spectral-norm C gcc #8 program

/* The Computer Language Benchmarks Game
 * https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
 *
 * Contributed by Sebastien Loisel
 */

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

double eval_A(int i, int j) { return 1.0/((i+j)*(i+j+1)/2+i+1); }

void eval_A_times_u(int N, const double u[], double Au[])
{
  int i,j;
  for(i=0;i<N;i++)
    {
      Au[i]=0;
      for(j=0;j<N;j++) Au[i]+=eval_A(i,j)*u[j];
    }
}

void eval_At_times_u(int N, const double u[], double Au[])
{
  int i,j;
  for(i=0;i<N;i++)
    {
      Au[i]=0;
      for(j=0;j<N;j++) Au[i]+=eval_A(j,i)*u[j];
    }
}

void eval_AtA_times_u(int N, const double u[], double AtAu[])
{ double v[N]; eval_A_times_u(N,u,v); eval_At_times_u(N,v,AtAu); }

int main(int argc, char *argv[])
{
  int i;
  const int N = ((argc == 2) ? atoi(argv[1]) : 100);
  double u[N],v[N],vBv,vv;
  for(i=0;i<N;i++) u[i]=1;
  for(i=0;i<10;i++)
    {
      eval_AtA_times_u(N,u,v);
      eval_AtA_times_u(N,v,u);
    }
  vBv=vv=0;
  for(i=0;i<N;i++) { vBv+=u[i]*v[i]; vv+=v[i]*v[i]; }
  printf("%0.9f\n",sqrt(vBv/vv));
  return 0;
}

    

NOTES:
64-bit Ubuntu quad core
gcc (Ubuntu 14.2.0-4ubuntu2) 14.2.0


 Tue, 22 Oct 2024 19:25:08 GMT

MAKE:
/usr/bin/gcc -pipe -Wall -O3 -fomit-frame-pointer -march=ivybridge  spectralnorm.gcc-8.c -o spectralnorm.gcc-8.gcc_run -lm
rm spectralnorm.gcc-8.c

2.74s to complete and log all make actions

COMMAND LINE:
 ./spectralnorm.gcc-8.gcc_run 5500

PROGRAM OUTPUT:
1.274224153