Index: head/lib/msun/ld128/k_expl.h =================================================================== --- head/lib/msun/ld128/k_expl.h (revision 358346) +++ head/lib/msun/ld128/k_expl.h (revision 358347) @@ -1,322 +1,323 @@ /* from: FreeBSD: head/lib/msun/ld128/s_expl.c 251345 2013-06-03 20:09:22Z kargl */ /*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * Copyright (c) 2009-2013 Steven G. Kargl * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice unmodified, this list of conditions, and the following * disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. * * Optimized by Bruce D. Evans. */ #include __FBSDID("$FreeBSD$"); /* * ld128 version of k_expl.h. See ../ld80/s_expl.c for most comments. * * See ../src/e_exp.c and ../src/k_exp.h for precision-independent comments * about the secondary kernels. */ #define INTERVALS 128 #define LOG2_INTERVALS 7 #define BIAS (LDBL_MAX_EXP - 1) static const double /* * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest * bits zero so that multiplication of it by n is exact. */ INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */ L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */ static const long double /* 0x1.62e42fefa39ef35793c768000000p-8 */ L1 = 5.41521234812457272982212595914567508e-3L; /* * XXX values in hex in comments have been lost (or were never present) * from here. */ static const long double /* * Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]: * |exp(x) - p(x)| < 2**-124.9 * (0.002708 is ln2/(2*INTERVALS) rounded up a little). * * XXX the coeffs aren't very carefully rounded, and I get 3.6 more bits. */ A2 = 0.5, A3 = 1.66666666666666666666666666651085500e-1L, A4 = 4.16666666666666666666666666425885320e-2L, A5 = 8.33333333333333333334522877160175842e-3L, A6 = 1.38888888888888888889971139751596836e-3L; static const double A7 = 1.9841269841269470e-4, /* 0x1.a01a01a019f91p-13 */ A8 = 2.4801587301585286e-5, /* 0x1.71de3ec75a967p-19 */ A9 = 2.7557324277411235e-6, /* 0x1.71de3ec75a967p-19 */ A10 = 2.7557333722375069e-7; /* 0x1.27e505ab56259p-22 */ static const struct { /* * hi must be rounded to at most 106 bits so that multiplication * by r1 in expm1l() is exact, but it is rounded to 88 bits due to * historical accidents. * * XXX it is wasteful to use long double for both hi and lo. ld128 * exp2l() uses only float for lo (in a very differently organized * table; ld80 exp2l() is different again. It uses 2 doubles in a * table organized like this one. 1 double and 1 float would * suffice). There are different packing/locality/alignment/caching * problems with these methods. * * XXX C's bad %a format makes the bits unreadable. They happen * to all line up for the hi values 1 before the point and 88 * in 22 nybbles, but for the low values the nybbles are shifted * randomly. */ long double hi; long double lo; } tbl[INTERVALS] = { 0x1p0L, 0x0p0L, 0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L, 0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L, 0x1.04315e86e7f84bd738f9a2p0L, 0xd.a47e6ed040bb4bfc05af6455e9b8p-96L, 0x1.059b0d31585743ae7c548ep0L, 0xb.68ca417fe53e3495f7df4baf84a0p-92L, 0x1.0706b29ddf6ddc6dc403a8p0L, 0x1.d87b27ed07cb8b092ac75e311753p-88L, 0x1.0874518759bc808c35f25cp0L, 0x1.9427fa2b041b2d6829d8993a0d01p-88L, 0x1.09e3ecac6f3834521e060cp0L, 0x5.84d6b74ba2e023da730e7fccb758p-92L, 0x1.0b5586cf9890f6298b92b6p0L, 0x1.1842a98364291408b3ceb0a2a2bbp-88L, 0x1.0cc922b7247f7407b705b8p0L, 0x9.3dc5e8aac564e6fe2ef1d431fd98p-92L, 0x1.0e3ec32d3d1a2020742e4ep0L, 0x1.8af6a552ac4b358b1129e9f966a4p-88L, 0x1.0fb66affed31af232091dcp0L, 0x1.8a1426514e0b627bda694a400a27p-88L, 0x1.11301d0125b50a4ebbf1aep0L, 0xd.9318ceac5cc47ab166ee57427178p-92L, 0x1.12abdc06c31cbfb92bad32p0L, 0x4.d68e2f7270bdf7cedf94eb1cb818p-92L, 0x1.1429aaea92ddfb34101942p0L, 0x1.b2586d01844b389bea7aedd221d4p-88L, 0x1.15a98c8a58e512480d573cp0L, 0x1.d5613bf92a2b618ee31b376c2689p-88L, 0x1.172b83c7d517adcdf7c8c4p0L, 0x1.0eb14a792035509ff7d758693f24p-88L, 0x1.18af9388c8de9bbbf70b9ap0L, 0x3.c2505c97c0102e5f1211941d2840p-92L, 0x1.1a35beb6fcb753cb698f68p0L, 0x1.2d1c835a6c30724d5cfae31b84e5p-88L, 0x1.1bbe084045cd39ab1e72b4p0L, 0x4.27e35f9acb57e473915519a1b448p-92L, 0x1.1d4873168b9aa7805b8028p0L, 0x9.90f07a98b42206e46166cf051d70p-92L, 0x1.1ed5022fcd91cb8819ff60p0L, 0x1.121d1e504d36c47474c9b7de6067p-88L, 0x1.2063b88628cd63b8eeb028p0L, 0x1.50929d0fc487d21c2b84004264dep-88L, 0x1.21f49917ddc962552fd292p0L, 0x9.4bdb4b61ea62477caa1dce823ba0p-92L, 0x1.2387a6e75623866c1fadb0p0L, 0x1.c15cb593b0328566902df69e4de2p-88L, 0x1.251ce4fb2a63f3582ab7dep0L, 0x9.e94811a9c8afdcf796934bc652d0p-92L, 0x1.26b4565e27cdd257a67328p0L, 0x1.d3b249dce4e9186ddd5ff44e6b08p-92L, 0x1.284dfe1f5638096cf15cf0p0L, 0x3.ca0967fdaa2e52d7c8106f2e262cp-92L, 0x1.29e9df51fdee12c25d15f4p0L, 0x1.a24aa3bca890ac08d203fed80a07p-88L, 0x1.2b87fd0dad98ffddea4652p0L, 0x1.8fcab88442fdc3cb6de4519165edp-88L, 0x1.2d285a6e4030b40091d536p0L, 0xd.075384589c1cd1b3e4018a6b1348p-92L, 0x1.2ecafa93e2f5611ca0f45cp0L, 0x1.523833af611bdcda253c554cf278p-88L, 0x1.306fe0a31b7152de8d5a46p0L, 0x3.05c85edecbc27343629f502f1af2p-92L, 0x1.32170fc4cd8313539cf1c2p0L, 0x1.008f86dde3220ae17a005b6412bep-88L, 0x1.33c08b26416ff4c9c8610cp0L, 0x1.96696bf95d1593039539d94d662bp-88L, 0x1.356c55f929ff0c94623476p0L, 0x3.73af38d6d8d6f9506c9bbc93cbc0p-92L, 0x1.371a7373aa9caa7145502ep0L, 0x1.4547987e3e12516bf9c699be432fp-88L, 0x1.38cae6d05d86585a9cb0d8p0L, 0x1.bed0c853bd30a02790931eb2e8f0p-88L, 0x1.3a7db34e59ff6ea1bc9298p0L, 0x1.e0a1d336163fe2f852ceeb134067p-88L, 0x1.3c32dc313a8e484001f228p0L, 0xb.58f3775e06ab66353001fae9fca0p-92L, 0x1.3dea64c12342235b41223ep0L, 0x1.3d773fba2cb82b8244267c54443fp-92L, 0x1.3fa4504ac801ba0bf701aap0L, 0x4.1832fb8c1c8dbdff2c49909e6c60p-92L, 0x1.4160a21f72e29f84325b8ep0L, 0x1.3db61fb352f0540e6ba05634413ep-88L, 0x1.431f5d950a896dc7044394p0L, 0x1.0ccec81e24b0caff7581ef4127f7p-92L, 0x1.44e086061892d03136f408p0L, 0x1.df019fbd4f3b48709b78591d5cb5p-88L, 0x1.46a41ed1d005772512f458p0L, 0x1.229d97df404ff21f39c1b594d3a8p-88L, 0x1.486a2b5c13cd013c1a3b68p0L, 0x1.062f03c3dd75ce8757f780e6ec99p-88L, 0x1.4a32af0d7d3de672d8bcf4p0L, 0x6.f9586461db1d878b1d148bd3ccb8p-92L, 0x1.4bfdad5362a271d4397afep0L, 0xc.42e20e0363ba2e159c579f82e4b0p-92L, 0x1.4dcb299fddd0d63b36ef1ap0L, 0x9.e0cc484b25a5566d0bd5f58ad238p-92L, 0x1.4f9b2769d2ca6ad33d8b68p0L, 0x1.aa073ee55e028497a329a7333dbap-88L, 0x1.516daa2cf6641c112f52c8p0L, 0x4.d822190e718226177d7608d20038p-92L, 0x1.5342b569d4f81df0a83c48p0L, 0x1.d86a63f4e672a3e429805b049465p-88L, 0x1.551a4ca5d920ec52ec6202p0L, 0x4.34ca672645dc6c124d6619a87574p-92L, 0x1.56f4736b527da66ecb0046p0L, 0x1.64eb3c00f2f5ab3d801d7cc7272dp-88L, 0x1.58d12d497c7fd252bc2b72p0L, 0x1.43bcf2ec936a970d9cc266f0072fp-88L, 0x1.5ab07dd48542958c930150p0L, 0x1.91eb345d88d7c81280e069fbdb63p-88L, 0x1.5c9268a5946b701c4b1b80p0L, 0x1.6986a203d84e6a4a92f179e71889p-88L, 0x1.5e76f15ad21486e9be4c20p0L, 0x3.99766a06548a05829e853bdb2b52p-92L, 0x1.605e1b976dc08b076f592ap0L, 0x4.86e3b34ead1b4769df867b9c89ccp-92L, 0x1.6247eb03a5584b1f0fa06ep0L, 0x1.d2da42bb1ceaf9f732275b8aef30p-88L, 0x1.6434634ccc31fc76f8714cp0L, 0x4.ed9a4e41000307103a18cf7a6e08p-92L, 0x1.66238825522249127d9e28p0L, 0x1.b8f314a337f4dc0a3adf1787ff74p-88L, 0x1.68155d44ca973081c57226p0L, 0x1.b9f32706bfe4e627d809a85dcc66p-88L, 0x1.6a09e667f3bcc908b2fb12p0L, 0x1.66ea957d3e3adec17512775099dap-88L, 0x1.6c012750bdabeed76a9980p0L, 0xf.4f33fdeb8b0ecd831106f57b3d00p-96L, 0x1.6dfb23c651a2ef220e2cbep0L, 0x1.bbaa834b3f11577ceefbe6c1c411p-92L, 0x1.6ff7df9519483cf87e1b4ep0L, 0x1.3e213bff9b702d5aa477c12523cep-88L, 