Why can GCC not vectorize this function and loop?

Question

I'm attempting to make a function SIMD-enabled and vectorize the loop with a function call.

#include <cmath>

#pragma omp declare simd
double BlackBoxFunction(const double x) {
    return 1.0/sqrt(x);
}

double ComputeIntegral(const int n, const double a, const double b) {
    const double dx = (b - a)/n;
    double I = 0.0;
    #pragma omp simd reduction(+: I)

    for (int i = 0; i < n; i++) {
      const double xip12 = a + dx*(double(i) + 0.5);
      const double yip12 = BlackBoxFunction(xip12);
      const double dI = yip12*dx;
      I += dI; 
  }
  return I;
}

For the code above, if I compile it with icpc:

icpc worker.cc -qopenmp -qopt-report=5 -c

The opt-report shows that the function and loop are both vectorized. However, if I try to compile it with g++ 6.5:

g++ worker.cc -O3 -fopenmp -fopt-info-vec-missed -funsafe-math-optimizations -c

The output shows note:not vectorized: control flow in loop. and note: bad loop form, and the loop cannot be vectorized.

How can I vectorize the loop with GCC?

EDIT :

If I write the function into a separate file,

worker.cc:

#include "library.h"

double ComputeIntegral(const int n, const double a, const double b) {
    const double dx = (b - a)/n;
    double I = 0.0;
    #pragma omp simd reduction(+: I)

    for (int i = 0; i < n; i++) {
      const double xip12 = a + dx*(double(i) + 0.5);
      const double yip12 = BlackBoxFunction(xip12);
      const double dI = yip12*dx;
      I += dI; 
  }
  return I;
}

library.h:

#ifndef __INCLUDED_LIBRARY_H__
#define __INCLUDED_LIBRARY_H__

#pragma omp declare simd
double BlackBoxFunction(const double x); 

#endif

and library.cc:

#include <cmath>

#pragma omp declare simd
double BlackBoxFunction(const double x) {
  return 1.0/sqrt(x);
}

Then I compile it with GCC:

g++ worker.cc library.cc -O3 -fopenmp -fopt-info-vec-missed -funsafe-math-optimizations -c

It shows:

worker.cc:9:31: note: loop vectorized

but

library.cc:5:18: note:not vectorized: control flow in loop.
library.cc:5:18: note:bad loop form.

It makes me confused. I wonder whether it is already vectorized.

Answer 1

Vectorization is possible with gcc, after some slight modifications of the code:

#include <cmath>

double BlackBoxFunction(const double x) {
    return 1.0/sqrt(x);
}

double ComputeIntegral(const int n, const double a, const double b) {
    const double dx = (b - a)/n;
    double I = 0.0;
    double d_i = 0.0;
    for (int i = 0; i < n; i++) {
      const double xip12 = a + dx*(d_i + 0.5);
      d_i = d_i + 1.0;
      const double yip12 = BlackBoxFunction(xip12);
      const double dI = yip12*dx;
      I += dI; 
  }
  return I;
}

This was compiled with the compiler options: -Ofast -march=haswell -fopt-info-vec-missed -funsafe-math-optimizations. The main loop compiles to

.L7:
    vaddpd  ymm2, ymm4, ymm7
    inc     eax
    vaddpd  ymm4, ymm4, ymm8
    vfmadd132pd     ymm2, ymm9, ymm5
    vsqrtpd ymm2, ymm2
    vdivpd  ymm2, ymm6, ymm2
    vfmadd231pd     ymm3, ymm5, ymm2
    cmp     eax, edx
    jne     .L7

See the following Godbolt link

I removed the #pragma omp ..., because they didn't improve the vectorization, but they did not made the vectorization worse either.

Note that only changing the compiler option from -O3 to -Ofast is sufficient to enable vectorization. Nevertheless, it is more efficient to use a double counter than an int counter which is converted to double each iteration.

Note also that the vectorization reports are quite misleading. Inspect the generated assembly code to see whether or not the vectorization was successful.