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Diffstat (limited to 'inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/zeta.hpp')
| -rw-r--r-- | inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/zeta.hpp | 1100 |
1 files changed, 0 insertions, 1100 deletions
diff --git a/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/zeta.hpp b/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/zeta.hpp deleted file mode 100644 index 91b83c1b2..000000000 --- a/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/zeta.hpp +++ /dev/null @@ -1,1100 +0,0 @@ -// Copyright John Maddock 2007, 2014. -// 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_ZETA_HPP -#define BOOST_MATH_ZETA_HPP - -#ifdef _MSC_VER -#pragma once -#endif - -#include <boost/math/special_functions/math_fwd.hpp> -#include <boost/math/tools/precision.hpp> -#include <boost/math/tools/series.hpp> -#include <boost/math/tools/big_constant.hpp> -#include <boost/math/policies/error_handling.hpp> -#include <boost/math/special_functions/gamma.hpp> -#include <boost/math/special_functions/factorials.hpp> -#include <boost/math/special_functions/sin_pi.hpp> - -namespace boost{ namespace math{ namespace detail{ - -#if 0 -// -// This code is commented out because we have a better more rapidly converging series -// now. Retained for future reference and in case the new code causes any issues down the line.... -// - -template <class T, class Policy> -struct zeta_series_cache_size -{ - // - // Work how large to make our cache size when evaluating the series - // evaluation: normally this is just large enough for the series - // to have converged, but for arbitrary precision types we need a - // really large cache to achieve reasonable precision in a reasonable - // time. This is important when constructing rational approximations - // to zeta for example. - // - typedef typename boost::math::policies::precision<T,Policy>::type precision_type; - typedef typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<0> >, - mpl::int_<5000>, - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<64> >, - mpl::int_<70>, - typename mpl::if_< - mpl::less_equal<precision_type, mpl::int_<113> >, - mpl::int_<100>, - mpl::int_<5000> - >::type - >::type - >::type type; -}; - -template <class T, class Policy> -T zeta_series_imp(T s, T sc, const Policy&) -{ - // - // Series evaluation from: - // Havil, J. Gamma: Exploring Euler's Constant. - // Princeton, NJ: Princeton University Press, 2003. - // - // See also http://mathworld.wolfram.com/RiemannZetaFunction.html - // - BOOST_MATH_STD_USING - T sum = 0; - T mult = 0.5; - T change; - typedef typename zeta_series_cache_size<T,Policy>::type cache_size; - T powers[cache_size::value] = { 0, }; - unsigned n = 0; - do{ - T binom = -static_cast<T>(n); - T nested_sum = 1; - if(n < sizeof(powers) / sizeof(powers[0])) - powers[n] = pow(static_cast<T>(n + 1), -s); - for(unsigned k = 1; k <= n; ++k) - { - T p; - if(k < sizeof(powers) / sizeof(powers[0])) - { - p = powers[k]; - //p = pow(k + 1, -s); - } - else - p = pow(static_cast<T>(k + 1), -s); - nested_sum += binom * p; - binom *= (k - static_cast<T>(n)) / (k + 1); - } - change = mult * nested_sum; - sum += change; - mult /= 2; - ++n; - }while(fabs(change / sum) > tools::epsilon<T>()); - - return sum * 1 / -boost::math::powm1(T(2), sc); -} - -// -// Classical p-series: -// -template <class T> -struct zeta_series2 -{ - typedef T result_type; - zeta_series2(T _s) : s(-_s), k(1){} - T operator()() - { - BOOST_MATH_STD_USING - return pow(static_cast<T>(k++), s); - } -private: - T s; - unsigned k; -}; - -template <class T, class Policy> -inline T zeta_series2_imp(T s, const Policy& pol) -{ - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();; - zeta_series2<T> f(s); - T result = tools::sum_series( - f, - policies::get_epsilon<T, Policy>(), - max_iter); - policies::check_series_iterations<T>("boost::math::zeta_series2<%1%>(%1%)", max_iter, pol); - return result; -} -#endif - -template <class T, class Policy> -T zeta_polynomial_series(T s, T sc, Policy const &) -{ - // - // This is algorithm 3 from: - // - // "An Efficient Algorithm for the Riemann Zeta Function", P. Borwein, - // Canadian Mathematical Society, Conference Proceedings. - // See: http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf - // - BOOST_MATH_STD_USING - int n = itrunc(T(log(boost::math::tools::epsilon<T>()) / -2)); - T sum = 0; - T two_n = ldexp(T(1), n); - int ej_sign = 1; - for(int j = 0; j < n; ++j) - { - sum += ej_sign * -two_n / pow(T(j + 1), s); - ej_sign = -ej_sign; - } - T ej_sum = 1; - T ej_term = 1; - for(int j = n; j <= 2 * n - 1; ++j) - { - sum += ej_sign * (ej_sum - two_n) / pow(T(j + 1), s); - ej_sign = -ej_sign; - ej_term *= 2 * n - j; - ej_term /= j - n + 1; - ej_sum += ej_term; - } - return -sum / (two_n * (-powm1(T(2), sc))); -} - -template <class T, class Policy> -T zeta_imp_prec(T s, T sc, const Policy& pol, const mpl::int_<0>&) -{ - BOOST_MATH_STD_USING - T result; - if(s >= policies::digits<T, Policy>()) - return 1; - result = zeta_polynomial_series(s, sc, pol); -#if 0 - // Old code archived for future reference: - - // - // Only use power series if it will converge in 100 - // iterations or less: the more iterations it consumes - // the slower convergence becomes so we have to be very - // careful in it's usage. - // - if (s > -log(tools::epsilon<T>()) / 4.5) - result = detail::zeta_series2_imp(s, pol); - else - result = detail::zeta_series_imp(s, sc, pol); -#endif - return result; -} - -template <class T, class Policy> -inline T zeta_imp_prec(T s, T sc, const Policy&, const mpl::int_<53>&) -{ - BOOST_MATH_STD_USING - T result; - if(s < 1) - { - // Rational Approximation - // Maximum Deviation Found: 2.020e-18 - // Expected Error Term: -2.020e-18 - // Max error found at double precision: 3.994987e-17 - static const T P[6] = { - static_cast<T>(0.24339294433593750202L), - static_cast<T>(-0.49092470516353571651L), - static_cast<T>(0.0557616214776046784287L), - static_cast<T>(-0.00320912498879085894856L), - static_cast<T>(0.000451534528645796438704L), - static_cast<T>(-0.933241270357061460782e-5L), - }; - static const T Q[6] = { - static_cast<T>(1L), - static_cast<T>(-0.279960334310344432495L), - static_cast<T>(0.0419676223309986037706L), - static_cast<T>(-0.00413421406552171059003L), - static_cast<T>(0.00024978985622317935355L), - static_cast<T>(-0.101855788418564031874e-4L), - }; - result = tools::evaluate_polynomial(P, sc) / tools::evaluate_polynomial(Q, sc); - result -= 1.2433929443359375F; - result += (sc); - result /= (sc); - } - else if(s <= 2) - { - // Maximum Deviation Found: 9.007e-20 - // Expected Error Term: 9.007e-20 - static const T P[6] = { - static_cast<T>(0.577215664901532860516L), - static_cast<T>(0.243210646940107164097L), - static_cast<T>(0.0417364673988216497593L), - static_cast<T>(0.00390252087072843288378L), - static_cast<T>(0.000249606367151877175456L), - static_cast<T>(0.110108440976732897969e-4L), - }; - static const T Q[6] = { - static_cast<T>(1.0), - static_cast<T>(0.295201277126631761737L), - static_cast<T>(0.043460910607305495864L), - static_cast<T>(0.00434930582085826330659L), - static_cast<T>(0.000255784226140488490982L), - static_cast<T>(0.10991819782396112081e-4L), - }; - result = tools::evaluate_polynomial(P, T(-sc)) / tools::evaluate_polynomial(Q, T(-sc)); - result += 1 / (-sc); - } - else if(s <= 4) - { - // Maximum Deviation Found: 5.946e-22 - // Expected Error Term: -5.946e-22 - static const float Y = 0.6986598968505859375; - static const T P[6] = { - static_cast<T>(-0.0537258300023595030676L), - static_cast<T>(0.0445163473292365591906L), - static_cast<T>(0.0128677673534519952905L), - static_cast<T>(0.00097541770457391752726L), - static_cast<T>(0.769875101573654070925e-4L), - static_cast<T>(0.328032510000383084155e-5L), - }; - static const T Q[7] = { - 1.0f, - static_cast<T>(0.33383194553034051422L), - static_cast<T>(0.0487798431291407621462L), - static_cast<T>(0.00479039708573558490716L), - static_cast<T>(0.000270776703956336357707L), - static_cast<T>(0.106951867532057341359e-4L), - static_cast<T>(0.236276623974978646399e-7L), - }; - result = tools::evaluate_polynomial(P, T(s - 2)) / tools::evaluate_polynomial(Q, T(s - 2)); - result += Y + 1 / (-sc); - } - else if(s <= 7) - { - // Maximum Deviation Found: 2.955e-17 - // Expected Error Term: 2.955e-17 - // Max error found at double precision: 2.009135e-16 - - static const T P[6] = { - static_cast<T>(-2.49710190602259410021L), - static_cast<T>(-2.60013301809475665334L), - static_cast<T>(-0.939260435377109939261L), - static_cast<T>(-0.138448617995741530935L), - static_cast<T>(-0.00701721240549802377623L), - static_cast<T>(-0.229257310594893932383e-4L), - }; - static const T Q[9] = { - 1.0f, - static_cast<T>(0.706039025937745133628L), - static_cast<T>(0.15739599649558626358L), - static_cast<T>(0.0106117950976845084417L), - static_cast<T>(-0.36910273311764618902e-4L), - static_cast<T>(0.493409563927590008943e-5L), - static_cast<T>(-0.234055487025287216506e-6L), - static_cast<T>(0.718833729365459760664e-8L), - static_cast<T>(-0.1129200113474947419e-9L), - }; - result = tools::evaluate_polynomial(P, T(s - 4)) / tools::evaluate_polynomial(Q, T(s - 4)); - result = 1 + exp(result); - } - else if(s < 15) - { - // Maximum Deviation Found: 7.117e-16 - // Expected Error Term: 7.117e-16 - // Max error found at double precision: 9.387771e-16 - static const T P[7] = { - static_cast<T>(-4.78558028495135619286L), - static_cast<T>(-1.89197364881972536382L), - static_cast<T>(-0.211407134874412820099L), - static_cast<T>(-0.000189204758260076688518L), - static_cast<T>(0.00115140923889178742086L), - static_cast<T>(0.639949204213164496988e-4L), - static_cast<T>(0.139348932445324888343e-5L), - }; - static const T Q[9] = { - 1.0f, - static_cast<T>(0.244345337378188557777L), - static_cast<T>(0.00873370754492288653669L), - static_cast<T>(-0.00117592765334434471562L), - static_cast<T>(-0.743743682899933180415e-4L), - static_cast<T>(-0.21750464515767984778e-5L), - static_cast<T>(0.471001264003076486547e-8L), - static_cast<T>(-0.833378440625385520576e-10L), - static_cast<T>(0.699841545204845636531e-12L), - }; - result = tools::evaluate_polynomial(P, T(s - 7)) / tools::evaluate_polynomial(Q, T(s - 7)); - result = 1 + exp(result); - } - else if(s < 36) - { - // Max error in interpolated form: 1.668e-17 - // Max error found at long double precision: 1.669714e-17 - static const T P[8] = { - static_cast<T>(-10.3948950573308896825L), - static_cast<T>(-2.85827219671106697179L), - static_cast<T>(-0.347728266539245787271L), - static_cast<T>(-0.0251156064655346341766L), - static_cast<T>(-0.00119459173416968685689L), - static_cast<T>(-0.382529323507967522614e-4L), - static_cast<T>(-0.785523633796723466968e-6L), - static_cast<T>(-0.821465709095465524192e-8L), - }; - static const T Q[10] = { - 1.0f, - static_cast<T>(0.208196333572671890965L), - static_cast<T>(0.0195687657317205033485L), - static_cast<T>(0.00111079638102485921877L), - static_cast<T>(0.408507746266039256231e-4L), - static_cast<T>(0.955561123065693483991e-6L), - static_cast<T>(0.118507153474022900583e-7L), - static_cast<T>(0.222609483627352615142e-14L), - }; - result = tools::evaluate_polynomial(P, T(s - 15)) / tools::evaluate_polynomial(Q, T(s - 15)); - result = 1 + exp(result); - } - else if(s < 56) - { - result = 1 + pow(T(2), -s); - } - else - { - result = 1; - } - return result; -} - -template <class T, class Policy> -T zeta_imp_prec(T s, T sc, const Policy&, const mpl::int_<64>&) -{ - BOOST_MATH_STD_USING - T result; - if(s < 1) - { - // Rational Approximation - // Maximum Deviation Found: 3.099e-20 - // Expected Error Term: 3.099e-20 - // Max error found at long double precision: 5.890498e-20 - static const T P[6] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 0.243392944335937499969), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.496837806864865688082), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0680008039723709987107), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.00511620413006619942112), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000455369899250053003335), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.279496685273033761927e-4), - }; - static const T Q[7] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.30425480068225790522), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.050052748580371598736), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.00519355671064700627862), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000360623385771198350257), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.159600883054550987633e-4), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.339770279812410586032e-6), - }; - result = tools::evaluate_polynomial(P, sc) / tools::evaluate_polynomial(Q, sc); - result -= 1.2433929443359375F; - result += (sc); - result /= (sc); - } - else if(s <= 2) - { - // Maximum Deviation Found: 1.059e-21 - // Expected Error Term: 1.059e-21 - // Max error found at long double precision: 1.626303e-19 - - static const T P[6] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 0.577215664901532860605), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.222537368917162139445), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0356286324033215682729), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00304465292366350081446), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000178102511649069421904), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.700867470265983665042e-5), - }; - static const T Q[7] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.259385759149531030085), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0373974962106091316854), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00332735159183332820617), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000188690420706998606469), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.635994377921861930071e-5), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.226583954978371199405e-7), - }; - result = tools::evaluate_polynomial(P, T(-sc)) / tools::evaluate_polynomial(Q, T(-sc)); - result += 1 / (-sc); - } - else if(s <= 4) - { - // Maximum Deviation Found: 5.946e-22 - // Expected Error Term: -5.946e-22 - static const float Y = 0.6986598968505859375; - static const T P[7] = { - BOOST_MATH_BIG_CONSTANT(T, 64, -0.053725830002359501027), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0470551187571475844778), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0101339410415759517471), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00100240326666092854528), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.685027119098122814867e-4), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.390972820219765942117e-5), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.540319769113543934483e-7), - }; - static const T Q[8] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.286577739726542730421), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0447355811517733225843), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00430125107610252363302), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000284956969089786662045), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.116188101609848411329e-4), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.278090318191657278204e-6), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.19683620233222028478e-8), - }; - result = tools::evaluate_polynomial(P, T(s - 2)) / tools::evaluate_polynomial(Q, T(s - 2)); - result += Y + 1 / (-sc); - } - else if(s <= 7) - { - // Max error found at long double precision: 8.132216e-19 - static const T P[8] = { - BOOST_MATH_BIG_CONSTANT(T, 64, -2.49710190602259407065), - BOOST_MATH_BIG_CONSTANT(T, 64, -3.36664913245960625334), - BOOST_MATH_BIG_CONSTANT(T, 64, -1.77180020623777595452), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.464717885249654313933), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.0643694921293579472583), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.00464265386202805715487), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.000165556579779704340166), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.252884970740994069582e-5), - }; - static const T Q[9] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 1.01300131390690459085), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.387898115758643503827), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0695071490045701135188), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00586908595251442839291), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000217752974064612188616), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.397626583349419011731e-5), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.927884739284359700764e-8), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.119810501805618894381e-9), - }; - result = tools::evaluate_polynomial(P, T(s - 4)) / tools::evaluate_polynomial(Q, T(s - 4)); - result = 1 + exp(result); - } - else if(s < 15) - { - // Max error in interpolated form: 1.133e-18 - // Max error found at long double precision: 2.183198e-18 - static const T P[9] = { - BOOST_MATH_BIG_CONSTANT(T, 64, -4.78558028495135548083), - BOOST_MATH_BIG_CONSTANT(T, 64, -3.23873322238609358947), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.892338582881021799922), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.131326296217965913809), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.0115651591773783712996), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.000657728968362695775205), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.252051328129449973047e-4), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.626503445372641798925e-6), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.815696314790853893484e-8), - }; - static const T Q[9] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.525765665400123515036), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.10852641753657122787), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0115669945375362045249), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.000732896513858274091966), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.30683952282420248448e-4), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.819649214609633126119e-6), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.117957556472335968146e-7), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.193432300973017671137e-12), - }; - result = tools::evaluate_polynomial(P, T(s - 7)) / tools::evaluate_polynomial(Q, T(s - 7)); - result = 1 + exp(result); - } - else if(s < 42) - { - // Max error in interpolated form: 1.668e-17 - // Max error found at long double precision: 1.669714e-17 - static const T P[9] = { - BOOST_MATH_BIG_CONSTANT(T, 64, -10.3948950573308861781), - BOOST_MATH_BIG_CONSTANT(T, 64, -2.82646012777913950108), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.342144362739570333665), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.0249285145498722647472), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.00122493108848097114118), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.423055371192592850196e-4), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.1025215577185967488e-5), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.165096762663509467061e-7), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.145392555873022044329e-9), - }; - static