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bbd578b38d
The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows better performance compared to the generic expm1f. The code was adapted to glibc style and to use the definition of math_config.h (to handle errno, overflow, and underflow). Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1, gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1): Latency master patched improvement x86_64 96.7402 36.4026 62.37% x86_64v2 97.5391 33.4625 65.69% x86_64v3 82.1778 30.8668 62.44% i686 120.58 94.8302 21.35% aarch64 32.3558 12.8881 60.17% power10 23.5087 9.8574 58.07% powerpc 23.4776 9.06325 61.40% reciprocal-throughput master patched improvement x86_64 27.8224 15.9255 42.76% x86_64v2 27.8364 9.6438 65.36% x86_64v3 20.3227 9.6146 52.69% i686 63.5629 59.4718 6.44% aarch64 17.4838 7.1082 59.34% power10 12.4644 8.7829 29.54% powerpc 14.2152 5.94765 58.16% Signed-off-by: Alexei Sibidanov <sibid@uvic.ca> Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr> Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org> Reviewed-by: DJ Delorie <dj@redhat.com>
192 lines
6 KiB
C
192 lines
6 KiB
C
/* Correctly-rounded base-2 exponent function biased by 1 for binary32 value.
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Copyright (c) 2022-2024 Alexei Sibidanov.
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The original version of this file was copied from the CORE-MATH
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project (file src/binary32/exp2m1/exp2m1f.c, revision baf5f6b).
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#include <fenv.h>
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#include <math.h>
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#include "math_config.h"
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#include <libm-alias-float.h>
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#include <math-narrow-eval.h>
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#include <float.h>
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float
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__exp2m1f (float x)
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{
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double z = x;
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uint32_t ux = asuint (x);
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uint32_t ax = ux & (~0u >> 1);
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if (__glibc_unlikely (ux >= 0xc1c80000u))
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{ /* x <= -25 */
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if (ax > (0xffu << 23))
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return x + x; /* nan */
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return (ux == 0xff800000) ? -0x1p+0 : -0x1p+0 + 0x1p-26f;
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}
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else if (__glibc_unlikely (ax >= 0x43000000u))
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{ /* x >= 128 */
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if (ax >= asuint (INFINITY))
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return x + x; /* +Inf or NaN */
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/* exp2m1 (MAX_EXP) should not overflow when rounding towards zero
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or towards -Inf. We round FLT_MAX + 2^103 which is in the middle
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between FLT_MAX and 2^128 (the next number with unbounded range). */
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float ret = math_narrow_eval (FLT_MAX + 0x1p103f);
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if (x == FLT_MAX_EXP && ret == FLT_MAX)
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return ret;
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return __math_oflowf (0);
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}
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else if (__glibc_unlikely (ax < 0x3df95f1fu))
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{ /* |x| < 8.44e-2/log(2) */
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double z2 = z * z, r;
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if (__glibc_unlikely (ax < 0x3d67a4ccu))
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{ /* |x| < 3.92e-2/log(2) */
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if (__glibc_unlikely (ax < 0x3caa2feeu))
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{ /* |x| < 1.44e-2/log(2) */
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if (__glibc_unlikely (ax < 0x3bac1405u))
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{ /* |x| < 3.64e-3/log(2) */
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if (__glibc_unlikely (ax < 0x3a358876u))
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{ /* |x| < 4.8e-4/log(2) */
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if (__glibc_unlikely (ax < 0x37d32ef6u))
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{ /* |x| < 1.745e-5/log(2) */
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if (__glibc_unlikely (ax < 0x331fdd82u))
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{ /* |x| < 2.58e-8/log(2) */
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if (__glibc_unlikely (ax < 0x2538aa3bu))
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/* |x| < 1.60171e-16 */
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r = 0x1.62e42fefa39efp-1;
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else
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r = 0x1.62e42fefa39fp-1
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+ z * 0x1.ebfbdff82c58fp-3;
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}
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else
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{
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if (__glibc_unlikely (ux == 0xb3d85005u))
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return -0x1.2bdf76p-24 - 0x1.8p-77;
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if (__glibc_unlikely (ux == 0x3338428du))
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return 0x1.fee08ap-26 + 0x1p-80;
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static const double c[] =
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{
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0x1.62e42fefa39efp-1, 0x1.ebfbdff8548fdp-3,
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0x1.c6b08d704a06dp-5
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};
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r = c[0] + z * (c[1] + z * c[2]);
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}
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}
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else
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{
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if (__glibc_unlikely (ux == 0x388bca4fu))
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return 0x1.839702p-15 - 0x1.8p-68;
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static const double c[] =
