spectral-norm Intel C #5 program

/* The Computer Language Benchmarks Game
 * https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
 *
 * contributed by Ledrug
 * algorithm is a straight copy from Steve Decker et al's Fortran code
 * with GCC SSE2 intrinsics
 */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <malloc.h>
#include <emmintrin.h>

inline double A(int i, int j) {
   return ((i+j) * (i+j+1) / 2 + i + 1);
}

double dot(double * v, double * u, int n) {
   int i;
   double sum = 0;
   for (i = 0; i < n; i++)
      sum += v[i] * u[i];
   return sum;
}

void mult_Av(double * v, double * out, const int n) {
   int i;

#pragma omp parallel for
   for (i = 0; i < n; i++) {
      __m128d sum = _mm_setzero_pd();

      int j;
      for (j = 0; j < n; j += 2) {
         __m128d b = _mm_set_pd(v[j],v[j+1]);
         __m128d a = _mm_set_pd(A(i,j), A(i,j+1));
         sum = _mm_add_pd(sum, _mm_div_pd(b, a));
      }
      out[i] = sum[0] + sum[1];
   }
}

void mult_Atv(double * v, double * out, const int n) {
   int i;

#pragma omp parallel for
   for (i = 0; i < n; i++) {
      __m128d sum = _mm_setzero_pd();

      int j;
      for (j = 0; j < n; j += 2) {
         __m128d b = _mm_set_pd(v[j], v[j+1]);
         __m128d a = _mm_set_pd(A(j,i), A(j+1,i));
         sum = _mm_add_pd(sum, _mm_div_pd(b, a));
      }
      out[i] = sum[0] + sum[1];
   }
}

double *tmp;
void mult_AtAv(double *v, double *out, const int n) {
   mult_Av(v, tmp, n);
   mult_Atv(tmp, out, n);
}

int main(int argc, char**argv) {
   int n = atoi(argv[1]);
   if (n <= 0) n = 2000;
   if (n & 1) n++;   // make it multiple of two

   double *u, *v;
   u = memalign(16, n * sizeof(double));
   v = memalign(16, n * sizeof(double));
   tmp = memalign(16, n * sizeof(double));

   int i;
   for (i = 0; i < n; i++) u[i] = 1;
   for (i = 0; i < 10; i++) {
      mult_AtAv(u, v, n);
      mult_AtAv(v, u, n);
   }

   printf("%.9f\n", sqrt(dot(u,v, n) / dot(v,v,n)));

   return 0;
}
    

NOTES:
64-bit Ubuntu quad core
Intel(R) oneAPI DPC++/C++ Compiler
2024.1.0.20240308


 Thu, 06 Jun 2024 22:40:17 GMT

MAKE:
~/intel/oneapi/compiler/latest/bin/icx -pipe -Wall -O3 -fomit-frame-pointer -march=ivybridge -qopenmp spectralnorm.icx-5.c -o spectralnorm.icx-5.icx_run -lm
rm spectralnorm.icx-5.c

5.36s to complete and log all make actions

COMMAND LINE:
 ./spectralnorm.icx-5.icx_run 5500

PROGRAM OUTPUT:
1.274224153