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newlib-cygwin/newlib/libm/common/pow_log_data.c

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New pow implementation The new implementation is provided under !__OBSOLETE_MATH, it uses ISO C99 code. With default settings the worst case error in nearest rounding mode is 0.54 ULP with inlined fma and fma contraction. It uses a 4 KB lookup table in addition to the table in exp_data.c, on aarch64 .text+.rodata size of libm.a is increased by 2295 bytes. Improvements on Cortex-A72: latency: 3.3x thruput: 4.9x
2018-06-26 23:25:12 +08:00
/* Data for the log part of 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.
2018-09-28 01:03:32 +08:00
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS'' AND ANY EXPRESS OR IMPLIED
New pow implementation The new implementation is provided under !__OBSOLETE_MATH, it uses ISO C99 code. With default settings the worst case error in nearest rounding mode is 0.54 ULP with inlined fma and fma contraction. It uses a 4 KB lookup table in addition to the table in exp_data.c, on aarch64 .text+.rodata size of libm.a is increased by 2295 bytes. Improvements on Cortex-A72: latency: 3.3x thruput: 4.9x
2018-06-26 23:25:12 +08:00
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.
2018-09-28 01:03:32 +08:00
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
New pow implementation The new implementation is provided under !__OBSOLETE_MATH, it uses ISO C99 code. With default settings the worst case error in nearest rounding mode is 0.54 ULP with inlined fma and fma contraction. It uses a 4 KB lookup table in addition to the table in exp_data.c, on aarch64 .text+.rodata size of libm.a is increased by 2295 bytes. Improvements on Cortex-A72: latency: 3.3x thruput: 4.9x
2018-06-26 23:25:12 +08:00
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 << POW_LOG_TABLE_BITS)
const struct pow_log_data __pow_log_data = {
.ln2hi = 0x1.62e42fefa3800p-1,
.ln2lo = 0x1.ef35793c76730p-45,
.poly = {
#if N == 128 && POW_LOG_POLY_ORDER == 8
// relative error: 0x1.11922ap-70
// in -0x1.6bp-8 0x1.6bp-8
// Coefficients are scaled to match the scaling during evaluation.
-0x1p-1,
0x1.555555555556p-2 * -2,
-0x1.0000000000006p-2 * -2,
0x1.999999959554ep-3 * 4,
-0x1.555555529a47ap-3 * 4,
0x1.2495b9b4845e9p-3 * -8,
-0x1.0002b8b263fc3p-3 * -8,
#endif
},
Document the log table generation method Add comments with enough detail so the log lookup tables can be recreated.
2018-09-05 19:15:55 +08:00
/* Algorithm:
x = 2^k z
log(x) = k ln2 + log(c) + log(z/c)
log(z/c) = poly(z/c - 1)
where z is in [0x1.69555p-1; 0x1.69555p0] which is split into N subintervals
and z falls into the ith one, then table entries are computed as
tab[i].invc = 1/c
tab[i].logc = round(0x1p43*log(c))/0x1p43
tab[i].logctail = (double)(log(c) - logc)
where c is chosen near the center of the subinterval such that 1/c has only a
few precision bits so z/c - 1 is exactly representible as double:
1/c = center < 1 ? round(N/center)/N : round(2*N/center)/N/2
Note: |z/c - 1| < 1/N for the chosen c, |log(c) - logc - logctail| < 0x1p-97,
