Re: floating-point bug?

[Eli Zaretskii]

> From: "Linda Riewe" <address@hidden>
> Date: Wed, 10 Nov 2004 15:21:53 -0800
> Cc: 
> 
> BEGIN {
> 
>  x = 3000 * 8.87
>  y = 8.87 * 3000
>  a = 3 * 8870
>  b = 0.3 * 88700
>  z = 26610.00
>  w = 26610
>  print "a=" a " b=" b " w=" w " x=" x " y=" y " z=" z
>  print "x == y " ((x == y) ? "true" : "false")
>  print "x == z " ((x == z) ? "true" : "false")
>  print "x == a " ((x == a) ? "true" : "false")
>  print "x == b " ((x == b) ? "true" : "false")
>  print "x == w " ((x == w) ? "true" : "false")
> }
> 
> but instead, it prints:
> 
> > gawk -f tryit
> a=26610 b=26610 w=26610 x=26610 y=26610 z=26610
> x == y true
> x == z false
> x == a false
> x == b false
> x == w false

Welcome to the wonderful world of floating-point computations, where
comparing numbers for equality is a risky business.

These values are not ``equal'' because small differences in fractional
digits (that don't show when you use `print', but will probably show
if you use `printf' with sufficient number of digits after the decimal
point) make them different.

The way to compare floating-point numbers is to do something like
this:

      print "x == y " (abs(x - y) < eps ? "true" : "false")

where abs() is a function that returns the absolute value of its
argument, and eps is a small (machine-dependent) number, like 1.e-15.