[libc-commits] [libc] [llvm] [libc][math] Refactor acos implementation to header-only in src/__support/math folder. (PR #148409)
Muhammad Bassiouni via libc-commits
libc-commits at lists.llvm.org
Fri Jul 18 10:46:58 PDT 2025
https://github.com/bassiounix updated https://github.com/llvm/llvm-project/pull/148409
>From ec9e21faaaa9f0efd1086ec039d564d8ead856c4 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Fri, 18 Jul 2025 20:08:22 +0300
Subject: [PATCH 1/3] [libc][math] Refactor acos implementation to header-only
in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/acos.h | 23 ++
libc/src/__support/math/CMakeLists.txt | 33 ++
libc/src/__support/math/acos.h | 285 ++++++++++++++++++
.../generic => __support/math}/asin_utils.h | 34 +--
libc/src/math/generic/CMakeLists.txt | 28 +-
libc/src/math/generic/acos.cpp | 266 +---------------
libc/src/math/generic/asin.cpp | 2 +-
.../llvm-project-overlay/libc/BUILD.bazel | 39 +++
9 files changed, 403 insertions(+), 308 deletions(-)
create mode 100644 libc/shared/math/acos.h
create mode 100644 libc/src/__support/math/acos.h
rename libc/src/{math/generic => __support/math}/asin_utils.h (96%)
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 26f69d6fa43ea..8dcfaf0352339 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -11,6 +11,7 @@
#include "libc_common.h"
+#include "math/acos.h"
#include "math/exp.h"
#include "math/exp10.h"
#include "math/exp10f.h"
diff --git a/libc/shared/math/acos.h b/libc/shared/math/acos.h
new file mode 100644
index 0000000000000..73c6b512e16f4
--- /dev/null
+++ b/libc/shared/math/acos.h
@@ -0,0 +1,23 @@
+//===-- Shared acos 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_ACOS_H
+#define LLVM_LIBC_SHARED_MATH_ACOS_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/acos.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acos;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOS_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 77a47c65489dd..4a29c2975d523 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -1,3 +1,36 @@
+add_header_library(
+ acos
+ HDRS
+ acos.h
+ DEPENDS
+ .asin_utils
+ libc.src.__support.math.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.types
+ libc.src.__support.macros.properties.cpu_features
+)
+
+add_header_library(
+ asin_utils
+ HDRS
+ asin_utils.h
+ DEPENDS
+ libc.src.__support.integer_literals
+ libc.src.__support.FPUtil.double_double
+ libc.src.__support.FPUtil.dyadic_float
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.nearest_integer
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.macros.optimization
+)
+
add_header_library(
exp_float_constants
HDRS
diff --git a/libc/src/__support/math/acos.h b/libc/src/__support/math/acos.h
new file mode 100644
index 0000000000000..a7287f11aa302
--- /dev/null
+++ b/libc/src/__support/math/acos.h
@@ -0,0 +1,285 @@
+//===-- Implementation header for acos --------------------------*- 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_ACOS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_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
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+using DoubleDouble = fputil::DoubleDouble;
+using Float128 = fputil::DyadicFloat<128>;
+
+static constexpr double acos(double x) {
+ 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^-55.
+ if (LIBC_UNLIKELY(x_exp < FPBits::EXP_BIAS - 55)) {
+ // When |x| < 2^-55, acos(x) = pi/2
+#if defined(LIBC_MATH_HAS_SKIP_ACCURATE_PASS)
+ return PI_OVER_TWO.hi;
+#else
+ // Force the evaluation and prevent constant propagation so that it
+ // is rounded correctly for FE_UPWARD rounding mode.
+ return (xbits.abs().get_val() + 0x1.0p-160) + PI_OVER_TWO.hi;
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ }
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ // acos(x) = pi/2 - asin(x)
+ // = pi/2 - x * P(x^2)
+ double p = asin_eval(x * x);
+ return PI_OVER_TWO.hi + fputil::multiply_add(-x, p, PI_OVER_TWO.lo);
+#else
+ 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)/x
+ DoubleDouble p = asin_eval(x_sq, idx, err);
+ // asin(x) ~ x * p
+ DoubleDouble r0 = fputil::exact_mult(x, p.hi);
+ // acos(x) = pi/2 - asin(x)
+ // ~ pi/2 - x * p
+ // = pi/2 - x * (p.hi + p.lo)
+ double r_hi = fputil::multiply_add(-x, p.hi, PI_OVER_TWO.hi);
+ // Use Dekker's 2SUM algorithm to compute the lower part.
