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libc/newlib/libm/common/exp_data.c

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New exp and exp2 implementations The new implementations are provided under !__OBSOLETE_MATH, they use ISO C99 code. There are several settings, with the default one the worst case error in nearest rounding mode is 0.509 ULP for exp and 0.507 ULP for exp2 when a multiply and add is contracted into an fma. They use a shared 2 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased by 1868 bytes. The w_*.c wrappers are disabled for the new code as it takes care of error handling inline. The old exp2(x) code used to be just pow(2,x) so the speedup there is more significant. The file name has no special prefix to avoid any name collision with existing files. Improvements on Cortex-A72: exp latency: 3.2x exp thruput: 4.1x exp2 latency: 7.8x exp2 thruput: 18.8x
2018-06-22 19:12:26 +02:00
/* Shared data between exp, exp2 and pow.
Copyright (c) 2018 Arm Ltd. All rights reserved.
SPDX-License-Identifier: BSD-3-Clause
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.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
Update Arm copyright notices in new math files While working on the strstr patch I noticed several copyright headers of the new math functions are missing closing quotes after ``AS IS. I've added these. Also update spellings of Arm Ltd in a few places (but still use ARM LTD in upper case portion). Finally add SPDX identifiers to make everything consistent.
2018-09-27 19:03:32 +02:00
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS'' AND ANY EXPRESS OR IMPLIED
New exp and exp2 implementations The new implementations are provided under !__OBSOLETE_MATH, they use ISO C99 code. There are several settings, with the default one the worst case error in nearest rounding mode is 0.509 ULP for exp and 0.507 ULP for exp2 when a multiply and add is contracted into an fma. They use a shared 2 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased by 1868 bytes. The w_*.c wrappers are disabled for the new code as it takes care of error handling inline. The old exp2(x) code used to be just pow(2,x) so the speedup there is more significant. The file name has no special prefix to avoid any name collision with existing files. Improvements on Cortex-A72: exp latency: 3.2x exp thruput: 4.1x exp2 latency: 7.8x exp2 thruput: 18.8x
2018-06-22 19:12:26 +02:00
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
Update Arm copyright notices in new math files While working on the strstr patch I noticed several copyright headers of the new math functions are missing closing quotes after ``AS IS. I've added these. Also update spellings of Arm Ltd in a few places (but still use ARM LTD in upper case portion). Finally add SPDX identifiers to make everything consistent.
2018-09-27 19:03:32 +02:00
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
New exp and exp2 implementations The new implementations are provided under !__OBSOLETE_MATH, they use ISO C99 code. There are several settings, with the default one the worst case error in nearest rounding mode is 0.509 ULP for exp and 0.507 ULP for exp2 when a multiply and add is contracted into an fma. They use a shared 2 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased by 1868 bytes. The w_*.c wrappers are disabled for the new code as it takes care of error handling inline. The old exp2(x) code used to be just pow(2,x) so the speedup there is more significant. The file name has no special prefix to avoid any name collision with existing files. Improvements on Cortex-A72: exp latency: 3.2x exp thruput: 4.1x exp2 latency: 7.8x exp2 thruput: 18.8x
2018-06-22 19:12:26 +02:00
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 "fdlibm.h"
#if !__OBSOLETE_MATH
#include "math_config.h"
#define N (1 << EXP_TABLE_BITS)
const struct exp_data __exp_data = {
// N/ln2
.invln2N = 0x1.71547652b82fep0 * N,
// -ln2/N
#if N == 64
.negln2hiN = -0x1.62e42fefa0000p-7,
.negln2loN = -0x1.cf79abc9e3b3ap-46,
#elif N == 128
.negln2hiN = -0x1.62e42fefa0000p-8,
.negln2loN = -0x1.cf79abc9e3b3ap-47,
#elif N == 256
.negln2hiN = -0x1.62e42fefc0000p-9,
.negln2loN = 0x1.c610ca86c3899p-45,
#endif
// Used for rounding when !TOINT_INTRINSICS
#if EXP_USE_TOINT_NARROW
.shift = 0x1800000000.8p0,
#else
.shift = 0x1.8p52,
#endif
// exp polynomial coefficients.
