[libc-commits] [libc] [libc][math][c23] implement C23 math function asinpif16 (PR #146226)
via libc-commits
libc-commits at lists.llvm.org
Sat Jun 28 09:27:50 PDT 2025
llvmbot wrote:
<!--LLVM PR SUMMARY COMMENT-->
@llvm/pr-subscribers-libc
Author: Mohamed Emad (hulxv)
<details>
<summary>Changes</summary>
The function is implemented using the following Taylor series that's generated using python-sympy, and it is very accurate for x $$\in [0, 0.5]$$ and has been verified using Geogebra. The range reduction is used for the rest range (0.5, 1].
$$
\frac{\arcsin(x)}{\pi} \approx
\begin{aligned}[t]
& 0.318309886183791x \\
& + 0.0530516476972984x^3 \\
& + 0.0238732414637843x^5 \\
& + 0.0142102627760621x^7 \\
& + 0.00967087327815336x^9 \\
& + 0.00712127941391293x^{11} \\
& + 0.00552355646848375x^{13} \\
& + 0.00444514782463692x^{15} \\
& + 0.00367705242846804x^{17} \\
& + 0.00310721681820837x^{19} + O(x^{21})
\end{aligned}
$$
### Geogebra graph
Closes #<!-- -->132210
---
Full diff: https://github.com/llvm/llvm-project/pull/146226.diff
10 Files Affected:
- (modified) libc/config/linux/aarch64/entrypoints.txt (+1)
- (modified) libc/config/linux/x86_64/entrypoints.txt (+1)
- (modified) libc/docs/headers/math/index.rst (+1-1)
- (modified) libc/include/math.yaml (+8-1)
- (modified) libc/src/math/CMakeLists.txt (+2)
- (added) libc/src/math/asinpif16.h (+21)
- (modified) libc/src/math/generic/CMakeLists.txt (+16)
- (added) libc/src/math/generic/asinpif16.cpp (+177)
- (modified) libc/test/src/math/CMakeLists.txt (+13)
- (added) libc/test/src/math/asinpif16_test.cpp (+110)
``````````diff
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index be5f5a66016b5..240d48f5bcdb8 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -651,6 +651,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
list(APPEND TARGET_LIBM_ENTRYPOINTS
# math.h C23 _Float16 entrypoints
# libc.src.math.acoshf16
+ libc.src.math.asinpif16
libc.src.math.canonicalizef16
libc.src.math.ceilf16
libc.src.math.copysignf16
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 73dfeae1a2c94..c9e5b0096099f 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -664,6 +664,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
libc.src.math.acoshf16
libc.src.math.asinf16
libc.src.math.asinhf16
+ libc.src.math.asinpif16
libc.src.math.canonicalizef16
libc.src.math.ceilf16
libc.src.math.copysignf16
diff --git a/libc/docs/headers/math/index.rst b/libc/docs/headers/math/index.rst
index 947bd4b60b391..aaacc3ca92832 100644
--- a/libc/docs/headers/math/index.rst
+++ b/libc/docs/headers/math/index.rst
@@ -259,7 +259,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| asinh | |check| | | | |check| | | 7.12.5.2 | F.10.2.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| asinpi | | | | | | 7.12.4.9 | F.10.1.9 |
+| asinpi | | | | |check| | | 7.12.4.9 | F.10.1.9 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atan | |check| | 1 ULP | | | | 7.12.4.3 | F.10.1.3 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/include/math.yaml b/libc/include/math.yaml
index fef829422244d..b49c17b871a93 100644
--- a/libc/include/math.yaml
+++ b/libc/include/math.yaml
@@ -71,7 +71,14 @@ functions:
- stdc
return_type: double
arguments:
- - type: double
+ - type: double
+ - name: asinpif16
+ standards:
+ - stdc
+ return_type: _Float16
+ arguments:
+ - type: _Float16
+ guard: LIBC_TYPES_HAS_FLOAT16
- name: atan2
standards:
- stdc
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index d177ff79141c0..e7ccb3726c54c 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -56,6 +56,8 @@ add_math_entrypoint_object(asinh)
add_math_entrypoint_object(asinhf)
add_math_entrypoint_object(asinhf16)
+add_math_entrypoint_object(asinpif16)
+
add_math_entrypoint_object(atan)
add_math_entrypoint_object(atanf)
