mirror of git://sourceware.org/git/glibc.git
math: Use binary search on lgammaf slow path
And remove some unused entries of the fallback table. Checked on x86_64-linux-gnu and aarch64-linux-gnu. Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
This commit is contained in:
Adhemerval Zanella
parent
6610a293b3
commit
850d93f514
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@ -6933,6 +6933,9 @@ lgamma 0x1p-16494
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lgamma -0x1p-16494
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# the next value generates larger error bounds on x86_64 (binary32)
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lgamma -0x3.ec4298p+0
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lgamma 0x1.ecf3fep-73
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lgamma 0x1.58ace8p+112
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lgamma -0x1.efc2a2p+14
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# Values +/- 10ulp from overflow threshold. (Values very close to
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# overflow threshold produce results very close of that threshold,
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@ -2226,6 +2226,81 @@ lgamma -0x3.ec4298p+0
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= lgamma tonearest ibm128 -0x3.ec4298p+0 : -0x7.d809ecd340fc16da6722ad1166p-4 1 : inexact-ok
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= lgamma towardzero ibm128 -0x3.ec4298p+0 : -0x7.d809ecd340fc16da6722ad1166p-4 1 : inexact-ok
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= lgamma upward ibm128 -0x3.ec4298p+0 : -0x7.d809ecd340fc16da6722ad1166p-4 1 : inexact-ok
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lgamma 0x1.ecf3fep-73
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= lgamma downward binary32 0xf.679ffp-76 : 0x3.1f1cbp+4 1 : inexact-ok
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= lgamma tonearest binary32 0xf.679ffp-76 : 0x3.1f1cb4p+4 1 : inexact-ok
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= lgamma towardzero binary32 0xf.679ffp-76 : 0x3.1f1cbp+4 1 : inexact-ok
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= lgamma upward binary32 0xf.679ffp-76 : 0x3.1f1cb4p+4 1 : inexact-ok
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= lgamma downward binary64 0xf.679ffp-76 : 0x3.1f1cb3ffffffep+4 1 : inexact-ok
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= lgamma tonearest binary64 0xf.679ffp-76 : 0x3.1f1cb4p+4 1 : inexact-ok
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= lgamma towardzero binary64 0xf.679ffp-76 : 0x3.1f1cb3ffffffep+4 1 : inexact-ok
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= lgamma upward binary64 0xf.679ffp-76 : 0x3.1f1cb4p+4 1 : inexact-ok
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= lgamma downward intel96 0xf.679ffp-76 : 0x3.1f1cb3fffffff08cp+4 1 : inexact-ok
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= lgamma tonearest intel96 0xf.679ffp-76 : 0x3.1f1cb3fffffff08cp+4 1 : inexact-ok
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= lgamma towardzero intel96 0xf.679ffp-76 : 0x3.1f1cb3fffffff08cp+4 1 : inexact-ok
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= lgamma upward intel96 0xf.679ffp-76 : 0x3.1f1cb3fffffff09p+4 1 : inexact-ok
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= lgamma downward m68k96 0xf.679ffp-76 : 0x3.1f1cb3fffffff08cp+4 1 : inexact-ok
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= lgamma tonearest m68k96 0xf.679ffp-76 : 0x3.1f1cb3fffffff08cp+4 1 : inexact-ok
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= lgamma towardzero m68k96 0xf.679ffp-76 : 0x3.1f1cb3fffffff08cp+4 1 : inexact-ok
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= lgamma upward m68k96 0xf.679ffp-76 : 0x3.1f1cb3fffffff09p+4 1 : inexact-ok
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= lgamma downward binary128 0xf.679ffp-76 : 0x3.1f1cb3fffffff08c0c4788f0c8a8p+4 1 : inexact-ok
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= lgamma tonearest binary128 0xf.679ffp-76 : 0x3.1f1cb3fffffff08c0c4788f0c8a8p+4 1 : inexact-ok
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= lgamma towardzero binary128 0xf.679ffp-76 : 0x3.1f1cb3fffffff08c0c4788f0c8a8p+4 1 : inexact-ok
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= lgamma upward binary128 0xf.679ffp-76 : 0x3.1f1cb3fffffff08c0c4788f0c8aap+4 1 : inexact-ok
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= lgamma downward ibm128 0xf.679ffp-76 : 0x3.1f1cb3fffffff08c0c4788f0c8p+4 1 : inexact-ok
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= lgamma tonearest ibm128 0xf.679ffp-76 : 0x3.1f1cb3fffffff08c0c4788f0c9p+4 1 : inexact-ok
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= lgamma towardzero ibm128 0xf.679ffp-76 : 0x3.1f1cb3fffffff08c0c4788f0c8p+4 1 : inexact-ok
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= lgamma upward ibm128 0xf.679ffp-76 : 0x3.1f1cb3fffffff08c0c4788f0c9p+4 1 : inexact-ok
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lgamma 0x1.58ace8p+112
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= lgamma downward binary32 0x1.58ace8p+112 : 0x6.793d9p+116 1 : inexact-ok
