[libc-commits] [libc] 1bb0302 - [libc][math][c23] implement double-precision asinpi (#188158)
via libc-commits
libc-commits at lists.llvm.org
Sun Mar 29 07:18:12 PDT 2026
Author: Mohamed Emad
Date: 2026-03-29T10:18:07-04:00
New Revision: 1bb03026b6aa332863de65a7d245c4ecf3a99645
URL: https://github.com/llvm/llvm-project/commit/1bb03026b6aa332863de65a7d245c4ecf3a99645
DIFF: https://github.com/llvm/llvm-project/commit/1bb03026b6aa332863de65a7d245c4ecf3a99645.diff
LOG: [libc][math][c23] implement double-precision asinpi (#188158)
Implement the double precision version of the asinpi c23 math function
Added:
libc/shared/math/asinpi.h
libc/src/__support/math/asinpi.h
libc/src/math/asinpi.h
libc/src/math/generic/asinpi.cpp
libc/test/src/math/asinpi_test.cpp
libc/test/src/math/smoke/asinpi_test.cpp
Modified:
libc/config/baremetal/aarch64/entrypoints.txt
libc/config/baremetal/arm/entrypoints.txt
libc/config/baremetal/riscv/entrypoints.txt
libc/config/darwin/aarch64/entrypoints.txt
libc/config/gpu/amdgpu/entrypoints.txt
libc/config/gpu/nvptx/entrypoints.txt
libc/config/linux/aarch64/entrypoints.txt
libc/config/linux/arm/entrypoints.txt
libc/config/linux/riscv/entrypoints.txt
libc/config/linux/x86_64/entrypoints.txt
libc/config/windows/entrypoints.txt
libc/docs/headers/math/index.rst
libc/include/math.yaml
libc/shared/math.h
libc/src/__support/math/CMakeLists.txt
libc/src/__support/math/asin_utils.h
libc/src/math/CMakeLists.txt
libc/src/math/generic/CMakeLists.txt
libc/test/shared/CMakeLists.txt
libc/test/shared/shared_math_test.cpp
libc/test/src/math/CMakeLists.txt
libc/test/src/math/smoke/CMakeLists.txt
utils/bazel/llvm-project-overlay/libc/BUILD.bazel
Removed:
################################################################################
diff --git a/libc/config/baremetal/aarch64/entrypoints.txt b/libc/config/baremetal/aarch64/entrypoints.txt
index 19f3fb189de78..ed84bdff8ce1e 100644
--- a/libc/config/baremetal/aarch64/entrypoints.txt
+++ b/libc/config/baremetal/aarch64/entrypoints.txt
@@ -349,6 +349,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan2
libc.src.math.atan2f
diff --git a/libc/config/baremetal/arm/entrypoints.txt b/libc/config/baremetal/arm/entrypoints.txt
index 902f6ed44179b..43ba426b8ca09 100644
--- a/libc/config/baremetal/arm/entrypoints.txt
+++ b/libc/config/baremetal/arm/entrypoints.txt
@@ -359,6 +359,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan2
libc.src.math.atan2f
diff --git a/libc/config/baremetal/riscv/entrypoints.txt b/libc/config/baremetal/riscv/entrypoints.txt
index 5c2b5c24e158d..79fbd1e4b0de2 100644
--- a/libc/config/baremetal/riscv/entrypoints.txt
+++ b/libc/config/baremetal/riscv/entrypoints.txt
@@ -355,6 +355,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.acospif
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan2
libc.src.math.atan2f
diff --git a/libc/config/darwin/aarch64/entrypoints.txt b/libc/config/darwin/aarch64/entrypoints.txt
index 8e0d2fb01966f..71881d23c7a06 100644
--- a/libc/config/darwin/aarch64/entrypoints.txt
+++ b/libc/config/darwin/aarch64/entrypoints.txt
@@ -168,6 +168,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan2
libc.src.math.atan2f
diff --git a/libc/config/gpu/amdgpu/entrypoints.txt b/libc/config/gpu/amdgpu/entrypoints.txt
index 028d57b521165..e327d9ac6f3d3 100644
--- a/libc/config/gpu/amdgpu/entrypoints.txt
+++ b/libc/config/gpu/amdgpu/entrypoints.txt
@@ -287,6 +287,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan
libc.src.math.atan2
diff --git a/libc/config/gpu/nvptx/entrypoints.txt b/libc/config/gpu/nvptx/entrypoints.txt
index feae60547beda..efc784d23e301 100644
--- a/libc/config/gpu/nvptx/entrypoints.txt
+++ b/libc/config/gpu/nvptx/entrypoints.txt
@@ -287,6 +287,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan
libc.src.math.atan2
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 49288ce0699a3..4311ba624e6d8 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -443,6 +443,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan2
libc.src.math.atan2f
