FM / detail

/usr/include/boost/math/special_functions/detail/

/usr/include/boost/math/special_functions/detail

Name	Size	Mode	Actions
airy_ai_bi_zero.hpp	6294	0644	edit dl rm
bernoulli_details.hpp	26513	0644	edit dl rm
bessel_derivatives_linear.hpp	3378	0644	edit dl rm
bessel_i0.hpp	28135	0644	edit dl rm
bessel_i1.hpp	29933	0644	edit dl rm
bessel_ik.hpp	13917	0644	edit dl rm
bessel_j0.hpp	8585	0644	edit dl rm
bessel_j1.hpp	8951	0644	edit dl rm
bessel_jn.hpp	3909	0644	edit dl rm
bessel_jy.hpp	21868	0644	edit dl rm
bessel_jy_asym.hpp	6488	0644	edit dl rm
bessel_jy_derivatives_asym.hpp	4649	0644	edit dl rm
bessel_jy_derivatives_series.hpp	6944	0644	edit dl rm
bessel_jy_series.hpp	7241	0644	edit dl rm
bessel_jy_zero.hpp	24967	0644	edit dl rm
bessel_k0.hpp	22178	0644	edit dl rm
bessel_k1.hpp	25465	0644	edit dl rm
bessel_kn.hpp	2249	0644	edit dl rm
bessel_y0.hpp	10805	0644	edit dl rm
bessel_y1.hpp	9458	0644	edit dl rm
bessel_yn.hpp	3118	0644	edit dl rm
daubechies_scaling_integer_grid.hpp	233788	0644	edit dl rm
erf_inv.hpp	22738	0644	edit dl rm
fp_traits.hpp	17193	0644	edit dl rm
gamma_inva.hpp	7066	0644	edit dl rm
hypergeometric_0F1_bessel.hpp	1543	0644	edit dl rm
hypergeometric_1F1_addition_theorems_on_z.hpp	12980	0644	edit dl rm
hypergeometric_1F1_bessel.hpp	32781	0644	edit dl rm
hypergeometric_1F1_by_ratios.hpp	33540	0644	edit dl rm
hypergeometric_1F1_cf.hpp	1830	0644	edit dl rm
hypergeometric_1F1_large_a.hpp	1159	0644	edit dl rm
hypergeometric_1F1_large_abz.hpp	22101	0644	edit dl rm
hypergeometric_1F1_negative_b_regions.hpp	33376	0644	edit dl rm
hypergeometric_1F1_recurrence.hpp	17295	0644	edit dl rm
hypergeometric_1F1_scaled_series.hpp	2183	0644	edit dl rm
hypergeometric_1F1_small_a_negative_b_by_ratio.hpp	3893	0644	edit dl rm
hypergeometric_asym.hpp	5902	0644	edit dl rm
hypergeometric_cf.hpp	5826	0644	edit dl rm
hypergeometric_pade.hpp	3837	0644	edit dl rm
hypergeometric_pFq_checked_series.hpp	27943	0644	edit dl rm
hypergeometric_rational.hpp	5068	0644	edit dl rm
hypergeometric_separated_series.hpp	1449	0644	edit dl rm
hypergeometric_series.hpp	14422	0644	edit dl rm
ibeta_inverse.hpp	34072	0644	edit dl rm
ibeta_inv_ab.hpp	10363	0644	edit dl rm
iconv.hpp	1009	0644	edit dl rm
igamma_inverse.hpp	17414	0644	edit dl rm
igamma_large.hpp	39534	0644	edit dl rm
lambert_w_lookup_table.ipp	15601	0644	edit dl rm
lanczos_sse2.hpp	8916	0644	edit dl rm
lgamma_small.hpp	23295	0644	edit dl rm
polygamma.hpp	22596	0644	edit dl rm
round_fwd.hpp	2794	0644	edit dl rm
t_distribution_inv.hpp	17735	0644	edit dl rm
unchecked_bernoulli.hpp	76437	0644	edit dl rm
unchecked_factorial.hpp	46290	0644	edit dl rm

Edit: /usr/include/boost/math/special_functions/detail/lanczos_sse2.hpp (8916B)

#ifndef BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS_SSE2
#define BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS_SSE2

