[Bug libc/16151] New: strtod() incorrectly rounds 2^-1075 to 0x0.0000000000001p-1022

[Bug libc/16151] New: strtod() incorrectly rounds 2^-1075 to 0x0.0000000000001p-1022

[exploringbinary at gmail dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=16151

            Bug ID: 16151
           Summary: strtod() incorrectly rounds 2^-1075 to
                    0x0.0000000000001p-1022
           Product: glibc
           Version: 2.18
            Status: NEW
          Severity: minor
          Priority: P2
         Component: libc
          Assignee: unassigned at sourceware dot org
          Reporter: exploringbinary at gmail dot com
                CC: drepper.fsp at gmail dot com

Given the decimal string that represents 2^-1075, strtod() returns an
incorrectly rounded result: it returns 0x0.0000000000001p-1022 instead of the
correct answer, 0x0p+0 (zero). 2^-1075 is half the smallest double precision
value, 2^-1074.

I did a little tracing to help isolate the bug. It appears that the division is
correct and that this is just a rounding problem. In /stdlib/strtod_l.c,
round_and_return() calls round_away() with half_bit == true, last_digit_odd ==
false, and more_bits == true. This causes it to round up (case FE_TONEAREST).
more_bits should be false, which would make it round correctly to even. 

This program demonstrates the problem:

#include <stdio.h>
#include <stdlib.h>
int main (void)
{ 
 double d =
strtod("0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000024703282292062327208828439643411068618252990130716238221279284125033775363510437593264991818081799618989828234772285886546332835517796989819938739800539093906315035659515570226392290858392449105184435931802849936536152500319370457678249219365623669863658480757001585769269903706311928279558551332927834338409351978015531246597263579574622766465272827220056374006485499977096599470454020828166226237857393450736339007967761930577506740176324673600968951340535537458516661134223766678604162159680461914467291840300530057530849048765391711386591646239524912623653881879636239373280423891018672348497668235089863388587925628302755995657524455507255189313690836254779186948667994968324049705821028513185451396213837722826145437693412532098591327667236328125",NULL);
 printf("%a\n",d);
}

(I used PARI/GP to generate that string: 2.^-1075)


(I am submitting this bug report on behalf of Water Qian, who discovered this
bug and reported it on my blog:
http://www.exploringbinary.com/how-glibc-strtod-works/#comment-6892 .)

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[Bug libc/16151] strtod() incorrectly rounds 2^-1075 to 0x0.0000000000001p-1022

[jsm28 at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=16151

Joseph Myers <jsm28 at gcc dot gnu.org> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
             Status|NEW                         |ASSIGNED
           Assignee|unassigned at sourceware dot org   |jsm28 at gcc dot gnu.org

--- Comment #1 from Joseph Myers <jsm28 at gcc dot gnu.org> ---
Testing a patch.  This only applies to input that is exactly (plus or minus)
half the least subnormal and only if an entire normal mantissa fits in one MP
limb; in that case, the loop testing for extra bits set in the MANT_DIG initial
mantissa bits should have i < RETURN_LIMB_SIZE - 1 not RETURN_LIMB_SIZE (the
loop for the multiple-limb case has the correct bound).

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[Bug libc/16151] strtod() incorrectly rounds 2^-1075 to 0x0.0000000000001p-1022

[jsm28 at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=16151

--- Comment #2 from Joseph Myers <jsm28 at gcc dot gnu.org> ---
(Actually, "only if an entire normal mantissa fits in one MP limb" is not a
condition for this bug; the following loop for shifts of more than one limb is
for other cases, but gets the loop bound right.)

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[Bug libc/16151] strtod() incorrectly rounds 2^-1075 to 0x0.0000000000001p-1022

[exploringbinary at gmail dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=16151

--- Comment #3 from Rick Regan <exploringbinary at gmail dot com> ---
For reference, my slightly more refined description of the problem is here:
http://www.exploringbinary.com/glibc-strtod-incorrectly-converts-2-to-the-negative-1075/
.

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[Bug libc/16151] strtod() incorrectly rounds 2^-1075 to 0x0.0000000000001p-1022

[cvs-commit at gcc dot gnu.org]

http://sourceware.org/bugzilla/show_bug.cgi?id=16151

--- Comment #4 from cvs-commit at gcc dot gnu.org <cvs-commit at gcc dot gnu.org> ---
This is an automated email from the git hooks/post-receive script. It was
generated because a ref change was pushed to the repository containing
the project "GNU C Library master sources".

The branch, master has been updated
       via  9310c284ae91f13247c9dd7ff58fc2683b9c523d (commit)
      from  7a2ad8cf392acfcaef319e722dda9101d4d8b6bd (commit)

Those revisions listed above that are new to this repository have
not appeared on any other notification email; so we list those
revisions in full, below.

- Log -----------------------------------------------------------------
https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=9310c284ae91f13247c9dd7ff58fc2683b9c523d

commit 9310c284ae91f13247c9dd7ff58fc2683b9c523d
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Wed Nov 13 12:59:54 2013 +0000

    Fix strtod rounding of half the least subnormal (bug 16151).

-----------------------------------------------------------------------

Summary of changes:
 ChangeLog                    |    9 ++
 NEWS                         |    3 +-
 stdlib/strtod_l.c            |    2 +-
 stdlib/tst-strtod-round-data |    8 ++
 stdlib/tst-strtod-round.c    |  288 ++++++++++++++++++++++++++++++++++++++++++
 5 files changed, 308 insertions(+), 2 deletions(-)

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[Bug libc/16151] strtod() incorrectly rounds 2^-1075 to 0x0.0000000000001p-1022

[jsm28 at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=16151

Joseph Myers <jsm28 at gcc dot gnu.org> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
             Status|ASSIGNED                    |RESOLVED
         Resolution|---                         |FIXED

--- Comment #5 from Joseph Myers <jsm28 at gcc dot gnu.org> ---
Fixed for 2.19.

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[Bug libc/16151] strtod() incorrectly rounds 2^-1075 to 0x0.0000000000001p-1022

[exploringbinary at gmail dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=16151

--- Comment #6 from Rick Regan <exploringbinary at gmail dot com> ---
Thanks. I tested it and it works.

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[Bug libc/16151] strtod() incorrectly rounds 2^-1075 to 0x0.0000000000001p-1022

[fweimer at redhat dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=16151

Florian Weimer <fweimer at redhat dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
              Flags|                            |security-

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