glibc/sysdeps/ieee754/dbl-64/e_log_data.c

348 lines
14 KiB
C
Raw Normal View History

Add new log implementation Optimized log using carefully generated lookup table with 1/c and log(c) values for small intervalls around 1. The log(c) is very near a double precision value, it has about 62 bits precision. The algorithm is log(2^k x) = k log(2) + log(c) + log(x/c), where the last term is approximated by a polynomial of x/c - 1. Near 1 a single polynomial of x - 1 is used. There is separate code path when fma instruction is not available for computing x/c - 1 precisely, in which case the table size is doubled. The code uses __builtin_fma under __FP_FAST_FMA to ensure it is inlined as an instruction. With the default configuration settings the worst case error is 0.519 ULP (and 0.520 without fma), the rodata size is 2192 bytes (4240 without fma). The non-nearest rounding error is less than 1 ULP. Improvements on Cortex-A72 compared to current glibc master: log thruput: 3.28x in [0.01 11.1] log latency: 2.23x in [0.01 11.1] log thruput: 1.56x in [0.999 1.001] log latency: 1.57x in [0.999 1.001] Tested on aarch64-linux-gnu (defined __FP_FAST_FMA) arm-linux-gnueabihf (!defined __FP_FAST_FMA) x86_64-linux-gnu (!defined __FP_FAST_FMA) powerpc64le-linux-gnu (defined __FP_FAST_FMA) targets. * NEWS: Mention log improvement. * math/Makefile (type-double-routines): Add e_log_data. * sysdeps/i386/fpu/e_log_data.c: New file. * sysdeps/ia64/fpu/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/e_log.c: Rewrite. * sysdeps/ieee754/dbl-64/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/math_config.h (__log_data): Add. * sysdeps/ieee754/dbl-64/ulog.h: Remove. * sysdeps/ieee754/dbl-64/ulog.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_log_data.c: New file.
2018-06-13 16:40:19 +00:00
/* Data for log.
Copyright (C) 2018-2023 Free Software Foundation, Inc.
Add new log implementation Optimized log using carefully generated lookup table with 1/c and log(c) values for small intervalls around 1. The log(c) is very near a double precision value, it has about 62 bits precision. The algorithm is log(2^k x) = k log(2) + log(c) + log(x/c), where the last term is approximated by a polynomial of x/c - 1. Near 1 a single polynomial of x - 1 is used. There is separate code path when fma instruction is not available for computing x/c - 1 precisely, in which case the table size is doubled. The code uses __builtin_fma under __FP_FAST_FMA to ensure it is inlined as an instruction. With the default configuration settings the worst case error is 0.519 ULP (and 0.520 without fma), the rodata size is 2192 bytes (4240 without fma). The non-nearest rounding error is less than 1 ULP. Improvements on Cortex-A72 compared to current glibc master: log thruput: 3.28x in [0.01 11.1] log latency: 2.23x in [0.01 11.1] log thruput: 1.56x in [0.999 1.001] log latency: 1.57x in [0.999 1.001] Tested on aarch64-linux-gnu (defined __FP_FAST_FMA) arm-linux-gnueabihf (!defined __FP_FAST_FMA) x86_64-linux-gnu (!defined __FP_FAST_FMA) powerpc64le-linux-gnu (defined __FP_FAST_FMA) targets. * NEWS: Mention log improvement. * math/Makefile (type-double-routines): Add e_log_data. * sysdeps/i386/fpu/e_log_data.c: New file. * sysdeps/ia64/fpu/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/e_log.c: Rewrite. * sysdeps/ieee754/dbl-64/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/math_config.h (__log_data): Add. * sysdeps/ieee754/dbl-64/ulog.h: Remove. * sysdeps/ieee754/dbl-64/ulog.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_log_data.c: New file.