diff --git a/libc/config/linux/arm/entrypoints.txt b/libc/config/linux/arm/entrypoints.txt
index 9fd45329ad0f9..a10dc0c82e36f 100644
--- a/libc/config/linux/arm/entrypoints.txt
+++ b/libc/config/linux/arm/entrypoints.txt
@@ -268,6 +268,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan2
libc.src.math.atan2f
diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
index 2f5a742a272d7..17efa2e368ede 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/libc/config/linux/riscv/entrypoints.txt
@@ -447,6 +447,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan2
libc.src.math.atan2f
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 2d7de065d8119..eeaccc863dbc3 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -497,6 +497,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan2
libc.src.math.atan2f
diff --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt
index ee8072a3465e5..e594f6bbb1fd5 100644
--- a/libc/config/windows/entrypoints.txt
+++ b/libc/config/windows/entrypoints.txt
@@ -148,6 +148,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.asin
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.asinpi
libc.src.math.asinpif
libc.src.math.atan2
libc.src.math.atan2f
diff --git a/libc/docs/headers/math/index.rst b/libc/docs/headers/math/index.rst
index 88b284d1e63fd..f9614c6d19d22 100644
--- a/libc/docs/headers/math/index.rst
+++ b/libc/docs/headers/math/index.rst
@@ -269,7 +269,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+
| asinh | |check| | | | |check| | | | 7.12.5.2 | F.10.2.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+
-| asinpi | |check| | | | |check| | | | 7.12.4.9 | F.10.1.9 |
+| asinpi | |check| | |check| | | |check| | | | 7.12.4.9 | F.10.1.9 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+
| atan | |check| | 1 ULP | | |check| | | |check| | 7.12.4.3 | F.10.1.3 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/include/math.yaml b/libc/include/math.yaml
index dbb8479b1d0db..3984a665b234b 100644
--- a/libc/include/math.yaml
+++ b/libc/include/math.yaml
@@ -79,6 +79,18 @@ functions:
arguments:
- type: _Float16
guard: LIBC_TYPES_HAS_FLOAT16
+ - name: asinpi
+ standards:
+ - stdc
+ return_type: double
+ arguments:
+ - type: double
+ - name: asinpif
+ standards:
+ - stdc
+ return_type: float
+ arguments:
+ - type: float
- name: asinpif16
standards:
- stdc
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 71da66d37baba..08a4c994283c5 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -23,6 +23,7 @@
#include "math/asinf16.h"
#include "math/asinhf.h"
#include "math/asinhf16.h"
+#include "math/asinpi.h"
#include "math/asinpif.h"
#include "math/asinpif16.h"
#include "math/atan.h"
diff --git a/libc/shared/math/asinpi.h b/libc/shared/math/asinpi.h
new file mode 100644
index 0000000000000..42ada49e0a1ae
--- /dev/null
+++ b/libc/shared/math/asinpi.h
@@ -0,0 +1,23 @@
+//===-- Shared asinpi header ------------------------------------*- 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_ASINPI_H
+#define LLVM_LIBC_SHARED_MATH_ASINPI_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/asinpi.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::asinpi;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_ASINPI_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 187ff4f124b20..10329830a004b 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -189,6 +189,23 @@ add_header_library(
libc.src.__support.macros.optimization
)
+add_header_library(
+ asinpi
+ HDRS
+ asinpi.h
+ DEPENDS
+ .asin_utils
+ libc.src.__support.FPUtil.double_double
+ libc.src.__support.FPUtil.dyadic_float
+ 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.cpu_features
+)
+
add_header_library(
asinpif
HDRS
diff --git a/libc/src/__support/math/asin_utils.h b/libc/src/__support/math/asin_utils.h
index 2feb1485ec667..4f64ad5291711 100644
--- a/libc/src/__support/math/asin_utils.h
+++ b/libc/src/__support/math/asin_utils.h
@@ -63,6 +63,47 @@ LIBC_INLINE double asin_eval(double u) {
return fputil::polyeval(u4, d0, d1, d2);
}
+// Coefficients for the polynomial approximation of asin(x)/(pi*x) on [0, 0.5].
+// Generated by Sollya:
+// > prec = 200;
+// > g = asin(x) / (pi * x);
+// > P = fpminimax(g, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22|],
+// > [|D...|], [0, 0.5]);
+// > print("Error:", dirtyinfnorm(P - g, [1e-30; 0.25]));
+// Error : 0x1.a53f84eafa3ea69bb81b6c52b3278872083fca2c757bd778acp-54 ~= 2^-54
+LIBC_INLINE_VAR constexpr double ASINPI_COEFFS[12] = {
+ 0x1.45f306dc9c881p-2, // x^0
+ 0x1.b2995e7b7e756p-5, // x^2
+ 0x1.8723a1d12f828p-6, // x^4
+ 0x1.d1a45564b9545p-7, // x^6
+ 0x1.3ce4ceaa0e1e9p-7, // x^8
+ 0x1.d2c305898ea13p-8, // x^10
+ 0x1.692212e27a5f9p-8, // x^12
+ 0x1.2b22cc744d25bp-8, // x^14
+ 0x1.8427b864479ffp-9, // x^16
+ 0x1.815522d7a2bf1p-8, // x^18
+ -0x1.f6df98438aef4p-9, // x^20
+ 0x1.4b50c2eb13708p-7, // x^22
+};
+
+// Evaluate P(u) where P(u) ~ asin(sqrt(u))/(pi*sqrt(u)), using Estrin's scheme.
+LIBC_INLINE double asinpi_eval(double u) {
+ double u2 = u * u;
+ double c0 = fputil::multiply_add(u, ASINPI_COEFFS[1], ASINPI_COEFFS[0]);
+ double c1 = fputil::multiply_add(u, ASINPI_COEFFS[3], ASINPI_COEFFS[2]);
+ double c2 = fputil::multiply_add(u, ASINPI_COEFFS[5], ASINPI_COEFFS[4]);
+ double c3 = fputil::multiply_add(u, ASINPI_COEFFS[7], ASINPI_COEFFS[6]);
+ double c4 = fputil::multiply_add(u, ASINPI_COEFFS[9], ASINPI_COEFFS[8]);
+ double c5 = fputil::multiply_add(u, ASINPI_COEFFS[11], ASINPI_COEFFS[10]);
+
+ double u4 = u2 * u2;
+ double d0 = fputil::multiply_add(u2, c1, c0);
+ double d1 = fputil::multiply_add(u2, c3, c2);
+ double d2 = fputil::multiply_add(u2, c5, c4);
+
+ return fputil::polyeval(u4, d0, d1, d2);
+}
+
#else
// The Taylor expansion of asin(x) around 0 is:
@@ -565,6 +606,35 @@ LIBC_INLINE constexpr Float128 asin_eval(const Float128 &u, unsigned idx) {
ASIN_COEFFS_F128[idx][14], ASIN_COEFFS_F128[idx][15]);
}
+// 1/pi as DoubleDouble (~106 bits of precision).
+LIBC_INLINE_VAR constexpr DoubleDouble ONE_OVER_PI_DD = {-0x1.6b01ec5417056p-56,
+ 0x1.45f306dc9c883p-2};
+
+// 1/pi as Float128 (~128 bits of precision).
+LIBC_INLINE_VAR constexpr Float128 ONE_OVER_PI_F128 = {
+ Sign::POS, -129, 0xa2f9836e'4e441529'fc2757d1'f534ddc0_u128};
+
+// 0.5 as Float128 (exact).
+LIBC_INLINE_VAR constexpr Float128 HALF_F128 = {
+ Sign::POS, -128, 0x80000000'00000000'00000000'00000000_u128};
+
+// Compute asin(sqrt(u))/(pi*sqrt(u)) in DoubleDouble precision by wrapping
+// asin_eval and multiplying by 1/pi.
+LIBC_INLINE DoubleDouble asinpi_eval(const DoubleDouble &u, unsigned &idx,
+ double &err) {
+ DoubleDouble p = asin_eval(u, idx, err);
+ DoubleDouble result = fputil::quick_mult(p, ONE_OVER_PI_DD);
+ // Scale error by ~1/pi and add multiplication rounding error.
+ err = err * 0x1.46p-2 + 0x1.0p-98;
+ return result;
+}
+
+// Compute asin(sqrt(u))/(pi*sqrt(u)) in Float128 precision.
+LIBC_INLINE constexpr Float128 asinpi_eval(const Float128 &u, unsigned idx) {
+ Float128 p = asin_eval(u, idx);
+ return fputil::quick_mul(p, ONE_OVER_PI_F128);
+}
+
#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
} // namespace asin_internal
diff --git a/libc/src/__support/math/asinpi.h b/libc/src/__support/math/asinpi.h
new file mode 100644
index 0000000000000..a088ae322ad79
--- /dev/null
+++ b/libc/src/__support/math/asinpi.h
@@ -0,0 +1,291 @@
+//===-- Implementation header for asinpi ------------------------*- 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_ASINPI_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ASINPI_H
+
+#include "asin_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
+#include "src/__support/math/asin_utils.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+LIBC_INLINE double asinpi(double x) {
+ using namespace asin_internal;
+ using FPBits = fputil::FPBits<double>;
+
+ FPBits xbits(x);
+ int x_exp = xbits.get_biased_exponent();
+
+ // |x| < 0.5.
+ if (x_exp < FPBits::EXP_BIAS - 1) {
+ // |x| < 2^-26.
+ if (LIBC_UNLIKELY(x_exp < FPBits::EXP_BIAS - 26)) {
+ // asinpi(+-0) = +-0.
+ if (LIBC_UNLIKELY(xbits.abs().uintval() == 0))
+ return x;
+ // When |x| < 2^-26, asinpi(x) ~ x/pi.
+ // The relative error of x/pi is:
+ // |asinpi(x) - x/pi| / |asinpi(x)| < x^2/6 < 2^-54.
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ return x * ASINPI_COEFFS[0];
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ }
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ return x * asinpi_eval(x * x);
+#else
+ using Float128 = fputil::DyadicFloat<128>;
+ using DoubleDouble = fputil::DoubleDouble;
+
+ // For |x| < 2^-511, x^2 would underflow to subnormal, raising a
+ // spurious underflow exception. Since asinpi(x) = x/pi with correction
+ // x^2/(6*pi) < 2^-1024 relative (negligible), compute x/pi directly
+ // in Float128.
+ if (LIBC_UNLIKELY(x_exp < 512)) {
+ Float128 x_f128(x);
+ Float128 r = fputil::quick_mul(x_f128, ONE_OVER_PI_F128);
+ double result = static_cast<double>(r);
+
+ // IEEE 754 "after rounding" tininess: the 53-bit unlimited-exponent
+ // result is strictly between +-2^-1022. DyadicFloat's conversion
+ // checks the *IEEE subnormal* result (52-bit at the boundary), not
+ // the 53-bit unlimited-exponent result, so we detect it here.
+ int exp_hi = r.exponent + 127 + FPBits::EXP_BIAS;
+ if (LIBC_UNLIKELY(exp_hi <= 0) && !r.mantissa.is_zero()) {
+ bool raise_underflow = true;
+ // When exp_hi == 0, a carry in 53-bit rounding can push the
+ // result to exactly 2^-1022 (not tiny). Check for this.
+ if (exp_hi == 0) {
+ constexpr unsigned SHIFT_53 = 128 - FPBits::SIG_LEN - 1;
+ using MantT = typename Float128::MantissaType;
+ MantT m53 = r.mantissa >> SHIFT_53;
+ constexpr MantT ALL_ONES_53 = (MantT(1) << (FPBits::SIG_LEN + 1)) - 1;
+ if (m53 == ALL_ONES_53) {
+ // All 53 bits set. carry happens if rounding rounds away
+ // from zero at this precision.
+ bool round_bit =
+ static_cast<bool>((r.mantissa >> (SHIFT_53 - 1)) & 1);
+ MantT sticky_mask = (MantT(1) << (SHIFT_53 - 1)) - 1;
+ bool sticky = (r.mantissa & sticky_mask) != 0;
+ bool lsb = static_cast<bool>(m53 & 1);
+ switch (fputil::quick_get_round()) {
+ case FE_TONEAREST:
+ // Carry if round_bit && (lsb || sticky) (round half to even).
+ raise_underflow = !(round_bit && (lsb || sticky));
+ break;
+ case FE_UPWARD:
+ raise_underflow = xbits.is_neg() || !(round_bit || sticky);
+ break;
+ case FE_DOWNWARD:
+ raise_underflow = !xbits.is_neg() || !(round_bit || sticky);
+ break;
+ case FE_TOWARDZERO:
+ default:
+ raise_underflow = true; // truncation never carries
+ break;
+ }
+ }
+ }
+ if (raise_underflow)
+ fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
+ }
+ return result;
+ }
+
+ unsigned idx = 0;
+ DoubleDouble x_sq = fputil::exact_mult(x, x);
+ double err = xbits.abs().get_val() * 0x1.0p-51;
+ // Polynomial approximation:
+ // p ~ asin(x)/(pi*x)
+
+ DoubleDouble p = asinpi_eval(x_sq, idx, err);
+ // asinpi(x) ~ x * p
+ DoubleDouble r0 = fputil::exact_mult(x, p.hi);
+ double r_lo = fputil::multiply_add(x, p.lo, r0.lo);
+
+ // Ziv's accuracy test.
