[libc][math] Refactor acosf16 implementation to header-only in src/__support/math folder. #148412
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bassiounix
requested review from
rupprecht,
keith and
aaronmondal
as code owners
This was referenced Jul 13, 2025
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@llvm/pr-subscribers-libc Author: Muhammad Bassiouni (bassiounix) ChangesPart of #147386 in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450 Please merge #148411 first Full diff: https://github.com/llvm/llvm-project/pull/148412.diff 7 Files Affected:
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 617e46602de8c..baec05b08a25d 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -13,6 +13,7 @@
#include "math/acos.h"
#include "math/acosf.h"
+#include "math/acosf16.h"
#include "math/exp.h"
#include "math/exp10.h"
#include "math/exp10f.h"
diff --git a/libc/shared/math/acosf16.h b/libc/shared/math/acosf16.h
new file mode 100644
index 0000000000000..aaf6ed9922556
--- /dev/null
+++ b/libc/shared/math/acosf16.h
@@ -0,0 +1,29 @@
+//===-- Shared acosf16 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_ACOSF16_H
+#define LLVM_LIBC_SHARED_MATH_ACOSF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "shared/libc_common.h"
+#include "src/__support/math/acosf16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acosf16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOSF16_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index fbe7e2c3125ce..fc2c8a65340cc 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -31,6 +31,22 @@ add_header_library(
libc.src.__support.macros.optimization
)
+add_header_library(
+ acosf16
+ HDRS
+ acosf16.h
+ DEPENDS
+ libc.src.__support.FPUtil.cast
+ libc.src.__support.FPUtil.except_value_utils
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.macros.optimization
+ libc.src.__support.macros.properties.types
+)
+
add_header_library(
asin_utils
HDRS
diff --git a/libc/src/__support/math/acosf16.h b/libc/src/__support/math/acosf16.h
new file mode 100644
index 0000000000000..47946704fe891
--- /dev/null
+++ b/libc/src/__support/math/acosf16.h
@@ -0,0 +1,163 @@
+//===-- Implementation header for acosf16 -----------------------*- 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_ACOSF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+// Generated by Sollya using the following command:
+// > round(pi/2, SG, RN);
+// > round(pi, SG, RN);
+static constexpr float PI_OVER_2 = 0x1.921fb6p0f;
+static constexpr float PI = 0x1.921fb6p1f;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr size_t N_EXCEPTS = 2;
+
+static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSF16_EXCEPTS{{
+ // (input, RZ output, RU offset, RD offset, RN offset)
+ {0xacaf, 0x3e93, 1, 0, 0},
+ {0xb874, 0x4052, 1, 0, 1},
+}};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+static constexpr float16 acosf16(float16 x) {
+ using FPBits = fputil::FPBits<float16>;
+ FPBits xbits(x);
+
+ uint16_t x_u = xbits.uintval();
+ uint16_t x_abs = x_u & 0x7fff;
+ uint16_t x_sign = x_u >> 15;
+
+ // |x| > 0x1p0, |x| > 1, or x is NaN.
+ if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
+ // acosf16(NaN) = NaN
+ if (xbits.is_nan()) {
+ if (xbits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ return x;
+ }
+
+ // 1 < |x| <= +/-inf
+ fputil::raise_except_if_required(FE_INVALID);
+ fputil::set_errno_if_required(EDOM);
+
+ return FPBits::quiet_nan().get_val();
+ }
+
+ float xf = x;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ // Handle exceptional values
+ if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+ return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+ // |x| == 0x1p0, x is 1 or -1
+ // if x is (-)1, return pi, else
+ // if x is (+)1, return 0
+ if (LIBC_UNLIKELY(x_abs == 0x3c00))
+ return fputil::cast<float16>(x_sign ? PI : 0.0f);
+
+ float xsq = xf * xf;
+
+ // |x| <= 0x1p-1, |x| <= 0.5
+ if (x_abs <= 0x3800) {
+ // if x is 0, return pi/2
+ if (LIBC_UNLIKELY(x_abs == 0))
+ return fputil::cast<float16>(PI_OVER_2);
+
+ // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
+ // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
+ // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+ float interm =
+ fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
+ 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+ return fputil::cast<float16>(fputil::multiply_add(-xf, interm, PI_OVER_2));
+ }
+
+ // When |x| > 0.5, assume that 0.5 < |x| <= 1
+ //
+ // Step-by-step range-reduction proof:
+ // 1: Let y = asin(x), such that, x = sin(y)
+ // 2: From complimentary angle identity:
+ // x = sin(y) = cos(pi/2 - y)
+ // 3: Let z = pi/2 - y, such that x = cos(z)
+ // 4: From double angle formula; cos(2A) = 1 - 2 * sin^2(A):
+ // z = 2A, z/2 = A
+ // cos(z) = 1 - 2 * sin^2(z/2)
+ // 5: Make sin(z/2) subject of the formula:
+ // sin(z/2) = sqrt((1 - cos(z))/2)
+ // 6: Recall [3]; x = cos(z). Therefore:
+ // sin(z/2) = sqrt((1 - x)/2)
+ // 7: Let u = (1 - x)/2
+ // 8: Therefore:
+ // asin(sqrt(u)) = z/2
+ // 2 * asin(sqrt(u)) = z
+ // 9: Recall [3]; z = pi/2 - y. Therefore:
+ // y = pi/2 - z
+ // y = pi/2 - 2 * asin(sqrt(u))
+ // 10: Recall [1], y = asin(x). Therefore:
+ // asin(x) = pi/2 - 2 * asin(sqrt(u))
+ // 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
+ // Therefore:
+ // acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u)))
+ // acos(x) = 2 * asin(sqrt(u))
+ //
+ // THE RANGE REDUCTION, HOW?
+ // 12: Recall [7], u = (1 - x)/2
+ // 13: Since 0.5 < x <= 1, therefore:
+ // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
+ //
+ // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
+ // Step [11] as `sqrt(u)` is in range.
+ // When -1 < x <= -0.5, the identity:
+ // acos(x) = pi - acos(-x)
+ // allows us to compute for the negative x value (lhs)
+ // with a positive x value instead (rhs).
+
+ float xf_abs = (xf < 0 ? -xf : xf);
+ float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
+ float sqrt_u = fputil::sqrt<float>(u);
+
+ // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
+ // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+ float asin_sqrt_u =
+ sqrt_u * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
+ 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+
+ return fputil::cast<float16>(
+ x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index c90665d5aa2a5..9ea024f48fa7e 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4040,17 +4040,8 @@ add_entrypoint_object(
HDRS
../acosf16.h
DEPENDS
- libc.hdr.errno_macros
- libc.hdr.fenv_macros
- libc.src.__support.FPUtil.cast
- libc.src.__support.FPUtil.except_value_utils
- libc.src.__support.FPUtil.fenv_impl
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.FPUtil.sqrt
- libc.src.__support.macros.optimization
- libc.src.__support.macros.properties.types
+ libc.src.__support.math.acosf16
+ libc.src.errno.errno
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/acosf16.cpp b/libc/src/math/generic/acosf16.cpp
index 202a950fbb5dd..0bf85f84c842c 100644
--- a/libc/src/math/generic/acosf16.cpp
+++ b/libc/src/math/generic/acosf16.cpp
@@ -8,144 +8,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/acosf16.h"
-#include "hdr/errno_macros.h"
-#include "hdr/fenv_macros.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/cast.h"
-#include "src/__support/FPUtil/except_value_utils.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/sqrt.h"
-#include "src/__support/macros/optimization.h"
+#include "src/__support/math/acosf16.h"
namespace LIBC_NAMESPACE_DECL {
-// Generated by Sollya using the following command:
-// > round(pi/2, SG, RN);
-// > round(pi, SG, RN);
-static constexpr float PI_OVER_2 = 0x1.921fb6p0f;
-static constexpr float PI = 0x1.921fb6p1f;
+LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) { return math::acosf16(x); }
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-static constexpr size_t N_EXCEPTS = 2;
-
-static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSF16_EXCEPTS{{
- // (input, RZ output, RU offset, RD offset, RN offset)
- {0xacaf, 0x3e93, 1, 0, 0},
- {0xb874, 0x4052, 1, 0, 1},
-}};
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) {
- using FPBits = fputil::FPBits<float16>;
- FPBits xbits(x);
-
- uint16_t x_u = xbits.uintval();
- uint16_t x_abs = x_u & 0x7fff;
- uint16_t x_sign = x_u >> 15;
-
- // |x| > 0x1p0, |x| > 1, or x is NaN.
- if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
- // acosf16(NaN) = NaN
- if (xbits.is_nan()) {
- if (xbits.is_signaling_nan()) {
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- return x;
- }
-
- // 1 < |x| <= +/-inf
- fputil::raise_except_if_required(FE_INVALID);
- fputil::set_errno_if_required(EDOM);
-
- return FPBits::quiet_nan().get_val();
- }
-
- float xf = x;
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- // Handle exceptional values
- if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
- return r.value();
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
- // |x| == 0x1p0, x is 1 or -1
- // if x is (-)1, return pi, else
- // if x is (+)1, return 0
- if (LIBC_UNLIKELY(x_abs == 0x3c00))
- return fputil::cast<float16>(x_sign ? PI : 0.0f);
-
- float xsq = xf * xf;
-
- // |x| <= 0x1p-1, |x| <= 0.5
- if (x_abs <= 0x3800) {
- // if x is 0, return pi/2
- if (LIBC_UNLIKELY(x_abs == 0))
- return fputil::cast<float16>(PI_OVER_2);
-
- // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
- // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
- // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
- float interm =
- fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
- 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
- return fputil::cast<float16>(fputil::multiply_add(-xf, interm, PI_OVER_2));
- }
-
- // When |x| > 0.5, assume that 0.5 < |x| <= 1
- //
- // Step-by-step range-reduction proof:
- // 1: Let y = asin(x), such that, x = sin(y)
- // 2: From complimentary angle identity:
- // x = sin(y) = cos(pi/2 - y)
- // 3: Let z = pi/2 - y, such that x = cos(z)
- // 4: From double angle formula; cos(2A) = 1 - 2 * sin^2(A):
- // z = 2A, z/2 = A
- // cos(z) = 1 - 2 * sin^2(z/2)
- // 5: Make sin(z/2) subject of the formula:
- // sin(z/2) = sqrt((1 - cos(z))/2)
- // 6: Recall [3]; x = cos(z). Therefore:
- // sin(z/2) = sqrt((1 - x)/2)
- // 7: Let u = (1 - x)/2
- // 8: Therefore:
- // asin(sqrt(u)) = z/2
- // 2 * asin(sqrt(u)) = z
- // 9: Recall [3]; z = pi/2 - y. Therefore:
- // y = pi/2 - z
- // y = pi/2 - 2 * asin(sqrt(u))
- // 10: Recall [1], y = asin(x). Therefore:
- // asin(x) = pi/2 - 2 * asin(sqrt(u))
- // 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
- // Therefore:
- // acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u)))
- // acos(x) = 2 * asin(sqrt(u))
- //
- // THE RANGE REDUCTION, HOW?
- // 12: Recall [7], u = (1 - x)/2
- // 13: Since 0.5 < x <= 1, therefore:
- // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
- //
- // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
- // Step [11] as `sqrt(u)` is in range.
- // When -1 < x <= -0.5, the identity:
- // acos(x) = pi - acos(-x)
- // allows us to compute for the negative x value (lhs)
- // with a positive x value instead (rhs).
-
- float xf_abs = (xf < 0 ? -xf : xf);
- float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
- float sqrt_u = fputil::sqrt<float>(u);
-
- // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
- // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
- float asin_sqrt_u =
- sqrt_u * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
- 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
-
- return fputil::cast<float16>(
- x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u);
-}
} // 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 337423cfb96cb..4579000fd174f 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2093,6 +2093,20 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_acosf16",
+ hdrs = ["src/__support/math/acosf16.h"],
+ deps = [
+ ":__support_fputil_cast",
+ ":__support_fputil_fma",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_sqrt",
+ ":__support_macros_optimization",
+ ],
+)
+
libc_support_library(
name = "__support_math_asin_utils",
hdrs = ["src/__support/math/asin_utils.h"],
@@ -2611,14 +2625,8 @@ libc_math_function(
libc_math_function(
name = "acosf16",
additional_deps = [
- ":__support_fputil_cast",
- ":__support_fputil_fma",
- ":__support_fputil_multiply_add",
- ":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
- ":__support_fputil_sqrt",
- ":__support_macros_optimization",
- ":__support_math_inv_trigf_utils",
+ ":__support_math_acosf16",
+ ":errno",
],
)
|
…support/math folder.
lntue
reviewed
Jul 21, 2025
lntue
approved these changes
Jul 21, 2025
|
LLVM Buildbot has detected a new failure on builder Full details are available at: https://lab.llvm.org/buildbot/#/builders/153/builds/38828 Here is the relevant piece of the build log for the reference |
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Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
Please merge #148411 first