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[libc][math][c23] Add acosf16() function (#127731)

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- Implementation of acosf16 (inverse cosine) function for 16-bit inputs.
- Exhaustive tests across the 16-bit input range.
This commit is contained in:
wldfngrs
2025-02-23 19:46:46 +01:00
committed by GitHub
parent 8ea6b735a6
commit 3e284554a8
11 changed files with 302 additions and 1 deletions
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1
libc/config/linux/x86_64/entrypoints.txt
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@@ -649,6 +649,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
list(APPEND TARGET_LIBM_ENTRYPOINTS
# math.h C23 _Float16 entrypoints
libc.src.math.asinf16
libc.src.math.acosf16
libc.src.math.canonicalizef16
libc.src.math.ceilf16
libc.src.math.copysignf16

2
libc/docs/headers/math/index.rst
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@@ -250,7 +250,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| <Func> | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | C23 Definition Section | C23 Error Handling Section |
+===========+==================+=================+========================+======================+========================+========================+============================+
| acos | |check| | | | | | 7.12.4.1 | F.10.1.1 |
| acos | |check| | | | |check| | | 7.12.4.1 | F.10.1.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| acosh | |check| | | | | | 7.12.5.1 | F.10.2.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

7
libc/include/math.yaml
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@@ -14,6 +14,13 @@ functions:
return_type: float
arguments:
- type: float
- name: acosf16
standards:
- stdc
return_type: _Float16
arguments:
- type: _Float16
guard: LIBC_TYPES_HAS_FLOAT16
- name: acoshf
standards:
- stdc

2
libc/src/math/CMakeLists.txt
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@@ -42,6 +42,8 @@ endfunction()
add_math_entrypoint_object(acos)
add_math_entrypoint_object(acosf)
add_math_entrypoint_object(acosf16)
add_math_entrypoint_object(acosh)
add_math_entrypoint_object(acoshf)

21
libc/src/math/acosf16.h Normal file
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@@ -0,0 +1,21 @@
//===-- Implementation header for acosf16 -----------------------*- C++ -*-===//
//
// 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.
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_LIBC_SRC_MATH_ACOSF16_H
#define LLVM_LIBC_SRC_MATH_ACOSF16_H
#include "src/__support/macros/config.h"
#include "src/__support/macros/properties/types.h"
namespace LIBC_NAMESPACE_DECL {
float16 acosf16(float16 x);
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SRC_MATH_ACOSF16_H

20
libc/src/math/generic/CMakeLists.txt
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@@ -4034,6 +4034,26 @@ add_entrypoint_object(
.inv_trigf_utils
)
add_entrypoint_object(
acosf16
SRCS
acosf16.cpp
HDRS
../acosf16.h
DEPENDS
libc.hdr.errno_macros
libc.hdr.fenv_macros
libc.src.__support.FPUtil.cast
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.sqrt
libc.src.__support.macros.optimization
libc.src.__support.macros.properties.types
)
add_entrypoint_object(
atanf
SRCS

