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[libc][math] Implement double precision cos correctly rounded to all rounding modes. (#96591)
Sharing the same algorithm as double precision sin: #95736
1 parent ef05b03 commit 88f80ae

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15 files changed

+505
-174
lines changed

15 files changed

+505
-174
lines changed

‎libc/config/darwin/arm/entrypoints.txt‎

Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -130,6 +130,7 @@ set(TARGET_LIBM_ENTRYPOINTS
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libc.src.math.ceilf
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libc.src.math.ceill
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libc.src.math.coshf
133+
libc.src.math.cos
133134
libc.src.math.cosf
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libc.src.math.erff
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libc.src.math.exp

‎libc/config/linux/aarch64/entrypoints.txt‎

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@@ -344,6 +344,7 @@ set(TARGET_LIBM_ENTRYPOINTS
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libc.src.math.ceilf
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libc.src.math.ceill
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libc.src.math.coshf
347+
libc.src.math.cos
347348
libc.src.math.cosf
348349
libc.src.math.erff
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libc.src.math.exp

‎libc/config/linux/arm/entrypoints.txt‎

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@@ -218,6 +218,7 @@ set(TARGET_LIBM_ENTRYPOINTS
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libc.src.math.copysign
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libc.src.math.copysignf
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libc.src.math.copysignl
221+
libc.src.math.cos
221222
libc.src.math.cosf
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libc.src.math.coshf
223224
libc.src.math.erff

‎libc/config/linux/riscv/entrypoints.txt‎

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Original file line numberDiff line numberDiff line change
@@ -352,6 +352,7 @@ set(TARGET_LIBM_ENTRYPOINTS
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libc.src.math.ceilf
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libc.src.math.ceill
354354
libc.src.math.coshf
355+
libc.src.math.cos
355356
libc.src.math.cosf
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libc.src.math.erff
357358
libc.src.math.exp

‎libc/docs/math/index.rst‎

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -266,7 +266,7 @@ Higher Math Functions
266266
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
267267
| compoundn | | | | | | 7.12.7.2 | F.10.4.2 |
268268
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
269-
| cos | |check| | large | | | | 7.12.4.5 | F.10.1.5 |
269+
| cos | |check| | |check| | | | | 7.12.4.5 | F.10.1.5 |
270270
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
271271
| cosh | |check| | | | | | 7.12.5.4 | F.10.2.4 |
272272
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

‎libc/src/math/generic/CMakeLists.txt‎

Lines changed: 34 additions & 11 deletions
Original file line numberDiff line numberDiff line change
@@ -142,14 +142,14 @@ add_header_library(
142142
range_reduction_double_fma.h
143143
range_reduction_double_nofma.h
144144
DEPENDS
145-
libc.src.__support.FPUtil.double_double
146-
libc.src.__support.FPUtil.dyadic_float
147-
libc.src.__support.FPUtil.fp_bits
148-
libc.src.__support.FPUtil.fma
149-
libc.src.__support.FPUtil.multiply_add
150-
libc.src.__support.FPUtil.nearest_integer
151-
libc.src.__support.common
152-
libc.src.__support.integer_literals
145+
libc.src.__support.FPUtil.double_double
146+
libc.src.__support.FPUtil.dyadic_float
147+
libc.src.__support.FPUtil.fp_bits
148+
libc.src.__support.FPUtil.fma
149+
libc.src.__support.FPUtil.multiply_add
150+
libc.src.__support.FPUtil.nearest_integer
151+
libc.src.__support.common
152+
libc.src.__support.integer_literals
153153
)
154154

155155
add_header_library(
@@ -169,7 +169,31 @@ add_header_library(
169169
sincos_eval.h
170170
DEPENDS
171171
libc.src.__support.FPUtil.double_double
172+
libc.src.__support.FPUtil.dyadic_float
172173
libc.src.__support.FPUtil.multiply_add
174+
libc.src.__support.FPUtil.polyeval
175+
libc.src.__support.integer_literals
176+
)
177+
178+
add_entrypoint_object(
179+
cos
180+
SRCS
181+
cos.cpp
182+
HDRS
183+
../cos.h
184+
DEPENDS
185+
.range_reduction_double
186+
.sincos_eval
187+
libc.hdr.errno_macros
188+
libc.src.errno.errno
189+
libc.src.__support.FPUtil.double_double
190+
libc.src.__support.FPUtil.dyadic_float
191+
libc.src.__support.FPUtil.except_value_utils
192+
libc.src.__support.FPUtil.fenv_impl
193+
libc.src.__support.FPUtil.fp_bits
194+
libc.src.__support.macros.optimization
195+
COMPILE_OPTIONS
196+
-O3
173197
)
174198

