1/* Shared data between exp, exp2 and pow.
2 Copyright (C) 2018-2019 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <http://www.gnu.org/licenses/>. */
18
19#include "math_config.h"
20
21#define N (1 << EXP_TABLE_BITS)
22
23const struct exp_data __exp_data = {
24// N/ln2
25.invln2N = 0x1.71547652b82fep0 * N,
26// -ln2/N
27#if N == 128
28.negln2hiN = -0x1.62e42fefa0000p-8,
29.negln2loN = -0x1.cf79abc9e3b3ap-47,
30#endif
31// Used for rounding when !TOINT_INTRINSICS
32.shift = 0x1.8p52,
33// exp polynomial coefficients.
34.poly = {
35#if N == 128 && EXP_POLY_ORDER == 5
36// abs error: 1.555*2^-66
37// ulp error: 0.509 (0.511 without fma)
38// if |x| < ln2/256+eps
39// abs error if |x| < ln2/128: 1.7145*2^-56
400x1.ffffffffffdbdp-2,
410x1.555555555543cp-3,
420x1.55555cf172b91p-5,
430x1.1111167a4d017p-7,
44#endif
45},
46.exp2_shift = 0x1.8p52 / N,
47// exp2 polynomial coefficients.
48.exp2_poly = {
49#if N == 128 && EXP2_POLY_ORDER == 5
50// abs error: 1.2195*2^-65
51// ulp error: 0.507 (0.511 without fma)
52// if |x| < 1/256
53// abs error if |x| < 1/128: 1.9941*2^-56
540x1.62e42fefa39efp-1,
550x1.ebfbdff82c424p-3,
560x1.c6b08d70cf4b5p-5,
570x1.3b2abd24650ccp-7,
580x1.5d7e09b4e3a84p-10,
59#endif
60},
61// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N)
62// tab[2*k] = asuint64(T[k])
63// tab[2*k+1] = asuint64(H[k]) - (k << 52)/N
64.tab = {
65#if N == 128
660x0, 0x3ff0000000000000,
670x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
680xbc7160139cd8dc5d, 0x3fefec9a3e778061,
690xbc905e7a108766d1, 0x3fefe315e86e7f85,
700x3c8cd2523567f613, 0x3fefd9b0d3158574,
710xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
720x3c60f74e61e6c861, 0x3fefc74518759bc8,
730x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
740x3c979aa65d837b6d, 0x3fefb5586cf9890f,
750x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
760x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
770xbc6a033489906e0b, 0x3fef9b66affed31b,
780xbc9556522a2fbd0e, 0x3fef9301d0125b51,
790xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
800xbc91c923b9d5f416, 0x3fef829aaea92de0,
810x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
820xbc801b15eaa59348, 0x3fef72b83c7d517b,
830xbc8f1ff055de323d, 0x3fef6af9388c8dea,
840x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
850xbc96d99c7611eb26, 0x3fef5be084045cd4,
860x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
870xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
880x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
890x3c807a05b0e4047d, 0x3fef3f49917ddc96,
900x3c968efde3a8a894, 0x3fef387a6e756238,
910x3c875e18f274487d, 0x3fef31ce4fb2a63f,
920x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
930xbc96b87b3f71085e, 0x3fef24dfe1f56381,
940x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
950xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
960x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
970x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
980x3c834d754db0abb6, 0x3fef06fe0a31b715,
990x3c864201e2ac744c, 0x3fef0170fc4cd831,
1000x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
1010xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
1020xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
1030xbc9907f81b512d8e, 0x3feeecae6d05d866,
1040xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
1050xbc991919b3ce1b15, 0x3feee32dc313a8e5,
1060x3c859f48a72a4c6d, 0x3feedea64c123422,
1070xbc9312607a28698a, 0x3feeda4504ac801c,
1080xbc58a78f4817895b, 0x3feed60a21f72e2a,
1090xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
1100x3c4363ed60c2ac11, 0x3feece086061892d,
1110x3c9666093b0664ef, 0x3feeca41ed1d0057,
1120x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
1130x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
1140x3c7690cebb7aafb0, 0x3feebfdad5362a27,
1150x3c931dbdeb54e077, 0x3feebcb299fddd0d,
1160xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
1170xbc87deccdc93a349, 0x3feeb6daa2cf6642,
1180xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
1190xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
1200x3c93350518fdd78e, 0x3feeaf4736b527da,
1210x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
1220x3c9063e1e21c5409, 0x3feeab07dd485429,
1230x3c34c7855019c6ea, 0x3feea9268a5946b7,
1240x3c9432e62b64c035, 0x3feea76f15ad2148,
1250xbc8ce44a6199769f, 0x3feea5e1b976dc09,
1260xbc8c33c53bef4da8, 0x3feea47eb03a5585,
1270xbc845378892be9ae, 0x3feea34634ccc320,
1280xbc93cedd78565858, 0x3feea23882552225,
1290x3c5710aa807e1964, 0x3feea155d44ca973,
1300xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
1310xbc6a12ad8734b982, 0x3feea012750bdabf,
1320xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
1330xbc80dc3d54e08851, 0x3fee9f7df9519484,
1340xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
1350xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
1360xbc8619321e55e68a, 0x3fee9feb564267c9,
1370x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
1380xbc7b32dcb94da51d, 0x3feea11473eb0187,
1390x3c94ecfd5467c06b, 0x3feea1ed0130c132,
1400x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
1410xbc88a1c52fb3cf42, 0x3feea427543e1a12,
1420xbc9369b6f13b3734, 0x3feea589994cce13,
1430xbc805e843a19ff1e, 0x3feea71a4623c7ad,
1440xbc94d450d872576e, 0x3feea8d99b4492ed,
1450x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
1460x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
1470xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
1480x3c7bf68359f35f44, 0x3feeb1ae99157736,
1490xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
1500xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
1510xbc6c23f97c90b959, 0x3feeba44cbc8520f,
1520xbc92434322f4f9aa, 0x3feebd829fde4e50,
1530xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
1540x3c71affc2b91ce27, 0x3feec49182a3f090,
1550x3c6dd235e10a73bb, 0x3feec86319e32323,
1560xbc87c50422622263, 0x3feecc667b5de565,
1570x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
1580xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
1590x3c90cc319cee31d2, 0x3feed99e1330b358,
1600x3c8469846e735ab3, 0x3feede6b5579fdbf,
1610xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
1620x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
1630xbc907b8f4ad1d9fa, 0x3feeee07298db666,
1640xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
1650xbc90a40e3da6f640, 0x3feef9728de5593a,
1660xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
1670xbc91eee26b588a35, 0x3fef05b030a1064a,
1680x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
1690xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
1700x3c736eae30af0cb3, 0x3fef199bdd85529c,
1710x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
1720x3c84e08fd10959ac, 0x3fef27f12e57d14b,
1730x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
1740x3c676b2c6c921968, 0x3fef3720dcef9069,
1750xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
1760xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
1770xbc900dae3875a949, 0x3fef4f87080d89f2,
1780x3c74a385a63d07a7, 0x3fef5818dcfba487,
1790xbc82919e2040220f, 0x3fef60e316c98398,
1800x3c8e5a50d5c192ac, 0x3fef69e603db3285,
1810x3c843a59ac016b4b, 0x3fef7321f301b460,
1820xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
1830xbc892ab93b470dc9, 0x3fef864614f5a129,
1840x3c74b604603a88d3, 0x3fef902ee78b3ff6,
1850x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
1860xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
1870xbc8dae98e223747d, 0x3fefaf482d8e67f1,
1880x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
1890x3c842b94c3a9eb32, 0x3fefc52b376bba97,
1900x3c8a64a931d185ee, 0x3fefd0765b6e4540,
1910xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
1920x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
1930x3c5305c14160cc89, 0x3feff3c22b8f71f1,
194#endif
195},
196};
197