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{
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0x1.62e42fefa39efp-1, 0x1.ebfbdff82c58fp-3,
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0x1.c6b08dc82b347p-5, 0x1.3b2ab6fbad172p-7
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};
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r = (c[0] + z * c[1]) + z2 * (c[2] + z * c[3]);
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}
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}
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else
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{
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static const double c[] =
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{
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0x1.62e42fefa39efp-1, 0x1.ebfbdff82c068p-3,
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0x1.c6b08d704a6dcp-5, 0x1.3b2ac262c3eedp-7,
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0x1.5d87fe7af779ap-10
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};
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r = (c[0] + z * c[1])
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+ z2 * (c[2] + z * (c[3] + z * c[4]));
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}
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}
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else
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{
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static const double c[] =
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{
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0x1.62e42fefa39fp-1, 0x1.ebfbdff82c58dp-3,
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0x1.c6b08d7011d13p-5, 0x1.3b2ab6fbd267dp-7,
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0x1.5d88a81cea49ep-10, 0x1.430912ea9b963p-13
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};
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r = (c[0] + z * c[1])
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+ z2 * ((c[2] + z * c[3]) + z2 * (c[4] + z * c[5]));
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}
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}
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else
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{
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static const double c[] =
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{
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0x1.62e42fefa39efp-1, 0x1.ebfbdff82c639p-3,
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0x1.c6b08d7049f1cp-5, 0x1.3b2ab6f5243bdp-7,
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0x1.5d87fe80a9e6cp-10, 0x1.430d0b9257fa8p-13,
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0x1.ffcbfc4cf0952p-17
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};
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r = (c[0] + z * c[1])
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+ z2 * ((c[2] + z * c[3])
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+ z2 * (c[4] + z * (c[5] + z * c[6])));
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}
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}
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else
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{
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static const double c[] =
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{
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0x1.62e42fefa39efp-1, 0x1.ebfbdff82c591p-3,
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0x1.c6b08d704cf6bp-5, 0x1.3b2ab6fba00cep-7,
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0x1.5d87fdfdaadb4p-10, 0x1.4309137333066p-13,
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0x1.ffe5e90daf7ddp-17, 0x1.62c0220eed731p-20
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};
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r = ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3]))
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+ (z2 * z2) * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7]));
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}
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r *= z;
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return r;
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}
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else
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{
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static const double c[] =
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{
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0x1.62e42fefa398bp-5, 0x1.ebfbdff84555ap-11,
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0x1.c6b08d4ad86d3p-17, 0x1.3b2ad1b1716a2p-23,
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0x1.5d7472718ce9dp-30, 0x1.4a1d7f457ac56p-37
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};
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static const double tb[] =
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{
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0x1p+0, 0x1.0b5586cf9890fp+0, 0x1.172b83c7d517bp+0,
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0x1.2387a6e756238p+0, 0x1.306fe0a31b715p+0, 0x1.3dea64c123422p+0,
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0x1.4bfdad5362a27p+0, 0x1.5ab07dd485429p+0, 0x1.6a09e667f3bcdp+0,
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0x1.7a11473eb0187p+0, 0x1.8ace5422aa0dap+0, 0x1.9c49182a3f09p+0,
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0x1.ae89f995ad3adp+0, 0x1.c199bdd85529cp+0, 0x1.d5818dcfba487p+0,
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0x1.ea4afa2a490dap+0
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};
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double a = 16.0 * z;
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double ia = floor (a);
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double h = a - ia;
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double h2 = h * h;
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int64_t i = ia, j = i & 0xf, e = i - j;
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e >>= 4;
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double s = tb[j];
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s *= asdouble ((e + 0x3ffull) << 52);
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double c0 = c[0] + h * c[1];
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double c2 = c[2] + h * c[3];
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double c4 = c[4] + h * c[5];
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c0 += h2 * (c2 + h2 * c4);
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double w = s * h;
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return (s - 1.0) + w * c0;
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}
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}
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libm_alias_float (__exp2m1, exp2m1)
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