Tengo el siguiente código C. La primera parte solo lee en una matriz de números complejos desde estándar en matriz llamadaM. La parte interesante es la segunda parte.

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

int main() {
    int n, m, c, d;
    float re, im;

    scanf("%d %d", &n, &m);
    assert(n==m);
    complex float M[n][n];

    for(c=0; c<n; c++) {
      for(d=0; d<n; d++) {
    scanf("%f%fi", &re, &im);
    M[c][d] = re + im * I;
      }
    }

    for(c=0; c<n; c++) {
      for(d=0; d<n; d++) {
        printf("%.2f%+.2fi ", creal(M[c][d]), cimag(M[c][d]));
      }
      printf("\n");
    }
/*
Example:input   
2 3
1+2i 2+3i 74-4i
3+4i 4+5i -7-8i
*/
    /* Part 2. M is now an n by n matrix of complex numbers */
    int s=1, i, j;
    int *f = malloc(n * sizeof *f);
    complex float *delta = malloc(n * sizeof *delta);
    complex float *v = malloc(n * sizeof *v);
    complex float p = 1, prod;

    for (i = 0; i < n; i++) {
      v[i] = 0;
      for (j = 0; j <n; j++) {
        v[i] += M[j][i];
      }
      p *= v[i];
      f[i] = i;
      delta[i] = 1;
    }
    j = 0;
    while (j < n-1) {
      prod = 1.;
      for (i = 0; i < n; i++) {
        v[i] -= 2.*delta[j]*M[j][i];
        prod *= v[i];
      }
      delta[j] = -delta[j];
      s = -s;            
      p += s*prod;
      f[0] = 0;
      f[j] = f[j+1];
      f[j+1] = j+1;
      j = f[0];
    }
    free(delta);
    free(f);
    free(v);
    printf("%f + i%f\n", creal(p/pow(2.,(n-1))), cimag(p/pow(2.,(n-1))));
    return 0;
}

Compilo congcc -fopt-info-vec-all -O3 -ffast-math -march=bdver2 permanent-in-c.c -lm. Esto me explica por qué casi ninguno de los bucles se está vectorizando.

La parte más importante para el rendimiento son las líneas 47 a 50, que son:

for (i = 0; i < n; i++) {
    v[i] -= 2.*delta[j]*M[j][i];
    prod *= v[i];
}

gcc me dice:

permanent-in-c.c:47:7: note: reduction used in loop.
permanent-in-c.c:47:7: note: Unknown def-use cycle pattern.
permanent-in-c.c:47:7: note: reduction used in loop.
permanent-in-c.c:47:7: note: Unknown def-use cycle pattern.
permanent-in-c.c:47:7: note: Unsupported pattern.
permanent-in-c.c:47:7: note: not vectorized: unsupported use in stmt.
permanent-in-c.c:47:7: note: unexpected pattern.
[...]
permanent-in-c.c:48:26: note: SLP: step doesn't divide the vector-size.
permanent-in-c.c:48:26: note: Unknown alignment for access: IMAGPART_EXPR <*M.4_40[j_202]{lb: 0 sz: pretmp_291 * 4}[i_200]>
permanent-in-c.c:48:26: note: SLP: step doesn't divide the vector-size.
permanent-in-c.c:48:26: note: Unknown alignment for access: REALPART_EXPR <*M.4_40[j_202]{lb: 0 sz: pretmp_291 * 4}[i_200]>
[...]
permanent-in-c.c:48:26: note: Build SLP failed: unrolling required in basic block SLP
permanent-in-c.c:48:26: note: Failed to SLP the basic block.
permanent-in-c.c:48:26: note: not vectorized: failed to find SLP opportunities in basic block.

¿Cómo puedo solucionar los problemas que impiden que esta parte se vectorice?

Curiosamente, esta parte está vectorizada, pero no estoy seguro de por qué:

for (j = 0; j <n; j++) {
    v[i] += M[j][i];

La salida completa de gcc -fopt-info-vec-all -O3 -ffast-math -march = bdver2 permanent-in-c.c -lm está enhttps://bpaste.net/show/18ebc3d66a53.