diff --git a/libc/src/math/asinpif16.h b/libc/src/math/asinpif16.h
new file mode 100644
index 0000000000000..67ccb4ff4ac3d
--- /dev/null
+++ b/libc/src/math/asinpif16.h
@@ -0,0 +1,21 @@
+//===-- Implementation header for asinpif16 ---------------------*- 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_ASINFPI16_H
+#define LLVM_LIBC_SRC_MATH_ASINFPI16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 asinpif16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_ASINPIF16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index adbed5b2de48c..76accf72058d3 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4017,6 +4017,22 @@ add_entrypoint_object(
libc.src.__support.macros.properties.types
)
+add_entrypoint_object(
+ asinpif16
+ SRCS
+ asinpif16.cpp
+ HDRS
+ ../asinpif16.h
+ DEPENDS
+ libc.hdr.errno_macros
+ libc.hdr.fenv_macros
+ libc.src.__support.FPUtil.cast
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.macros.optimization
+)
+
add_entrypoint_object(
atanhf
SRCS
diff --git a/libc/src/math/generic/asinpif16.cpp b/libc/src/math/generic/asinpif16.cpp
new file mode 100644
index 0000000000000..34b0b7e7779fc
--- /dev/null
+++ b/libc/src/math/generic/asinpif16.cpp
@@ -0,0 +1,177 @@
+//===-- Half-precision asinf16(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/asinpif16.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 {
+
+static constexpr float16 ONE_OVER_TWO = 0.5f16;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr size_t N_ASINFPI_EXCEPTS = 3;
+static constexpr float16 ONE_OVER_SIX = 0.166748046875f16;
+
+static constexpr fputil::ExceptValues<float16, N_ASINFPI_EXCEPTS>
+ ASINFPI_EXCEPTS{{
+ // (input_hex, RZ_output_hex, RU_offset, RD_offset, RN_offset)
+ // x = 0.0, asinfpi(0.0) = 0.0
+ {0x0000, 0x0000, 0, 0, 0},
+
+ // x = 1.0, asinfpi(1.0) = 0.5
+ {(fputil::FPBits<float16>(1.0f16)).uintval(),
+ (fputil::FPBits<float16>(ONE_OVER_TWO)).uintval(), 0, 0, 0},
+
+ // x = 0.5, asinfpi(0.5) = 1/6
+ {(fputil::FPBits<float16>(0.5f16)).uintval(),
+ (fputil::FPBits<float16>(ONE_OVER_SIX)).uintval(), 0, 0, 0},
+
+ }};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+LLVM_LIBC_FUNCTION(float16, asinpif16, (float16 x)) {
+ using FPBits = fputil::FPBits<float16>;
+
+ FPBits xbits(x);
+ uint16_t x_uint = xbits.uintval();
+ bool is_neg = static_cast<bool>(x_uint >> 15);
+ float16 x_abs = is_neg ? -x : x;
+
+ auto __signed_result = [is_neg](float16 r) -> float16 {
+ return is_neg ? -r : r;
+ };
+
+ if (LIBC_UNLIKELY(x_abs > 1.0f16)) {
+ // aspinf16(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();
+ }
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ // exceptional values
+ if (auto r = ASINFPI_EXCEPTS.lookup(x_uint); LIBC_UNLIKELY(r.has_value())) {
+ return (r.value());
+ }
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+ // zero
+ if (LIBC_UNLIKELY(x_abs == 0.0f16)) {
+ return 0.0f16;
+ }
+
+ // +/-1.0
+ // if x is +/-1.0, return +/-0.5
+ if (LIBC_UNLIKELY(x_abs == 1.0f16)) {
+ return fputil::cast<float16>(__signed_result(ONE_OVER_TWO));
+ }
+
+ // the coefficients for the polynomial approximation of asin(x)/pi in the
+ // range [0, 0.5] extracted using python-sympy
+ //
+ // Python code to generate the coefficients:
+ // > from sympy import *
+ // > import math
+ // > x = symbols('x')
+ // > print(series(asin(x)/math.pi, x, 0, 21))
+ //
+ // OUTPUT:
+ //
+ // 0.318309886183791*x + 0.0530516476972984*x**3 + 0.0238732414637843*x**5 +
+ // 0.0142102627760621*x**7 + 0.00967087327815336*x**9 +
+ // 0.00712127941391293*x**11 + 0.00552355646848375*x**13 +
+ // 0.00444514782463692*x**15 + 0.00367705242846804*x**17 +
+ // 0.00310721681820837*x**19 + O(x**21)
+ //
+ // it's very accurate in the range [0, 0.5] and has a maximum error of
+ // 0.0000000000000001 in the range [0, 0.5].