175199
add_entrypoint_object(
@@ -200,16 +224,15 @@ add_entrypoint_object(
200224
HDRS
201225
../sin.h
202226
DEPENDS
227+
.range_reduction_double
228+
.sincos_eval
203229
libc.hdr.errno_macros
204230
libc.src.errno.errno
205231
libc.src.__support.FPUtil.double_double
206232
libc.src.__support.FPUtil.dyadic_float
207233
libc.src.__support.FPUtil.fenv_impl
208234
libc.src.__support.FPUtil.fp_bits
209-
libc.src.__support.FPUtil.fma
210235
libc.src.__support.FPUtil.multiply_add
211-
libc.src.__support.FPUtil.nearest_integer
212-
libc.src.__support.FPUtil.polyeval
213236
libc.src.__support.FPUtil.rounding_mode
214237
libc.src.__support.macros.optimization
215238
COMPILE_OPTIONS

‎libc/src/math/generic/cos.cpp‎

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,197 @@
1+
//===-- Double-precision cos function -------------------------------------===//
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+
#include "src/math/cos.h"
10+
#include "hdr/errno_macros.h"
11+
#include "src/__support/FPUtil/FEnvImpl.h"
12+
#include "src/__support/FPUtil/FPBits.h"
13+
#include "src/__support/FPUtil/double_double.h"
14+
#include "src/__support/FPUtil/dyadic_float.h"
15+
#include "src/__support/FPUtil/except_value_utils.h"
16+
#include "src/__support/common.h"
17+
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
18+
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
19+
#include "src/math/generic/sincos_eval.h"
20+
21+
#ifdef LIBC_TARGET_CPU_HAS_FMA
22+
#include "range_reduction_double_fma.h"
23+
24+
using LIBC_NAMESPACE::fma::FAST_PASS_EXPONENT;
25+
using LIBC_NAMESPACE::fma::ONE_TWENTY_EIGHT_OVER_PI;
26+
using LIBC_NAMESPACE::fma::range_reduction_small;
27+
using LIBC_NAMESPACE::fma::SIN_K_PI_OVER_128;
28+
29+
LIBC_INLINE constexpr bool NO_FMA = false;
30+
#else
31+
#include "range_reduction_double_nofma.h"
32+
33+
using LIBC_NAMESPACE::nofma::FAST_PASS_EXPONENT;
34+
using LIBC_NAMESPACE::nofma::ONE_TWENTY_EIGHT_OVER_PI;
35+
using LIBC_NAMESPACE::nofma::range_reduction_small;
36+
using LIBC_NAMESPACE::nofma::SIN_K_PI_OVER_128;
37+
38+
LIBC_INLINE constexpr bool NO_FMA = true;
39+
#endif // LIBC_TARGET_CPU_HAS_FMA
40+
41+
// TODO: We might be able to improve the performance of large range reduction of
42+
// non-FMA targets further by operating directly on 25-bit chunks of 128/pi and
43+
// pre-split SIN_K_PI_OVER_128, but that might double the memory footprint of
44+
// those lookup table.
45+
#include "range_reduction_double_common.h"
46+
47+
#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0)
48+
#define LIBC_MATH_COS_SKIP_ACCURATE_PASS
49+
#endif
50+
51+
namespace LIBC_NAMESPACE {
52+
53+
using DoubleDouble = fputil::DoubleDouble;
54+
using Float128 = typename fputil::DyadicFloat<128>;
55+
56+
LLVM_LIBC_FUNCTION(double, cos, (double x)) {
57+
using FPBits = typename fputil::FPBits<double>;
58+
FPBits xbits(x);
59+
60+
uint16_t x_e = xbits.get_biased_exponent();
61+
62+
DoubleDouble y;
63+
unsigned k;
64+
generic::LargeRangeReduction<NO_FMA> range_reduction_large;
65+
66+
// |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)
67+
if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
68+
// |x| < 2^-27
69+
if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {
70+
// Signed zeros.
71+
if (LIBC_UNLIKELY(x == 0.0))
72+
return 1.0;
73+
74+
// For |x| < 2^-27, |cos(x) - 1| < |x|^2/2 < 2^-54 = ulp(1 - 2^-53)/2.
75+
return fputil::round_result_slightly_down(1.0);
76+
}
77+
78+
// // Small range reduction.
79+
k = range_reduction_small(x, y);
80+
} else {
81+
// Inf or NaN
82+
if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
83+
// sin(+-Inf) = NaN
84+
if (xbits.get_mantissa() == 0) {
85+
fputil::set_errno_if_required(EDOM);
86+
fputil::raise_except_if_required(FE_INVALID);
87+
}
88+
return x + FPBits::quiet_nan().get_val();
89+
}
90+
91+
// Large range reduction.
92+
k = range_reduction_large.compute_high_part(x);
93+
y = range_reduction_large.fast();
