[Bug middle-end/21718] real.c rounding not perfect

["neil at gcc dot gnu dot org" <gcc-bugzilla at gcc dot gnu dot org>]

------- Comment #6 from neil at gcc dot gnu dot org  2007-10-18 15:24 -------
(In reply to comment #5)

> I believe more than 160 bits are required to get even single-precision numbers
> right with DECIMAL_DIG digits precision and an exponent.  I'm going to try and
> prove this by finding an example.  It could be hard as I believe 160 is only
> just below the required number.

Here's an example to prove this assertion.  When compiled with GCC 4.1.2 or
4.1.3 with -std=c99, assuming a correctly-rounding libc (e.g. NetBSD's; glibc
also seems to get this correct) you get the following output:

0x1.8p-147 0x1.4p-147 8.40779078594890243e-45

So not only is it rounded incorrectly, but the number it is rounded to, when
converted back to decimal, does not even match the input number in the first
digit.

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

int main (void)
{
  float f1 = 7.7071415537864938e-45;
  float f2 = strtof ("7.7071415537864938e-45", NULL);

  printf( "%a %a %0.18g\n", f1, f2, f1);

  return 0;
}


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http://gcc.gnu.org/bugzilla/show_bug.cgi?id=21718