const T Q[10] = { - BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.205135978585281988052), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.0192359357875879453602), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.00111496452029715514119), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.434928449016693986857e-4), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.116911068726610725891e-5), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.206704342290235237475e-7), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.209772836100827647474e-9), - BOOST_MATH_BIG_CONSTANT(T, 64, -0.939798249922234703384e-16), - BOOST_MATH_BIG_CONSTANT(T, 64, 0.264584017421245080294e-18), - }; - result = tools::evaluate_polynomial(P, T(s - 15)) / tools::evaluate_polynomial(Q, T(s - 15)); - result = 1 + exp(result); - } - else if(s < 63) - { - result = 1 + pow(T(2), -s); - } - else - { - result = 1; - } - return result; -} - -template <class T, class Policy> -T zeta_imp_prec(T s, T sc, const Policy&, const mpl::int_<113>&) -{ - BOOST_MATH_STD_USING - T result; - if(s < 1) - { - // Rational Approximation - // Maximum Deviation Found: 9.493e-37 - // Expected Error Term: 9.492e-37 - // Max error found at long double precision: 7.281332e-31 - - static const T P[10] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0353008629988648122808504280990313668), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0107795651204927743049369868548706909), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000523961870530500751114866884685172975), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.661805838304910731947595897966487515e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.658932670403818558510656304189164638e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.103437265642266106533814021041010453e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.116818787212666457105375746642927737e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.660690993901506912123512551294239036e-9), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.113103113698388531428914333768142527e-10), - }; - static const T Q[11] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.387483472099602327112637481818565459), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0802265315091063135271497708694776875), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0110727276164171919280036408995078164), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00112552716946286252000434849173787243), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.874554160748626916455655180296834352e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.530097847491828379568636739662278322e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.248461553590496154705565904497247452e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.881834921354014787309644951507523899e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.217062446168217797598596496310953025e-9), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.315823200002384492377987848307151168e-11), - }; - result = tools::evaluate_polynomial(P, sc) / tools::evaluate_polynomial(Q, sc); - result += (sc); - result /= (sc); - } - else if(s <= 2) - { - // Maximum Deviation Found: 1.616e-37 - // Expected Error Term: -1.615e-37 - - static const T P[10] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 0.577215664901532860606512090082402431), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.255597968739771510415479842335906308), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0494056503552807274142218876983542205), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00551372778611700965268920983472292325), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00043667616723970574871427830895192731), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.268562259154821957743669387915239528e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.109249633923016310141743084480436612e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.273895554345300227466534378753023924e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.583103205551702720149237384027795038e-9), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.835774625259919268768735944711219256e-11), - }; - static const T Q[11] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.316661751179735502065583176348292881), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0540401806533507064453851182728635272), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00598621274107420237785899476374043797), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000474907812321704156213038740142079615), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.272125421722314389581695715835862418e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.112649552156479800925522445229212933e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.301838975502992622733000078063330461e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.422960728687211282539769943184270106e-9), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.377105263588822468076813329270698909e-11), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.581926559304525152432462127383600681e-13), - }; - result = tools::evaluate_polynomial(P, T(-sc)) / tools::evaluate_polynomial(Q, T(-sc)); - result += 1 / (-sc); - } - else if(s <= 4) - { - // Maximum Deviation Found: 1.891e-36 - // Expected Error Term: -1.891e-36 - // Max error found: 2.171527e-35 - - static const float Y = 0.6986598968505859375; - static const T P[11] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0537258300023595010275848333539748089), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0429086930802630159457448174466342553), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0136148228754303412510213395034056857), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00190231601036042925183751238033763915), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000186880390916311438818302549192456581), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.145347370745893262394287982691323657e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.805843276446813106414036600485884885e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.340818159286739137503297172091882574e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.115762357488748996526167305116837246e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.231904754577648077579913403645767214e-10), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.340169592866058506675897646629036044e-12), - }; - static