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msvcrt: Use the log2()/log2f() implementation from the bundled musl library.
This commit is contained in:
Alexandre Julliard
parent
714874ba46
commit
21cbe74b88
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@ -5496,344 +5496,6 @@ void __cdecl __libm_sse2_sqrt_precise(void)
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#if _MSVCR_VER>=120
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/*********************************************************************
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* log2 (MSVCR120.@)
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*
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* Copied from musl: src/math/log2.c
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*/
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double CDECL log2(double x)
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{
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static const double invln2hi = 0x1.7154765200000p+0,
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invln2lo = 0x1.705fc2eefa200p-33;
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static const double A[] = {
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-0x1.71547652b8339p-1,
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0x1.ec709dc3a04bep-2,
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-0x1.7154764702ffbp-2,
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0x1.2776c50034c48p-2,
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-0x1.ec7b328ea92bcp-3,
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0x1.a6225e117f92ep-3
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};
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static const double B[] = {
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-0x1.71547652b82fep-1,
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0x1.ec709dc3a03f7p-2,
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-0x1.71547652b7c3fp-2,
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0x1.2776c50f05be4p-2,
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-0x1.ec709dd768fe5p-3,
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0x1.a61761ec4e736p-3,
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-0x1.7153fbc64a79bp-3,
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0x1.484d154f01b4ap-3,
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-0x1.289e4a72c383cp-3,
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0x1.0b32f285aee66p-3
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};
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static const struct {
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double invc, logc;
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} T[] = {
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{0x1.724286bb1acf8p+0, -0x1.1095feecdb000p-1},
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{0x1.6e1f766d2cca1p+0, -0x1.08494bd76d000p-1},
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{0x1.6a13d0e30d48ap+0, -0x1.00143aee8f800p-1},
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{0x1.661ec32d06c85p+0, -0x1.efec5360b4000p-2},
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{0x1.623fa951198f8p+0, -0x1.dfdd91ab7e000p-2},
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{0x1.5e75ba4cf026cp+0, -0x1.cffae0cc79000p-2},
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{0x1.5ac055a214fb8p+0, -0x1.c043811fda000p-2},
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{0x1.571ed0f166e1ep+0, -0x1.b0b67323ae000p-2},
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{0x1.53909590bf835p+0, -0x1.a152f5a2db000p-2},
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{0x1.5014fed61adddp+0, -0x1.9217f5af86000p-2},
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{0x1.4cab88e487bd0p+0, -0x1.8304db0719000p-2},
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{0x1.49539b4334feep+0, -0x1.74189f9a9e000p-2},
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{0x1.460cbdfafd569p+0, -0x1.6552bb5199000p-2},
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{0x1.42d664ee4b953p+0, -0x1.56b23a29b1000p-2},
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{0x1.3fb01111dd8a6p+0, -0x1.483650f5fa000p-2},
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{0x1.3c995b70c5836p+0, -0x1.39de937f6a000p-2},
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{0x1.3991c4ab6fd4ap+0, -0x1.2baa1538d6000p-2},
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{0x1.3698e0ce099b5p+0, -0x1.1d98340ca4000p-2},
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{0x1.33ae48213e7b2p+0, -0x1.0fa853a40e000p-2},
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{0x1.30d191985bdb1p+0, -0x1.01d9c32e73000p-2},
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{0x1.2e025cab271d7p+0, -0x1.e857da2fa6000p-3},
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{0x1.2b404cf13cd82p+0, -0x1.cd3c8633d8000p-3},
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{0x1.288b02c7ccb50p+0, -0x1.b26034c14a000p-3},
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{0x1.25e2263944de5p+0, -0x1.97c1c2f4fe000p-3},
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{0x1.234563d8615b1p+0, -0x1.7d6023f800000p-3},
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{0x1.20b46e33eaf38p+0, -0x1.633a71a05e000p-3},
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{0x1.1e2eefdcda3ddp+0, -0x1.494f5e9570000p-3},
