Bug#175809: Strange or incorrect floating point behaviour

[gwesp@cosy.sbg.ac.at (Gerhard Wesp)]

Package: g++-3.2
Version: 3.2.2 20021212 (Debian prerelease)

Note that this problem most likely is present in other g++ versions, and
also, in similar forms, in other gcc languages.

It was discussed in comp.lang.c++.moderated, cf.
news:<atq355$9or$1@esel.cosy.sbg.ac.at> and the followup postings.
Posters suggested it might be a bug in the implementation of
-ffloat-store and/or related to floating point expressions evaluated at
compile-time and at runtime with different precisions.

Mathematically, a >= b implies ka >= kb for k >= 0.  While I'm well
aware that not all properties of the reals carry over to floating point
arithmetic, I certainly would expect this *particular* implication to
carry over.  However, g++ -O3 thinks otherwise.

In the code below, the last assertion fails under certain circumstances.
It's these circumstances which make the behaviour really mysterious:

The assertion does *not* fail if *any* of the following conditions is
satisfied:
1) The bound() template is replaced by a function.  (Change the #if 1 to
#if 0.)
2) Lines (1) or (2) are commented out.
3) 2.5 is replaced by other values, e.g. 4.
4) -O2 is specified instead of -O3 (it *does*, however, fail with 
-O2 -ffloat-store).

My first guess was that this has something to do with internal usage of
80 bit floating point values, but this doesn't go well with observation
4).



#include <cassert>

#if 1
  template< typename T > inline void bound( T     & x , T      const& u
) {
#else
                         inline void bound( double& x , double const& u
) {
#endif
  assert( 1. <= u ) ;            // (1)
  if( x < 1. ) { x = 1. ; }      // (2)
  if( x > u  ) { x = u  ; }
}

int main() {
  const double u = 2.1 ;
  double x = 3 ;

  bound( x , u ) ;

  assert( u >= x ) ;
  assert( 2.5*u >= 2.5*x ) ;  // fails!!!
}




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