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[libc][math] Refactor acospif16 implementation to header-only in src/__support/math folder. (#148574)

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Part of #147386

in preparation for:
https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
This commit is contained in:
Muhammad Bassiouni 2025-07-25 21:28:27 +03:00 committed by GitHub
parent 0844812b2e
commit 47e2de0d50
No known key found for this signature in database
GPG Key ID: B5690EEEBB952194
9 changed files with 223 additions and 129 deletions
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1
libc/shared/math.h
View File

@ -16,6 +16,7 @@
#include "math/acosf16.h"
#include "math/acoshf.h"
#include "math/acoshf16.h"
#include "math/acospif16.h"
#include "math/erff.h"
#include "math/exp.h"
#include "math/exp10.h"

29
libc/shared/math/acospif16.h Normal file
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@ -0,0 +1,29 @@
//===-- Shared acospif16 function -------------------------------*- 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_SHARED_MATH_ACOSPIF16_H
#define LLVM_LIBC_SHARED_MATH_ACOSPIF16_H
#include "include/llvm-libc-macros/float16-macros.h"
#ifdef LIBC_TYPES_HAS_FLOAT16
#include "shared/libc_common.h"
#include "src/__support/math/acospif16.h"
namespace LIBC_NAMESPACE_DECL {
namespace shared {
using math::acospif16;
} // namespace shared
} // namespace LIBC_NAMESPACE_DECL
#endif // LIBC_TYPES_HAS_FLOAT16
#endif // LLVM_LIBC_SHARED_MATH_ACOSPIF16_H

15
libc/src/__support/math/CMakeLists.txt
View File

@ -95,6 +95,21 @@ add_header_library(
libc.src.__support.macros.optimization
)
add_header_library(
acospif16
HDRS
acospif16.h
DEPENDS
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.FPUtil.polyeval
libc.src.__support.FPUtil.sqrt
libc.src.__support.macros.optimization
libc.src.__support.macros.properties.types
)
add_header_library(
asin_utils
HDRS

147
libc/src/__support/math/acospif16.h Normal file
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@ -0,0 +1,147 @@
//===-- Implementation header for acospif16 ---------------------*- 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___SUPPORT_MATH_ACOSPIF16_H
#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSPIF16_H
#include "include/llvm-libc-macros/float16-macros.h"
#ifdef LIBC_TYPES_HAS_FLOAT16
#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/multiply_add.h"
#include "src/__support/FPUtil/sqrt.h"
#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
namespace math {
static constexpr float16 acospif16(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)) {
// acospif16(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();
}
// |x| == 0x1p0, x is 1 or -1
// if x is (-)1, return 1
// if x is (+)1, return 0
if (LIBC_UNLIKELY(x_abs == 0x3c00))
return fputil::cast<float16>(x_sign ? 1.0f : 0.0f);
float xf = x;
float xsq = xf * xf;
// Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya
// with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0,
// 0.5]);
constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f,
0x1.897e36p-6f, 0x1.9efafcp-7f,
0x1.06d884p-6f};
// |x| <= 0x1p-1, |x| <= 0.5
if (x_abs <= 0x3800) {
// if x is 0, return 0.5
if (LIBC_UNLIKELY(x_abs == 0))
return fputil::cast<float16>(0.5f);
// Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x), then
// acospi(x) = 0.5 - asin(x)/pi
float interm =
fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2],
POLY_COEFFS[3], POLY_COEFFS[4]);
return fputil::cast<float16>(fputil::multiply_add(-xf, interm, 0.5f));
}
// 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))
// acospi(x) = 2 * (asin(sqrt(u)) / pi)
//
// 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)
// acospi(x) = 1 - acos(-x)/pi
// 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);
float asin_sqrt_u =
sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1],
POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]);
// Same as acos(x), but devided the expression with pi
return fputil::cast<float16>(
x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f)
: 2.0f * asin_sqrt_u);
}
} // namespace math
} // namespace LIBC_NAMESPACE_DECL
#endif // LIBC_TYPES_HAS_FLOAT16
#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSPIF16_H

12
libc/src/math/generic/CMakeLists.txt
View File

@ -4043,16 +4043,8 @@ add_entrypoint_object(
HDRS
../acospif16.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.FPUtil.polyeval
libc.src.__support.FPUtil.sqrt
libc.src.__support.macros.optimization
libc.src.__support.macros.properties.types
libc.src.__support.math.acospif16
libc.src.errno.errno
)
add_header_library(

122
libc/src/math/generic/acospif16.cpp
View File

@ -7,128 +7,12 @@
//===----------------------------------------------------------------------===//
#include "src/math/acospif16.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/multiply_add.h"
#include "src/__support/FPUtil/sqrt.h"
#include "src/__support/macros/optimization.h"
#include "src/__support/math/acospif16.h"
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float16, acospif16, (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)) {
// acospif16(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();
}
// |x| == 0x1p0, x is 1 or -1
// if x is (-)1, return 1
// if x is (+)1, return 0
if (LIBC_UNLIKELY(x_abs == 0x3c00))
return fputil::cast<float16>(x_sign ? 1.0f : 0.0f);
float xf = x;
float xsq = xf * xf;
// Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya
// with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0,
// 0.5]);
constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f,
0x1.897e36p-6f, 0x1.9efafcp-7f,
0x1.06d884p-6f};
// |x| <= 0x1p-1, |x| <= 0.5
if (x_abs <= 0x3800) {
// if x is 0, return 0.5
if (LIBC_UNLIKELY(x_abs == 0))
return fputil::cast<float16>(0.5f);
// Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x), then
// acospi(x) = 0.5 - asin(x)/pi
float interm =
fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2],
POLY_COEFFS[3], POLY_COEFFS[4]);
return fputil::cast<float16>(fputil::multiply_add(-xf, interm, 0.5f));
}
// 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))
// acospi(x) = 2 * (asin(sqrt(u)) / pi)
//
// 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)
// acospi(x) = 1 - acos(-x)/pi
// 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);
float asin_sqrt_u =
sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1],
POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]);
// Same as acos(x), but devided the expression with pi
return fputil::cast<float16>(
x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f)
: 2.0f * asin_sqrt_u);
return math::acospif16(x);
}
} // namespace LIBC_NAMESPACE_DECL

1
libc/test/shared/CMakeLists.txt
View File

@ -12,6 +12,7 @@ add_fp_unittest(
libc.src.__support.math.acosf16
libc.src.__support.math.acoshf
libc.src.__support.math.acoshf16
libc.src.__support.math.acospif16
libc.src.__support.math.erff
libc.src.__support.math.exp
libc.src.__support.math.exp10

2
libc/test/shared/shared_math_test.cpp
View File

@ -8,6 +8,7 @@
#include "shared/math.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
#ifdef LIBC_TYPES_HAS_FLOAT16
@ -15,6 +16,7 @@ TEST(LlvmLibcSharedMathTest, AllFloat16) {
int exponent;
EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::acoshf16(1.0f16));
EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::acospif16(1.0f16));
EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::exp10f16(0.0f16));

23
utils/bazel/llvm-project-overlay/libc/BUILD.bazel
View File

@ -2184,6 +2184,21 @@ libc_support_library(
],
)
libc_support_library(
name = "__support_math_acospif16",
hdrs = ["src/__support/math/acospif16.h"],
deps = [
":__support_fputil_cast",
":__support_fputil_fenv_impl",
":__support_fputil_fp_bits",
":__support_fputil_multiply_add",
":__support_fputil_polyeval",
":__support_fputil_sqrt",
":__support_macros_optimization",
":__support_macros_properties_types",
],
)
libc_support_library(
name = "__support_math_asin_utils",
hdrs = ["src/__support/math/asin_utils.h"],
@ -2735,6 +2750,14 @@ libc_math_function(
],
)
libc_math_function(
name = "acospif16",
additional_deps = [
":__support_math_acospif16",
":errno",
],
)
libc_math_function(
name = "asinf",
additional_deps = [