#ifdef _MSC_VER
#pragma once
#endif

#include <emmintrin.h>

#if defined(__GNUC__) || defined(__PGI) || defined(__SUNPRO_CC)
#define ALIGN16 __attribute__((__aligned__(16)))
#else
#define ALIGN16 __declspec(align(16))
#endif

namespace boost{ namespace math{ namespace lanczos{

template <>
inline double lanczos13m53::lanczos_sum<double>(const double& x)
{
   static const ALIGN16 double coeff[26] = {
      static_cast<double>(2.506628274631000270164908177133837338626L),
      static_cast<double>(1u),
      static_cast<double>(210.8242777515793458725097339207133627117L),
      static_cast<double>(66u),
      static_cast<double>(8071.672002365816210638002902272250613822L),
      static_cast<double>(1925u),
      static_cast<double>(186056.2653952234950402949897160456992822L),
      static_cast<double>(32670u),
      static_cast<double>(2876370.628935372441225409051620849613599L),
      static_cast<double>(357423u),
      static_cast<double>(31426415.58540019438061423162831820536287L),
      static_cast<double>(2637558u),
      static_cast<double>(248874557.8620541565114603864132294232163L),
      static_cast<double>(13339535u),
      static_cast<double>(1439720407.311721673663223072794912393972L),
      static_cast<double>(45995730u),
      static_cast<double>(6039542586.35202800506429164430729792107L),
      static_cast<double>(105258076u),
      static_cast<double>(17921034426.03720969991975575445893111267L),
      static_cast<double>(150917976u),
      static_cast<double>(35711959237.35566804944018545154716670596L),
      static_cast<double>(120543840u),
      static_cast<double>(42919803642.64909876895789904700198885093L),
      static_cast<double>(39916800u),
      static_cast<double>(23531376880.41075968857200767445163675473L),
      static_cast<double>(0u)
   };

static const double lim = 4.31965e+25; // By experiment, the largest x for which the SSE2 code does not go bad.

if (x > lim)
   {
      double z = 1 / x;
      return ((((((((((((coeff[24] * z + coeff[22]) * z + coeff[20]) * z + coeff[18]) * z + coeff[16]) * z + coeff[14]) * z + coeff[12]) * z + coeff[10]) * z + coeff[8]) * z + coeff[6]) * z + coeff[4]) * z + coeff[2]) * z + coeff[0]) / ((((((((((((coeff[25] * z + coeff[23]) * z + coeff[21]) * z + coeff[19]) * z + coeff[17]) * z + coeff[15]) * z + coeff[13]) * z + coeff[11]) * z + coeff[9]) * z + coeff[7]) * z + coeff[5]) * z + coeff[3]) * z + coeff[1]);
   }

__m128d vx = _mm_load1_pd(&x);
   __m128d sum_even = _mm_load_pd(coeff);
   __m128d sum_odd = _mm_load_pd(coeff+2);
   __m128d nc_odd, nc_even;
   __m128d vx2 = _mm_mul_pd(vx, vx);

sum_even = _mm_mul_pd(sum_even, vx2);
   nc_even = _mm_load_pd(coeff + 4);
   sum_odd = _mm_mul_pd(sum_odd, vx2);
   nc_odd = _mm_load_pd(coeff + 6);
   sum_even = _mm_add_pd(sum_even, nc_even);
   sum_odd = _mm_add_pd(sum_odd, nc_odd);

sum_even = _mm_mul_pd(sum_even, vx2);
   nc_even = _mm_load_pd(coeff + 8);
   sum_odd = _mm_mul_pd(sum_odd, vx2);
   nc_odd = _mm_load_pd(coeff + 10);
   sum_even = _mm_add_pd(sum_even, nc_even);
   sum_odd = _mm_add_pd(sum_odd, nc_odd);

sum_even = _mm_mul_pd(sum_even, vx2);
   nc_even = _mm_load_pd(coeff + 12);
   sum_odd = _mm_mul_pd(sum_odd, vx2);
   nc_odd = _mm_load_pd(coeff + 14);
   sum_even = _mm_add_pd(sum_even, nc_even);
   sum_odd = _mm_add_pd(sum_odd, nc_odd);

sum_even = _mm_mul_pd(sum_even, vx2);
   nc_even = _mm_load_pd(coeff + 16);
   sum_odd = _mm_mul_pd(sum_odd, vx2);
   nc_odd = _mm_load_pd(coeff + 18);
   sum_even = _mm_add_pd(sum_even, nc_even);
   sum_odd = _mm_add_pd(sum_odd, nc_odd);

sum_even = _mm_mul_pd(sum_even, vx2);
   nc_even = _mm_load_pd(coeff + 20);
   sum_odd = _mm_mul_pd(sum_odd, vx2);
   nc_odd = _mm_load_pd(coeff + 22);
   sum_even = _mm_add_pd(sum_even, nc_even);
   sum_odd = _mm_add_pd(sum_odd, nc_odd);

sum_even = _mm_mul_pd(sum_even, vx2);
   nc_even = _mm_load_pd(coeff + 24);
   sum_odd = _mm_mul_pd(sum_odd, vx);
   sum_even = _mm_add_pd(sum_even, nc_even);
   sum_even = _mm_add_pd(sum_even, sum_odd);

