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[libc][math][c23] Implement C23 math function asinpif16 (llvm#146226)
The function is implemented using the following Taylor series that's generated using [python-sympy](https://www.sympy.org/en/index.html), 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 ![28-06-2025-1913-eDP-1](https://github.com/user-attachments/assets/f70818e1-1b34-406e-962a-a30fdc909f18) Closes llvm#132210
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‎libc/config/linux/aarch64/entrypoints.txt‎

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@@ -660,6 +660,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
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list(APPEND TARGET_LIBM_ENTRYPOINTS
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# math.h C23 _Float16 entrypoints
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# libc.src.math.acoshf16
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libc.src.math.asinpif16
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libc.src.math.canonicalizef16
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libc.src.math.ceilf16
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libc.src.math.copysignf16

‎libc/config/linux/x86_64/entrypoints.txt‎

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@@ -703,6 +703,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
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libc.src.math.acospif16
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libc.src.math.asinf16
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libc.src.math.asinhf16
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libc.src.math.asinpif16
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libc.src.math.atanf16
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libc.src.math.atanhf16
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libc.src.math.canonicalizef16

‎libc/docs/headers/math/index.rst‎

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@@ -259,7 +259,7 @@ Higher Math Functions
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| asinh | |check| | | | |check| | | 7.12.5.2 | F.10.2.2 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| asinpi | | | | | | 7.12.4.9 | F.10.1.9 |
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| asinpi | | | | |check| | | 7.12.4.9 | F.10.1.9 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| atan | |check| | 1 ULP | | |check| | | 7.12.4.3 | F.10.1.3 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

‎libc/include/math.yaml‎

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arguments:
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- type: _Float16
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guard: LIBC_TYPES_HAS_FLOAT16
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- name: asinpif16
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standards:
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- stdc
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return_type: _Float16
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arguments:
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- type: _Float16
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guard: LIBC_TYPES_HAS_FLOAT16
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- name: atan
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standards:
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- stdc

‎libc/src/math/CMakeLists.txt‎

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@@ -58,6 +58,8 @@ add_math_entrypoint_object(asinh)
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add_math_entrypoint_object(asinhf)
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add_math_entrypoint_object(asinhf16)
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add_math_entrypoint_object(asinpif16)
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add_math_entrypoint_object(atan)
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add_math_entrypoint_object(atanf)
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add_math_entrypoint_object(atanf16)

‎libc/src/math/asinpif16.h‎

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//===-- Implementation header for asinpif16 ---------------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception.
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//
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_SRC_MATH_ASINPIF16_H
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#define LLVM_LIBC_SRC_MATH_ASINPIF16_H
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#include "src/__support/macros/config.h"
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#include "src/__support/macros/properties/types.h"
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namespace LIBC_NAMESPACE_DECL {
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float16 asinpif16(float16 x);
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LLVM_LIBC_SRC_MATH_ASINPIF16_H

‎libc/src/math/generic/CMakeLists.txt‎

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@@ -3918,6 +3918,25 @@ add_entrypoint_object(
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libc.src.__support.macros.properties.types
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)
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add_entrypoint_object(
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asinpif16
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SRCS
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asinpif16.cpp
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HDRS
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../asinpif16.h
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DEPENDS
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libc.hdr.errno_macros
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libc.hdr.fenv_macros
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libc.src.__support.FPUtil.cast
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libc.src.__support.FPUtil.except_value_utils
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libc.src.__support.FPUtil.fenv_impl
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libc.src.__support.FPUtil.fp_bits
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libc.src.__support.FPUtil.multiply_add
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libc.src.__support.FPUtil.polyeval
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libc.src.__support.FPUtil.sqrt
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libc.src.__support.macros.optimization
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)
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add_entrypoint_object(
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atanhf
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SRCS