147
libc/src/math/generic/acosf16.cpp Normal file
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@@ -0,0 +1,147 @@
//===-- Half-precision acosf16(x) 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/acosf16.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/cast.h"
#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/sqrt.h"
#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
// Generated by Sollya using the following command:
// > round(pi/2, SG, RN);
// > round(pi, SG, RN);
static constexpr float PI_OVER_2 = 0x1.921fb6p0f;
static constexpr float PI = 0x1.921fb6p1f;
static constexpr size_t N_EXCEPTS = 2;
static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSF16_EXCEPTS{{
// (input, RZ output, RU offset, RD offset, RN offset)
{0xacaf, 0x3e93, 1, 0, 0},
{0xb874, 0x4052, 1, 0, 1},
}};
LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) {
using FPBits = fputil::FPBits<float16>;
FPBits xbits(x);
uint16_t x_u = xbits.uintval();
uint16_t x_abs = x_u & 0x7fff;
uint16_t x_sign = x_u >> 15;
// |x| > 0x1p0, |x| > 1, or x is NaN.
if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
// acosf16(NaN) = NaN
if (xbits.is_nan()) {
if (xbits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
return x;
}
// 1 < |x| <= +/-inf
fputil::raise_except_if_required(FE_INVALID);
fputil::set_errno_if_required(EDOM);
return FPBits::quiet_nan().get_val();
}
float xf = x;
// Handle exceptional values
if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();
// |x| == 0x1p0, x is 1 or -1
// if x is (-)1, return pi, else
// if x is (+)1, return 0
if (LIBC_UNLIKELY(x_abs == 0x3c00))
return fputil::cast<float16>(x_sign ? PI : 0.0f);
float xsq = xf * xf;
// |x| <= 0x1p-1, |x| <= 0.5
if (x_abs <= 0x3800) {
// if x is 0, return pi/2
if (LIBC_UNLIKELY(x_abs == 0))
return fputil::cast<float16>(PI_OVER_2);
// Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
// Degree-6 minimax polynomial of asin(x) generated by Sollya with:
// > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
float interm =
fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
return fputil::cast<float16>(fputil::multiply_add(-xf, interm, PI_OVER_2));
}
// When |x| > 0.5, assume that 0.5 < |x| <= 1
//
// Step-by-step range-reduction proof:
// 1: Let y = asin(x), such that, x = sin(y)
// 2: From complimentary angle identity:
// x = sin(y) = cos(pi/2 - y)
// 3: Let z = pi/2 - y, such that x = cos(z)
// 4: From double angle formula; cos(2A) = 1 - 2 * sin^2(A):
// z = 2A, z/2 = A
// cos(z) = 1 - 2 * sin^2(z/2)
// 5: Make sin(z/2) subject of the formula:
// sin(z/2) = sqrt((1 - cos(z))/2)
// 6: Recall [3]; x = cos(z). Therefore:
// sin(z/2) = sqrt((1 - x)/2)
// 7: Let u = (1 - x)/2
// 8: Therefore:
// asin(sqrt(u)) = z/2
// 2 * asin(sqrt(u)) = z
// 9: Recall [3]; z = pi/2 - y. Therefore:
// y = pi/2 - z
// y = pi/2 - 2 * asin(sqrt(u))
// 10: Recall [1], y = asin(x). Therefore:
// asin(x) = pi/2 - 2 * asin(sqrt(u))
// 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
// Therefore:
// acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u)))
// acos(x) = 2 * asin(sqrt(u))
//
// THE RANGE REDUCTION, HOW?
// 12: Recall [7], u = (1 - x)/2
// 13: Since 0.5 < x <= 1, therefore:
// 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
//
// Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
// Step [11] as `sqrt(u)` is in range.
// When -1 < x <= -0.5, the identity:
// acos(x) = pi - acos(-x)
// allows us to compute for the negative x value (lhs)
// with a positive x value instead (rhs).
float xf_abs = (xf < 0 ? -xf : xf);
float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
float sqrt_u = fputil::sqrt<float>(u);
// Degree-6 minimax polynomial of asin(x) generated by Sollya with:
// > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
float asin_sqrt_u =
sqrt_u * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
return fputil::cast<float16>(
x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u);
}
} // namespace LIBC_NAMESPACE_DECL

11
libc/test/src/math/CMakeLists.txt
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@@ -2210,6 +2210,17 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
add_fp_unittest(
acosf16_test
NEED_MPFR
SUITE
libc-math-unittests
SRCS
acosf16_test.cpp
DEPENDS
libc.src.math.acosf16
)
add_fp_unittest(
atanf_test
NEED_MPFR

42
libc/test/src/math/acosf16_test.cpp Normal file
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@@ -0,0 +1,42 @@
//===-- Exhaustive test for acosf16 ---------------------------------------===//
//
// 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/acosf16.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
#include "utils/MPFRWrapper/MPFRUtils.h"
using LlvmLibcAcosf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
// Range: [0, Inf]
static constexpr uint16_t POS_START = 0x0000U;
static constexpr uint16_t POS_STOP = 0x7c00U;
// Range: [-Inf, 0]
static constexpr uint16_t NEG_START = 0x8000U;
static constexpr uint16_t NEG_STOP = 0xfc00U;
TEST_F(LlvmLibcAcosf16Test, PositiveRange) {
for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
float16 x = FPBits(v).get_val();
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
LIBC_NAMESPACE::acosf16(x), 0.5);
}
}
TEST_F(LlvmLibcAcosf16Test, NegativeRange) {
for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
float16 x = FPBits(v).get_val();
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
LIBC_NAMESPACE::acosf16(x), 0.5);
}
}

11
libc/test/src/math/smoke/CMakeLists.txt
View File

@@ -3980,6 +3980,17 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
add_fp_unittest(
acosf16_test
SUITE
libc-math-smoke-tests
SRCS
acosf16_test.cpp
DEPENDS
libc.src.errno.errno
libc.src.math.acosf16
)
add_fp_unittest(
atanf_test
SUITE

39
libc/test/src/math/smoke/acosf16_test.cpp Normal file
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@@ -0,0 +1,39 @@
//===-- Unittests for acosf16 ---------------------------------------------===//
//
//
// 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/errno/libc_errno.h"
#include "src/math/acosf16.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
using LlvmLibcAcosf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
TEST_F(LlvmLibcAcosf16Test, SpecialNumbers) {
LIBC_NAMESPACE::libc_errno = 0;
EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(aNaN));
EXPECT_MATH_ERRNO(0);
EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::acosf16(sNaN), FE_INVALID);
EXPECT_MATH_ERRNO(0);
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::acosf16(1.0f));
EXPECT_MATH_ERRNO(0);
EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(inf));
EXPECT_MATH_ERRNO(EDOM);
EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(neg_inf));
EXPECT_MATH_ERRNO(EDOM);
EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(2.0f));
EXPECT_MATH_ERRNO(EDOM);
EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(-2.0f));
EXPECT_MATH_ERRNO(EDOM);
}