0x1.71f75e8ec5f73dd2370f2ep0L, 0xf.0acd6cb434b562d9e8a20adda648p-92L, 0x1.73f9a48a58173bd5c9a4e6p0L, 0x8.ab1182ae217f3a7681759553e840p-92L, 0x1.75feb564267c8bf6e9aa32p0L, 0x1.a48b27071805e61a17b954a2dad8p-88L, 0x1.780694fde5d3f619ae0280p0L, 0x8.58b2bb2bdcf86cd08e35fb04c0f0p-92L, 0x1.7a11473eb0186d7d51023ep0L, 0x1.6cda1f5ef42b66977960531e821bp-88L, 0x1.7c1ed0130c1327c4933444p0L, 0x1.937562b2dc933d44fc828efd4c9cp-88L, 0x1.7e2f336cf4e62105d02ba0p0L, 0x1.5797e170a1427f8fcdf5f3906108p-88L, 0x1.80427543e1a11b60de6764p0L, 0x9.a354ea706b8e4d8b718a672bf7c8p-92L, 0x1.82589994cce128acf88afap0L, 0xb.34a010f6ad65cbbac0f532d39be0p-92L, 0x1.8471a4623c7acce52f6b96p0L, 0x1.c64095370f51f48817914dd78665p-88L, 0x1.868d99b4492ec80e41d90ap0L, 0xc.251707484d73f136fb5779656b70p-92L, 0x1.88ac7d98a669966530bcdep0L, 0x1.2d4e9d61283ef385de170ab20f96p-88L, 0x1.8ace5422aa0db5ba7c55a0p0L, 0x1.92c9bb3e6ed61f2733304a346d8fp-88L, 0x1.8cf3216b5448bef2aa1cd0p0L, 0x1.61c55d84a9848f8c453b3ca8c946p-88L, 0x1.8f1ae991577362b982745cp0L, 0x7.2ed804efc9b4ae1458ae946099d4p-92L, 0x1.9145b0b91ffc588a61b468p0L, 0x1.f6b70e01c2a90229a4c4309ea719p-88L, 0x1.93737b0cdc5e4f4501c3f2p0L, 0x5.40a22d2fc4af581b63e8326efe9cp-92L, 0x1.95a44cbc8520ee9b483694p0L, 0x1.a0fc6f7c7d61b2b3a22a0eab2cadp-88L, 0x1.97d829fde4e4f8b9e920f8p0L, 0x1.1e8bd7edb9d7144b6f6818084cc7p-88L, 0x1.9a0f170ca07b9ba3109b8cp0L, 0x4.6737beb19e1eada6825d3c557428p-92L, 0x1.9c49182a3f0901c7c46b06p0L, 0x1.1f2be58ddade50c217186c90b457p-88L, 0x1.9e86319e323231824ca78ep0L, 0x6.4c6e010f92c082bbadfaf605cfd4p-92L, 0x1.a0c667b5de564b29ada8b8p0L, 0xc.ab349aa0422a8da7d4512edac548p-92L, 0x1.a309bec4a2d3358c171f76p0L, 0x1.0daad547fa22c26d168ea762d854p-88L, 0x1.a5503b23e255c8b424491cp0L, 0xa.f87bc8050a405381703ef7caff50p-92L, 0x1.a799e1330b3586f2dfb2b0p0L, 0x1.58f1a98796ce8908ae852236ca94p-88L, 0x1.a9e6b5579fdbf43eb243bcp0L, 0x1.ff4c4c58b571cf465caf07b4b9f5p-88L, 0x1.ac36bbfd3f379c0db966a2p0L, 0x1.1265fc73e480712d20f8597a8e7bp-88L, 0x1.ae89f995ad3ad5e8734d16p0L, 0x1.73205a7fbc3ae675ea440b162d6cp-88L, 0x1.b0e07298db66590842acdep0L, 0x1.c6f6ca0e5dcae2aafffa7a0554cbp-88L, 0x1.b33a2b84f15faf6bfd0e7ap0L, 0x1.d947c2575781dbb49b1237c87b6ep-88L, 0x1.b59728de559398e3881110p0L, 0x1.64873c7171fefc410416be0a6525p-88L, 0x1.b7f76f2fb5e46eaa7b081ap0L, 0xb.53c5354c8903c356e4b625aacc28p-92L, 0x1.ba5b030a10649840cb3c6ap0L, 0xf.5b47f297203757e1cc6eadc8bad0p-92L, 0x1.bcc1e904bc1d2247ba0f44p0L, 0x1.b3d08cd0b20287092bd59be4ad98p-88L, 0x1.bf2c25bd71e088408d7024p0L, 0x1.18e3449fa073b356766dfb568ff4p-88L, 0x1.c199bdd85529c2220cb12ap0L, 0x9.1ba6679444964a36661240043970p-96L, 0x1.c40ab5fffd07a6d14df820p0L, 0xf.1828a5366fd387a7bdd54cdf7300p-92L, 0x1.c67f12e57d14b4a2137fd2p0L, 0xf.2b301dd9e6b151a6d1f9d5d5f520p-96L, 0x1.c8f6d9406e7b511acbc488p0L, 0x5.c442ddb55820171f319d9e5076a8p-96L, 0x1.cb720dcef90691503cbd1ep0L, 0x9.49db761d9559ac0cb6dd3ed599e0p-92L, 0x1.cdf0b555dc3f9c44f8958ep0L, 0x1.ac51be515f8c58bdfb6f5740a3a4p-88L, 0x1.d072d4a07897b8d0f22f20p0L, 0x1.a158e18fbbfc625f09f4cca40874p-88L, 0x1.d2f87080d89f18ade12398p0L, 0x9.ea2025b4c56553f5cdee4c924728p-92L, 0x1.d5818dcfba48725da05aeap0L, 0x1.66e0dca9f589f559c0876ff23830p-88L, 0x1.d80e316c98397bb84f9d04p0L, 0x8.805f84bec614de269900ddf98d28p-92L, 0x1.da9e603db3285708c01a5ap0L, 0x1.6d4c97f6246f0ec614ec95c99392p-88L, 0x1.dd321f301b4604b695de3cp0L, 0x6.30a393215299e30d4fb73503c348p-96L, 0x1.dfc97337b9b5eb968cac38p0L, 0x1.ed291b7225a944efd5bb5524b927p-88L, 0x1.e264614f5a128a12761fa0p0L, 0x1.7ada6467e77f73bf65e04c95e29dp-88L, 0x1.e502ee78b3ff6273d13014p0L, 0x1.3991e8f49659e1693be17ae1d2f9p-88L, 0x1.e7a51fbc74c834b548b282p0L, 0x1.23786758a84f4956354634a416cep-88L, 0x1.ea4afa2a490d9858f73a18p0L, 0xf.5db301f86dea20610ceee13eb7b8p-92L, 0x1.ecf482d8e67f08db0312fap0L, 0x1.949cef462010bb4bc4ce72a900dfp-88L, 0x1.efa1bee615a27771fd21a8p0L, 0x1.2dac1f6dd5d229ff68e46f27e3dfp-88L, 0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L, 0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L, 0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L, 0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L, 0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L }; /* * Kernel for expl(x). x must be finite and not tiny or huge. * "tiny" is anything that would make us underflow (|A6*x^6| < ~LDBL_MIN). * "huge" is anything that would make fn*L1 inexact (|x| > ~2**17*ln2). */ static inline void __k_expl(long double x, long double *hip, long double *lop, int *kp) { long double q, r, r1, t; double dr, fn, r2; int n, n2; /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */ fn = rnint((double)x * INV_L); n = irint(fn); n2 = (unsigned)n % INTERVALS; /* Depend on the sign bit being propagated: */ *kp = n >> LOG2_INTERVALS; r1 = x - fn * L1; r2 = fn * -L2; r = r1 + r2; /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */ dr = r; q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 + dr * (A7 + dr * (A8 + dr * (A9 + dr * A10)))))))); t = tbl[n2].lo + tbl[n2].hi; *hip = tbl[n2].hi; *lop = tbl[n2].lo + t * (q + r1); } /* * XXX: the rest of the functions are identical for ld80 and ld128. * However, we should use scalbnl() for ld128, since long double - * multiplication is very slow on the only supported ld128 arch (sparc64). + * multiplication was very slow on sparc64 and no new evaluation has + * been made for aarch64 and/or riscv. */ static inline void k_hexpl(long double x, long double *hip, long double *lop) { float twopkm1; int k; __k_expl(x, hip, lop, &k); SET_FLOAT_WORD(twopkm1, 0x3f800000 + ((k - 1) << 23)); *hip *= twopkm1; *lop *= twopkm1; } static inline long double hexpl(long double x) { long double hi, lo, twopkm2; int k; twopkm2 = 1; __k_expl(x, &hi, &lo, &k); SET_LDBL_EXPSIGN(twopkm2, BIAS + k - 2); return (lo + hi) * 2 * twopkm2; } #ifdef _COMPLEX_H /* * See ../src/k_exp.c for details. */ static inline long double complex __ldexp_cexpl(long double complex z, int expt) { long double exp_x, hi, lo; long double x, y, scale1, scale2; int half_expt, k; x = creall(z); y = cimagl(z); __k_expl(x, &hi, &lo, &k); exp_x = (lo + hi) * 0x1p16382; expt += k - 16382; scale1 = 1; half_expt = expt / 2; SET_LDBL_EXPSIGN(scale1, BIAS + half_expt); scale2 = 1; SET_LDBL_EXPSIGN(scale1, BIAS + expt - half_expt); return (CMPLXL(cos(y) * exp_x * scale1 * scale2, sinl(y) * exp_x * scale1 * scale2)); } #endif /* _COMPLEX_H */ Index: head/lib/msun/ld128/s_expl.c =================================================================== --- head/lib/msun/ld128/s_expl.c (revision 358346) +++ head/lib/msun/ld128/s_expl.c (revision 358347) @@ -1,323 +1,326 @@ /*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * Copyright (c) 2009-2013 Steven G. Kargl * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice unmodified, this list of conditions, and the following * disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. * * Optimized by Bruce D. Evans. */ #include __FBSDID("$FreeBSD$"); /* * ld128 version of s_expl.c. See ../ld80/s_expl.c for most comments. */ #include #include "fpmath.h" #include "math.h" #include "math_private.h" #include "k_expl.h" /* XXX Prevent compilers from erroneously constant folding these: */ static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L; static const long double twom10000 = 0x1p-10000L; static const long double /* log(2**16384 - 0.5) rounded towards zero: */ /* log(2**16384 - 0.5 + 1) rounded towards zero for expm1l() is the same: */ o_threshold = 11356.523406294143949491931077970763428L, /* log(2**(-16381-64-1)) rounded towards zero: */ u_threshold = -11433.462743336297878837243843452621503L; long double expl(long double x) { union IEEEl2bits u; long double hi, lo, t, twopk; int k; uint16_t hx, ix; DOPRINT_START(&x); /* Filter out exceptional cases. */ u.e = x; hx = u.xbits.expsign; ix = hx & 0x7fff; if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */ if (ix == BIAS + LDBL_MAX_EXP) { if (hx & 0x8000) /* x is -Inf or -NaN */ RETURNP(-1 / x); RETURNP(x + x); /* x is +Inf or +NaN */ } if (x > o_threshold) RETURNP(huge * huge); if (x < u_threshold) RETURNP(tiny * tiny); } else if (ix < BIAS - 114) { /* |x| < 0x1p-114 */ RETURN2P(1, x); /* 1 with inexact iff x != 0 */ } ENTERI(); twopk = 1; __k_expl(x, &hi, &lo, &k); t = SUM2P(hi, lo); /* Scale by 2**k. */ - /* XXX sparc64 multiplication is so slow that scalbnl() is faster. */ + /* + * XXX sparc64 multiplication was so slow that scalbnl() is faster, + * but performance on aarch64 and riscv hasn't yet been quantified. + */ if (k >= LDBL_MIN_EXP) { if (k == LDBL_MAX_EXP) RETURNI(t * 2 * 0x1p16383L); SET_LDBL_EXPSIGN(twopk, BIAS + k); RETURNI(t * twopk); } else { SET_LDBL_EXPSIGN(twopk, BIAS + k + 10000); RETURNI(t * twopk * twom10000); } } /* * Our T1 and T2 are chosen to be approximately the points where method * A and method B have the same accuracy. Tang's T1 and T2 are the * points where method A's accuracy changes by a full bit. For Tang, * this drop in accuracy makes method A immediately less accurate than * method B, but our larger INTERVALS makes method A 2 bits more * accurate so it remains the most accurate method significantly * closer to the origin despite losing the full bit in our extended * range for it. * * Split the interval [T1, T2] into two intervals [T1, T3] and [T3, T2]. * Setting T3 to 0 would require the |x| < 0x1p-113 condition to appear * in both subintervals, so set T3 = 2**-5, which places the condition * into the [T1, T3] interval. * * XXX we now do this more to (partially) balance the number of terms * in the C and D polys than to avoid checking the condition in both * intervals. * * XXX these micro-optimizations are excessive. */ static const double T1 = -0.1659, /* ~-30.625/128 * log(2) */ T2 = 0.1659, /* ~30.625/128 * log(2) */ T3 = 0.03125; /* * Domain [-0.1659, 0.03125], range ~[2.9134e-44, 1.8404e-37]: * |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-122.03 * * XXX none of the long double C or D coeffs except C10 is correctly printed. * If you re-print their values in %.35Le format, the result is always * different. For example, the last 2 digits in C3 should be 59, not 67. * 67 is apparently from rounding an extra-precision value to 36 decimal * places. */ static const long double C3 = 1.66666666666666666666666666666666667e-1L, C4 = 4.16666666666666666666666666666666645e-2L, C5 = 8.33333333333333333333333333333371638e-3L, C6 = 1.38888888888888888888888888891188658e-3L, C7 = 1.98412698412698412698412697235950394e-4L, C8 = 2.48015873015873015873015112487849040e-5L, C9 = 2.75573192239858906525606685484412005e-6L, C10 = 2.75573192239858906612966093057020362e-7L, C11 = 2.50521083854417203619031960151253944e-8L, C12 = 2.08767569878679576457272282566520649e-9L, C13 = 1.60590438367252471783548748824255707e-10L; /* * XXX this has 1 more coeff than needed. * XXX can start the double coeffs but not the double mults at C10. * With my coeffs (C10-C17 double; s = best_s): * Domain [-0.1659, 0.03125], range ~[-1.1976e-37, 1.1976e-37]: * |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65 */ static const double C14 = 1.1470745580491932e-11, /* 0x1.93974a81dae30p-37 */ C15 = 7.6471620181090468e-13, /* 0x1.ae7f3820adab1p-41 */ C16 = 4.7793721460260450e-14, /* 0x1.ae7cd18a18eacp-45 */ C17 = 2.8074757356658877e-15, /* 0x1.949992a1937d9p-49 */ C18 = 1.4760610323699476e-16; /* 0x1.545b43aabfbcdp-53 */ /* * Domain [0.03125, 0.1659], range ~[-2.7676e-37, -1.0367e-38]: * |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-121.44 */ static const long double D3 = 1.66666666666666666666666666666682245e-1L, D4 = 4.16666666666666666666666666634228324e-2L, D5 = 8.33333333333333333333333364022244481e-3L, D6 = 1.38888888888888888888887138722762072e-3L, D7 = 1.98412698412698412699085805424661471e-4L, D8 = 2.48015873015873015687993712101479612e-5L, D9 = 2.75573192239858944101036288338208042e-6L, D10 = 2.75573192239853161148064676533754048e-7L, D11 = 2.50521083855084570046480450935267433e-8L, D12 = 2.08767569819738524488686318024854942e-9L, D13 = 1.60590442297008495301927448122499313e-10L; /* * XXX this has 1 more coeff than needed. * XXX can start the double coeffs but not the double mults at D11. * With my coeffs (D11-D16 double): * Domain [0.03125, 0.1659], range ~[-1.1980e-37, 1.1980e-37]: * |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65 */ static const double D14 = 1.1470726176204336e-11, /* 0x1.93971dc395d9ep-37 */ D15 = 7.6478532249581686e-13, /* 0x1.ae892e3D16fcep-41 */ D16 = 4.7628892832607741e-14, /* 0x1.ad00Dfe41feccp-45 */ D17 = 3.0524857220358650e-15; /* 0x1.D7e8d886Df921p-49 */ long double expm1l(long double x) { union IEEEl2bits u, v; long double hx2_hi, hx2_lo, q, r, r1, t, twomk, twopk, x_hi; long double x_lo, x2; double dr, dx, fn, r2; int k, n, n2; uint16_t hx, ix; DOPRINT_START(&x); /* Filter out exceptional cases. */ u.e = x; hx = u.xbits.expsign; ix = hx & 0x7fff; if (ix >= BIAS + 7) { /* |x| >= 128 or x is NaN */ if (ix == BIAS + LDBL_MAX_EXP) { if (hx & 0x8000) /* x is -Inf or -NaN */ RETURNP(-1 / x - 1); RETURNP(x + x); /* x is +Inf or +NaN */ } if (x > o_threshold) RETURNP(huge * huge); /* * expm1l() never underflows, but it must avoid * unrepresentable large negative exponents. We used a * much smaller threshold for large |x| above than in * expl() so as to handle not so large negative exponents * in the same way as large ones here. */ if (hx & 0x8000) /* x <= -128 */ RETURN2P(tiny, -1); /* good for x < -114ln2 - eps */ } ENTERI(); if (T1 < x && x < T2) { x2 = x * x; dx = x; if (x < T3) { if (ix < BIAS - 113) { /* |x| < 0x1p-113 */ /* x (rounded) with inexact if x != 0: */ RETURNPI(x == 0 ? x : (0x1p200 * x + fabsl(x)) * 0x1p-200); } q = x * x2 * C3 + x2 * x2 * (C4 + x * (C5 + x * (C6 + x * (C7 + x * (C8 + x * (C9 + x * (C10 + x * (C11 + x * (C12 + x * (C13 + dx * (C14 + dx * (C15 + dx * (C16 + dx * (C17 + dx * C18)))))))))))))); } else { q = x * x2 * D3 + x2 * x2 * (D4 + x * (D5 + x * (D6 + x * (D7 + x * (D8 + x * (D9 + x * (D10 + x * (D11 + x * (D12 + x * (D13 + dx * (D14 + dx * (D15 + dx * (D16 + dx * D17))))))))))))); } x_hi = (float)x; x_lo = x - x_hi; hx2_hi = x_hi * x_hi / 2; hx2_lo = x_lo * (x + x_hi) / 2; if (ix >= BIAS - 7) RETURN2PI(hx2_hi + x_hi, hx2_lo + x_lo + q); else RETURN2PI(x, hx2_lo + q + hx2_hi); } /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */ fn = rnint((double)x * INV_L); n = irint(fn); n2 = (unsigned)n % INTERVALS; k = n >> LOG2_INTERVALS; r1 = x - fn * L1; r2 = fn * -L2; r = r1 + r2; /* Prepare scale factor. */ v.e = 1; v.xbits.expsign = BIAS + k; twopk = v.e; /* * Evaluate lower terms of * expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */ dr = r; q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 + dr * (A7 + dr * (A8 + dr * (A9 + dr * A10)))))))); t = tbl[n2].lo + tbl[n2].hi; if (k == 0) { t = SUM2P(tbl[n2].hi - 1, tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1); RETURNI(t); } if (k == -1) { t = SUM2P(tbl[n2].hi - 2, tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1); RETURNI(t / 2); } if (k < -7) { t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1)); RETURNI(t * twopk - 1); } if (k > 2 * LDBL_MANT_DIG - 1) { t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1)); if (k == LDBL_MAX_EXP) RETURNI(t * 2 * 0x1p16383L - 1); RETURNI(t * twopk - 1); } v.xbits.expsign = BIAS - k; twomk = v.e; if (k > LDBL_MANT_DIG - 1) t = SUM2P(tbl[n2].hi, tbl[n2].lo - twomk + t * (q + r1)); else t = SUM2P(tbl[n2].hi - twomk, tbl[n2].lo + t * (q + r1)); RETURNI(t * twopk); } Index: head/lib/msun/ld128/s_logl.c =================================================================== --- head/lib/msun/ld128/s_logl.c (revision 358346) +++ head/lib/msun/ld128/s_logl.c (revision 358347) @@ -1,739 +1,740 @@ /*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * Copyright (c) 2007-2013 Bruce D. Evans * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice unmodified, this list of conditions, and the following * disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #include __FBSDID("$FreeBSD$"); /** * Implementation of the natural logarithm of x for 128-bit format. * * First decompose x into its base 2 representation: * * log(x) = log(X * 2**k), where X is in [1, 2) * = log(X) + k * log(2). * * Let X = X_i + e, where X_i is the center of one of the intervals * [-1.0/256, 1.0/256), [1.0/256, 3.0/256), .... [2.0-1.0/256, 2.0+1.0/256) * and X is in this interval. Then * * log(X) = log(X_i + e) * = log(X_i * (1 + e / X_i)) * = log(X_i) + log(1 + e / X_i). * * The values log(X_i) are tabulated below. Let d = e / X_i and use * * log(1 + d) = p(d) * * where p(d) = d - 0.5*d*d + ... is a special minimax polynomial of * suitably high degree. * * To get sufficiently small roundoff errors, k * log(2), log(X_i), and * sometimes (if |k| is not large) the first term in p(d) must be evaluated * and added up in extra precision. Extra precision is not needed for the * rest of p(d). In the worst case when k = 0 and log(X_i) is 0, the final * error is controlled mainly by the error in the second term in p(d). The * error in this term itself is at most 0.5 ulps from the d*d operation in * it. The error in this term relative to the first term is thus at most * 0.5 * |-0.5| * |d| < 1.0/1024 ulps. We aim for an accumulated error of * at most twice this at the point of the final rounding step. Thus the * final error should be at most 0.5 + 1.0/512 = 0.5020 ulps. Exhaustive * testing of a float variant of this function showed a maximum final error * of 0.5008 ulps. Non-exhaustive testing of a double variant of this * function showed a maximum final error of 0.5078 ulps (near 1+1.0/256). * * We made the maximum of |d| (and thus the total relative error and the * degree of p(d)) small by using a large number of intervals. Using * centers of intervals instead of endpoints reduces this maximum by a * factor of 2 for a given number of intervals. p(d) is special only * in beginning with the Taylor coefficients 0 + 1*d, which tends to happen * naturally. The most accurate minimax polynomial of a given degree might * be different, but then we wouldn't want it since we would have to do * extra work to avoid roundoff error (especially for P0*d instead of d). */ #ifdef DEBUG #include #include #endif #include "fpmath.h" #include "math.h" #ifndef NO_STRUCT_RETURN #define STRUCT_RETURN #endif #include "math_private.h" #if !defined(NO_UTAB) && !defined(NO_UTABL) #define USE_UTAB #endif /* * Domain [-0.005280, 0.004838], range ~[-1.1577e-37, 1.1582e-37]: * |log(1 + d)/d - p(d)| < 2**-122.7 */ static const long double P2 = -0.5L, P3 = 3.33333333333333333333333333333233795e-1L, /* 0x15555555555555555555555554d42.0p-114L */ P4 = -2.49999999999999999999999999941139296e-1L, /* -0x1ffffffffffffffffffffffdab14e.0p-115L */ P5 = 2.00000000000000000000000085468039943e-1L, /* 0x19999999999999999999a6d3567f4.0p-115L */ P6 = -1.66666666666666666666696142372698408e-1L, /* -0x15555555555555555567267a58e13.0p-115L */ P7 = 1.42857142857142857119522943477166120e-1L, /* 0x1249249249249248ed79a0ae434de.0p-115L */ P8 = -1.24999999999999994863289015033581301e-1L; /* -0x1fffffffffffffa13e91765e46140.0p-116L */ /* Double precision gives ~ 53 + log2(P9 * max(|d|)**8) ~= 120 bits. */ static const double P9 = 1.1111111111111401e-1, /* 0x1c71c71c71c7ed.0p-56 */ P10 = -1.0000000000040135e-1, /* -0x199999999a0a92.0p-56 */ P11 = 9.0909090728136258e-2, /* 0x1745d173962111.0p-56 */ P12 = -8.3333318851855284e-2, /* -0x1555551722c7a3.0p-56 */ P13 = 7.6928634666404178e-2, /* 0x13b1985204a4ae.0p-56 */ P14 = -7.1626810078462499e-2; /* -0x12562276cdc5d0.0p-56 */ static volatile const double zero = 0; #define INTERVALS 128 #define LOG2_INTERVALS 7 #define TSIZE (INTERVALS + 1) #define G(i) (T[(i)].G) #define F_hi(i) (T[(i)].F_hi) #define F_lo(i) (T[(i)].F_lo) #define ln2_hi F_hi(TSIZE - 1) #define ln2_lo F_lo(TSIZE - 1) #define E(i) (U[(i)].E) #define H(i) (U[(i)].H) static const struct { float G; /* 1/(1 + i/128) rounded to 8/9 bits */ float F_hi; /* log(1 / G_i) rounded (see below) */ /* The compiler will insert 8 bytes of padding here. */ long double F_lo; /* next 113 bits for log(1 / G_i) */ } T[TSIZE] = { /* * ln2_hi and each F_hi(i) are rounded to a number of bits that * makes F_hi(i) + dk*ln2_hi exact for all i and all dk. * * The last entry (for X just below 2) is used to define ln2_hi * and ln2_lo, to ensure that F_hi(i) and F_lo(i) cancel exactly * with dk*ln2_hi and dk*ln2_lo, respectively, when dk = -1. * This is needed for accuracy when x is just below 1. (To avoid * special cases, such x are "reduced" strangely to X just below * 2 and dk = -1, and then the exact cancellation is needed * because any the error from any non-exactness would be too * large). * * The relevant range of dk is [-16445, 16383]. The maximum number * of bits in F_hi(i) that works is very dependent on i but has * a minimum of 93. We only need about 12 bits in F_hi(i) for * it to provide enough extra precision. * * We round F_hi(i) to 24 bits so that it can have type float, * mainly to minimize the size of the table. Using all 24 bits * in a float for it automatically satisfies the above constraints. */ 0x800000.0p-23, 0, 0, 0xfe0000.0p-24, 0x8080ac.0p-30, -0x14ee431dae6674afa0c4bfe16e8fd.0p-144L, 0xfc0000.0p-24, 0x8102b3.0p-29, -0x1db29ee2d83717be918e1119642ab.0p-144L, 0xfa0000.0p-24, 0xc24929.0p-29, 0x1191957d173697cf302cc9476f561.0p-143L, 0xf80000.0p-24, 0x820aec.0p-28, 0x13ce8888e02e78eba9b1113bc1c18.0p-142L, 0xf60000.0p-24, 0xa33577.0p-28, -0x17a4382ce6eb7bfa509bec8da5f22.0p-142L, 0xf48000.0p-24, 0xbc42cb.0p-28, -0x172a21161a107674986dcdca6709c.0p-143L, 0xf30000.0p-24, 0xd57797.0p-28, -0x1e09de07cb958897a3ea46e84abb3.0p-142L, 0xf10000.0p-24, 0xf7518e.0p-28, 0x1ae1eec1b036c484993c549c4bf40.0p-151L, 0xef0000.0p-24, 0x8cb9df.0p-27, -0x1d7355325d560d9e9ab3d6ebab580.0p-141L, 0xed8000.0p-24, 0x999ec0.0p-27, -0x1f9f02d256d5037108f4ec21e48cd.0p-142L, 0xec0000.0p-24, 0xa6988b.0p-27, -0x16fc0a9d12c17a70f7a684c596b12.0p-143L, 0xea0000.0p-24, 0xb80698.0p-27, 0x15d581c1e8da99ded322fb08b8462.0p-141L, 0xe80000.0p-24, 0xc99af3.0p-27, -0x1535b3ba8f150ae09996d7bb4653e.0p-143L, 0xe70000.0p-24, 0xd273b2.0p-27, 0x163786f5251aefe0ded34c8318f52.0p-145L, 0xe50000.0p-24, 0xe442c0.0p-27, 0x1bc4b2368e32d56699c1799a244d4.0p-144L, 0xe38000.0p-24, 0xf1b83f.0p-27, 0x1c6090f684e6766abceccab1d7174.0p-141L, 0xe20000.0p-24, 0xff448a.0p-27, -0x1890aa69ac9f4215f93936b709efb.0p-142L, 0xe08000.0p-24, 0x8673f6.0p-26, 0x1b9985194b6affd511b534b72a28e.0p-140L, 0xdf0000.0p-24, 0x8d515c.0p-26, -0x1dc08d61c6ef1d9b2ef7e68680598.0p-143L, 0xdd8000.0p-24, 0x943a9e.0p-26, -0x1f72a2dac729b3f46662238a9425a.0p-142L, 