.poly = {
#if N == 64 && EXP_POLY_ORDER == 5 && !EXP_POLY_WIDE
// abs error: 1.5543*2^-60
// ulp error: 0.529 (0.533 without fma)
// if |x| < ln2/128+eps
// abs error if |x| < ln2/64: 1.7157*2^-50
0x1.fffffffffdbcdp-2,
0x1.555555555444cp-3,
0x1.555573c6a9f7dp-5,
0x1.1111266d28935p-7,
#elif N == 64 && EXP_POLY_ORDER == 6 && EXP_POLY_WIDE
// abs error: 1.6735*2^-64
// ulp error: 0.518 (0.522 without fma)
// if |x| < ln2/64
0x1.5555555548f9ap-3,
0x1.555555554bf5dp-5,
0x1.11115b75f0f4dp-7,
0x1.6c171a6b6303ep-10,
#elif N == 128 && EXP_POLY_ORDER == 5 && !EXP_POLY_WIDE
// abs error: 1.555*2^-66
// ulp error: 0.509 (0.511 without fma)
// if |x| < ln2/256+eps
// abs error if |x| < ln2/256+0x1p-15: 1.09*2^-65
// abs error if |x| < ln2/128: 1.7145*2^-56
0x1.ffffffffffdbdp-2,
0x1.555555555543cp-3,
0x1.55555cf172b91p-5,
0x1.1111167a4d017p-7,
#elif N == 128 && EXP_POLY_ORDER == 5 && EXP_POLY_WIDE
// abs error: 1.5542*2^-60
// ulp error: 0.521 (0.523 without fma)
// if |x| < ln2/128
0x1.fffffffffdbcep-2,
0x1.55555555543c2p-3,
0x1.555573c64f2e3p-5,
0x1.111126b4eff73p-7,
#elif N == 128 && EXP_POLY_ORDER == 6 && EXP_POLY_WIDE
// abs error: 1.6861*2^-71
// ulp error: 0.509 (0.511 without fma)
// if |x| < ln2/128
0x1.55555555548fdp-3,
0x1.555555555658fp-5,
0x1.111123a859bb6p-7,
0x1.6c16ba6920cabp-10,
#elif N == 256 && EXP_POLY_ORDER == 4 && !EXP_POLY_WIDE
// abs error: 1.43*2^-58
// ulp error: 0.549 (0.550 without fma)
// if |x| < ln2/512
0x1p0, // unused
0x1.fffffffffffd4p-2,
0x1.5555571d6ef9p-3,
0x1.5555576a5adcep-5,
#elif N == 256 && EXP_POLY_ORDER == 5 && EXP_POLY_WIDE
// abs error: 1.5547*2^-66
// ulp error: 0.505 (0.506 without fma)
// if |x| < ln2/256
0x1.ffffffffffdbdp-2,
0x1.555555555543cp-3,
0x1.55555cf16e1edp-5,
0x1.1111167a4b553p-7,
#endif
},
.exp2_shift = 0x1.8p52 / N,
// exp2 polynomial coefficients.
