[libc-commits] [libc] [libc][math] Implement double precision cos correctly rounded to all rounding modes. (PR #96591)
via libc-commits
libc-commits at lists.llvm.org
Mon Jun 24 21:48:22 PDT 2024
https://github.com/lntue created https://github.com/llvm/llvm-project/pull/96591
Sharing the same algorithm as double precision sin: https://github.com/llvm/llvm-project/pull/95736
>From aca8eb34aff1cc79ea0938a6c4eff28a309215b6 Mon Sep 17 00:00:00 2001
From: Tue Ly <lntue.h at gmail.com>
Date: Tue, 25 Jun 2024 04:44:08 +0000
Subject: [PATCH] [libc][math] Implement double precision cos correctly rounded
to all rounding modes.
---
libc/config/darwin/arm/entrypoints.txt | 1 +
libc/config/linux/aarch64/entrypoints.txt | 1 +
libc/config/linux/arm/entrypoints.txt | 1 +
libc/config/linux/riscv/entrypoints.txt | 1 +
libc/docs/math/index.rst | 2 +-
libc/src/math/generic/CMakeLists.txt | 45 +++-
libc/src/math/generic/cos.cpp | 197 ++++++++++++++++++
.../generic/range_reduction_double_common.h | 68 ++++++
libc/src/math/generic/sin.cpp | 132 ++----------
libc/src/math/generic/sincos_eval.h | 43 ++++
libc/src/math/x86_64/CMakeLists.txt | 10 -
libc/src/math/x86_64/cos.cpp | 19 --
libc/test/src/math/cos_test.cpp | 120 +++++++++--
libc/test/src/math/smoke/CMakeLists.txt | 10 +
libc/test/src/math/smoke/cos_test.cpp | 26 +++
15 files changed, 502 insertions(+), 174 deletions(-)
create mode 100644 libc/src/math/generic/cos.cpp
delete mode 100644 libc/src/math/x86_64/cos.cpp
create mode 100644 libc/test/src/math/smoke/cos_test.cpp
diff --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt
index d486916a542d6..2843c469559ba 100644
--- a/libc/config/darwin/arm/entrypoints.txt
+++ b/libc/config/darwin/arm/entrypoints.txt
@@ -130,6 +130,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.ceilf
libc.src.math.ceill
libc.src.math.coshf
+ libc.src.math.cos
libc.src.math.cosf
libc.src.math.erff
libc.src.math.exp
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 2d2e1b58c0b27..132a1589ed9d6 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -344,6 +344,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.ceilf
libc.src.math.ceill
libc.src.math.coshf
+ libc.src.math.cos
libc.src.math.cosf
libc.src.math.erff
libc.src.math.exp
diff --git a/libc/config/linux/arm/entrypoints.txt b/libc/config/linux/arm/entrypoints.txt
index 53cdcc3caab1c..6133ccf4976b1 100644
--- a/libc/config/linux/arm/entrypoints.txt
+++ b/libc/config/linux/arm/entrypoints.txt
@@ -218,6 +218,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.copysign
libc.src.math.copysignf
libc.src.math.copysignl
+ libc.src.math.cos
libc.src.math.cosf
libc.src.math.coshf
libc.src.math.erff
diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
index 18968f5b07b59..70102a08f1255 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/libc/config/linux/riscv/entrypoints.txt
@@ -352,6 +352,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.ceilf
libc.src.math.ceill
libc.src.math.coshf
+ libc.src.math.cos
libc.src.math.cosf
libc.src.math.erff
libc.src.math.exp
diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
index 29723be7ce752..dad3a0f2b0362 100644
--- a/libc/docs/math/index.rst
+++ b/libc/docs/math/index.rst
@@ -264,7 +264,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| compoundn | | | | | | 7.12.7.2 | F.10.4.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| cos | |check| | large | | | | 7.12.4.5 | F.10.1.5 |
+| cos | |check| | |check| | | | | 7.12.4.5 | F.10.1.5 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| cosh | |check| | | | | | 7.12.5.4 | F.10.2.4 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 54a5b6ac0a70c..3110166e6ceaf 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -142,14 +142,14 @@ add_header_library(
range_reduction_double_fma.h
range_reduction_double_nofma.h
DEPENDS
- libc.src.__support.FPUtil.double_double
- libc.src.__support.FPUtil.dyadic_float
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.fma
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.nearest_integer
- libc.src.__support.common
- libc.src.__support.integer_literals
+ libc.src.__support.FPUtil.double_double
+ libc.src.__support.FPUtil.dyadic_float
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.fma
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.nearest_integer
+ libc.src.__support.common
+ libc.src.__support.integer_literals
)
add_header_library(
@@ -169,7 +169,31 @@ add_header_library(
sincos_eval.h
DEPENDS
libc.src.__support.FPUtil.double_double
+ libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.integer_literals
+)
+
+add_entrypoint_object(
+ cos
+ SRCS
+ cos.cpp
+ HDRS
+ ../cos.h
+ DEPENDS
+ .range_reduction_double
+ .sincos_eval
+ libc.hdr.errno_macros
+ libc.src.errno.errno
+ libc.src.__support.FPUtil.double_double
+ libc.src.__support.FPUtil.dyadic_float
+ libc.src.__support.FPUtil.except_value_utils
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.macros.optimization
+ COMPILE_OPTIONS
+ -O3
)
add_entrypoint_object(
@@ -200,16 +224,15 @@ add_entrypoint_object(
HDRS
../sin.h
DEPENDS
+ .range_reduction_double
+ .sincos_eval
libc.hdr.errno_macros
libc.src.errno.errno
libc.src.__support.FPUtil.double_double
libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.fma
libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.nearest_integer
- libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
COMPILE_OPTIONS
diff --git a/libc/src/math/generic/cos.cpp b/libc/src/math/generic/cos.cpp
new file mode 100644
index 0000000000000..a2cfe758fe4cc
--- /dev/null
+++ b/libc/src/math/generic/cos.cpp
@@ -0,0 +1,197 @@
+//===-- Double-precision cos function -------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/cos.h"
+#include "hdr/errno_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
+#include "src/math/generic/sincos_eval.h"
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+#include "range_reduction_double_fma.h"
+
+using LIBC_NAMESPACE::fma::FAST_PASS_EXPONENT;
+using LIBC_NAMESPACE::fma::ONE_TWENTY_EIGHT_OVER_PI;
+using LIBC_NAMESPACE::fma::range_reduction_small;
+using LIBC_NAMESPACE::fma::SIN_K_PI_OVER_128;
+
+LIBC_INLINE constexpr bool NO_FMA = false;
+#else
+#include "range_reduction_double_nofma.h"
+
+using LIBC_NAMESPACE::nofma::FAST_PASS_EXPONENT;
+using LIBC_NAMESPACE::nofma::ONE_TWENTY_EIGHT_OVER_PI;
+using LIBC_NAMESPACE::nofma::range_reduction_small;
+using LIBC_NAMESPACE::nofma::SIN_K_PI_OVER_128;
+
+LIBC_INLINE constexpr bool NO_FMA = true;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
+// TODO: We might be able to improve the performance of large range reduction of
+// non-FMA targets further by operating directly on 25-bit chunks of 128/pi and
+// pre-split SIN_K_PI_OVER_128, but that might double the memory footprint of
+// those lookup table.
