356 lines · c
1//===-- Range reduction for double precision sin/cos/tan --------*- 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_NOFMA_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_NOFMA_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/common.h"17#include "src/__support/macros/config.h"18#include "src/__support/macros/optimization.h"19#include "src/__support/math/range_reduction_double_common.h"20 21namespace LIBC_NAMESPACE_DECL {22 23namespace math {24 25namespace range_reduction_double_internal {26 27using fputil::DoubleDouble;28 29LIBC_INLINE unsigned LargeRangeReduction::fast(double x, DoubleDouble &u) {30 using FPBits = typename fputil::FPBits<double>;31 FPBits xbits(x);32 33 int x_e_m62 = xbits.get_biased_exponent() - (FPBits::EXP_BIAS + 62);34 idx = static_cast<unsigned>((x_e_m62 >> 4) + 3);35 // Scale x down by 2^(-(16 * (idx - 3))36 xbits.set_biased_exponent((x_e_m62 & 15) + FPBits::EXP_BIAS + 62);37 // 2^62 <= |x_reduced| < 2^(62 + 16) = 2^7838 x_reduced = xbits.get_val();39 // x * c_hi = ph.hi + ph.lo exactly.40 DoubleDouble x_split = fputil::split(x_reduced);41 DoubleDouble ph = fputil::exact_mult<double, SPLIT>(42 x_split, x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][0]);43 // x * c_mid = pm.hi + pm.lo exactly.44 DoubleDouble pm = fputil::exact_mult<double, SPLIT>(45 x_split, x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][1]);46 // x * c_lo = pl.hi + pl.lo exactly.47 DoubleDouble pl = fputil::exact_mult<double, SPLIT>(48 x_split, x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][2]);49 // Extract integral parts and fractional parts of (ph.lo + pm.hi).50 double sum_hi = ph.lo + pm.hi;51 double kd = fputil::nearest_integer(sum_hi);52 53 // x * 128/pi mod 1 ~ y_hi + y_mid + y_lo54 y_hi = (ph.lo - kd) + pm.hi; // Exact55 y_mid = fputil::exact_add(pm.lo, pl.hi);56 y_lo = pl.lo;57 58 // y_l = x * c_lo_2 + pl.lo59 double y_l =60 fputil::multiply_add(x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][3], y_lo);61 DoubleDouble y = fputil::exact_add(y_hi, y_mid.hi);62 y.lo += (y_mid.lo + y_l);63 64 // Digits of pi/128, generated by Sollya with:65 // > a = round(pi/128, D, RN);66 // > b = round(pi/128 - a, D, RN);67 constexpr DoubleDouble PI_OVER_128_DD = {0x1.1a62633145c07p-60,68 0x1.921fb54442d18p-6};69 70 // Error bound: with {a} denote the fractional part of a, i.e.:71 // {a} = a - round(a)72 // Then,73 // | {x * 128/pi} - (y_hi + y_lo) | <= ulp(ulp(y_hi)) <= 2^-10574 // | {x mod pi/128} - (u.hi + u.lo) | < 2 * 2^-6 * 2^-105 = 2^-11075 u = fputil::quick_mult<SPLIT>(y, PI_OVER_128_DD);76 77 return static_cast<unsigned>(static_cast<int64_t>(kd));78}79 80// Lookup table for sin(k * pi / 128) with k = 0, ..., 255.81// Table is