.exp2_poly = {
#if N == 64 && EXP2_POLY_ORDER == 6 && EXP2_POLY_WIDE
// abs error: 1.3054*2^-63
// ulp error: 0.515
// if |x| < 1/64
0x1.62e42fefa39efp-1,
0x1.ebfbdff82c58fp-3,
0x1.c6b08d7045cf1p-5,
0x1.3b2ab6fb8fd0ep-7,
0x1.5d884afec48d7p-10,
0x1.43097dc684ae1p-13,
#elif N == 128 && EXP2_POLY_ORDER == 5 && !EXP2_POLY_WIDE
// abs error: 1.2195*2^-65
// ulp error: 0.507 (0.511 without fma)
// if |x| < 1/256
// abs error if |x| < 1/128: 1.9941*2^-56
0x1.62e42fefa39efp-1,
0x1.ebfbdff82c424p-3,
0x1.c6b08d70cf4b5p-5,
0x1.3b2abd24650ccp-7,
0x1.5d7e09b4e3a84p-10,
#elif N == 256 && EXP2_POLY_ORDER == 5 && EXP2_POLY_WIDE
// abs error: 1.2195*2^-65
// ulp error: 0.504 (0.508 without fma)
// if |x| < 1/256
0x1.62e42fefa39efp-1,
0x1.ebfbdff82c424p-3,
0x1.c6b08d70cf4b5p-5,
0x1.3b2abd24650ccp-7,
0x1.5d7e09b4e3a84p-10,
#endif
},
// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N)
// tab[2*k] = asuint64(T[k])
// tab[2*k+1] = asuint64(H[k]) - (k << 52)/N
.tab = {
#if N == 64
0x0, 0x3ff0000000000000,
0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
0x3c8cd2523567f613, 0x3fefd9b0d3158574,
0x3c60f74e61e6c861, 0x3fefc74518759bc8,
0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
0xbc91c923b9d5f416, 0x3fef829aaea92de0,
0xbc801b15eaa59348, 0x3fef72b83c7d517b,
0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
0x3c968efde3a8a894, 0x3fef387a6e756238,
0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
0x3c834d754db0abb6, 0x3fef06fe0a31b715,
0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
0x3c859f48a72a4c6d, 0x3feedea64c123422,
0xbc58a78f4817895b, 0x3feed60a21f72e2a,
0x3c4363ed60c2ac11, 0x3feece086061892d,
0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
0x3c93350518fdd78e, 0x3feeaf4736b527da,
0x3c9063e1e21c5409, 0x3feeab07dd485429,
0x3c9432e62b64c035, 0x3feea76f15ad2148,
0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
0xbc93cedd78565858, 0x3feea23882552225,
0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
0xbc8619321e55e68a, 0x3fee9feb564267c9,
0xbc7b32dcb94da51d, 0x3feea11473eb0187,
0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
0xbc9369b6f13b3734, 0x3feea589994cce13,
0xbc94d450d872576e, 0x3feea8d99b4492ed,
0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
0x3c7bf68359f35f44, 0x3feeb1ae99157736,
0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
0xbc92434322f4f9aa, 0x3feebd829fde4e50,
0x3c71affc2b91ce27, 0x3feec49182a3f090,
0xbc87c50422622263, 0x3feecc667b5de565,
0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
0x3c8469846e735ab3, 0x3feede6b5579fdbf,
0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
0x3c736eae30af0cb3, 0x3fef199bdd85529c,
0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
0x3c676b2c6c921968, 0x3fef3720dcef9069,
0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
0x3c74a385a63d07a7, 0x3fef5818dcfba487,
0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
#elif N == 128
0x0, 0x3ff0000000000000,
0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
0xbc905e7a108766d1, 0x3fefe315e86e7f85,
0x3c8cd2523567f613, 0x3fefd9b0d3158574,
0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
0x3c60f74e61e6c861, 0x3fefc74518759bc8,
0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
0xbc6a033489906e0b, 0x3fef9b66affed31b,
0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
0xbc91c923b9d5f416, 0x3fef829aaea92de0,
0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
0xbc801b15eaa59348, 0x3fef72b83c7d517b,
0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
0xbc96d99c7611eb26, 0x3fef5be084045cd4,
0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