the last few bits of logc are rounded away so k*ln2hi + logc has no rounding
error and the interval for z is selected such that near x == 1, where log(x)
is tiny, large cancellation error is avoided in logc + poly(z/c - 1). */
New pow implementation The new implementation is provided under !__OBSOLETE_MATH, it uses ISO C99 code. With default settings the worst case error in nearest rounding mode is 0.54 ULP with inlined fma and fma contraction. It uses a 4 KB lookup table in addition to the table in exp_data.c, on aarch64 .text+.rodata size of libm.a is increased by 2295 bytes. Improvements on Cortex-A72: latency: 3.3x thruput: 4.9x
2018-06-26 23:25:12 +08:00
.tab = {
#if N == 128
#define A(a,b,c) {a,0,b,c},
A(0x1.6a00000000000p+0, -0x1.62c82f2b9c800p-2, 0x1.ab42428375680p-48)
A(0x1.6800000000000p+0, -0x1.5d1bdbf580800p-2, -0x1.ca508d8e0f720p-46)
A(0x1.6600000000000p+0, -0x1.5767717455800p-2, -0x1.362a4d5b6506dp-45)
A(0x1.6400000000000p+0, -0x1.51aad872df800p-2, -0x1.684e49eb067d5p-49)
A(0x1.6200000000000p+0, -0x1.4be5f95777800p-2, -0x1.41b6993293ee0p-47)
A(0x1.6000000000000p+0, -0x1.4618bc21c6000p-2, 0x1.3d82f484c84ccp-46)
A(0x1.5e00000000000p+0, -0x1.404308686a800p-2, 0x1.c42f3ed820b3ap-50)
A(0x1.5c00000000000p+0, -0x1.3a64c55694800p-2, 0x1.0b1c686519460p-45)
A(0x1.5a00000000000p+0, -0x1.347dd9a988000p-2, 0x1.5594dd4c58092p-45)
A(0x1.5800000000000p+0, -0x1.2e8e2bae12000p-2, 0x1.67b1e99b72bd8p-45)
A(0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46)
A(0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46)
A(0x1.5400000000000p+0, -0x1.22941fbcf7800p-2, -0x1.65a242853da76p-46)
A(0x1.5200000000000p+0, -0x1.1c898c1699800p-2, -0x1.fafbc68e75404p-46)
A(0x1.5000000000000p+0, -0x1.1675cababa800p-2, 0x1.f1fc63382a8f0p-46)
A(0x1.4e00000000000p+0, -0x1.1058bf9ae4800p-2, -0x1.6a8c4fd055a66p-45)
A(0x1.4c00000000000p+0, -0x1.0a324e2739000p-2, -0x1.c6bee7ef4030ep-47)
A(0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48)
A(0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48)
A(0x1.4800000000000p+0, -0x1.fb9186d5e4000p-3, 0x1.d572aab993c87p-47)
A(0x1.4600000000000p+0, -0x1.ef0adcbdc6000p-3, 0x1.b26b79c86af24p-45)
A(0x1.4400000000000p+0, -0x1.e27076e2af000p-3, -0x1.72f4f543fff10p-46)
A(0x1.4200000000000p+0, -0x1.d5c216b4fc000p-3, 0x1.1ba91bbca681bp-45)
A(0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45)
A(0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45)
A(0x1.3e00000000000p+0, -0x1.bc286742d9000p-3, 0x1.94eb0318bb78fp-46)
A(0x1.3c00000000000p+0, -0x1.af3c94e80c000p-3, 0x1.a4e633fcd9066p-52)
A(0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45)
A(0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45)
A(0x1.3800000000000p+0, -0x1.9525a9cf45000p-3, -0x1.ad1d904c1d4e3p-45)
A(0x1.3600000000000p+0, -0x1.87fa06520d000p-3, 0x1.bbdbf7fdbfa09p-45)
A(0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45)
A(0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45)
A(0x1.3200000000000p+0, -0x1.6d60fe719d000p-3, -0x1.0e46aa3b2e266p-46)
A(0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46)