+ double r_lo = ((PI_OVER_TWO.hi - r_hi) - r0.hi) - r0.lo;
+ r_lo = fputil::multiply_add(-x, p.lo, r_lo + PI_OVER_TWO.lo);
+
+ // Ziv's accuracy test.
+
+ double r_upper = r_hi + (r_lo + err);
+ double r_lower = r_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));
+
+ // Get x^2 - idx/64 exactly. When FMA is available, double-double
+ // multiplication will be correct for all rounding modes. Otherwise we use
+ // Float128 directly.
+ Float128 x_f128(x);
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ // u = x^2 - idx/64
+ 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 = asin_eval(u, idx);
+ // Flip the sign of x_f128 to perform subtraction.
+ x_f128.sign = x_f128.sign.negate();
+ Float128 r =
+ fputil::quick_add(PI_OVER_TWO_F128, 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, asin(x) = +- pi/2
+ if (x_abs == 1.0) {
+ // x = 1, acos(x) = 0,
+ // x = -1, acos(x) = pi
+ return x == 1.0 ? 0.0 : fputil::multiply_add(-x_sign, PI.hi, PI.lo);
+ }
+ // |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:
+ //
+ // When 0.5 <= x < 1, let:
+ // y = acos(x)
+ // We will use the double angle formula:
+ // cos(2y) = 1 - 2 sin^2(y)
+ // and the complement angle identity:
+ // x = cos(y) = 1 - 2 sin^2 (y/2)
+ // So:
+ // sin(y/2) = sqrt( (1 - x)/2 )
+ // And hence:
+ // y/2 = asin( sqrt( (1 - x)/2 ) )
+ // Equivalently:
+ // acos(x) = y = 2 * asin( sqrt( (1 - x)/2 ) )
+ // Let u = (1 - x)/2, then:
+ // acos(x) = 2 * asin( sqrt(u) )
+ // Moreover, since 0.5 <= x < 1:
+ // 0 < u <= 1/4, and 0 < sqrt(u) <= 0.5,
+ // And hence we can reuse the same polynomial approximation of asin(x) when
+ // |x| <= 0.5:
+ // acos(x) ~ 2 * sqrt(u) * P(u).
+ //
+ // When -1 < x <= -0.5, we reduce to the previous case using the formula:
+ // acos(x) = pi - acos(-x)
+ // = pi - 2 * asin ( sqrt( (1 + x)/2 ) )
+ // ~ pi - 2 * sqrt(u) * P(u),
+ // where u = (1 - |x|)/2.
+
+ // u = (1 - |x|)/2
+ double u = fputil::multiply_add(x_abs, -0.5, 0.5);
+ // v_hi + v_lo ~ sqrt(u).
+ // Let:
+ // h = u - v_hi^2 = (sqrt(u) - v_hi) * (sqrt(u) + v_hi)
+ // Then:
+ // sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
+ // ~ v_hi + h / (2 * v_hi)
+ // So we can use:
+ // v_lo = h / (2 * v_hi).
+ double v_hi = fputil::sqrt<double>(u);
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ constexpr DoubleDouble CONST_TERM[2] = {{0.0, 0.0}, PI};
+ DoubleDouble const_term = CONST_TERM[xbits.is_neg()];
+
+ double p = asin_eval(u);
+ double scale = x_sign * 2.0 * v_hi;
+ double r = const_term.hi + fputil::multiply_add(scale, p, const_term.lo);
+ return r;
+#else
+
+#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))/sqrt(u)
+ unsigned idx = 0;
+ double err = vh * 0x1.0p-51;
+
+ DoubleDouble p = asin_eval(DoubleDouble{0.0, u}, idx, err);
+
+ // Perform computations in double-double arithmetic:
+ // asin(x) = pi/2 - (v_hi + v_lo) * (ASIN_COEFFS[idx][0] + p)
+ DoubleDouble r0 = fputil::quick_mult(DoubleDouble{vl, vh}, p);
+
+ double r_hi = 0, r_lo = 0;
+ if (xbits.is_pos()) {
+ r_hi = r0.hi;
+ r_lo = r0.lo;
+ } else {
+ DoubleDouble r = fputil::exact_add(PI.hi, -r0.hi);
+ r_hi = r.hi;
+ r_lo = (PI.lo - r0.lo) + r.lo;
+ }
+
+ // Ziv's accuracy test.