0x3c968efde3a8a894, 0x3fef387a6e756238,
0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
0x3c834d754db0abb6, 0x3fef06fe0a31b715,
0x3c864201e2ac744c, 0x3fef0170fc4cd831,
0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
0xbc9907f81b512d8e, 0x3feeecae6d05d866,
0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
0x3c859f48a72a4c6d, 0x3feedea64c123422,
0xbc9312607a28698a, 0x3feeda4504ac801c,
0xbc58a78f4817895b, 0x3feed60a21f72e2a,
0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
0x3c4363ed60c2ac11, 0x3feece086061892d,
0x3c9666093b0664ef, 0x3feeca41ed1d0057,
0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
0x3c93350518fdd78e, 0x3feeaf4736b527da,
0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
0x3c9063e1e21c5409, 0x3feeab07dd485429,
0x3c34c7855019c6ea, 0x3feea9268a5946b7,
0x3c9432e62b64c035, 0x3feea76f15ad2148,
0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
0xbc845378892be9ae, 0x3feea34634ccc320,
0xbc93cedd78565858, 0x3feea23882552225,
0x3c5710aa807e1964, 0x3feea155d44ca973,
0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
0xbc6a12ad8734b982, 0x3feea012750bdabf,
0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
0xbc80dc3d54e08851, 0x3fee9f7df9519484,
0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
0xbc8619321e55e68a, 0x3fee9feb564267c9,
0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
0xbc7b32dcb94da51d, 0x3feea11473eb0187,
0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
0xbc9369b6f13b3734, 0x3feea589994cce13,
0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
0xbc94d450d872576e, 0x3feea8d99b4492ed,
0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
0x3c7bf68359f35f44, 0x3feeb1ae99157736,
0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
0xbc92434322f4f9aa, 0x3feebd829fde4e50,
0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
0x3c71affc2b91ce27, 0x3feec49182a3f090,
0x3c6dd235e10a73bb, 0x3feec86319e32323,
0xbc87c50422622263, 0x3feecc667b5de565,
0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
0x3c90cc319cee31d2, 0x3feed99e1330b358,
0x3c8469846e735ab3, 0x3feede6b5579fdbf,
0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
0xbc90a40e3da6f640, 0x3feef9728de5593a,
0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
0xbc91eee26b588a35, 0x3fef05b030a1064a,
0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
0x3c736eae30af0cb3, 0x3fef199bdd85529c,
0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
0x3c676b2c6c921968, 0x3fef3720dcef9069,
0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
0xbc900dae3875a949, 0x3fef4f87080d89f2,
0x3c74a385a63d07a7, 0x3fef5818dcfba487,
0xbc82919e2040220f, 0x3fef60e316c98398,
0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
0x3c843a59ac016b4b, 0x3fef7321f301b460,
0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
0xbc892ab93b470dc9, 0x3fef864614f5a129,
0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
#elif N == 256
0x0, 0x3ff0000000000000,
0xbc84e82fc61851ac, 0x3feffb1afa5abcbf,
0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
0xbc82985dd8521d32, 0x3feff168143b0281,
0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
0x3c651e617061bfbd, 0x3fefe7d42e11bbcc,
0xbc905e7a108766d1, 0x3fefe315e86e7f85,
0x3c845fad437fa426, 0x3fefde5f72f654b1,
0x3c8cd2523567f613, 0x3fefd9b0d3158574,
0xbc954529642b232f, 0x3fefd50a0e3c1f89,
0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
0x3c8293708ef5c32e, 0x3fefcbd42b72a836,
0x3c60f74e61e6c861, 0x3fefc74518759bc8,
0xbc95b9280905b2a4, 0x3fefc2bdf66607e0,
0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
0x3c84f31f32c4b7e7, 0x3fefb9c79b1f3919,