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= lgamma tonearest binary32 0x1.58ace8p+112 : 0x6.793d98p+116 1 : inexact-ok
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= lgamma towardzero binary32 0x1.58ace8p+112 : 0x6.793d9p+116 1 : inexact-ok
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= lgamma upward binary32 0x1.58ace8p+112 : 0x6.793d98p+116 1 : inexact-ok
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= lgamma downward binary64 0x1.58ace8p+112 : 0x6.793d94p+116 1 : inexact-ok
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= lgamma tonearest binary64 0x1.58ace8p+112 : 0x6.793d940000004p+116 1 : inexact-ok
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= lgamma towardzero binary64 0x1.58ace8p+112 : 0x6.793d94p+116 1 : inexact-ok
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= lgamma upward binary64 0x1.58ace8p+112 : 0x6.793d940000004p+116 1 : inexact-ok
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= lgamma downward intel96 0x1.58ace8p+112 : 0x6.793d940000003d2p+116 1 : inexact-ok
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= lgamma tonearest intel96 0x1.58ace8p+112 : 0x6.793d940000003d28p+116 1 : inexact-ok
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= lgamma towardzero intel96 0x1.58ace8p+112 : 0x6.793d940000003d2p+116 1 : inexact-ok
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= lgamma upward intel96 0x1.58ace8p+112 : 0x6.793d940000003d28p+116 1 : inexact-ok
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= lgamma downward m68k96 0x1.58ace8p+112 : 0x6.793d940000003d2p+116 1 : inexact-ok
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= lgamma tonearest m68k96 0x1.58ace8p+112 : 0x6.793d940000003d28p+116 1 : inexact-ok
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= lgamma towardzero m68k96 0x1.58ace8p+112 : 0x6.793d940000003d2p+116 1 : inexact-ok
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= lgamma upward m68k96 0x1.58ace8p+112 : 0x6.793d940000003d28p+116 1 : inexact-ok
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= lgamma downward binary128 0x1.58ace8p+112 : 0x6.793d940000003d252ede096c3f0cp+116 1 : inexact-ok
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= lgamma tonearest binary128 0x1.58ace8p+112 : 0x6.793d940000003d252ede096c3f0cp+116 1 : inexact-ok
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= lgamma towardzero binary128 0x1.58ace8p+112 : 0x6.793d940000003d252ede096c3f0cp+116 1 : inexact-ok
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= lgamma upward binary128 0x1.58ace8p+112 : 0x6.793d940000003d252ede096c3f1p+116 1 : inexact-ok
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= lgamma downward ibm128 0x1.58ace8p+112 : 0x6.793d940000003d252ede096c3ep+116 1 : inexact-ok
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= lgamma tonearest ibm128 0x1.58ace8p+112 : 0x6.793d940000003d252ede096c4p+116 1 : inexact-ok
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= lgamma towardzero ibm128 0x1.58ace8p+112 : 0x6.793d940000003d252ede096c3ep+116 1 : inexact-ok
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= lgamma upward ibm128 0x1.58ace8p+112 : 0x6.793d940000003d252ede096c4p+116 1 : inexact-ok
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lgamma -0x1.efc2a2p+14
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= lgamma downward binary32 -0x7.bf0a88p+12 : -0x4.88b6f8p+16 -1 : inexact-ok
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= lgamma tonearest binary32 -0x7.bf0a88p+12 : -0x4.88b6fp+16 -1 : inexact-ok
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= lgamma towardzero binary32 -0x7.bf0a88p+12 : -0x4.88b6fp+16 -1 : inexact-ok
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= lgamma upward binary32 -0x7.bf0a88p+12 : -0x4.88b6fp+16 -1 : inexact-ok
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= lgamma downward binary64 -0x7.bf0a88p+12 : -0x4.88b6f00000008p+16 -1 : inexact-ok
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= lgamma tonearest binary64 -0x7.bf0a88p+12 : -0x4.88b6f00000004p+16 -1 : inexact-ok
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= lgamma towardzero binary64 -0x7.bf0a88p+12 : -0x4.88b6f00000004p+16 -1 : inexact-ok
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= lgamma upward binary64 -0x7.bf0a88p+12 : -0x4.88b6f00000004p+16 -1 : inexact-ok
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= lgamma downward intel96 -0x7.bf0a88p+12 : -0x4.88b6f00000005978p+16 -1 : inexact-ok
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= lgamma tonearest intel96 -0x7.bf0a88p+12 : -0x4.88b6f0000000597p+16 -1 : inexact-ok
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= lgamma towardzero intel96 -0x7.bf0a88p+12 : -0x4.88b6f0000000597p+16 -1 : inexact-ok
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= lgamma upward intel96 -0x7.bf0a88p+12 : -0x4.88b6f0000000597p+16 -1 : inexact-ok
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= lgamma downward m68k96 -0x7.bf0a88p+12 : -0x4.88b6f00000005978p+16 -1 : inexact-ok
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= lgamma tonearest m68k96 -0x7.bf0a88p+12 : -0x4.88b6f0000000597p+16 -1 : inexact-ok
