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From: "vincent-srcware at vinc17 dot net" <sourceware-bugzilla@sourceware.org>
To: glibc-bugs@sources.redhat.com
Subject: [Bug math/13658] New: sincos() is inaccurate for large inputs on x86_64
Date: Fri, 03 Feb 2012 14:42:00 -0000
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http://sourceware.org/bugzilla/show_bug.cgi?id=13658

             Bug #: 13658
           Summary: sincos() is inaccurate for large inputs on x86_64
           Product: glibc
           Version: 2.13
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
        AssignedTo: aj@suse.de
        ReportedBy: vincent-srcware@vinc17.net
    Classification: Unclassified


sincos() is inaccurate for large inputs on x86_64: with glibc 2.13,

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

int main (void)
{
  volatile double x = 1.0e22;
  double s1, s2, c1;

  sincos (x, &s1, &c1);
  s2 = sin (x);
  printf ("s1 = %.17g\n", s1);
  printf ("s2 = %.17g\n", s2);
  return 0;
}

outputs:

s1 = 0.46261304076460175
s2 = -0.85220084976718879

(s2 is the correct value). I suppose that contrary to the other trig functions,
glibc uses the hardware sincos instruction, which has never been meant to be
used directly by a C library (the hardware elementary functions of the x86
processors were designed for small inputs, and they must not be used by code
where inputs can be large, like here). The sincos() function can simply be
implemented by a call to sin() and a call to cos() on this target.

Ditto for sincosf() and sincosl().

Note: x86 (32 bits) has the same problem, but it has been claimed that users
don't care about correctness on this target.

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