A(0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46)
A(0x1.2e00000000000p+0, -0x1.526e5e3a1b000p-3, -0x1.0de8b90075b8fp-45)
A(0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46)
A(0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46)
A(0x1.2a00000000000p+0, -0x1.371fc201e9000p-3, 0x1.178864d27543ap-48)
A(0x1.2800000000000p+0, -0x1.29552f81ff000p-3, -0x1.48d301771c408p-45)
A(0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45)
A(0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45)
A(0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47)
A(0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47)
A(0x1.2200000000000p+0, -0x1.fec9131dbe000p-4, -0x1.575545ca333f2p-45)
A(0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45)
A(0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45)
A(0x1.1e00000000000p+0, -0x1.c5e548f5bc000p-4, -0x1.d0c57585fbe06p-46)
A(0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45)
A(0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45)
A(0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46)
A(0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46)
A(0x1.1800000000000p+0, -0x1.6f0d28ae56000p-4, -0x1.69737c93373dap-45)
A(0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46)
A(0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46)
A(0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45)
A(0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45)
A(0x1.1200000000000p+0, -0x1.16536eea38000p-4, 0x1.47c5e768fa309p-46)
A(0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45)
A(0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45)
A(0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46)
A(0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46)
A(0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45)
A(0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45)
A(0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48)
A(0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48)
A(0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45)
A(0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45)
A(0x1.0600000000000p+0, -0x1.7b91b07d58000p-6, -0x1.88d5493faa639p-45)
A(0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50)
A(0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50)
A(0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46)
A(0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46)
A(0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0)
A(0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0)
A(0x1.fc00000000000p-1, 0x1.0101575890000p-7, -0x1.0c76b999d2be8p-46)
A(0x1.f800000000000p-1, 0x1.0205658938000p-6, -0x1.3dc5b06e2f7d2p-45)
A(0x1.f400000000000p-1, 0x1.8492528c90000p-6, -0x1.aa0ba325a0c34p-45)
A(0x1.f000000000000p-1, 0x1.0415d89e74000p-5, 0x1.111c05cf1d753p-47)
A(0x1.ec00000000000p-1, 0x1.466aed42e0000p-5, -0x1.c167375bdfd28p-45)
A(0x1.e800000000000p-1, 0x1.894aa149fc000p-5, -0x1.97995d05a267dp-46)
A(0x1.e400000000000p-1, 0x1.ccb73cdddc000p-5, -0x1.a68f247d82807p-46)
A(0x1.e200000000000p-1, 0x1.eea31c006c000p-5, -0x1.e113e4fc93b7bp-47)