2018-06-13 16:40:19 +00:00
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
Prefer https to http for gnu.org and fsf.org URLs Also, change sources.redhat.com to sourceware.org. This patch was automatically generated by running the following shell script, which uses GNU sed, and which avoids modifying files imported from upstream: sed -ri ' s,(http|ftp)(://(.*\.)?(gnu|fsf|sourceware)\.org($|[^.]|\.[^a-z])),https\2,g s,(http|ftp)(://(.*\.)?)sources\.redhat\.com($|[^.]|\.[^a-z]),https\2sourceware.org\4,g ' \ $(find $(git ls-files) -prune -type f \ ! -name '*.po' \ ! -name 'ChangeLog*' \ ! -path COPYING ! -path COPYING.LIB \ ! -path manual/fdl-1.3.texi ! -path manual/lgpl-2.1.texi \ ! -path manual/texinfo.tex ! -path scripts/config.guess \ ! -path scripts/config.sub ! -path scripts/install-sh \ ! -path scripts/mkinstalldirs ! -path scripts/move-if-change \ ! -path INSTALL ! -path locale/programs/charmap-kw.h \ ! -path po/libc.pot ! -path sysdeps/gnu/errlist.c \ ! '(' -name configure \ -execdir test -f configure.ac -o -f configure.in ';' ')' \ ! '(' -name preconfigure \ -execdir test -f preconfigure.ac ';' ')' \ -print) and then by running 'make dist-prepare' to regenerate files built from the altered files, and then executing the following to cleanup: chmod a+x sysdeps/unix/sysv/linux/riscv/configure # Omit irrelevant whitespace and comment-only changes, # perhaps from a slightly-different Autoconf version. git checkout -f \ sysdeps/csky/configure \ sysdeps/hppa/configure \ sysdeps/riscv/configure \ sysdeps/unix/sysv/linux/csky/configure # Omit changes that caused a pre-commit check to fail like this: # remote: *** error: sysdeps/powerpc/powerpc64/ppc-mcount.S: trailing lines git checkout -f \ sysdeps/powerpc/powerpc64/ppc-mcount.S \ sysdeps/unix/sysv/linux/s390/s390-64/syscall.S # Omit change that caused a pre-commit check to fail like this: # remote: *** error: sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S: last line does not end in newline git checkout -f sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S
2019-09-07 05:40:42 +00:00
<https://www.gnu.org/licenses/>. */
Add new log implementation Optimized log using carefully generated lookup table with 1/c and log(c) values for small intervalls around 1. The log(c) is very near a double precision value, it has about 62 bits precision. The algorithm is log(2^k x) = k log(2) + log(c) + log(x/c), where the last term is approximated by a polynomial of x/c - 1. Near 1 a single polynomial of x - 1 is used. There is separate code path when fma instruction is not available for computing x/c - 1 precisely, in which case the table size is doubled. The code uses __builtin_fma under __FP_FAST_FMA to ensure it is inlined as an instruction. With the default configuration settings the worst case error is 0.519 ULP (and 0.520 without fma), the rodata size is 2192 bytes (4240 without fma). The non-nearest rounding error is less than 1 ULP. Improvements on Cortex-A72 compared to current glibc master: log thruput: 3.28x in [0.01 11.1] log latency: 2.23x in [0.01 11.1] log thruput: 1.56x in [0.999 1.001] log latency: 1.57x in [0.999 1.001] Tested on aarch64-linux-gnu (defined __FP_FAST_FMA) arm-linux-gnueabihf (!defined __FP_FAST_FMA) x86_64-linux-gnu (!defined __FP_FAST_FMA) powerpc64le-linux-gnu (defined __FP_FAST_FMA) targets. * NEWS: Mention log improvement. * math/Makefile (type-double-routines): Add e_log_data. * sysdeps/i386/fpu/e_log_data.c: New file. * sysdeps/ia64/fpu/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/e_log.c: Rewrite. * sysdeps/ieee754/dbl-64/e_log_data.c: New file. * sysdeps/ieee754/dbl-64/math_config.h (__log_data): Add. * sysdeps/ieee754/dbl-64/ulog.h: Remove. * sysdeps/ieee754/dbl-64/ulog.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_log_data.c: New file.