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{0x1.1bb4a580b3930p+0, -0x1.2f9e424e0a000p-3},
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{0x1.19453847f2200p+0, -0x1.162595afdc000p-3},
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{0x1.16e06c0d5d73cp+0, -0x1.f9c9a75bd8000p-4},
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{0x1.1485f47b7e4c2p+0, -0x1.c7b575bf9c000p-4},
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{0x1.12358ad0085d1p+0, -0x1.960c60ff48000p-4},
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{0x1.0fef00f532227p+0, -0x1.64ce247b60000p-4},
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{0x1.0db2077d03a8fp+0, -0x1.33f78b2014000p-4},
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{0x1.0b7e6d65980d9p+0, -0x1.0387d1a42c000p-4},
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{0x1.0953efe7b408dp+0, -0x1.a6f9208b50000p-5},
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{0x1.07325cac53b83p+0, -0x1.47a954f770000p-5},
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{0x1.05197e40d1b5cp+0, -0x1.d23a8c50c0000p-6},
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{0x1.03091c1208ea2p+0, -0x1.16a2629780000p-6},
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{0x1.0101025b37e21p+0, -0x1.720f8d8e80000p-8},
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{0x1.fc07ef9caa76bp-1, 0x1.6fe53b1500000p-7},
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{0x1.f4465d3f6f184p-1, 0x1.11ccce10f8000p-5},
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{0x1.ecc079f84107fp-1, 0x1.c4dfc8c8b8000p-5},
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{0x1.e573a99975ae8p-1, 0x1.3aa321e574000p-4},
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{0x1.de5d6f0bd3de6p-1, 0x1.918a0d08b8000p-4},
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{0x1.d77b681ff38b3p-1, 0x1.e72e9da044000p-4},
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{0x1.d0cb5724de943p-1, 0x1.1dcd2507f6000p-3},
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{0x1.ca4b2dc0e7563p-1, 0x1.476ab03dea000p-3},
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{0x1.c3f8ee8d6cb51p-1, 0x1.7074377e22000p-3},
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{0x1.bdd2b4f020c4cp-1, 0x1.98ede8ba94000p-3},
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{0x1.b7d6c006015cap-1, 0x1.c0db86ad2e000p-3},
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{0x1.b20366e2e338fp-1, 0x1.e840aafcee000p-3},
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{0x1.ac57026295039p-1, 0x1.0790ab4678000p-2},
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{0x1.a6d01bc2731ddp-1, 0x1.1ac056801c000p-2},
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{0x1.a16d3bc3ff18bp-1, 0x1.2db11d4fee000p-2},
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{0x1.9c2d14967feadp-1, 0x1.406464ec58000p-2},
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{0x1.970e4f47c9902p-1, 0x1.52dbe093af000p-2},
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{0x1.920fb3982bcf2p-1, 0x1.651902050d000p-2},
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{0x1.8d30187f759f1p-1, 0x1.771d2cdeaf000p-2},
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{0x1.886e5ebb9f66dp-1, 0x1.88e9c857d9000p-2},
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{0x1.83c97b658b994p-1, 0x1.9a80155e16000p-2},
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{0x1.7f405ffc61022p-1, 0x1.abe186ed3d000p-2},
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{0x1.7ad22181415cap-1, 0x1.bd0f2aea0e000p-2},
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{0x1.767dcf99eff8cp-1, 0x1.ce0a43dbf4000p-2}
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};
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static const struct {
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double chi, clo;
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} T2[] = {
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{0x1.6200012b90a8ep-1, 0x1.904ab0644b605p-55},
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{0x1.66000045734a6p-1, 0x1.1ff9bea62f7a9p-57},
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{0x1.69fffc325f2c5p-1, 0x1.27ecfcb3c90bap-55},
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{0x1.6e00038b95a04p-1, 0x1.8ff8856739326p-55},
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{0x1.71fffe09994e3p-1, 0x1.afd40275f82b1p-55},
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{0x1.7600015590e1p-1, -0x1.2fd75b4238341p-56},
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{0x1.7a00012655bd5p-1, 0x1.808e67c242b76p-56},
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{0x1.7e0003259e9a6p-1, -0x1.208e426f622b7p-57},
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{0x1.81fffedb4b2d2p-1, -0x1.402461ea5c92fp-55},
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{0x1.860002dfafcc3p-1, 0x1.df7f4a2f29a1fp-57},
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{0x1.89ffff78c6b5p-1, -0x1.e0453094995fdp-55},
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{0x1.8e00039671566p-1, -0x1.a04f3bec77b45p-55},
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{0x1.91fffe2bf1745p-1, -0x1.7fa34400e203cp-56},
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{0x1.95fffcc5c9fd1p-1, -0x1.6ff8005a0695dp-56},
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{0x1.9a0003bba4767p-1, 0x1.0f8c4c4ec7e03p-56},
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{0x1.9dfffe7b92da5p-1, 0x1.e7fd9478c4602p-55},