0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
0x3c9407fb30d06420, 0x3fefb0f145e46c85,
0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
0xbc9a5d04b3b9911b, 0x3fefa83b23395dec,
0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
0xbc937a01f0739546, 0x3fef9fa55fdfa9c5,
0xbc6a033489906e0b, 0x3fef9b66affed31b,
0x3c8b8268b04ef0a5, 0x3fef973028d7233e,
0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
0xbc9ac46e44a2ebcc, 0x3fef8edbab5e2ab6,
0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
0xbc65704e90c9f860, 0x3fef86a814f204ab,
0xbc91c923b9d5f416, 0x3fef829aaea92de0,
0xbc897cea57e46280, 0x3fef7e95934f312e,
0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
0x3c56f01429e2b9d2, 0x3fef76a45471c3c2,
0xbc801b15eaa59348, 0x3fef72b83c7d517b,
0x3c6e653b2459034b, 0x3fef6ed48695bbc0,
0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
0x3c92cc7ea345b7dc, 0x3fef672658375d2f,
0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
0x3c957bfb2876ea9e, 0x3fef5f99f8138a1c,
0xbc96d99c7611eb26, 0x3fef5be084045cd4,
0x3c8cdc1873af2155, 0x3fef582f95281c6b,
0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
0xbc9493684653a131, 0x3fef50e75eb44027,
0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
0xbc98e2899077520a, 0x3fef49c18438ce4d,
0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
0x3c9120fcd4f59273, 0x3fef42be3578a819,
0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
0x3c89b788c188c9b8, 0x3fef3bdda27912d1,
0x3c968efde3a8a894, 0x3fef387a6e756238,
0x3c877afbca90ef84, 0x3fef351ffb82140a,
0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
0x3c91512f082876ee, 0x3fef2e85711ece75,
0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
0x3c9a02f0c7d75ec6, 0x3fef280e341ddf29,
0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
0xbc803297e78260bf, 0x3fef21ba7591bb70,
0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
0xbc95b77e5ccd9fbf, 0x3fef1b8a66d10f13,
0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
0xbc91e75c40b4251e, 0x3fef157e39771b2f,
0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
0x3c98a911f1f7785a, 0x3fef0f961f641589,
0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
0xbc61e7c998db7dbb, 0x3fef09d24abd886b,
0x3c834d754db0abb6, 0x3fef06fe0a31b715,
0x3c85425c11faadf4, 0x3fef0432edeeb2fd,
0x3c864201e2ac744c, 0x3fef0170fc4cd831,
0xbc979517a03e2847, 0x3feefeb83ba8ea32,
0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
0xbc800e2a46da4bee, 0x3feef96266e3fa2d,
0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
0xbc87430803972b34, 0x3feef431a2de883b,
0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
0xbc954de30ae02d94, 0x3feeef26231e754a,
0xbc9907f81b512d8e, 0x3feeecae6d05d866,
0xbc94f2487e1c03ec, 0x3feeea401b7140ef,
0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
0x3c914a5432fcb2f4, 0x3feee57fbfec6cf4,
0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
0x3c79c3bba5562a2f, 0x3feee0e544ede173,
0x3c859f48a72a4c6d, 0x3feedea64c123422,
0xbc85a71612e21658, 0x3feedc70df1c5175,
0xbc9312607a28698a, 0x3feeda4504ac801c,
0x3c86421f6f1d24d6, 0x3feed822c367a024,
0xbc58a78f4817895b, 0x3feed60a21f72e2a,
0xbc9348a6815fce65, 0x3feed3fb2709468a,
0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
0x3c835c43984d9871, 0x3feecffa3f84b9d4,
0x3c4363ed60c2ac11, 0x3feece086061892d,
0xbc632afc8d9473a0, 0x3feecc2042a7d232,
0x3c9666093b0664ef, 0x3feeca41ed1d0057,
0xbc95fc5e44de020e, 0x3feec86d668b3237,
0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
0xbc7ea0148327c42f, 0x3feec4e1e192aed2,
0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
0xbc7a843ad1a88022, 0x3feec17dea6db7d7,