2018-06-13 16:40:19 +00:00
#include "math_config.h"
#define N (1 << LOG_TABLE_BITS)
const struct log_data __log_data = {
.ln2hi = 0x1.62e42fefa3800p-1,
.ln2lo = 0x1.ef35793c76730p-45,
.poly1 = {
#if LOG_POLY1_ORDER == 12
// relative error: 0x1.c04d76cp-63
// in -0x1p-4 0x1.09p-4 (|log(1+x)| > 0x1p-4 outside the interval)
-0x1p-1,
0x1.5555555555577p-2,
-0x1.ffffffffffdcbp-3,
0x1.999999995dd0cp-3,
-0x1.55555556745a7p-3,
0x1.24924a344de3p-3,
-0x1.fffffa4423d65p-4,
0x1.c7184282ad6cap-4,
-0x1.999eb43b068ffp-4,
0x1.78182f7afd085p-4,
-0x1.5521375d145cdp-4,
#endif
},
.poly = {
#if N == 128 && LOG_POLY_ORDER == 6
// relative error: 0x1.926199e8p-56
// abs error: 0x1.882ff33p-65
// in -0x1.fp-9 0x1.fp-9
-0x1.0000000000001p-1,
0x1.555555551305bp-2,
-0x1.fffffffeb459p-3,
0x1.999b324f10111p-3,
-0x1.55575e506c89fp-3,
#endif
},
/* 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 [1.6p-1; 1.6p0] 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 = (double)log(c)
tab2[i].chi = (double)c
tab2[i].clo = (double)(c - (double)c)
where c is near the center of the subinterval and is chosen by trying +-2^29
floating point invc candidates around 1/center and selecting one for which
1) the rounding error in 0x1.8p9 + logc is 0,
2) the rounding error in z - chi - clo is < 0x1p-66 and
3) the rounding error in (double)log(c) is minimized (< 0x1p-66).
Note: 1) ensures that k*ln2hi + logc can be computed without rounding error,
2) ensures that z/c - 1 can be computed as (z - chi - clo)*invc with close to
a single rounding error when there is no fast fma for z*invc - 1, 3) ensures
that logc + poly(z/c - 1) has small error, however near x == 1 when
|log(x)| < 0x1p-4, this is not enough so that is special cased. */
.tab = {
#if N == 128
{0x1.734f0c3e0de9fp+0, -0x1.7cc7f79e69000p-2},
{0x1.713786a2ce91fp+0, -0x1.76feec20d0000p-2},
{0x1.6f26008fab5a0p+0, -0x1.713e31351e000p-2},
{0x1.6d1a61f138c7dp+0, -0x1.6b85b38287800p-2},
{0x1.6b1490bc5b4d1p+0, -0x1.65d5590807800p-2},
{0x1.69147332f0cbap+0, -0x1.602d076180000p-2},
{0x1.6719f18224223p+0, -0x1.5a8ca86909000p-2},
{0x1.6524f99a51ed9p+0, -0x1.54f4356035000p-2},
{0x1.63356aa8f24c4p+0, -0x1.4f637c36b4000p-2},
{0x1.614b36b9ddc14p+0, -0x1.49da7fda85000p-2},
{0x1.5f66452c65c4cp+0, -0x1.445923989a800p-2},
{0x1.5d867b5912c4fp+0, -0x1.3edf439b0b800p-2},