+
+ double r_upper = r_hi + (r_lo + err);
+ double r_lower = r_hi + (r_lo - err);
+
+ 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), we have
+ // that:
+ // sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
+ // v_lo = h / (2 * v_hi)
+ // With error:
+ // sqrt(u) - (v_hi + v_lo) = h * ( 1/(sqrt(u) + v_hi) - 1/(2*v_hi) )
+ // = -h^2 / (2*v * (sqrt(u) + v)^2).
+ // Since:
+ // (sqrt(u) + v_hi)^2 ~ (2sqrt(u))^2 = 4u,
+ // we can add another correction term to (v_hi + v_lo) that is:
+ // v_ll = -h^2 / (2*v_hi * 4u)
+ // = -v_lo * (h / 4u)
+ // = -vl * (h / 8u),
+ // making the errors:
+ // sqrt(u) - (v_hi + v_lo + v_ll) = O(h^3)
+ // well beyond 128-bit precision needed.
+
+ // Get the rounding error of vl = 2 * v_lo ~ h / vh
+ // Get full product of vh * vl
+#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 = xbits.sign();
+
+ // Perform computations in Float128:
+ // acos(x) = (v_hi + v_lo + vll) * P(u) , when 0.5 <= x < 1,
+ // = pi - (v_hi + v_lo + vll) * P(u) , when -1 < x <= -0.5.
+ Float128 y_f128(fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, u));
+
+ Float128 p_f128 = asin_eval(y_f128, idx);
+ Float128 r_f128 = fputil::quick_mul(m_v, p_f128);
+
+ if (xbits.is_neg())
+ r_f128 = fputil::quick_add(PI_F128, r_f128);
+
+ 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_ACOS_H
diff --git a/libc/src/math/generic/asin_utils.h b/libc/src/__support/math/asin_utils.h
similarity index 96%
rename from libc/src/math/generic/asin_utils.h
rename to libc/src/__support/math/asin_utils.h
index 44913d573de2c..4e0179e43298b 100644
--- a/libc/src/math/generic/asin_utils.h
+++ b/libc/src/__support/math/asin_utils.h
@@ -6,8 +6,8 @@
//
//===----------------------------------------------------------------------===//
-#ifndef LLVM_LIBC_SRC_MATH_GENERIC_ASIN_UTILS_H
-#define LLVM_LIBC_SRC_MATH_GENERIC_ASIN_UTILS_H
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ASIN_UTILS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ASIN_UTILS_H
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/double_double.h"
@@ -16,7 +16,6 @@
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/integer_literals.h"
#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
@@ -25,10 +24,10 @@ namespace {
using DoubleDouble = fputil::DoubleDouble;
using Float128 = fputil::DyadicFloat<128>;
-constexpr DoubleDouble PI = {0x1.1a62633145c07p-53, 0x1.921fb54442d18p1};
+static constexpr DoubleDouble PI = {0x1.1a62633145c07p-53, 0x1.921fb54442d18p1};
-constexpr DoubleDouble PI_OVER_TWO = {0x1.1a62633145c07p-54,
- 0x1.921fb54442d18p0};
+static constexpr DoubleDouble PI_OVER_TWO = {0x1.1a62633145c07p-54,
+ 0x1.921fb54442d18p0};
#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
@@ -39,14 +38,14 @@ constexpr DoubleDouble PI_OVER_TWO = {0x1.1a62633145c07p-54,
// > dirtyinfnorm(asin(x)/x - P, [0, 0.5]);
// 0x1.1a71ef0a0f26a9fb7ed7e41dee788b13d1770db3dp-52
-constexpr double ASIN_COEFFS[12] = {
+static constexpr double ASIN_COEFFS[12] = {
0x1.0000000000000p0, 0x1.5555555556dcfp-3, 0x1.3333333082e11p-4,
0x1.6db6dd14099edp-5, 0x1.f1c69b35bf81fp-6, 0x1.6e97194225a67p-6,
