[Bug math/23395] New: fmod repeated subtraction algorithm introduces round off errors

["irv at princeton dot com" <sourceware-bugzilla at sourceware dot org>]

https://sourceware.org/bugzilla/show_bug.cgi?id=23395

            Bug ID: 23395
           Summary: fmod repeated subtraction algorithm introduces round
                    off errors
           Product: glibc
           Version: unspecified
            Status: UNCONFIRMED
          Severity: normal
          Priority: P2
         Component: math
          Assignee: unassigned at sourceware dot org
          Reporter: irv at princeton dot com
  Target Milestone: ---

Created attachment 11120
  --> https://sourceware.org/bugzilla/attachment.cgi?id=11120&action=edit
Source code that illustrates the problem.

Consider the attached source code that computes fmod(x, y) for the values
x=100, 10, ..., 1.0e-6, y = x/100.  The result should always be close to 0. The
problem is that the fmod() implementation in sysdeps/ieee754/dbl-64/e_fmod.c
does repeated subtraction, which causes round off error to accumulate.

For the case where x > 0, y > 0, y < x, I show a different algorithm in
newfmod() that avoids that round off error.

This is on Intel chips, under Ubuntu (but it happens for any distribution on
Intel).

Since the implementation of fmod() is 25 years old, it ought to be fixed.

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