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gradient_avx.cpp
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Wed, Dec 11, 09:06

gradient_avx.cpp
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#include <iostream>
#include <string.h>
#include <cuda_runtime.h>
#include <math.h>
#include <sys/time.h>
#include <fstream>
#include <immintrin.h>
//
#include "structure_hpc.h"
#include "simd_math_avx.h"
#include "gradient.hpp"
//
//#include "iacaMarks.h"
//
//
//
void print256(__m256d __reg)
{
printf("%f\n", ((double*) &__reg)[0]);
printf("%f\n", ((double*) &__reg)[1]);
printf("%f\n", ((double*) &__reg)[2]);
printf("%f\n", ((double*) &__reg)[3]);
}
//
//
//
//
//
//
inline
static
void rotateCoordinateSystem_avx(__m256d Q_x, __m256d Q_y, const __m256d P_x, const __m256d P_y, double* angles)
{
//
__m256d theta = _mm256_loadu_pd(angles);
/*positionning at the potential center*/
__m256d cos_theta = _mm256_cos_pd(theta);
__m256d sin_theta = _mm256_sin_pd(theta);
// rotation: 6 ops
Q_x = P_x*cos_theta + P_y*sin_theta;
Q_y = P_y*cos_theta - P_x*sin_theta;
}
//
//
//
struct point module_potentialDerivatives_totalGradient_SOA_AVX(const struct point *pImage, const struct Potential_SOA *lens, const int nhalos)
{
struct point grad, clumpgrad;
grad.x = 0;
grad.y = 0;
//
// smearing the image coordinates on registers
__m256d image_x = _mm256_set1_pd(pImage->x);
__m256d image_y = _mm256_set1_pd(pImage->y);
//
__m256d __grad_x = _mm256_set1_pd(0.);
__m256d __grad_y = _mm256_set1_pd(0.);
//
int i;
//#pragma unroll
for(i = 0; i < nhalos - nhalos%4; i = i + 4)
{
//IACA_START;
//
__m256d two = _mm256_set1_pd( 2. );
__m256d one = _mm256_set1_pd( 1. );
__m256d zero = _mm256_set1_pd( 0. );
__m256d half = _mm256_set1_pd( 0.5);
__m256d mhalf = _mm256_set1_pd(-0.5);
//
// 2 loads
__m256d true_coord_x = _mm256_sub_pd(image_x, _mm256_loadu_pd(&lens->position_x[i]));
__m256d true_coord_y = _mm256_sub_pd(image_y, _mm256_loadu_pd(&lens->position_y[i]));
// 2 loafs
__m256d rc = _mm256_loadu_pd(&lens->rcore[i]);
__m256d b0 = _mm256_loadu_pd(&lens->b0[i]);
// 2 loads
__m256d eps = _mm256_loadu_pd(&lens->ellipticity_potential[i]);
//
__m256d one_minus_eps = _mm256_sub_pd(one, eps);
__m256d one_plus_eps = _mm256_add_pd(one, eps);
__m256d one_plus_eps_rcp = __INV(one_plus_eps);
// 1 load
__m256d theta = _mm256_loadu_pd(&lens->ellipticity_angle[i]);
/*positionning at the potential center*/
__m256d cos_theta = _mm256_cos_pd(theta);
__m256d sin_theta = _mm256_sin_pd(theta);
// rotation: 6 ops
__m256d x = _mm256_add_pd(_mm256_mul_pd(true_coord_x, cos_theta), _mm256_mul_pd(true_coord_y, sin_theta));
__m256d y = _mm256_sub_pd(_mm256_mul_pd(true_coord_y, cos_theta), _mm256_mul_pd(true_coord_x, sin_theta));
//
__m256d sqe = __SQRT(eps);
//