‎libc/src/math/generic/asinpif16.cpp‎

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//===-- Half-precision asinpif16(x) function ------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception.
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//
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//===----------------------------------------------------------------------===//
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#include "src/math/asinpif16.h"
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#include "hdr/errno_macros.h"
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#include "hdr/fenv_macros.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FPBits.h"
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#include "src/__support/FPUtil/PolyEval.h"
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#include "src/__support/FPUtil/cast.h"
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#include "src/__support/FPUtil/except_value_utils.h"
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#include "src/__support/FPUtil/multiply_add.h"
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#include "src/__support/FPUtil/sqrt.h"
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#include "src/__support/macros/optimization.h"
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namespace LIBC_NAMESPACE_DECL {
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LLVM_LIBC_FUNCTION(float16, asinpif16, (float16 x)) {
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using FPBits = fputil::FPBits<float16>;
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FPBits xbits(x);
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bool is_neg = xbits.is_neg();
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double x_abs = fputil::cast<double>(xbits.abs().get_val());
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auto signed_result = [is_neg](auto r) -> auto { return is_neg ? -r : r; };
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if (LIBC_UNLIKELY(x_abs > 1.0)) {
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// aspinf16(NaN) = NaN
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if (xbits.is_nan()) {
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if (xbits.is_signaling_nan()) {
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fputil::raise_except_if_required(FE_INVALID);
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return FPBits::quiet_nan().get_val();
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}
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return x;
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}
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// 1 < |x| <= +/-inf
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fputil::raise_except_if_required(FE_INVALID);
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fputil::set_errno_if_required(EDOM);
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return FPBits::quiet_nan().get_val();
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}
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// the coefficients for the polynomial approximation of asin(x)/pi in the
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// range [0, 0.5] extracted using python-sympy
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//
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// Python code to generate the coefficients:
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// > from sympy import *
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// > import math
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// > x = symbols('x')
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// > print(series(asin(x)/math.pi, x, 0, 21))
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//
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// OUTPUT:
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//
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// 0.318309886183791*x + 0.0530516476972984*x**3 + 0.0238732414637843*x**5 +
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// 0.0142102627760621*x**7 + 0.00967087327815336*x**9 +
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// 0.00712127941391293*x**11 + 0.00552355646848375*x**13 +
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// 0.00444514782463692*x**15 + 0.00367705242846804*x**17 +
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// 0.00310721681820837*x**19 + O(x**21)
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//
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// it's very accurate in the range [0, 0.5] and has a maximum error of
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// 0.0000000000000001 in the range [0, 0.5].
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constexpr double POLY_COEFFS[] = {
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0x1.45f306dc9c889p-2, // x^1
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0x1.b2995e7b7b5fdp-5, // x^3
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0x1.8723a1d588a36p-6, // x^5
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0x1.d1a452f20430dp-7, // x^7
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0x1.3ce52a3a09f61p-7, // x^9
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0x1.d2b33e303d375p-8, // x^11
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0x1.69fde663c674fp-8, // x^13
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0x1.235134885f19bp-8, // x^15
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};
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// polynomial evaluation using horner's method
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// work only for |x| in [0, 0.5]
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auto asinpi_polyeval = [](double x) -> double {
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return x * fputil::polyeval(x * x, POLY_COEFFS[0], POLY_COEFFS[1],
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POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4],
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POLY_COEFFS[5], POLY_COEFFS[6], POLY_COEFFS[7]);
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};
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// if |x| <= 0.5:
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if (LIBC_UNLIKELY(x_abs <= 0.5)) {
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// Use polynomial approximation of asin(x)/pi in the range [0, 0.5]
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double result = asinpi_polyeval(fputil::cast<double>(x));
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return fputil::cast<float16>(result);
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}
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// If |x| > 0.5, we need to use the range reduction method:
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// y = asin(x) => x = sin(y)
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// because: sin(a) = cos(pi/2 - a)
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// therefore:
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// x = cos(pi/2 - y)
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// let z = pi/2 - y,
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// x = cos(z)
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// because: cos(2a) = 1 - 2 * sin^2(a), z = 2a, a = z/2
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// therefore:
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// cos(z) = 1 - 2 * sin^2(z/2)
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// sin(z/2) = sqrt((1 - cos(z))/2)
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// sin(z/2) = sqrt((1 - x)/2)
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// let u = (1 - x)/2
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// then:
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// sin(z/2) = sqrt(u)
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// z/2 = asin(sqrt(u))
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// z = 2 * asin(sqrt(u))
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// pi/2 - y = 2 * asin(sqrt(u))
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// y = pi/2 - 2 * asin(sqrt(u))
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// y/pi = 1/2 - 2 * asin(sqrt(u))/pi
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//
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// Finally, we can write:
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// asinpi(x) = 1/2 - 2 * asinpi(sqrt(u))
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// where u = (1 - x) /2
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// = 0.5 - 0.5 * x
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// = multiply_add(-0.5, x, 0.5)
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double u = fputil::multiply_add(-0.5, x_abs, 0.5);
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double asinpi_sqrt_u = asinpi_polyeval(fputil::sqrt<double>(u));
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double result = fputil::multiply_add(-2.0, asinpi_sqrt_u, 0.5);
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return fputil::cast<float16>(signed_result(result));
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}
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} // namespace LIBC_NAMESPACE_DECL

‎libc/test/src/math/CMakeLists.txt‎

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libc.src.math.asinf16
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)
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add_fp_unittest(
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asinpif16_test
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NEED_MPFR
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SUITE
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libc-math-unittests
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SRCS
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asinpif16_test.cpp
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DEPENDS
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libc.src.math.asinpif16
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)
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add_fp_unittest(
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acosf_test
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NEED_MPFR

‎libc/test/src/math/asinpif16_test.cpp‎

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//===-- Exhaustive test for asinpif16 -------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#include "src/math/asinpif16.h"
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#include "test/UnitTest/FPMatcher.h"
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#include "test/UnitTest/Test.h"
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#include "utils/MPFRWrapper/MPFRUtils.h"
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using LlvmLibcAsinpif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
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namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
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// Range: [0, Inf]
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static constexpr uint16_t POS_START = 0x0000U;
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static constexpr uint16_t POS_STOP = 0x7c00U;
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// Range: [-Inf, 0]
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static constexpr uint16_t NEG_START = 0x8000U;
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static constexpr uint16_t NEG_STOP = 0xfc00U;
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TEST_F(LlvmLibcAsinpif16Test, PositiveRange) {
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for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
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float16 x = FPBits(v).get_val();
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EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asinpi, x,
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LIBC_NAMESPACE::asinpif16(x), 0.5);
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}
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}
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TEST_F(LlvmLibcAsinpif16Test, NegativeRange) {
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for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
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float16 x = FPBits(v).get_val();
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EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asinpi, x,
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LIBC_NAMESPACE::asinpif16(x), 0.5);
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}
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}

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