boost/math/special_functions/detail/lanczos_sse2.hpp
// (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 <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. 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 static_assert(sizeof(double) == sizeof(long double), "sizeof(long double) != sizeof(double) is not supported"); 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