0x1.1babddb82ce12p-6, 0x1.d55bd078600d6p-7, 0x1.33328959e63d6p-7,
0x1.2b5993bda1d9bp-6, -0x1.806aff270bf25p-7, 0x1.02614e5ed3936p-5,
};
-LIBC_INLINE double asin_eval(double u) {
+LIBC_INLINE static constexpr double asin_eval(double u) {
double u2 = u * u;
double c0 = fputil::multiply_add(u, ASIN_COEFFS[1], ASIN_COEFFS[0]);
double c1 = fputil::multiply_add(u, ASIN_COEFFS[3], ASIN_COEFFS[2]);
@@ -124,7 +123,7 @@ LIBC_INLINE double asin_eval(double u) {
// > dirtyinfnorm(asin(x)/x - P, [-1/64, 1/64]);
// 0x1.999075402cafp-83
-constexpr double ASIN_COEFFS[9][12] = {
+static constexpr double ASIN_COEFFS[9][12] = {
{1.0, 0.0, 0x1.5555555555555p-3, 0x1.5555555555555p-57,
0x1.3333333333333p-4, 0x1.6db6db6db6db7p-5, 0x1.f1c71c71c71c7p-6,
0x1.6e8ba2e8ba2e9p-6, 0x1.1c4ec4ec4ec4fp-6, 0x1.c99999999999ap-7,
@@ -164,8 +163,8 @@ constexpr double ASIN_COEFFS[9][12] = {
};
// We calculate the lower part of the approximation P(u).
-LIBC_INLINE DoubleDouble asin_eval(const DoubleDouble &u, unsigned &idx,
- double &err) {
+LIBC_INLINE static constexpr DoubleDouble
+asin_eval(const DoubleDouble &u, unsigned &idx, double &err) {
using fputil::multiply_add;
// k = round(u * 32).
double k = fputil::nearest_integer(u.hi * 0x1.0p5);
@@ -239,7 +238,7 @@ LIBC_INLINE DoubleDouble asin_eval(const DoubleDouble &u, unsigned &idx,
// + (676039 x^24)/104857600 + (1300075 x^26)/226492416 +
// + (5014575 x^28)/973078528 + (9694845 x^30)/2080374784.
-constexpr Float128 ASIN_COEFFS_F128[17][16] = {
+static constexpr Float128 ASIN_COEFFS_F128[17][16] = {
{
{Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128},
{Sign::POS, -130, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128},
@@ -548,13 +547,14 @@ constexpr Float128 ASIN_COEFFS_F128[17][16] = {
},
};
-constexpr Float128 PI_OVER_TWO_F128 = {
+static constexpr Float128 PI_OVER_TWO_F128 = {
Sign::POS, -127, 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
-constexpr Float128 PI_F128 = {Sign::POS, -126,
- 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
+static constexpr Float128 PI_F128 = {
+ Sign::POS, -126, 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
-LIBC_INLINE Float128 asin_eval(const Float128 &u, unsigned idx) {
+LIBC_INLINE static constexpr Float128 asin_eval(const Float128 &u,
+ unsigned idx) {
return fputil::polyeval(u, ASIN_COEFFS_F128[idx][0], ASIN_COEFFS_F128[idx][1],
ASIN_COEFFS_F128[idx][2], ASIN_COEFFS_F128[idx][3],
ASIN_COEFFS_F128[idx][4], ASIN_COEFFS_F128[idx][5],
@@ -571,4 +571,4 @@ LIBC_INLINE Float128 asin_eval(const Float128 &u, unsigned idx) {
} // namespace LIBC_NAMESPACE_DECL
-#endif // LLVM_LIBC_SRC_MATH_GENERIC_ASIN_UTILS_H
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ASIN_UTILS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index fb253a4502700..7e6a32b7cdf16 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4016,20 +4016,6 @@ add_entrypoint_object(
libc.src.__support.macros.properties.types
)
-add_header_library(
- asin_utils
- HDRS
- atan_utils.h
- DEPENDS
- libc.src.__support.integer_literals
- libc.src.__support.FPUtil.double_double
