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libc/newlib/libm/common/log2_data.c
Szabolcs Nagy 07e2c32828 New log2 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 0.547 ULP with inlined fma and fma contraction.  It uses
a 1 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased
by 1584 bytes.

Note that the math.h header defines log2(x) to be log(x)/Ln2, this is
not changed, so the new code is only used if that macro is suppressed.

Improvements on Cortex-A72:
latency: 2.0x
thruput: 2.2x
2018-06-27 15:40:49 +02:00

209 lines
8.4 KiB
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/* Data for log2.
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.
THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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 << LOG2_TABLE_BITS)
const struct log2_data __log2_data = {
// First coefficient: 0x1.71547652b82fe1777d0ffda0d24p0
.invln2hi = 0x1.7154765200000p+0,
.invln2lo = 0x1.705fc2eefa200p-33,
.poly1 = {
#if LOG2_POLY1_ORDER == 11
// relative error: 0x1.2fad8188p-63
// in -0x1.5b51p-5 0x1.6ab2p-5
-0x1.71547652b82fep-1,
0x1.ec709dc3a03f7p-2,
-0x1.71547652b7c3fp-2,
0x1.2776c50f05be4p-2,
-0x1.ec709dd768fe5p-3,
0x1.a61761ec4e736p-3,
-0x1.7153fbc64a79bp-3,
0x1.484d154f01b4ap-3,
-0x1.289e4a72c383cp-3,
0x1.0b32f285aee66p-3,
#endif
},
.poly = {
#if N == 64 && LOG2_POLY_ORDER == 7
// relative error: 0x1.a72c2bf8p-58
// abs error: 0x1.67a552c8p-66
// in -0x1.f45p-8 0x1.f45p-8
-0x1.71547652b8339p-1,
0x1.ec709dc3a04bep-2,
-0x1.7154764702ffbp-2,
0x1.2776c50034c48p-2,
-0x1.ec7b328ea92bcp-3,
0x1.a6225e117f92ep-3,
#endif
},
.tab = {
#if N == 64
{0x1.724286bb1acf8p+0, -0x1.1095feecdb000p-1},
{0x1.6e1f766d2cca1p+0, -0x1.08494bd76d000p-1},
{0x1.6a13d0e30d48ap+0, -0x1.00143aee8f800p-1},
{0x1.661ec32d06c85p+0, -0x1.efec5360b4000p-2},
{0x1.623fa951198f8p+0, -0x1.dfdd91ab7e000p-2},
{0x1.5e75ba4cf026cp+0, -0x1.cffae0cc79000p-2},
{0x1.5ac055a214fb8p+0, -0x1.c043811fda000p-2},
{0x1.571ed0f166e1ep+0, -0x1.b0b67323ae000p-2},
{0x1.53909590bf835p+0, -0x1.a152f5a2db000p-2},
{0x1.5014fed61adddp+0, -0x1.9217f5af86000p-2},
{0x1.4cab88e487bd0p+0, -0x1.8304db0719000p-2},
{0x1.49539b4334feep+0, -0x1.74189f9a9e000p-2},
{0x1.460cbdfafd569p+0, -0x1.6552bb5199000p-2},
{0x1.42d664ee4b953p+0, -0x1.56b23a29b1000p-2},
{0x1.3fb01111dd8a6p+0, -0x1.483650f5fa000p-2},
{0x1.3c995b70c5836p+0, -0x1.39de937f6a000p-2},
{0x1.3991c4ab6fd4ap+0, -0x1.2baa1538d6000p-2},
{0x1.3698e0ce099b5p+0, -0x1.1d98340ca4000p-2},
{0x1.33ae48213e7b2p+0, -0x1.0fa853a40e000p-2},
{0x1.30d191985bdb1p+0, -0x1.01d9c32e73000p-2},
{0x1.2e025cab271d7p+0, -0x1.e857da2fa6000p-3},