+#include "range_reduction_double_common.h"
+
+#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0)
+#define LIBC_MATH_COS_SKIP_ACCURATE_PASS
+#endif
+
+namespace LIBC_NAMESPACE {
+
+using DoubleDouble = fputil::DoubleDouble;
+using Float128 = typename fputil::DyadicFloat<128>;
+
+LLVM_LIBC_FUNCTION(double, cos, (double x)) {
+ using FPBits = typename fputil::FPBits<double>;
+ FPBits xbits(x);
+
+ uint16_t x_e = xbits.get_biased_exponent();
+
+ DoubleDouble y;
+ unsigned k;
+ generic::LargeRangeReduction<NO_FMA> range_reduction_large;
+
+ // |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)
+ if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
+ // |x| < 2^-27
+ if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {
+ // Signed zeros.
+ if (LIBC_UNLIKELY(x == 0.0))
+ return 1.0;
+
+ // For |x| < 2^-27, |cos(x) - 1| < |x|^2/2 < 2^-54 = ulp(1 - 2^-53)/2.
+ return fputil::round_result_slightly_down(1.0);
+ }
+
+ // // Small range reduction.
+ k = range_reduction_small(x, y);
+ } else {
+ // Inf or NaN
+ if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
+ // sin(+-Inf) = NaN
+ if (xbits.get_mantissa() == 0) {
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ }
+ return x + FPBits::quiet_nan().get_val();
+ }
+
+ // Large range reduction.
+ k = range_reduction_large.compute_high_part(x);
+ y = range_reduction_large.fast();
+ }
+
+ DoubleDouble sin_y, cos_y;
+
+ generic::sincos_eval(y, sin_y, cos_y);
+
+ // Look up sin(k * pi/128) and cos(k * pi/128)
+ // Memory saving versions:
+
+ // Use 128-entry table instead:
+ // DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 127];
+ // uint64_t sin_s = static_cast<uint64_t>((k + 128) & 128) << (63 - 7);
+ // sin_k.hi = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
+ // sin_k.lo = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
+ // DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 127];
+ // uint64_t cos_s = static_cast<uint64_t>((k + 64) & 128) << (63 - 7);
+ // cos_k.hi = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
+ // cos_k.lo = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
+
+ // Use 64-entry table instead:
+ // auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
+ // unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
+ // DoubleDouble ans = SIN_K_PI_OVER_128[idx];
+ // if (kk & 128) {
+ // ans.hi = -ans.hi;
+ // ans.lo = -ans.lo;
+ // }
+ // return ans;
+ // };
+ // DoubleDouble sin_k = get_idx_dd(k + 128);
+ // DoubleDouble cos_k = get_idx_dd(k + 64);
+
+ // Fast look up version, but needs 256-entry table.
+ // -sin(k * pi/128) = sin((k + 128) * pi/128)
+ // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
+ DoubleDouble msin_k = SIN_K_PI_OVER_128[(k + 128) & 255];
+ DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
+
+ // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
+ // So k is an integer and -pi / 256 <= y <= pi / 256.
+ // Then cos(x) = cos((k * pi/128 + y)
+ // = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)
+ DoubleDouble cos_k_cos_y = fputil::quick_mult<NO_FMA>(cos_y, cos_k);
+ DoubleDouble msin_k_sin_y = fputil::quick_mult<NO_FMA>(sin_y, msin_k);
+
+ DoubleDouble rr = fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi);
+ rr.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;
+
+#ifdef LIBC_MATH_COS_SKIP_ACCURATE_PASS
+ return rr.hi + rr.lo;
+#else
+
+ // Accurate test and pass for correctly rounded implementation.
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+ constexpr double ERR = 0x1.0p-70;
+#else
+ // TODO: Improve non-FMA fast pass accuracy.
+ constexpr double ERR = 0x1.0p-66;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
+ double rlp = rr.lo + ERR;
+ double rlm = rr.lo - ERR;
+
+ double r_upper = rr.hi + rlp; // (rr.lo + ERR);
+ double r_lower = rr.hi + rlm; // (rr.lo - ERR);
+
+ // Ziv's rounding test.
+ if (LIBC_LIKELY(r_upper == r_lower))
+ return r_upper;
+
+ Float128 u_f128, sin_u, cos_u;
+ if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
+ u_f128 = generic::range_reduction_small_f128(x);
+ else
+ u_f128 = range_reduction_large.accurate();
+
+ generic::sincos_eval(u_f128, sin_u, cos_u);
+
+ auto get_sin_k = [](unsigned kk) -> Float128 {
+ unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
+ Float128 ans = generic::SIN_K_PI_OVER_128_F128[idx];
+ if (kk & 128)
+ ans.sign = Sign::NEG;
+ return ans;
+ };
+
+ // -sin(k * pi/128) = sin((k + 128) * pi/128)
+ // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
+ Float128 msin_k_f128 = get_sin_k(k + 128);
+ Float128 cos_k_f128 = get_sin_k(k + 64);
+
+ // cos(x) = cos((k * pi/128 + u)
+ // = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)
+ Float128 r = fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u),
+ fputil::quick_mul(msin_k_f128, sin_u));
+
+ // TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
+ // https://github.com/llvm/llvm-project/issues/96452.