0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
0x3c892ca3bf144e63, 0x3feebe41b817c114,
0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
0xbc902c99b04aa8b0, 0x3feebb2d81d8abff,
0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
0x3c73e34f67e67118, 0x3feeb8417f4531ee,
0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
0xbc75a3b1197ba0f0, 0x3feeb57de83f4eef,
0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
0x3c81bd2888075068, 0x3feeb2e2f4f6ad27,
0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
0xbc896be8ae89ef8f, 0x3feeb070dde910d2,
0x3c93350518fdd78e, 0x3feeaf4736b527da,
0xbc88e6ac90348602, 0x3feeae27dbe2c4cf,
0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
0xbc91af7f1365c3ac, 0x3feeac0827ff07cc,
0x3c9063e1e21c5409, 0x3feeab07dd485429,
0xbc943a3540d1898a, 0x3feeaa11fba87a03,
0x3c34c7855019c6ea, 0x3feea9268a5946b7,
0xbc951f58ddaa8090, 0x3feea84590998b93,
0x3c9432e62b64c035, 0x3feea76f15ad2148,
0xbc82e1648e50a17c, 0x3feea6a320dceb71,
0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
0x3c95f30eda98a575, 0x3feea52ae6cdf6f4,
0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
0x3c917ecda8a72159, 0x3feea3dd1d1929fd,
0xbc845378892be9ae, 0x3feea34634ccc320,
0xbc9345f3cee1ae6e, 0x3feea2b9febc8fb7,
0xbc93cedd78565858, 0x3feea23882552225,
0xbc85c33fdf910406, 0x3feea1c1c70833f6,
0x3c5710aa807e1964, 0x3feea155d44ca973,
0x3c81079ab5789604, 0x3feea0f4b19e9538,
0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
0x3c727df161cd7778, 0x3feea052fa75173e,
0xbc6a12ad8734b982, 0x3feea012750bdabf,
0x3c93f9924a05b767, 0x3fee9fdcddd47645,
0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
0xbc87557939a8b5ef, 0x3fee9f9298593ae5,
0xbc80dc3d54e08851, 0x3fee9f7df9519484,
0x3c51ed2f56fa9d1a, 0x3fee9f7466f42e87,
0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
0xbc88e67a9006c909, 0x3fee9f8286ead08a,
0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
0x3c86597566977ac8, 0x3fee9fbd35d7cbfd,
0xbc8619321e55e68a, 0x3fee9feb564267c9,
0x3c92c0b7028a5c3a, 0x3feea024b1ab6e09,
0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
0x3c8a30faf49cc78c, 0x3feea0b938ac1cf6,
0xbc7b32dcb94da51d, 0x3feea11473eb0187,
0xbc92dad3519d7b5b, 0x3feea17b0976cfdb,
0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
0x3c87d51410fd15c2, 0x3feea26a62ff86f0,
0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
0xbc760a3629969871, 0x3feea3878491c491,
0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
0x3c8b18c6e3fdef5d, 0x3feea4d2add106d9,
0xbc9369b6f13b3734, 0x3feea589994cce13,
0x3c90ec1ddcb1390a, 0x3feea64c1eb941f7,
0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
0xbc522cea4f3afa1e, 0x3feea7f4179f5b21,
0xbc94d450d872576e, 0x3feea8d99b4492ed,
0x3c7c88549b958471, 0x3feea9cad931a436,
0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
0x3c931143962f7877, 0x3feeabd0a478580f,
0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
0x3c93e9e96f112479, 0x3feeae05bad61778,
0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
0xbc8dac42a4a38df0, 0x3feeb06a5e0866d9,
0x3c7bf68359f35f44, 0x3feeb1ae99157736,
0x3c8b99dd98b1ed84, 0x3feeb2fed0282c8a,
0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
0xbc7885ad50cbb750, 0x3feeb5c353aa2fe2,
0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
0xbc82d5e85f3e0301, 0x3feeb8b82b5f98e5,
0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
0xbc51669428996971, 0x3feebbdd9a7670b3,
0xbc92434322f4f9aa, 0x3feebd829fde4e50,
0x3c71f2b2c1c4c014, 0x3feebf33e47a22a2,
0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
0xbc9294f304f166b6, 0x3feec2bb4d53fe0d,
0x3c71affc2b91ce27, 0x3feec49182a3f090,