A(0x1.de00000000000p-1, 0x1.1973bd1466000p-4, -0x1.5325d560d9e9bp-45)
A(0x1.da00000000000p-1, 0x1.3bdf5a7d1e000p-4, 0x1.cc85ea5db4ed7p-45)
A(0x1.d600000000000p-1, 0x1.5e95a4d97a000p-4, -0x1.c69063c5d1d1ep-45)
A(0x1.d400000000000p-1, 0x1.700d30aeac000p-4, 0x1.c1e8da99ded32p-49)
A(0x1.d000000000000p-1, 0x1.9335e5d594000p-4, 0x1.3115c3abd47dap-45)
A(0x1.cc00000000000p-1, 0x1.b6ac88dad6000p-4, -0x1.390802bf768e5p-46)
A(0x1.ca00000000000p-1, 0x1.c885801bc4000p-4, 0x1.646d1c65aacd3p-45)
A(0x1.c600000000000p-1, 0x1.ec739830a2000p-4, -0x1.dc068afe645e0p-45)
A(0x1.c400000000000p-1, 0x1.fe89139dbe000p-4, -0x1.534d64fa10afdp-45)
A(0x1.c000000000000p-1, 0x1.1178e8227e000p-3, 0x1.1ef78ce2d07f2p-45)
A(0x1.be00000000000p-1, 0x1.1aa2b7e23f000p-3, 0x1.ca78e44389934p-45)
A(0x1.ba00000000000p-1, 0x1.2d1610c868000p-3, 0x1.39d6ccb81b4a1p-47)
A(0x1.b800000000000p-1, 0x1.365fcb0159000p-3, 0x1.62fa8234b7289p-51)
A(0x1.b400000000000p-1, 0x1.4913d8333b000p-3, 0x1.5837954fdb678p-45)
A(0x1.b200000000000p-1, 0x1.527e5e4a1b000p-3, 0x1.633e8e5697dc7p-45)
A(0x1.ae00000000000p-1, 0x1.6574ebe8c1000p-3, 0x1.9cf8b2c3c2e78p-46)
A(0x1.ac00000000000p-1, 0x1.6f0128b757000p-3, -0x1.5118de59c21e1p-45)
A(0x1.aa00000000000p-1, 0x1.7898d85445000p-3, -0x1.c661070914305p-46)
A(0x1.a600000000000p-1, 0x1.8beafeb390000p-3, -0x1.73d54aae92cd1p-47)
A(0x1.a400000000000p-1, 0x1.95a5adcf70000p-3, 0x1.7f22858a0ff6fp-47)
A(0x1.a000000000000p-1, 0x1.a93ed3c8ae000p-3, -0x1.8724350562169p-45)
A(0x1.9e00000000000p-1, 0x1.b31d8575bd000p-3, -0x1.c358d4eace1aap-47)
A(0x1.9c00000000000p-1, 0x1.bd087383be000p-3, -0x1.d4bc4595412b6p-45)
A(0x1.9a00000000000p-1, 0x1.c6ffbc6f01000p-3, -0x1.1ec72c5962bd2p-48)
A(0x1.9600000000000p-1, 0x1.db13db0d49000p-3, -0x1.aff2af715b035p-45)
A(0x1.9400000000000p-1, 0x1.e530effe71000p-3, 0x1.212276041f430p-51)
A(0x1.9200000000000p-1, 0x1.ef5ade4dd0000p-3, -0x1.a211565bb8e11p-51)
A(0x1.9000000000000p-1, 0x1.f991c6cb3b000p-3, 0x1.bcbecca0cdf30p-46)
A(0x1.8c00000000000p-1, 0x1.07138604d5800p-2, 0x1.89cdb16ed4e91p-48)
A(0x1.8a00000000000p-1, 0x1.0c42d67616000p-2, 0x1.7188b163ceae9p-45)
A(0x1.8800000000000p-1, 0x1.1178e8227e800p-2, -0x1.c210e63a5f01cp-45)
A(0x1.8600000000000p-1, 0x1.16b5ccbacf800p-2, 0x1.b9acdf7a51681p-45)
A(0x1.8400000000000p-1, 0x1.1bf99635a6800p-2, 0x1.ca6ed5147bdb7p-45)
A(0x1.8200000000000p-1, 0x1.214456d0eb800p-2, 0x1.a87deba46baeap-47)
A(0x1.7e00000000000p-1, 0x1.2bef07cdc9000p-2, 0x1.a9cfa4a5004f4p-45)
A(0x1.7c00000000000p-1, 0x1.314f1e1d36000p-2, -0x1.8e27ad3213cb8p-45)
A(0x1.7a00000000000p-1, 0x1.36b6776be1000p-2, 0x1.16ecdb0f177c8p-46)
A(0x1.7800000000000p-1, 0x1.3c25277333000p-2, 0x1.83b54b606bd5cp-46)
A(0x1.7600000000000p-1, 0x1.419b423d5e800p-2, 0x1.8e436ec90e09dp-47)
A(0x1.7400000000000p-1, 0x1.4718dc271c800p-2, -0x1.f27ce0967d675p-45)
A(0x1.7200000000000p-1, 0x1.4c9e09e173000p-2, -0x1.e20891b0ad8a4p-45)
A(0x1.7000000000000p-1, 0x1.522ae0738a000p-2, 0x1.ebe708164c759p-45)
A(0x1.6e00000000000p-1, 0x1.57bf753c8d000p-2, 0x1.fadedee5d40efp-46)
A(0x1.6c00000000000p-1, 0x1.5d5bddf596000p-2, -0x1.a0b2a08a465dcp-47)
#endif
},
};
#endif /* __OBSOLETE_MATH */