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= lgamma towardzero m68k96 -0x7.bf0a88p+12 : -0x4.88b6f0000000597p+16 -1 : inexact-ok
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= lgamma upward m68k96 -0x7.bf0a88p+12 : -0x4.88b6f0000000597p+16 -1 : inexact-ok
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= lgamma downward binary128 -0x7.bf0a88p+12 : -0x4.88b6f00000005971e29c3b8dd834p+16 -1 : inexact-ok
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= lgamma tonearest binary128 -0x7.bf0a88p+12 : -0x4.88b6f00000005971e29c3b8dd834p+16 -1 : inexact-ok
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= lgamma towardzero binary128 -0x7.bf0a88p+12 : -0x4.88b6f00000005971e29c3b8dd83p+16 -1 : inexact-ok
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= lgamma upward binary128 -0x7.bf0a88p+12 : -0x4.88b6f00000005971e29c3b8dd83p+16 -1 : inexact-ok
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= lgamma downward ibm128 -0x7.bf0a88p+12 : -0x4.88b6f00000005971e29c3b8ddap+16 -1 : inexact-ok
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= lgamma tonearest ibm128 -0x7.bf0a88p+12 : -0x4.88b6f00000005971e29c3b8dd8p+16 -1 : inexact-ok
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= lgamma towardzero ibm128 -0x7.bf0a88p+12 : -0x4.88b6f00000005971e29c3b8dd8p+16 -1 : inexact-ok
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= lgamma upward ibm128 -0x7.bf0a88p+12 : -0x4.88b6f00000005971e29c3b8dd8p+16 -1 : inexact-ok
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lgamma 0x3.12be0cp+120
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= lgamma downward binary32 0x3.12be0cp+120 : 0xf.ffff1p+124 1 : inexact-ok
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= lgamma tonearest binary32 0x3.12be0cp+120 : 0xf.ffff1p+124 1 : inexact-ok
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@ -116,41 +116,34 @@ __ieee754_lgammaf_r (float x, int *signgamp)
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float f;
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float df;
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} tb[] = {
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{ -0x1.efc2a2p+14, -0x1.222dbcp+18, -0x1p-7 },
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{ -0x1.627346p+7, -0x1.73235ep+9, -0x1p-16 },
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{ -0x1.08b14p+4, -0x1.f0cbe6p+4, -0x1p-21 },
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{ -0x1.69d628p+3, -0x1.0eac2ap+4, -0x1p-21 },
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{ -0x1.904902p+2, -0x1.65532cp+2, 0x1p-23 },
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{ -0x1.9272d2p+1, -0x1.170b98p-8, 0x1p-33 },
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{ -0x1.625edap+1, 0x1.6a6c4ap-5, -0x1p-30 },
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{ -0x1.5fc2aep+1, 0x1.c0a484p-11, -0x1p-36 },
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{ -0x1.5fb43ep+1, 0x1.5b697p-17, 0x1p-42 },
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{ -0x1.5fa20cp+1, -0x1.132f7ap-10, 0x1p-35 },
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{ -0x1.580c1ep+1, -0x1.5787c6p-4, 0x1p-29 },
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{ -0x1.3a7fcap+1, -0x1.e4cf24p-24, -0x1p-49 },
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{ -0x1.c2f04p-30, 0x1.43a6f6p+4, 0x1p-21 },
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{ -0x1.ade594p-30, 0x1.446ab2p+4, -0x1p-21 },
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{ -0x1.437e74p-40, 0x1.b7dec2p+4, -0x1p-21 },
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{ -0x1.d85bfep-43, 0x1.d31592p+4, -0x1p-21 },
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{ -0x1.f51c8ep-49, 0x1.0a572ap+5, -0x1p-20 },
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{ -0x1.108a5ap-66, 0x1.6d7b18p+5, -0x1p-20 },
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{ -0x1.ecf3fep-73, 0x1.8f8e5ap+5, -0x1p-20 },
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{ -0x1.25cb66p-123, 0x1.547a44p+6, -0x1p-19 },
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{ 0x1.ecf3fep-73, 0x1.8f8e5ap+5, -0x1p-20 },
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{ 0x1.108a5ap-66, 0x1.6d7b18p+5, -0x1p-20 },
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{ 0x1.a68bbcp-42, 0x1.c9c6e8p+4, 0x1p-21 },
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{ 0x1.ddfd06p-12, 0x1.ec5ba8p+2, -0x1p-23 },
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{ 0x1.f8a754p-9, 0x1.63acc2p+2, 0x1p-23 },
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{ 0x1.8d16b2p+5, 0x1.1e4b4ep+7, 0x1p-18 },
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{ 0x1.359e0ep+10, 0x1.d9ad02p+12, -0x1p-13 },
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{ 0x1.a82a2cp+13, 0x1.c38036p+16, 0x1p-9 },
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{ 0x1.62c646p+14, 0x1.9075bep+17, -0x1p-8 },
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{ 0x1.7f298p+31, 0x1.f44946p+35, -0x1p+10 },
