[libc-commits] [libc] [llvm] [libc][math] Refactor acosf implementation to header-only in src/__support/math folder. (PR #148411)
Muhammad Bassiouni via libc-commits
libc-commits at lists.llvm.org
Fri Jul 18 19:56:57 PDT 2025
https://github.com/bassiounix updated https://github.com/llvm/llvm-project/pull/148411
>From 6939b188bc48a7ae3cfc01bcaf8eb7b2d9e3b11f Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sat, 19 Jul 2025 05:33:41 +0300
Subject: [PATCH 1/3] [libc][math] Refactor acosf implementation to header-only
in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/acosf.h | 23 +++
libc/src/__support/math/CMakeLists.txt | 24 +++
libc/src/__support/math/acosf.h | 139 ++++++++++++++++++
.../math/inv_trigf_utils.h} | 100 ++++++++++++-
libc/src/math/generic/CMakeLists.txt | 26 +---
libc/src/math/generic/acosf.cpp | 121 +--------------
libc/src/math/generic/asinf.cpp | 2 +-
libc/src/math/generic/atan2f.cpp | 2 +-
libc/src/math/generic/atanf.cpp | 2 +-
libc/src/math/generic/inv_trigf_utils.h | 110 --------------
.../llvm-project-overlay/libc/BUILD.bazel | 58 ++++----
12 files changed, 323 insertions(+), 285 deletions(-)
create mode 100644 libc/shared/math/acosf.h
create mode 100644 libc/src/__support/math/acosf.h
rename libc/src/{math/generic/inv_trigf_utils.cpp => __support/math/inv_trigf_utils.h} (57%)
delete mode 100644 libc/src/math/generic/inv_trigf_utils.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 8dcfaf0352339..617e46602de8c 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -12,6 +12,7 @@
#include "libc_common.h"
#include "math/acos.h"
+#include "math/acosf.h"
#include "math/exp.h"
#include "math/exp10.h"
#include "math/exp10f.h"
diff --git a/libc/shared/math/acosf.h b/libc/shared/math/acosf.h
new file mode 100644
index 0000000000000..7cdd64e7b379a
--- /dev/null
+++ b/libc/shared/math/acosf.h
@@ -0,0 +1,23 @@
+//===-- Shared acosf 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_ACOSF_H
+#define LLVM_LIBC_SHARED_MATH_ACOSF_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/acosf.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acosf;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOSF_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 4a29c2975d523..fbe7e2c3125ce 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -17,6 +17,20 @@ add_header_library(
libc.src.__support.macros.properties.cpu_features
)
+add_header_library(
+ acosf
+ HDRS
+ acosf.h
+ DEPENDS
+ .inv_trigf_utils
+ libc.src.__support.FPUtil.except_value_utils
+ 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
+)
+
add_header_library(
asin_utils
HDRS
@@ -98,6 +112,16 @@ add_header_library(
libc.src.__support.FPUtil.manipulation_functions
)
+add_header_library(
+ inv_trigf_utils
+ HDRS
+ inv_trigf_utils.h
+ DEPENDS
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.common
+)
+
add_header_library(
frexpf16
HDRS
diff --git a/libc/src/__support/math/acosf.h b/libc/src/__support/math/acosf.h
new file mode 100644
index 0000000000000..941c39f6c3eb6
--- /dev/null
+++ b/libc/src/__support/math/acosf.h
@@ -0,0 +1,139 @@
+//===-- Implementation header for acosf -------------------------*- 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_ACOSF_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF_H
+
+#include "inv_trigf_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/except_value_utils.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
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr size_t N_EXCEPTS = 4;
+
+// Exceptional values when |x| <= 0.5
+static constexpr fputil::ExceptValues<float, N_EXCEPTS> ACOSF_EXCEPTS = {{
+ // (inputs, RZ output, RU offset, RD offset, RN offset)
+ // x = 0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
+ {0x328885a3, 0x3fc90fda, 1, 0, 1},
+ // x = -0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
+ {0xb28885a3, 0x3fc90fda, 1, 0, 1},
+ // x = 0x1.04c444p-12, acosf(x) = 0x1.920f68p0 (RZ)
+ {0x39826222, 0x3fc907b4, 1, 0, 1},
+ // x = -0x1.04c444p-12, acosf(x) = 0x1.923p0 (RZ)
+ {0xb9826222, 0x3fc91800, 1, 0, 1},
