353 lines · c
1//===-- Range reduction for double precision sin/cos/tan w/ FMA -*- C++ -*-===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8 9#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_FMA_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_FMA_H11 12#include "src/__support/FPUtil/FPBits.h"13#include "src/__support/FPUtil/double_double.h"14#include "src/__support/FPUtil/multiply_add.h"15#include "src/__support/FPUtil/nearest_integer.h"16#include "src/__support/macros/config.h"17#include "src/__support/math/range_reduction_double_common.h"18 19namespace LIBC_NAMESPACE_DECL {20 21namespace math {22 23namespace range_reduction_double_internal {24 25using LIBC_NAMESPACE::fputil::DoubleDouble;26 27LIBC_INLINE unsigned LargeRangeReduction::fast(double x, DoubleDouble &u) {28 using FPBits = typename fputil::FPBits<double>;29 FPBits xbits(x);30 31 int x_e_m62 = xbits.get_biased_exponent() - (FPBits::EXP_BIAS + 62);32 idx = static_cast<unsigned>((x_e_m62 >> 4) + 3);33 // Scale x down by 2^(-(16 * (idx - 3))34 xbits.set_biased_exponent((x_e_m62 & 15) + FPBits::EXP_BIAS + 62);35 // 2^62 <= |x_reduced| < 2^(62 + 16) = 2^7836 x_reduced = xbits.get_val();37 // x * c_hi = ph.hi + ph.lo exactly.38 DoubleDouble ph = fputil::exact_mult<double, SPLIT>(39 x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][0]);40 // x * c_mid = pm.hi + pm.lo exactly.41 DoubleDouble pm = fputil::exact_mult<double, SPLIT>(42 x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][1]);43 // x * c_lo = pl.hi + pl.lo exactly.44 DoubleDouble pl = fputil::exact_mult<double, SPLIT>(45 x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][2]);46 // Extract integral parts and fractional parts of (ph.lo + pm.hi).47 double sum_hi = ph.lo + pm.hi;48 double kd = fputil::nearest_integer(sum_hi);49 50 // x * 128/pi mod 1 ~ y_hi + y_mid + y_lo51 y_hi = (ph.lo - kd) + pm.hi; // Exact52 y_mid = fputil::exact_add(pm.lo, pl.hi);53 y_lo = pl.lo;54 55 // y_l = x * c_lo_2 + pl.lo56 double y_l =57 fputil::multiply_add(x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][3], y_lo);58 DoubleDouble y = fputil::exact_add(y_hi, y_mid.hi);59 y.lo += (y_mid.lo + y_l);60 61 // Digits of pi/128, generated by Sollya with:62 // > a = round(pi/128, D, RN);63 // > b = round(pi/128 - a, D, RN);64 constexpr DoubleDouble PI_OVER_128_DD = {0x1.1a62633145c07p-60,65 0x1.921fb54442d18p-6};66 67 // Error bound: with {a} denote the fractional part of a, i.e.:68 // {a} = a - round(a)69 // Then,70 // | {x * 128/pi} - (y_hi + y_lo) | <= ulp(ulp(y_hi)) <= 2^-10571 // | {x mod pi/128} - (u.hi + u.lo) | < 2 * 2^-6 * 2^-105 = 2^-11072 u = fputil::quick_mult<SPLIT>(y, PI_OVER_128_DD);73 74 return static_cast<unsigned>(static_cast<int64_t>(kd));75}76 77// Lookup