{0x1.5babccb5b90dep+0, -0x1.396ce448f7000p-2},
{0x1.59d61f2d91a78p+0, -0x1.3401e17bda000p-2},
{0x1.5805612465687p+0, -0x1.2e9e2ef468000p-2},
{0x1.56397cee76bd3p+0, -0x1.2941b3830e000p-2},
{0x1.54725e2a77f93p+0, -0x1.23ec58cda8800p-2},
{0x1.52aff42064583p+0, -0x1.1e9e129279000p-2},
{0x1.50f22dbb2bddfp+0, -0x1.1956d2b48f800p-2},
{0x1.4f38f4734ded7p+0, -0x1.141679ab9f800p-2},
{0x1.4d843cfde2840p+0, -0x1.0edd094ef9800p-2},
{0x1.4bd3ec078a3c8p+0, -0x1.09aa518db1000p-2},
{0x1.4a27fc3e0258ap+0, -0x1.047e65263b800p-2},
{0x1.4880524d48434p+0, -0x1.feb224586f000p-3},
{0x1.46dce1b192d0bp+0, -0x1.f474a7517b000p-3},
{0x1.453d9d3391854p+0, -0x1.ea4443d103000p-3},
{0x1.43a2744b4845ap+0, -0x1.e020d44e9b000p-3},
{0x1.420b54115f8fbp+0, -0x1.d60a22977f000p-3},
{0x1.40782da3ef4b1p+0, -0x1.cc00104959000p-3},
{0x1.3ee8f5d57fe8fp+0, -0x1.c202956891000p-3},
{0x1.3d5d9a00b4ce9p+0, -0x1.b81178d811000p-3},
{0x1.3bd60c010c12bp+0, -0x1.ae2c9ccd3d000p-3},
{0x1.3a5242b75dab8p+0, -0x1.a45402e129000p-3},
{0x1.38d22cd9fd002p+0, -0x1.9a877681df000p-3},
{0x1.3755bc5847a1cp+0, -0x1.90c6d69483000p-3},
{0x1.35dce49ad36e2p+0, -0x1.87120a645c000p-3},
{0x1.34679984dd440p+0, -0x1.7d68fb4143000p-3},
{0x1.32f5cceffcb24p+0, -0x1.73cb83c627000p-3},
{0x1.3187775a10d49p+0, -0x1.6a39a9b376000p-3},
{0x1.301c8373e3990p+0, -0x1.60b3154b7a000p-3},
{0x1.2eb4ebb95f841p+0, -0x1.5737d76243000p-3},
{0x1.2d50a0219a9d1p+0, -0x1.4dc7b8fc23000p-3},
{0x1.2bef9a8b7fd2ap+0, -0x1.4462c51d20000p-3},
{0x1.2a91c7a0c1babp+0, -0x1.3b08abc830000p-3},
{0x1.293726014b530p+0, -0x1.31b996b490000p-3},
{0x1.27dfa5757a1f5p+0, -0x1.2875490a44000p-3},
{0x1.268b39b1d3bbfp+0, -0x1.1f3b9f879a000p-3},
{0x1.2539d838ff5bdp+0, -0x1.160c8252ca000p-3},
{0x1.23eb7aac9083bp+0, -0x1.0ce7f57f72000p-3},
{0x1.22a012ba940b6p+0, -0x1.03cdc49fea000p-3},
{0x1.2157996cc4132p+0, -0x1.f57bdbc4b8000p-4},
{0x1.201201dd2fc9bp+0, -0x1.e370896404000p-4},
{0x1.1ecf4494d480bp+0, -0x1.d17983ef94000p-4},
{0x1.1d8f5528f6569p+0, -0x1.bf9674ed8a000p-4},
{0x1.1c52311577e7cp+0, -0x1.adc79202f6000p-4},
{0x1.1b17c74cb26e9p+0, -0x1.9c0c3e7288000p-4},
{0x1.19e010c2c1ab6p+0, -0x1.8a646b372c000p-4},
{0x1.18ab07bb670bdp+0, -0x1.78d01b3ac0000p-4},
{0x1.1778a25efbcb6p+0, -0x1.674f145380000p-4},
{0x1.1648d354c31dap+0, -0x1.55e0e6d878000p-4},
{0x1.151b990275fddp+0, -0x1.4485cdea1e000p-4},