double ALIGN16 t[2];
   _mm_store_pd(t, sum_even);
   
   return t[0] / t[1];
}

template <>
inline double lanczos13m53::lanczos_sum_expG_scaled<double>(const double& x)
{
   static const ALIGN16 double coeff[26] = {
         static_cast<double>(0.006061842346248906525783753964555936883222L),
         static_cast<double>(1u),
         static_cast<double>(0.5098416655656676188125178644804694509993L),
         static_cast<double>(66u),
         static_cast<double>(19.51992788247617482847860966235652136208L),
         static_cast<double>(1925u),
         static_cast<double>(449.9445569063168119446858607650988409623L),
         static_cast<double>(32670u),
         static_cast<double>(6955.999602515376140356310115515198987526L),
         static_cast<double>(357423u),
         static_cast<double>(75999.29304014542649875303443598909137092L),
         static_cast<double>(2637558u),
         static_cast<double>(601859.6171681098786670226533699352302507L),
         static_cast<double>(13339535u),
         static_cast<double>(3481712.15498064590882071018964774556468L),
         static_cast<double>(45995730u),
         static_cast<double>(14605578.08768506808414169982791359218571L),
         static_cast<double>(105258076u),
         static_cast<double>(43338889.32467613834773723740590533316085L),
         static_cast<double>(150917976u),
         static_cast<double>(86363131.28813859145546927288977868422342L),
         static_cast<double>(120543840u),
         static_cast<double>(103794043.1163445451906271053616070238554L),
         static_cast<double>(39916800u),
         static_cast<double>(56906521.91347156388090791033559122686859L),
         static_cast<double>(0u)
   };

static const double lim = 4.76886e+25; // By experiment, the largest x for which the SSE2 code does not go bad.

__m128d vx = _mm_load1_pd(&x);
   __m128d sum_even = _mm_load_pd(coeff);
   __m128d sum_odd = _mm_load_pd(coeff+2);
   __m128d nc_odd, nc_even;
   __m128d vx2 = _mm_mul_pd(vx, vx);

double ALIGN16 t[2];
   _mm_store_pd(t, sum_even);
   
   return t[0] / t[1];
}

#ifdef _MSC_VER

BOOST_STATIC_ASSERT(sizeof(double) == sizeof(long double));

template <>
inline long double lanczos13m53::lanczos_sum<long double>(const long double& x)
{
   return lanczos_sum<double>(static_cast<double>(x));
}
template <>
inline long double lanczos13m53::lanczos_sum_expG_scaled<long double>(const long double& x)
{
   return lanczos_sum_expG_scaled<double>(static_cast<double>(x));
}
#endif