0xdc0000.0p-24, 0x9b2fe6.0p-26, -0x1fd4dfd3a0afb9691aed4d5e3df94.0p-140L, 0xda8000.0p-24, 0xa2315d.0p-26, -0x11b26121629c46c186384993e1c93.0p-142L, 0xd90000.0p-24, 0xa93f2f.0p-26, 0x1286d633e8e5697dc6a402a56fce1.0p-141L, 0xd78000.0p-24, 0xb05988.0p-26, 0x16128eba9367707ebfa540e45350c.0p-144L, 0xd60000.0p-24, 0xb78094.0p-26, 0x16ead577390d31ef0f4c9d43f79b2.0p-140L, 0xd50000.0p-24, 0xbc4c6c.0p-26, 0x151131ccf7c7b75e7d900b521c48d.0p-141L, 0xd38000.0p-24, 0xc3890a.0p-26, -0x115e2cd714bd06508aeb00d2ae3e9.0p-140L, 0xd20000.0p-24, 0xcad2d7.0p-26, -0x1847f406ebd3af80485c2f409633c.0p-142L, 0xd10000.0p-24, 0xcfb620.0p-26, 0x1c2259904d686581799fbce0b5f19.0p-141L, 0xcf8000.0p-24, 0xd71653.0p-26, 0x1ece57a8d5ae54f550444ecf8b995.0p-140L, 0xce0000.0p-24, 0xde843a.0p-26, -0x1f109d4bc4595412b5d2517aaac13.0p-141L, 0xcd0000.0p-24, 0xe37fde.0p-26, 0x1bc03dc271a74d3a85b5b43c0e727.0p-141L, 0xcb8000.0p-24, 0xeb050c.0p-26, -0x1bf2badc0df841a71b79dd5645b46.0p-145L, 0xca0000.0p-24, 0xf29878.0p-26, -0x18efededd89fbe0bcfbe6d6db9f66.0p-147L, 0xc90000.0p-24, 0xf7ad6f.0p-26, 0x1373ff977baa6911c7bafcb4d84fb.0p-141L, 0xc80000.0p-24, 0xfcc8e3.0p-26, 0x196766f2fb328337cc050c6d83b22.0p-140L, 0xc68000.0p-24, 0x823f30.0p-25, 0x19bd076f7c434e5fcf1a212e2a91e.0p-139L, 0xc58000.0p-24, 0x84d52c.0p-25, -0x1a327257af0f465e5ecab5f2a6f81.0p-139L, 0xc40000.0p-24, 0x88bc74.0p-25, 0x113f23def19c5a0fe396f40f1dda9.0p-141L, 0xc30000.0p-24, 0x8b5ae6.0p-25, 0x1759f6e6b37de945a049a962e66c6.0p-139L, 0xc20000.0p-24, 0x8dfccb.0p-25, 0x1ad35ca6ed5147bdb6ddcaf59c425.0p-141L, 0xc10000.0p-24, 0x90a22b.0p-25, 0x1a1d71a87deba46bae9827221dc98.0p-139L, 0xbf8000.0p-24, 0x94a0d8.0p-25, -0x139e5210c2b730e28aba001a9b5e0.0p-140L, 0xbe8000.0p-24, 0x974f16.0p-25, -0x18f6ebcff3ed72e23e13431adc4a5.0p-141L, 0xbd8000.0p-24, 0x9a00f1.0p-25, -0x1aa268be39aab7148e8d80caa10b7.0p-139L, 0xbc8000.0p-24, 0x9cb672.0p-25, -0x14c8815839c5663663d15faed7771.0p-139L, 0xbb0000.0p-24, 0xa0cda1.0p-25, 0x1eaf46390dbb2438273918db7df5c.0p-141L, 0xba0000.0p-24, 0xa38c6e.0p-25, 0x138e20d831f698298adddd7f32686.0p-141L, 0xb90000.0p-24, 0xa64f05.0p-25, -0x1e8d3c41123615b147a5d47bc208f.0p-142L, 0xb80000.0p-24, 0xa91570.0p-25, 0x1ce28f5f3840b263acb4351104631.0p-140L, 0xb70000.0p-24, 0xabdfbb.0p-25, -0x186e5c0a42423457e22d8c650b355.0p-139L, 0xb60000.0p-24, 0xaeadef.0p-25, -0x14d41a0b2a08a465dc513b13f567d.0p-143L, 0xb50000.0p-24, 0xb18018.0p-25, 0x16755892770633947ffe651e7352f.0p-139L, 0xb40000.0p-24, 0xb45642.0p-25, -0x16395ebe59b15228bfe8798d10ff0.0p-142L, 0xb30000.0p-24, 0xb73077.0p-25, 0x1abc65c8595f088b61a335f5b688c.0p-140L, 0xb20000.0p-24, 0xba0ec4.0p-25, -0x1273089d3dad88e7d353e9967d548.0p-139L, 0xb10000.0p-24, 0xbcf133.0p-25, 0x10f9f67b1f4bbf45de06ecebfaf6d.0p-139L, 0xb00000.0p-24, 0xbfd7d2.0p-25, -0x109fab904864092b34edda19a831e.0p-140L, 0xaf0000.0p-24, 0xc2c2ac.0p-25, -0x1124680aa43333221d8a9b475a6ba.0p-139L, 0xae8000.0p-24, 0xc439b3.0p-25, -0x1f360cc4710fbfe24b633f4e8d84d.0p-140L, 0xad8000.0p-24, 0xc72afd.0p-25, -0x132d91f21d89c89c45003fc5d7807.0p-140L, 0xac8000.0p-24, 0xca20a2.0p-25, -0x16bf9b4d1f8da8002f2449e174504.0p-139L, 0xab8000.0p-24, 0xcd1aae.0p-25, 0x19deb5ce6a6a8717d5626e16acc7d.0p-141L, 0xaa8000.0p-24, 0xd0192f.0p-25, 0x1a29fb48f7d3ca87dabf351aa41f4.0p-139L, 0xaa0000.0p-24, 0xd19a20.0p-25, 0x1127d3c6457f9d79f51dcc73014c9.0p-141L, 0xa90000.0p-24, 0xd49f6a.0p-25, -0x1ba930e486a0ac42d1bf9199188e7.0p-141L, 0xa80000.0p-24, 0xd7a94b.0p-25, -0x1b6e645f31549dd1160bcc45c7e2c.0p-139L, 0xa70000.0p-24, 0xdab7d0.0p-25, 0x1118a425494b610665377f15625b6.0p-140L, 0xa68000.0p-24, 0xdc40d5.0p-25, 0x1966f24d29d3a2d1b2176010478be.0p-140L, 0xa58000.0p-24, 0xdf566d.0p-25, -0x1d8e52eb2248f0c95dd83626d7333.0p-142L, 0xa48000.0p-24, 0xe270ce.0p-25, -0x1ee370f96e6b67ccb006a5b9890ea.0p-140L, 0xa40000.0p-24, 0xe3ffce.0p-25, 0x1d155324911f56db28da4d629d00a.0p-140L, 0xa30000.0p-24, 0xe72179.0p-25, -0x1fe6e2f2f867d8f4d60c713346641.0p-140L, 0xa20000.0p-24, 0xea4812.0p-25, 0x1b7be9add7f4d3b3d406b6cbf3ce5.0p-140L, 0xa18000.0p-24, 0xebdd3d.0p-25, 0x1b3cfb3f7511dd73692609040ccc2.0p-139L, 0xa08000.0p-24, 0xef0b5b.0p-25, -0x1220de1f7301901b8ad85c25afd09.0p-139L, 0xa00000.0p-24, 0xf0a451.0p-25, -0x176364c9ac81cc8a4dfb804de6867.0p-140L, 0x9f0000.0p-24, 0xf3da16.0p-25, 0x1eed6b9aafac8d42f78d3e65d3727.0p-141L, 0x9e8000.0p-24, 0xf576e9.0p-25, 0x1d593218675af269647b783d88999.0p-139L, 0x9d8000.0p-24, 0xf8b47c.0p-25, -0x13e8eb7da053e063714615f7cc91d.0p-144L, 0x9d0000.0p-24, 0xfa553f.0p-25, 0x1c063259bcade02951686d5373aec.0p-139L, 0x9c0000.0p-24, 0xfd9ac5.0p-25, 0x1ef491085fa3c1649349630531502.0p-139L, 0x9b8000.0p-24, 0xff3f8c.0p-25, 0x1d607a7c2b8c5320619fb9433d841.0p-139L, 0x9a8000.0p-24, 0x814697.0p-24, -0x12ad3817004f3f0bdff99f932b273.0p-138L, 0x9a0000.0p-24, 0x821b06.0p-24, -0x189fc53117f9e54e78103a2bc1767.0p-141L, 0x990000.0p-24, 0x83c5f8.0p-24, 0x14cf15a048907b7d7f47ddb45c5a3.0p-139L, 0x988000.0p-24, 0x849c7d.0p-24, 0x1cbb1d35fb82873b04a9af1dd692c.0p-138L, 0x978000.0p-24, 0x864ba6.0p-24, 0x1128639b814f9b9770d8cb6573540.0p-138L, 0x970000.0p-24, 0x87244c.0p-24, 0x184733853300f002e836dfd47bd41.0p-139L, 0x968000.0p-24, 0x87fdaa.0p-24, 0x109d23aef77dd5cd7cc94306fb3ff.0p-140L, 0x958000.0p-24, 0x89b293.0p-24, -0x1a81ef367a59de2b41eeebd550702.0p-138L, 0x950000.0p-24, 0x8a8e20.0p-24, -0x121ad3dbb2f45275c917a30df4ac9.0p-138L, 0x948000.0p-24, 0x8b6a6a.0p-24, -0x1cfb981628af71a89df4e6df2e93b.0p-139L, 0x938000.0p-24, 0x8d253a.0p-24, -0x1d21730ea76cfdec367828734cae5.0p-139L, 0x930000.0p-24, 0x8e03c2.0p-24, 0x135cc00e566f76b87333891e0dec4.0p-138L, 0x928000.0p-24, 0x8ee30d.0p-24, -0x10fcb5df257a263e3bf446c6e3f69.0p-140L, 0x918000.0p-24, 0x90a3ee.0p-24, -0x16e171b15433d723a4c7380a448d8.0p-139L, 0x910000.0p-24, 0x918587.0p-24, -0x1d050da07f3236f330972da2a7a87.0p-139L, 0x908000.0p-24, 0x9267e7.0p-24, 0x1be03669a5268d21148c6002becd3.0p-139L, 0x8f8000.0p-24, 0x942f04.0p-24, 0x10b28e0e26c336af90e00533323ba.0p-139L, 0x8f0000.0p-24, 0x9513c3.0p-24, 0x1a1d820da57cf2f105a89060046aa.0p-138L, 0x8e8000.0p-24, 0x95f950.0p-24, -0x19ef8f13ae3cf162409d8ea99d4c0.0p-139L, 0x8e0000.0p-24, 0x96dfab.0p-24, -0x109e417a6e507b9dc10dac743ad7a.0p-138L, 0x8d0000.0p-24, 0x98aed2.0p-24, 0x10d01a2c5b0e97c4990b23d9ac1f5.0p-139L, 0x8c8000.0p-24, 0x9997a2.0p-24, -0x1d6a50d4b61ea74540bdd2aa99a42.0p-138L, 0x8c0000.0p-24, 0x9a8145.0p-24, 0x1b3b190b83f9527e6aba8f2d783c1.0p-138L, 0x8b8000.0p-24, 0x9b6bbf.0p-24, 0x13a69fad7e7abe7ba81c664c107e0.0p-138L, 0x8b0000.0p-24, 0x9c5711.0p-24, -0x11cd12316f576aad348ae79867223.0p-138L, 0x8a8000.0p-24, 0x9d433b.0p-24, 0x1c95c444b807a246726b304ccae56.0p-139L, 0x898000.0p-24, 0x9f1e22.0p-24, -0x1b9c224ea698c2f9b47466d6123fe.0p-139L, 0x890000.0p-24, 0xa00ce1.0p-24, 0x125ca93186cf0f38b4619a2483399.0p-141L, 0x888000.0p-24, 0xa0fc80.0p-24, -0x1ee38a7bc228b3597043be78eaf49.0p-139L, 0x880000.0p-24, 0xa1ed00.0p-24, -0x1a0db876613d204147dc69a07a649.0p-138L, 0x878000.0p-24, 0xa2de62.0p-24, 0x193224e8516c008d3602a7b41c6e8.0p-139L, 0x870000.0p-24, 0xa3d0a9.0p-24, 0x1fa28b4d2541aca7d5844606b2421.0p-139L, 0x868000.0p-24, 0xa4c3d6.0p-24, 0x1c1b5760fb4571acbcfb03f16daf4.0p-138L, 0x858000.0p-24, 0xa6acea.0p-24, 0x1fed5d0f65949c0a345ad743ae1ae.0p-140L, 0x850000.0p-24, 0xa7a2d4.0p-24, 0x1ad270c9d749362382a7688479e24.0p-140L, 0x848000.0p-24, 0xa899ab.0p-24, 0x199ff15ce532661ea9643a3a2d378.0p-139L, 0x840000.0p-24, 0xa99171.0p-24, 0x1a19e15ccc45d257530a682b80490.0p-139L, 0x838000.0p-24, 0xaa8a28.0p-24, -0x121a14ec532b35ba3e1f868fd0b5e.0p-140L, 0x830000.0p-24, 0xab83d1.0p-24, 0x1aee319980bff3303dd481779df69.0p-139L, 0x828000.0p-24, 