const T Q[12] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.363755247765087100018556983050520554), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0696581979014242539385695131258321598), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00882208914484611029571547753782014817), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000815405623261946661762236085660996718), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.571366167062457197282642344940445452e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.309278269271853502353954062051797838e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.12822982083479010834070516053794262e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.397876357325018976733953479182110033e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.8484432107648683277598472295289279e-10), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.105677416606909614301995218444080615e-11), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.547223964564003701979951154093005354e-15), - }; - result = tools::evaluate_polynomial(P, T(s - 2)) / tools::evaluate_polynomial(Q, T(s - 2)); - result += Y + 1 / (-sc); - } - else if(s <= 6) - { - // Max error in interpolated form: 1.510e-37 - // Max error found at long double precision: 2.769266e-34 - - static const T Y = 3.28348541259765625F; - - static const T P[13] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 0.786383506575062179339611614117697622), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.495766593395271370974685959652073976), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.409116737851754766422360889037532228), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.57340744006238263817895456842655987), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.280479899797421910694892949057963111), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0753148409447590257157585696212649869), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0122934003684672788499099362823748632), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.00126148398446193639247961370266962927), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.828465038179772939844657040917364896e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.361008916706050977143208468690645684e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.109879825497910544424797771195928112e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.214539416789686920918063075528797059e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.15090220092460596872172844424267351e-10), - }; - static const T Q[14] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.69490865837142338462982225731926485), - BOOST_MATH_BIG_CONSTANT(T, 113, 1.22697696630994080733321401255942464), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.495409420862526540074366618006341533), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.122368084916843823462872905024259633), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0191412993625268971656513890888208623), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00191401538628980617753082598351559642), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000123318142456272424148930280876444459), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.531945488232526067889835342277595709e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.161843184071894368337068779669116236e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.305796079600152506743828859577462778e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.233582592298450202680170811044408894e-10), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.275363878344548055574209713637734269e-13), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.221564186807357535475441900517843892e-15), - }; - result = tools::evaluate_polynomial(P, T(s - 4)) / tools::evaluate_polynomial(Q, T(s - 4)); - result -= Y; - result = 1 + exp(result); - } - else if(s < 10) - { - // Max error in interpolated form: 1.999e-34 - // Max error found at long double precision: 2.156186e-33 - - static const T P[13] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -4.0545627381873738086704293881227365), - BOOST_MATH_BIG_CONSTANT(T, 113, -4.70088348734699134347906176097717782), - BOOST_MATH_BIG_CONSTANT(T, 113, -2.36921550900925512951976617607678789), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.684322583796369508367726293719322866), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.126026534540165129870721937592996324), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.015636903921778316147260572008619549), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.00135442294754728549644376325814460807), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.842793965853572134365031384646117061e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.385602133791111663372015460784978351e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.130458500394692067189883214401478539e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.315861074947230418778143153383660035e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.500334720512030826996373077844707164e-10), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.420204769185233365849253969097184005e-12), - }; - static const T Q[14] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.97663511666410096104783358493318814), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.40878780231201806504987368939673249), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0963890666609396058945084107597727252), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0142207619090854604824116070866614505), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00139010220902667918476773423995750877), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.940669540194694997889636696089994734e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.458220848507517004399292480807026602e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.16345521617741789012782420625435495e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.414007452533083304371566316901024114e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.68701473543366328016953742622661377e-10), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.603461891080716585087883971886075863e-12), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.294670713571839023181857795866134957e-16), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.147003914536437243143096875069813451e-18), - }; - result = tools::evaluate_polynomial(P, T(s - 6)) / tools::evaluate_polynomial(Q, T(s - 6)); - result = 1 + exp(result); - } - else if(s < 17) - { - // Max error in interpolated form: 1.641e-32 - // Max error found at long double precision: 1.696121e-32 - static const T P[13] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -6.91319491921722925920883787894829678), - BOOST_MATH_BIG_CONSTANT(T, 113, -3.65491257639481960248690596951049048), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.813557553449954526442644544105257881), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0994317301685870959473658713841138083), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.00726896610245676520248617014211734906), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.000317253318715075854811266230916762929), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.66851422826636750855184211580127133e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.879464154730985406003332577806849971e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.113838903158254250631678791998294628e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.379184410304927316385211327537817583e-9), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.612992858643904887150527613446403867e-11), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.347873737198164757035457841688594788e-13), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.289187187441625868404494665572279364e-15), - }; - static const T Q[14] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.427310044448071818775721584949868806), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.074602514873055756201435421385243062), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00688651562174480772901425121653945942), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000360174847635115036351323894321880445), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.973556847713307543918865405758248777e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.853455848314516117964634714780874197e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.118203513654855112421673192194622826e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.462521662511754117095006543363328159e-9), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.834212591919475633107355719369463143e-11), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.5354594751002702935740220218582929e-13), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.406451690742991192964889603000756203e-15), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.887948682401000153828241615760146728e-19), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.34980761098820347103967203948619072e-21), - }; - result = tools::evaluate_polynomial(P, T(s - 10)) / tools::evaluate_polynomial(Q, T(s - 10)); - result = 1 + exp(result); - } - else if(s < 30) - { - // Max error in interpolated form: 1.563e-31 - // Max error found at long double precision: 1.562725e-31 - - static const T P[13] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -11.7824798233959252791987402769438322), - BOOST_MATH_BIG_CONSTANT(T, 113, -4.36131215284987731928174218354118102), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.732260980060982349410898496846972204), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0744985185694913074484248803015717388), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.00517228281320594683022294996292250527), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.000260897206152101522569969046299309939), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.989553462123121764865178453128769948e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.286916799741891410827712096608826167e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.637262477796046963617949532211619729e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.106796831465628373325491288787760494e-9), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.129343095511091870860498356205376823e-11), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.102397936697965977221267881716672084e-13), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.402663128248642002351627980255756363e-16), - }; - static const T Q[14] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.311288325355705609096155335186466508), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0438318468940415543546769437752132748), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.00374396349183199548610264222242269536), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.000218707451200585197339671707189281302), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.927578767487930747532953583797351219e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.294145760625753561951137473484889639e-6), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.704618586690874460082739479535985395e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.126333332872897336219649130062221257e-9), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.16317315713773503718315435769352765e-11), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.137846712823719515148344938160275695e-13), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.580975420554224366450994232723910583e-16), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.291354445847552426900293580511392459e-22), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.73614324724785855925025452085443636e-25), - }; - result = tools::evaluate_polynomial(P, T(s - 17)) / tools::evaluate_polynomial(Q, T(s - 17)); - result = 1 + exp(result); - } - else if(s < 74) - { - // Max error in interpolated form: 2.311e-27 - // Max error found at long double precision: 2.297544e-27 - static const T P[14] = { - BOOST_MATH_BIG_CONSTANT(T, 113, -20.7944102007844314586649688802236072), - BOOST_MATH_BIG_CONSTANT(T, 