- libc.src.__support.FPUtil.dyadic_float
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.nearest_integer
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.macros.optimization
-)
-
add_entrypoint_object(
asin
SRCS
@@ -4037,7 +4023,7 @@ add_entrypoint_object(
HDRS
../asin.h
DEPENDS
- .asin_utils
+ libc.src.__support.math.asin_utils
libc.src.__support.FPUtil.double_double
libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.fenv_impl
@@ -4092,17 +4078,7 @@ add_entrypoint_object(
HDRS
../acos.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.types
- libc.src.__support.macros.properties.cpu_features
+ libc.src.__support.math.acos
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/acos.cpp b/libc/src/math/generic/acos.cpp
index c14721faef3ce..3a5964290cdd3 100644
--- a/libc/src/math/generic/acos.cpp
+++ b/libc/src/math/generic/acos.cpp
@@ -7,272 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/acos.h"
-#include "asin_utils.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.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/acos.h"
namespace LIBC_NAMESPACE_DECL {
-using DoubleDouble = fputil::DoubleDouble;
-using Float128 = fputil::DyadicFloat<128>;
-
-LLVM_LIBC_FUNCTION(double, acos, (double x)) {
- 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^-55.
- if (LIBC_UNLIKELY(x_exp < FPBits::EXP_BIAS - 55)) {
- // When |x| < 2^-55, acos(x) = pi/2
-#if defined(LIBC_MATH_HAS_SKIP_ACCURATE_PASS)
- return PI_OVER_TWO.hi;
-#else
- // Force the evaluation and prevent constant propagation so that it
- // is rounded correctly for FE_UPWARD rounding mode.
- return (xbits.abs().get_val() + 0x1.0p-160) + PI_OVER_TWO.hi;
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- }
-
-#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- // acos(x) = pi/2 - asin(x)
- // = pi/2 - x * P(x^2)
- double p = asin_eval(x * x);
- return PI_OVER_TWO.hi + fputil::multiply_add(-x, p, PI_OVER_TWO.lo);
-#else
- unsigned idx;
- DoubleDouble x_sq = fputil::exact_mult(x, x);
- double err = xbits.abs().get_val() * 0x1.0p-51;
- // Polynomial approximation:
- // p ~ asin(x)/x
- DoubleDouble p = asin_eval(x_sq, idx, err);
- // asin(x) ~ x * p
- DoubleDouble r0 = fputil::exact_mult(x, p.hi);
- // acos(x) = pi/2 - asin(x)
- // ~ pi/2 - x * p
- // = pi/2 - x * (p.hi + p.lo)
- double r_hi = fputil::multiply_add(-x, p.hi, PI_OVER_TWO.hi);
- // Use Dekker's 2SUM algorithm to compute the lower part.
- double r_lo = ((PI_OVER_TWO.hi - r_hi) - r0.hi) - r0.lo;
- r_lo = fputil::multiply_add(-x, p.lo, r_lo + PI_OVER_TWO.lo);
-
- // Ziv's accuracy test.
-
- double r_upper = r_hi + (r_lo + err);
- double r_lower = r_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));
-
- // Get x^2 - idx/64 exactly. When FMA is available, double-double
- // multiplication will be correct for all rounding modes. Otherwise we use
- // Float128 directly.
- Float128 x_f128(x);
-
-#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
- // u = x^2 - idx/64
- 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 = asin_eval(u, idx);
- // Flip the sign of x_f128 to perform subtraction.
