type).name()); - BOOST_MATH_INSTRUMENT_CODE("value_type = " << typeid(value_type).name()); - BOOST_MATH_INSTRUMENT_CODE("precision_type = " << typeid(precision_type).name()); - - typedef typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<0> >, - mpl::int_<0>, - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<53> >, - mpl::int_<53>, // double - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<64> >, - mpl::int_<64>, // 80-bit long double - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<113> >, - mpl::int_<113>, // 128-bit long double - mpl::int_<0> // too many bits, use generic version. - >::type - >::type - >::type - >::type tag_type; - - BOOST_MATH_INSTRUMENT_CODE("tag_type = " << typeid(tag_type).name()); - - detail::erf_initializer<value_type, forwarding_policy, tag_type>::force_instantiate(); // Force constants to be initialized before main - - return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::erf_imp( - static_cast<value_type>(z), - false, - forwarding_policy(), - tag_type()), "boost::math::erf<%1%>(%1%, %1%)"); -} - -template <class T, class Policy> -inline typename tools::promote_args<T>::type erfc(T z, const Policy& /* pol */) -{ - typedef typename tools::promote_args<T>::type result_type; - typedef typename policies::evaluation<result_type, Policy>::type value_type; - typedef typename policies::precision<result_type, Policy>::type precision_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - BOOST_MATH_INSTRUMENT_CODE("result_type = " << typeid(result_type).name()); - BOOST_MATH_INSTRUMENT_CODE("value_type = " << typeid(value_type).name()); - BOOST_MATH_INSTRUMENT_CODE("precision_type = " << typeid(precision_type).name()); - - typedef typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<0> >, - mpl::int_<0>, - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<53> >, - mpl::int_<53>, // double - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<64> >, - mpl::int_<64>, // 80-bit long double - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<113> >, - mpl::int_<113>, // 128-bit long double - mpl::int_<0> // too many bits, use generic version. - >::type - >::type - >::type - >::type tag_type; - - BOOST_MATH_INSTRUMENT_CODE("tag_type = " << typeid(tag_type).name()); - - detail::erf_initializer<value_type, forwarding_policy, tag_type>::force_instantiate(); // Force constants to be initialized before main - - return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::erf_imp( - static_cast<value_type>(z), - true, - forwarding_policy(), - tag_type()), "boost::math::erfc<%1%>(%1%, %1%)"); -} - -template <class T> -inline typename tools::promote_args<T>::type erf(T z) -{ - return boost::math::erf(z, policies::policy<>()); -} - -template <class T> -inline typename tools::promote_args<T>::type erfc(T z) -{ - return boost::math::erfc(z, policies::policy<>()); -} - -} // namespace math -} // namespace boost - -#include <boost/math/special_functions/detail/erf_inv.hpp> - -#endif // BOOST_MATH_SPECIAL_ERF_HPP - - - - |