[Bug manual/31322] New: Section 9.1 should document that the comparison function used in the example is not transitive

["vincent-srcware at vinc17 dot net" <sourceware-bugzilla@sourceware.org>]

https://sourceware.org/bugzilla/show_bug.cgi?id=31322

            Bug ID: 31322
           Summary: Section 9.1 should document that the comparison
                    function used in the example is not transitive
           Product: glibc
           Version: 2.38
            Status: UNCONFIRMED
          Severity: normal
          Priority: P2
         Component: manual
          Assignee: unassigned at sourceware dot org
          Reporter: vincent-srcware at vinc17 dot net
                CC: mtk.manpages at gmail dot com
  Target Milestone: ---

Section 9.1 gives an example of a comparison function on floating-point numbers
of type "double" that is not transitive due to possible NaN values. This can be
shown by the following program:

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

int
compare_doubles (const void *a, const void *b)
{
  const double *da = (const double *) a;
  const double *db = (const double *) b;

  return (*da > *db) - (*da < *db);
}

int main (void)
{
  double t[3] = { 1.0, NAN, 2.0 };
  printf ("%d\n", compare_doubles(t+0, t+1));
  printf ("%d\n", compare_doubles(t+1, t+2));
  printf ("%d\n", compare_doubles(t+0, t+2));
  return 0;
}

which gives

0
0
-1

while the initial 0 0 implies a third 0 with a transitive comparison function.

This should be documented.

Apparently, this is not clear to everyone:
  https://sourceware.org/pipermail/libc-alpha/2024-January/154350.html

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