- x_f128.sign = x_f128.sign.negate();
- Float128 r =
- fputil::quick_add(PI_OVER_TWO_F128, 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, asin(x) = +- pi/2
- if (x_abs == 1.0) {
- // x = 1, acos(x) = 0,
- // x = -1, acos(x) = pi
- return x == 1.0 ? 0.0 : fputil::multiply_add(-x_sign, PI.hi, PI.lo);
- }
- // |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:
- //
- // When 0.5 <= x < 1, let:
- // y = acos(x)
- // We will use the double angle formula:
- // cos(2y) = 1 - 2 sin^2(y)
- // and the complement angle identity:
- // x = cos(y) = 1 - 2 sin^2 (y/2)
- // So:
- // sin(y/2) = sqrt( (1 - x)/2 )
- // And hence:
- // y/2 = asin( sqrt( (1 - x)/2 ) )
- // Equivalently:
- // acos(x) = y = 2 * asin( sqrt( (1 - x)/2 ) )
- // Let u = (1 - x)/2, then:
- // acos(x) = 2 * asin( sqrt(u) )
- // Moreover, since 0.5 <= x < 1:
- // 0 < u <= 1/4, and 0 < sqrt(u) <= 0.5,
- // And hence we can reuse the same polynomial approximation of asin(x) when
- // |x| <= 0.5:
- // acos(x) ~ 2 * sqrt(u) * P(u).
- //
- // When -1 < x <= -0.5, we reduce to the previous case using the formula:
- // acos(x) = pi - acos(-x)
- // = pi - 2 * asin ( sqrt( (1 + x)/2 ) )
- // ~ pi - 2 * sqrt(u) * P(u),
- // where u = (1 - |x|)/2.
-
- // u = (1 - |x|)/2
- double u = fputil::multiply_add(x_abs, -0.5, 0.5);
- // v_hi + v_lo ~ sqrt(u).
- // Let:
- // h = u - v_hi^2 = (sqrt(u) - v_hi) * (sqrt(u) + v_hi)
- // Then:
- // sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
- // ~ v_hi + h / (2 * v_hi)
- // So we can use:
- // v_lo = h / (2 * v_hi).
- double v_hi = fputil::sqrt<double>(u);
-
-#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- constexpr DoubleDouble CONST_TERM[2] = {{0.0, 0.0}, PI};
- DoubleDouble const_term = CONST_TERM[xbits.is_neg()];
-
- double p = asin_eval(u);
- double scale = x_sign * 2.0 * v_hi;
- double r = const_term.hi + fputil::multiply_add(scale, p, const_term.lo);
- return r;
-#else
-
-#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))/sqrt(u)
- unsigned idx;
- double err = vh * 0x1.0p-51;
-
- DoubleDouble p = asin_eval(DoubleDouble{0.0, u}, idx, err);
-
- // Perform computations in double-double arithmetic:
- // asin(x) = pi/2 - (v_hi + v_lo) * (ASIN_COEFFS[idx][0] + p)
- DoubleDouble r0 = fputil::quick_mult(DoubleDouble{vl, vh}, p);
-
- double r_hi, r_lo;
- if (xbits.is_pos()) {
- r_hi = r0.hi;
- r_lo = r0.lo;
- } else {
- DoubleDouble r = fputil::exact_add(PI.hi, -r0.hi);
- r_hi = r.hi;
- r_lo = (PI.lo - r0.lo) + r.lo;
- }
-
- // Ziv's accuracy test.
-
- double r_upper = r_hi + (r_lo + err);
- double r_lower = r_hi + (r_lo - err);
-
- 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), we have
- // that:
- // sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
- // v_lo = h / (2 * v_hi)
- // With error:
- // sqrt(u) - (v_hi + v_lo) = h * ( 1/(sqrt(u) + v_hi) - 1/(2*v_hi) )
- // = -h^2 / (2*v * (sqrt(u) + v)^2).
- // Since:
- // (sqrt(u) + v_hi)^2 ~ (2sqrt(u))^2 = 4u,
- // we can add another correction term to (v_hi + v_lo) that is:
- // v_ll = -h^2 / (2*v_hi * 4u)
- // = -v_lo * (h / 4u)
- // = -vl * (h / 8u),
- // making the errors:
- // sqrt(u) - (v_hi + v_lo + v_ll) = O(h^3)
- // well beyond 128-bit precision needed.
-
- // Get the rounding error of vl = 2 * v_lo ~ h / vh
- // Get full product of vh * vl
-#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 = xbits.sign();
-
- // Perform computations in Float128:
- // acos(x) = (v_hi + v_lo + vll) * P(u) , when 0.5 <= x < 1,
- // = pi - (v_hi + v_lo + vll) * P(u) , when -1 < x <= -0.5.
- Float128 y_f128(fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, u));
-
- Float128 p_f128 = asin_eval(y_f128, idx);
- Float128 r_f128 = fputil::quick_mul(m_v, p_f128);
-
- if (xbits.is_neg())
- r_f128 = fputil::quick_add(PI_F128, r_f128);
-
- return static_cast<double>(r_f128);
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-}
+LLVM_LIBC_FUNCTION(double, acos, (double x)) { return math::acos(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/asin.cpp b/libc/src/math/generic/asin.cpp
index ad77683d1f880..c033597334345 100644
--- a/libc/src/math/generic/asin.cpp
+++ b/libc/src/math/generic/asin.cpp
@@ -7,7 +7,6 @@
//===----------------------------------------------------------------------===//
#include "src/math/asin.h"
-#include "asin_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
@@ -18,6 +17,7 @@
#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 {
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index f0b45a99aae40..1d9989debdcdb 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2077,6 +2077,38 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_acos",
+ hdrs = ["src/__support/math/acos.h"],
+ deps = [
+ ":__support_math_asin_utils",
+ ":__support_fputil_double_double",
+ ":__support_fputil_dyadic_float",
+ ":__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",
+ ":__support_macros_properties_cpu_features",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_asin_utils",
+ hdrs = ["src/__support/math/asin_utils.h"],
+ deps = [
+ ":__support_integer_literals",
+ ":__support_fputil_double_double",
+ ":__support_fputil_dyadic_float",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_polyeval",
+ ":__support_macros_optimization",
+ ],
+)
+
libc_support_library(
name = "__support_math_exp_float_constants",
hdrs = ["src/__support/math/exp_float_constants.h"],
@@ -2554,6 +2586,13 @@ libc_function(
################################ math targets ##################################
+libc_math_function(
+ name = "acos",
+ additional_deps = [
+ ":__support_math_acos",
+ ],
+)
+
libc_math_function(
name = "acosf",
additional_deps = [
>From c944a92426c262be38c5ba8b16310b590ca6efc9 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Fri, 18 Jul 2025 20:12:52 +0300
Subject: [PATCH 2/3] make gcc happy
---
libc/src/__support/math/asin_utils.h | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/libc/src/__support/math/asin_utils.h b/libc/src/__support/math/asin_utils.h
index 4e0179e43298b..84403a98821e4 100644
--- a/libc/src/__support/math/asin_utils.h
+++ b/libc/src/__support/math/asin_utils.h
@@ -163,7 +163,7 @@ static constexpr double ASIN_COEFFS[9][12] = {
};
// We calculate the lower part of the approximation P(u).
-LIBC_INLINE static constexpr DoubleDouble
+LIBC_INLINE static DoubleDouble
asin_eval(const DoubleDouble &u, unsigned &idx, double &err) {
using fputil::multiply_add;
// k = round(u * 32).
>From 049fe9837798fe071f318e1eb6f50cf1ac9ae3e1 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Fri, 18 Jul 2025 20:46:45 +0300
Subject: [PATCH 3/3] fix style
---
libc/src/__support/math/asin_utils.h | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/libc/src/__support/math/asin_utils.h b/libc/src/__support/math/asin_utils.h
index 84403a98821e4..3146444afc51f 100644
--- a/libc/src/__support/math/asin_utils.h
+++ b/libc/src/__support/math/asin_utils.h
@@ -163,8 +163,8 @@ static constexpr double ASIN_COEFFS[9][12] = {
};
// We calculate the lower part of the approximation P(u).
-LIBC_INLINE static DoubleDouble
-asin_eval(const DoubleDouble &u, unsigned &idx, double &err) {
+LIBC_INLINE static DoubleDouble asin_eval(const DoubleDouble &u, unsigned &idx,
+ double &err) {
using fputil::multiply_add;
// k = round(u * 32).
double k = fputil::nearest_integer(u.hi * 0x1.0p5);
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