RE: [Caml-list] float number

["T. Kurt Bond" <tkb@tkb.mpl.com>]

Vincent Barichard writes:
> Hi,
> 
> I've observed a strange behaviour of ocaml :
> 
> let x = asin (-0.587527525714) in (x,x = (-0.628));;
> - : float * bool = (-0.628, false)
> 
> Why x doesn't equal to -0.628 ??
> 
> Thanks

Because x isn't equal to -0.628, even though it prints as -0.628.  The
output routine doesn't print the value of x accurately.  The same
thing happens in C.  O'Caml uses the C routine sprintf to format
floating point numbers (see the function format_float in
byterun/floats.c), and inherits poor float-printing routines from the
C runtime library..

Asking CMU Common Lisp (with *read-default-float-format* set to
DOUBLE-FLOAT, since O'Caml represents floating point numbers as
doubles) for the value of (asin -0.587527525714) gives
-0.6280000000001337, as does MzScheme.  

Here's a short (and non-portable) program that shows the problem
occuring in C:

    #include <stdio.h>
    #include <math.h>

    int
    main (int argc, char **argv)
    {
      double x = asin (-0.587527525714);
      double y = -0.628;

      int *xp = &x;
      int *yp = &y;

      printf ("x: %g, x == (-0.628): %d\n", x, x == (-0.628));
      printf ("*xp: %x *(xp+1): %x\n", *xp, *(xp+1));
      printf ("*yp: %x *(yp+1): %x\n", *yp, *(yp+1));

      exit (1);
    }

On FreeBSD 4.6 running on a Pentium II I compiled it like this:

    cc -O -pipe   x.c -lm -o x

and the output was:

    x: -0.628, x == (-0.628): 0
    *xp: 74bc6f33 *(xp+1): bfe41893
    *yp: 74bc6a7f *(yp+1): bfe41893

Notice that *xp and *yp are not equal.

More information on print floating point numbers can be found in the
paper "Printing Floating-Point Numbers Quickly and Accurately"; see

    http://citeseer.nj.nec.com/28233.html

-- 
T. Kurt Bond, tkb@tkb.mpl.com

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