113, -4.95759941987499442499908748130192187), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.563290752832461751889194629200298688), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0406197001137935911912457120706122877), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.0020846534789473022216888863613422293), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.808095978462109173749395599401375667e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.244706022206249301640890603610060959e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.589477682919645930544382616501666572e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.113699573675553496343617442433027672e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.174767860183598149649901223128011828e-10), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.210051620306761367764549971980026474e-12), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.189187969537370950337212675466400599e-14), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.116313253429564048145641663778121898e-16), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.376708747782400769427057630528578187e-19), - }; - static const T Q[16] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.205076752981410805177554569784219717), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.0202526722696670378999575738524540269), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.001278305290005994980069466658219057), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.576404779858501791742255670403304787e-4), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.196477049872253010859712483984252067e-5), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.521863830500876189501054079974475762e-7), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.109524209196868135198775445228552059e-8), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.181698713448644481083966260949267825e-10), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.234793316975091282090312036524695562e-12), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.227490441461460571047545264251399048e-14), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.151500292036937400913870642638520668e-16), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.543475775154780935815530649335936121e-19), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.241647013434111434636554455083309352e-28), - BOOST_MATH_BIG_CONSTANT(T, 113, -0.557103423021951053707162364713587374e-31), - BOOST_MATH_BIG_CONSTANT(T, 113, 0.618708773442584843384712258199645166e-34), - }; - result = tools::evaluate_polynomial(P, T(s - 30)) / tools::evaluate_polynomial(Q, T(s - 30)); - result = 1 + exp(result); - } - else if(s < 117) - { - result = 1 + pow(T(2), -s); - } - else - { - result = 1; - } - return result; -} - -template <class T, class Policy> -T zeta_imp_odd_integer(int s, const T&, const Policy&, const mpl::true_&) -{ - static const T results[] = { - BOOST_MATH_BIG_CONSTANT(T, 113, 1.2020569031595942853997381615114500), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0369277551433699263313654864570342), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0083492773819228268397975498497968), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0020083928260822144178527692324121), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0004941886041194645587022825264699), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0001227133475784891467518365263574), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000305882363070204935517285106451), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000076371976378997622736002935630), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000019082127165539389256569577951), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000004769329867878064631167196044), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000001192199259653110730677887189), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000298035035146522801860637051), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000074507117898354294919810042), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000018626597235130490064039099), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000004656629065033784072989233), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000001164155017270051977592974), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000291038504449709968692943), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000072759598350574810145209), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000018189896503070659475848), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000004547473783042154026799), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000001136868407680227849349), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000284217097688930185546), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000071054273952108527129), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000017763568435791203275), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000004440892103143813364), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000001110223025141066134), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000277555756213612417), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000069388939045441537), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000017347234760475766), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000004336808690020650), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000001084202172494241), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000271050543122347), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000067762635780452), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000016940658945098), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000004235164736273), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000001058791184068), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000264697796017), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000066174449004), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000016543612251), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000004135903063), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000001033975766), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000258493941), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000064623485), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000016155871), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000004038968), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000001009742), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000252435), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000063109), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000015777), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000003944), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000000986), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000000247), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000000062), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000000015), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000000004), BOOST_MATH_BIG_CONSTANT(T, 113, 1.0000000000000000000000000000000001), - }; - return s > 113 ? 