[Bug math/18211] New: atan2 inaccuracy

[jsm28 at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=18211

            Bug ID: 18211
           Summary: atan2 inaccuracy
           Product: glibc
           Version: 2.21
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
          Assignee: unassigned at sourceware dot org
          Reporter: jsm28 at gcc dot gnu.org

The dbl-64 version of atan2 is inaccurate in non-default rounding modes beyond
the 9ulp maximum considered acceptable by libm-test.inc.  For example, on
x86_64:

Failure: Test: atan2_downward (0x1.47239ep+68, 0xa.3ac3cp+68)
Result:
 is:          1.24277371224459629028e-01   0x1.fd0a44d0aba530000000p-4
 should be:   1.24277371224459420862e-01   0x1.fd0a44d0aba440000000p-4
 difference:  2.08166817117216851329e-16   0x1.e0000000000000000000p-53
 ulp       :  15.0000
 max.ulp   :  5.0000

Failure: Test: atan2_towardzero (0x1.47239ep+68, 0xa.3ac3cp+68)
Result:
 is:          1.24277371224459629028e-01   0x1.fd0a44d0aba530000000p-4
 should be:   1.24277371224459420862e-01   0x1.fd0a44d0aba440000000p-4
 difference:  2.08166817117216851329e-16   0x1.e0000000000000000000p-53
 ulp       :  15.0000
 max.ulp   :  5.0000

Failure: Test: atan2_upward (-0x6.b0794p-4, 0x3.8ff10cp+0)
Result:
 is:         -1.16830070183739129219e-01  -0x1.de89352a0e8470000000p-4
 should be:  -1.16830070183738934930e-01  -0x1.de89352a0e8390000000p-4
 difference:  1.94289029309402394575e-16   0x1.c0000000000000000000p-53
 ulp       :  14.0000
 max.ulp   :  8.0000

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