Re: optimization/9654: extra-precision fp comparisons are less accurate

[<rearnsha at gcc dot gnu dot org>]

The following reply was made to PR optimization/9654; it has been noted by GNATS.

From: <rearnsha@gcc.gnu.org>
To: richard@wetafx.co.nz, gcc-gnats@gcc.gnu.org, gcc-bugs@gcc.gnu.org
Cc:  
Subject: Re: optimization/9654: extra-precision fp comparisons are less accurate
Date: Wed, 12 Feb 2003 17:49:17 +0000

 http://gcc.gnu.org/cgi-bin/gnatsweb.pl?cmd=view%20audit-trail&database=gcc&pr=9654
 
 I think it's very dangerous to assume that
 
 acos(something-nearly-equal-to-1)
 
 won't return 0, or, more importantly
 
 sin (acos(something-nearly-equal-to-1)
 
 won't.
 
 A simple test after the assignment of o would suffice to avoid this 
 problem, eg:
 
 #include <math.h>
 
 double s(double t) throw()
 {
    double d = 0.75+t;
    double o = d < 1.0 ? acos(d) : 1.0/67108864.0;
    if (o == 0.0) o = 1.0 / 67108864.0;
    return sin(o*0.5)/sin(o);
 }
 
 int main(void)
 {
    return isnan(s(0.25-1.0/18014398509481984.0));
 }
 
 If you are really paranoid, then a range check on small o and applying 
 L'Hoptial's Rule might not be a bad idea.
 
 I really don't think you'd like the alternatives to -ffloat-store any 
 more than you like -ffloat-store.