cblas: compatibility for compilers without C99 complex number support (e.g. Visual Studio)

[zchothia]

Hello Xianyi,

Visual Studio is unable to compile <cblas.h> included with OpenBLAS, due to its
use of the _Complex type which assumes C99 support. Here is a patch which switches
to a binary-compatible structure in cases where the complex number type is not available: https://gist.github.com/2470335.

With this change in place, this test program can now be built with Visual Studio 2010:

#include <stdio.h>

#include <openblas/cblas.h>

int main(void) {
  int N = 2, incX = 1, incY = 1;
  double x[] = {1.0, 2.0, 3.0, 4.0};
  double y[] = {1.0, 2.0, 3.0, 4.0};
  openblas_complex_double result = cblas_zdotu(N, x, incX, y, incY);
  printf("result = %lf + %lfi\n", openblas_complex_double_real(result),
                                  openblas_complex_double_imag(result));
  // Expected output: -10.000000 + 28.000000i
  return 0;
}

I have tested this change on Linux and Windows (MinGW) and have not observed any adverse effects.

Best,

--Zaheer

Additional notes:

• <f77blas.h> has the same issue, but already contains a workaround, so I didn't make any changes.

• The approach I have used is similar to that used in LAPACKE (see <lapacke_config.h>).
  There are several utility routines (make_complex, *_real, *_imag) included, which
  are not strictly necessary, but permit writing code which works with either complex type.

  It should be noted that OPENBLAS_COMPLEX_STRUCT is not a drop-in replacement
  for OPENBLAS_COMPLEX_C99. For instance, this snippet works with C99's _Complex,
  but fails to compile with the struct form:

  openblas_complex_double z1 = openblas_make_complex_double(1.0, 2.0);
  openblas_complex_double z2 = openblas_make_complex_double(3.0, 4.0);
  openblas_complex_double z3 = z1 + z2;

  For this reason, it may be preferrable to entirely drop the C99 _Complex type and
  always use the struct form, leaving conversion to client code. This is the approach
  taken by Intel's MKL, which is described in more detail here.

[xianyi]

Hi Zaheer,

Thank you for your effort and patch on CBLAS complex issue.

Xianyi