+
+ return static_cast<double>(r);
+#endif // !LIBC_MATH_COS_SKIP_ACCURATE_PASS
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/range_reduction_double_common.h b/libc/src/math/generic/range_reduction_double_common.h
index 0e9edf811891d..150118fba0ba0 100644
--- a/libc/src/math/generic/range_reduction_double_common.h
+++ b/libc/src/math/generic/range_reduction_double_common.h
@@ -155,6 +155,74 @@ LIBC_INLINE Float128 range_reduction_small_f128(double x) {
return fputil::quick_mul(y, PI_OVER_128_F128);
}
+LIBC_INLINE constexpr Float128 SIN_K_PI_OVER_128_F128[65] = {
+ {Sign::POS, 0, 0},
+ {Sign::POS, -133, 0xc90a'afbd'1b33'efc9'c539'edcb'fda0'cf2c_u128},
+ {Sign::POS, -132, 0xc8fb'2f88'6ec0'9f37'6a17'954b'2b7c'5171_u128},
+ {Sign::POS, -131, 0x96a9'0496'70cf'ae65'f775'7409'4d3c'35c4_u128},
+ {Sign::POS, -131, 0xc8bd'35e1'4da1'5f0e'c739'6c89'4bbf'7389_u128},
+ {Sign::POS, -131, 0xfab2'72b5'4b98'71a2'7047'29ae'56d7'8a37_u128},
+ {Sign::POS, -130, 0x9640'8374'7309'd113'000a'89a1'1e07'c1fe_u128},
+ {Sign::POS, -130, 0xaf10'a224'59fe'32a6'3fee'f3bb'58b1'f10d_u128},
+ {Sign::POS, -130, 0xc7c5'c1e3'4d30'55b2'5cc8'c00e'4fcc'd850_u128},
+ {Sign::POS, -130, 0xe05c'1353'f27b'17e5'0ebc'61ad'e6ca'83cd_u128},
+ {Sign::POS, -130, 0xf8cf'cbd9'0af8'd57a'4221'dc4b'a772'598d_u128},
+ {Sign::POS, -129, 0x888e'9315'8fb3'bb04'9841'56f5'5334'4306_u128},
+ {Sign::POS, -129, 0x94a0'3176'acf8'2d45'ae4b'a773'da6b'f754_u128},
+ {Sign::POS, -129, 0xa09a'e4a0'bb30'0a19'2f89'5f44'a303'cc0b_u128},
+ {Sign::POS, -129, 0xac7c'd3ad'58fe'e7f0'811f'9539'84ef'f83e_u128},
+ {Sign::POS, -129, 0xb844'2987'd22c'f576'9cc3'ef36'746d'e3b8_u128},
+ {Sign::POS, -129, 0xc3ef'1535'754b'168d'3122'c2a5'9efd'dc37_u128},
+ {Sign::POS, -129, 0xcf7b'ca1d'476c'516d'a812'90bd'baad'62e4_u128},
+ {Sign::POS, -129, 0xdae8'804f'0ae6'015b'362c'b974'182e'3030_u128},
+ {Sign::POS, -129, 0xe633'74c9'8e22'f0b4'2872'ce1b'fc7a'd1cd_u128},
+ {Sign::POS, -129, 0xf15a'e9c0'37b1'd8f0'6c48'e9e3'420b'0f1e_u128},
+ {Sign::POS, -129, 0xfc5d'26df'c4d5'cfda'27c0'7c91'1290'b8d1_u128},
+ {Sign::POS, -128, 0x839c'3cc9'17ff'6cb4'bfd7'9717'f288'0abf_u128},
+ {Sign::POS, -128, 0x88f5'9aa0'da59'1421'b892'ca83'61d8'c84c_u128},
+ {Sign::POS, -128, 0x8e39'd9cd'7346'4364'bba4'cfec'bff5'4867_u128},
+ {Sign::POS, -128, 0x9368'2a66'e896'f544'b178'2191'1e71'c16e_u128},
+ {Sign::POS, -128, 0x987f'bfe7'0b81'a708'19ce'c845'ac87'a5c6_u128},
+ {Sign::POS, -128, 0x9d7f'd149'0285'c9e3'e25e'3954'9638'ae68_u128},
+ {Sign::POS, -128, 0xa267'9928'48ee'b0c0'3b51'67ee'359a'234e_u128},
+ {Sign::POS, -128, 0xa736'55df'1f2f'489e'149f'6e75'9934'68a3_u128},
+ {Sign::POS, -128, 0xabeb'49a4'6764'fd15'1bec'da80'89c1'a94c_u128},
+ {Sign::POS, -128, 0xb085'baa8'e966'f6da'e4ca'd00d'5c94'bcd2_u128},
+ {Sign::POS, -128, 0xb504'f333'f9de'6484'597d'89b3'754a'be9f_u128},
+ {Sign::POS, -128, 0xb968'41bf'7ffc'b21a'9de1'e3b2'2b8b'f4db_u128},
+ {Sign::POS, -128, 0xbdae'f913'557d'76f0'ac85'320f'528d'6d5d_u128},
+ {Sign::POS, -128, 0xc1d8'705f'fcbb'6e90'bdf0'715c'b8b2'0bd7_u128},
+ {Sign::POS, -128, 0xc5e4'0358'a8ba'05a7'43da'25d9'9267'326b_u128},
+ {Sign::POS, -128, 0xc9d1'124c'931f'da7a'8335'241b'e169'3225_u128},
+ {Sign::POS, -128, 0xcd9f'023f'9c3a'059e'23af'31db'7179'a4aa_u128},
+ {Sign::POS, -128, 0xd14d'3d02'313c'0eed'744f'ea20'e8ab'ef92_u128},
+ {Sign::POS, -128, 0xd4db'3148'750d'1819'f630'e8b6'dac8'3e69_u128},
+ {Sign::POS, -128, 0xd848'52c0'a80f'fcdb'24b9'fe00'6635'74a4_u128},
