other/10417: Inconsistent results in floating point comparison.

[Craig S. Kaplan]

The following reply was made to PR other/10417; it has been noted by GNATS.

From: "Craig S. Kaplan" <csk@cgl.uwaterloo.ca>
To: tprince@computer.org
Cc: gcc-gnats@gcc.gnu.org
Subject: Re: other/10417: Inconsistent results in floating point comparison.
Date: Wed, 16 Apr 2003 10:40:02 -0400 (EDT)

 Tim,
 
 Thanks for the insights.  If you've got the time, I have some
 additional comments below.
 
 > > ---------------------
 > > #include <stdio.h>
 > > #include <stdlib.h>
 > >
 > > int main( int argc, char ** argv )
 > > {
 > >     double x = atof( argv[1] );
 > >     double d = x*x;
 > >
 > >     printf( "%d\n", (x*x<d) );
 > >     return 0;
 > > }
 > > -----------------------
 > >
 > > Ideally, this program should always print 0, since a number shouldn't be
 > > strictly less than itself.  When compiled without optimization, the program
 > > will print 0 or 1 depending on the input (I get 0.3 --> 0, 0.4 --> 1, for
 > > instance).
 > >
 > > Now I understand that floating point numbers are far from ideal, and that
 > > this behaviour might not be a bug.  Still, I would love to be able to
 > > characterize for which numbers the program will print 0 or 1.  Any
 > > thoughts?
 > If you ask the compiler to generate x87 code (the probable default for your
 > configuration), it could interpret the expression as
 > (long double)x*x < d;
 > so the expression would be 1 every time d has been rounded up.
 > If you use the command
 > gcc -march=pentium4 -mfpmath=sse *.c
 > as you might normally do for a P4, I doubt you could get the results you
 > mention.
 
 Surprisingly, I _do_ still get the strange behaviour with those
 switches.
 
 But I am beginning to understand where the behaviour may be coming
 from, based on your comments and the comments of another maintainer
 who emailed me (ebotcazou).  When d is stored in a variable, some
 extra bits of precision that existed in the FPU are discarded.  Now,
 you seem to suggest that the way the FPU does this is to _round_ d
 (rather than just truncating).  My simple program seems to generate
 random output for different floats, but actually I'm just seeing the
 FPU's rounding semantics -- its decision whether to round up or down.
 Does that sound believable to you?
 
 Of course, if this is the case, we shouldn't expect -mfpmath=sse
 to solve the 'problem' -- we're still rounding x*x to store the
 answer in d.  The other maintainer suggested that I needed
 '-ffloat-store' to guarantee strict IEEE semantics.  I tried that
 switch, and it seemed to make the behaviour a little more consistent.
 It does remove the randomness from the large program I'm working
 on, but amazingly it doesn't fix my toy example.  Using gcc 3.2.1,
 the only way I can make the short program above output 0 consistently
 is to compile it -O2.  The -ffloat-store, -march=pentium4, and
 -mfpmath=sse switches don't seem to do anything.  Any thoughts on
 why I'm not seeing a difference here?
 
 Thanks again.
 
 -- 
 Craig S. Kaplan                     ``Evolution drives a steamroller,
 School of Computer Science          disguised as a stationary bike.''
 University of Waterloo              http://www.cgl.uwaterloo.ca/~csk/