94+
}
95+
96+
DoubleDouble sin_y, cos_y;
97+
98+
generic::sincos_eval(y, sin_y, cos_y);
99+
100+
// Look up sin(k * pi/128) and cos(k * pi/128)
101+
// Memory saving versions:
102+
103+
// Use 128-entry table instead:
104+
// DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 127];
105+
// uint64_t sin_s = static_cast<uint64_t>((k + 128) & 128) << (63 - 7);
106+
// sin_k.hi = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
107+
// sin_k.lo = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
108+
// DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 127];
109+
// uint64_t cos_s = static_cast<uint64_t>((k + 64) & 128) << (63 - 7);
110+
// cos_k.hi = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
111+
// cos_k.lo = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
112+
113+
// Use 64-entry table instead:
114+
// auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
115+
// unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
116+
// DoubleDouble ans = SIN_K_PI_OVER_128[idx];
117+
// if (kk & 128) {
118+
// ans.hi = -ans.hi;
119+
// ans.lo = -ans.lo;
120+
// }
121+
// return ans;
122+
// };
123+
// DoubleDouble sin_k = get_idx_dd(k + 128);
124+
// DoubleDouble cos_k = get_idx_dd(k + 64);
125+
126+
// Fast look up version, but needs 256-entry table.
127+
// -sin(k * pi/128) = sin((k + 128) * pi/128)
128+
// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
129+
DoubleDouble msin_k = SIN_K_PI_OVER_128[(k + 128) & 255];
130+
DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
131+
132+
// After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
133+
// So k is an integer and -pi / 256 <= y <= pi / 256.
134+
// Then cos(x) = cos((k * pi/128 + y)
135+
// = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)
136+
DoubleDouble cos_k_cos_y = fputil::quick_mult<NO_FMA>(cos_y, cos_k);
137+
DoubleDouble msin_k_sin_y = fputil::quick_mult<NO_FMA>(sin_y, msin_k);
138+
139+
DoubleDouble rr = fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi);
140+
rr.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;
141+
142+
#ifdef LIBC_MATH_COS_SKIP_ACCURATE_PASS
143+
return rr.hi + rr.lo;
144+
#else
145+
146+
// Accurate test and pass for correctly rounded implementation.
147+
#ifdef LIBC_TARGET_CPU_HAS_FMA
148+
constexpr double ERR = 0x1.0p-70;
149+
#else
150+
// TODO: Improve non-FMA fast pass accuracy.
151+
constexpr double ERR = 0x1.0p-66;
152+
#endif // LIBC_TARGET_CPU_HAS_FMA
153+
154+
double rlp = rr.lo + ERR;
155+
double rlm = rr.lo - ERR;
156+
157+
double r_upper = rr.hi + rlp; // (rr.lo + ERR);
158+
double r_lower = rr.hi + rlm; // (rr.lo - ERR);
159+
160+
// Ziv's rounding test.
161+
if (LIBC_LIKELY(r_upper == r_lower))
162+
return r_upper;
163+
164+
Float128 u_f128, sin_u, cos_u;
165+
if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
166+
u_f128 = generic::range_reduction_small_f128(x);
167+
else
168+
u_f128 = range_reduction_large.accurate();
169+
170+
generic::sincos_eval(u_f128, sin_u, cos_u);
171+
172+
auto get_sin_k = [](unsigned kk) -> Float128 {
173+
unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
174+
Float128 ans = generic::SIN_K_PI_OVER_128_F128[idx];
175+
if (kk & 128)
176+
ans.sign = Sign::NEG;
177+
return ans;
178+
};
179+
180+
// -sin(k * pi/128) = sin((k + 128) * pi/128)
181+
// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
182+
Float128 msin_k_f128 = get_sin_k(k + 128);
183+
Float128 cos_k_f128 = get_sin_k(k + 64);
184+
185+
// cos(x) = cos((k * pi/128 + u)
186+
// = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)
187+
Float128 r = fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u),
188+
fputil::quick_mul(msin_k_f128, sin_u));
189+
190+
// TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
191+
// https://github.com/llvm/llvm-project/issues/96452.
192+
193+
return static_cast<double>(r);
194+
#endif // !LIBC_MATH_COS_SKIP_ACCURATE_PASS
195+
}
196+
197+
} // namespace LIBC_NAMESPACE

