floating point bug -- or misunderstanding?

floating point bug -- or misunderstanding?

[Derrick Bass]

I may have found a bug in egcs, but more likely I just don't
understand floating point math.

Can someone tell me enough about floating point (or point me to an
explanation) to explain the output of the following program?

#include <stdio.h>
main() {
  float a,b,c,d;
  
  a = 1;
  b = 3;
  c = a/b;
  d = c * b;

  printf("%g\n", a - c * b);	
  printf("%g\n", a - d);
}

I compiled the program with egcs-19980803 on a pentium pro linux
machine with no optimization and the output was
-2.98023e-08
0

Shouldn't these numbers be equal?

Derrick Bass

Re: floating point bug -- or misunderstanding?

[Alexandre Oliva]

Derrick Bass <derrick@tapir.Caltech.EDU> writes:

> I may have found a bug in egcs, but more likely I just don't
> understand floating point math.

The x86 FPU works with an internal precision higher than the one
offered by type double.  Thus, when it performs calculations
internally, without storing temporary values in memory, it usually
gets more accurate results than if it stores and loads values in
memory.  Your program is just getting rounding errors.

-- 
Alexandre Oliva
mailto:oliva@dcc.unicamp.br mailto:aoliva@acm.org
http://www.dcc.unicamp.br/~oliva
Universidade Estadual de Campinas, SP, Brasil