{0x1.2b404cf13cd82p+0, -0x1.cd3c8633d8000p-3},
{0x1.288b02c7ccb50p+0, -0x1.b26034c14a000p-3},
{0x1.25e2263944de5p+0, -0x1.97c1c2f4fe000p-3},
{0x1.234563d8615b1p+0, -0x1.7d6023f800000p-3},
{0x1.20b46e33eaf38p+0, -0x1.633a71a05e000p-3},
{0x1.1e2eefdcda3ddp+0, -0x1.494f5e9570000p-3},
{0x1.1bb4a580b3930p+0, -0x1.2f9e424e0a000p-3},
{0x1.19453847f2200p+0, -0x1.162595afdc000p-3},
{0x1.16e06c0d5d73cp+0, -0x1.f9c9a75bd8000p-4},
{0x1.1485f47b7e4c2p+0, -0x1.c7b575bf9c000p-4},
{0x1.12358ad0085d1p+0, -0x1.960c60ff48000p-4},
{0x1.0fef00f532227p+0, -0x1.64ce247b60000p-4},
{0x1.0db2077d03a8fp+0, -0x1.33f78b2014000p-4},
{0x1.0b7e6d65980d9p+0, -0x1.0387d1a42c000p-4},
{0x1.0953efe7b408dp+0, -0x1.a6f9208b50000p-5},
{0x1.07325cac53b83p+0, -0x1.47a954f770000p-5},
{0x1.05197e40d1b5cp+0, -0x1.d23a8c50c0000p-6},
{0x1.03091c1208ea2p+0, -0x1.16a2629780000p-6},
{0x1.0101025b37e21p+0, -0x1.720f8d8e80000p-8},
{0x1.fc07ef9caa76bp-1, 0x1.6fe53b1500000p-7},
{0x1.f4465d3f6f184p-1, 0x1.11ccce10f8000p-5},
{0x1.ecc079f84107fp-1, 0x1.c4dfc8c8b8000p-5},
{0x1.e573a99975ae8p-1, 0x1.3aa321e574000p-4},
{0x1.de5d6f0bd3de6p-1, 0x1.918a0d08b8000p-4},
{0x1.d77b681ff38b3p-1, 0x1.e72e9da044000p-4},
{0x1.d0cb5724de943p-1, 0x1.1dcd2507f6000p-3},
{0x1.ca4b2dc0e7563p-1, 0x1.476ab03dea000p-3},
{0x1.c3f8ee8d6cb51p-1, 0x1.7074377e22000p-3},
{0x1.bdd2b4f020c4cp-1, 0x1.98ede8ba94000p-3},
{0x1.b7d6c006015cap-1, 0x1.c0db86ad2e000p-3},
{0x1.b20366e2e338fp-1, 0x1.e840aafcee000p-3},
{0x1.ac57026295039p-1, 0x1.0790ab4678000p-2},
{0x1.a6d01bc2731ddp-1, 0x1.1ac056801c000p-2},
{0x1.a16d3bc3ff18bp-1, 0x1.2db11d4fee000p-2},
{0x1.9c2d14967feadp-1, 0x1.406464ec58000p-2},
{0x1.970e4f47c9902p-1, 0x1.52dbe093af000p-2},
{0x1.920fb3982bcf2p-1, 0x1.651902050d000p-2},
{0x1.8d30187f759f1p-1, 0x1.771d2cdeaf000p-2},
{0x1.886e5ebb9f66dp-1, 0x1.88e9c857d9000p-2},
{0x1.83c97b658b994p-1, 0x1.9a80155e16000p-2},
{0x1.7f405ffc61022p-1, 0x1.abe186ed3d000p-2},
{0x1.7ad22181415cap-1, 0x1.bd0f2aea0e000p-2},
{0x1.767dcf99eff8cp-1, 0x1.ce0a43dbf4000p-2},
#endif
},
#if !__HAVE_FAST_FMA
.tab2 = {
# if N == 64
{0x1.6200012b90a8ep-1, 0x1.904ab0644b605p-55},
{0x1.66000045734a6p-1, 0x1.1ff9bea62f7a9p-57},
{0x1.69fffc325f2c5p-1, 0x1.27ecfcb3c90bap-55},
{0x1.6e00038b95a04p-1, 0x1.8ff8856739326p-55},
{0x1.71fffe09994e3p-1, 0x1.afd40275f82b1p-55},
{0x1.7600015590e1p-1, -0x1.2fd75b4238341p-56},
{0x1.7a00012655bd5p-1, 0x1.808e67c242b76p-56},
{0x1.7e0003259e9a6p-1, -0x1.208e426f622b7p-57},
{0x1.81fffedb4b2d2p-1, -0x1.402461ea5c92fp-55},
{0x1.860002dfafcc3p-1, 0x1.df7f4a2f29a1fp-57},
{0x1.89ffff78c6b5p-1, -0x1.e0453094995fdp-55},
{0x1.8e00039671566p-1, -0x1.a04f3bec77b45p-55},