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{0x1.a1fffd72efdafp-1, -0x1.a0c554dcdae7ep-57},
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{0x1.a5fffde04ff95p-1, 0x1.67da98ce9b26bp-55},
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{0x1.a9fffca5e8d2bp-1, -0x1.284c9b54c13dep-55},
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{0x1.adfffddad03eap-1, 0x1.812c8ea602e3cp-58},
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{0x1.b1ffff10d3d4dp-1, -0x1.efaddad27789cp-55},
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{0x1.b5fffce21165ap-1, 0x1.3cb1719c61237p-58},
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{0x1.b9fffd950e674p-1, 0x1.3f7d94194cep-56},
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{0x1.be000139ca8afp-1, 0x1.50ac4215d9bcp-56},
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{0x1.c20005b46df99p-1, 0x1.beea653e9c1c9p-57},
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{0x1.c600040b9f7aep-1, -0x1.c079f274a70d6p-56},
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{0x1.ca0006255fd8ap-1, -0x1.a0b4076e84c1fp-56},
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{0x1.cdfffd94c095dp-1, 0x1.8f933f99ab5d7p-55},
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{0x1.d1ffff975d6cfp-1, -0x1.82c08665fe1bep-58},
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{0x1.d5fffa2561c93p-1, -0x1.b04289bd295f3p-56},
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{0x1.d9fff9d228b0cp-1, 0x1.70251340fa236p-55},
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{0x1.de00065bc7e16p-1, -0x1.5011e16a4d80cp-56},
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{0x1.e200002f64791p-1, 0x1.9802f09ef62ep-55},
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{0x1.e600057d7a6d8p-1, -0x1.e0b75580cf7fap-56},
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{0x1.ea00027edc00cp-1, -0x1.c848309459811p-55},
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{0x1.ee0006cf5cb7cp-1, -0x1.f8027951576f4p-55},
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{0x1.f2000782b7dccp-1, -0x1.f81d97274538fp-55},
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{0x1.f6000260c450ap-1, -0x1.071002727ffdcp-59},
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{0x1.f9fffe88cd533p-1, -0x1.81bdce1fda8bp-58},
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{0x1.fdfffd50f8689p-1, 0x1.7f91acb918e6ep-55},
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{0x1.0200004292367p+0, 0x1.b7ff365324681p-54},
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{0x1.05fffe3e3d668p+0, 0x1.6fa08ddae957bp-55},
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{0x1.0a0000a85a757p+0, -0x1.7e2de80d3fb91p-58},
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{0x1.0e0001a5f3fccp+0, -0x1.1823305c5f014p-54},
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{0x1.11ffff8afbaf5p+0, -0x1.bfabb6680bac2p-55},
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{0x1.15fffe54d91adp+0, -0x1.d7f121737e7efp-54},
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{0x1.1a00011ac36e1p+0, 0x1.c000a0516f5ffp-54},
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{0x1.1e00019c84248p+0, -0x1.082fbe4da5dap-54},
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{0x1.220000ffe5e6ep+0, -0x1.8fdd04c9cfb43p-55},
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{0x1.26000269fd891p+0, 0x1.cfe2a7994d182p-55},
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{0x1.2a00029a6e6dap+0, -0x1.00273715e8bc5p-56},
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{0x1.2dfffe0293e39p+0, 0x1.b7c39dab2a6f9p-54},
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{0x1.31ffff7dcf082p+0, 0x1.df1336edc5254p-56},
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{0x1.35ffff05a8b6p+0, -0x1.e03564ccd31ebp-54},
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{0x1.3a0002e0eaeccp+0, 0x1.5f0e74bd3a477p-56},
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{0x1.3e000043bb236p+0, 0x1.c7dcb149d8833p-54},
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{0x1.4200002d187ffp+0, 0x1.e08afcf2d3d28p-56},
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{0x1.460000d387cb1p+0, 0x1.20837856599a6p-55},
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{0x1.4a00004569f89p+0, -0x1.9fa5c904fbcd2p-55},
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{0x1.4e000043543f3p+0, -0x1.81125ed175329p-56},
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{0x1.51fffcc027f0fp+0, 0x1.883d8847754dcp-54},
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{0x1.55ffffd87b36fp+0, -0x1.709e731d02807p-55},
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{0x1.59ffff21df7bap+0, 0x1.7f79f68727b02p-55},
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{0x1.5dfffebfc3481p+0, -0x1.180902e30e93ep-54}
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};
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double z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p, rhi, rlo;
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UINT64 ix, iz, tmp;
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UINT32 top;
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int k, i;
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ix = *(UINT64*)&x;
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top = ix >> 48;
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if (ix - 0x3feea4af00000000ULL < 0x210aa00000000ULL) {
