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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-exception
6//
7//===----------------------------------------------------------------------===//
8
9#ifndef LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_NOFMA_H
10#define LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_NOFMA_H
11
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/math/generic/range_reduction_double_common.h"
20
21namespace LIBC_NAMESPACE_DECL {
22
23using fputil::DoubleDouble;
24
25LIBC_INLINE unsigned LargeRangeReduction::fast(double x, DoubleDouble &u) {
26 using FPBits = typename fputil::FPBits<double>;
27 FPBits xbits(x);
28
29 int x_e_m62 = xbits.get_biased_exponent() - (FPBits::EXP_BIAS + 62);
30 idx = static_cast<unsigned>((x_e_m62 >> 4) + 3);
31 // Scale x down by 2^(-(16 * (idx - 3))
32 xbits.set_biased_exponent((x_e_m62 & 15) + FPBits::EXP_BIAS + 62);
33 // 2^62 <= |x_reduced| < 2^(62 + 16) = 2^78
34 x_reduced = xbits.get_val();
35 // x * c_hi = ph.hi + ph.lo exactly.
36 DoubleDouble x_split = fputil::split(x_reduced);
37 DoubleDouble ph = fputil::exact_mult<double, SPLIT>(
38 x_split, x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][0]);
39 // x * c_mid = pm.hi + pm.lo exactly.
40 DoubleDouble pm = fputil::exact_mult<double, SPLIT>(
41 x_split, x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][1]);
42 // x * c_lo = pl.hi + pl.lo exactly.
43 DoubleDouble pl = fputil::exact_mult<double, SPLIT>(
44 x_split, x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][2]);
45 // Extract integral parts and fractional parts of (ph.lo + pm.hi).
46 double sum_hi = ph.lo + pm.hi;
47 double kd = fputil::nearest_integer(sum_hi);
48
49 // x * 128/pi mod 1 ~ y_hi + y_mid + y_lo
50 y_hi = (ph.lo - kd) + pm.hi; // Exact
51 y_mid = fputil::exact_add(pm.lo, pl.hi);
52 y_lo = pl.lo;
53
54 // y_l = x * c_lo_2 + pl.lo
55 double y_l =
56 fputil::multiply_add(x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][3], y_lo);
57 DoubleDouble y = fputil::exact_add(y_hi, y_mid.hi);
58 y.lo += (y_mid.lo + y_l);
59
60 // Digits of pi/128, generated by Sollya with:
61 // > a = round(pi/128, D, RN);
62 // > b = round(pi/128 - a, D, RN);
63 constexpr DoubleDouble PI_OVER_128_DD = {0x1.1a62633145c07p-60,
64 0x1.921fb54442d18p-6};
65
66 // Error bound: with {a} denote the fractional part of a, i.e.:
67 // {a} = a - round(a)
68 // Then,
69 // | {x * 128/pi} - (y_hi + y_lo) | <= ulp(ulp(y_hi)) <= 2^-105
70 // | {x mod pi/128} - (u.hi + u.lo) | < 2 * 2^-6 * 2^-105 = 2^-110
71 u = fputil::quick_mult<SPLIT>(y, PI_OVER_128_DD);
72
73 return static_cast<unsigned>(static_cast<int64_t>(kd));
74}
75
76// Lookup table for sin(k * pi / 128) with k = 0, ..., 255.