+ {Sign::POS, -128, 0xdb94'1a28'cb71'ec87'2c19'b632'53da'43fc_u128},
+ {Sign::POS, -128, 0xdebe'0563'7ca9'4cfb'4b19'aa71'fec3'ae6d_u128},
+ {Sign::POS, -128, 0xe1c5'978c'05ed'8691'f4e8'a837'2f8c'5810_u128},
+ {Sign::POS, -128, 0xe4aa'5909'a08f'a7b4'1227'85ae'67f5'515d_u128},
+ {Sign::POS, -128, 0xe76b'd7a1'e63b'9786'1251'2952'9d48'a92f_u128},
+ {Sign::POS, -128, 0xea09'a68a'6e49'cd62'15ad'45b4'a1b5'e823_u128},
+ {Sign::POS, -128, 0xec83'5e79'946a'3145'7e61'0231'ac1d'6181_u128},
+ {Sign::POS, -128, 0xeed8'9db6'6611'e307'86f8'c20f'b664'b01b_u128},
+ {Sign::POS, -128, 0xf109'0827'b437'25fd'6712'7db3'5b28'7316_u128},
+ {Sign::POS, -128, 0xf314'4762'4708'8f74'a548'6bdc'455d'56a2_u128},
+ {Sign::POS, -128, 0xf4fa'0ab6'316e'd2ec'163c'5c7f'03b7'18c5_u128},
+ {Sign::POS, -128, 0xf6ba'073b'424b'19e8'2c79'1f59'cc1f'fc23_u128},
+ {Sign::POS, -128, 0xf853'f7dc'9186'b952'c7ad'c6b4'9888'91bb_u128},
+ {Sign::POS, -128, 0xf9c7'9d63'272c'4628'4504'ae08'd19b'2980_u128},
+ {Sign::POS, -128, 0xfb14'be7f'bae5'8156'2172'a361'fd2a'722f_u128},
+ {Sign::POS, -128, 0xfc3b'27d3'8a5d'49ab'2567'78ff'cb5c'1769_u128},
+ {Sign::POS, -128, 0xfd3a'abf8'4528'b50b'eae6'bd95'1c1d'abbe_u128},
+ {Sign::POS, -128, 0xfe13'2387'0cfe'9a3d'90cd'1d95'9db6'74ef_u128},
+ {Sign::POS, -128, 0xfec4'6d1e'8929'2cf0'4139'0efd'c726'e9ef_u128},
+ {Sign::POS, -128, 0xff4e'6d68'0c41'd0a9'0f66'8633'f1ab'858a_u128},
+ {Sign::POS, -128, 0xffb1'0f1b'cb6b'ef1d'421e'8eda'af59'453e_u128},
+ {Sign::POS, -128, 0xffec'4304'2668'65d9'5657'5523'6696'1732_u128},
+ {Sign::POS, 0, 1},
+};
+
} // namespace generic
} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/sin.cpp b/libc/src/math/generic/sin.cpp
index 5f2d8e7bd2d64..207435d4385ae 100644
--- a/libc/src/math/generic/sin.cpp
+++ b/libc/src/math/generic/sin.cpp
@@ -10,11 +10,9 @@
#include "hdr/errno_macros.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/double_double.h"
#include "src/__support/FPUtil/dyadic_float.h"
#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/common.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
@@ -56,88 +54,6 @@ namespace LIBC_NAMESPACE {
using DoubleDouble = fputil::DoubleDouble;
using Float128 = typename fputil::DyadicFloat<128>;
-namespace {
-
-#ifndef LIBC_MATH_SIN_SKIP_ACCURATE_PASS
-LIBC_INLINE constexpr Float128 SIN_K_PI_OVER_128_F128[65] = {
- {Sign::POS, 0, 0},
- {Sign::POS, -133, 0xc90a'afbd'1b33'efc9'c539'edcb'fda0'cf2c_u128},
- {Sign::POS, -132, 0xc8fb'2f88'6ec0'9f37'6a17'954b'2b7c'5171_u128},
- {Sign::POS, -131, 0x96a9'0496'70cf'ae65'f775'7409'4d3c'35c4_u128},
- {Sign::POS, -131, 0xc8bd'35e1'4da1'5f0e'c739'6c89'4bbf'7389_u128},
- {Sign::POS, -131, 0xfab2'72b5'4b98'71a2'7047'29ae'56d7'8a37_u128},
- {Sign::POS, -130, 0x9640'8374'7309'd113'000a'89a1'1e07'c1fe_u128},
- {Sign::POS, -130, 0xaf10'a224'59fe'32a6'3fee'f3bb'58b1'f10d_u128},
- {Sign::POS, -130, 0xc7c5'c1e3'4d30'55b2'5cc8'c00e'4fcc'd850_u128},
- {Sign::POS, -130, 0xe05c'1353'f27b'17e5'0ebc'61ad'e6ca'83cd_u128},
- {Sign::POS, -130, 0xf8cf'cbd9'0af8'd57a'4221'dc4b'a772'598d_u128},
- {Sign::POS, -129, 0x888e'9315'8fb3'bb04'9841'56f5'5334'4306_u128},
- {Sign::POS, -129, 0x94a0'3176'acf8'2d45'ae4b'a773'da6b'f754_u128},
- {Sign::POS, -129, 0xa09a'e4a0'bb30'0a19'2f89'5f44'a303'cc0b_u128},
- {Sign::POS, -129, 0xac7c'd3ad'58fe'e7f0'811f'9539'84ef'f83e_u128},
- {Sign::POS, -129, 0xb844'2987'd22c'f576'9cc3'ef36'746d'e3b8_u128},
- {Sign::POS, -129, 0xc3ef'1535'754b'168d'3122'c2a5'9efd'dc37_u128},