0xbc8a1e58414c07d3, 0x3feec674194bb8d5,
0x3c6dd235e10a73bb, 0x3feec86319e32323,
0xbc79740b58a20091, 0x3feeca5e8d07f29e,
0xbc87c50422622263, 0x3feecc667b5de565,
0x3c9165830a2b96c2, 0x3feece7aed8eb8bb,
0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
0xbc903d5cbe27874b, 0x3feed2c980460ad8,
0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
0x3c5986178980fce0, 0x3feed74a8af46052,
0x3c90cc319cee31d2, 0x3feed99e1330b358,
0xbc89472975b1f2a5, 0x3feedbfe53c12e59,
0x3c8469846e735ab3, 0x3feede6b5579fdbf,
0x3c7d8157a34b7e7f, 0x3feee0e521356eba,
0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
0x3c8c8a4e231ebb7d, 0x3feee5ff3a3c2774,
0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
0xbc888c8d11a142e5, 0x3feeeb4ce622f2ff,
0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
0x3c889c2ea41433c7, 0x3feef0ce6c9a8952,
0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
0xbc7274aedac8ff80, 0x3feef68415b749b1,
0xbc90a40e3da6f640, 0x3feef9728de5593a,
0x3c85c620ce76df06, 0x3feefc6e29f1c52a,
0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
0xbc8fda52e1b51e41, 0x3fef028cf22749e4,
0xbc91eee26b588a35, 0x3fef05b030a1064a,
0xbc32141a7b3e2cd8, 0x3fef08e0b79a6f1f,
0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
0xbc302899507554e5, 0x3fef0f69c3f3a207,
0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
0xbc80dda2d4c0010c, 0x3fef16286141b33d,
0x3c736eae30af0cb3, 0x3fef199bdd85529c,
0xbc8a007daadf8d68, 0x3fef1d1cd9fa652c,
0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
0x3c836909391181d3, 0x3fef244778fafb22,
0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
0xbc811cd7dbdf9547, 0x3fef2ba88988c933,
0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
0xbc7ac28b7bef6621, 0x3fef33405751c4db,
0x3c676b2c6c921968, 0x3fef3720dcef9069,
0xbc7030587207b9e1, 0x3fef3b0f2e6d1675,
0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
0xbc8cc734592af7fc, 0x3fef43155b5bab74,
0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
0x3c87752a44f587e8, 0x3fef4b532b08c968,
0xbc900dae3875a949, 0x3fef4f87080d89f2,
0x3c85b66fefeef52e, 0x3fef53c8eacaa1d6,
0x3c74a385a63d07a7, 0x3fef5818dcfba487,
0x3c5159d9d908a96e, 0x3fef5c76e862e6d3,
0xbc82919e2040220f, 0x3fef60e316c98398,
0x3c8c254d16117a68, 0x3fef655d71ff6075,
0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
0xbc8d8c329fbd0e03, 0x3fef6e7cd63a8315,
0x3c843a59ac016b4b, 0x3fef7321f301b460,
0xbc8ea6e6fbd5f2a6, 0x3fef77d5641c0658,
0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
0xbc63e8e3eab2cbb4, 0x3fef81676b197d17,
0xbc892ab93b470dc9, 0x3fef864614f5a129,
0xbc8b7966cd0d2cd9, 0x3fef8b333b16ee12,
0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
0xbc776caa4c2ff1cf, 0x3fef953924676d76,
0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
0xbc81d5fc525d9940, 0x3fef9f7977cdb740,
0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
0x3c855cd8aaea3d21, 0x3fefa9f4867cca6e,
0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
0x3c8269947c2bed4a, 0x3fefb4aaa2188510,
0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
0xbc83b6137e9afe9e, 0x3fefbf9c1cb6412a,
0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
0xbc69fa74878ba7c7, 0x3fefcac948dd7274,
0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
0x3c901f3a75ee0efe, 0x3fefd632798844f8,
0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
0xbc516a9ce6ed84fa, 0x3fefe1d802243c89,
0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
0xbc699c7db2effc76, 0x3fefedba3692d514,
0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
0x3c64b458677f9840, 0x3feff9d96b2a23d9,
#endif
},
};
#endif /* __OBSOLETE_MATH */