generated with Sollya as follow:82// > display = hexadecimal;83// > for k from 0 to 255 do {84// a = round(sin(k * pi/128), 51, RN);85// b = round(sin(k * pi/128) - a, D, RN);86// print("{", b, ",", a, "},");87// };88LIBC_INLINE constexpr DoubleDouble SIN_K_PI_OVER_128[] = {89 {0, 0},90 {0x1.f938a73db97fbp-58, 0x1.92155f7a3667cp-6},91 {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},92 {0x1.ccbeeeae8129ap-56, 0x1.2d52092ce19f4p-4},93 {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},94 {-0x1.cbb1f71aca352p-56, 0x1.f564e56a9731p-4},95 {-0x1.dd9ffeaecbdc4p-55, 0x1.2c8106e8e613cp-3},96 {-0x1.ab3802218894fp-55, 0x1.5e214448b3fc8p-3},97 {-0x1.49b466e7fe36p-55, 0x1.8f8b83c69a60cp-3},98 {-0x1.035e2873ca432p-55, 0x1.c0b826a7e4f64p-3},99 {-0x1.50b7bbc4768b1p-55, 0x1.f19f97b215f1cp-3},100 {-0x1.3ed9efaa42ab3p-55, 0x1.111d262b1f678p-2},101 {0x1.a8b5c974ee7b5p-54, 0x1.294062ed59f04p-2},102 {0x1.4325f12be8946p-54, 0x1.4135c941766p-2},103 {0x1.fc2047e54e614p-55, 0x1.58f9a75ab1fdcp-2},104 {-0x1.512c678219317p-54, 0x1.7088530fa45ap-2},105 {-0x1.2e59dba7ab4c2p-54, 0x1.87de2a6aea964p-2},106 {-0x1.d24afdade848bp-54, 0x1.9ef7943a8ed8cp-2},107 {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},108 {-0x1.e97af1a63c807p-54, 0x1.cc66e9931c46p-2},109 {-0x1.c3e4edc5872f8p-55, 0x1.e2b5d3806f63cp-2},110 {0x1.fb44f80f92225p-54, 0x1.f8ba4dbf89ab8p-2},111 {0x1.9697faf2e2fe5p-53, 0x1.073879922ffecp-1},112 {-0x1.7bc8eda6af93cp-53, 0x1.11eb3541b4b24p-1},113 {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},114 {-0x1.5769d0fbcddc3p-53, 0x1.26d054cdd12ep-1},115 {0x1.c20673b2116b2p-54, 0x1.30ff7fce17034p-1},116 {0x1.3c7c4bc72a92cp-53, 0x1.3affa292050b8p-1},117 {-0x1.e7f895d302395p-53, 0x1.44cf325091dd8p-1},118 {0x1.13c293edceb32p-53, 0x1.4e6cabbe3e5e8p-1},119 {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},120 {-0x1.24a366a5fe547p-53, 0x1.610b7551d2cep-1},121 {0x1.21165f626cdd5p-54, 0x1.6a09e667f3bccp-1},122 {-0x1.bcac43c389ba9p-53, 0x1.72d0837efff98p-1},123 {-0x1.21ea6f59be15bp-53, 0x1.7b5df226aafbp-1},124 {0x1.d217be0e2b971p-53, 0x1.83b0e0bff976cp-1},125 {0x1.69d0f6897664ap-54, 0x1.8bc806b15174p-1},126 {-0x1.615f32b6f907ap-54, 0x1.93a22499263fcp-1},127 {0x1.6788ebcc76dc6p-54, 0x1.9b3e047f3874p-1},128 {0x1.ddae89fd441d1p-53, 0x1.a29a7a046278p-1},129 {-0x1.f98273c5d2495p-54, 0x1.a9b66290ea1a4p-1},130 {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},131 {0x1.90e58336c64a8p-53, 0x1.b728345196e3cp-1},132 {0x1.9f6963354e3fep-53, 0x1.bd7c0ac6f9528p-1},133 {0x1.a47d3a2a0dcbep-54, 0x1.c38b2f180bdbp-1},134 {0x1.ed0489e16b9ap-54, 0x1.c954b213411f4p-1},135 {-0x1.0f3db5dad5ac5p-53, 0x1.ced7af43cc774p-1},136 {0x1.ac42b5a8b6943p-53, 0x1.d4134d14dc938p-1},137 {-0x1.d75033dfb9ca8p-53, 