‎libc/src/math/generic/range_reduction_double_common.h‎

Lines changed: 68 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -155,6 +155,74 @@ LIBC_INLINE Float128 range_reduction_small_f128(double x) {
155155
return fputil::quick_mul(y, PI_OVER_128_F128);
156156
}
157157

158+
LIBC_INLINE constexpr Float128 SIN_K_PI_OVER_128_F128[65] = {
159+
{Sign::POS, 0, 0},
160+
{Sign::POS, -133, 0xc90a'afbd'1b33'efc9'c539'edcb'fda0'cf2c_u128},
161+
{Sign::POS, -132, 0xc8fb'2f88'6ec0'9f37'6a17'954b'2b7c'5171_u128},
162+
{Sign::POS, -131, 0x96a9'0496'70cf'ae65'f775'7409'4d3c'35c4_u128},
163+
{Sign::POS, -131, 0xc8bd'35e1'4da1'5f0e'c739'6c89'4bbf'7389_u128},
164+
{Sign::POS, -131, 0xfab2'72b5'4b98'71a2'7047'29ae'56d7'8a37_u128},
165+
{Sign::POS, -130, 0x9640'8374'7309'd113'000a'89a1'1e07'c1fe_u128},
166+
{Sign::POS, -130, 0xaf10'a224'59fe'32a6'3fee'f3bb'58b1'f10d_u128},
167+
{Sign::POS, -130, 0xc7c5'c1e3'4d30'55b2'5cc8'c00e'4fcc'd850_u128},
168+
{Sign::POS, -130, 0xe05c'1353'f27b'17e5'0ebc'61ad'e6ca'83cd_u128},
169+
{Sign::POS, -130, 0xf8cf'cbd9'0af8'd57a'4221'dc4b'a772'598d_u128},
170+
{Sign::POS, -129, 0x888e'9315'8fb3'bb04'9841'56f5'5334'4306_u128},
171+
{Sign::POS, -129, 0x94a0'3176'acf8'2d45'ae4b'a773'da6b'f754_u128},
172+
{Sign::POS, -129, 0xa09a'e4a0'bb30'0a19'2f89'5f44'a303'cc0b_u128},
173+
{Sign::POS, -129, 0xac7c'd3ad'58fe'e7f0'811f'9539'84ef'f83e_u128},
174+
{Sign::POS, -129, 0xb844'2987'd22c'f576'9cc3'ef36'746d'e3b8_u128},
175+
{Sign::POS, -129, 0xc3ef'1535'754b'168d'3122'c2a5'9efd'dc37_u128},
176+
{Sign::POS, -129, 0xcf7b'ca1d'476c'516d'a812'90bd'baad'62e4_u128},
177+
{Sign::POS, -129, 0xdae8'804f'0ae6'015b'362c'b974'182e'3030_u128},
178+
{Sign::POS, -129, 0xe633'74c9'8e22'f0b4'2872'ce1b'fc7a'd1cd_u128},
179+
{Sign::POS, -129, 0xf15a'e9c0'37b1'd8f0'6c48'e9e3'420b'0f1e_u128},
180+
{Sign::POS, -129, 0xfc5d'26df'c4d5'cfda'27c0'7c91'1290'b8d1_u128},
181+
{Sign::POS, -128, 0x839c'3cc9'17ff'6cb4'bfd7'9717'f288'0abf_u128},
182+
{Sign::POS, -128, 0x88f5'9aa0'da59'1421'b892'ca83'61d8'c84c_u128},
183+
{Sign::POS, -128, 0x8e39'd9cd'7346'4364'bba4'cfec'bff5'4867_u128},
184+
{Sign::POS, -128, 0x9368'2a66'e896'f544'b178'2191'1e71'c16e_u128},
185+
{Sign::POS, -128, 0x987f'bfe7'0b81'a708'19ce'c845'ac87'a5c6_u128},
186+
{Sign::POS, -128, 0x9d7f'd149'0285'c9e3'e25e'3954'9638'ae68_u128},
187+
{Sign::POS, -128, 0xa267'9928'48ee'b0c0'3b51'67ee'359a'234e_u128},
188+
{Sign::POS, -128, 0xa736'55df'1f2f'489e'149f'6e75'9934'68a3_u128},
189+
{Sign::POS, -128, 0xabeb'49a4'6764'fd15'1bec'da80'89c1'a94c_u128},
190+
{Sign::POS, -128, 0xb085'baa8'e966'f6da'e4ca'd00d'5c94'bcd2_u128},
191+