77// Table is generated with Sollya as follow:
78// > display = hexadecimal;
79// > for k from 0 to 255 do {
80// a = round(sin(k * pi/128), 51, RN);
81// b = round(sin(k * pi/128) - a, D, RN);
82// print("{", b, ",", a, "},");
83// };
84LIBC_INLINE constexpr DoubleDouble SIN_K_PI_OVER_128[] = {
85 {0, 0},
86 {0x1.f938a73db97fbp-58, 0x1.92155f7a3667cp-6},
87 {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},
88 {0x1.ccbeeeae8129ap-56, 0x1.2d52092ce19f4p-4},
89 {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},
90 {-0x1.cbb1f71aca352p-56, 0x1.f564e56a9731p-4},
91 {-0x1.dd9ffeaecbdc4p-55, 0x1.2c8106e8e613cp-3},
92 {-0x1.ab3802218894fp-55, 0x1.5e214448b3fc8p-3},
93 {-0x1.49b466e7fe36p-55, 0x1.8f8b83c69a60cp-3},
94 {-0x1.035e2873ca432p-55, 0x1.c0b826a7e4f64p-3},
95 {-0x1.50b7bbc4768b1p-55, 0x1.f19f97b215f1cp-3},
96 {-0x1.3ed9efaa42ab3p-55, 0x1.111d262b1f678p-2},
97 {0x1.a8b5c974ee7b5p-54, 0x1.294062ed59f04p-2},
98 {0x1.4325f12be8946p-54, 0x1.4135c941766p-2},
99 {0x1.fc2047e54e614p-55, 0x1.58f9a75ab1fdcp-2},
100 {-0x1.512c678219317p-54, 0x1.7088530fa45ap-2},
101 {-0x1.2e59dba7ab4c2p-54, 0x1.87de2a6aea964p-2},
102 {-0x1.d24afdade848bp-54, 0x1.9ef7943a8ed8cp-2},
103 {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},
104 {-0x1.e97af1a63c807p-54, 0x1.cc66e9931c46p-2},
105 {-0x1.c3e4edc5872f8p-55, 0x1.e2b5d3806f63cp-2},
106 {0x1.fb44f80f92225p-54, 0x1.f8ba4dbf89ab8p-2},
107 {0x1.9697faf2e2fe5p-53, 0x1.073879922ffecp-1},
108 {-0x1.7bc8eda6af93cp-53, 0x1.11eb3541b4b24p-1},
109 {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},
110 {-0x1.5769d0fbcddc3p-53, 0x1.26d054cdd12ep-1},
111 {0x1.c20673b2116b2p-54, 0x1.30ff7fce17034p-1},
112 {0x1.3c7c4bc72a92cp-53, 0x1.3affa292050b8p-1},
113 {-0x1.e7f895d302395p-53, 0x1.44cf325091dd8p-1},
114 {0x1.13c293edceb32p-53, 0x1.4e6cabbe3e5e8p-1},
115 {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},
116 {-0x1.24a366a5fe547p-53, 0x1.610b7551d2cep-1},
117 {0x1.21165f626cdd5p-54, 0x1.6a09e667f3bccp-1},
118 {-0x1.bcac43c389ba9p-53, 0x1.72d0837efff98p-1},
119 {-0x1.21ea6f59be15bp-53, 0x1.7b5df226aafbp-1},
120 {0x1.d217be0e2b971p-53, 0x1.83b0e0bff976cp-1},
121 {0x1.69d0f6897664ap-54, 0x1.8bc806b15174p-1},
122 {-0x1.615f32b6f907ap-54, 0x1.93a22499263fcp-1},
123 {0x1.6788ebcc76dc6p-54, 0x1.9b3e047f3874p-1},
124 {0x1.ddae89fd441d1p-53, 0x1.a29a7a046278p-1},
125 {-0x1.f98273c5d2495p-54, 0x1.a9b66290ea1a4p-1},
126 {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},
127 {0x1.90e58336c64a8p-53, 0x1.b728345196e3cp-1},
128 {0x1.9f6963354e3fep-53, 0x1.bd7c0ac6f9528p-1},
129 {0x1.a47d3a2a0dcbep-54, 0x1.c38b2f180bdbp-1},
130 {0x1.ed0489e16b9ap-54, 0x1.c954b213411f4p-1},
131 {-0x1.0f3db5dad5ac5p-53, 0x1.ced7af43cc774p-1},
132 {0x1.ac42b5a8b6943p-53, 0x1.d4134d14dc938p-1},
133 {-0x1.d75033dfb9ca8p-53, 0x1.d906bcf328d48p-1},