- {Sign::POS, -129, 0xcf7b'ca1d'476c'516d'a812'90bd'baad'62e4_u128},
- {Sign::POS, -129, 0xdae8'804f'0ae6'015b'362c'b974'182e'3030_u128},
- {Sign::POS, -129, 0xe633'74c9'8e22'f0b4'2872'ce1b'fc7a'd1cd_u128},
- {Sign::POS, -129, 0xf15a'e9c0'37b1'd8f0'6c48'e9e3'420b'0f1e_u128},
- {Sign::POS, -129, 0xfc5d'26df'c4d5'cfda'27c0'7c91'1290'b8d1_u128},
- {Sign::POS, -128, 0x839c'3cc9'17ff'6cb4'bfd7'9717'f288'0abf_u128},
- {Sign::POS, -128, 0x88f5'9aa0'da59'1421'b892'ca83'61d8'c84c_u128},
- {Sign::POS, -128, 0x8e39'd9cd'7346'4364'bba4'cfec'bff5'4867_u128},
- {Sign::POS, -128, 0x9368'2a66'e896'f544'b178'2191'1e71'c16e_u128},
- {Sign::POS, -128, 0x987f'bfe7'0b81'a708'19ce'c845'ac87'a5c6_u128},
- {Sign::POS, -128, 0x9d7f'd149'0285'c9e3'e25e'3954'9638'ae68_u128},
- {Sign::POS, -128, 0xa267'9928'48ee'b0c0'3b51'67ee'359a'234e_u128},
- {Sign::POS, -128, 0xa736'55df'1f2f'489e'149f'6e75'9934'68a3_u128},
- {Sign::POS, -128, 0xabeb'49a4'6764'fd15'1bec'da80'89c1'a94c_u128},
- {Sign::POS, -128, 0xb085'baa8'e966'f6da'e4ca'd00d'5c94'bcd2_u128},
- {Sign::POS, -128, 0xb504'f333'f9de'6484'597d'89b3'754a'be9f_u128},
- {Sign::POS, -128, 0xb968'41bf'7ffc'b21a'9de1'e3b2'2b8b'f4db_u128},
- {Sign::POS, -128, 0xbdae'f913'557d'76f0'ac85'320f'528d'6d5d_u128},
- {Sign::POS, -128, 0xc1d8'705f'fcbb'6e90'bdf0'715c'b8b2'0bd7_u128},
- {Sign::POS, -128, 0xc5e4'0358'a8ba'05a7'43da'25d9'9267'326b_u128},
- {Sign::POS, -128, 0xc9d1'124c'931f'da7a'8335'241b'e169'3225_u128},
- {Sign::POS, -128, 0xcd9f'023f'9c3a'059e'23af'31db'7179'a4aa_u128},
- {Sign::POS, -128, 0xd14d'3d02'313c'0eed'744f'ea20'e8ab'ef92_u128},
- {Sign::POS, -128, 0xd4db'3148'750d'1819'f630'e8b6'dac8'3e69_u128},
- {Sign::POS, -128, 0xd848'52c0'a80f'fcdb'24b9'fe00'6635'74a4_u128},
- {Sign::POS, -128, 0xdb94'1a28'cb71'ec87'2c19'b632'53da'43fc_u128},
- {Sign::POS, -128, 0xdebe'0563'7ca9'4cfb'4b19'aa71'fec3'ae6d_u128},
- {Sign::POS, -128, 0xe1c5'978c'05ed'8691'f4e8'a837'2f8c'5810_u128},
- {Sign::POS, -128, 0xe4aa'5909'a08f'a7b4'1227'85ae'67f5'515d_u128},
- {Sign::POS, -128, 0xe76b'd7a1'e63b'9786'1251'2952'9d48'a92f_u128},
- {Sign::POS, -128, 0xea09'a68a'6e49'cd62'15ad'45b4'a1b5'e823_u128},
- {Sign::POS, -128, 0xec83'5e79'946a'3145'7e61'0231'ac1d'6181_u128},
- {Sign::POS, -128, 0xeed8'9db6'6611'e307'86f8'c20f'b664'b01b_u128},
- {Sign::POS, -128, 0xf109'0827'b437'25fd'6712'7db3'5b28'7316_u128},
- {Sign::POS, -128, 0xf314'4762'4708'8f74'a548'6bdc'455d'56a2_u128},
- {Sign::POS, -128, 0xf4fa'0ab6'316e'd2ec'163c'5c7f'03b7'18c5_u128},
- {Sign::POS, -128, 0xf6ba'073b'424b'19e8'2c79'1f59'cc1f'fc23_u128},
- {Sign::POS, -128, 0xf853'f7dc'9186'b952'c7ad'c6b4'9888'91bb_u128},
- {Sign::POS, -128, 0xf9c7'9d63'272c'4628'4504'ae08'd19b'2980_u128},
- {Sign::POS, -128, 0xfb14'be7f'bae5'8156'2172'a361'fd2a'722f_u128},
- {Sign::POS, -128, 0xfc3b'27d3'8a5d'49ab'2567'78ff'cb5c'1769_u128},
- {Sign::POS, -128, 0xfd3a'abf8'4528'b50b'eae6'bd95'1c1d'abbe_u128},
- {Sign::POS, -128, 0xfe13'2387'0cfe'9a3d'90cd'1d95'9db6'74ef_u128},
- {Sign::POS, -128, 0xfec4'6d1e'8929'2cf0'4139'0efd'c726'e9ef_u128},
- {Sign::POS, -128, 0xff4e'6d68'0c41'd0a9'0f66'8633'f1ab'858a_u128},
- {Sign::POS, -128, 0xffb1'0f1b'cb6b'ef1d'421e'8eda'af59'453e_u128},
- {Sign::POS, -128, 0xffec'4304'2668'65d9'5657'5523'6696'1732_u128},
- {Sign::POS, 0, 1},
-};
-
-#ifdef LIBC_TARGET_CPU_HAS_FMA
-constexpr double ERR = 0x1.0p-70;
-#else
-// TODO: Improve non-FMA fast pass accuracy.