__m256d cx1 = one_minus_eps*one_plus_eps_rcp; // (1. - eps)/(1. + eps); 3 ops
__m256d cxro = one_plus_eps*one_plus_eps; // (1. + eps)*(1. + eps); 3 ops
__m256d cyro = one_minus_eps*one_minus_eps; // (1. - eps)*(1. - eps); 3 ops
__m256d rem2 = x*x*__INV(cxro) + y*y*__INV(cyro); // x*x/(cxro) + y*y/(cyro); ~5 ops
//
__m256d zci_re = zero;
__m256d zci_im = mhalf*(one - eps*eps)*__INV(sqe); // ~4 ops
// 2.*sqe*sqrt(rc*rc + rem2) - y/cx1, 7 ops
__m256d znum_re = cx1*x;
__m256d znum_im = two*sqe*__SQRT(rc*rc + rem2) - y*__INV(cx1); // ~4 ops
//
__m256d zden_re = x;
__m256d zden_im = _mm256_mul_pd(_mm256_set1_pd(2.), _mm256_mul_pd(rc, sqe));
//
zden_im = _mm256_sub_pd(zden_im, y);
//norm = (zden.re*zden.re + zden.im*zden.im); 3 ops
__m256d norm = (zden_re*zden_re + zden_im*zden_im);
__m256d zis_re = (znum_re*zden_re + znum_im*zden_im)*__INV(norm); // 3 ops
__m256d zis_im = (znum_im*zden_re - znum_re*zden_im)*__INV(norm); // 3 ops
//
norm = zis_re;
//
zis_re = _mm256_log_pd(__SQRT(norm*norm + zis_im*zis_im)); // 3 ops// ln(zis) = ln(|zis|)+i.Arg(zis)
zis_re = _mm256_log_pd(__SQRT(norm*norm + zis_im*zis_im)); // 3 ops// ln(zis) = ln(|zis|)+i.Arg(zis)
zis_im = _mm256_atan2_pd(zis_im, norm); //
//
__m256d zres_re = zci_re*zis_re - zci_im*zis_im; // Re( zci*ln(zis) ) 3 ops
__m256d zres_im = zci_im*zis_re + zis_im*zci_re; // Im( zci*ln(zis) ) 3 ops
/*
zis_re = zres_re;
zis_im = zres_im;
//
cos_theta = _mm256_cos_pd(- theta);
sin_theta = _mm256_sin_pd(- theta);
// rotation: 6 ops
zres_re = _mm256_add_pd(_mm256_mul_pd(zis_re, cos_theta), _mm256_mul_pd(zis_im, sin_theta));
zres_im = _mm256_sub_pd(_mm256_mul_pd(zis_im, cos_theta), _mm256_mul_pd(zis_re, sin_theta));
//
__grad_x += b0*zres_re;
__grad_y += b0*zres_im;
*/
zis_re = b0*zres_re;
zis_im = b0*zres_im;
//
cos_theta = _mm256_cos_pd(zero - theta);
sin_theta = _mm256_sin_pd(zero - theta);
// rotation: 6 ops
__grad_x = __grad_x + _mm256_add_pd(_mm256_mul_pd(zis_re, cos_theta), _mm256_mul_pd(zis_im, sin_theta));
__grad_y = __grad_y + _mm256_sub_pd(_mm256_mul_pd(zis_im, cos_theta), _mm256_mul_pd(zis_re, sin_theta));
//
//__grad_x += _mm256_add_pd(_mm256_mul_pd(zis_re, cos_theta), _mm256_mul_pd(zis_im, sin_theta));
//__grad_y += _mm256_sub_pd(_mm256_mul_pd(zis_im, cos_theta), _mm256_mul_pd(zis_re, sin_theta));
}
//
//
//
grad.x = ((double*) &__grad_x)[0];
grad.x += ((double*) &__grad_x)[1];
grad.x += ((double*) &__grad_x)[2];
grad.x += ((double*) &__grad_x)[3];
//
grad.y = ((double*) &__grad_y)[0];
grad.y += ((double*) &__grad_y)[1];
grad.y += ((double*) &__grad_y)[2];
grad.y += ((double*) &__grad_y)[3];
//
// end of peeling
//
if (nhalos%4 > 0)
{
struct point grad_peel;
grad_peel = module_potentialDerivatives_totalGradient_SOA(pImage, lens, i, nhalos);
//grad_peel = rotateCoordinateSystem(grad_peel, -theta);
//
grad.x += grad_peel.x;
grad.y += grad_peel.y;
}
//
//IACA_END;
//
return(grad);
}
//
//
//
struct point module_potentialDerivatives_totalGradient_81_SOA_AVX(const struct point *pImage, const struct Potential_SOA *lens,const int nhalos)
{
struct point grad, clumpgrad;