+}};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+static constexpr float acosf(float x) {
+ using FPBits = typename fputil::FPBits<float>;
+
+ FPBits xbits(x);
+ uint32_t x_uint = xbits.uintval();
+ uint32_t x_abs = xbits.uintval() & 0x7fff'ffffU;
+ uint32_t x_sign = x_uint >> 31;
+
+ // |x| <= 0.5
+ if (LIBC_UNLIKELY(x_abs <= 0x3f00'0000U)) {
+ // |x| < 0x1p-10
+ if (LIBC_UNLIKELY(x_abs < 0x3a80'0000U)) {
+ // When |x| < 2^-10, we use the following approximation:
+ // acos(x) = pi/2 - asin(x)
+ // ~ pi/2 - x - x^3 / 6
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ // Check for exceptional values
+ if (auto r = ACOSF_EXCEPTS.lookup(x_uint); LIBC_UNLIKELY(r.has_value()))
+ return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+ double xd = static_cast<double>(x);
+ return static_cast<float>(fputil::multiply_add(
+ -0x1.5555555555555p-3 * xd, xd * xd, M_MATH_PI_2 - xd));
+ }
+
+ // For |x| <= 0.5, we approximate acosf(x) by:
+ // acos(x) = pi/2 - asin(x) = pi/2 - x * P(x^2)
+ // Where P(X^2) = Q(X) is a degree-20 minimax even polynomial approximating
+ // asin(x)/x on [0, 0.5] generated by Sollya with:
+ // > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
+ // [|1, D...|], [0, 0.5]);
+ double xd = static_cast<double>(x);
+ double xsq = xd * xd;
+ double x3 = xd * xsq;
+ double r = asin_eval(xsq);
+ return static_cast<float>(fputil::multiply_add(-x3, r, M_MATH_PI_2 - xd));
+ }
+
+ // |x| >= 1, return 0, 2pi, or NaNs.
+ if (LIBC_UNLIKELY(x_abs >= 0x3f80'0000U)) {
+ if (x_abs == 0x3f80'0000U)
+ return x_sign ? /* x == -1.0f */ fputil::round_result_slightly_down(
+ 0x1.921fb6p+1f)
+ : /* x == 1.0f */ 0.0f;
+
+ if (xbits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ // |x| <= +/-inf
+ if (x_abs <= 0x7f80'0000U) {
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ }
+
+ return x + FPBits::quiet_nan().get_val();
+ }
+
+ // When 0.5 < |x| < 1, we perform range reduction as follow:
+ //
+ // Assume further that 0.5 < x <= 1, and let:
+ // y = acos(x)
+ // We use the double angle formula:
+ // 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 ) )
+ // 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 use the identity:
+ // acos(x) = pi - acos(-x)
+ // which is reduced to the postive case.
+
+ xbits.set_sign(Sign::POS);
+ double xd = static_cast<double>(xbits.get_val());
+ double u = fputil::multiply_add(-0.5, xd, 0.5);
+ double cv = 2 * fputil::sqrt<double>(u);
+
+ double r3 = asin_eval(u);
+ double r = fputil::multiply_add(cv * u, r3, cv);
+ return static_cast<float>(x_sign ? M_MATH_PI - r : r);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_H
diff --git a/libc/src/math/generic/inv_trigf_utils.cpp b/libc/src/__support/math/inv_trigf_utils.h
similarity index 57%
rename from libc/src/math/generic/inv_trigf_utils.cpp
rename to libc/src/__support/math/inv_trigf_utils.h
index f23028bb86b5c..a2811c09e9ee9 100644
--- a/libc/src/math/generic/inv_trigf_utils.cpp
+++ b/libc/src/__support/math/inv_trigf_utils.h
@@ -1,4 +1,4 @@
-//===-- Single-precision general exp/log functions ------------------------===//
+//===-- Single-precision general inverse trigonometric functions ----------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
@@ -6,11 +6,20 @@
//
//===----------------------------------------------------------------------===//
-#include "inv_trigf_utils.h"
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_INV_TRIGF_UTILS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_INV_TRIGF_UTILS_H
+
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/common.h"
#include "src/__support/macros/config.h"
namespace LIBC_NAMESPACE_DECL {
+// PI and PI / 2
+static constexpr double M_MATH_PI = 0x1.921fb54442d18p+1;
+static constexpr double M_MATH_PI_2 = 0x1.921fb54442d18p+0;
+
// Polynomial approximation for 0 <= x <= 1:
// atan(x) ~ atan((i/16) + (x - (i/16)) * Q(x - i/16)
// = P(x - i/16)
@@ -29,7 +38,7 @@ namespace LIBC_NAMESPACE_DECL {
// Notice that degree-7 is good enough for atanf, but degree-8 helps reduce the
// error bounds for atan2f's fast pass 16 times, and it does not affect the
// performance of atanf much.