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/* Handle close to 1.0 inputs separately. */
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/* Fix sign of zero with downward rounding when x==1. */
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if (ix == 0x3ff0000000000000ULL)
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return 0;
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r = x - 1.0;
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*(UINT64*)&rhi = *(UINT64*)&r & -1ULL << 32;
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rlo = r - rhi;
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hi = rhi * invln2hi;
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lo = rlo * invln2hi + r * invln2lo;
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r2 = r * r; /* rounding error: 0x1p-62. */
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r4 = r2 * r2;
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/* Worst-case error is less than 0.54 ULP (0.55 ULP without fma). */
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p = r2 * (B[0] + r * B[1]);
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y = hi + p;
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lo += hi - y + p;
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lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5]) +
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r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9])));
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y += lo;
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return y;
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}
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if (top - 0x0010 >= 0x7ff0 - 0x0010) {
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/* x < 0x1p-1022 or inf or nan. */
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if (ix * 2 == 0) {
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*_errno() = ERANGE;
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return -1.0 / x;
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}
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if (ix == 0x7ff0000000000000ULL) /* log(inf) == inf. */
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return x;
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if ((top & 0x7ff0) == 0x7ff0 && (ix & 0xfffffffffffffULL))
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return x;
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if (top & 0x8000) {
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*_errno() = EDOM;
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return (x - x) / (x - x);
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}
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/* x is subnormal, normalize it. */
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x *= 0x1p52;
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ix = *(UINT64*)&x;
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ix -= 52ULL << 52;
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}
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/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
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The range is split into N subintervals.
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The ith subinterval contains z and c is near its center. */
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tmp = ix - 0x3fe6000000000000ULL;
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i = (tmp >> (52 - 6)) % (1 << 6);
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k = (INT64)tmp >> 52; /* arithmetic shift */
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iz = ix - (tmp & 0xfffULL << 52);
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invc = T[i].invc;
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logc = T[i].logc;
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z = *(double*)&iz;
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kd = k;
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/* log2(x) = log2(z/c) + log2(c) + k. */
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/* r ~= z/c - 1, |r| < 1/(2*N). */
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/* rounding error: 0x1p-55/N + 0x1p-65. */
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r = (z - T2[i].chi - T2[i].clo) * invc;
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*(UINT64*)&rhi = *(UINT64*)&r & -1ULL << 32;
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rlo = r - rhi;
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t1 = rhi * invln2hi;
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t2 = rlo * invln2hi + r * invln2lo;
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/* hi + lo = r/ln2 + log2(c) + k. */
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t3 = kd + logc;
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hi = t3 + t1;
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lo = t3 - hi + t1 + t2;
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/* log2(r+1) = r/ln2 + r^2*poly(r). */
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/* Evaluation is optimized assuming superscalar pipelined execution. */
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r2 = r * r; /* rounding error: 0x1p-54/N^2. */
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r4 = r2 * r2;
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/* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