0xac7e6f.0p-24, -0x18ffd9e3900345a85d2d86161742e.0p-140L, 0x820000.0p-24, 0xad7a03.0p-24, -0x1e4db102ce29f79b026b64b42caa1.0p-140L, 0x818000.0p-24, 0xae768f.0p-24, 0x17c35c55a04a82ab19f77652d977a.0p-141L, 0x810000.0p-24, 0xaf7415.0p-24, 0x1448324047019b48d7b98c1cf7234.0p-138L, 0x808000.0p-24, 0xb07298.0p-24, -0x1750ee3915a197e9c7359dd94152f.0p-138L, 0x800000.0p-24, 0xb17218.0p-24, -0x105c610ca86c3898cff81a12a17e2.0p-141L, }; #ifdef USE_UTAB static const struct { float H; /* 1 + i/INTERVALS (exact) */ float E; /* H(i) * G(i) - 1 (exact) */ } U[TSIZE] = { 0x800000.0p-23, 0, 0x810000.0p-23, -0x800000.0p-37, 0x820000.0p-23, -0x800000.0p-35, 0x830000.0p-23, -0x900000.0p-34, 0x840000.0p-23, -0x800000.0p-33, 0x850000.0p-23, -0xc80000.0p-33, 0x860000.0p-23, -0xa00000.0p-36, 0x870000.0p-23, 0x940000.0p-33, 0x880000.0p-23, 0x800000.0p-35, 0x890000.0p-23, -0xc80000.0p-34, 0x8a0000.0p-23, 0xe00000.0p-36, 0x8b0000.0p-23, 0x900000.0p-33, 0x8c0000.0p-23, -0x800000.0p-35, 0x8d0000.0p-23, -0xe00000.0p-33, 0x8e0000.0p-23, 0x880000.0p-33, 0x8f0000.0p-23, -0xa80000.0p-34, 0x900000.0p-23, -0x800000.0p-35, 0x910000.0p-23, 0x800000.0p-37, 0x920000.0p-23, 0x900000.0p-35, 0x930000.0p-23, 0xd00000.0p-35, 0x940000.0p-23, 0xe00000.0p-35, 0x950000.0p-23, 0xc00000.0p-35, 0x960000.0p-23, 0xe00000.0p-36, 0x970000.0p-23, -0x800000.0p-38, 0x980000.0p-23, -0xc00000.0p-35, 0x990000.0p-23, -0xd00000.0p-34, 0x9a0000.0p-23, 0x880000.0p-33, 0x9b0000.0p-23, 0xe80000.0p-35, 0x9c0000.0p-23, -0x800000.0p-35, 0x9d0000.0p-23, 0xb40000.0p-33, 0x9e0000.0p-23, 0x880000.0p-34, 0x9f0000.0p-23, -0xe00000.0p-35, 0xa00000.0p-23, 0x800000.0p-33, 0xa10000.0p-23, -0x900000.0p-36, 0xa20000.0p-23, -0xb00000.0p-33, 0xa30000.0p-23, -0xa00000.0p-36, 0xa40000.0p-23, 0x800000.0p-33, 0xa50000.0p-23, -0xf80000.0p-35, 0xa60000.0p-23, 0x880000.0p-34, 0xa70000.0p-23, -0x900000.0p-33, 0xa80000.0p-23, -0x800000.0p-35, 0xa90000.0p-23, 0x900000.0p-34, 0xaa0000.0p-23, 0xa80000.0p-33, 0xab0000.0p-23, -0xac0000.0p-34, 0xac0000.0p-23, -0x800000.0p-37, 0xad0000.0p-23, 0xf80000.0p-35, 0xae0000.0p-23, 0xf80000.0p-34, 0xaf0000.0p-23, -0xac0000.0p-33, 0xb00000.0p-23, -0x800000.0p-33, 0xb10000.0p-23, -0xb80000.0p-34, 0xb20000.0p-23, -0x800000.0p-34, 0xb30000.0p-23, -0xb00000.0p-35, 0xb40000.0p-23, -0x800000.0p-35, 0xb50000.0p-23, -0xe00000.0p-36, 0xb60000.0p-23, -0x800000.0p-35, 0xb70000.0p-23, -0xb00000.0p-35, 0xb80000.0p-23, -0x800000.0p-34, 0xb90000.0p-23, -0xb80000.0p-34, 0xba0000.0p-23, -0x800000.0p-33, 0xbb0000.0p-23, -0xac0000.0p-33, 0xbc0000.0p-23, 0x980000.0p-33, 0xbd0000.0p-23, 0xbc0000.0p-34, 0xbe0000.0p-23, 0xe00000.0p-36, 0xbf0000.0p-23, -0xb80000.0p-35, 0xc00000.0p-23, -0x800000.0p-33, 0xc10000.0p-23, 0xa80000.0p-33, 0xc20000.0p-23, 0x900000.0p-34, 0xc30000.0p-23, -0x800000.0p-35, 0xc40000.0p-23, -0x900000.0p-33, 0xc50000.0p-23, 0x820000.0p-33, 0xc60000.0p-23, 0x800000.0p-38, 0xc70000.0p-23, -0x820000.0p-33, 0xc80000.0p-23, 0x800000.0p-33, 0xc90000.0p-23, -0xa00000.0p-36, 0xca0000.0p-23, -0xb00000.0p-33, 0xcb0000.0p-23, 0x840000.0p-34, 0xcc0000.0p-23, -0xd00000.0p-34, 0xcd0000.0p-23, 0x800000.0p-33, 0xce0000.0p-23, -0xe00000.0p-35, 0xcf0000.0p-23, 0xa60000.0p-33, 0xd00000.0p-23, -0x800000.0p-35, 0xd10000.0p-23, 0xb40000.0p-33, 0xd20000.0p-23, -0x800000.0p-35, 0xd30000.0p-23, 0xaa0000.0p-33, 0xd40000.0p-23, -0xe00000.0p-35, 0xd50000.0p-23, 0x880000.0p-33, 0xd60000.0p-23, -0xd00000.0p-34, 0xd70000.0p-23, 0x9c0000.0p-34, 0xd80000.0p-23, -0xb00000.0p-33, 0xd90000.0p-23, -0x800000.0p-38, 0xda0000.0p-23, 0xa40000.0p-33, 0xdb0000.0p-23, -0xdc0000.0p-34, 0xdc0000.0p-23, 0xc00000.0p-35, 0xdd0000.0p-23, 0xca0000.0p-33, 0xde0000.0p-23, -0xb80000.0p-34, 0xdf0000.0p-23, 0xd00000.0p-35, 0xe00000.0p-23, 0xc00000.0p-33, 0xe10000.0p-23, -0xf40000.0p-34, 0xe20000.0p-23, 0x800000.0p-37, 0xe30000.0p-23, 0x860000.0p-33, 0xe40000.0p-23, -0xc80000.0p-33, 0xe50000.0p-23, -0xa80000.0p-34, 0xe60000.0p-23, 0xe00000.0p-36, 0xe70000.0p-23, 0x880000.0p-33, 0xe80000.0p-23, -0xe00000.0p-33, 0xe90000.0p-23, -0xfc0000.0p-34, 0xea0000.0p-23, -0x800000.0p-35, 0xeb0000.0p-23, 0xe80000.0p-35, 0xec0000.0p-23, 0x900000.0p-33, 0xed0000.0p-23, 0xe20000.0p-33, 0xee0000.0p-23, -0xac0000.0p-33, 0xef0000.0p-23, -0xc80000.0p-34, 0xf00000.0p-23, -0x800000.0p-35, 0xf10000.0p-23, 0x800000.0p-35, 0xf20000.0p-23, 0xb80000.0p-34, 0xf30000.0p-23, 0x940000.0p-33, 0xf40000.0p-23, 0xc80000.0p-33, 0xf50000.0p-23, -0xf20000.0p-33, 0xf60000.0p-23, -0xc80000.0p-33, 0xf70000.0p-23, -0xa20000.0p-33, 0xf80000.0p-23, -0x800000.0p-33, 0xf90000.0p-23, -0xc40000.0p-34, 0xfa0000.0p-23, -0x900000.0p-34, 0xfb0000.0p-23, -0xc80000.0p-35, 0xfc0000.0p-23, -0x800000.0p-35, 0xfd0000.0p-23, -0x900000.0p-36, 0xfe0000.0p-23, -0x800000.0p-37, 0xff0000.0p-23, -0x800000.0p-39, 0x800000.0p-22, 0, }; #endif /* USE_UTAB */ #ifdef STRUCT_RETURN #define RETURN1(rp, v) do { \ (rp)->hi = (v); \ (rp)->lo_set = 0; \ return; \ } while (0) #define RETURN2(rp, h, l) do { \ (rp)->hi = (h); \ (rp)->lo = (l); \ (rp)->lo_set = 1; \ return; \ } while (0) struct ld { long double hi; long double lo; int lo_set; }; #else #define RETURN1(rp, v) RETURNF(v) #define RETURN2(rp, h, l) RETURNI((h) + (l)) #endif #ifdef STRUCT_RETURN static inline __always_inline void k_logl(long double x, struct ld *rp) #else long double logl(long double x) #endif { long double d, val_hi, val_lo; double dd, dk; uint64_t lx, llx; int i, k; uint16_t hx; EXTRACT_LDBL128_WORDS(hx, lx, llx, x); k = -16383; #if 0 /* Hard to do efficiently. Don't do it until we support all modes. */ if (x == 1) RETURN1(rp, 0); /* log(1) = +0 in all rounding modes */ #endif if (hx == 0 || hx >= 0x8000) { /* zero, negative or subnormal? */ if (((hx & 0x7fff) | lx | llx) == 0) RETURN1(rp, -1 / zero); /* log(+-0) = -Inf */ if (hx != 0) /* log(neg or NaN) = qNaN: */ RETURN1(rp, (x - x) / zero); x *= 0x1.0p113; /* subnormal; scale up x */ EXTRACT_LDBL128_WORDS(hx, lx, llx, x); k = -16383 - 113; } else if (hx >= 0x7fff) RETURN1(rp, x + x); /* log(Inf or NaN) = Inf or qNaN */ #ifndef STRUCT_RETURN ENTERI(); #endif k += hx; dk = k; /* Scale x to be in [1, 2). */ SET_LDBL_EXPSIGN(x, 0x3fff); /* 0 <= i <= INTERVALS: */ #define L2I (49 - LOG2_INTERVALS) i = (lx + (1LL << (L2I - 2))) >> (L2I - 1); /* * -0.005280 < d < 0.004838. In particular, the infinite- * precision |d| is <= 2**-7. Rounding of G(i) to 8 bits * ensures that d is representable without extra precision for * this bound on |d| (since when this calculation is expressed * as x*G(i)-1, the multiplication needs as many extra bits as * G(i) has and the subtraction cancels 8 bits). But for * most i (107 cases out of 129), the infinite-precision |d| * is <= 2**-8. G(i) is rounded to 9 bits for such i to give * better accuracy (this works by improving the bound on |d|, * which in turn allows rounding to 9 bits in more cases). * This is only important when the original x is near 1 -- it * lets us avoid using a special method to give the desired * accuracy for such x. */ if (0) d = x * G(i) - 1; else { #ifdef USE_UTAB d = (x - H(i)) * G(i) + E(i); #else long double x_hi; double x_lo; /* * Split x into x_hi + x_lo to calculate x*G(i)-1 exactly. * G(i) has at most 9 bits, so the splitting point is not * critical. */ INSERT_LDBL128_WORDS(x_hi, 0x3fff, lx, llx & 0xffffffffff000000ULL); x_lo = x - x_hi; d = x_hi * G(i) - 1 + x_lo * G(i); #endif } /* * Our algorithm depends on exact cancellation of F_lo(i) and * F_hi(i) with dk*ln_2_lo and dk*ln2_hi when k is -1 and i is * at the end of the table. This and other technical complications * make it difficult to avoid