Patch gcc-4.0 should not apply mathematical associative rules for addition or multiplication

[Richard Henderson]

On Thu, Oct 07, 2004 at 11:18:34PM +0000, Joseph S. Myers wrote:
> I can't find a reference to this discussion right now and I think it must 
> have been some other rounding mode, but the idea was that half the 
> smallest floating point value rounded to the same value but a quarter of 
> it rounded to zero

I modified my test program to iterate through all of the rounding
modes, and still couldn't find such a case.

For the record, and in case someone can identify a bug that would
have caused this case to be missed, the test program follows.  I
ran the test program on ia64 to avoid any possibility of mucking
up with extended precision on x86.



r~



#include <fenv.h>

#define hide(x) \
  ({ __typeof (x) x_ = (x); asm ("" : "=frg"(x_) : "0"(x_)); x_; })

void test(void)
{
  int i;
  union {
    float f;
    int i;
  } u;

  for (i = 0; i < 1<<24; i++)
    {
      float f, t0, t1, t2;
      u.i = i;
      f = u.f;

      t0 = hide(f * 0.5f);
      t1 = hide(t0 * 0.5f);
      t2 = hide(f * 0.25f);

      if (t1 != t2)
	{
	  printf ("%.10a: %.10a != %.10a\n", f, t1, t2);
	  abort ();
	}
    }
}

int main()
{
  int r;

  for (r = 0; r < 4; ++r)
    {
      int m;
      switch (r)
	{
	case 0:
	  m = FE_TOWARDZERO;
	  break;
	case 1:
	  m = FE_DOWNWARD;
	  break;
	case 2:
	  m = FE_TONEAREST;
	  break;
	case 3:
	  m = FE_UPWARD;
	  break;
	}
      fesetround (m);
      test ();
    }

  return 0;
}