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// (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)
};
__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)
};
__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<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
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