{0x1.91fffe2bf1745p-1, -0x1.7fa34400e203cp-56},
{0x1.95fffcc5c9fd1p-1, -0x1.6ff8005a0695dp-56},
{0x1.9a0003bba4767p-1, 0x1.0f8c4c4ec7e03p-56},
{0x1.9dfffe7b92da5p-1, 0x1.e7fd9478c4602p-55},
{0x1.a1fffd72efdafp-1, -0x1.a0c554dcdae7ep-57},
{0x1.a5fffde04ff95p-1, 0x1.67da98ce9b26bp-55},
{0x1.a9fffca5e8d2bp-1, -0x1.284c9b54c13dep-55},
{0x1.adfffddad03eap-1, 0x1.812c8ea602e3cp-58},
{0x1.b1ffff10d3d4dp-1, -0x1.efaddad27789cp-55},
{0x1.b5fffce21165ap-1, 0x1.3cb1719c61237p-58},
{0x1.b9fffd950e674p-1, 0x1.3f7d94194cep-56},
{0x1.be000139ca8afp-1, 0x1.50ac4215d9bcp-56},
{0x1.c20005b46df99p-1, 0x1.beea653e9c1c9p-57},
{0x1.c600040b9f7aep-1, -0x1.c079f274a70d6p-56},
{0x1.ca0006255fd8ap-1, -0x1.a0b4076e84c1fp-56},
{0x1.cdfffd94c095dp-1, 0x1.8f933f99ab5d7p-55},
{0x1.d1ffff975d6cfp-1, -0x1.82c08665fe1bep-58},
{0x1.d5fffa2561c93p-1, -0x1.b04289bd295f3p-56},
{0x1.d9fff9d228b0cp-1, 0x1.70251340fa236p-55},
{0x1.de00065bc7e16p-1, -0x1.5011e16a4d80cp-56},
{0x1.e200002f64791p-1, 0x1.9802f09ef62ep-55},
{0x1.e600057d7a6d8p-1, -0x1.e0b75580cf7fap-56},
{0x1.ea00027edc00cp-1, -0x1.c848309459811p-55},
{0x1.ee0006cf5cb7cp-1, -0x1.f8027951576f4p-55},
{0x1.f2000782b7dccp-1, -0x1.f81d97274538fp-55},
{0x1.f6000260c450ap-1, -0x1.071002727ffdcp-59},
{0x1.f9fffe88cd533p-1, -0x1.81bdce1fda8bp-58},
{0x1.fdfffd50f8689p-1, 0x1.7f91acb918e6ep-55},
{0x1.0200004292367p+0, 0x1.b7ff365324681p-54},
{0x1.05fffe3e3d668p+0, 0x1.6fa08ddae957bp-55},
{0x1.0a0000a85a757p+0, -0x1.7e2de80d3fb91p-58},
{0x1.0e0001a5f3fccp+0, -0x1.1823305c5f014p-54},
{0x1.11ffff8afbaf5p+0, -0x1.bfabb6680bac2p-55},
{0x1.15fffe54d91adp+0, -0x1.d7f121737e7efp-54},
{0x1.1a00011ac36e1p+0, 0x1.c000a0516f5ffp-54},
{0x1.1e00019c84248p+0, -0x1.082fbe4da5dap-54},
{0x1.220000ffe5e6ep+0, -0x1.8fdd04c9cfb43p-55},
{0x1.26000269fd891p+0, 0x1.cfe2a7994d182p-55},
{0x1.2a00029a6e6dap+0, -0x1.00273715e8bc5p-56},
{0x1.2dfffe0293e39p+0, 0x1.b7c39dab2a6f9p-54},
{0x1.31ffff7dcf082p+0, 0x1.df1336edc5254p-56},
{0x1.35ffff05a8b6p+0, -0x1.e03564ccd31ebp-54},
{0x1.3a0002e0eaeccp+0, 0x1.5f0e74bd3a477p-56},
{0x1.3e000043bb236p+0, 0x1.c7dcb149d8833p-54},
{0x1.4200002d187ffp+0, 0x1.e08afcf2d3d28p-56},
{0x1.460000d387cb1p+0, 0x1.20837856599a6p-55},
{0x1.4a00004569f89p+0, -0x1.9fa5c904fbcd2p-55},
{0x1.4e000043543f3p+0, -0x1.81125ed175329p-56},
{0x1.51fffcc027f0fp+0, 0x1.883d8847754dcp-54},
{0x1.55ffffd87b36fp+0, -0x1.709e731d02807p-55},
{0x1.59ffff21df7bap+0, 0x1.7f79f68727b02p-55},
{0x1.5dfffebfc3481p+0, -0x1.180902e30e93ep-54},
# endif
},
#endif /* !__HAVE_FAST_FMA */
};
#endif /* __OBSOLETE_MATH */
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