-double ATAN_COEFFS[17][9] = {
+static constexpr double ATAN_COEFFS[17][9] = {
{0.0, 1.0, 0x1.3f8d76d26d61bp-47, -0x1.5555555574cd8p-2,
0x1.0dde5d06878eap-29, 0x1.99997738acc77p-3, 0x1.2c43eac9797cap-16,
-0x1.25fb020007dbdp-3, 0x1.c1b6c31d7b0aep-7},
@@ -83,4 +92,89 @@ double ATAN_COEFFS[17][9] = {
0x1.555e31a1e15e9p-6, -0x1.245240d65e629p-7, -0x1.fa9ba66478903p-11},
};
+// Look-up table for atan(k/16) with k = 0..16.
+static constexpr double ATAN_K_OVER_16[17] = {
+ 0.0,
+ 0x1.ff55bb72cfdeap-5,
+ 0x1.fd5ba9aac2f6ep-4,
+ 0x1.7b97b4bce5b02p-3,
+ 0x1.f5b75f92c80ddp-3,
+ 0x1.362773707ebccp-2,
+ 0x1.6f61941e4def1p-2,
+ 0x1.a64eec3cc23fdp-2,
+ 0x1.dac670561bb4fp-2,
+ 0x1.0657e94db30dp-1,
+ 0x1.1e00babdefeb4p-1,
+ 0x1.345f01cce37bbp-1,
+ 0x1.4978fa3269ee1p-1,
+ 0x1.5d58987169b18p-1,
+ 0x1.700a7c5784634p-1,
+ 0x1.819d0b7158a4dp-1,
+ 0x1.921fb54442d18p-1,
+};
+
+// For |x| <= 1/32 and 0 <= i <= 16, return Q(x) such that:
+// Q(x) ~ (atan(x + i/16) - atan(i/16)) / x.
+LIBC_INLINE static constexpr double atan_eval(double x, unsigned i) {
+ double x2 = x * x;
+
+ double c0 = fputil::multiply_add(x, ATAN_COEFFS[i][2], ATAN_COEFFS[i][1]);
+ double c1 = fputil::multiply_add(x, ATAN_COEFFS[i][4], ATAN_COEFFS[i][3]);
+ double c2 = fputil::multiply_add(x, ATAN_COEFFS[i][6], ATAN_COEFFS[i][5]);
+ double c3 = fputil::multiply_add(x, ATAN_COEFFS[i][8], ATAN_COEFFS[i][7]);
+
+ double x4 = x2 * x2;
+ double d1 = fputil::multiply_add(x2, c1, c0);
+ double d2 = fputil::multiply_add(x2, c3, c2);
+ double p = fputil::multiply_add(x4, d2, d1);
+ return p;
+}
+
+// Evaluate atan without big lookup table.
