Chris@16: //  (C) Copyright John Maddock 2006.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS_SSE2
Chris@16: #define BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS_SSE2
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma once
Chris@16: #endif
Chris@16: 
Chris@16: #include <emmintrin.h>
Chris@16: 
Chris@16: #if defined(__GNUC__) || defined(__PGI)
Chris@16: #define ALIGN16 __attribute__((__aligned__(16)))
Chris@16: #else
Chris@16: #define ALIGN16 __declspec(align(16))
Chris@16: #endif
Chris@16: 
Chris@16: namespace boost{ namespace math{ namespace lanczos{
Chris@16: 
Chris@16: template <>
Chris@16: inline double lanczos13m53::lanczos_sum<double>(const double& x)
Chris@16: {
Chris@16:    static const ALIGN16 double coeff[26] = {
Chris@16:       static_cast<double>(2.506628274631000270164908177133837338626L),
Chris@16:       static_cast<double>(1u),
Chris@16:       static_cast<double>(210.8242777515793458725097339207133627117L),
Chris@16:       static_cast<double>(66u),
Chris@16:       static_cast<double>(8071.672002365816210638002902272250613822L),
Chris@16:       static_cast<double>(1925u),
Chris@16:       static_cast<double>(186056.2653952234950402949897160456992822L),
Chris@16:       static_cast<double>(32670u),
Chris@16:       static_cast<double>(2876370.628935372441225409051620849613599L),
Chris@16:       static_cast<double>(357423u),
Chris@16:       static_cast<double>(31426415.58540019438061423162831820536287L),
Chris@16:       static_cast<double>(2637558u),
Chris@16:       static_cast<double>(248874557.8620541565114603864132294232163L),
Chris@16:       static_cast<double>(13339535u),
Chris@16:       static_cast<double>(1439720407.311721673663223072794912393972L),
Chris@16:       static_cast<double>(45995730u),
Chris@16:       static_cast<double>(6039542586.35202800506429164430729792107L),
Chris@16:       static_cast<double>(105258076u),
Chris@16:       static_cast<double>(17921034426.03720969991975575445893111267L),
Chris@16:       static_cast<double>(150917976u),
Chris@16:       static_cast<double>(35711959237.35566804944018545154716670596L),
Chris@16:       static_cast<double>(120543840u),
Chris@16:       static_cast<double>(42919803642.64909876895789904700198885093L),
Chris@16:       static_cast<double>(39916800u),
Chris@16:       static_cast<double>(23531376880.41075968857200767445163675473L),
Chris@16:       static_cast<double>(0u)
Chris@16:    };
Chris@101:    __m128d vx = _mm_load1_pd(&x);
Chris@101:    __m128d sum_even = _mm_load_pd(coeff);
Chris@101:    __m128d sum_odd = _mm_load_pd(coeff+2);
Chris@101:    __m128d nc_odd, nc_even;
Chris@101:    __m128d vx2 = _mm_mul_pd(vx, vx);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 4);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 6);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 8);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 10);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 12);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 14);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 16);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 18);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 20);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 22);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 24);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_even = _mm_add_pd(sum_even, sum_odd);
Chris@16: 
Chris@16: 
Chris@16:    double ALIGN16 t[2];
Chris@16:    _mm_store_pd(t, sum_even);
Chris@16:    
Chris@16:    return t[0] / t[1];
Chris@16: }
Chris@16: 
Chris@16: template <>
Chris@16: inline double lanczos13m53::lanczos_sum_expG_scaled<double>(const double& x)
Chris@16: {
Chris@16:    static const ALIGN16 double coeff[26] = {
Chris@16:          static_cast<double>(0.006061842346248906525783753964555936883222L),
Chris@16:          static_cast<double>(1u),
Chris@16:          static_cast<double>(0.5098416655656676188125178644804694509993L),
Chris@16:          static_cast<double>(66u),
Chris@16:          static_cast<double>(19.51992788247617482847860966235652136208L),
Chris@16:          static_cast<double>(1925u),
Chris@16:          static_cast<double>(449.9445569063168119446858607650988409623L),
Chris@16:          static_cast<double>(32670u),
Chris@16:          static_cast<double>(6955.999602515376140356310115515198987526L),
Chris@16:          static_cast<double>(357423u),
Chris@16:          static_cast<double>(75999.29304014542649875303443598909137092L),
Chris@16:          static_cast<double>(2637558u),
Chris@16:          static_cast<double>(601859.6171681098786670226533699352302507L),
Chris@16:          static_cast<double>(13339535u),
Chris@16:          static_cast<double>(3481712.15498064590882071018964774556468L),
Chris@16:          static_cast<double>(45995730u),
Chris@16:          static_cast<double>(14605578.08768506808414169982791359218571L),
Chris@16:          static_cast<double>(105258076u),
Chris@16:          static_cast<double>(43338889.32467613834773723740590533316085L),
Chris@16:          static_cast<double>(150917976u),
Chris@16:          static_cast<double>(86363131.28813859145546927288977868422342L),
Chris@16:          static_cast<double>(120543840u),
Chris@16:          static_cast<double>(103794043.1163445451906271053616070238554L),
Chris@16:          static_cast<double>(39916800u),
Chris@16:          static_cast<double>(56906521.91347156388090791033559122686859L),
Chris@16:          static_cast<double>(0u)
Chris@16:    };
Chris@101:    __m128d vx = _mm_load1_pd(&x);
Chris@101:    __m128d sum_even = _mm_load_pd(coeff);
Chris@101:    __m128d sum_odd = _mm_load_pd(coeff+2);
Chris@101:    __m128d nc_odd, nc_even;
Chris@101:    __m128d vx2 = _mm_mul_pd(vx, vx);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 4);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 6);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 8);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 10);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 12);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 14);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 16);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 18);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 20);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx2);
Chris@16:    nc_odd = _mm_load_pd(coeff + 22);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_odd = _mm_add_pd(sum_odd, nc_odd);
Chris@16: 
Chris@16:    sum_even = _mm_mul_pd(sum_even, vx2);
Chris@16:    nc_even = _mm_load_pd(coeff + 24);
Chris@16:    sum_odd = _mm_mul_pd(sum_odd, vx);
Chris@16:    sum_even = _mm_add_pd(sum_even, nc_even);
Chris@16:    sum_even = _mm_add_pd(sum_even, sum_odd);
Chris@16: 
Chris@16: 
Chris@16:    double ALIGN16 t[2];
Chris@16:    _mm_store_pd(t, sum_even);
Chris@16:    
Chris@16:    return t[0] / t[1];
Chris@16: }
Chris@16: 
Chris@16: } // namespace lanczos
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #undef ALIGN16
Chris@16: 
Chris@16: #endif // BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: