Skip to content

Commit eed9b4e

Browse files
hulxvhulxv
authored
[libc][math][c23] Implement C23 math function asinpif16 (#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 #132210
1 parent 5d26e3c commit eed9b4e

File tree

16 files changed

+338
-1
lines changed

16 files changed

+338
-1
lines changed

‎libc/config/linux/aarch64/entrypoints.txt

Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -660,6 +660,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
660660
list(APPEND TARGET_LIBM_ENTRYPOINTS
661661
# math.h C23 _Float16 entrypoints
662662
# libc.src.math.acoshf16
663+
libc.src.math.asinpif16
663664
libc.src.math.canonicalizef16
664665
libc.src.math.ceilf16
665666
libc.src.math.copysignf16

‎libc/config/linux/x86_64/entrypoints.txt

Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -703,6 +703,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
703703
libc.src.math.acospif16
704704
libc.src.math.asinf16
705705
libc.src.math.asinhf16
706+
libc.src.math.asinpif16
706707
libc.src.math.atanf16
707708
libc.src.math.atanhf16
708709
libc.src.math.canonicalizef16

‎libc/docs/headers/math/index.rst

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -259,7 +259,7 @@ Higher Math Functions
259259
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
260260
| asinh | |check| | | | |check| | | 7.12.5.2 | F.10.2.2 |
261261
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
262-
| asinpi | | | | | | 7.12.4.9 | F.10.1.9 |
262+
| asinpi | | | | |check| | | 7.12.4.9 | F.10.1.9 |
263263
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
264264
| atan | |check| | 1 ULP | | |check| | | 7.12.4.3 | F.10.1.3 |
265265
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

‎libc/include/math.yaml

Lines changed: 7 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -79,6 +79,13 @@ functions:
7979
arguments:
8080
- type: _Float16
8181
guard: LIBC_TYPES_HAS_FLOAT16
82+
- name: asinpif16
83+
standards:
84+
- stdc
85+
return_type: _Float16
86+
arguments:
87+
- type: _Float16
88+
guard: LIBC_TYPES_HAS_FLOAT16
8289
- name: atan
8390
standards:
8491
- stdc

‎libc/src/math/CMakeLists.txt

Lines changed: 2 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -58,6 +58,8 @@ add_math_entrypoint_object(asinh)
5858
add_math_entrypoint_object(asinhf)
5959
add_math_entrypoint_object(asinhf16)
6060

61+
add_math_entrypoint_object(asinpif16)
62+
6163
add_math_entrypoint_object(atan)
6264
add_math_entrypoint_object(atanf)
6365
add_math_entrypoint_object(atanf16)

‎libc/src/math/asinpif16.h

Lines changed: 21 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,21 @@
1+
//===-- Implementation header for asinpif16 ---------------------*- C++ -*-===//
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+
#ifndef LLVM_LIBC_SRC_MATH_ASINPIF16_H
10+
#define LLVM_LIBC_SRC_MATH_ASINPIF16_H
11+
12+
#include "src/__support/macros/config.h"
13+
#include "src/__support/macros/properties/types.h"
14+
15+
namespace LIBC_NAMESPACE_DECL {
16+
17+
float16 asinpif16(float16 x);
18+
19+
} // namespace LIBC_NAMESPACE_DECL
20+
21+
#endif // LLVM_LIBC_SRC_MATH_ASINPIF16_H

‎libc/src/math/generic/CMakeLists.txt

Lines changed: 19 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -3918,6 +3918,25 @@ add_entrypoint_object(
39183918
libc.src.__support.macros.properties.types
39193919
)
39203920

3921+
add_entrypoint_object(
3922+
asinpif16
3923+
SRCS
3924+
asinpif16.cpp
3925+
HDRS
3926+
../asinpif16.h
3927+
DEPENDS
3928+
libc.hdr.errno_macros
3929+
libc.hdr.fenv_macros
3930+
libc.src.__support.FPUtil.cast
3931+
libc.src.__support.FPUtil.except_value_utils
3932+
libc.src.__support.FPUtil.fenv_impl
3933+
libc.src.__support.FPUtil.fp_bits
3934+
libc.src.__support.FPUtil.multiply_add
3935+
libc.src.__support.FPUtil.polyeval
3936+
libc.src.__support.FPUtil.sqrt
3937+
libc.src.__support.macros.optimization
3938+
)
3939+
39213940
add_entrypoint_object(
39223941
atanhf
39233942
SRCS