+// atan(n/d) - atan(k/16) = atan((n/d - k/16) / (1 + (n/d) * (k/16)))
+// = atan((n - d * k/16)) / (d + n * k/16))
+// So we let q = (n - d * k/16) / (d + n * k/16),
+// and approximate with Taylor polynomial:
+// atan(q) ~ q - q^3/3 + q^5/5 - q^7/7 + q^9/9
+LIBC_INLINE static constexpr double atan_eval_no_table(double num, double den,
+ double k_over_16) {
+ double num_r = fputil::multiply_add(den, -k_over_16, num);
+ double den_r = fputil::multiply_add(num, k_over_16, den);
+ double q = num_r / den_r;
+
+ constexpr double ATAN_TAYLOR[] = {
+ -0x1.5555555555555p-2,
+ 0x1.999999999999ap-3,
+ -0x1.2492492492492p-3,
+ 0x1.c71c71c71c71cp-4,
+ };
+ double q2 = q * q;
+ double q3 = q2 * q;
+ double q4 = q2 * q2;
+ double c0 = fputil::multiply_add(q2, ATAN_TAYLOR[1], ATAN_TAYLOR[0]);
+ double c1 = fputil::multiply_add(q2, ATAN_TAYLOR[3], ATAN_TAYLOR[2]);
+ double d = fputil::multiply_add(q4, c1, c0);
+ return fputil::multiply_add(q3, d, q);
+}
+
+// > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
+// [|1, D...|], [0, 0.5]);
+static constexpr double ASIN_COEFFS[10] = {
+ 0x1.5555555540fa1p-3, 0x1.333333512edc2p-4, 0x1.6db6cc1541b31p-5,
+ 0x1.f1caff324770ep-6, 0x1.6e43899f5f4f4p-6, 0x1.1f847cf652577p-6,
+ 0x1.9b60f47f87146p-7, 0x1.259e2634c494fp-6, -0x1.df946fa875ddp-8,
+ 0x1.02311ecf99c28p-5};
+
+// Evaluate P(x^2) - 1, where P(x^2) ~ asin(x)/x
+LIBC_INLINE static constexpr double asin_eval(double xsq) {
+ double x4 = xsq * xsq;
+ double r1 = fputil::polyeval(x4, ASIN_COEFFS[0], ASIN_COEFFS[2],
+ ASIN_COEFFS[4], ASIN_COEFFS[6], ASIN_COEFFS[8]);
+ double r2 = fputil::polyeval(x4, ASIN_COEFFS[1], ASIN_COEFFS[3],
+ ASIN_COEFFS[5], ASIN_COEFFS[7], ASIN_COEFFS[9]);
+ return fputil::multiply_add(xsq, r2, r1);
+}
+
} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_INV_TRIGF_UTILS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 7e6a32b7cdf16..c90665d5aa2a5 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -3969,18 +3969,6 @@ add_entrypoint_object(
libc.src.__support.macros.properties.types
)
-add_object_library(
- inv_trigf_utils
- HDRS
- inv_trigf_utils.h
- SRCS
- inv_trigf_utils.cpp
- DEPENDS
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.common
-)
-
add_entrypoint_object(
asinf
SRCS
@@ -3994,7 +3982,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.sqrt
libc.src.__support.macros.optimization
- .inv_trigf_utils
+ libc.src.__support.math.inv_trigf_utils
)
add_entrypoint_object(
@@ -4042,13 +4030,7 @@ add_entrypoint_object(
HDRS
../acosf.h
DEPENDS
- libc.src.__support.FPUtil.except_value_utils
- 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
- .inv_trigf_utils
+ libc.src.__support.math.acosf
)
add_entrypoint_object(
@@ -4120,7 +4102,6 @@ add_entrypoint_object(
HDRS
../atanf.h
DEPENDS
- .inv_trigf_utils
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
@@ -4128,6 +4109,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
+ libc.src.__support.math.inv_trigf_utils
)
add_entrypoint_object(
@@ -4176,7 +4158,6 @@ add_entrypoint_object(
../atan2f.h
atan2f_float.h
DEPENDS
- .inv_trigf_utils
libc.hdr.fenv_macros
libc.src.__support.FPUtil.double_double
libc.src.__support.FPUtil.fenv_impl
@@ -4186,6 +4167,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
+ libc.src.__support.math.inv_trigf_utils
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/acosf.cpp b/libc/src/math/generic/acosf.cpp