+ static constexpr float16 POLY_COEFFS[10] = {
+ 0.318309886183791f16, // x^1
+ 0.0530516476972984f16, // x^3
+ 0.0238732414637843f16, // x^5
+ 0.0142102627760621f16, // x^7
+ 0.00967087327815336f16, // x^9
+ 0.00712127941391293f16, // x^11
+ 0.00552355646848375f16, // x^13
+ 0.00444514782463692f16, // x^15
+ 0.00367705242846804f16, // x^17
+ 0.00310721681820837f16 // x^19
+ };
+
+ // polynomial evaluation using horner's method
+ // work only for |x| in [0, 0.5]
+ auto __asinpi_polyeval = [](float16 xsq) -> float16 {
+ return fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2],
+ POLY_COEFFS[3], POLY_COEFFS[4], POLY_COEFFS[5],
+ POLY_COEFFS[6], POLY_COEFFS[7], POLY_COEFFS[8],
+ POLY_COEFFS[9]);
+ };
+
+ // if |x| <= 0.5:
+ if (LIBC_UNLIKELY(x_abs <= ONE_OVER_TWO)) {
+ // Use polynomial approximation of asin(x)/pi in the range [0, 0.5]
+ float16 xsq = x * x;
+ float16 result = x * __asinpi_polyeval(xsq);
+ return fputil::cast<float16>(__signed_result(result));
+ }
+
+ // If |x| > 0.5, we need to use the range reduction method:
+ // y = asin(x) => x = sin(y)
+ // because: sin(a) = cos(pi/2 - a)
+ // therefore:
+ // x = cos(pi/2 - y)
+ // let z = pi/2 - y,
+ // x = cos(z)
+ // becuase: cos(2a) = 1 - 2 * sin^2(a), z = 2a, a = z/2
+ // therefore:
+ // cos(z) = 1 - 2 * sin^2(z/2)
+ // sin(z/2) = sqrt((1 - cos(z))/2)
+ // sin(z/2) = sqrt((1 - x)/2)
+ // let u = (1 - x)/2
+ // then:
+ // sin(z/2) = sqrt(u)
+ // z/2 = asin(sqrt(u))
+ // z = 2 * asin(sqrt(u))
+ // pi/2 - y = 2 * asin(sqrt(u))
+ // y = pi/2 - 2 * asin(sqrt(u))
+ // y/pi = 1/2 - 2 * asin(sqrt(u))/pi
+ //
+ // Finally, we can write:
+ // asinpi(x) = 1/2 - 2 * asinpi(sqrt(u))
+ // where u = (1 - x) /2
+ // = 0.5 - 0.5 * x
+ // = multiply_add(-0.5, x, 0.5)
+
+ float16 u = fputil::multiply_add(-ONE_OVER_TWO, x_abs, ONE_OVER_TWO);
+ float16 u_sqrt = fputil::sqrt<float16>(u);
+ float16 asinpi_sqrt_u = u_sqrt * __asinpi_polyeval(u);
+ float16 result = fputil::multiply_add(-2.0f16, asinpi_sqrt_u, ONE_OVER_TWO);
+
+ return fputil::cast<float16>(__signed_result(result));
+}
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index 7ee8b86135557..bd62b76817ceb 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -2245,6 +2245,19 @@ add_fp_unittest(
libc.src.math.asinf16
)
+add_fp_unittest(
+ asinpif16_test
+ NEED_MPFR
+ SUITE
+ libc-math-unittests
+ SRCS
+ asinpif16_test.cpp
+ DEPENDS
+ libc.src.math.fabs
+ libc.src.math.asinpif16
+ libc.src.__support.FPUtil.fp_bits
+)
+
add_fp_unittest(
acosf_test
NEED_MPFR
diff --git a/libc/test/src/math/asinpif16_test.cpp b/libc/test/src/math/asinpif16_test.cpp
new file mode 100644
index 0000000000000..6d8f76568902e
--- /dev/null
+++ b/libc/test/src/math/asinpif16_test.cpp
@@ -0,0 +1,110 @@
+//===-- Unittests for asinpif16 -------------------------------------------===//
+//
+// 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/asinpif16.h"
+#include "src/math/fabs.h"
+#include "test/UnitTest/FPMatcher.h"
+
+#include <errno.h>
