Re: c/8395: gcc 2.95.4 and 3.2 generate wrong code for double on intel

[Bruce Allen <ballen@aei.mpg.de>]

The following reply was made to PR c/8395; it has been noted by GNATS.

From: Bruce Allen <ballen@aei.mpg.de>
To: gcc-gnats@gcc.gnu.org, gcc-prs@gcc.gnu.org, bernardo@sti.uniurb.it,
   gcc-bugs@gcc.gnu.org, nobody@gcc.gnu.org
Cc:  
Subject: Re: c/8395: gcc 2.95.4 and 3.2 generate wrong code for double on
 intel
Date: Wed, 30 Oct 2002 18:25:15 +0100

 http://gcc.gnu.org/cgi-bin/gnatsweb.pl?cmd=view%20audit-trail&database=gcc&pr=8395
 
 There's nothing wrong here.  It's very reasonable for this code to 
 produce ~10^-16 for double.
 The reason is tha the number 1.2 can not be exactly represented as an 
 IEEE754 floating point number.
 The numbers 5 and -6 CAN be exactly represented.
 
 I suggest that you read the first 15 or so pages of "Numerical Recipes 
 in C" by Press, Teukolsky (and two others).
 They discuss this question.  Then look at 
 http://www.etsimo.uniovi.es/~antonio/uned/ieee754/IEEE-754.html
 
 The closest IEEE754 double to 1.2 is (in binary)
 1.0011001100110011001100110011001100110011001100110011
 =
 1.1999999999999999555910790149937383830547332763671875......
 in decimal.
 
 If we multiply this by 5 (which is exactly represented by an IEEE754 
 double) one gets
 5.9999999999999997779553950749686919152736663818359375
 
 which is not 6.  The difference is what you are seeing.
 
 #include <stdio.h>
 int main(void)
 {
     double x, y, z;
     long double lx, ly, lz;
 
     x = -6.0;
     y = -1.2;
     z = 5;
     printf("%g %g %g %g\n",
            x,
            y,
            z,
            x - y * z);
     lx = -6.0L;
     ly = -1.2L;
     lz = 5L;
     printf("%Lg %Lg %Lg %Lg\n",
            lx,
            ly,
            lz,
            lx - ly * lz);
     return(0);
 }