index 8dd6de2ce7474..7afc7d661d552 100644
--- a/libc/src/math/generic/acosf.cpp
+++ b/libc/src/math/generic/acosf.cpp
@@ -7,127 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/acosf.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/except_value_utils.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 "inv_trigf_utils.h"
+#include "src/__support/math/acosf.h"
namespace LIBC_NAMESPACE_DECL {
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-static constexpr size_t N_EXCEPTS = 4;
-
-// Exceptional values when |x| <= 0.5
-static constexpr fputil::ExceptValues<float, N_EXCEPTS> ACOSF_EXCEPTS = {{
- // (inputs, RZ output, RU offset, RD offset, RN offset)
- // x = 0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
- {0x328885a3, 0x3fc90fda, 1, 0, 1},
- // x = -0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
- {0xb28885a3, 0x3fc90fda, 1, 0, 1},
- // x = 0x1.04c444p-12, acosf(x) = 0x1.920f68p0 (RZ)
- {0x39826222, 0x3fc907b4, 1, 0, 1},
- // x = -0x1.04c444p-12, acosf(x) = 0x1.923p0 (RZ)
- {0xb9826222, 0x3fc91800, 1, 0, 1},
-}};
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-LLVM_LIBC_FUNCTION(float, acosf, (float x)) {
- using FPBits = typename fputil::FPBits<float>;
-
- FPBits xbits(x);
- uint32_t x_uint = xbits.uintval();
- uint32_t x_abs = xbits.uintval() & 0x7fff'ffffU;
- uint32_t x_sign = x_uint >> 31;
-
- // |x| <= 0.5
- if (LIBC_UNLIKELY(x_abs <= 0x3f00'0000U)) {
- // |x| < 0x1p-10
- if (LIBC_UNLIKELY(x_abs < 0x3a80'0000U)) {
- // When |x| < 2^-10, we use the following approximation:
- // acos(x) = pi/2 - asin(x)
- // ~ pi/2 - x - x^3 / 6
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- // Check for exceptional values
- if (auto r = ACOSF_EXCEPTS.lookup(x_uint); LIBC_UNLIKELY(r.has_value()))
- return r.value();
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
- double xd = static_cast<double>(x);
- return static_cast<float>(fputil::multiply_add(
- -0x1.5555555555555p-3 * xd, xd * xd, M_MATH_PI_2 - xd));
- }
-
- // For |x| <= 0.5, we approximate acosf(x) by:
- // acos(x) = pi/2 - asin(x) = pi/2 - x * P(x^2)
- // Where P(X^2) = Q(X) is a degree-20 minimax even polynomial approximating
- // asin(x)/x on [0, 0.5] generated by Sollya with:
- // > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
- // [|1, D...|], [0, 0.5]);
- double xd = static_cast<double>(x);
- double xsq = xd * xd;
- double x3 = xd * xsq;
- double r = asin_eval(xsq);
- return static_cast<float>(fputil::multiply_add(-x3, r, M_MATH_PI_2 - xd));
- }
-
- // |x| >= 1, return 0, 2pi, or NaNs.
- if (LIBC_UNLIKELY(x_abs >= 0x3f80'0000U)) {
- if (x_abs == 0x3f80'0000U)
- return x_sign ? /* x == -1.0f */ fputil::round_result_slightly_down(
- 0x1.921fb6p+1f)
- : /* x == 1.0f */ 0.0f;
-
- if (xbits.is_signaling_nan()) {
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- // |x| <= +/-inf
- if (x_abs <= 0x7f80'0000U) {
- fputil::set_errno_if_required(EDOM);
- fputil::raise_except_if_required(FE_INVALID);
- }
-
- return x + FPBits::quiet_nan().get_val();
- }
-
- // When 0.5 < |x| < 1, we perform range reduction as follow:
- //
- // Assume further that 0.5 < x <= 1, and let:
- // y = acos(x)
- // We use the double angle formula:
- // 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 ) )
- // 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 use the identity:
- // acos(x) = pi - acos(-x)
- // which is reduced to the postive case.