grad.x = 0;
grad.y = 0;
//
// smearing the image coordinates on registers
__m256d image_x = _mm256_set1_pd(pImage->x);
__m256d image_y = _mm256_set1_pd(pImage->y);
//
__m256d __grad_x = _mm256_set1_pd(0.);
__m256d __grad_y = _mm256_set1_pd(0.);
//
int i;
//#pragma unroll
for(i = 0; i < nhalos - nhalos%4; i = i + 4)
{
//IACA_START;
//
__m256d two = _mm256_set1_pd( 2. );
__m256d one = _mm256_set1_pd( 1. );
__m256d zero = _mm256_set1_pd( 0. );
__m256d half = _mm256_set1_pd( 0.5);
__m256d mhalf = _mm256_set1_pd(-0.5);
//
// 2 loads
__m256d true_coord_x = _mm256_sub_pd(image_x, _mm256_loadu_pd(&lens->position_x[i]));
__m256d true_coord_y = _mm256_sub_pd(image_y, _mm256_loadu_pd(&lens->position_y[i]));
// 2 loads
__m256d rc = _mm256_loadu_pd(&lens->rcore[i]);
__m256d rcut = _mm256_loadu_pd(&lens->rcut[i]);
__m256d b0 = _mm256_loadu_pd(&lens->b0[i]);
__m256d t05 = b0*rcut*__INV(rcut - rc);
//__m256d t05 = b0; //*rcut*__INV(rcut - rc);
// 2 loads
__m256d eps = _mm256_loadu_pd(&lens->ellipticity_potential[i]);
//
__m256d one_minus_eps = _mm256_sub_pd(one, eps);
__m256d one_plus_eps = _mm256_add_pd(one, eps);
__m256d one_plus_eps_rcp = __INV(one_plus_eps);
// 1 load
__m256d theta = _mm256_loadu_pd(&lens->ellipticity_angle[i]);
/*positionning at the potential center*/
__m256d cos_theta = _mm256_cos_pd(theta);
__m256d sin_theta = _mm256_sin_pd(theta);
// rotation: 6 ops
__m256d x = _mm256_add_pd(_mm256_mul_pd(true_coord_x, cos_theta), _mm256_mul_pd(true_coord_y, sin_theta));
__m256d y = _mm256_sub_pd(_mm256_mul_pd(true_coord_y, cos_theta), _mm256_mul_pd(true_coord_x, sin_theta));
//
__m256d sqe = __SQRT(eps);
//
__m256d cx1 = one_minus_eps*one_plus_eps_rcp; // (1. - eps)/(1. + eps); 3 ops
__m256d cxro = one_plus_eps*one_plus_eps; // (1. + eps)*(1. + eps); 3 ops
__m256d cyro = one_minus_eps*one_minus_eps; // (1. - eps)*(1. - eps); 3 ops
__m256d rem2 = x*x*__INV(cxro) + y*y*__INV(cyro); // x*x/(cxro) + y*y/(cyro); ~5 ops
//
__m256d zci_re = zero;
__m256d zci_im = mhalf*(one - eps*eps)*__INV(sqe); // ~4 ops
//
__m256d znum_re = zero, znum_im = zero;
__m256d zden_re = zero, zden_im = zero;
__m256d norm;
//
__m256d zis_re = zero, zis_im = zero;
__m256d zres_rc_re = zero, zres_rc_im = zero;
__m256d zres_rcut_re = zero, zres_rcut_im = zero;
//
// step 1
//
{
// 2.*sqe*sqrt(rc*rc + rem2) - y/cx1, 7 ops
znum_re = cx1*x;
znum_im = two*sqe*__SQRT(rc*rc + rem2) - y*__INV(cx1); // ~4 ops
//
zden_re = x;
zden_im = _mm256_mul_pd(_mm256_set1_pd(2.), _mm256_mul_pd(rc, sqe));
//
zden_im = _mm256_sub_pd(zden_im, y);
//norm = (zden.re*zden.re + zden.im*zden.im); 3 ops
norm = (zden_re*zden_re + zden_im*zden_im);
zis_re = (znum_re*zden_re + znum_im*zden_im)*__INV(norm); // 3 ops
zis_im = (znum_im*zden_re - znum_re*zden_im)*__INV(norm); // 3 ops
//
norm = zis_re;
//
zis_re = _mm256_log_pd(__SQRT(norm*norm + zis_im*zis_im)); // 3 ops// ln(zis) = ln(|zis|)+i.Arg(zis)