{0x1.13f0ea432d24cp+0, -0x1.333d94d6aa000p-4},
{0x1.12c8b7210f9dap+0, -0x1.22079f8c56000p-4},
{0x1.11a3028ecb531p+0, -0x1.10e4698622000p-4},
{0x1.107fbda8434afp+0, -0x1.ffa6c6ad20000p-5},
{0x1.0f5ee0f4e6bb3p+0, -0x1.dda8d4a774000p-5},
{0x1.0e4065d2a9fcep+0, -0x1.bbcece4850000p-5},
{0x1.0d244632ca521p+0, -0x1.9a1894012c000p-5},
{0x1.0c0a77ce2981ap+0, -0x1.788583302c000p-5},
{0x1.0af2f83c636d1p+0, -0x1.5715e67d68000p-5},
{0x1.09ddb98a01339p+0, -0x1.35c8a49658000p-5},
{0x1.08cabaf52e7dfp+0, -0x1.149e364154000p-5},
{0x1.07b9f2f4e28fbp+0, -0x1.e72c082eb8000p-6},
{0x1.06ab58c358f19p+0, -0x1.a55f152528000p-6},
{0x1.059eea5ecf92cp+0, -0x1.63d62cf818000p-6},
{0x1.04949cdd12c90p+0, -0x1.228fb8caa0000p-6},
{0x1.038c6c6f0ada9p+0, -0x1.c317b20f90000p-7},
{0x1.02865137932a9p+0, -0x1.419355daa0000p-7},
{0x1.0182427ea7348p+0, -0x1.81203c2ec0000p-8},
{0x1.008040614b195p+0, -0x1.0040979240000p-9},
{0x1.fe01ff726fa1ap-1, 0x1.feff384900000p-9},
{0x1.fa11cc261ea74p-1, 0x1.7dc41353d0000p-7},
{0x1.f6310b081992ep-1, 0x1.3cea3c4c28000p-6},
{0x1.f25f63ceeadcdp-1, 0x1.b9fc114890000p-6},
{0x1.ee9c8039113e7p-1, 0x1.1b0d8ce110000p-5},
{0x1.eae8078cbb1abp-1, 0x1.58a5bd001c000p-5},
{0x1.e741aa29d0c9bp-1, 0x1.95c8340d88000p-5},
{0x1.e3a91830a99b5p-1, 0x1.d276aef578000p-5},
{0x1.e01e009609a56p-1, 0x1.07598e598c000p-4},
{0x1.dca01e577bb98p-1, 0x1.253f5e30d2000p-4},
{0x1.d92f20b7c9103p-1, 0x1.42edd8b380000p-4},
{0x1.d5cac66fb5ccep-1, 0x1.606598757c000p-4},
{0x1.d272caa5ede9dp-1, 0x1.7da76356a0000p-4},
{0x1.cf26e3e6b2ccdp-1, 0x1.9ab434e1c6000p-4},
{0x1.cbe6da2a77902p-1, 0x1.b78c7bb0d6000p-4},
{0x1.c8b266d37086dp-1, 0x1.d431332e72000p-4},
{0x1.c5894bd5d5804p-1, 0x1.f0a3171de6000p-4},
{0x1.c26b533bb9f8cp-1, 0x1.067152b914000p-3},
{0x1.bf583eeece73fp-1, 0x1.147858292b000p-3},
{0x1.bc4fd75db96c1p-1, 0x1.2266ecdca3000p-3},
{0x1.b951e0c864a28p-1, 0x1.303d7a6c55000p-3},
{0x1.b65e2c5ef3e2cp-1, 0x1.3dfc33c331000p-3},
{0x1.b374867c9888bp-1, 0x1.4ba366b7a8000p-3},
{0x1.b094b211d304ap-1, 0x1.5933928d1f000p-3},
{0x1.adbe885f2ef7ep-1, 0x1.66acd2418f000p-3},
{0x1.aaf1d31603da2p-1, 0x1.740f8ec669000p-3},
{0x1.a82e63fd358a7p-1, 0x1.815c0f51af000p-3},
{0x1.a5740ef09738bp-1, 0x1.8e92954f68000p-3},
{0x1.a2c2a90ab4b27p-1, 0x1.9bb3602f84000p-3},
{0x1.a01a01393f2d1p-1, 0x1.a8bed1c2c0000p-3},
{0x1.9d79f24db3c1bp-1, 0x1.b5b515c01d000p-3},
