[Bug math/14412] Removal of sysdeps/x86_64/fpu/s_sincos.S causes regressions

["bugdal at aerifal dot cx" <sourceware-bugzilla@sourceware.org>]

http://sourceware.org/bugzilla/show_bug.cgi?id=14412

--- Comment #47 from Rich Felker <bugdal at aerifal dot cx> 2013-05-01 22:25:14 UTC ---
Another citation, from the C99 Rationale
(http://www.open-std.org/jtc1/sc22/wg14/www/C99RationaleV5.10.pdf), supporting
the option to give wrong results for trig functions:

Page 27, lines 9-13:

"Some math functions such as those that do argument reduction modulo an
approximation of π have good accuracy for small arguments, but poor accuracy
for large arguments. It is not unusual for an implementation of the
trigonometric functions to have zero bits correct in the computed result for
large arguments. For cases like this, an implementation might break the domain
of the function into disjoint regions and specify the accuracy in each region."

Note that an implementation should still document the accuracy, and in the case
of wrong argument reduction, the error could theoretically be as large as
2**1074 ULPs for some inputs of sin/cos (if the correct result were denormal
but the function returned 1.0 or -1.0) and much worse (even possibly infinite)
for tan.

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From: "jsm28 at gcc dot gnu.org" <sourceware-bugzilla@sourceware.org>
To: glibc-bugs@sourceware.org
Subject: [Bug math/15427] New: Spurious underflow from lgammaf
Date: Wed, 01 May 2013 22:26:00 -0000
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http://sourceware.org/bugzilla/show_bug.cgi?id\x15427

             Bug #: 15427
           Summary: Spurious underflow from lgammaf
           Product: glibc
           Version: 2.17
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
        AssignedTo: unassigned@sourceware.org
        ReportedBy: jsm28@gcc.gnu.org
    Classification: Unclassified


On x86_64, lgammaf (-0x1p-64) raises a spurious underflow exception.

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