‎libc/src/math/generic/asinpif16.cpp

Lines changed: 127 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,127 @@
1+
//===-- Half-precision asinpif16(x) 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/asinpif16.h"
10+
#include "hdr/errno_macros.h"
11+
#include "hdr/fenv_macros.h"
12+
#include "src/__support/FPUtil/FEnvImpl.h"
13+
#include "src/__support/FPUtil/FPBits.h"
14+
#include "src/__support/FPUtil/PolyEval.h"
15+
#include "src/__support/FPUtil/cast.h"
16+
#include "src/__support/FPUtil/except_value_utils.h"
17+
#include "src/__support/FPUtil/multiply_add.h"
18+
#include "src/__support/FPUtil/sqrt.h"
19+
#include "src/__support/macros/optimization.h"
20+
21+
namespace LIBC_NAMESPACE_DECL {
22+
23+
LLVM_LIBC_FUNCTION(float16, asinpif16, (float16 x)) {
24+
using FPBits = fputil::FPBits<float16>;
25+
26+
FPBits xbits(x);
27+
bool is_neg = xbits.is_neg();
28+
double x_abs = fputil::cast<double>(xbits.abs().get_val());
29+
30+
auto signed_result = [is_neg](auto r) -> auto { return is_neg ? -r : r; };
31+
32+
if (LIBC_UNLIKELY(x_abs > 1.0)) {
33+
// aspinf16(NaN) = NaN
34+
if (xbits.is_nan()) {
35+
if (xbits.is_signaling_nan()) {
36+
fputil::raise_except_if_required(FE_INVALID);
37+
return FPBits::quiet_nan().get_val();
38+
}
39+
return x;
40+
}
41+
42+
// 1 < |x| <= +/-inf
43+
fputil::raise_except_if_required(FE_INVALID);
44+
fputil::set_errno_if_required(EDOM);
45+
46+
return FPBits::quiet_nan().get_val();
47+
}
48+
49+
// the coefficients for the polynomial approximation of asin(x)/pi in the
50+
// range [0, 0.5] extracted using python-sympy
51+
//
52+
// Python code to generate the coefficients:
53+
// > from sympy import *
54+
// > import math
55+
// > x = symbols('x')
56+
// > print(series(asin(x)/math.pi, x, 0, 21))
57+
//
58+
// OUTPUT:
59+
//
60+
// 0.318309886183791*x + 0.0530516476972984*x**3 + 0.0238732414637843*x**5 +
61+
// 0.0142102627760621*x**7 + 0.00967087327815336*x**9 +
62+
// 0.00712127941391293*x**11 + 0.00552355646848375*x**13 +
63+
// 0.00444514782463692*x**15 + 0.00367705242846804*x**17 +
64+
// 0.00310721681820837*x**19 + O(x**21)
65+
//
66+
// it's very accurate in the range [0, 0.5] and has a maximum error of
67+
// 0.0000000000000001 in the range [0, 0.5].
68+
constexpr double POLY_COEFFS[] = {
69+
0x1.45f306dc9c889p-2, // x^1
70+
0x1.b2995e7b7b5fdp-5, // x^3
71+
0x1.8723a1d588a36p-6, // x^5
72+
0x1.d1a452f20430dp-7, // x^7
73+
0x1.3ce52a3a09f61p-7, // x^9
74+
0x1.d2b33e303d375p-8, // x^11
75+
0x1.69fde663c674fp-8, // x^13
76+
0x1.235134885f19bp-8, // x^15
77+
};
78+
// polynomial evaluation using horner's method
79+
// work only for |x| in [0, 0.5]
80+
auto asinpi_polyeval = [](double x) -> double {
81+
return x * fputil::polyeval(x * x, POLY_COEFFS[0], POLY_COEFFS[1],
82+
POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4],
83+
POLY_COEFFS[5], POLY_COEFFS[6], POLY_COEFFS[7]);
84+
};
85+
86+
// if |x| <= 0.5:
87+
if (LIBC_UNLIKELY(x_abs <= 0.5)) {
88+
// Use polynomial approximation of asin(x)/pi in the range [0, 0.5]
89+
double result = asinpi_polyeval(fputil::cast<double>(x));
90+
return fputil::cast<float16>(result);
91+
}
92+
93+
// If |x| > 0.5, we need to use the range reduction method:
94+
// y = asin(x) => x = sin(y)
95+
// because: sin(a) = cos(pi/2 - a)
96+
// therefore:
97+
// x = cos(pi/2 - y)
98+
// let z = pi/2 - y,
99+
// x = cos(z)
100+
// because: cos(2a) = 1 - 2 * sin^2(a), z = 2a, a = z/2
101+
// therefore:
102+
// cos(z) = 1 - 2 * sin^2(z/2)
103+
// sin(z/2) = sqrt((1 - cos(z))/2)
104+
// sin(z/2) = sqrt((1 - x)/2)
105+
// let u = (1 - x)/2
106+
// then:
107+
// sin(z/2) = sqrt(u)
108+
// z/2 = asin(sqrt(u))
109+
// z = 2 * asin(sqrt(u))
110+
// pi/2 - y = 2 * asin(sqrt(u))
111+
// y = pi/2 - 2 * asin(sqrt(u))
112+
// y/pi = 1/2 - 2 * asin(sqrt(u))/pi
113+
//
114+
// Finally, we can write:
115+
// asinpi(x) = 1/2 - 2 * asinpi(sqrt(u))
116+
// where u = (1 - x) /2
117+
// = 0.5 - 0.5 * x
118+
// = multiply_add(-0.5, x, 0.5)
119+
120+
double u = fputil::multiply_add(-0.5, x_abs, 0.5);
121+
double asinpi_sqrt_u = asinpi_polyeval(fputil::sqrt<double>(u));
122+
double result = fputil::multiply_add(-2.0, asinpi_sqrt_u, 0.5);
123+
124+
return fputil::cast<float16>(signed_result(result));
125+
}
126+
127+
} // namespace LIBC_NAMESPACE_DECL