{0x1.9ae2505c7b190p-1, 0x1.c2967ccbcc000p-3},
{0x1.9852ef297ce2fp-1, 0x1.cf635d5486000p-3},
{0x1.95cbaeea44b75p-1, 0x1.dc1bd3446c000p-3},
{0x1.934c69de74838p-1, 0x1.e8c01b8cfe000p-3},
{0x1.90d4f2f6752e6p-1, 0x1.f5509c0179000p-3},
{0x1.8e6528effd79dp-1, 0x1.00e6c121fb800p-2},
{0x1.8bfce9fcc007cp-1, 0x1.071b80e93d000p-2},
{0x1.899c0dabec30ep-1, 0x1.0d46b9e867000p-2},
{0x1.87427aa2317fbp-1, 0x1.13687334bd000p-2},
{0x1.84f00acb39a08p-1, 0x1.1980d67234800p-2},
{0x1.82a49e8653e55p-1, 0x1.1f8ffe0cc8000p-2},
{0x1.8060195f40260p-1, 0x1.2595fd7636800p-2},
{0x1.7e22563e0a329p-1, 0x1.2b9300914a800p-2},
{0x1.7beb377dcb5adp-1, 0x1.3187210436000p-2},
{0x1.79baa679725c2p-1, 0x1.377266dec1800p-2},
{0x1.77907f2170657p-1, 0x1.3d54ffbaf3000p-2},
{0x1.756cadbd6130cp-1, 0x1.432eee32fe000p-2},
#endif
},
#ifndef __FP_FAST_FMA
.tab2 = {
# if N == 128
{0x1.61000014fb66bp-1, 0x1.e026c91425b3cp-56},
{0x1.63000034db495p-1, 0x1.dbfea48005d41p-55},
{0x1.650000d94d478p-1, 0x1.e7fa786d6a5b7p-55},
{0x1.67000074e6fadp-1, 0x1.1fcea6b54254cp-57},
{0x1.68ffffedf0faep-1, -0x1.c7e274c590efdp-56},
{0x1.6b0000763c5bcp-1, -0x1.ac16848dcda01p-55},
{0x1.6d0001e5cc1f6p-1, 0x1.33f1c9d499311p-55},
{0x1.6efffeb05f63ep-1, -0x1.e80041ae22d53p-56},
{0x1.710000e86978p-1, 0x1.bff6671097952p-56},
{0x1.72ffffc67e912p-1, 0x1.c00e226bd8724p-55},
{0x1.74fffdf81116ap-1, -0x1.e02916ef101d2p-57},
{0x1.770000f679c9p-1, -0x1.7fc71cd549c74p-57},
{0x1.78ffffa7ec835p-1, 0x1.1bec19ef50483p-55},
{0x1.7affffe20c2e6p-1, -0x1.07e1729cc6465p-56},
{0x1.7cfffed3fc9p-1, -0x1.08072087b8b1cp-55},
{0x1.7efffe9261a76p-1, 0x1.dc0286d9df9aep-55},
{0x1.81000049ca3e8p-1, 0x1.97fd251e54c33p-55},
{0x1.8300017932c8fp-1, -0x1.afee9b630f381p-55},
{0x1.850000633739cp-1, 0x1.9bfbf6b6535bcp-55},
{0x1.87000204289c6p-1, -0x1.bbf65f3117b75p-55},
{0x1.88fffebf57904p-1, -0x1.9006ea23dcb57p-55},
{0x1.8b00022bc04dfp-1, -0x1.d00df38e04b0ap-56},
{0x1.8cfffe50c1b8ap-1, -0x1.8007146ff9f05p-55},
{0x1.8effffc918e43p-1, 0x1.3817bd07a7038p-55},
{0x1.910001efa5fc7p-1, 0x1.93e9176dfb403p-55},
{0x1.9300013467bb9p-1, 0x1.f804e4b980276p-56},
{0x1.94fffe6ee076fp-1, -0x1.f7ef0d9ff622ep-55},
{0x1.96fffde3c12d1p-1, -0x1.082aa962638bap-56},
{0x1.98ffff4458a0dp-1, -0x1.7801b9164a8efp-55},
{0x1.9afffdd982e3ep-1, -0x1.740e08a5a9337p-55},
{0x1.9cfffed49fb66p-1, 0x1.fce08c19bep-60},