-constexpr double ERR = 0x1.0p-66;
-#endif // LIBC_TARGET_CPU_HAS_FMA
-
-#endif // !LIBC_MATH_SIN_SKIP_ACCURATE_PASS
-
-} // anonymous namespace
-
LLVM_LIBC_FUNCTION(double, sin, (double x)) {
using FPBits = typename fputil::FPBits<double>;
FPBits xbits(x);
@@ -191,7 +107,7 @@ LLVM_LIBC_FUNCTION(double, sin, (double x)) {
DoubleDouble sin_y, cos_y;
- sincos_eval(y, sin_y, cos_y);
+ generic::sincos_eval(y, sin_y, cos_y);
// Look up sin(k * pi/128) and cos(k * pi/128)
// Memory saving versions:
@@ -231,8 +147,6 @@ LLVM_LIBC_FUNCTION(double, sin, (double x)) {
DoubleDouble sin_k_cos_y = fputil::quick_mult<NO_FMA>(cos_y, sin_k);
DoubleDouble cos_k_sin_y = fputil::quick_mult<NO_FMA>(sin_y, cos_k);
- FPBits sk_cy(sin_k_cos_y.hi);
- FPBits ck_sy(cos_k_sin_y.hi);
DoubleDouble rr = fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi);
rr.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;
@@ -240,6 +154,14 @@ LLVM_LIBC_FUNCTION(double, sin, (double x)) {
return rr.hi + rr.lo;
#else
// Accurate test and pass for correctly rounded implementation.
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+ constexpr double ERR = 0x1.0p-70;
+#else
+ // TODO: Improve non-FMA fast pass accuracy.
+ constexpr double ERR = 0x1.0p-66;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
double rlp = rr.lo + ERR;
double rlm = rr.lo - ERR;
@@ -250,47 +172,17 @@ LLVM_LIBC_FUNCTION(double, sin, (double x)) {
if (LIBC_LIKELY(r_upper == r_lower))
return r_upper;
- Float128 u_f128;
+ Float128 u_f128, sin_u, cos_u;
if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
u_f128 = generic::range_reduction_small_f128(x);
else
u_f128 = range_reduction_large.accurate();
- Float128 u_sq = fputil::quick_mul(u_f128, u_f128);
-
- // sin(u) ~ x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - x^11/11! + x^13/13!
- constexpr Float128 SIN_COEFFS[] = {
- {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1
- {Sign::NEG, -130, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // -1/3!
- {Sign::POS, -134, 0x88888888'88888888'88888888'88888889_u128}, // 1/5!
- {Sign::NEG, -140, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // -1/7!
- {Sign::POS, -146, 0xb8ef1d2a'b6399c7d'560e4472'800b8ef2_u128}, // 1/9!
- {Sign::NEG, -153, 0xd7322b3f'aa271c7f'3a3f25c1'bee38f10_u128}, // -1/11!
- {Sign::POS, -160, 0xb092309d'43684be5'1c198e91'd7b4269e_u128}, // 1/13!
- };
-
- // cos(u) ~ 1 - x^2/2 + x^4/4! - x^6/6! + x^8/8! - x^10/10! + x^12/12!
- constexpr Float128 COS_COEFFS[] = {
- {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
- {Sign::NEG, -128, 0x80000000'00000000'00000000'00000000_u128}, // 1/2
- {Sign::POS, -132, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/4!
- {Sign::NEG, -137, 0xb60b60b6'0b60b60b'60b60b60'b60b60b6_u128}, // 1/6!
- {Sign::POS, -143, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // 1/8!
- {Sign::NEG, -149, 0x93f27dbb'c4fae397'780b69f5'333c725b_u128}, // 1/10!
- {Sign::POS, -156, 0x8f76c77f'c6c4bdaa'26d4c3d6'7f425f60_u128}, // 1/12!
- };
-
- Float128 sin_u = fputil::quick_mul(
- u_f128, fputil::polyeval(u_sq, SIN_COEFFS[0], SIN_COEFFS[1],
- SIN_COEFFS[2], SIN_COEFFS[3], SIN_COEFFS[4],
- SIN_COEFFS[5], SIN_COEFFS[6]));
- Float128 cos_u = fputil::polyeval(u_sq, COS_COEFFS[0], COS_COEFFS[1],
- COS_COEFFS[2], COS_COEFFS[3], COS_COEFFS[4],
- COS_COEFFS[5], COS_COEFFS[6]);
+ generic::sincos_eval(u_f128, sin_u, cos_u);
auto get_sin_k = [](unsigned kk) -> Float128 {
unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
- Float128 ans = SIN_K_PI_OVER_128_F128[idx];
+ Float128 ans = generic::SIN_K_PI_OVER_128_F128[idx];
if (kk & 128)
ans.sign = Sign::NEG;
return ans;
diff --git a/libc/src/math/generic/sincos_eval.h b/libc/src/math/generic/sincos_eval.h
index d5db18f04a8f1..5b4f3b8563cff 100644
--- a/libc/src/math/generic/sincos_eval.h
+++ b/libc/src/math/generic/sincos_eval.h
@@ -9,12 +9,18 @@
#ifndef LLVM_LIBC_SRC_MATH_GENERIC_SINCOS_EVAL_H
#define LLVM_LIBC_SRC_MATH_GENERIC_SINCOS_EVAL_H
+#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.h"
#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/integer_literals.h"
namespace LIBC_NAMESPACE {
+namespace generic {
+
using fputil::DoubleDouble;
+using Float128 = fputil::DyadicFloat<128>;
LIBC_INLINE void sincos_eval(const DoubleDouble &u, DoubleDouble &sin_u,
DoubleDouble &cos_u) {
@@ -76,6 +82,43 @@ LIBC_INLINE void sincos_eval(const DoubleDouble &u, DoubleDouble &sin_u,
cos_u = fputil::exact_add(v_hi, cos_lo);
}
+LIBC_INLINE void sincos_eval(const Float128 &u, Float128 &sin_u,
+ Float128 &cos_u) {
+ Float128 u_sq = fputil::quick_mul(u, u);
+
+ // sin(u) ~ x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - x^11/11! + x^13/13!
