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197 lines
6.9 KiB
C
197 lines
6.9 KiB
C
/* Shared data between exp, exp2 and pow.
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Copyright (C) 2018-2020 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "math_config.h"
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#define N (1 << EXP_TABLE_BITS)
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const struct exp_data __exp_data = {
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// N/ln2
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.invln2N = 0x1.71547652b82fep0 * N,
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// -ln2/N
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#if N == 128
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.negln2hiN = -0x1.62e42fefa0000p-8,
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.negln2loN = -0x1.cf79abc9e3b3ap-47,
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#endif
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// Used for rounding when !TOINT_INTRINSICS
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.shift = 0x1.8p52,
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// exp polynomial coefficients.
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.poly = {
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#if N == 128 && EXP_POLY_ORDER == 5
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// abs error: 1.555*2^-66
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// ulp error: 0.509 (0.511 without fma)
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// if |x| < ln2/256+eps
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// abs error if |x| < ln2/128: 1.7145*2^-56
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0x1.ffffffffffdbdp-2,
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0x1.555555555543cp-3,
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0x1.55555cf172b91p-5,
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0x1.1111167a4d017p-7,
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#endif
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},
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.exp2_shift = 0x1.8p52 / N,
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// exp2 polynomial coefficients.
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.exp2_poly = {
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#if N == 128 && EXP2_POLY_ORDER == 5
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// abs error: 1.2195*2^-65
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// ulp error: 0.507 (0.511 without fma)
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// if |x| < 1/256
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// abs error if |x| < 1/128: 1.9941*2^-56
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0x1.62e42fefa39efp-1,
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0x1.ebfbdff82c424p-3,
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0x1.c6b08d70cf4b5p-5,
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0x1.3b2abd24650ccp-7,
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0x1.5d7e09b4e3a84p-10,
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#endif
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},
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// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N)
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// tab[2*k] = asuint64(T[k])
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// tab[2*k+1] = asuint64(H[k]) - (k << 52)/N
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.tab = {
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#if N == 128
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0x0, 0x3ff0000000000000,
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0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
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0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
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0xbc905e7a108766d1, 0x3fefe315e86e7f85,
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0x3c8cd2523567f613, 0x3fefd9b0d3158574,
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0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
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0x3c60f74e61e6c861, 0x3fefc74518759bc8,
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0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
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0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
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0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
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0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
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0xbc6a033489906e0b, 0x3fef9b66affed31b,
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0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
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0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
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0xbc91c923b9d5f416, 0x3fef829aaea92de0,
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0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
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0xbc801b15eaa59348, 0x3fef72b83c7d517b,
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0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
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0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
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0xbc96d99c7611eb26, 0x3fef5be084045cd4,
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0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
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0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
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0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
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0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
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0x3c968efde3a8a894, 0x3fef387a6e756238,
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0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
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0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
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0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
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0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
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0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
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0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
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0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
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0x3c834d754db0abb6, 0x3fef06fe0a31b715,
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0x3c864201e2ac744c, 0x3fef0170fc4cd831,
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0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
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0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
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0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
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0xbc9907f81b512d8e, 0x3feeecae6d05d866,
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0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
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0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
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0x3c859f48a72a4c6d, 0x3feedea64c123422,
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0xbc9312607a28698a, 0x3feeda4504ac801c,
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0xbc58a78f4817895b, 0x3feed60a21f72e2a,
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0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
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0x3c4363ed60c2ac11, 0x3feece086061892d,
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0x3c9666093b0664ef, 0x3feeca41ed1d0057,
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0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
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0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
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0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
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0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
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0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
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0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
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0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
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0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
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0x3c93350518fdd78e, 0x3feeaf4736b527da,
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0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
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0x3c9063e1e21c5409, 0x3feeab07dd485429,
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0x3c34c7855019c6ea, 0x3feea9268a5946b7,
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0x3c9432e62b64c035, 0x3feea76f15ad2148,
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0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
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0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
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0xbc845378892be9ae, 0x3feea34634ccc320,
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0xbc93cedd78565858, 0x3feea23882552225,
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0x3c5710aa807e1964, 0x3feea155d44ca973,
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0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
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0xbc6a12ad8734b982, 0x3feea012750bdabf,
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0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
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0xbc80dc3d54e08851, 0x3fee9f7df9519484,
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0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
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0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
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0xbc8619321e55e68a, 0x3fee9feb564267c9,
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0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
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0xbc7b32dcb94da51d, 0x3feea11473eb0187,
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0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
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0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
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0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
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0xbc9369b6f13b3734, 0x3feea589994cce13,
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0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
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0xbc94d450d872576e, 0x3feea8d99b4492ed,
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0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
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0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
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0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
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0x3c7bf68359f35f44, 0x3feeb1ae99157736,
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0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
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0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
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0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
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0xbc92434322f4f9aa, 0x3feebd829fde4e50,
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0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
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0x3c71affc2b91ce27, 0x3feec49182a3f090,
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0x3c6dd235e10a73bb, 0x3feec86319e32323,
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0xbc87c50422622263, 0x3feecc667b5de565,
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0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
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0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
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0x3c90cc319cee31d2, 0x3feed99e1330b358,
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0x3c8469846e735ab3, 0x3feede6b5579fdbf,
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0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
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0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
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0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
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0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
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0xbc90a40e3da6f640, 0x3feef9728de5593a,
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0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
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0xbc91eee26b588a35, 0x3fef05b030a1064a,
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0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
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0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
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0x3c736eae30af0cb3, 0x3fef199bdd85529c,
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0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
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0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
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0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
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0x3c676b2c6c921968, 0x3fef3720dcef9069,
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0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
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0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
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0xbc900dae3875a949, 0x3fef4f87080d89f2,
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0x3c74a385a63d07a7, 0x3fef5818dcfba487,
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0xbc82919e2040220f, 0x3fef60e316c98398,
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0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
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0x3c843a59ac016b4b, 0x3fef7321f301b460,
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0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
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0xbc892ab93b470dc9, 0x3fef864614f5a129,
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0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
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0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
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0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
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0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
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0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
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0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
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0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
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0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
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0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
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0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
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#endif
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},
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};
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