the double scaling in (dk*ln2) * * log(base) for base != e without losing more accuracy and/or * efficiency than is gained. */ /* - * Use double precision operations wherever possible, since long - * double operations are emulated and are very slow on the only - * known machines that support ld128 (sparc64). Also, don't try - * to improve parallelism by increasing the number of operations, - * since any parallelism on such machines is needed for the - * emulation. Horner's method is good for this, and is also good - * for accuracy. Horner's method doesn't handle the `lo' term - * well, either for efficiency or accuracy. However, for accuracy - * we evaluate d * d * P2 separately to take advantage of - * by P2 being exact, and this gives a good place to sum the 'lo' + * Use double precision operations wherever possible, since + * long double operations are emulated and were very slow on + * the old sparc64 and unknown on the newer aarch64 and riscv + * machines. Also, don't try to improve parallelism by + * increasing the number of operations, since any parallelism + * on such machines is needed for the emulation. Horner's + * method is good for this, and is also good for accuracy. + * Horner's method doesn't handle the `lo' term well, either + * for efficiency or accuracy. However, for accuracy we + * evaluate d * d * P2 separately to take advantage of by P2 + * being exact, and this gives a good place to sum the 'lo' * term too. */ dd = (double)d; val_lo = d * d * d * (P3 + d * (P4 + d * (P5 + d * (P6 + d * (P7 + d * (P8 + dd * (P9 + dd * (P10 + dd * (P11 + dd * (P12 + dd * (P13 + dd * P14))))))))))) + (F_lo(i) + dk * ln2_lo) + d * d * P2; val_hi = d; #ifdef DEBUG if (fetestexcept(FE_UNDERFLOW)) breakpoint(); #endif _3sumF(val_hi, val_lo, F_hi(i) + dk * ln2_hi); RETURN2(rp, val_hi, val_lo); } long double log1pl(long double x) { long double d, d_hi, f_lo, val_hi, val_lo; long double f_hi, twopminusk; double d_lo, dd, dk; uint64_t lx, llx; int i, k; int16_t ax, hx; DOPRINT_START(&x); EXTRACT_LDBL128_WORDS(hx, lx, llx, x); if (hx < 0x3fff) { /* x < 1, or x neg NaN */ ax = hx & 0x7fff; if (ax >= 0x3fff) { /* x <= -1, or x neg NaN */ if (ax == 0x3fff && (lx | llx) == 0) RETURNP(-1 / zero); /* log1p(-1) = -Inf */ /* log1p(x < 1, or x NaN) = qNaN: */ RETURNP((x - x) / (x - x)); } if (ax <= 0x3f8d) { /* |x| < 2**-113 */ if ((int)x == 0) RETURNP(x); /* x with inexact if x != 0 */ } f_hi = 1; f_lo = x; } else if (hx >= 0x7fff) { /* x +Inf or non-neg NaN */ RETURNP(x + x); /* log1p(Inf or NaN) = Inf or qNaN */ } else if (hx < 0x40e1) { /* 1 <= x < 2**226 */ f_hi = x; f_lo = 1; } else { /* 2**226 <= x < +Inf */ f_hi = x; f_lo = 0; /* avoid underflow of the P3 term */ } ENTERI(); x = f_hi + f_lo; f_lo = (f_hi - x) + f_lo; EXTRACT_LDBL128_WORDS(hx, lx, llx, x); k = -16383; k += hx; dk = k; SET_LDBL_EXPSIGN(x, 0x3fff); twopminusk = 1; SET_LDBL_EXPSIGN(twopminusk, 0x7ffe - (hx & 0x7fff)); f_lo *= twopminusk; i = (lx + (1LL << (L2I - 2))) >> (L2I - 1); /* * x*G(i)-1 (with a reduced x) can be represented exactly, as * above, but now we need to evaluate the polynomial on d = * (x+f_lo)*G(i)-1 and extra precision is needed for that. * Since x+x_lo is a hi+lo decomposition and subtracting 1 * doesn't lose too many bits, an inexact calculation for * f_lo*G(i) is good enough. */ if (0) d_hi = x * G(i) - 1; else { #ifdef USE_UTAB d_hi = (x - H(i)) * G(i) + E(i); #else long double x_hi; double x_lo; INSERT_LDBL128_WORDS(x_hi, 0x3fff, lx, llx & 0xffffffffff000000ULL); x_lo = x - x_hi; d_hi = x_hi * G(i) - 1 + x_lo * G(i); #endif } d_lo = f_lo * G(i); /* * This is _2sumF(d_hi, d_lo) inlined. The condition * (d_hi == 0 || |d_hi| >= |d_lo|) for using _2sumF() is not * always satisifed, so it is not clear that this works, but * it works in practice. It works even if it gives a wrong * normalized d_lo, since |d_lo| > |d_hi| implies that i is * nonzero and d is tiny, so the F(i) term dominates d_lo. * In float precision: * (By exhaustive testing, the worst case is d_hi = 0x1.bp-25. * And if d is only a little tinier than that, we would have * another underflow problem for the P3 term; this is also ruled * out by exhaustive testing.) */ d = d_hi + d_lo; d_lo = d_hi - d + d_lo; d_hi = d; dd = (double)d; val_lo = d * d * d * (P3 + d * (P4 + d * (P5 + d * (P6 + d * (P7 + d * (P8 + dd * (P9 + dd * (P10 + dd * (P11 + dd * (P12 + dd * (P13 + dd * P14))))))))))) + (F_lo(i) + dk * ln2_lo + d_lo) + d * d * P2; val_hi = d_hi; #ifdef DEBUG if (fetestexcept(FE_UNDERFLOW)) breakpoint(); #endif _3sumF(val_hi, val_lo, F_hi(i) + dk * ln2_hi); RETURN2PI(val_hi, val_lo); } #ifdef STRUCT_RETURN long double logl(long double x) { struct ld r; ENTERI(); DOPRINT_START(&x); k_logl(x, &r); RETURNSPI(&r); } /* * 29+113 bit decompositions. The bits are distributed so that the products * of the hi terms are exact in double precision. The types are chosen so * that the products of the hi terms are done in at least double precision, * without any explicit conversions. More natural choices would require a * slow long double precision multiplication. */ static const double invln10_hi = 4.3429448176175356e-1, /* 0x1bcb7b15000000.0p-54 */ invln2_hi = 1.4426950402557850e0; /* 0x17154765000000.0p-52 */ static const long double invln10_lo = 1.41498268538580090791605082294397000e-10L, /* 0x137287195355baaafad33dc323ee3.0p-145L */ invln2_lo = 6.33178418956604368501892137426645911e-10L; /* 0x15c17f0bbbe87fed0691d3e88eb57.0p-143L */ long double log10l(long double x) { struct ld r; long double lo; float hi; ENTERI(); DOPRINT_START(&x); k_logl(x, &r); if (!r.lo_set) RETURNPI(r.hi); _2sumF(r.hi, r.lo); hi = r.hi; lo = r.lo + (r.hi - hi); RETURN2PI(invln10_hi * hi, (invln10_lo + invln10_hi) * lo + invln10_lo * hi); } long double log2l(long double x) { struct ld r; long double lo; float hi; ENTERI(); DOPRINT_START(&x); k_logl(x, &r); if (!r.lo_set) RETURNPI(r.hi); _2sumF(r.hi, r.lo); hi = r.hi; lo = r.lo + (r.hi - hi); RETURN2PI(invln2_hi * hi, (invln2_lo + invln2_hi) * lo + invln2_lo * hi); } #endif /* STRUCT_RETURN */ Index: head/lib/msun/sparc64/Symbol.map =================================================================== --- head/lib/msun/sparc64/Symbol.map (revision 358346) +++ head/lib/msun/sparc64/Symbol.map (nonexistent) @@ -1,13 +0,0 @@ -/* - * $FreeBSD$ - */ -FBSD_1.0 { -}; - -FBSD_1.3 { - fesetexceptflag; - feraiseexcept; - fegetenv; - feholdexcept; - feupdateenv; -}; Property changes on: head/lib/msun/sparc64/Symbol.map ___________________________________________________________________ Deleted: svn:keywords ## -1 +0,0 ## -FreeBSD=%H \ No newline at end of property Index: head/lib/msun/sparc64/Makefile.inc =================================================================== --- head/lib/msun/sparc64/Makefile.inc (revision 358346) +++ head/lib/msun/sparc64/Makefile.inc (nonexistent) @@ -1,5 +0,0 @@ -# $FreeBSD$ - -ARCH_SRCS= e_sqrt.S e_sqrtf.S -LDBL_PREC= 113 -SYM_MAPS+= ${.CURDIR}/sparc64/Symbol.map Property changes on: head/lib/msun/sparc64/Makefile.inc ___________________________________________________________________ Deleted: svn:keywords ## -1 +0,0 ## -FreeBSD=%H \ No newline at end of property Index: head/lib/msun/sparc64/fenv.h =================================================================== --- head/lib/msun/sparc64/fenv.h (revision 358346) +++ head/lib/msun/sparc64/fenv.h (nonexistent) @@ -1,262 +0,0 @@ -/*- - * SPDX-License-Identifier: BSD-2-Clause-FreeBSD - * - * Copyright (c) 2004-2005 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - * - * $FreeBSD$ - */ - -#ifndef _FENV_H_ -#define _FENV_H_ - -#include - -#ifndef __fenv_static -#define __fenv_static static -#endif - -typedef __uint64_t fenv_t; -typedef __uint64_t fexcept_t; - -/* Exception flags */ -#define FE_INVALID 0x00000200 -#define FE_DIVBYZERO 0x00000040 -#define FE_OVERFLOW 0x00000100 -#define FE_UNDERFLOW 0x00000080 -#define FE_INEXACT 0x00000020 -#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_INEXACT | \ - FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW) - -/* - * Rounding modes - * - * We can't just use the hardware bit values here, because that would - * make FE_UPWARD and FE_DOWNWARD negative, which is not allowed. - */ -#define FE_TONEAREST 0x0 -#define FE_TOWARDZERO 0x1 -#define FE_UPWARD 0x2 -#define FE_DOWNWARD 0x3 -#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \ - FE_UPWARD | FE_TOWARDZERO) -#define _ROUND_SHIFT 30 - -__BEGIN_DECLS - -/* Default floating-point environment */ -extern const fenv_t __fe_dfl_env; -#define FE_DFL_ENV (&__fe_dfl_env) - -/* We need to be able to map status flag positions to mask flag positions */ -#define _FPUSW_SHIFT 18 -#define _ENABLE_MASK (FE_ALL_EXCEPT << _FPUSW_SHIFT) - -#define __ldxfsr(__r) __asm __volatile("ldx %0, %%fsr" : : "m" (__r)) -#define __stxfsr(__r) __asm __volatile("stx %%fsr, %0" : "=m" (*(__r))) - -__fenv_static __inline int -feclearexcept(int __excepts) -{ - fexcept_t __r; - - __stxfsr(&__r); - __r &= ~__excepts; - __ldxfsr(__r); - return (0); -} - -__fenv_static inline int -fegetexceptflag(fexcept_t *__flagp, int __excepts) -{ - fexcept_t __r; - - __stxfsr(&__r); - *__flagp = __r & __excepts; - return (0); -} - -__fenv_static inline int -fesetexceptflag(const fexcept_t *__flagp, int __excepts) -{ - fexcept_t __r; - - __stxfsr(&__r); - __r &= ~__excepts; - __r |= *__flagp & __excepts; - __ldxfsr(__r); - return (0); -} - -/* - * It seems to be worthwhile to inline this function even when the - * arguments are not compile-time constants. Perhaps this depends - * on the register window. - */ -__fenv_static inline int -feraiseexcept(int __excepts) -{ - volatile double d; - - /* - * With a compiler that supports the FENV_ACCESS pragma - * properly, simple expressions like '0.0 / 0.0' should - * be sufficient to generate traps. Unfortunately, we - * need to bring a volatile variable into the equation - * to prevent incorrect optimizations. - */ - if (__excepts & FE_INVALID) { - d = 0.0; - d = 0.0 / d; - } - if (__excepts & FE_DIVBYZERO) { - d = 0.0; - d = 1.0 / d; - } - if (__excepts & FE_OVERFLOW) { - d = 0x1.ffp1023; - d *= 2.0; - } - if (__excepts & FE_UNDERFLOW) { - d = 0x1p-1022; - d /= 0x1p1023; - } - if (__excepts & FE_INEXACT) { - d = 0x1p-1022; - d += 1.0; - } - return (0); -} - -__fenv_static inline int -fetestexcept(int __excepts) -{ - fexcept_t __r; - - __stxfsr(&__r); - return (__r & __excepts); -} - -__fenv_static inline int -fegetround(void) -{ - fenv_t __r; - - __stxfsr(&__r); - return ((__r >> _ROUND_SHIFT) & _ROUND_MASK); -} - -__fenv_static inline int -fesetround(int __round) -{ - fenv_t __r; - - if (__round & ~_ROUND_MASK) - return (-1); - __stxfsr(&__r); - __r &= ~(_ROUND_MASK << _ROUND_SHIFT); - __r |= __round << _ROUND_SHIFT; - __ldxfsr(__r); - return (0); -} - -__fenv_static inline int -fegetenv(fenv_t *__envp) -{ - - __stxfsr(__envp); - return (0); -} - -__fenv_static inline int -feholdexcept(fenv_t *__envp) -{ - fenv_t __r; - - __stxfsr(&__r); - *__envp = __r; - __r &= ~(FE_ALL_EXCEPT | _ENABLE_MASK); - __ldxfsr(__r); - return (0); -} - -__fenv_static inline int -fesetenv(const fenv_t *__envp) -{ - - __ldxfsr(*__envp); - return (0); -} - -__fenv_static inline int -feupdateenv(const fenv_t *__envp) -{ - fexcept_t __r; - - __stxfsr(&__r); - __ldxfsr(*__envp); - feraiseexcept(__r & FE_ALL_EXCEPT); - return (0); -} - -#if __BSD_VISIBLE - -/* We currently provide no external definitions of the functions below. */ - -static inline int -feenableexcept(int __mask) -{ - fenv_t __old_r, __new_r; - - __stxfsr(&__old_r); - __new_r = __old_r | ((__mask & FE_ALL_EXCEPT) << _FPUSW_SHIFT); - __ldxfsr(__new_r); - return ((__old_r >> _FPUSW_SHIFT) & FE_ALL_EXCEPT); -} - -static inline int -fedisableexcept(int __mask) -{ - fenv_t __old_r, __new_r; - - __stxfsr(&__old_r); - __new_r = __old_r & ~((__mask & FE_ALL_EXCEPT) << _FPUSW_SHIFT); - __ldxfsr(__new_r); - return ((__old_r >> _FPUSW_SHIFT) & FE_ALL_EXCEPT); -} - -static inline int -fegetexcept(void) -{ - fenv_t __r; - - __stxfsr(&__r); - return ((__r & _ENABLE_MASK) >> _FPUSW_SHIFT); -} - -#endif /* __BSD_VISIBLE */ - -__END_DECLS - -#endif /* !_FENV_H_ */ Property changes on: head/lib/msun/sparc64/fenv.h ___________________________________________________________________ Deleted: svn:keywords ## -1 +0,0 ## -FreeBSD=%H \ No newline at end of property Index: head/lib/msun/sparc64/e_sqrtf.S =================================================================== --- head/lib/msun/sparc64/e_sqrtf.S (revision 358346) +++ head/lib/msun/sparc64/e_sqrtf.S (nonexistent) @@ -1,33 +0,0 @@ -/*- - * Copyright (c) 2005 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - -#include -__FBSDID("$FreeBSD$") - -ENTRY(sqrtf) - retl - fsqrts %f1, %f0 -END(sqrtf) Property changes on: head/lib/msun/sparc64/e_sqrtf.S ___________________________________________________________________ Deleted: svn:keywords ## -1 +0,0 ## -FreeBSD=%H \ No newline at end of property Index: head/lib/msun/sparc64/e_sqrt.S =================================================================== --- head/lib/msun/sparc64/e_sqrt.S (revision 358346) +++ head/lib/msun/sparc64/e_sqrt.S (nonexistent) @@ -1,33 +0,0 @@ -/*- - * Copyright (c) 2005 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - -#include -__FBSDID("$FreeBSD$") - -ENTRY(sqrt) - retl - fsqrtd %f0, %f0 -END(sqrt) Property changes on: head/lib/msun/sparc64/e_sqrt.S ___________________________________________________________________ Deleted: svn:keywords ## -1 +0,0 ## -FreeBSD=%H \ No newline at end of property Index: head/lib/msun/sparc64/fenv.c =================================================================== --- head/lib/msun/sparc64/fenv.c (revision 358346) +++ head/lib/msun/sparc64/fenv.c (nonexistent) @@ -1,55 +0,0 @@ -/*- - * SPDX-License-Identifier: BSD-2-Clause-FreeBSD - * - * Copyright (c) 2004 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - * - * $FreeBSD$ - */ - -#define __fenv_static -#include "fenv.h" - -#ifdef __GNUC_GNU_INLINE__ -#error "This file must be compiled with C99 'inline' semantics" -#endif - -/* - * The FSR_version field may be different on different - * implementations, but it is immutable and opaque to the - * application. Thus, 0 is valid as the default environment. - */ -const fenv_t __fe_dfl_env = 0; - -extern inline int feclearexcept(int __excepts); -extern inline int fegetexceptflag(fexcept_t *__flagp, int __excepts); -extern inline int fesetexceptflag(const fexcept_t *__flagp, int __excepts); -extern inline int feraiseexcept(int __excepts); -extern inline int fetestexcept(int __excepts); -extern inline int fegetround(void); -extern inline int fesetround(int __round); -extern inline int fegetenv(fenv_t *__envp); -extern inline int feholdexcept(fenv_t *__envp); -extern inline int fesetenv(const fenv_t *__envp); -extern inline int feupdateenv(const fenv_t *__envp); Property changes on: head/lib/msun/sparc64/fenv.c ___________________________________________________________________ Deleted: svn:keywords ## -1 +0,0 ## -FreeBSD=%H \ No newline at end of property