134 {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},
135 {0x1.7f59c49f6cd6dp-54, 0x1.e212104f686e4p-1},
136 {0x1.ee94a90d7b88bp-53, 0x1.e6288ec48e11p-1},
137 {-0x1.a27d3874701f9p-53, 0x1.e9f4156c62ddcp-1},
138 {-0x1.85f4e1b8298dp-54, 0x1.ed740e7684964p-1},
139 {-0x1.ab4e148e52d9ep-54, 0x1.f0a7efb9230d8p-1},
140 {0x1.8a11412b82346p-54, 0x1.f38f3ac64e588p-1},
141 {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},
142 {0x1.3564acef1ff97p-53, 0x1.f8764fa714ba8p-1},
143 {-0x1.5e82a3284d5c8p-53, 0x1.fa7557f08a518p-1},
144 {-0x1.709bccb89a989p-54, 0x1.fc26470e19fd4p-1},
145 {0x1.9e082721dfb8ep-53, 0x1.fd88da3d12524p-1},
146 {-0x1.eade132f3981dp-53, 0x1.fe9cdad01883cp-1},
147 {0x1.e3a843d1db55fp-53, 0x1.ff621e3796d7cp-1},
148 {0x1.765595d548d9ap-54, 0x1.ffd886084cd0cp-1},
149 {0, 1},
150#ifndef LIBC_MATH_HAS_SMALL_TABLES
151 {0x1.765595d548d9ap-54, 0x1.ffd886084cd0cp-1},
152 {0x1.e3a843d1db55fp-53, 0x1.ff621e3796d7cp-1},
153 {-0x1.eade132f3981dp-53, 0x1.fe9cdad01883cp-1},
154 {0x1.9e082721dfb8ep-53, 0x1.fd88da3d12524p-1},
155 {-0x1.709bccb89a989p-54, 0x1.fc26470e19fd4p-1},
156 {-0x1.5e82a3284d5c8p-53, 0x1.fa7557f08a518p-1},
157 {0x1.3564acef1ff97p-53, 0x1.f8764fa714ba8p-1},
158 {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},
159 {0x1.8a11412b82346p-54, 0x1.f38f3ac64e588p-1},
160 {-0x1.ab4e148e52d9ep-54, 0x1.f0a7efb9230d8p-1},
161 {-0x1.85f4e1b8298dp-54, 0x1.ed740e7684964p-1},
162 {-0x1.a27d3874701f9p-53, 0x1.e9f4156c62ddcp-1},
163 {0x1.ee94a90d7b88bp-53, 0x1.e6288ec48e11p-1},
164 {0x1.7f59c49f6cd6dp-54, 0x1.e212104f686e4p-1},
165 {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},
166 {-0x1.d75033dfb9ca8p-53, 0x1.d906bcf328d48p-1},
167 {0x1.ac42b5a8b6943p-53, 0x1.d4134d14dc938p-1},
168 {-0x1.0f3db5dad5ac5p-53, 0x1.ced7af43cc774p-1},
169 {0x1.ed0489e16b9ap-54, 0x1.c954b213411f4p-1},
170 {0x1.a47d3a2a0dcbep-54, 0x1.c38b2f180bdbp-1},
171 {0x1.9f6963354e3fep-53, 0x1.bd7c0ac6f9528p-1},
172 {0x1.90e58336c64a8p-53, 0x1.b728345196e3cp-1},
173 {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},
174 {-0x1.f98273c5d2495p-54, 0x1.a9b66290ea1a4p-1},
175 {0x1.ddae89fd441d1p-53, 0x1.a29a7a046278p-1},
176 {0x1.6788ebcc76dc6p-54, 0x1.9b3e047f3874p-1},
177 {-0x1.615f32b6f907ap-54, 0x1.93a22499263fcp-1},
178 {0x1.69d0f6897664ap-54, 0x1.8bc806b15174p-1},
179 {0x1.d217be0e2b971p-53, 0x1.83b0e0bff976cp-1},
180 {-0x1.21ea6f59be15bp-53, 0x1.7b5df226aafbp-1},
181 {-0x1.bcac43c389ba9p-53, 0x1.72d0837efff98p-1},
182 {0x1.21165f626cdd5p-54, 0x1.6a09e667f3bccp-1},
183 {-0x1.24a366a5fe547p-53, 0x1.610b7551d2cep-1},
184 {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},
185 {0x1.13c293edceb32p-53, 0x1.4e6cabbe3e5e8p-1},
186 {-0x1.e7f895d302395p-53, 0x1.44cf325091dd8p-1},
187 {0x1.3c7c4bc72a92cp-53, 0x1.3affa292050b8p-1},
