| // (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) |
| #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) |
| }; |
| register __m128d vx = _mm_load1_pd(&x); |
| register __m128d sum_even = _mm_load_pd(coeff); |
| register __m128d sum_odd = _mm_load_pd(coeff+2); |
| register __m128d nc_odd, nc_even; |
| register __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) |
| }; |
| register __m128d vx = _mm_load1_pd(&x); |
| register __m128d sum_even = _mm_load_pd(coeff); |
| register __m128d sum_odd = _mm_load_pd(coeff+2); |
| register __m128d nc_odd, nc_even; |
| register __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]; |
| } |
| |
| } // namespace lanczos |
| } // namespace math |
| } // namespace boost |
| |
| #endif // BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS |
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