} // namespace lanczos
} // namespace math
} // namespace boost

#undef ALIGN16

#endif // BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS

// (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_FUNCTIONS_LANCZOS_SSE2 #define BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS_SSE2 #ifdef _MSC_VER #pragma once #endif #include #if defined(__GNUC__) || defined(__PGI) || defined(__SUNPRO_CC) #define ALIGN16 __attribute__((__aligned__(16))) #else #define ALIGN16 __declspec(align(16)) #endif namespace boost{ namespace math{ namespace lanczos{ template <> inline double lanczos13m53::lanczos_sum(const double& x) { static const ALIGN16 double coeff[26] = { static_cast(2.506628274631000270164908177133837338626L), static_cast(1u), static_cast(210.8242777515793458725097339207133627117L), static_cast(66u), static_cast(8071.672002365816210638002902272250613822L), static_cast(1925u), static_cast(186056.2653952234950402949897160456992822L), static_cast(32670u), static_cast(2876370.628935372441225409051620849613599L), static_cast(357423u), static_cast(31426415.58540019438061423162831820536287L), static_cast(2637558u), static_cast(248874557.8620541565114603864132294232163L), static_cast(13339535u), static_cast(1439720407.311721673663223072794912393972L), static_cast(45995730u), static_cast(6039542586.35202800506429164430729792107L), static_cast(105258076u), static_cast(17921034426.03720969991975575445893111267L), static_cast(150917976u), static_cast(35711959237.35566804944018545154716670596L), static_cast(120543840u), static_cast(42919803642.64909876895789904700198885093L), static_cast(39916800u), static_cast(23531376880.41075968857200767445163675473L), static_cast(0u) }; static const double lim = 4.31965e+25; // By experiment, the largest x for which the SSE2 code does not go bad. if (x > lim) { double z = 1 / x; return ((((((((((((coeff[24] * z + coeff[22]) * z + coeff[20]) * z + coeff[18]) * z + coeff[16]) * z + coeff[14]) * z + coeff[12]) * z + coeff[10]) * z + coeff[8]) * z + coeff[6]) * z + coeff[4]) * z + coeff[2]) * z + coeff[0]) / ((((((((((((coeff[25] * z + coeff[23]) * z + coeff[21]) * z + coeff[19]) * z + coeff[17]) * z + coeff[15]) * z + coeff[13]) * z + coeff[11]) * z + coeff[9]) * z + coeff[7]) * z + coeff[5]) * z + coeff[3]) * z + coeff[1]); } __m128d vx = _mm_load1_pd(&x); __m128d sum_even = _mm_load_pd(coeff); __m128d sum_odd = _mm_load_pd(coeff+2); __m128d nc_odd, nc_even; __m128d vx2 = _mm_mul_pd(vx, vx); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 4); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 6); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 8); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 10); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 12); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 14); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 16); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 18); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 20); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 22); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 24); sum_odd = _mm_mul_pd(sum_odd, vx); sum_even = _mm_add_pd(sum_even, nc_even); sum_even = _mm_add_pd(sum_even, sum_odd); double ALIGN16 t[2]; _mm_store_pd(t, sum_even); return t[0] / t[1]; } template <> inline double lanczos13m53::lanczos_sum_expG_scaled(const double& x) { static const ALIGN16 double coeff[26] = { static_cast(0.006061842346248906525783753964555936883222L), static_cast(1u), static_cast(0.5098416655656676188125178644804694509993L), static_cast(66u), static_cast(19.51992788247617482847860966235652136208L), static_cast(1925u), static_cast(449.9445569063168119446858607650988409623L), static_cast(32670u), static_cast(6955.999602515376140356310115515198987526L), static_cast(357423u), static_cast(75999.29304014542649875303443598909137092L), static_cast(2637558u), static_cast(601859.6171681098786670226533699352302507L), static_cast(13339535u), static_cast(3481712.15498064590882071018964774556468L), static_cast(45995730u), static_cast(14605578.08768506808414169982791359218571L), static_cast(105258076u), static_cast(43338889.32467613834773723740590533316085L), static_cast(150917976u), static_cast(86363131.28813859145546927288977868422342L), static_cast(120543840u), static_cast(103794043.1163445451906271053616070238554L), static_cast(39916800u), static_cast(56906521.91347156388090791033559122686859L), static_cast(0u) }; static const double lim = 4.76886e+25; // By experiment, the largest x for which the SSE2 code does not go bad. if (x > lim) { double z = 1 / x; return ((((((((((((coeff[24] * z + coeff[22]) * z + coeff[20]) * z + coeff[18]) * z + coeff[16]) * z + coeff[14]) * z + coeff[12]) * z + coeff[10]) * z + coeff[8]) * z + coeff[6]) * z + coeff[4]) * z + coeff[2]) * z + coeff[0]) / ((((((((((((coeff[25] * z + coeff[23]) * z + coeff[21]) * z + coeff[19]) * z + coeff[17]) * z + coeff[15]) * z + coeff[13]) * z + coeff[11]) * z + coeff[9]) * z + coeff[7]) * z + coeff[5]) * z + coeff[3]) * z + coeff[1]); } __m128d vx = _mm_load1_pd(&x); __m128d sum_even = _mm_load_pd(coeff); __m128d sum_odd = _mm_load_pd(coeff+2); __m128d nc_odd, nc_even; __m128d vx2 = _mm_mul_pd(vx, vx); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 4); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 6); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 8); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 10); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 12); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 14); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 16); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 18); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 20); sum_odd = _mm_mul_pd(sum_odd, vx2); nc_odd = _mm_load_pd(coeff + 22); sum_even = _mm_add_pd(sum_even, nc_even); sum_odd = _mm_add_pd(sum_odd, nc_odd); sum_even = _mm_mul_pd(sum_even, vx2); nc_even = _mm_load_pd(coeff + 24); sum_odd = _mm_mul_pd(sum_odd, vx); sum_even = _mm_add_pd(sum_even, nc_even); sum_even = _mm_add_pd(sum_even, sum_odd); double ALIGN16 t[2]; _mm_store_pd(t, sum_even); return t[0] / t[1]; } #ifdef _MSC_VER BOOST_STATIC_ASSERT(sizeof(double) == sizeof(long double)); template <> inline long double lanczos13m53::lanczos_sum(const long double& x) { return lanczos_sum(static_cast(x)); } template <> inline long double lanczos13m53::lanczos_sum_expG_scaled(const long double& x) { return lanczos_sum_expG_scaled(static_cast(x)); } #endif } // namespace lanczos } // namespace math } // namespace boost #undef ALIGN16 #endif // BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS