v_pow_exp_data.c

/*
 * Shared data between exp, exp2 and pow.
 *
 * Copyright (c) 2018-2024, Arm Limited.
 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
 */

#include "math_config.h"

#define N (1 << V_POW_EXP_TABLE_BITS)

const struct v_pow_exp_data __v_pow_exp_data = {
// exp polynomial coefficients.
.poly = {
// abs error: 1.43*2^-58
// ulp error: 0.549 (0.550 without fma)
// if |x| < ln2/512
0x1.fffffffffffd4p-2,
0x1.5555571d6ef9p-3,
0x1.5555576a5adcep-5,
},
// N/ln2
.n_over_ln2 = 0x1.71547652b82fep0 * N,
// ln2/N
.ln2_over_n_hi = 0x1.62e42fefc0000p-9,
.ln2_over_n_lo = -0x1.c610ca86c3899p-45,
// Used for rounding to nearest integer without using intrinsics.
.shift = 0x1.8p52,
// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N)
// sbits[k] = asuint64(H[k]) - (k << 52)/N
.sbits = {
0x3ff0000000000000,
0x3feffb1afa5abcbf,
0x3feff63da9fb3335,
0x3feff168143b0281,
0x3fefec9a3e778061,
0x3fefe7d42e11bbcc,
0x3fefe315e86e7f85,
0x3fefde5f72f654b1,
0x3fefd9b0d3158574,
0x3fefd50a0e3c1f89,
0x3fefd06b29ddf6de,
0x3fefcbd42b72a836,
0x3fefc74518759bc8,
0x3fefc2bdf66607e0,
0x3fefbe3ecac6f383,
0x3fefb9c79b1f3919,
0x3fefb5586cf9890f,
0x3fefb0f145e46c85,
0x3fefac922b7247f7,
0x3fefa83b23395dec,
0x3fefa3ec32d3d1a2,
0x3fef9fa55fdfa9c5,
0x3fef9b66affed31b,
0x3fef973028d7233e,
0x3fef9301d0125b51,
0x3fef8edbab5e2ab6,
0x3fef8abdc06c31cc,
0x3fef86a814f204ab,
0x3fef829aaea92de0,
0x3fef7e95934f312e,
0x3fef7a98c8a58e51,
0x3fef76a45471c3c2,
0x3fef72b83c7d517b,
0x3fef6ed48695bbc0,
0x3fef6af9388c8dea,
0x3fef672658375d2f,
0x3fef635beb6fcb75,
0x3fef5f99f8138a1c,
0x3fef5be084045cd4,
0x3fef582f95281c6b,
0x3fef54873168b9aa,
0x3fef50e75eb44027,
0x3fef4d5022fcd91d,
0x3fef49c18438ce4d,
0x3fef463b88628cd6,
0x3fef42be3578a819,
0x3fef3f49917ddc96,
0x3fef3bdda27912d1,
0x3fef387a6e756238,
0x3fef351ffb82140a,
0x3fef31ce4fb2a63f,
0x3fef2e85711ece75,
0x3fef2b4565e27cdd,
0x3fef280e341ddf29,
0x3fef24dfe1f56381,
0x3fef21ba7591bb70,
0x3fef1e9df51fdee1,
0x3fef1b8a66d10f13,
0x3fef187fd0dad990,
0x3fef157e39771b2f,
0x3fef1285a6e4030b,
0x3fef0f961f641589,
0x3fef0cafa93e2f56,
0x3fef09d24abd886b,
0x3fef06fe0a31b715,
0x3fef0432edeeb2fd,
0x3fef0170fc4cd831,
0x3feefeb83ba8ea32,
0x3feefc08b26416ff,
0x3feef96266e3fa2d,
0x3feef6c55f929ff1,
0x3feef431a2de883b,
0x3feef1a7373aa9cb,
0x3feeef26231e754a,
0x3feeecae6d05d866,
0x3feeea401b7140ef,
0x3feee7db34e59ff7,
0x3feee57fbfec6cf4,
0x3feee32dc313a8e5,
0x3feee0e544ede173,
0x3feedea64c123422,
0x3feedc70df1c5175,
0x3feeda4504ac801c,
0x3feed822c367a024,
0x3feed60a21f72e2a,
0x3feed3fb2709468a,
0x3feed1f5d950a897,
0x3feecffa3f84b9d4,
0x3feece086061892d,
0x3feecc2042a7d232,
0x3feeca41ed1d0057,
0x3feec86d668b3237,
0x3feec6a2b5c13cd0,
0x3feec4e1e192aed2,
0x3feec32af0d7d3de,
0x3feec17dea6db7d7,
0x3feebfdad5362a27,
0x3feebe41b817c114,
0x3feebcb299fddd0d,
0x3feebb2d81d8abff,
0x3feeb9b2769d2ca7,
0x3feeb8417f4531ee,
0x3feeb6daa2cf6642,
0x3feeb57de83f4eef,
0x3feeb42b569d4f82,
0x3feeb2e2f4f6ad27,
0x3feeb1a4ca5d920f,
0x3feeb070dde910d2,
0x3feeaf4736b527da,
0x3feeae27dbe2c4cf,
0x3feead12d497c7fd,
0x3feeac0827ff07cc,
0x3feeab07dd485429,
0x3feeaa11fba87a03,
0x3feea9268a5946b7,
0x3feea84590998b93,
0x3feea76f15ad2148,
0x3feea6a320dceb71,
0x3feea5e1b976dc09,
0x3feea52ae6cdf6f4,
0x3feea47eb03a5585,
0x3feea3dd1d1929fd,
0x3feea34634ccc320,
0x3feea2b9febc8fb7,
0x3feea23882552225,
0x3feea1c1c70833f6,
0x3feea155d44ca973,
0x3feea0f4b19e9538,
0x3feea09e667f3bcd,
0x3feea052fa75173e,
0x3feea012750bdabf,
0x3fee9fdcddd47645,
0x3fee9fb23c651a2f,
0x3fee9f9298593ae5,
0x3fee9f7df9519484,
0x3fee9f7466f42e87,
0x3fee9f75e8ec5f74,
0x3fee9f8286ead08a,
0x3fee9f9a48a58174,
0x3fee9fbd35d7cbfd,
0x3fee9feb564267c9,
0x3feea024b1ab6e09,
0x3feea0694fde5d3f,
0x3feea0b938ac1cf6,
0x3feea11473eb0187,
0x3feea17b0976cfdb,
0x3feea1ed0130c132,
0x3feea26a62ff86f0,
0x3feea2f336cf4e62,
0x3feea3878491c491,
0x3feea427543e1a12,
0x3feea4d2add106d9,
0x3feea589994cce13,
0x3feea64c1eb941f7,
0x3feea71a4623c7ad,
0x3feea7f4179f5b21,
0x3feea8d99b4492ed,
0x3feea9cad931a436,
0x3feeaac7d98a6699,
0x3feeabd0a478580f,
0x3feeace5422aa0db,
0x3feeae05bad61778,
0x3feeaf3216b5448c,
0x3feeb06a5e0866d9,
0x3feeb1ae99157736,
0x3feeb2fed0282c8a,
0x3feeb45b0b91ffc6,
0x3feeb5c353aa2fe2,
0x3feeb737b0cdc5e5,
0x3feeb8b82b5f98e5,
0x3feeba44cbc8520f,
0x3feebbdd9a7670b3,
0x3feebd829fde4e50,
0x3feebf33e47a22a2,
0x3feec0f170ca07ba,
0x3feec2bb4d53fe0d,
0x3feec49182a3f090,
0x3feec674194bb8d5,
0x3feec86319e32323,
0x3feeca5e8d07f29e,
0x3feecc667b5de565,
0x3feece7aed8eb8bb,
0x3feed09bec4a2d33,
0x3feed2c980460ad8,
0x3feed503b23e255d,
0x3feed74a8af46052,
0x3feed99e1330b358,
0x3feedbfe53c12e59,
0x3feede6b5579fdbf,
0x3feee0e521356eba,
0x3feee36bbfd3f37a,
0x3feee5ff3a3c2774,
0x3feee89f995ad3ad,
0x3feeeb4ce622f2ff,
0x3feeee07298db666,
0x3feef0ce6c9a8952,
0x3feef3a2b84f15fb,
0x3feef68415b749b1,
0x3feef9728de5593a,
0x3feefc6e29f1c52a,
0x3feeff76f2fb5e47,
0x3fef028cf22749e4,
0x3fef05b030a1064a,
0x3fef08e0b79a6f1f,
0x3fef0c1e904bc1d2,
0x3fef0f69c3f3a207,
0x3fef12c25bd71e09,
0x3fef16286141b33d,
0x3fef199bdd85529c,
0x3fef1d1cd9fa652c,
0x3fef20ab5fffd07a,
0x3fef244778fafb22,
0x3fef27f12e57d14b,
0x3fef2ba88988c933,
0x3fef2f6d9406e7b5,
0x3fef33405751c4db,
0x3fef3720dcef9069,
0x3fef3b0f2e6d1675,
0x3fef3f0b555dc3fa,
0x3fef43155b5bab74,
0x3fef472d4a07897c,
0x3fef4b532b08c968,
0x3fef4f87080d89f2,
0x3fef53c8eacaa1d6,
0x3fef5818dcfba487,
0x3fef5c76e862e6d3,
0x3fef60e316c98398,
0x3fef655d71ff6075,
0x3fef69e603db3285,
0x3fef6e7cd63a8315,
0x3fef7321f301b460,
0x3fef77d5641c0658,
0x3fef7c97337b9b5f,
0x3fef81676b197d17,
0x3fef864614f5a129,
0x3fef8b333b16ee12,
0x3fef902ee78b3ff6,
0x3fef953924676d76,
0x3fef9a51fbc74c83,
0x3fef9f7977cdb740,
0x3fefa4afa2a490da,
0x3fefa9f4867cca6e,
0x3fefaf482d8e67f1,
0x3fefb4aaa2188510,
0x3fefba1bee615a27,
0x3fefbf9c1cb6412a,
0x3fefc52b376bba97,
0x3fefcac948dd7274,
0x3fefd0765b6e4540,
0x3fefd632798844f8,
0x3fefdbfdad9cbe14,
0x3fefe1d802243c89,
0x3fefe7c1819e90d8,
0x3fefedba3692d514,
0x3feff3c22b8f71f1,
0x3feff9d96b2a23d9,
},
};