{0x1.9f00020f19c51p-1, -0x1.a3faa27885b0ap-55},
{0x1.a10001145b006p-1, 0x1.4ff489958da56p-56},
{0x1.a300007bbf6fap-1, 0x1.cbeab8a2b6d18p-55},
{0x1.a500010971d79p-1, 0x1.8fecadd78793p-55},
{0x1.a70001df52e48p-1, -0x1.f41763dd8abdbp-55},
{0x1.a90001c593352p-1, -0x1.ebf0284c27612p-55},
{0x1.ab0002a4f3e4bp-1, -0x1.9fd043cff3f5fp-57},
{0x1.acfffd7ae1ed1p-1, -0x1.23ee7129070b4p-55},
{0x1.aefffee510478p-1, 0x1.a063ee00edea3p-57},
{0x1.b0fffdb650d5bp-1, 0x1.a06c8381f0ab9p-58},
{0x1.b2ffffeaaca57p-1, -0x1.9011e74233c1dp-56},
{0x1.b4fffd995badcp-1, -0x1.9ff1068862a9fp-56},
{0x1.b7000249e659cp-1, 0x1.aff45d0864f3ep-55},
{0x1.b8ffff987164p-1, 0x1.cfe7796c2c3f9p-56},
{0x1.bafffd204cb4fp-1, -0x1.3ff27eef22bc4p-57},
{0x1.bcfffd2415c45p-1, -0x1.cffb7ee3bea21p-57},
{0x1.beffff86309dfp-1, -0x1.14103972e0b5cp-55},
{0x1.c0fffe1b57653p-1, 0x1.bc16494b76a19p-55},
{0x1.c2ffff1fa57e3p-1, -0x1.4feef8d30c6edp-57},
{0x1.c4fffdcbfe424p-1, -0x1.43f68bcec4775p-55},
{0x1.c6fffed54b9f7p-1, 0x1.47ea3f053e0ecp-55},
{0x1.c8fffeb998fd5p-1, 0x1.383068df992f1p-56},
{0x1.cb0002125219ap-1, -0x1.8fd8e64180e04p-57},
{0x1.ccfffdd94469cp-1, 0x1.e7ebe1cc7ea72p-55},
{0x1.cefffeafdc476p-1, 0x1.ebe39ad9f88fep-55},
{0x1.d1000169af82bp-1, 0x1.57d91a8b95a71p-56},
{0x1.d30000d0ff71dp-1, 0x1.9c1906970c7dap-55},
{0x1.d4fffea790fc4p-1, -0x1.80e37c558fe0cp-58},
{0x1.d70002edc87e5p-1, -0x1.f80d64dc10f44p-56},
{0x1.d900021dc82aap-1, -0x1.47c8f94fd5c5cp-56},
{0x1.dafffd86b0283p-1, 0x1.c7f1dc521617ep-55},
{0x1.dd000296c4739p-1, 0x1.8019eb2ffb153p-55},
{0x1.defffe54490f5p-1, 0x1.e00d2c652cc89p-57},
{0x1.e0fffcdabf694p-1, -0x1.f8340202d69d2p-56},
{0x1.e2fffdb52c8ddp-1, 0x1.b00c1ca1b0864p-56},
{0x1.e4ffff24216efp-1, 0x1.2ffa8b094ab51p-56},
{0x1.e6fffe88a5e11p-1, -0x1.7f673b1efbe59p-58},
{0x1.e9000119eff0dp-1, -0x1.4808d5e0bc801p-55},
{0x1.eafffdfa51744p-1, 0x1.80006d54320b5p-56},
{0x1.ed0001a127fa1p-1, -0x1.002f860565c92p-58},
{0x1.ef00007babcc4p-1, -0x1.540445d35e611p-55},
{0x1.f0ffff57a8d02p-1, -0x1.ffb3139ef9105p-59},
{0x1.f30001ee58ac7p-1, 0x1.a81acf2731155p-55},
{0x1.f4ffff5823494p-1, 0x1.a3f41d4d7c743p-55},
{0x1.f6ffffca94c6bp-1, -0x1.202f41c987875p-57},
{0x1.f8fffe1f9c441p-1, 0x1.77dd1f477e74bp-56},
{0x1.fafffd2e0e37ep-1, -0x1.f01199a7ca331p-57},
{0x1.fd0001c77e49ep-1, 0x1.181ee4bceacb1p-56},
{0x1.feffff7e0c331p-1, -0x1.e05370170875ap-57},
