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computepi.c
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computepi.c
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#include <stdio.h>
#include <immintrin.h>
#include <omp.h>
#include "computepi.h"
double compute_pi_baseline(size_t N)
{
double pi = 0.0;
double dt = 1.0 / N; // dt = (b-a)/N, b = 1, a = 0
for (size_t i = 0; i < N; i++) {
double x = (double) i / N; // x = ti = a+(b-a)*i/N = i/N
pi += dt / (1.0 + x * x); // integrate 1/(1+x^2), i = 0....N
}
return pi * 4.0;
}
double compute_pi_openmp(size_t N, int threads)
{
double pi = 0.0;
double dt = 1.0 / N;
double x;
#pragma omp parallel num_threads(threads)
{
#pragma omp for private(x) reduction(+:pi)
for (size_t i = 0; i < N; i++) {
x = (double) i / N;
pi += dt / (1.0 + x * x);
}
}
return pi * 4.0;
}
double compute_pi_avx(size_t N)
{
double pi = 0.0;
double dt = 1.0 / N;
register __m256d ymm0, ymm1, ymm2, ymm3, ymm4;
ymm0 = _mm256_set1_pd(1.0);
ymm1 = _mm256_set1_pd(dt);
ymm2 = _mm256_set_pd(dt * 3, dt * 2, dt * 1, 0.0);
ymm4 = _mm256_setzero_pd(); // sum of pi
for (int i = 0; i <= N - 4; i += 4) {
ymm3 = _mm256_set1_pd(i * dt); // i*dt, i*dt, i*dt, i*dt
ymm3 = _mm256_add_pd(ymm3, ymm2); // x = i*dt+3*dt, i*dt+2*dt, i*dt+dt, i*dt+0.0
ymm3 = _mm256_mul_pd(ymm3, ymm3); // x^2 = (i*dt+3*dt)^2, (i*dt+2*dt)^2, ...
ymm3 = _mm256_add_pd(ymm0, ymm3); // 1+x^2 = 1+(i*dt+3*dt)^2, 1+(i*dt+2*dt)^2, ...
ymm3 = _mm256_div_pd(ymm1, ymm3); // dt/(1+x^2)
ymm4 = _mm256_add_pd(ymm4, ymm3); // pi += dt/(1+x^2)
}
double tmp[4] __attribute__((aligned(32)));
_mm256_store_pd(tmp, ymm4); // move packed float64 values to 256-bit aligned memory location
pi += tmp[0] + tmp[1] + tmp[2] + tmp[3];
return pi * 4.0;
}
double compute_pi_avx_unroll(size_t N)
{
double pi = 0.0;
double dt = 1.0 / N;
register __m256d ymm0, ymm1, ymm2, ymm3, ymm4,
ymm5, ymm6, ymm7, ymm8, ymm9,
ymm10,ymm11, ymm12, ymm13, ymm14;
ymm0 = _mm256_set1_pd(1.0);
ymm1 = _mm256_set1_pd(dt);
ymm2 = _mm256_set_pd(dt * 3, dt * 2, dt * 1, 0.0);
ymm3 = _mm256_set_pd(dt * 7, dt * 6, dt * 5, dt * 4);
ymm4 = _mm256_set_pd(dt * 11, dt * 10, dt * 9, dt * 8);
ymm5 = _mm256_set_pd(dt * 15, dt * 14, dt * 13, dt * 12);
ymm6 = _mm256_setzero_pd(); // first sum of pi
ymm7 = _mm256_setzero_pd(); // second sum of pi
ymm8 = _mm256_setzero_pd(); // third sum of pi
ymm9 = _mm256_setzero_pd(); // fourth sum of pi
for (int i = 0; i <= N - 16; i += 16) {
ymm14 = _mm256_set1_pd(i * dt);
ymm10 = _mm256_add_pd(ymm14, ymm2);
ymm11 = _mm256_add_pd(ymm14, ymm3);
ymm12 = _mm256_add_pd(ymm14, ymm4);
ymm13 = _mm256_add_pd(ymm14, ymm5);
ymm10 = _mm256_mul_pd(ymm10, ymm10);
ymm11 = _mm256_mul_pd(ymm11, ymm11);
ymm12 = _mm256_mul_pd(ymm12, ymm12);
ymm13 = _mm256_mul_pd(ymm13, ymm13);
ymm10 = _mm256_add_pd(ymm0, ymm10);
ymm11 = _mm256_add_pd(ymm0, ymm11);
ymm12 = _mm256_add_pd(ymm0, ymm12);
ymm13 = _mm256_add_pd(ymm0, ymm13);
ymm10 = _mm256_div_pd(ymm1, ymm10);
ymm11 = _mm256_div_pd(ymm1, ymm11);
ymm12 = _mm256_div_pd(ymm1, ymm12);
ymm13 = _mm256_div_pd(ymm1, ymm13);
ymm6 = _mm256_add_pd(ymm6, ymm10);
ymm7 = _mm256_add_pd(ymm7, ymm11);
ymm8 = _mm256_add_pd(ymm8, ymm12);
ymm9 = _mm256_add_pd(ymm9, ymm13);
}
double tmp1[4] __attribute__((aligned(32)));
double tmp2[4] __attribute__((aligned(32)));
double tmp3[4] __attribute__((aligned(32)));
double tmp4[4] __attribute__((aligned(32)));
_mm256_store_pd(tmp1, ymm6);
_mm256_store_pd(tmp2, ymm7);
_mm256_store_pd(tmp3, ymm8);
_mm256_store_pd(tmp4, ymm9);
pi += tmp1[0] + tmp1[1] + tmp1[2] + tmp1[3] +
tmp2[0] + tmp2[1] + tmp2[2] + tmp2[3] +
tmp3[0] + tmp3[1] + tmp3[2] + tmp3[3] +
tmp4[0] + tmp4[1] + tmp4[2] + tmp4[3];
return pi * 4.0;
}
double arctan(double x , size_t N,int threads)
{
double atan = 0.0;
double dz = x / N;
double z;
#pragma omp parallel num_threads(threads)
{
#pragma omp for private(z) reduction(+:atan)
for(size_t i = 0; i<N; i++) {
z = (double) x*i / N;
atan += dz / (1.0 + z*z );
}
}
return atan;
}
double compute_pi_machin(size_t N, int threads)
{
double pi = 4.0 * arctan((double)0.2,N,threads) - arctan((double)1.0/239,N,threads);
return pi * 4.0;
}