188 {0x1.c20673b2116b2p-54, 0x1.30ff7fce17034p-1},
189 {-0x1.5769d0fbcddc3p-53, 0x1.26d054cdd12ep-1},
190 {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},
191 {-0x1.7bc8eda6af93cp-53, 0x1.11eb3541b4b24p-1},
192 {0x1.9697faf2e2fe5p-53, 0x1.073879922ffecp-1},
193 {0x1.fb44f80f92225p-54, 0x1.f8ba4dbf89ab8p-2},
194 {-0x1.c3e4edc5872f8p-55, 0x1.e2b5d3806f63cp-2},
195 {-0x1.e97af1a63c807p-54, 0x1.cc66e9931c46p-2},
196 {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},
197 {-0x1.d24afdade848bp-54, 0x1.9ef7943a8ed8cp-2},
198 {-0x1.2e59dba7ab4c2p-54, 0x1.87de2a6aea964p-2},
199 {-0x1.512c678219317p-54, 0x1.7088530fa45ap-2},
200 {0x1.fc2047e54e614p-55, 0x1.58f9a75ab1fdcp-2},
201 {0x1.4325f12be8946p-54, 0x1.4135c941766p-2},
202 {0x1.a8b5c974ee7b5p-54, 0x1.294062ed59f04p-2},
203 {-0x1.3ed9efaa42ab3p-55, 0x1.111d262b1f678p-2},
204 {-0x1.50b7bbc4768b1p-55, 0x1.f19f97b215f1cp-3},
205 {-0x1.035e2873ca432p-55, 0x1.c0b826a7e4f64p-3},
206 {-0x1.49b466e7fe36p-55, 0x1.8f8b83c69a60cp-3},
207 {-0x1.ab3802218894fp-55, 0x1.5e214448b3fc8p-3},
208 {-0x1.dd9ffeaecbdc4p-55, 0x1.2c8106e8e613cp-3},
209 {-0x1.cbb1f71aca352p-56, 0x1.f564e56a9731p-4},
210 {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},
211 {0x1.ccbeeeae8129ap-56, 0x1.2d52092ce19f4p-4},
212 {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},
213 {0x1.f938a73db97fbp-58, 0x1.92155f7a3667cp-6},
214 {0, 0},
215 {-0x1.f938a73db97fbp-58, -0x1.92155f7a3667cp-6},
216 {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},
217 {-0x1.ccbeeeae8129ap-56, -0x1.2d52092ce19f4p-4},
218 {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},
219 {0x1.cbb1f71aca352p-56, -0x1.f564e56a9731p-4},
220 {0x1.dd9ffeaecbdc4p-55, -0x1.2c8106e8e613cp-3},
221 {0x1.ab3802218894fp-55, -0x1.5e214448b3fc8p-3},
222 {0x1.49b466e7fe36p-55, -0x1.8f8b83c69a60cp-3},
223 {0x1.035e2873ca432p-55, -0x1.c0b826a7e4f64p-3},
224 {0x1.50b7bbc4768b1p-55, -0x1.f19f97b215f1cp-3},
225 {0x1.3ed9efaa42ab3p-55, -0x1.111d262b1f678p-2},
226 {-0x1.a8b5c974ee7b5p-54, -0x1.294062ed59f04p-2},
227 {-0x1.4325f12be8946p-54, -0x1.4135c941766p-2},
228 {-0x1.fc2047e54e614p-55, -0x1.58f9a75ab1fdcp-2},
229 {0x1.512c678219317p-54, -0x1.7088530fa45ap-2},
230 {0x1.2e59dba7ab4c2p-54, -0x1.87de2a6aea964p-2},
231 {0x1.d24afdade848bp-54, -0x1.9ef7943a8ed8cp-2},
232 {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},
233 {0x1.e97af1a63c807p-54, -0x1.cc66e9931c46p-2},
234 {0x1.c3e4edc5872f8p-55, -0x1.e2b5d3806f63cp-2},
235 {-0x1.fb44f80f92225p-54, -0x1.f8ba4dbf89ab8p-2},
236 {-0x1.9697faf2e2fe5p-53, -0x1.073879922ffecp-1},
237 {0x1.7bc8eda6af93cp-53, -0x1.11eb3541b4b24p-1},
238 {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},
239 {0x1.5769d0fbcddc3p-53, -0x1.26d054cdd12ep-1},
240 {-0x1.c20673b2116b2p-54, -0x1.30ff7fce17034p-1},
241 {-0x1.3c7c4bc72a92cp-53, -0x1.3affa292050b8p-1},