-
- xbits.set_sign(Sign::POS);
- double xd = static_cast<double>(xbits.get_val());
- double u = fputil::multiply_add(-0.5, xd, 0.5);
- double cv = 2 * fputil::sqrt<double>(u);
-
- double r3 = asin_eval(u);
- double r = fputil::multiply_add(cv * u, r3, cv);
- return static_cast<float>(x_sign ? M_MATH_PI - r : r);
-}
+LLVM_LIBC_FUNCTION(float, acosf, (float x)) { return math::acosf(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/asinf.cpp b/libc/src/math/generic/asinf.cpp
index 12383bf6dacae..c8d6b38ab1560 100644
--- a/libc/src/math/generic/asinf.cpp
+++ b/libc/src/math/generic/asinf.cpp
@@ -17,7 +17,7 @@
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
-#include "inv_trigf_utils.h"
+#include "src/__support/math/inv_trigf_utils.h"
namespace LIBC_NAMESPACE_DECL {
diff --git a/libc/src/math/generic/atan2f.cpp b/libc/src/math/generic/atan2f.cpp
index c04b0eb1cc589..0a768494baa64 100644
--- a/libc/src/math/generic/atan2f.cpp
+++ b/libc/src/math/generic/atan2f.cpp
@@ -8,7 +8,6 @@
#include "src/math/atan2f.h"
#include "hdr/fenv_macros.h"
-#include "inv_trigf_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/FPUtil/rounding_mode.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/math/inv_trigf_utils.h"
#if defined(LIBC_MATH_HAS_SKIP_ACCURATE_PASS) && \
defined(LIBC_MATH_HAS_INTERMEDIATE_COMP_IN_FLOAT)
diff --git a/libc/src/math/generic/atanf.cpp b/libc/src/math/generic/atanf.cpp
index 46196dbe4162c..d12456c591016 100644
--- a/libc/src/math/generic/atanf.cpp
+++ b/libc/src/math/generic/atanf.cpp
@@ -7,7 +7,6 @@
//===----------------------------------------------------------------------===//
#include "src/math/atanf.h"
-#include "inv_trigf_utils.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/except_value_utils.h"
@@ -16,6 +15,7 @@
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/math/inv_trigf_utils.h"
namespace LIBC_NAMESPACE_DECL {
diff --git a/libc/src/math/generic/inv_trigf_utils.h b/libc/src/math/generic/inv_trigf_utils.h
deleted file mode 100644
index 8b47aba342995..0000000000000
--- a/libc/src/math/generic/inv_trigf_utils.h
+++ /dev/null
@@ -1,110 +0,0 @@
-//===-- Single-precision general inverse trigonometric functions ----------===//
-//
-// 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_GENERIC_INV_TRIGF_UTILS_H
-#define LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H
-
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
-
-namespace LIBC_NAMESPACE_DECL {
-
-// PI and PI / 2
-static constexpr double M_MATH_PI = 0x1.921fb54442d18p+1;
-static constexpr double M_MATH_PI_2 = 0x1.921fb54442d18p+0;
-
-extern double ATAN_COEFFS[17][9];
-
-// Look-up table for atan(k/16) with k = 0..16.
-static constexpr double ATAN_K_OVER_16[17] = {
- 0.0,
- 0x1.ff55bb72cfdeap-5,
- 0x1.fd5ba9aac2f6ep-4,
- 0x1.7b97b4bce5b02p-3,
- 0x1.f5b75f92c80ddp-3,
- 0x1.362773707ebccp-2,
- 0x1.6f61941e4def1p-2,
- 0x1.a64eec3cc23fdp-2,
- 0x1.dac670561bb4fp-2,
- 0x1.0657e94db30dp-1,
- 0x1.1e00babdefeb4p-1,
- 0x1.345f01cce37bbp-1,
- 0x1.4978fa3269ee1p-1,
- 0x1.5d58987169b18p-1,
- 0x1.700a7c5784634p-1,
- 0x1.819d0b7158a4dp-1,
- 0x1.921fb54442d18p-1,
-};
-
-// For |x| <= 1/32 and 0 <= i <= 16, return Q(x) such that:
-// Q(x) ~ (atan(x + i/16) - atan(i/16)) / x.
-LIBC_INLINE static double atan_eval(double x, unsigned i) {
- double x2 = x * x;
-
- double c0 = fputil::multiply_add(x, ATAN_COEFFS[i][2], ATAN_COEFFS[i][1]);
- double c1 = fputil::multiply_add(x, ATAN_COEFFS[i][4], ATAN_COEFFS[i][3]);
- double c2 = fputil::multiply_add(x, ATAN_COEFFS[i][6], ATAN_COEFFS[i][5]);
- double c3 = fputil::multiply_add(x, ATAN_COEFFS[i][8], ATAN_COEFFS[i][7]);
-
- double x4 = x2 * x2;
- double d1 = fputil::multiply_add(x2, c1, c0);
- double d2 = fputil::multiply_add(x2, c3, c2);
- double p = fputil::multiply_add(x4, d2, d1);
- return p;
-}
-
-// Evaluate atan without big lookup table.
-// atan(n/d) - atan(k/16) = atan((n/d - k/16) / (1 + (n/d) * (k/16)))
-// = atan((n - d * k/16)) / (d + n * k/16))
-// So we let q = (n - d * k/16) / (d + n * k/16),
-// and approximate with Taylor polynomial:
-// atan(q) ~ q - q^3/3 + q^5/5 - q^7/7 + q^9/9
-LIBC_INLINE static double atan_eval_no_table(double num, double den,
- double k_over_16) {
- double num_r = fputil::multiply_add(den, -k_over_16, num);
- double den_r = fputil::multiply_add(num, k_over_16, den);
- double q = num_r / den_r;
-
- constexpr double ATAN_TAYLOR[] = {
- -0x1.5555555555555p-2,
- 0x1.999999999999ap-3,
- -0x1.2492492492492p-3,
- 0x1.c71c71c71c71cp-4,
- };
- double q2 = q * q;
- double q3 = q2 * q;
- double q4 = q2 * q2;
- double c0 = fputil::multiply_add(q2, ATAN_TAYLOR[1], ATAN_TAYLOR[0]);
- double c1 = fputil::multiply_add(q2, ATAN_TAYLOR[3], ATAN_TAYLOR[2]);
- double d = fputil::multiply_add(q4, c1, c0);
- return fputil::multiply_add(q3, d, q);
-}
-
-// > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
-// [|1, D...|], [0, 0.5]);
-static constexpr double ASIN_COEFFS[10] = {
- 0x1.5555555540fa1p-3, 0x1.333333512edc2p-4, 0x1.6db6cc1541b31p-5,
- 0x1.f1caff324770ep-6, 0x1.6e43899f5f4f4p-6, 0x1.1f847cf652577p-6,
- 0x1.9b60f47f87146p-7, 0x1.259e2634c494fp-6, -0x1.df946fa875ddp-8,
- 0x1.02311ecf99c28p-5};
-
-// Evaluate P(x^2) - 1, where P(x^2) ~ asin(x)/x
-LIBC_INLINE static double asin_eval(double xsq) {
- double x4 = xsq * xsq;
- double r1 = fputil::polyeval(x4, ASIN_COEFFS[0], ASIN_COEFFS[2],
- ASIN_COEFFS[4], ASIN_COEFFS[6], ASIN_COEFFS[8]);
- double r2 = fputil::polyeval(x4, ASIN_COEFFS[1], ASIN_COEFFS[3],
- ASIN_COEFFS[5], ASIN_COEFFS[7], ASIN_COEFFS[9]);
- return fputil::multiply_add(xsq, r2, r1);
-}
-
-} // namespace LIBC_NAMESPACE_DECL
-
-#endif // LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 1d9989debdcdb..337423cfb96cb 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2009,22 +2009,6 @@ libc_support_library(
],
)
-libc_support_library(
- name = "inv_trigf_utils",
- srcs = ["src/math/generic/inv_trigf_utils.cpp"],
- hdrs = [
- "src/math/generic/inv_trigf_utils.h",
- ],
- deps = [
- ":__support_common",
- ":__support_fputil_double_double",
- ":__support_fputil_fma",
- ":__support_fputil_multiply_add",
- ":__support_fputil_polyeval",
- ":__support_integer_literals",
- ],
-)
-
libc_support_library(
name = "atan_utils",
hdrs = ["src/math/generic/atan_utils.h"],
@@ -2095,6 +2079,20 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_acosf",
+ hdrs = ["src/__support/math/acosf.h"],
+ deps = [
+ ":__support_math_inv_trigf_utils",
+ ":__support_fputil_except_value_utils",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_sqrt",
+ ":__support_macros_optimization",
+ ],
+)
+
libc_support_library(
name = "__support_math_asin_utils",
hdrs = ["src/__support/math/asin_utils.h"],
@@ -2177,6 +2175,16 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_inv_trigf_utils",
+ hdrs = ["src/__support/math/inv_trigf_utils.h"],
+ deps = [
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_polyeval",
+ ":__support_common",
+ ],
+)
+
libc_support_library(
name = "__support_math_frexpf16",
hdrs = ["src/__support/math/frexpf16.h"],
@@ -2596,13 +2604,7 @@ libc_math_function(
libc_math_function(
name = "acosf",
additional_deps = [
- ":__support_fputil_fma",
- ":__support_fputil_multiply_add",
- ":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
- ":__support_fputil_sqrt",
- ":__support_macros_optimization",
- ":inv_trigf_utils",
+ ":__support_math_acosf",
],
)
@@ -2616,7 +2618,7 @@ libc_math_function(
":__support_fputil_polyeval",
":__support_fputil_sqrt",