0x1.d906bcf328d48p-1},138 {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},139 {0x1.7f59c49f6cd6dp-54, 0x1.e212104f686e4p-1},140 {0x1.ee94a90d7b88bp-53, 0x1.e6288ec48e11p-1},141 {-0x1.a27d3874701f9p-53, 0x1.e9f4156c62ddcp-1},142 {-0x1.85f4e1b8298dp-54, 0x1.ed740e7684964p-1},143 {-0x1.ab4e148e52d9ep-54, 0x1.f0a7efb9230d8p-1},144 {0x1.8a11412b82346p-54, 0x1.f38f3ac64e588p-1},145 {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},146 {0x1.3564acef1ff97p-53, 0x1.f8764fa714ba8p-1},147 {-0x1.5e82a3284d5c8p-53, 0x1.fa7557f08a518p-1},148 {-0x1.709bccb89a989p-54, 0x1.fc26470e19fd4p-1},149 {0x1.9e082721dfb8ep-53, 0x1.fd88da3d12524p-1},150 {-0x1.eade132f3981dp-53, 0x1.fe9cdad01883cp-1},151 {0x1.e3a843d1db55fp-53, 0x1.ff621e3796d7cp-1},152 {0x1.765595d548d9ap-54, 0x1.ffd886084cd0cp-1},153 {0, 1},154#ifndef LIBC_MATH_HAS_SMALL_TABLES155 {0x1.765595d548d9ap-54, 0x1.ffd886084cd0cp-1},156 {0x1.e3a843d1db55fp-53, 0x1.ff621e3796d7cp-1},157 {-0x1.eade132f3981dp-53, 0x1.fe9cdad01883cp-1},158 {0x1.9e082721dfb8ep-53, 0x1.fd88da3d12524p-1},159 {-0x1.709bccb89a989p-54, 0x1.fc26470e19fd4p-1},160 {-0x1.5e82a3284d5c8p-53, 0x1.fa7557f08a518p-1},161 {0x1.3564acef1ff97p-53, 0x1.f8764fa714ba8p-1},162 {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},163 {0x1.8a11412b82346p-54, 0x1.f38f3ac64e588p-1},164 {-0x1.ab4e148e52d9ep-54, 0x1.f0a7efb9230d8p-1},165 {-0x1.85f4e1b8298dp-54, 0x1.ed740e7684964p-1},166 {-0x1.a27d3874701f9p-53, 0x1.e9f4156c62ddcp-1},167 {0x1.ee94a90d7b88bp-53, 0x1.e6288ec48e11p-1},168 {0x1.7f59c49f6cd6dp-54, 0x1.e212104f686e4p-1},169 {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},170 {-0x1.d75033dfb9ca8p-53, 0x1.d906bcf328d48p-1},171 {0x1.ac42b5a8b6943p-53, 0x1.d4134d14dc938p-1},172 {-0x1.0f3db5dad5ac5p-53, 0x1.ced7af43cc774p-1},173 {0x1.ed0489e16b9ap-54, 0x1.c954b213411f4p-1},174 {0x1.a47d3a2a0dcbep-54, 0x1.c38b2f180bdbp-1},175 {0x1.9f6963354e3fep-53, 0x1.bd7c0ac6f9528p-1},176 {0x1.90e58336c64a8p-53, 0x1.b728345196e3cp-1},177 {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},178 {-0x1.f98273c5d2495p-54, 0x1.a9b66290ea1a4p-1},179 {0x1.ddae89fd441d1p-53, 0x1.a29a7a046278p-1},180 {0x1.6788ebcc76dc6p-54, 0x1.9b3e047f3874p-1},181 {-0x1.615f32b6f907ap-54, 0x1.93a22499263fcp-1},182 {0x1.69d0f6897664ap-54, 0x1.8bc806b15174p-1},183 {0x1.d217be0e2b971p-53, 0x1.83b0e0bff976cp-1},184 {-0x1.21ea6f59be15bp-53, 0x1.7b5df226aafbp-1},185 {-0x1.bcac43c389ba9p-53, 0x1.72d0837efff98p-1},186 {0x1.21165f626cdd5p-54, 0x1.6a09e667f3bccp-1},187 {-0x1.24a366a5fe547p-53, 0x1.610b7551d2cep-1},188 {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},189 {0x1.13c293edceb32p-53, 0x1.4e6cabbe3e5e8p-1},190 {-0x1.e7f895d302395p-53, 0x1.44cf325091dd8p-1},191 {0x1.3c7c4bc72a92cp-53, 0x1.3affa292050b8p-1},192 {0x1.c20673b2116b2p-54, 0x1.30ff7fce17034p-1},193 {-0x1.5769d0fbcddc3p-53, 0x1.26d054cdd12ep-1},194 {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},195 {-0x1.7bc8eda6af93cp-53, 0x1.11eb3541b4b24p-1},196 {0x1.9697faf2e2fe5p-53, 0x1.073879922ffecp-1},197 {0x1.fb44f80f92225p-54, 0x1.f8ba4dbf89ab8p-2},198 {-0x1.c3e4edc5872f8p-55, 0x1.e2b5d3806f63cp-2},199 {-0x1.e97af1a63c807p-54, 0x1.cc66e9931c46p-2},200 {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},201 {-0x1.d24afdade848bp-54, 0x1.9ef7943a8ed8cp-2},202 {-0x1.2e59dba7ab4c2p-54, 0x1.87de2a6aea964p-2},203 {-0x1.512c678219317p-54, 0x1.7088530fa45ap-2},204 {0x1.fc2047e54e614p-55, 0x1.58f9a75ab1fdcp-2},205 {0x1.4325f12be8946p-54, 0x1.4135c941766p-2},206 {0x1.a8b5c974ee7b5p-54, 0x1.294062ed59f04p-2},207 {-0x1.3ed9efaa42ab3p-55, 0x1.111d262b1f678p-2},208 {-0x1.50b7bbc4768b1p-55, 0x1.f19f97b215f1cp-3},209 {-0x1.035e2873ca432p-55, 0x1.c0b826a7e4f64p-3},210 {-0x1.49b466e7fe36p-55, 0x1.8f8b83c69a60cp-3},211 {-0x1.ab3802218894fp-55, 0x1.5e214448b3fc8p-3},212 {-0x1.dd9ffeaecbdc4p-55, 0x1.2c8106e8e613cp-3},213 {-0x1.cbb1f71aca352p-56, 0x1.f564e56a9731p-4},214 {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},215 {0x1.ccbeeeae8129ap-56, 0x1.2d52092ce19f4p-4},216 {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},217 {0x1.f938a73db97fbp-58, 0x1.92155f7a3667cp-6},218 {0, 0},219 {-0x1.f938a73db97fbp-58, -0x1.92155f7a3667cp-6},220 {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},221 {-0x1.ccbeeeae8129ap-56, -0x1.2d52092ce19f4p-4},222 {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},223 {0x1.cbb1f71aca352p-56, -0x1.f564e56a9731p-4},224 {0x1.dd9ffeaecbdc4p-55, -0x1.2c8106e8e613cp-3},225 {0x1.ab3802218894fp-55, -0x1.5e214448b3fc8p-3},226 {0x1.49b466e7fe36p-55, -0x1.8f8b83c69a60cp-3},227 {0x1.035e2873ca432p-55, -0x1.c0b826a7e4f64p-3},228 {0x1.50b7bbc4768b1p-55, -0x1.f19f97b215f1cp-3},229 {0x1.3ed9efaa42ab3p-55, -0x1.111d262b1f678p-2},230 {-0x1.a8b5c974ee7b5p-54, -0x1.294062ed59f04p-2},231 {-0x1.4325f12be8946p-54, -0x1.4135c941766p-2},232 {-0x1.fc2047e54e614p-55, -0x1.58f9a75ab1fdcp-2},233 {0x1.512c678219317p-54, -0x1.7088530fa45ap-2},234 {0x1.2e59dba7ab4c2p-54, -0x1.87de2a6aea964p-2},235 {0x1.d24afdade848bp-54, -0x1.9ef7943a8ed8cp-2},236 {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},237 {0x1.e97af1a63c807p-54, -0x1.cc66e9931c46p-2},238 {0x1.c3e4edc5872f8p-55, -0x1.e2b5d3806f63cp-2},239 {-0x1.fb44f80f92225p-54, -0x1.f8ba4dbf89ab8p-2},240 {-0x1.9697faf2e2fe5p-53, -0x1.073879922ffecp-1},241 {0x1.7bc8eda6af93cp-53, -0x1.11eb3541b4b24p-1},242 {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},243 {0x1.5769d0fbcddc3p-53, -0x1.26d054cdd12ep-1},244 {-0x1.c20673b2116b2p-54, -0x1.30ff7fce17034p-1},245 {-0x1.3c7c4bc72a92cp-53, -0x1.3affa292050b8p-1},246 {0x1.e7f895d302395p-53, -0x1.44cf325091dd8p-1},247 {-0x1.13c293edceb32p-53, -0x1.4e6cabbe3e5e8p-1},248 {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},249 {0x1.24a366a5fe547p-53, -0x1.610b7551d2cep-1},250 {-0x1.21165f626cdd5p-54, -0x1.6a09e667f3bccp-1},251 {0x1.bcac43c389ba9p-53, -0x1.72d0837efff98p-1},252 {0x1.21ea6f59be15bp-53, -0x1.7b5df226aafbp-1},253 {-0x1.d217be0e2b971p-53, -0x1.83b0e0bff976cp-1},254 {-0x1.69d0f6897664ap-54, -0x1.8bc806b15174p-1},255 {0x1.615f32b6f907ap-54, -0x1.93a22499263fcp-1},256 {-0x1.6788ebcc76dc6p-54, -0x1.9b3e047f3874p-1},257 {-0x1.ddae89fd441d1p-53, -0x1.a29a7a046278p-1},258 {0x1.f98273c5d2495p-54, -0x1.a9b66290ea1a4p-1},259 {0x1.926da300ffccep-55, -0x1.b090a581502p-1},260 {-0x1.90e58336c64a8p-53, -0x1.b728345196e3cp-1},261 {-0x1.9f6963354e3fep-53, -0x1.bd7c0ac6f9528p-1},262 {-0x1.a47d3a2a0dcbep-54, -0x1.c38b2f180bdbp-1},263 {-0x1.ed0489e16b9ap-54, -0x1.c954b213411f4p-1},264 {0x1.0f3db5dad5ac5p-53, -0x1.ced7af43cc774p-1},265 {-0x1.ac42b5a8b6943p-53, -0x1.d4134d14dc938p-1},266 {0x1.d75033dfb9ca8p-53, -0x1.d906bcf328d48p-1},267 {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},268 {-0x1.7f59c49f6cd6dp-54, -0x1.e212104f686e4p-1},269 {-0x1.ee94a90d7b88bp-53, -0x1.e6288ec48e11p-1},270 {0x1.a27d3874701f9p-53, -0x1.e9f4156c62ddcp-1},271 {0x1.85f4e1b8298dp-54, -0x1.ed740e7684964p-1},272 {0x1.ab4e148e52d9ep-54, -0x1.f0a7efb9230d8p-1},273 {-0x1.8a11412b82346p-54, -0x1.f38f3ac64e588p-1},274 {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},275 {-0x1.3564acef1ff97p-53, -0x1.f8764fa714ba8p-1},276 {0x1.5e82a3284d5c8p-53, -0x1.fa7557f08a518p-1},277 {0x1.709bccb89a989p-54, -0x1.fc26470e19fd4p-1},278 {-0x1.9e082721dfb8ep-53, -0x1.fd88da3d12524p-1},279 {0x1.eade132f3981dp-53, -0x1.fe9cdad01883cp-1},280 {-0x1.e3a843d1db55fp-53, -0x1.ff621e3796d7cp-1},281 {-0x1.765595d548d9ap-54, -0x1.ffd886084cd0cp-1},282 {0, -1},283 {-0x1.765595d548d9ap-54, -0x1.ffd886084cd0cp-1},284 {-0x1.e3a843d1db55fp-53, -0x1.ff621e3796d7cp-1},285 {0x1.eade132f3981dp-53, -0x1.fe9cdad01883cp-1},286 {-0x1.9e082721dfb8ep-53, -0x1.fd88da3d12524p-1},287 {0x1.709bccb89a989p-54, -0x1.fc26470e19fd4p-1},288 {0x1.5e82a3284d5c8p-53, -0x1.fa7557f08a518p-1},289 {-0x1.3564acef1ff97p-53, -0x1.f8764fa714ba8p-1},290 {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},291 {-0x1.8a11412b82346p-54, -0x1.f38f3ac64e588p-1},292 {0x1.ab4e148e52d9ep-54, -0x1.f0a7efb9230d8p-1},293 {0x1.85f4e1b8298dp-54, -0x1.ed740e7684964p-1},294 {0x1.a27d3874701f9p-53, -0x1.e9f4156c62ddcp-1},295 {-0x1.ee94a90d7b88bp-53, -0x1.e6288ec48e11p-1},296 {-0x1.7f59c49f6cd6dp-54, -0x1.e212104f686e4p-1},297 {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},298 {0x1.d75033dfb9ca8p-53, -0x1.d906bcf328d48p-1},299 {-0x1.ac42b5a8b6943p-53, -0x1.d4134d14dc938p-1},300 {0x1.0f3db5dad5ac5p-53, -0x1.ced7af43cc774p-1},301 {-0x1.ed0489e16b9ap-54, -0x1.c954b213411f4p-1},302 {-0x1.a47d3a2a0dcbep-54, -0x1.c38b2f180bdbp-1},303 {-0x1.9f6963354e3fep-53, -0x1.bd7c0ac6f9528p-1},304 {-0x1.90e58336c64a8p-53, -0x1.b728345196e3cp-1},305 {0x1.926da300ffccep-55, -0x1.b090a581502p-1},306 {0x1.f98273c5d2495p-54, -0x1.a9b66290ea1a4p-1},307 {-0x1.ddae89fd441d1p-53, -0x1.a29a7a046278p-1},308 {-0x1.6788ebcc76dc6p-54, -0x1.9b3e047f3874p-1},309 {0x1.615f32b6f907ap-54, -0x1.93a22499263fcp-1},310 {-0x1.69d0f6897664ap-54, -0x1.8bc806b15174p-1},311 {-0x1.d217be0e2b971p-53, -0x1.83b0e0bff976cp-1},312 {0x1.21ea6f59be15bp-53, -0x1.7b5df226aafbp-1},313 {0x1.bcac43c389ba9p-53, -0x1.72d0837efff98p-1},314 {-0x1.21165f626cdd5p-54, -0x1.6a09e667f3bccp-1},315 {0x1.24a366a5fe547p-53, -0x1.610b7551d2cep-1},316 {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},317 {-0x1.13c293edceb32p-53, -0x1.4e6cabbe3e5e8p-1},318 {0x1.e7f895d302395p-53, -0x1.44cf325091dd8p-1},319 {-0x1.3c7c4bc72a92cp-53, -0x1.3affa292050b8p-1},320 {-0x1.c20673b2116b2p-54, -0x1.30ff7fce17034p-1},321 {0x1.5769d0fbcddc3p-53, -0x1.26d054cdd12ep-1},322 {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},323 {0x1.7bc8eda6af93cp-53, -0x1.11eb3541b4b24p-1},324 {-0x1.9697faf2e2fe5p-53, -0x1.073879922ffecp-1},325 {-0x1.fb44f80f92225p-54, -0x1.f8ba4dbf89ab8p-2},326 {0x1.c3e4edc5872f8p-55, -0x1.e2b5d3806f63cp-2},327 {0x1.e97af1a63c807p-54, -0x1.cc66e9931c46p-2},328 {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},329 {0x1.d24afdade848bp-54, -0x1.9ef7943a8ed8cp-2},330 {0x1.2e59dba7ab4c2p-54, -0x1.87de2a6aea964p-2},331 {0x1.512c678219317p-54, -0x1.7088530fa45ap-2},332 {-0x1.fc2047e54e614p-55, -0x1.58f9a75ab1fdcp-2},333 {-0x1.4325f12be8946p-54, -0x1.4135c941766p-2},334 {-0x1.a8b5c974ee7b5p-54, -0x1.294062ed59f04p-2},335 {0x1.3ed9efaa42ab3p-55, -0x1.111d262b1f678p-2},336 {0x1.50b7bbc4768b1p-55, -0x1.f19f97b215f1cp-3},337 {0x1.035e2873ca432p-55, -0x1.c0b826a7e4f64p-3},338 {0x1.49b466e7fe36p-55, -0x1.8f8b83c69a60cp-3},339 {0x1.ab3802218894fp-55, -0x1.5e214448b3fc8p-3},340 {0x1.dd9ffeaecbdc4p-55, -0x1.2c8106e8e613cp-3},341 {0x1.cbb1f71aca352p-56, -0x1.f564e56a9731p-4},342 {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},343 {-0x1.ccbeeeae8129ap-56, -0x1.2d52092ce19f4p-4},344 {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},345 {-0x1.f938a73db97fbp-58, -0x1.92155f7a3667cp-6},346#endif // !LIBC_MATH_HAS_SMALL_TABLES347};348 349} // namespace range_reduction_double_internal350 351} // namespace math352 353} // namespace LIBC_NAMESPACE_DECL354 355#endif // LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_NOFMA_H356