table for sin(k * pi / 128) with k = 0, ..., 255.78// Table is generated with Sollya as follow:79// > display = hexadecimal;80// > for k from 0 to 255 do {81// a = D(sin(k * pi/128)); };82// b = D(sin(k * pi/128) - a);83// print("{", b, ",", a, "},");84// };85LIBC_INLINE constexpr DoubleDouble SIN_K_PI_OVER_128[] = {86 {0, 0},87 {-0x1.b1d63091a013p-64, 0x1.92155f7a3667ep-6},88 {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},89 {-0x1.9a088a8bf6b2cp-59, 0x1.2d52092ce19f6p-4},90 {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},91 {0x1.a2704729ae56dp-59, 0x1.f564e56a9730ep-4},92 {0x1.13000a89a11ep-58, 0x1.2c8106e8e613ap-3},93 {0x1.531ff779ddac6p-57, 0x1.5e214448b3fc6p-3},94 {-0x1.26d19b9ff8d82p-57, 0x1.8f8b83c69a60bp-3},95 {-0x1.af1439e521935p-62, 0x1.c0b826a7e4f63p-3},96 {-0x1.42deef11da2c4p-57, 0x1.f19f97b215f1bp-3},97 {0x1.824c20ab7aa9ap-56, 0x1.111d262b1f677p-2},98 {-0x1.5d28da2c4612dp-56, 0x1.294062ed59f06p-2},99 {0x1.0c97c4afa2518p-56, 0x1.4135c94176601p-2},100 {-0x1.efdc0d58cf62p-62, 0x1.58f9a75ab1fddp-2},101 {-0x1.44b19e0864c5dp-56, 0x1.7088530fa459fp-2},102 {-0x1.72cedd3d5a61p-57, 0x1.87de2a6aea963p-2},103 {0x1.6da81290bdbabp-57, 0x1.9ef7943a8ed8ap-2},104 {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},105 {0x1.6850e59c37f8fp-58, 0x1.cc66e9931c45ep-2},106 {0x1.e0d891d3c6841p-58, 0x1.e2b5d3806f63bp-2},107 {-0x1.2ec1fc1b776b8p-60, 0x1.f8ba4dbf89abap-2},108 {-0x1.a5a014347406cp-55, 0x1.073879922ffeep-1},109 {-0x1.ef23b69abe4f1p-55, 0x1.11eb3541b4b23p-1},110 {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},111 {-0x1.5da743ef3770cp-55, 0x1.26d054cdd12dfp-1},112 {-0x1.efcc626f74a6fp-57, 0x1.30ff7fce17035p-1},113 {0x1.e3e25e3954964p-56, 0x1.3affa292050b9p-1},114 {0x1.8076a2cfdc6b3p-57, 0x1.44cf325091dd6p-1},115 {0x1.3c293edceb327p-57, 0x1.4e6cabbe3e5e9p-1},116 {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},117 {-0x1.251b352ff2a37p-56, 0x1.610b7551d2cdfp-1},118 {-0x1.bdd3413b26456p-55, 0x1.6a09e667f3bcdp-1},119 {0x1.0d4ef0f1d915cp-55, 0x1.72d0837efff96p-1},120 {-0x1.0f537acdf0ad7p-56, 0x1.7b5df226aafafp-1},121 {-0x1.6f420f8ea3475p-56, 0x1.83b0e0bff976ep-1},122 {-0x1.2c5e12ed1336dp-55, 0x1.8bc806b151741p-1},123 {0x1.3d419a920df0bp-55, 0x1.93a22499263fbp-1},124 {-0x1.30ee286712474p-55, 0x1.9b3e047f38741p-1},125 {-0x1.128bb015df175p-56, 0x1.a29a7a0462782p-1},126 {0x1.9f630e8b6dac8p-60, 0x1.a9b66290ea1a3p-1},127 {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},128 {-0x1.bc69f324e6d61p-55, 0x1.b728345196e3ep-1},129 {-0x1.825a732ac700ap-55, 0x1.bd7c0ac6f952ap-1},130 {-0x1.6e0b1757c8d07p-56, 0x1.c38b2f180bdb1p-1},131 {-0x1.2fb761e946603p-58, 0x1.c954b213411f5p-1},132 {-0x1.e7b6bb5ab58aep-58, 0x1.ced7af43cc773p-1},133 {-0x1.4ef5295d25af2p-55, 0x1.d4134d14dc93ap-1},134 {0x1.457e610231ac2p-56, 0x1.d906bcf328d46p-1},135 {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},136 {-0x1.014c76c126527p-55, 0x1.e212104f686e5p-1},137 {-0x1.16b56f2847754p-57, 0x1.e6288ec48e112p-1},138 {0x1.760b1e2e3f81ep-55, 0x1.e9f4156c62ddap-1},139 {0x1.e82c791f59cc2p-56, 0x1.ed740e7684963p-1},140 {0x1.52c7adc6b4989p-56, 0x1.f0a7efb9230d7p-1},141 {-0x1.d7bafb51f72e6p-56, 0x1.f38f3ac64e589p-1},142 {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},143 {0x1.ab256778ffcb6p-56, 0x1.f8764fa714ba9p-1},144 {-0x1.7a0a8ca13571fp-55, 0x1.fa7557f08a517p-1},145 {0x1.1ec8668ecaceep-55, 0x1.fc26470e19fd3p-1},146 {-0x1.87df6378811c7p-55, 0x1.fd88da3d12526p-1},147 {0x1.521ecd0c67e35p-57, 0x1.fe9cdad01883ap-1},148 {-0x1.c57bc2e24aa15p-57, 0x1.ff621e3796d7ep-1},149 {-0x1.1354d4556e4cbp-55, 0x1.ffd886084cd0dp-1},150 {0, 1},151#ifndef LIBC_MATH_HAS_SMALL_TABLES152 {-0x1.1354d4556e4cbp-55, 0x1.ffd886084cd0dp-1},153 {-0x1.c57bc2e24aa15p-57, 0x1.ff621e3796d7ep-1},154 {0x1.521ecd0c67e35p-57, 0x1.fe9cdad01883ap-1},155 {-0x1.87df6378811c7p-55, 0x1.fd88da3d12526p-1},156 {0x1.1ec8668ecaceep-55, 0x1.fc26470e19fd3p-1},157 {-0x1.7a0a8ca13571fp-55, 0x1.fa7557f08a517p-1},158 {0x1.ab256778ffcb6p-56, 0x1.f8764fa714ba9p-1},159 {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},160 {-0x1.d7bafb51f72e6p-56, 0x1.f38f3ac64e589p-1},161 {0x1.52c7adc6b4989p-56, 0x1.f0a7efb9230d7p-1},162 {0x1.e82c791f59cc2p-56, 0x1.ed740e7684963p-1},163 {0x1.760b1e2e3f81ep-55, 0x1.e9f4156c62ddap-1},164 {-0x1.16b56f2847754p-57, 0x1.e6288ec48e112p-1},165 {-0x1.014c76c126527p-55, 0x1.e212104f686e5p-1},166 {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},167 {0x1.457e610231ac2p-56, 0x1.d906bcf328d46p-1},168 {-0x1.4ef5295d25af2p-55, 0x1.d4134d14dc93ap-1},169 {-0x1.e7b6bb5ab58aep-58, 0x1.ced7af43cc773p-1},170 {-0x1.2fb761e946603p-58, 0x1.c954b213411f5p-1},171 {-0x1.6e0b1757c8d07p-56, 0x1.c38b2f180bdb1p-1},172 {-0x1.825a732ac700ap-55, 0x1.bd7c0ac6f952ap-1},173 {-0x1.bc69f324e6d61p-55, 0x1.b728345196e3ep-1},174 {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},175 {0x1.9f630e8b6dac8p-60, 0x1.a9b66290ea1a3p-1},176 {-0x1.128bb015df175p-56, 0x1.a29a7a0462782p-1},177 {-0x1.30ee286712474p-55, 0x1.9b3e047f38741p-1},178 {0x1.3d419a920df0bp-55, 0x1.93a22499263fbp-1},179 {-0x1.2c5e12ed1336dp-55, 0x1.8bc806b151741p-1},180 {-0x1.6f420f8ea3475p-56, 0x1.83b0e0bff976ep-1},181 {-0x1.0f537acdf0ad7p-56, 0x1.7b5df226aafafp-1},182 {0x1.0d4ef0f1d915cp-55, 0x1.72d0837efff96p-1},183 {-0x1.bdd3413b26456p-55, 0x1.6a09e667f3bcdp-1},184 {-0x1.251b352ff2a37p-56, 0x1.610b7551d2cdfp-1},185 {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},186 {0x1.3c293edceb327p-57, 0x1.4e6cabbe3e5e9p-1},187 {0x1.8076a2cfdc6b3p-57, 0x1.44cf325091dd6p-1},188 {0x1.e3e25e3954964p-56, 0x1.3affa292050b9p-1},189 {-0x1.efcc626f74a6fp-57, 0x1.30ff7fce17035p-1},190 {-0x1.5da743ef3770cp-55, 0x1.26d054cdd12dfp-1},191 {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},192 {-0x1.ef23b69abe4f1p-55, 0x1.11eb3541b4b23p-1},193 {-0x1.a5a014347406cp-55, 0x1.073879922ffeep-1},194 {-0x1.2ec1fc1b776b8p-60, 0x1.f8ba4dbf89abap-2},195 {0x1.e0d891d3c6841p-58, 0x1.e2b5d3806f63bp-2},196 {0x1.6850e59c37f8fp-58, 0x1.cc66e9931c45ep-2},197 {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},198 {0x1.6da81290bdbabp-57, 0x1.9ef7943a8ed8ap-2},199 {-0x1.72cedd3d5a61p-57, 0x1.87de2a6aea963p-2},200 {-0x1.44b19e0864c5dp-56, 0x1.7088530fa459fp-2},201 {-0x1.efdc0d58cf62p-62, 0x1.58f9a75ab1fddp-2},202 {0x1.0c97c4afa2518p-56, 0x1.4135c94176601p-2},203 {-0x1.5d28da2c4612dp-56, 0x1.294062ed59f06p-2},204 {0x1.824c20ab7aa9ap-56, 0x1.111d262b1f677p-2},205 {-0x1.42deef11da2c4p-57, 0x1.f19f97b215f1bp-3},206 {-0x1.af1439e521935p-62, 0x1.c0b826a7e4f63p-3},207 {-0x1.26d19b9ff8d82p-57, 0x1.8f8b83c69a60bp-3},208 {0x1.531ff779ddac6p-57, 0x1.5e214448b3fc6p-3},209 {0x1.13000a89a11ep-58, 0x1.2c8106e8e613ap-3},210 {0x1.a2704729ae56dp-59, 0x1.f564e56a9730ep-4},211 {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},212 {-0x1.9a088a8bf6b2cp-59, 0x1.2d52092ce19f6p-4},213 {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},214 {-0x1.b1d63091a013p-64, 0x1.92155f7a3667ep-6},215 {0, 0},216 {0x1.b1d63091a013p-64, -0x1.92155f7a3667ep-6},217 {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},218 {0x1.9a088a8bf6b2cp-59, -0x1.2d52092ce19f6p-4},219 {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},220 {-0x1.a2704729ae56dp-59, -0x1.f564e56a9730ep-4},221 {-0x1.13000a89a11ep-58, -0x1.2c8106e8e613ap-3},222 {-0x1.531ff779ddac6p-57, -0x1.5e214448b3fc6p-3},223 {0x1.26d19b9ff8d82p-57, -0x1.8f8b83c69a60bp-3},224 {0x1.af1439e521935p-62, -0x1.c0b826a7e4f63p-3},225 {0x1.42deef11da2c4p-57, -0x1.f19f97b215f1bp-3},226 {-0x1.824c20ab7aa9ap-56, -0x1.111d262b1f677p-2},227 {0x1.5d28da2c4612dp-56, -0x1.294062ed59f06p-2},228 {-0x1.0c97c4afa2518p-56, -0x1.4135c94176601p-2},229 {0x1.efdc0d58cf62p-62, -0x1.58f9a75ab1fddp-2},230 {0x1.44b19e0864c5dp-56, -0x1.7088530fa459fp-2},231 {0x1.72cedd3d5a61p-57, -0x1.87de2a6aea963p-2},232 {-0x1.6da81290bdbabp-57, -0x1.9ef7943a8ed8ap-2},233 {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},234 {-0x1.6850e59c37f8fp-58, -0x1.cc66e9931c45ep-2},235 {-0x1.e0d891d3c6841p-58, -0x1.e2b5d3806f63bp-2},236 {0x1.2ec1fc1b776b8p-60, -0x1.f8ba4dbf89abap-2},237 {0x1.a5a014347406cp-55, -0x1.073879922ffeep-1},238 {0x1.ef23b69abe4f1p-55, -0x1.11eb3541b4b23p-1},239 {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},240 {0x1.5da743ef3770cp-55, -0x1.26d054cdd12dfp-1},241 {0x1.efcc626f74a6fp-57, -0x1.30ff7fce17035p-1},242 {-0x1.e3e25e3954964p-56, -0x1.3affa292050b9p-1},243 {-0x1.8076a2cfdc6b3p-57, -0x1.44cf325091dd6p-1},244 {-0x1.3c293edceb327p-57, -0x1.4e6cabbe3e5e9p-1},245 {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},246 {0x1.251b352ff2a37p-56, -0x1.610b7551d2cdfp-1},247 {0x1.bdd3413b26456p-55, -0x1.6a09e667f3bcdp-1},248 {-0x1.0d4ef0f1d915cp-55, -0x1.72d0837efff96p-1},249 {0x1.0f537acdf0ad7p-56, -0x1.7b5df226aafafp-1},250 {0x1.6f420f8ea3475p-56, -0x1.83b0e0bff976ep-1},251 {0x1.2c5e12ed1336dp-55, -0x1.8bc806b151741p-1},252 {-0x1.3d419a920df0bp-55, -0x1.93a22499263fbp-1},253 {0x1.30ee286712474p-55, -0x1.9b3e047f38741p-1},254 {0x1.128bb015df175p-56, -0x1.a29a7a0462782p-1},255 {-0x1.9f630e8b6dac8p-60, -0x1.a9b66290ea1a3p-1},256 {0x1.926da300ffccep-55, -0x1.b090a581502p-1},257 {0x1.bc69f324e6d61p-55, -0x1.b728345196e3ep-1},258 {0x1.825a732ac700ap-55, -0x1.bd7c0ac6f952ap-1},259 {0x1.6e0b1757c8d07p-56, -0x1.c38b2f180bdb1p-1},260 {0x1.2fb761e946603p-58, -0x1.c954b213411f5p-1},261 {0x1.e7b6bb5ab58aep-58, -0x1.ced7af43cc773p-1},262 {0x1.4ef5295d25af2p-55, -0x1.d4134d14dc93ap-1},263 {-0x1.457e610231ac2p-56, -0x1.d906bcf328d46p-1},264 {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},265 {0x1.014c76c126527p-55, -0x1.e212104f686e5p-1},266 {0x1.16b56f2847754p-57, -0x1.e6288ec48e112p-1},267 {-0x1.760b1e2e3f81ep-55, -0x1.e9f4156c62ddap-1},268 {-0x1.e82c791f59cc2p-56, -0x1.ed740e7684963p-1},269 {-0x1.52c7adc6b4989p-56, -0x1.f0a7efb9230d7p-1},270 {0x1.d7bafb51f72e6p-56, -0x1.f38f3ac64e589p-1},271 {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},272 {-0x1.ab256778ffcb6p-56, -0x1.f8764fa714ba9p-1},273 {0x1.7a0a8ca13571fp-55, -0x1.fa7557f08a517p-1},274 {-0x1.1ec8668ecaceep-55, -0x1.fc26470e19fd3p-1},275 {0x1.87df6378811c7p-55, -0x1.fd88da3d12526p-1},276 {-0x1.521ecd0c67e35p-57, -0x1.fe9cdad01883ap-1},277 {0x1.c57bc2e24aa15p-57, -0x1.ff621e3796d7ep-1},278 {0x1.1354d4556e4cbp-55, -0x1.ffd886084cd0dp-1},279 {0, -1},280 {0x1.1354d4556e4cbp-55, -0x1.ffd886084cd0dp-1},281 {0x1.c57bc2e24aa15p-57, -0x1.ff621e3796d7ep-1},282 {-0x1.521ecd0c67e35p-57, -0x1.fe9cdad01883ap-1},283 {0x1.87df6378811c7p-55, -0x1.fd88da3d12526p-1},284 {-0x1.1ec8668ecaceep-55, -0x1.fc26470e19fd3p-1},285 {0x1.7a0a8ca13571fp-55, -0x1.fa7557f08a517p-1},286 {-0x1.ab256778ffcb6p-56, -0x1.f8764fa714ba9p-1},287 {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},288 {0x1.d7bafb51f72e6p-56, -0x1.f38f3ac64e589p-1},289 {-0x1.52c7adc6b4989p-56, -0x1.f0a7efb9230d7p-1},290 {-0x1.e82c791f59cc2p-56, -0x1.ed740e7684963p-1},291 {-0x1.760b1e2e3f81ep-55, -0x1.e9f4156c62ddap-1},292 {0x1.16b56f2847754p-57, -0x1.e6288ec48e112p-1},293 {0x1.014c76c126527p-55, -0x1.e212104f686e5p-1},294 {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},295 {-0x1.457e610231ac2p-56, -0x1.d906bcf328d46p-1},296 {0x1.4ef5295d25af2p-55, -0x1.d4134d14dc93ap-1},297 {0x1.e7b6bb5ab58aep-58, -0x1.ced7af43cc773p-1},298 {0x1.2fb761e946603p-58, -0x1.c954b213411f5p-1},299 {0x1.6e0b1757c8d07p-56, -0x1.c38b2f180bdb1p-1},300 {0x1.825a732ac700ap-55, -0x1.bd7c0ac6f952ap-1},301 {0x1.bc69f324e6d61p-55, -0x1.b728345196e3ep-1},302 {0x1.926da300ffccep-55, -0x1.b090a581502p-1},303 {-0x1.9f630e8b6dac8p-60, -0x1.a9b66290ea1a3p-1},304 {0x1.128bb015df175p-56, -0x1.a29a7a0462782p-1},305 {0x1.30ee286712474p-55, -0x1.9b3e047f38741p-1},306 {-0x1.3d419a920df0bp-55, -0x1.93a22499263fbp-1},307 {0x1.2c5e12ed1336dp-55, -0x1.8bc806b151741p-1},308 {0x1.6f420f8ea3475p-56, -0x1.83b0e0bff976ep-1},309 {0x1.0f537acdf0ad7p-56, -0x1.7b5df226aafafp-1},310 {-0x1.0d4ef0f1d915cp-55, -0x1.72d0837efff96p-1},311 {0x1.bdd3413b26456p-55, -0x1.6a09e667f3bcdp-1},312 {0x1.251b352ff2a37p-56, -0x1.610b7551d2cdfp-1},313 {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},314 {-0x1.3c293edceb327p-57, -0x1.4e6cabbe3e5e9p-1},315 {-0x1.8076a2cfdc6b3p-57, -0x1.44cf325091dd6p-1},316 {-0x1.e3e25e3954964p-56, -0x1.3affa292050b9p-1},317 {0x1.efcc626f74a6fp-57, -0x1.30ff7fce17035p-1},318 {0x1.5da743ef3770cp-55, -0x1.26d054cdd12dfp-1},319 {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},320 {0x1.ef23b69abe4f1p-55, -0x1.11eb3541b4b23p-1},321 {0x1.a5a014347406cp-55, -0x1.073879922ffeep-1},322 {0x1.2ec1fc1b776b8p-60, -0x1.f8ba4dbf89abap-2},323 {-0x1.e0d891d3c6841p-58, -0x1.e2b5d3806f63bp-2},324 {-0x1.6850e59c37f8fp-58, -0x1.cc66e9931c45ep-2},325 {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},326 {-0x1.6da81290bdbabp-57, -0x1.9ef7943a8ed8ap-2},327 {0x1.72cedd3d5a61p-57, -0x1.87de2a6aea963p-2},328 {0x1.44b19e0864c5dp-56, -0x1.7088530fa459fp-2},329 {0x1.efdc0d58cf62p-62, -0x1.58f9a75ab1fddp-2},330 {-0x1.0c97c4afa2518p-56, -0x1.4135c94176601p-2},331 {0x1.5d28da2c4612dp-56, -0x1.294062ed59f06p-2},332 {-0x1.824c20ab7aa9ap-56, -0x1.111d262b1f677p-2},333 {0x1.42deef11da2c4p-57, -0x1.f19f97b215f1bp-3},334 {0x1.af1439e521935p-62, -0x1.c0b826a7e4f63p-3},335 {0x1.26d19b9ff8d82p-57, -0x1.8f8b83c69a60bp-3},336 {-0x1.531ff779ddac6p-57, -0x1.5e214448b3fc6p-3},337 {-0x1.13000a89a11ep-58, -0x1.2c8106e8e613ap-3},338 {-0x1.a2704729ae56dp-59, -0x1.f564e56a9730ep-4},339 {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},340 {0x1.9a088a8bf6b2cp-59, -0x1.2d52092ce19f6p-4},341 {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},342 {0x1.b1d63091a013p-64, -0x1.92155f7a3667ep-6},343#endif // !LIBC_MATH_HAS_SMALL_TABLES344};345 346} // namespace range_reduction_double_internal347 348} // namespace math349 350} // namespace LIBC_NAMESPACE_DECL351 352#endif // LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_FMA_H353