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{ 0x1.a45ea4p+33, 0x1.25dcbcp+38, -0x1p+13 },
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{ 0x1.f9413ep+76, 0x1.9d5ab4p+82, -0x1p+57 },
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{ 0x1.dcbbaap+99, 0x1.fc5772p+105, 0x1p+80 },
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{ 0x1.58ace8p+112, 0x1.9e4f66p+118, -0x1p+93 },
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{ 0x1.87bdfp+115, 0x1.e465aep+121, 0x1p+96 },
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/* NB: the entries should be sorted by the asuint (x) value. */
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{ 0x1.ecf3fep-73f, 0x1.8f8e5ap+5f, -0x1p-20f },
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{ 0x1.108a5ap-66f, 0x1.6d7b18p+5f, -0x1p-20f },
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{ 0x1.a68bbcp-42f, 0x1.c9c6e8p+4f, 0x1p-21f },
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{ 0x1.ddfd06p-12f, 0x1.ec5ba8p+2f, -0x1p-23f },
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{ 0x1.f8a754p-9f, 0x1.63acc2p+2f, 0x1p-23f },
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{ 0x1.8d16b2p+5f, 0x1.1e4b4ep+7f, 0x1p-18f },
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{ 0x1.359e0ep+10f, 0x1.d9ad02p+12f, -0x1p-13f },
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{ 0x1.a82a2cp+13f, 0x1.c38036p+16f, 0x1p-9f },
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{ 0x1.62c646p+14f, 0x1.9075bep+17f, -0x1p-8f },
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{ 0x1.7f298p+31f, 0x1.f44946p+35f, -0x1p+10f },
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{ 0x1.a45ea4p+33f, 0x1.25dcbcp+38f, -0x1p+13f },
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{ 0x1.f9413ep+76f, 0x1.9d5ab4p+82f, -0x1p+57f },
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{ 0x1.dcbbaap+99f, 0x1.fc5772p+105f, 0x1p+80f },
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{ 0x1.58ace8p+112f, 0x1.9e4f66p+118f, -0x1p+93f },
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{ 0x1.87bdfp+115f, 0x1.e465aep+121f, 0x1p+96f },
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{ -0x1.25cb66p-123f, 0x1.547a44p+6f, -0x1p-19f },
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{ -0x1.ecf3fep-73f, 0x1.8f8e5ap+5f, -0x1p-20f },
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{ -0x1.108a5ap-66f, 0x1.6d7b18p+5f, -0x1p-20f },
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{ -0x1.f51c8ep-49f, 0x1.0a572ap+5f, -0x1p-20f },
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{ -0x1.d85bfep-43f, 0x1.d31592p+4f, -0x1p-21f },
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{ -0x1.437e74p-40f, 0x1.b7dec2p+4f, -0x1p-21f },
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{ -0x1.ade594p-30f, 0x1.446ab2p+4f, -0x1p-21f },
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{ -0x1.c2f04p-30f, 0x1.43a6f6p+4f, 0x1p-21f },
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{ -0x1.580c1ep+1f, -0x1.5787c6p-4f, 0x1p-29f },
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{ -0x1.69d628p+3f, -0x1.0eac2ap+4f, -0x1p-21f },
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{ -0x1.627346p+7f, -0x1.73235ep+9f, -0x1p-16f },
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{ -0x1.efc2a2p+14f, -0x1.222dbcp+18f, -0x1p-7f }
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};
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float fx = floor (x);
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@ -355,11 +348,18 @@ __ieee754_lgammaf_r (float x, int *signgamp)
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if (__glibc_unlikely (tl <= 31u))
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{
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t = asuint (x);
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for (unsigned i = 0; i < array_length (tb); i++)
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{
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if (t == asuint (tb[i].x))
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return tb[i].f + tb[i].df;
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int a = 0, b = array_length (tb) - 1;
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while (a < b)
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{ /* Binary search. */
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int m = (a + b) >> 1;
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uint32_t tbi = asuint (tb[m].x);
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if (t > tbi)
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a = m + 1;
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else
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b = m;
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}
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if (t == asuint (tb[a].x))
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return tb[a].f + tb[a].df;
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}
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return r;
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}
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