The Computer Language
24.11 Benchmarks Game

spectral-norm Intel C #7 program

source code

/* The Computer Language Benchmarks Game
 * https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
 *
 * Contributed by Bogdan Sharkov 
 * Optimized memory access (SSE2 intrinsics), compile with -march=native -fopenmp for best results 
 *
 * Contributed by Mr Ledrug 
 * Algorithm lifted from Intel Fortran #2 code by Steve Decker et al.
*/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <malloc.h>
#include <x86intrin.h>

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

void mult_Av(double * v, double * out, const int n) {
   __m128i ONE = _mm_set1_epi32(1);  
   __m128i FOUR = _mm_set1_epi32(4);
   unsigned int i, j;
   #pragma omp parallel for schedule(static)
   for (i = 1; i <= n; i++) {
	   
	   j = i-1;
	   int k = n+j;
	   __m128i m = _mm_set1_epi32(i);
	   __m128d mysum =_mm_setzero_pd();
	   __m128i x = _mm_setr_epi32(j, j + 1, j + 2, j + 3);	   
		
		for (double* pv = v; j < k; j+=4, pv+=2) {
			__m128i y = _mm_add_epi32(x, ONE);
			__m128i a = _mm_mullo_epi32(x, y);
			x = _mm_add_epi32(x, FOUR);
			a = _mm_srli_epi32(a, 1);
			a = _mm_add_epi32(a, m);
			 
			__m128d  mul = _mm_cvtepi32_pd(a);
			__m128d  src = _mm_load_pd(pv);			
			pv+=2;
			__m128d  res = _mm_div_pd(src, mul);
			mysum = _mm_add_pd(mysum, res);
			
		    a = _mm_shuffle_epi32(a, _MM_SHUFFLE(1, 0, 3, 2));			
			mul = _mm_cvtepi32_pd(a);
			src = _mm_load_pd(pv);
			res = _mm_div_pd(src, mul);
			mysum = _mm_add_pd(mysum, res);			
		}    
	  
  	  out[i-1] = ((double*)&mysum)[0] + ((double*)&mysum)[1];
   }
	out[n] = out[n+1] =out[n+2] = 0.0;
}

void mult_Atv(double * v, double * out,  const int n) {
   __m128i ONE = _mm_set1_epi32(1);  
   __m128i FOUR = _mm_set1_epi32(4);
   int i;
   
  #pragma omp parallel for schedule(static)
   for (i = 0; i < n; i++) {
	   double* pv = v;
	  __m128d mysum =_mm_setzero_pd();
	  __m128i x = _mm_setr_epi32(i, i + 1, i + 2, i + 3);
	  __m128i aj = _mm_setr_epi32(1, 2, 3, 4);
	  for (int j=0;j < n;j+=4){
		  
			__m128i y = _mm_add_epi32(x, ONE);
			__m128i a = _mm_mullo_epi32(x, y);
			x = _mm_add_epi32(x, FOUR);
			a = _mm_srli_epi32(a, 1);
			a = _mm_add_epi32(a, aj);
			aj = _mm_add_epi32(aj, FOUR);
			 
			__m128d  mul = _mm_cvtepi32_pd(a);
			__m128d  src = _mm_load_pd(pv);
			pv+=2;
			__m128d  res = _mm_div_pd(src, mul);	
			mysum = _mm_add_pd(mysum, res);
			
			a = _mm_shuffle_epi32(a, _MM_SHUFFLE(1, 0, 3, 2));			
			mul = _mm_cvtepi32_pd(a);
			src = _mm_load_pd(pv);
			pv+=2;
			res = _mm_div_pd(src, mul);	
			mysum = _mm_add_pd(mysum, res);			
	  }		  
	  out[i] = ((double*)&mysum)[0] + ((double*)&mysum)[1];
   }
   
    out[n] = out[n+1] = out[n+2] = 0.0;
}

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 = 2000;
   if (argc >= 2) n = atoi(argv[1]);

   double *u, *v;
   u = _mm_malloc((n+3) * sizeof(double),sizeof(__m128d));
   v = _mm_malloc((n+3) * sizeof(double),sizeof(__m128d));
   tmp = _mm_malloc((n+3) * sizeof(double),sizeof(__m128d));
   
   int i;
   for (i = 0; i < n; i++) u[i] = 1;
   u[n] = u[n+1] = u[n+2] = 0.0;
   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)));

	_mm_free(u);
	_mm_free(v);
	_mm_free(tmp);

   return 0; 
}
    
    

notes, command-line, and program output

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


 Thu, 06 Jun 2024 22:41:44 GMT

MAKE:
~/intel/oneapi/compiler/latest/bin/icx -pipe -Wall -O3 -fomit-frame-pointer -march=ivybridge -qopenmp spectralnorm.icx-7.c -o spectralnorm.icx-7.icx_run -lm
rm spectralnorm.icx-7.c

6.20s to complete and log all make actions

COMMAND LINE:
 ./spectralnorm.icx-7.icx_run 5500

PROGRAM OUTPUT:
1.274224153