1 : results[(s - 3) / 2]; -} - -template <class T, class Policy> -T zeta_imp_odd_integer(int s, const T& sc, const Policy& pol, const mpl::false_&) -{ - static BOOST_MATH_THREAD_LOCAL bool is_init = false; - static BOOST_MATH_THREAD_LOCAL T results[50] = {}; - static BOOST_MATH_THREAD_LOCAL int digits = tools::digits<T>(); - int current_digits = tools::digits<T>(); - if(digits != current_digits) - { - // Oh my precision has changed... - is_init = false; - } - if(!is_init) - { - is_init = true; - digits = current_digits; - for(unsigned k = 0; k < sizeof(results) / sizeof(results[0]); ++k) - { - T arg = k * 2 + 3; - T c_arg = 1 - arg; - results[k] = zeta_polynomial_series(arg, c_arg, pol); - } - } - unsigned index = (s - 3) / 2; - return index >= sizeof(results) / sizeof(results[0]) ? zeta_polynomial_series(T(s), sc, pol): results[index]; -} - -template <class T, class Policy, class Tag> -T zeta_imp(T s, T sc, const Policy& pol, const Tag& tag) -{ - BOOST_MATH_STD_USING - static const char* function = "boost::math::zeta<%1%>"; - if(sc == 0) - return policies::raise_pole_error<T>( - function, - "Evaluation of zeta function at pole %1%", - s, pol); - T result; - // - // Trivial case: - // - if(s > policies::digits<T, Policy>()) - return 1; - // - // Start by seeing if we have a simple closed form: - // - if(floor(s) == s) - { -#ifndef BOOST_NO_EXCEPTIONS - // Without exceptions we expect itrunc to return INT_MAX on overflow - // and we fall through anyway. - try - { -#endif - int v = itrunc(s); - if(v == s) - { - if(v < 0) - { - if(((-v) & 1) == 0) - return 0; - int n = (-v + 1) / 2; - if(n <= (int)boost::math::max_bernoulli_b2n<T>::value) - return T((-v & 1) ? -1 : 1) * boost::math::unchecked_bernoulli_b2n<T>(n) / (1 - v); - } - else if((v & 1) == 0) - { - if(((v / 2) <= (int)boost::math::max_bernoulli_b2n<T>::value) && (v <= (int)boost::math::max_factorial<T>::value)) - return T(((v / 2 - 1) & 1) ? -1 : 1) * ldexp(T(1), v - 1) * pow(constants::pi<T, Policy>(), v) * - boost::math::unchecked_bernoulli_b2n<T>(v / 2) / boost::math::unchecked_factorial<T>(v); - return T(((v / 2 - 1) & 1) ? -1 : 1) * ldexp(T(1), v - 1) * pow(constants::pi<T, Policy>(), v) * - boost::math::bernoulli_b2n<T>(v / 2) / boost::math::factorial<T>(v); - } - else - return zeta_imp_odd_integer(v, sc, pol, mpl::bool_<(Tag::value <= 113) && Tag::value>()); - } -#ifndef BOOST_NO_EXCEPTIONS - } - catch(const boost::math::rounding_error&){} // Just fall through, s is too large to round - catch(const std::overflow_error&){} -#endif - } - - if(fabs(s) < tools::root_epsilon<T>()) - { - result = -0.5f - constants::log_root_two_pi<T, Policy>() * s; - } - else if(s < 0) - { - std::swap(s, sc); - if(floor(sc/2) == sc/2) - result = 0; - else - { - if(s > max_factorial<T>::value) - { - T mult = boost::math::sin_pi(0.5f * sc, pol) * 2 * zeta_imp(s, sc, pol, tag); - result = boost::math::lgamma(s, pol); - result -= s * log(2 * constants::pi<T>()); - if(result > tools::log_max_value<T>()) - return sign(mult) * policies::raise_overflow_error<T>(function, 0, pol); - result = exp(result); - if(tools::max_value<T>() / fabs(mult) < result) - return boost::math::sign(mult) * policies::raise_overflow_error<T>(function, 0, pol); - result *= mult; - } - else - { - result = boost::math::sin_pi(0.5f * sc, pol) - * 2 * pow(2 * constants::pi<T>(), -s) - * boost::math::tgamma(s, pol) - * zeta_imp(s, sc, pol, tag); - } - } - } - else - { - result = zeta_imp_prec(s, sc, pol, tag); - } - return result; -} - -template <class T, class Policy, class tag> -struct zeta_initializer -{ - struct init - { - init() - { - do_init(tag()); - } - static void do_init(const mpl::int_<0>&){ boost::math::zeta(static_cast<T>(5), Policy()); } - static void do_init(const mpl::int_<53>&){ boost::math::zeta(static_cast<T>(5), Policy()); } - static void do_init(const mpl::int_<64>&) - { - boost::math::zeta(static_cast<T>(0.5), Policy()); - boost::math::zeta(static_cast<T>(1.5), Policy()); - boost::math::zeta(static_cast<T>(3.5), Policy()); - boost::math::zeta(static_cast<T>(6.5), Policy()); - boost::math::zeta(static_cast<T>(14.5), Policy()); - boost::math::zeta(static_cast<T>(40.5), Policy()); - - boost::math::zeta(static_cast<T>(5), Policy()); - } - static void do_init(const mpl::int_<113>&) - { - boost::math::zeta(static_cast<T>(0.5), Policy()); - boost::math::zeta(static_cast<T>(1.5), Policy()); - boost::math::zeta(static_cast<T>(3.5), Policy()); - boost::math::zeta(static_cast<T>(5.5), Policy()); - boost::math::zeta(static_cast<T>(9.5), Policy()); - boost::math::zeta(static_cast<T>(16.5), Policy()); - boost::math::zeta(static_cast<T>(25.5), Policy()); - boost::math::zeta(static_cast<T>(70.5), Policy()); - - boost::math::zeta(static_cast<T>(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 zeta_initializer<T, Policy, tag>::init zeta_initializer<T, Policy, tag>::initializer; - -} // detail - -template <class T, class Policy> -inline typename tools::promote_args<T>::type zeta(T s, const Policy&) -{ - 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; - 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; - //typedef mpl::int_<0> tag_type; - - detail::zeta_initializer<value_type, forwarding_policy, tag_type>::force_instantiate(); - - return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::zeta_imp( - static_cast<value_type>(s), - static_cast<value_type>(1 - static_cast<value_type>(s)), - forwarding_policy(), - tag_type()), "boost::math::zeta<%1%>(%1%)"); -} - -template <class T> -inline typename tools::promote_args<T>::type zeta(T s) -{ - return zeta(s, policies::policy<>()); -} - -}} // namespaces - -#endif // BOOST_MATH_ZETA_HPP - - - |