+ double r_upper = r0.hi + (r_lo + err);
+ double r_lower = r0.hi + (r_lo - err);
+
+ if (LIBC_LIKELY(r_upper == r_lower))
+ return r_upper;
+
+ // Ziv's accuracy test failed, perform 128-bit calculation.
+
+ // Recalculate mod 1/64.
+ idx = static_cast<unsigned>(fputil::nearest_integer(x_sq.hi * 0x1.0p6));
+
+ Float128 x_f128(x);
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ Float128 u_hi(
+ fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, x_sq.hi));
+ Float128 u = fputil::quick_add(u_hi, Float128(x_sq.lo));
+#else
+ Float128 x_sq_f128 = fputil::quick_mul(x_f128, x_f128);
+ Float128 u = fputil::quick_add(
+ x_sq_f128, Float128(static_cast<double>(idx) * (-0x1.0p-6)));
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+
+ Float128 p_f128 = asinpi_eval(u, idx);
+ Float128 r = fputil::quick_mul(x_f128, p_f128);
+
+ return static_cast<double>(r);
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ }
+ // |x| >= 0.5
+
+ double x_abs = xbits.abs().get_val();
+
+ // Maintaining the sign:
+ constexpr double SIGN[2] = {1.0, -1.0};
+ double x_sign = SIGN[xbits.is_neg()];
+
+ // |x| >= 1
+ if (LIBC_UNLIKELY(x_exp >= FPBits::EXP_BIAS)) {
+ // x = +-1, asinpi(x) = +- 0.5
+ if (x_abs == 1.0) {
+ return x_sign * 0.5;
+ }
+ // |x| > 1, return NaN.
+ if (xbits.is_quiet_nan())
+ return x;
+
+ // Set domain error for non-NaN input.
+ if (!xbits.is_nan())
+ fputil::set_errno_if_required(EDOM);
+
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ // When |x| >= 0.5, we perform range reduction as follow:
+ //
+ // Assume further that 0.5 <= x < 1, and let:
+ // y = asin(x)
+ // Using the identity:
+ // asin(x) = pi/2 - 2 * asin( sqrt( (1 - x)/2 ) )
+ // We get:
+ // asinpi(x) = asin(x)/pi = 0.5 - 2 * asin(sqrt(u)) / pi
+ // = 0.5 - 2 * sqrt(u) * [asin(sqrt(u)) / (pi * sqrt(u))]
+ // = 0.5 - 2 * sqrt(u) * asinpi_eval(u)
+ // where u = (1 - |x|) / 2.
+
+ // u = (1 - |x|)/2
+ double u = fputil::multiply_add(x_abs, -0.5, 0.5);
+ // v_hi ~ sqrt(u).
+ double v_hi = fputil::sqrt<double>(u);
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ double p = asinpi_eval(u);
+ double r = x_sign * fputil::multiply_add(-2.0 * v_hi, p, 0.5);
+ return r;
+#else
+ using Float128 = fputil::DyadicFloat<128>;
+ using DoubleDouble = fputil::DoubleDouble;
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double h = fputil::multiply_add(v_hi, -v_hi, u);
+#else
+ DoubleDouble v_hi_sq = fputil::exact_mult(v_hi, v_hi);
+ double h = (u - v_hi_sq.hi) - v_hi_sq.lo;
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+
+ // Scale v_lo and v_hi by 2 from the formula:
+ // vh = v_hi * 2
+ // vl = 2*v_lo = h / v_hi.
+ double vh = v_hi * 2.0;
+ double vl = h / v_hi;
+
+ // Polynomial approximation:
+ // p ~ asin(sqrt(u))/(pi*sqrt(u))
+ unsigned idx = 0;
+ double err = vh * 0x1.0p-51;
+
+ DoubleDouble p = asinpi_eval(DoubleDouble{0.0, u}, idx, err);
+
+ // Perform computations in double-double arithmetic:
+ // asinpi(x) = 0.5 - (vh + vl) * p
+ DoubleDouble r0 = fputil::quick_mult(DoubleDouble{vl, vh}, p);
+ DoubleDouble r = fputil::exact_add(0.5, -r0.hi);
+
+ double r_lo = -r0.lo + r.lo;
+
+ // Ziv's accuracy test.
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double r_upper = fputil::multiply_add(
+ r.hi, x_sign, fputil::multiply_add(r_lo, x_sign, err));
+ double r_lower = fputil::multiply_add(
+ r.hi, x_sign, fputil::multiply_add(r_lo, x_sign, -err));
+#else
+ r_lo *= x_sign;
+ r.hi *= x_sign;
+ double r_upper = r.hi + (r_lo + err);
+ double r_lower = r.hi + (r_lo - err);
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+
+ if (LIBC_LIKELY(r_upper == r_lower))
+ return r_upper;
+
+ // Ziv's accuracy test failed, we redo the computations in Float128.
+ // Recalculate mod 1/64.
+ idx = static_cast<unsigned>(fputil::nearest_integer(u * 0x1.0p6));
+
+ // After the first step of Newton-Raphson approximating v = sqrt(u):
+ // sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
+ // v_lo = h / (2 * v_hi)
+ // Add second-order correction:
+ // v_ll = -v_lo * (h / (4u))
+
+ // Get the rounding error of vl = 2 * v_lo ~ h / vh
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double vl_lo = fputil::multiply_add(-v_hi, vl, h) / v_hi;
+#else
+ DoubleDouble vh_vl = fputil::exact_mult(v_hi, vl);
+ double vl_lo = ((h - vh_vl.hi) - vh_vl.lo) / v_hi;
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ // vll = 2*v_ll = -vl * (h / (4u)).
+ double t = h * (-0.25) / u;
+ double vll = fputil::multiply_add(vl, t, vl_lo);
+ // m_v = -(v_hi + v_lo + v_ll).
+ Float128 m_v = fputil::quick_add(
+ Float128(vh), fputil::quick_add(Float128(vl), Float128(vll)));
+ m_v.sign = Sign::NEG;
+
+ // Perform computations in Float128:
+ // asinpi(x) = 0.5 - (v_hi + v_lo + vll) * P_pi(u).
+ Float128 y_f128(fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, u));
+
+ Float128 p_f128 = asinpi_eval(y_f128, idx);
+ Float128 r0_f128 = fputil::quick_mul(m_v, p_f128);
+ Float128 r_f128 = fputil::quick_add(HALF_F128, r0_f128);
+
+ if (xbits.is_neg())
+ r_f128.sign = Sign::NEG;
+
+ return static_cast<double>(r_f128);
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ASINPI_H
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index c7ded04aad7c6..ebba3f04b8d56 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -59,6 +59,7 @@ add_math_entrypoint_object(asinh)
add_math_entrypoint_object(asinhf)
add_math_entrypoint_object(asinhf16)
+add_math_entrypoint_object(asinpi)
add_math_entrypoint_object(asinpif)
add_math_entrypoint_object(asinpif16)
diff --git a/libc/src/math/asinpi.h b/libc/src/math/asinpi.h
new file mode 100644
index 0000000000000..7b8770b5e52a9
--- /dev/null
+++ b/libc/src/math/asinpi.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for asinpi ------------------------*- 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_ASINPI_H
+#define LLVM_LIBC_SRC_MATH_ASINPI_H
+
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+double asinpi(double x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_ASINPI_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index ad05fd83cadb9..30f33749d165e 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4037,6 +4037,16 @@ add_entrypoint_object(
libc.src.__support.math.asinhf16
)
+add_entrypoint_object(
+ asinpi
+ SRCS
+ asinpi.cpp
+ HDRS
+ ../asinpi.h
+ DEPENDS
+ libc.src.__support.math.asinpi
+)
+
add_entrypoint_object(
asinpif
SRCS
diff --git a/libc/src/math/generic/asinpi.cpp b/libc/src/math/generic/asinpi.cpp
new file mode 100644
index 0000000000000..20b76ff1ffd6f
--- /dev/null
+++ b/libc/src/math/generic/asinpi.cpp
@@ -0,0 +1,16 @@
+//===-- Double-precision asinpi 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/asinpi.h"
+#include "src/__support/math/asinpi.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+LLVM_LIBC_FUNCTION(double, asinpi, (double x)) { return math::asinpi(x); }
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/test/shared/CMakeLists.txt b/libc/test/shared/CMakeLists.txt
index b807ea9ac602f..c3795d366a588 100644
--- a/libc/test/shared/CMakeLists.txt
+++ b/libc/test/shared/CMakeLists.txt
@@ -20,6 +20,7 @@ add_fp_unittest(
libc.src.__support.math.asinf16
libc.src.__support.math.asinhf
libc.src.__support.math.asinhf16
+ libc.src.__support.math.asinpi
libc.src.__support.math.asinpif
libc.src.__support.math.asinpif16
libc.src.__support.math.atan
diff --git a/libc/test/shared/shared_math_test.cpp b/libc/test/shared/shared_math_test.cpp
index 31b14bbe204c7..b52abc6d8e990 100644
--- a/libc/test/shared/shared_math_test.cpp
+++ b/libc/test/shared/shared_math_test.cpp
@@ -242,6 +242,7 @@ TEST(LlvmLibcSharedMathTest, AllDouble) {
EXPECT_FP_EQ(0x1.921fb54442d18p+0, LIBC_NAMESPACE::shared::acos(0.0));
EXPECT_FP_EQ(0x0p+0, LIBC_NAMESPACE::shared::asin(0.0));
+ EXPECT_FP_EQ(0x0p+0, LIBC_NAMESPACE::shared::asinpi(0.0));
EXPECT_FP_EQ(0x0p+0, LIBC_NAMESPACE::shared::atan(0.0));
EXPECT_FP_EQ(0x0p+0, LIBC_NAMESPACE::shared::atan2(0.0, 0.0));
EXPECT_FP_EQ(0x0p+0, LIBC_NAMESPACE::shared::cbrt(0.0));
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index e157b0463bbdb..2fd77f964e4d6 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -2523,6 +2523,17 @@ add_fp_unittest(
libc.src.math.asinf16
)
+add_fp_unittest(
+ asinpi_test
+ NEED_MPFR
+ SUITE
+ libc-math-unittests
+ SRCS
+ asinpi_test.cpp
+ DEPENDS
+ libc.src.math.asinpi
+)
+
add_fp_unittest(
asinpif_test
NEED_MPFR
diff --git a/libc/test/src/math/asinpi_test.cpp b/libc/test/src/math/asinpi_test.cpp
new file mode 100644
index 0000000000000..75dfbc6608eac
--- /dev/null
+++ b/libc/test/src/math/asinpi_test.cpp
@@ -0,0 +1,92 @@
+//===-- Unittests for asinpi ----------------------------------------------===//
+//
+// 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/__support/macros/optimization.h"
+#include "src/math/asinpi.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+#define TOLERANCE 6
+#else
+#define TOLERANCE 0
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+using LlvmLibcAsinpiTest = LIBC_NAMESPACE::testing::FPTest<double>;
+
+namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
+
+using LIBC_NAMESPACE::testing::tlog;
+
+TEST_F(LlvmLibcAsinpiTest, InDoubleRange) {
+ constexpr uint64_t COUNT = 123'451;
+ uint64_t START = FPBits(0x1.0p-60).uintval();
+ uint64_t STOP = FPBits(1.0).uintval();
+ uint64_t STEP = (STOP - START) / COUNT;
+
+ auto test = [&](mpfr::RoundingMode rounding_mode) {
+ mpfr::ForceRoundingMode __r(rounding_mode);
+ if (!__r.success)
+ return;
+
+ uint64_t fails = 0;
+ uint64_t count = 0;
+ uint64_t cc = 0;
+ double mx = 0.0, mr = 0.0;
+ double tol = 0.5;
+
+ for (uint64_t i = 0, v = START; i <= COUNT; ++i, v += STEP) {
+ double x = FPBits(v).get_val();
+ if (FPBits(v).is_nan() || FPBits(v).is_inf())
+ continue;
+ libc_errno = 0;
+ double result = LIBC_NAMESPACE::asinpi(x);
+ ++cc;
+ if (FPBits(result).is_nan() || FPBits(result).is_inf())
+ continue;
+
+ ++count;
+
+ if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Asinpi, x, result,
+ TOLERANCE + 0.5, rounding_mode)) {
+ ++fails;
+ while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Asinpi, x,
+ result, tol, rounding_mode)) {
+ mx = x;
+ mr = result;
+
+ if (tol > 1000.0)
+ break;
+
+ tol *= 2.0;
+ }
+ }
+ }
+ if (fails) {
+ tlog << " Asinpi failed: " << fails << "/" << count << "/" << cc
+ << " tests.\n";
+ tlog << " Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
+ EXPECT_MPFR_MATCH(mpfr::Operation::Asinpi, mx, mr, 0.5, rounding_mode);
+ }
+ };
+
+ tlog << " Test Rounding To Nearest...\n";
+ test(mpfr::RoundingMode::Nearest);
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ tlog << " Test Rounding Downward...\n";
+ test(mpfr::RoundingMode::Downward);
+
+ tlog << " Test Rounding Upward...\n";
+ test(mpfr::RoundingMode::Upward);
+
+ tlog << " Test Rounding Toward Zero...\n";
+ test(mpfr::RoundingMode::TowardZero);
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+}
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index 544425a39d340..79f2ea4806377 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -4757,6 +4757,18 @@ add_fp_unittest(
libc.src.math.asinhf16
)
+add_fp_unittest(
+ asinpi_test
+ SUITE
+ libc-math-smoke-tests
+ SRCS
+ asinpi_test.cpp
+ DEPENDS
+ libc.hdr.fenv_macros
+ libc.src.math.asinpi
+ libc.src.__support.FPUtil.fp_bits
+)
+
add_fp_unittest(
asinpif_test
SUITE
diff --git a/libc/test/src/math/smoke/asinpi_test.cpp b/libc/test/src/math/smoke/asinpi_test.cpp
new file mode 100644
index 0000000000000..fcd3dd3e5ddc3
--- /dev/null
+++ b/libc/test/src/math/smoke/asinpi_test.cpp
@@ -0,0 +1,52 @@
+//===-- Unittests for asinpi ----------------------------------------------===//
+//
+// 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 "hdr/fenv_macros.h"
+#include "src/math/asinpi.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcAsinpiTest = LIBC_NAMESPACE::testing::FPTest<double>;
+
+TEST_F(LlvmLibcAsinpiTest, SpecialNumbers) {
+ EXPECT_FP_EQ_WITH_EXCEPTION_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::asinpi(sNaN),
+ FE_INVALID);
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::asinpi(aNaN));
+ EXPECT_FP_EQ_ALL_ROUNDING(zero, LIBC_NAMESPACE::asinpi(zero));
+ EXPECT_FP_EQ_ALL_ROUNDING(neg_zero, LIBC_NAMESPACE::asinpi(neg_zero));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::asinpi(inf));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::asinpi(neg_inf));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::asinpi(2.0));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::asinpi(-2.0));
+ EXPECT_FP_EQ(0.5, LIBC_NAMESPACE::asinpi(1.0));
+ EXPECT_FP_EQ(-0.5, LIBC_NAMESPACE::asinpi(-1.0));
+}
+
+#ifdef LIBC_TEST_FTZ_DAZ
+
+using namespace LIBC_NAMESPACE::testing;
+
+TEST_F(LlvmLibcAsinpiTest, FTZMode) {
+ ModifyMXCSR mxcsr(FTZ);
+
+ EXPECT_TRUE(zero == LIBC_NAMESPACE::asinpi(min_denormal));
+}
+
+TEST_F(LlvmLibcAsinpiTest, DAZMode) {
+ ModifyMXCSR mxcsr(DAZ);
+
+ EXPECT_TRUE(zero == LIBC_NAMESPACE::asinpi(min_denormal));
+}
+
+TEST_F(LlvmLibcAsinpiTest, FTZDAZMode) {
+ ModifyMXCSR mxcsr(FTZ | DAZ);
+
+ EXPECT_TRUE(zero == LIBC_NAMESPACE::asinpi(min_denormal));
+}
+
+#endif
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 29792cec1149e..a69ebcdb63fa7 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -3189,6 +3189,25 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_asinpi",
+ hdrs = ["src/__support/math/asinpi.h"],
+ deps = [
+ ":__support_fputil_cast",
+ ":__support_fputil_double_double",
+ ":__support_fputil_except_value_utils",
+ ":__support_fputil_fenv_impl",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_rounding_mode",
+ ":__support_fputil_sqrt",
+ ":__support_macros_config",
+ ":__support_macros_optimization",
+ ":__support_math_asin_utils",
+ ],
+)
+
libc_support_library(
name = "__support_math_asinpif",
hdrs = ["src/__support/math/asinpif.h"],
@@ -6566,6 +6585,13 @@ libc_math_function(
],
)
+libc_math_function(
+ name = "asinpi",
+ additional_deps = [
+ ":__support_math_asinpi",
+ ],
+)
+
libc_math_function(
name = "asinpif",
additional_deps = [
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