‎libc/test/src/math/CMakeLists.txt

Lines changed: 11 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -2282,6 +2282,17 @@ add_fp_unittest(
22822282
libc.src.math.asinf16
22832283
)
22842284

2285+
add_fp_unittest(
2286+
asinpif16_test
2287+
NEED_MPFR
2288+
SUITE
2289+
libc-math-unittests
2290+
SRCS
2291+
asinpif16_test.cpp
2292+
DEPENDS
2293+
libc.src.math.asinpif16
2294+
)
2295+
22852296
add_fp_unittest(
22862297
acosf_test
22872298
NEED_MPFR

‎libc/test/src/math/asinpif16_test.cpp

Lines changed: 40 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,40 @@
1+
//===-- Exhaustive test for asinpif16 -------------------------------------===//
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/asinpif16.h"
10+
#include "test/UnitTest/FPMatcher.h"
11+
#include "test/UnitTest/Test.h"
12+
#include "utils/MPFRWrapper/MPFRUtils.h"
13+
14+
using LlvmLibcAsinpif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
15+
16+
namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
17+
18+
// Range: [0, Inf]
19+
static constexpr uint16_t POS_START = 0x0000U;
20+
static constexpr uint16_t POS_STOP = 0x7c00U;
21+
22+
// Range: [-Inf, 0]
23+
static constexpr uint16_t NEG_START = 0x8000U;
24+
static constexpr uint16_t NEG_STOP = 0xfc00U;
25+
26+
TEST_F(LlvmLibcAsinpif16Test, PositiveRange) {
27+
for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
28+
float16 x = FPBits(v).get_val();
29+
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asinpi, x,
30+
LIBC_NAMESPACE::asinpif16(x), 0.5);
31+
}
32+
}
33+
34+
TEST_F(LlvmLibcAsinpif16Test, NegativeRange) {
35+
for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
36+
float16 x = FPBits(v).get_val();
37+
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asinpi, x,
38+
LIBC_NAMESPACE::asinpif16(x), 0.5);
39+
}
40+
}

0 commit comments

Comments
 (0)