[Bug math/14032] New: sqrt is not correctly rounded on x86

[Bug math/14032] New: sqrt is not correctly rounded on x86

[bugdal at aerifal dot cx]

http://sourceware.org/bugzilla/show_bug.cgi?id=14032

             Bug #: 14032
           Summary: sqrt is not correctly rounded on x86
           Product: glibc
           Version: unspecified
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
        AssignedTo: unassigned@sourceware.org
        ReportedBy: bugdal@aerifal.cx
    Classification: Unclassified


Created attachment 6381
  --> http://sourceware.org/bugzilla/attachment.cgi?id=6381
test case and example workaround code

glibc's 387 asm for sqrt() simply uses the fsqrt instruction, yielding results
that may not be correctly rounded, which violates the IEEE requirements for the
sqrt operation. The cause is double-rounding due to the fact that the fsqrt
operation is performed in extended 80-bit precision (and gives
correctly-rounded results at this precision), then rounded again when it's
converted to 64-bit double precision. Naturally this is very problematic for
any algorithm that depends on the result of sqrt being correctly rounded.

Until recently, the bug was almost always masked by the corresponding bug in
gcc (which generates fsqrt for __builtin_sqrt), gcc bug #52593:

http://gcc.gnu.org/bugzilla/show_bug.cgi?id=52593

But since -fexcess-precision=standard was added (and made default for -std=c99
and -std=c11) somewhere in the gcc 4.5 series, the library function will be
called when correct standards-conformance is desired, only to repeat the exact
same mistake in the library code.

Using the C sqrt code would fix the problem, but I think that's highly
undesirable. I have an algorithm we're using in musl that uses fsqrt and only
fixes up the result in cases where the double-rounding could have an effect on
the result; it uses the floating point status word to determine the direction
of the rounding that takes place and biases the 80-bit value so that the result
will be correctly rounded to double precision after store and load:

http://git.etalabs.net/cgi-bin/gitweb.cgi?p=musl;a=blob;f=src/math/i386/sqrt.s

Attached is test code by Szabolcs Nagy (nsz) which demonstrates incorrectly
rounded results and includes a C function d_sqrt() which patches up the results
of an incorrectly-rounded underlying sqrt.

Finally, note that sqrtf() is not affected. It can be shown (left as an
exercise for the reader) that the correctly-rounded 80-bit result of fsqrt
subsequently rounded to 32-bit single precision is also the correctly-rounded
single-precision square root.

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[Bug math/14032] sqrt is not correctly rounded on x86

[ppluzhnikov at google dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=14032

Paul Pluzhnikov <ppluzhnikov at google dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
                 CC|                            |ppluzhnikov at google dot
                   |                            |com

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[Bug math/14032] sqrt is not correctly rounded on x86

[bugdal at aerifal dot cx]

https://sourceware.org/bugzilla/show_bug.cgi?id=14032

--- Comment #1 from Rich Felker <bugdal at aerifal dot cx> ---
Ping.

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[Bug math/14032] sqrt is not correctly rounded on x86

[cvs-commit at gcc dot gnu.org]

http://sourceware.org/bugzilla/show_bug.cgi?id=14032

--- Comment #2 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  ea3bc4e821e20e70b093c9a33e54f99c79e0d847 (commit)
      from  0712c9d861f4e861313a7f9fad06609bd1afb263 (commit)

Those revisions listed above that are new to this repository have
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- Log -----------------------------------------------------------------
https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=ea3bc4e821e20e70b093c9a33e54f99c79e0d847

commit ea3bc4e821e20e70b093c9a33e54f99c79e0d847
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Fri Nov 29 16:31:16 2013 +0000

    Fix x86 sqrt rounding (bug 14032).

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

Summary of changes:
 ChangeLog                 |    7 +
 NEWS                      |   20 +-
 math/auto-libm-test-in    |   57 +
 math/auto-libm-test-out   | 3669 +++++++++++++++++++++++++++++++++++++++++++++
 sysdeps/i386/fpu/e_sqrt.S |   10 +
 sysdeps/i386/fpu/w_sqrt.c |    8 +
 6 files changed, 3761 insertions(+), 10 deletions(-)
 create mode 100644 sysdeps/i386/fpu/w_sqrt.c

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[Bug math/14032] sqrt is not correctly rounded on x86

[jsm28 at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=14032

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

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

--- Comment #3 from Joseph Myers <jsm28 at gcc dot gnu.org> ---
Fixed for 2.19.

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[Bug math/14032] sqrt is not correctly rounded on x86

[fweimer at redhat dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=14032

Florian Weimer <fweimer at redhat dot com> changed:

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

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