":__support_macros_optimization",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
@@ -2644,7 +2646,7 @@ libc_math_function(
":__support_fputil_sqrt",
":__support_macros_optimization",
":__support_macros_properties_cpu_features",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
@@ -2658,7 +2660,7 @@ libc_math_function(
":__support_fputil_polyeval",
":__support_fputil_sqrt",
":__support_macros_optimization",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
@@ -2685,7 +2687,7 @@ libc_math_function(
":__support_fputil_polyeval",
":__support_fputil_rounding_mode",
":__support_macros_optimization",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
@@ -2704,7 +2706,7 @@ libc_math_function(
additional_deps = [
":__support_fputil_double_double",
":__support_fputil_nearest_integer",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
>From e10df27794843fba42f666f7805bb6a5eddb0a35 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sat, 19 Jul 2025 05:50:37 +0300
Subject: [PATCH 2/3] make gcc happy
---
libc/src/__support/math/inv_trigf_utils.h | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/libc/src/__support/math/inv_trigf_utils.h b/libc/src/__support/math/inv_trigf_utils.h
index a2811c09e9ee9..b3f0e458cad5f 100644
--- a/libc/src/__support/math/inv_trigf_utils.h
+++ b/libc/src/__support/math/inv_trigf_utils.h
@@ -115,7 +115,7 @@ static constexpr double ATAN_K_OVER_16[17] = {
// For |x| <= 1/32 and 0 <= i <= 16, return Q(x) such that:
// Q(x) ~ (atan(x + i/16) - atan(i/16)) / x.
-LIBC_INLINE static constexpr double atan_eval(double x, unsigned i) {
+LIBC_INLINE static double atan_eval(double x, unsigned i) {
double x2 = x * x;
double c0 = fputil::multiply_add(x, ATAN_COEFFS[i][2], ATAN_COEFFS[i][1]);
@@ -136,7 +136,7 @@ LIBC_INLINE static constexpr double atan_eval(double x, unsigned i) {
// So we let q = (n - d * k/16) / (d + n * k/16),
// and approximate with Taylor polynomial:
// atan(q) ~ q - q^3/3 + q^5/5 - q^7/7 + q^9/9
-LIBC_INLINE static constexpr double atan_eval_no_table(double num, double den,
+LIBC_INLINE static double atan_eval_no_table(double num, double den,
double k_over_16) {
double num_r = fputil::multiply_add(den, -k_over_16, num);
double den_r = fputil::multiply_add(num, k_over_16, den);
@@ -166,7 +166,7 @@ static constexpr double ASIN_COEFFS[10] = {
0x1.02311ecf99c28p-5};
// Evaluate P(x^2) - 1, where P(x^2) ~ asin(x)/x
-LIBC_INLINE static constexpr double asin_eval(double xsq) {
+LIBC_INLINE static double asin_eval(double xsq) {
double x4 = xsq * xsq;
double r1 = fputil::polyeval(x4, ASIN_COEFFS[0], ASIN_COEFFS[2],
ASIN_COEFFS[4], ASIN_COEFFS[6], ASIN_COEFFS[8]);
>From 2d6f0a33fc9304c3f41cca874074cbdaee10c019 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sat, 19 Jul 2025 05:56:45 +0300
Subject: [PATCH 3/3] fix style
---
libc/src/__support/math/inv_trigf_utils.h | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/libc/src/__support/math/inv_trigf_utils.h b/libc/src/__support/math/inv_trigf_utils.h
index b3f0e458cad5f..b8f4914eeb9e5 100644
--- a/libc/src/__support/math/inv_trigf_utils.h
+++ b/libc/src/__support/math/inv_trigf_utils.h
@@ -137,7 +137,7 @@ LIBC_INLINE static double atan_eval(double x, unsigned i) {
// and approximate with Taylor polynomial:
// atan(q) ~ q - q^3/3 + q^5/5 - q^7/7 + q^9/9
LIBC_INLINE static double atan_eval_no_table(double num, double den,
- double k_over_16) {
+ double k_over_16) {
double num_r = fputil::multiply_add(den, -k_over_16, num);
double den_r = fputil::multiply_add(num, k_over_16, den);
double q = num_r / den_r;
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