+ constexpr Float128 SIN_COEFFS[] = {
+ {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1
+ {Sign::NEG, -130, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // -1/3!
+ {Sign::POS, -134, 0x88888888'88888888'88888888'88888889_u128}, // 1/5!
+ {Sign::NEG, -140, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // -1/7!
+ {Sign::POS, -146, 0xb8ef1d2a'b6399c7d'560e4472'800b8ef2_u128}, // 1/9!
+ {Sign::NEG, -153, 0xd7322b3f'aa271c7f'3a3f25c1'bee38f10_u128}, // -1/11!
+ {Sign::POS, -160, 0xb092309d'43684be5'1c198e91'd7b4269e_u128}, // 1/13!
+ };
+
+ // cos(u) ~ 1 - x^2/2 + x^4/4! - x^6/6! + x^8/8! - x^10/10! + x^12/12!
+ constexpr Float128 COS_COEFFS[] = {
+ {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
+ {Sign::NEG, -128, 0x80000000'00000000'00000000'00000000_u128}, // 1/2
+ {Sign::POS, -132, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/4!
+ {Sign::NEG, -137, 0xb60b60b6'0b60b60b'60b60b60'b60b60b6_u128}, // 1/6!
+ {Sign::POS, -143, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // 1/8!
+ {Sign::NEG, -149, 0x93f27dbb'c4fae397'780b69f5'333c725b_u128}, // 1/10!
+ {Sign::POS, -156, 0x8f76c77f'c6c4bdaa'26d4c3d6'7f425f60_u128}, // 1/12!
+ };
+
+ sin_u = fputil::quick_mul(u, fputil::polyeval(u_sq, SIN_COEFFS[0],
+ SIN_COEFFS[1], SIN_COEFFS[2],
+ SIN_COEFFS[3], SIN_COEFFS[4],
+ SIN_COEFFS[5], SIN_COEFFS[6]));
+ cos_u = fputil::polyeval(u_sq, COS_COEFFS[0], COS_COEFFS[1], COS_COEFFS[2],
+ COS_COEFFS[3], COS_COEFFS[4], COS_COEFFS[5],
+ COS_COEFFS[6]);
+}
+
+} // namespace generic
+
} // namespace LIBC_NAMESPACE
#endif // LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF_EVAL_H
diff --git a/libc/src/math/x86_64/CMakeLists.txt b/libc/src/math/x86_64/CMakeLists.txt
index 882181b33b9f8..3cfc422e56d49 100644
--- a/libc/src/math/x86_64/CMakeLists.txt
+++ b/libc/src/math/x86_64/CMakeLists.txt
@@ -1,13 +1,3 @@
-add_entrypoint_object(
- cos
- SRCS
- cos.cpp
- HDRS
- ../cos.h
- COMPILE_OPTIONS
- -O2
-)
-
add_entrypoint_object(
tan
SRCS
diff --git a/libc/src/math/x86_64/cos.cpp b/libc/src/math/x86_64/cos.cpp
deleted file mode 100644
index 2cb8db4b7a859..0000000000000
--- a/libc/src/math/x86_64/cos.cpp
+++ /dev/null
@@ -1,19 +0,0 @@
-//===-- Implementation of the cos function for x86_64 ---------------------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-#include "src/math/cos.h"
-#include "src/__support/common.h"
-
-namespace LIBC_NAMESPACE {
-
-LLVM_LIBC_FUNCTION(double, cos, (double x)) {
- __asm__ __volatile__("fcos" : "+t"(x));
- return x;
-}
-
-} // namespace LIBC_NAMESPACE
diff --git a/libc/test/src/math/cos_test.cpp b/libc/test/src/math/cos_test.cpp
index 9a39616ed16f8..08cf28c0c140a 100644
--- a/libc/test/src/math/cos_test.cpp
+++ b/libc/test/src/math/cos_test.cpp
@@ -6,27 +6,121 @@
//
//===----------------------------------------------------------------------===//
+#include "src/__support/FPUtil/FPBits.h"
#include "src/math/cos.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
#include "utils/MPFRWrapper/MPFRUtils.h"
-#include "hdr/math_macros.h"
-
using LlvmLibcCosTest = LIBC_NAMESPACE::testing::FPTest<double>;
namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
-TEST_F(LlvmLibcCosTest, Range) {
- static constexpr double _2pi = 6.283185307179586;
- constexpr StorageType COUNT = 100'000;
- constexpr StorageType STEP = STORAGE_MAX / COUNT;
- for (StorageType i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
- double x = FPBits(v).get_val();
- // TODO: Expand the range of testing after range reduction is implemented.