242 {0x1.e7f895d302395p-53, -0x1.44cf325091dd8p-1},
243 {-0x1.13c293edceb32p-53, -0x1.4e6cabbe3e5e8p-1},
244 {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},
245 {0x1.24a366a5fe547p-53, -0x1.610b7551d2cep-1},
246 {-0x1.21165f626cdd5p-54, -0x1.6a09e667f3bccp-1},
247 {0x1.bcac43c389ba9p-53, -0x1.72d0837efff98p-1},
248 {0x1.21ea6f59be15bp-53, -0x1.7b5df226aafbp-1},
249 {-0x1.d217be0e2b971p-53, -0x1.83b0e0bff976cp-1},
250 {-0x1.69d0f6897664ap-54, -0x1.8bc806b15174p-1},
251 {0x1.615f32b6f907ap-54, -0x1.93a22499263fcp-1},
252 {-0x1.6788ebcc76dc6p-54, -0x1.9b3e047f3874p-1},
253 {-0x1.ddae89fd441d1p-53, -0x1.a29a7a046278p-1},
254 {0x1.f98273c5d2495p-54, -0x1.a9b66290ea1a4p-1},
255 {0x1.926da300ffccep-55, -0x1.b090a581502p-1},
256 {-0x1.90e58336c64a8p-53, -0x1.b728345196e3cp-1},
257 {-0x1.9f6963354e3fep-53, -0x1.bd7c0ac6f9528p-1},
258 {-0x1.a47d3a2a0dcbep-54, -0x1.c38b2f180bdbp-1},
259 {-0x1.ed0489e16b9ap-54, -0x1.c954b213411f4p-1},
260 {0x1.0f3db5dad5ac5p-53, -0x1.ced7af43cc774p-1},
261 {-0x1.ac42b5a8b6943p-53, -0x1.d4134d14dc938p-1},
262 {0x1.d75033dfb9ca8p-53, -0x1.d906bcf328d48p-1},
263 {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},
264 {-0x1.7f59c49f6cd6dp-54, -0x1.e212104f686e4p-1},
265 {-0x1.ee94a90d7b88bp-53, -0x1.e6288ec48e11p-1},
266 {0x1.a27d3874701f9p-53, -0x1.e9f4156c62ddcp-1},
267 {0x1.85f4e1b8298dp-54, -0x1.ed740e7684964p-1},
268 {0x1.ab4e148e52d9ep-54, -0x1.f0a7efb9230d8p-1},
269 {-0x1.8a11412b82346p-54, -0x1.f38f3ac64e588p-1},
270 {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},
271 {-0x1.3564acef1ff97p-53, -0x1.f8764fa714ba8p-1},
272 {0x1.5e82a3284d5c8p-53, -0x1.fa7557f08a518p-1},
273 {0x1.709bccb89a989p-54, -0x1.fc26470e19fd4p-1},
274 {-0x1.9e082721dfb8ep-53, -0x1.fd88da3d12524p-1},
275 {0x1.eade132f3981dp-53, -0x1.fe9cdad01883cp-1},
276 {-0x1.e3a843d1db55fp-53, -0x1.ff621e3796d7cp-1},
277 {-0x1.765595d548d9ap-54, -0x1.ffd886084cd0cp-1},
278 {0, -1},
279 {-0x1.765595d548d9ap-54, -0x1.ffd886084cd0cp-1},
280 {-0x1.e3a843d1db55fp-53, -0x1.ff621e3796d7cp-1},
281 {0x1.eade132f3981dp-53, -0x1.fe9cdad01883cp-1},
282 {-0x1.9e082721dfb8ep-53, -0x1.fd88da3d12524p-1},
283 {0x1.709bccb89a989p-54, -0x1.fc26470e19fd4p-1},
284 {0x1.5e82a3284d5c8p-53, -0x1.fa7557f08a518p-1},
285 {-0x1.3564acef1ff97p-53, -0x1.f8764fa714ba8p-1},
286 {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},
287 {-0x1.8a11412b82346p-54, -0x1.f38f3ac64e588p-1},
288 {0x1.ab4e148e52d9ep-54, -0x1.f0a7efb9230d8p-1},
289 {0x1.85f4e1b8298dp-54, -0x1.ed740e7684964p-1},
290 {0x1.a27d3874701f9p-53, -0x1.e9f4156c62ddcp-1},
291 {-0x1.ee94a90d7b88bp-53, -0x1.e6288ec48e11p-1},
292 {-0x1.7f59c49f6cd6dp-54, -0x1.e212104f686e4p-1},
293 {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},
294 {0x1.d75033dfb9ca8p-53, -0x1.d906bcf328d48p-1},