+#include <stdint.h>
+
+using LlvmLibcAsinpif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+
+TEST_F(LlvmLibcAsinpif16Test, SpecialNumbers) {
+ using FPBits = LIBC_NAMESPACE::fputil::FPBits<float16>;
+
+ // zero
+ EXPECT_FP_EQ(0.0f16, LIBC_NAMESPACE::asinpif16(0.0f16));
+
+ // +/-1
+ EXPECT_FP_EQ(float16(0.5), LIBC_NAMESPACE::asinpif16(float16(1.0)));
+ EXPECT_FP_EQ(float16(-0.5), LIBC_NAMESPACE::asinpif16(float16(-1.0)));
+
+ // NaN inputs
+ EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+ LIBC_NAMESPACE::asinpif16(FPBits::quiet_nan().get_val()));
+
+ EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+ LIBC_NAMESPACE::asinpif16(FPBits::signaling_nan().get_val()));
+
+ // infinity inputs -> should return NaN
+ errno = 0;
+ EXPECT_FP_EQ(FPBits::quiet_nan().get_val(), LIBC_NAMESPACE::asinpif16(inf));
+ EXPECT_MATH_ERRNO(EDOM);
+
+ errno = 0;
+ EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+ LIBC_NAMESPACE::asinpif16(neg_inf));
+ EXPECT_MATH_ERRNO(EDOM);
+}
+
+TEST_F(LlvmLibcAsinpif16Test, OutOfRange) {
+ using FPBits = LIBC_NAMESPACE::fputil::FPBits<float16>;
+
+ // Test values > 1
+ errno = 0;
+ EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+ LIBC_NAMESPACE::asinpif16(float16(1.5)));
+ EXPECT_MATH_ERRNO(EDOM);
+
+ errno = 0;
+ EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+ LIBC_NAMESPACE::asinpif16(float16(2.0)));
+ EXPECT_MATH_ERRNO(EDOM);
+
+ // Test values < -1
+ errno = 0;
+ EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+ LIBC_NAMESPACE::asinpif16(float16(-1.5)));
+ EXPECT_MATH_ERRNO(EDOM);
+
+ errno = 0;
+ EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+ LIBC_NAMESPACE::asinpif16(float16(-2.0)));
+ EXPECT_MATH_ERRNO(EDOM);
+
+ // Test maximum normal value (should be > 1 for float16)
+ errno = 0;
+ EXPECT_FP_EQ(FPBits::quiet_nan().get_val(),
+ LIBC_NAMESPACE::asinpif16(FPBits::max_normal().get_val()));
+ EXPECT_MATH_ERRNO(EDOM);
+}
+
+TEST_F(LlvmLibcAsinpif16Test, SymmetryProperty) {
+ // Test that asinpi(-x) = -asinpi(x)
+ constexpr float16 test_vals[] = {0.1f16, 0.25f16, 0.5f16, 0.75f16,
+ 0.9f16, 0.99f16, 1.0f16};
+
+ for (float16 x : test_vals) {
+ if (x <= 1.0) {
+ float16 pos_result = LIBC_NAMESPACE::asinpif16(x);
+ float16 neg_result = LIBC_NAMESPACE::asinpif16(-x);
+
+ EXPECT_FP_EQ(pos_result, LIBC_NAMESPACE::fabs(neg_result));
+ }
+ }
+}
+
+TEST_F(LlvmLibcAsinpif16Test, RangeValidation) {
+ // Test that output is always in [-0.5, 0.5] for valid inputs
+ constexpr int num_tests = 1000;
+
+ for (int i = 0; i <= num_tests; ++i) {
+ float16 t = -1.0f16 + (2.0f16 * static_cast<float16>(i)) /
+ static_cast<float16>(num_tests);
+
+ if (LIBC_NAMESPACE::fabs(t) <= 1.0) {
+ float16 result = LIBC_NAMESPACE::asinpif16(t);
+
+ // should be in [-0.5, 0.5]
+ EXPECT_TRUE(result >= -0.5f16);
+ EXPECT_TRUE(result <= 0.5f16);
+ }
+ }
+}
``````````
</details>
https://github.com/llvm/llvm-project/pull/146226
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