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~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma). */
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p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]);
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y = lo + r2 * p + hi;
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return y;
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}
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/*********************************************************************
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* log2f (MSVCR120.@)
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*
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* Copied from musl: src/math/log2f.c
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*/
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float CDECL log2f(float x)
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{
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static const double A[] = {
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-0x1.712b6f70a7e4dp-2,
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0x1.ecabf496832ep-2,
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-0x1.715479ffae3dep-1,
|
||||
0x1.715475f35c8b8p0
|
||||
};
|
||||
static const struct {
|
||||
double invc, logc;
|
||||
} T[] = {
|
||||
{ 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 },
|
||||
{ 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 },
|
||||
{ 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 },
|
||||
{ 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 },
|
||||
{ 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 },
|
||||
{ 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 },
|
||||
{ 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 },
|
||||
{ 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 },
|
||||
{ 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 },
|
||||
{ 0x1p+0, 0x0p+0 },
|
||||
{ 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 },
|
||||
{ 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 },
|
||||
{ 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 },
|
||||
{ 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 },
|
||||
{ 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 },
|
||||
{ 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 }
|
||||
};
|
||||
|
||||
double z, r, r2, p, y, y0, invc, logc;
|
||||
UINT32 ix, iz, top, tmp;
|
||||
int k, i;
|
||||
|
||||
ix = *(UINT32*)&x;
|
||||
/* Fix sign of zero with downward rounding when x==1. */
|
||||
if (ix == 0x3f800000)
|
||||
return 0;
|
||||
if (ix - 0x00800000 >= 0x7f800000 - 0x00800000) {
|
||||
/* x < 0x1p-126 or inf or nan. */
|
||||
if (ix * 2 == 0) {
|
||||
*_errno() = ERANGE;
|
||||
return -1.0f / x;
|
||||
}
|
||||
if (ix == 0x7f800000) /* log2(inf) == inf. */
|
||||
return x;
|
||||
if (ix * 2 > 0xff000000)
|
||||
return x;
|
||||
if (ix & 0x80000000) {
|
||||
*_errno() = EDOM;
|
||||
return (x - x) / (x - x);
|
||||
}
|
||||
/* x is subnormal, normalize it. */
|
||||
x *= 0x1p23f;
|
||||
ix = *(UINT32*)&x;
|
||||
ix -= 23 << 23;
|
||||
}
|
||||
|
||||
/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
|
||||
The range is split into N subintervals.
|
||||
The ith subinterval contains z and c is near its center. */
|
||||
tmp = ix - 0x3f330000;
|
||||
i = (tmp >> (23 - 4)) % (1 << 4);
|
||||
top = tmp & 0xff800000;
|
||||
iz = ix - top;
|
||||
k = (INT32)tmp >> 23; /* arithmetic shift */
|
||||
invc = T[i].invc;
|
||||
logc = T[i].logc;
|
||||
z = *(float*)&iz;
|
||||
|
||||
/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
|
||||
r = z * invc - 1;
|
||||
y0 = logc + (double)k;
|
||||
|
||||
/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
|
||||
r2 = r * r;
|
||||
y = A[1] * r + A[2];
|
||||
y = A[0] * r2 + y;
|
||||
p = A[3] * r + y0;
|
||||
y = y * r2 + p;
|
||||
return y;
|
||||
}
|
||||
|
||||
/*********************************************************************
|
||||
* rint (MSVCR120.@)
|
||||
*/
|
||||
|
|
|
|||
|
|
@ -65,12 +65,18 @@ double __cdecl log2(double x)
|
|||
}
|
||||
if (predict_false(top - 0x0010 >= 0x7ff0 - 0x0010)) {
|
||||
/* x < 0x1p-1022 or inf or nan. */
|
||||
if (ix * 2 == 0)
|
||||
if (ix * 2 == 0) {
|
||||
errno = ERANGE;
|
||||
return __math_divzero(1);
|
||||
}
|
||||
if (ix == asuint64(INFINITY)) /* log(inf) == inf. */
|
||||
return x;
|
||||
if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
|
||||
if ((top & 0x7ff0) == 0x7ff0 && (ix & 0xfffffffffffffULL))
|
||||
return x;
|
||||
if (top & 0x8000) {
|
||||
errno = EDOM;
|
||||
return __math_invalid(x);
|
||||
}
|
||||
/* x is subnormal, normalize it. */
|
||||
ix = asuint64(x * 0x1p52);
|
||||
ix -= 52ULL << 52;
|
||||
|
|
|
|||
|
|
@ -35,12 +35,18 @@ float __cdecl log2f(float x)
|
|||
return 0;
|
||||
if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
|
||||
/* x < 0x1p-126 or inf or nan. */
|
||||
if (ix * 2 == 0)
|
||||
if (ix * 2 == 0) {
|
||||
errno = ERANGE;
|
||||
return __math_divzerof(1);
|
||||
}
|
||||
if (ix == 0x7f800000) /* log2(inf) == inf. */
|
||||
return x;
|
||||
if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
|
||||
if (ix * 2 > 0xff000000)
|
||||
return x;
|
||||
if (ix & 0x80000000) {
|
||||
errno = EDOM;
|
||||
return __math_invalidf(x);
|
||||
}
|
||||
/* x is subnormal, normalize it. */
|
||||
ix = asuint(x * 0x1p23f);
|
||||
ix -= 23 << 23;
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user