295 {-0x1.ac42b5a8b6943p-53, -0x1.d4134d14dc938p-1},
296 {0x1.0f3db5dad5ac5p-53, -0x1.ced7af43cc774p-1},
297 {-0x1.ed0489e16b9ap-54, -0x1.c954b213411f4p-1},
298 {-0x1.a47d3a2a0dcbep-54, -0x1.c38b2f180bdbp-1},
299 {-0x1.9f6963354e3fep-53, -0x1.bd7c0ac6f9528p-1},
300 {-0x1.90e58336c64a8p-53, -0x1.b728345196e3cp-1},
301 {0x1.926da300ffccep-55, -0x1.b090a581502p-1},
302 {0x1.f98273c5d2495p-54, -0x1.a9b66290ea1a4p-1},
303 {-0x1.ddae89fd441d1p-53, -0x1.a29a7a046278p-1},
304 {-0x1.6788ebcc76dc6p-54, -0x1.9b3e047f3874p-1},
305 {0x1.615f32b6f907ap-54, -0x1.93a22499263fcp-1},
306 {-0x1.69d0f6897664ap-54, -0x1.8bc806b15174p-1},
307 {-0x1.d217be0e2b971p-53, -0x1.83b0e0bff976cp-1},
308 {0x1.21ea6f59be15bp-53, -0x1.7b5df226aafbp-1},
309 {0x1.bcac43c389ba9p-53, -0x1.72d0837efff98p-1},
310 {-0x1.21165f626cdd5p-54, -0x1.6a09e667f3bccp-1},
311 {0x1.24a366a5fe547p-53, -0x1.610b7551d2cep-1},
312 {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},
313 {-0x1.13c293edceb32p-53, -0x1.4e6cabbe3e5e8p-1},
314 {0x1.e7f895d302395p-53, -0x1.44cf325091dd8p-1},
315 {-0x1.3c7c4bc72a92cp-53, -0x1.3affa292050b8p-1},
316 {-0x1.c20673b2116b2p-54, -0x1.30ff7fce17034p-1},
317 {0x1.5769d0fbcddc3p-53, -0x1.26d054cdd12ep-1},
318 {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},
319 {0x1.7bc8eda6af93cp-53, -0x1.11eb3541b4b24p-1},
320 {-0x1.9697faf2e2fe5p-53, -0x1.073879922ffecp-1},
321 {-0x1.fb44f80f92225p-54, -0x1.f8ba4dbf89ab8p-2},
322 {0x1.c3e4edc5872f8p-55, -0x1.e2b5d3806f63cp-2},
323 {0x1.e97af1a63c807p-54, -0x1.cc66e9931c46p-2},
324 {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},
325 {0x1.d24afdade848bp-54, -0x1.9ef7943a8ed8cp-2},
326 {0x1.2e59dba7ab4c2p-54, -0x1.87de2a6aea964p-2},
327 {0x1.512c678219317p-54, -0x1.7088530fa45ap-2},
328 {-0x1.fc2047e54e614p-55, -0x1.58f9a75ab1fdcp-2},
329 {-0x1.4325f12be8946p-54, -0x1.4135c941766p-2},
330 {-0x1.a8b5c974ee7b5p-54, -0x1.294062ed59f04p-2},
331 {0x1.3ed9efaa42ab3p-55, -0x1.111d262b1f678p-2},
332 {0x1.50b7bbc4768b1p-55, -0x1.f19f97b215f1cp-3},
333 {0x1.035e2873ca432p-55, -0x1.c0b826a7e4f64p-3},
334 {0x1.49b466e7fe36p-55, -0x1.8f8b83c69a60cp-3},
335 {0x1.ab3802218894fp-55, -0x1.5e214448b3fc8p-3},
336 {0x1.dd9ffeaecbdc4p-55, -0x1.2c8106e8e613cp-3},
337 {0x1.cbb1f71aca352p-56, -0x1.f564e56a9731p-4},
338 {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},
339 {-0x1.ccbeeeae8129ap-56, -0x1.2d52092ce19f4p-4},
340 {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},
341 {-0x1.f938a73db97fbp-58, -0x1.92155f7a3667cp-6},
342#endif // !LIBC_MATH_HAS_SMALL_TABLES
343};
344
345} // namespace LIBC_NAMESPACE_DECL
346
347#endif // LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_NOFMA_H
348

Warning: This file is not a C or C++ file. It does not have highlighting.

source code of libc/src/math/generic/range_reduction_double_nofma.h