{0x1.00ffff465606ep+0, -0x1.a7ead491c0adap-55},
{0x1.02ffff3867a58p+0, -0x1.77f69c3fcb2ep-54},
{0x1.04ffffdfc0d17p+0, 0x1.7bffe34cb945bp-54},
{0x1.0700003cd4d82p+0, 0x1.20083c0e456cbp-55},
{0x1.08ffff9f2cbe8p+0, -0x1.dffdfbe37751ap-57},
{0x1.0b000010cda65p+0, -0x1.13f7faee626ebp-54},
{0x1.0d00001a4d338p+0, 0x1.07dfa79489ff7p-55},
{0x1.0effffadafdfdp+0, -0x1.7040570d66bcp-56},
{0x1.110000bbafd96p+0, 0x1.e80d4846d0b62p-55},
{0x1.12ffffae5f45dp+0, 0x1.dbffa64fd36efp-54},
{0x1.150000dd59ad9p+0, 0x1.a0077701250aep-54},
{0x1.170000f21559ap+0, 0x1.dfdf9e2e3deeep-55},
{0x1.18ffffc275426p+0, 0x1.10030dc3b7273p-54},
{0x1.1b000123d3c59p+0, 0x1.97f7980030188p-54},
{0x1.1cffff8299eb7p+0, -0x1.5f932ab9f8c67p-57},
{0x1.1effff48ad4p+0, 0x1.37fbf9da75bebp-54},
{0x1.210000c8b86a4p+0, 0x1.f806b91fd5b22p-54},
{0x1.2300003854303p+0, 0x1.3ffc2eb9fbf33p-54},
{0x1.24fffffbcf684p+0, 0x1.601e77e2e2e72p-56},
{0x1.26ffff52921d9p+0, 0x1.ffcbb767f0c61p-56},
{0x1.2900014933a3cp+0, -0x1.202ca3c02412bp-56},
{0x1.2b00014556313p+0, -0x1.2808233f21f02p-54},
{0x1.2cfffebfe523bp+0, -0x1.8ff7e384fdcf2p-55},
{0x1.2f0000bb8ad96p+0, -0x1.5ff51503041c5p-55},
{0x1.30ffffb7ae2afp+0, -0x1.10071885e289dp-55},
{0x1.32ffffeac5f7fp+0, -0x1.1ff5d3fb7b715p-54},
{0x1.350000ca66756p+0, 0x1.57f82228b82bdp-54},
{0x1.3700011fbf721p+0, 0x1.000bac40dd5ccp-55},
{0x1.38ffff9592fb9p+0, -0x1.43f9d2db2a751p-54},
{0x1.3b00004ddd242p+0, 0x1.57f6b707638e1p-55},
{0x1.3cffff5b2c957p+0, 0x1.a023a10bf1231p-56},
{0x1.3efffeab0b418p+0, 0x1.87f6d66b152bp-54},
{0x1.410001532aff4p+0, 0x1.7f8375f198524p-57},
{0x1.4300017478b29p+0, 0x1.301e672dc5143p-55},
{0x1.44fffe795b463p+0, 0x1.9ff69b8b2895ap-55},
{0x1.46fffe80475ep+0, -0x1.5c0b19bc2f254p-54},
{0x1.48fffef6fc1e7p+0, 0x1.b4009f23a2a72p-54},
{0x1.4afffe5bea704p+0, -0x1.4ffb7bf0d7d45p-54},
{0x1.4d000171027dep+0, -0x1.9c06471dc6a3dp-54},
{0x1.4f0000ff03ee2p+0, 0x1.77f890b85531cp-54},
{0x1.5100012dc4bd1p+0, 0x1.004657166a436p-57},
{0x1.530001605277ap+0, -0x1.6bfcece233209p-54},
{0x1.54fffecdb704cp+0, -0x1.902720505a1d7p-55},
{0x1.56fffef5f54a9p+0, 0x1.bbfe60ec96412p-54},
{0x1.5900017e61012p+0, 0x1.87ec581afef9p-55},
{0x1.5b00003c93e92p+0, -0x1.f41080abf0ccp-54},
{0x1.5d0001d4919bcp+0, -0x1.8812afb254729p-54},
{0x1.5efffe7b87a89p+0, -0x1.47eb780ed6904p-54},
#endif
},
#endif /* __FP_FAST_FMA */
};