Re: weird optimization in sin+cos, x86 backend

[Vincent Lefevre <vincent+gcc at vinc17 dot org>]

On 2012-02-03 17:40:05 +0100, Dominique Dhumieres wrote:
> While I fail to see how the "correct value" of 
> cos(4.47460300787e+182)+sin(4.47460300787e+182)
> can be defined in the 'double' world, cos^2(x)+sin^2(x)=1 and 
> sin(2*x)=2*sin(x)*cos(x) seems to be verified (at least for this value)
> even if the actual values of sin and cos depends on the optimisation level.

Actually this depends on the context. It is even worse: the value
of sin(some_value) depends on the context. Consider the following
program:

#include <stdio.h>
#include <math.h>

int main (void)
{
  double x, c, s;
  volatile double v;

  x = 1.0e22;
  s = sin (x);
  printf ("sin(%.17g) = %.17g\n", x, s);

  v = x;
  x = v;
  c = cos (x);
  s = sin (x);
  printf ("sin(%.17g) = %.17g\n", x, s);

  return c == 0;
}

With "gcc -O" on x86_64 with glibc 2.13, one gets:

sin(1e+22) = -0.85220084976718879
sin(1e+22) = 0.46261304076460175

In the program, you can replace 1.0e22 by 4.47460300787e+182 or
whatever large constant you want. You'll get the same problem.

-- 
Vincent Lefèvre <vincent@vinc17.net> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)