zis_im = _mm256_atan2_pd(zis_im, norm); //
//
zres_rc_re = zci_re*zis_re - zci_im*zis_im; // Re( zci*ln(zis) ) 3 ops
zres_rc_im = zci_im*zis_re + zis_im*zci_re; // Im( zci*ln(zis) ) 3 ops
}
//
// step 2
//
{
// 2.*sqe*sqrt(rcut*rcut + rem2) - y/cx1, 7 ops
znum_re = cx1*x;
znum_im = two*sqe*__SQRT(rcut*rcut + rem2) - y*__INV(cx1); // ~4 ops
//
zden_re = x;
zden_im = _mm256_mul_pd(_mm256_set1_pd(2.), _mm256_mul_pd(rcut, sqe));
zden_im = _mm256_sub_pd(zden_im, y);
//
norm = (zden_re*zden_re + zden_im*zden_im); // 3 ops
//
zis_re = (znum_re*zden_re + znum_im*zden_im)*__INV(norm); // 3 ops
zis_im = (znum_im*zden_re - znum_re*zden_im)*__INV(norm); // 3 ops
//
norm = zis_re;
//
zis_re = _mm256_log_pd(__SQRT(norm*norm + zis_im*zis_im)); // 3 ops// ln(zis) = ln(|zis|)+i.Arg(zis)
zis_im = _mm256_atan2_pd(zis_im, norm); //
//
zres_rcut_re = (zci_re*zis_re - zci_im*zis_im); // Re( zci*ln(zis) ) 3 ops
zres_rcut_im = (zci_im*zis_re + zis_im*zci_re); // Im( zci*ln(zis) ) 3 ops
}
//
// postlogue
//
zis_re = t05*(zres_rc_re - zres_rcut_re);
zis_im = t05*(zres_rc_im - zres_rcut_im);
//
cos_theta = _mm256_cos_pd(zero - theta);
sin_theta = _mm256_sin_pd(zero - theta);
// rotation: 6 ops
__grad_x = __grad_x + _mm256_add_pd(_mm256_mul_pd(zis_re, cos_theta), _mm256_mul_pd(zis_im, sin_theta));
__grad_y = __grad_y + _mm256_sub_pd(_mm256_mul_pd(zis_im, cos_theta), _mm256_mul_pd(zis_re, sin_theta));
}
//
//
//
grad.x = ((double*) &__grad_x)[0];
grad.x += ((double*) &__grad_x)[1];
grad.x += ((double*) &__grad_x)[2];
grad.x += ((double*) &__grad_x)[3];
//
grad.y = ((double*) &__grad_y)[0];
grad.y += ((double*) &__grad_y)[1];
grad.y += ((double*) &__grad_y)[2];
grad.y += ((double*) &__grad_y)[3];
//
// end of peeling
/*
if (nhalos%4 > 0)
{
struct point grad_peel;
grad_peel = module_potentialDerivatives_totalGradient_SOA(pImage, lens, i, nhalos);
//grad_peel = rotateCoordinateSystem(grad_peel, -theta);
//
grad.x += grad_peel.x;
grad.y += grad_peel.y;
}
*/
for (; i < nhalos; ++i)
{
struct point true_coord;
true_coord.x = pImage->x - lens->position_x[i];
true_coord.y = pImage->y - lens->position_y[i];
//printf("x, y = %f, %f\n", lens->position.x, lens->position.y);
struct point true_coord_rot = rotateCoordinateSystem(true_coord, lens->ellipticity_angle[i]);
//
complex zis, zis_cut;
double t05 = lens->b0[i]*lens->rcut[i]/(lens->rcut[i] - lens->rcore[i]);
zis = piemd_1derivatives_ci05(true_coord_rot.x, true_coord_rot.y, lens->ellipticity_potential[i], lens->rcore[i]);
//
zis_cut = piemd_1derivatives_ci05(true_coord_rot.x, true_coord_rot.y, lens->ellipticity_potential[i], lens->rcut[i]);
struct point clumpgrad;
clumpgrad.x = t05*(zis.re - zis_cut.re);
clumpgrad.y = t05*(zis.im - zis_cut.im);
clumpgrad = rotateCoordinateSystem(clumpgrad, -lens->ellipticity_angle[i]);
//
grad.x += clumpgrad.x;
grad.y += clumpgrad.y;
}
//IACA_END;
//
return(grad);
}

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