- if (isnan(x) || isinf(x) || x > _2pi || x < -_2pi)
- continue;
-
- ASSERT_MPFR_MATCH(mpfr::Operation::Cos, x, LIBC_NAMESPACE::cos(x), 1.0);
+using LIBC_NAMESPACE::testing::tlog;
+
+TEST_F(LlvmLibcCosTest, TrickyInputs) {
+ constexpr double INPUTS[] = {
+ 0x1.8000000000009p-23, 0x1.8000000000024p-22,
+ 0x1.800000000009p-21, 0x1.20000000000f3p-20,
+ 0x1.800000000024p-20, 0x1.e0000000001c2p-20,
+ 0x1.940c877fb7dacp-7, -0x1.f42fb19b5b9b2p-6,
+ -0x1.0285070f9f1bcp-5, 0x1.23f40dccdef72p+0,
+ 0x1.43cf16358c9d7p+0, 0x1.addf3b9722265p+0,
+ 0x1.ae78d360afa15p+0, 0x1.e31b55306f22cp+2,
+ 0x1.e639103a05997p+2, -0x1.f7898d5a756ddp+2,
+ 0x1.1685973506319p+3, 0x1.5f09cad750ab1p+3,
+ -0x1.aaf85537ea4c7p+3, 0x1.4f2b874135d27p+4,
+ 0x1.13114266f9764p+4, 0x1.a211877de55dbp+4,
+ -0x1.a5eece87e8606p+4, 0x1.a65d441ea6dcep+4,
+ 0x1.1ffb509f3db15p+5, 0x1.2345d1e090529p+5,
+ 0x1.c96e28eb679f8p+5, 0x1.be886d9c2324dp+6,
+ -0x1.ab514bfc61c76p+7, -0x1.14823229799c2p+7,
+ 0x1.48ff1782ca91dp+8, 0x1.dcbfda0c7559ep+8,
+ 0x1.dcbfda0c7559ep+8, 0x1.2e566149bf5fdp+9,
+ 0x1.cb996c60f437ep+9, 0x1.ae945054939c2p+10,
+ -0x1.119471e9216cdp+10, 0x1.ae945054939c2p+10,
+ 0x1.fffffffffdb6p+24, 0x1.fd4da4ef37075p+29,
+ 0x1.55202aefde314p+31, 0x1.b951f1572eba5p+31,
+ 0x1.7776c2343ba4ep+101, 0x1.85fc0f04c0128p+101,
+ 0x1.678309fa50d58p+110, 0x1.fffffffffef4ep+199,
+ 0x1.3eec5912ea7cdp+331, -0x1.3eec5912ea7cdp+331,
+ -0x1.6deb37da81129p+205, 0x1.08087e9aad90bp+887,
+ -0x1.08087e9aad90bp+887, -0x1.8bb5847d49973p+845,
+ 0x1.6ac5b262ca1ffp+849, 0x1.f08b14e1c4d0fp+890,
+ 0x1.2b5fe88a9d8d5p+903, 0x1.f6d7518808571p+1023,
+ -0x1.a880417b7b119p+1023,
+
+ };
+ constexpr int N = sizeof(INPUTS) / sizeof(INPUTS[0]);
+
+ for (int i = 0; i < N; ++i) {
+ double x = INPUTS[i];
+ ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cos, x,
+ LIBC_NAMESPACE::cos(x), 0.5);
}
}
+
+TEST_F(LlvmLibcCosTest, InDoubleRange) {
+ constexpr uint64_t COUNT = 1'234'51;
+ uint64_t START = LIBC_NAMESPACE::fputil::FPBits<double>(0x1.0p-50).uintval();
+ uint64_t STOP = LIBC_NAMESPACE::fputil::FPBits<double>(0x1.0p200).uintval();
+ uint64_t STEP = (STOP - START) / COUNT;
+
+ auto test = [&](mpfr::RoundingMode rounding_mode) {
+ mpfr::ForceRoundingMode __r(rounding_mode);
+ if (!__r.success)
+ return;
+
+ uint64_t fails = 0;
+ uint64_t count = 0;
+ uint64_t cc = 0;
+ double mx, mr = 0.0;
+ double tol = 0.5;
+
+ for (uint64_t i = 0, v = START; i <= COUNT; ++i, v += STEP) {
+ double x = FPBits(v).get_val();
+ if (isnan(x) || isinf(x))
+ continue;
+ LIBC_NAMESPACE::libc_errno = 0;
+ double result = LIBC_NAMESPACE::cos(x);
+ ++cc;
+ if (isnan(result) || isinf(result))
+ continue;
+
+ ++count;
+
+ if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Cos, x, result,
+ 0.5, rounding_mode)) {
+ ++fails;
+ while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Cos, x,
+ result, tol, rounding_mode)) {
+ mx = x;
+ mr = result;
+
+ if (tol > 1000.0)
+ break;
+
+ tol *= 2.0;
+ }
+ }
+ }
+ if (fails) {
+ tlog << " Cos failed: " << fails << "/" << count << "/" << cc
+ << " tests.\n";
+ tlog << " Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
+ EXPECT_MPFR_MATCH(mpfr::Operation::Cos, mx, mr, 0.5, rounding_mode);
+ }
+ };
+
+ tlog << " Test Rounding To Nearest...\n";
+ test(mpfr::RoundingMode::Nearest);
+
+ tlog << " Test Rounding Downward...\n";
+ test(mpfr::RoundingMode::Downward);
+
+ tlog << " Test Rounding Upward...\n";
+ test(mpfr::RoundingMode::Upward);
+
+ tlog << " Test Rounding Toward Zero...\n";
+ test(mpfr::RoundingMode::TowardZero);
+}
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index ffa8ba138e309..d5668c3f2ce69 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -3663,3 +3663,13 @@ add_fp_unittest(
DEPENDS
libc.src.math.sin
)
+
+add_fp_unittest(
+ cos_test
+ SUITE
+ libc-math-smoke-tests
+ SRCS
+ cos_test.cpp
+ DEPENDS
+ libc.src.math.cos
+)
diff --git a/libc/test/src/math/smoke/cos_test.cpp b/libc/test/src/math/smoke/cos_test.cpp
new file mode 100644
index 0000000000000..81c8612dba26e
--- /dev/null
+++ b/libc/test/src/math/smoke/cos_test.cpp
@@ -0,0 +1,26 @@
+//===-- Unittests for cos -------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/cos.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcCosTest = LIBC_NAMESPACE::testing::FPTest<double>;
+
+using LIBC_NAMESPACE::testing::tlog;
+
+TEST_F(LlvmLibcCosTest, SpecialNumbers) {
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::cos(aNaN));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::cos(inf));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::cos(neg_inf));
+ EXPECT_FP_EQ_ALL_ROUNDING(1.0, LIBC_NAMESPACE::cos(zero));
+ EXPECT_FP_EQ_ALL_ROUNDING(1.0, LIBC_NAMESPACE::cos(neg_zero));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::cos(0x1.0p-50));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::cos(min_normal));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::cos(min_denormal));
+}
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