{Sign::POS, -128, 0xb504'f333'f9de'6484'597d'89b3'754a'be9f_u128},
192+
{Sign::POS, -128, 0xb968'41bf'7ffc'b21a'9de1'e3b2'2b8b'f4db_u128},
193+
{Sign::POS, -128, 0xbdae'f913'557d'76f0'ac85'320f'528d'6d5d_u128},
194+
{Sign::POS, -128, 0xc1d8'705f'fcbb'6e90'bdf0'715c'b8b2'0bd7_u128},
195+
{Sign::POS, -128, 0xc5e4'0358'a8ba'05a7'43da'25d9'9267'326b_u128},
196+
{Sign::POS, -128, 0xc9d1'124c'931f'da7a'8335'241b'e169'3225_u128},
197+
{Sign::POS, -128, 0xcd9f'023f'9c3a'059e'23af'31db'7179'a4aa_u128},
198+
{Sign::POS, -128, 0xd14d'3d02'313c'0eed'744f'ea20'e8ab'ef92_u128},
199+
{Sign::POS, -128, 0xd4db'3148'750d'1819'f630'e8b6'dac8'3e69_u128},
200+
{Sign::POS, -128, 0xd848'52c0'a80f'fcdb'24b9'fe00'6635'74a4_u128},
201+
{Sign::POS, -128, 0xdb94'1a28'cb71'ec87'2c19'b632'53da'43fc_u128},
202+
{Sign::POS, -128, 0xdebe'0563'7ca9'4cfb'4b19'aa71'fec3'ae6d_u128},
203+
{Sign::POS, -128, 0xe1c5'978c'05ed'8691'f4e8'a837'2f8c'5810_u128},
204+
{Sign::POS, -128, 0xe4aa'5909'a08f'a7b4'1227'85ae'67f5'515d_u128},
205+
{Sign::POS, -128, 0xe76b'd7a1'e63b'9786'1251'2952'9d48'a92f_u128},
206+
{Sign::POS, -128, 0xea09'a68a'6e49'cd62'15ad'45b4'a1b5'e823_u128},
207+
{Sign::POS, -128, 0xec83'5e79'946a'3145'7e61'0231'ac1d'6181_u128},
208+
{Sign::POS, -128, 0xeed8'9db6'6611'e307'86f8'c20f'b664'b01b_u128},
209+
{Sign::POS, -128, 0xf109'0827'b437'25fd'6712'7db3'5b28'7316_u128},
210+
{Sign::POS, -128, 0xf314'4762'4708'8f74'a548'6bdc'455d'56a2_u128},
211+
{Sign::POS, -128, 0xf4fa'0ab6'316e'd2ec'163c'5c7f'03b7'18c5_u128},
212+
{Sign::POS, -128, 0xf6ba'073b'424b'19e8'2c79'1f59'cc1f'fc23_u128},
213+
{Sign::POS, -128, 0xf853'f7dc'9186'b952'c7ad'c6b4'9888'91bb_u128},
214+
{Sign::POS, -128, 0xf9c7'9d63'272c'4628'4504'ae08'd19b'2980_u128},
215+
{Sign::POS, -128, 0xfb14'be7f'bae5'8156'2172'a361'fd2a'722f_u128},
216+
{Sign::POS, -128, 0xfc3b'27d3'8a5d'49ab'2567'78ff'cb5c'1769_u128},
217+
{Sign::POS, -128, 0xfd3a'abf8'4528'b50b'eae6'bd95'1c1d'abbe_u128},
218+
{Sign::POS, -128, 0xfe13'2387'0cfe'9a3d'90cd'1d95'9db6'74ef_u128},
219+
{Sign::POS, -128, 0xfec4'6d1e'8929'2cf0'4139'0efd'c726'e9ef_u128},
220+
{Sign::POS, -128, 0xff4e'6d68'0c41'd0a9'0f66'8633'f1ab'858a_u128},
221+
{Sign::POS, -128, 0xffb1'0f1b'cb6b'ef1d'421e'8eda'af59'453e_u128},
222+
{Sign::POS, -128, 0xffec'4304'2668'65d9'5657'5523'6696'1732_u128},
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{Sign::POS, 0, 1},
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};
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158226
} // namespace generic
159227

160228
} // namespace LIBC_NAMESPACE

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