[libc][math][c23] Add acosf16() function #127731
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wldfngrs
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Feb 19, 2025
wldfngrs
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- Implementation of acosf16 (inverse cosine) function for 16-bit inputs.
- Exhaustive tests across the 16-bit input range.
|
@llvm/pr-subscribers-libc Author: wldfngrs (wldfngrs) Changes
Full diff: https://github.com/llvm/llvm-project/pull/127731.diff 11 Files Affected:
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index a4f6671a59789..b38fe7520e293 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -648,6 +648,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
list(APPEND TARGET_LIBM_ENTRYPOINTS
# math.h C23 _Float16 entrypoints
libc.src.math.asinf16
+ libc.src.math.acosf16
libc.src.math.canonicalizef16
libc.src.math.ceilf16
libc.src.math.copysignf16
diff --git a/libc/docs/headers/math/index.rst b/libc/docs/headers/math/index.rst
index 3e45e3e618abb..3010f9457ae11 100644
--- a/libc/docs/headers/math/index.rst
+++ b/libc/docs/headers/math/index.rst
@@ -250,7 +250,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| <Func> | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | C23 Definition Section | C23 Error Handling Section |
+===========+==================+=================+========================+======================+========================+========================+============================+
-| acos | |check| | | | | | 7.12.4.1 | F.10.1.1 |
+| acos | |check| | | | |check| | | 7.12.4.1 | F.10.1.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| acosh | |check| | | | | | 7.12.5.1 | F.10.2.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/include/math.yaml b/libc/include/math.yaml
index b98bc55f6cc53..a66f981030864 100644
--- a/libc/include/math.yaml
+++ b/libc/include/math.yaml
@@ -14,6 +14,13 @@ functions:
return_type: float
arguments:
- type: float
+ - name: acosf16
+ standards:
+ - stdc
+ return_type: _Float16
+ arguments:
+ - type: _Float16
+ guard: LIBC_TYPES_HAS_FLOAT16
- name: acoshf
standards:
- stdc
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index 82551a4b57f45..f18a73d46f9aa 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -42,6 +42,8 @@ endfunction()
add_math_entrypoint_object(acos)
add_math_entrypoint_object(acosf)
+add_math_entrypoint_object(acosf16)
+
add_math_entrypoint_object(acosh)
add_math_entrypoint_object(acoshf)
diff --git a/libc/src/math/acosf16.h b/libc/src/math/acosf16.h
new file mode 100644
index 0000000000000..df30be2c537c9
--- /dev/null
+++ b/libc/src/math/acosf16.h
@@ -0,0 +1,21 @@
+//===-- 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_MATH_ACOSF16_H
+#define LLVM_LIBC_SRC_MATH_ACOSF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 acosf16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_ACOSF16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 537d5b5ad94ed..5ea23436ea9b1 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4034,6 +4034,25 @@ add_entrypoint_object(
.inv_trigf_utils
)
+add_entrypoint_object(
+ acosf16
+ SRCS
+ acosf16.cpp
+ HDRS
+ ../acosf16.h
+ DEPENDS
+ libc.hdr.errno_macros
+ libc.hdr.fenv_macros
+ libc.src.__support.FPUtil.cast
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.macros.optimization
+ libc.src.__support.macros.properties.types
+)
+
add_entrypoint_object(
atanf
SRCS
diff --git a/libc/src/math/generic/acosf16.cpp b/libc/src/math/generic/acosf16.cpp
new file mode 100644
index 0000000000000..4f9e9a2fb752d
--- /dev/null
+++ b/libc/src/math/generic/acosf16.cpp
@@ -0,0 +1,146 @@
+//===-- Half-precision acosf16(x) 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/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"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Generated by Sollya using the following command:
+// > round(pi/2, D, RN);
+// > round(pi, D, RN);
+static constexpr float PI_2 = 0x1.921fb54442d18p0f;
+static constexpr float PI = 0x1.921fb54442d18p1f;
+
+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},
+}};
+
+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;
+ float xf = x;
+
+ // Handle exceptional values
+ if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+ return r.value();
+
+ // |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 ? 0x1.921fb54442d18p1 : 0.0f);
+
+ // |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 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_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_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 - 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/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index 6a3dd8c9deff0..53ddd301900c0 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -2210,6 +2210,17 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
+add_fp_unittest(
+ acosf16_test
+ NEED_MPFR
+ SUITE
+ libc-math-unittests
+ SRCS
+ acosf16_test.cpp
+ DEPENDS
+ libc.src.math.acosf16
+)
+
add_fp_unittest(
atanf_test
NEED_MPFR
diff --git a/libc/test/src/math/acosf16_test.cpp b/libc/test/src/math/acosf16_test.cpp
new file mode 100644
index 0000000000000..f4890c81b0bcb
--- /dev/null
+++ b/libc/test/src/math/acosf16_test.cpp
@@ -0,0 +1,42 @@
+//===-- Exhaustive test for acosf16 ---------------------------------------===//
+//
+// 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/acosf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcAcosf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+
+namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
+
+// Range: [0, Inf]
+static constexpr uint16_t POS_START = 0x0000U;
+static constexpr uint16_t POS_STOP = 0x7c00U;
+
+// Range: [-Inf, 0]
+static constexpr uint16_t NEG_START = 0x8000U;
+static constexpr uint16_t NEG_STOP = 0xfc00U;
+
+TEST_F(LlvmLibcAcosf16Test, PositiveRange) {
+ for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
+ float16 x = FPBits(v).get_val();
+
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
+ LIBC_NAMESPACE::acosf16(x), 0.5);
+ }
+}
+
+TEST_F(LlvmLibcAcosf16Test, NegativeRange) {
+ for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
+ float16 x = FPBits(v).get_val();
+
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
+ LIBC_NAMESPACE::acosf16(x), 0.5);
+ }
+}
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index 14447728fb18a..6f94440d826d9 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -3980,6 +3980,17 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
+add_fp_unittest(
+ acosf16_test
+ SUITE
+ libc-math-smoke-tests
+ SRCS
+ acosf16_test.cpp
+ DEPENDS
+ libc.src.errno.errno
+ libc.src.math.acosf16
+)
+
add_fp_unittest(
atanf_test
SUITE
diff --git a/libc/test/src/math/smoke/acosf16_test.cpp b/libc/test/src/math/smoke/acosf16_test.cpp
new file mode 100644
index 0000000000000..c4274b8245092
--- /dev/null
+++ b/libc/test/src/math/smoke/acosf16_test.cpp
@@ -0,0 +1,39 @@
+//===-- Unittests for acosf16 ---------------------------------------------===//
+//
+//
+// 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/errno/libc_errno.h"
+#include "src/math/acosf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcAcosf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+
+TEST_F(LlvmLibcAcosf16Test, SpecialNumbers) {
+ LIBC_NAMESPACE::libc_errno = 0;
+ EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(aNaN));
+ EXPECT_MATH_ERRNO(0);
+
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::acosf16(sNaN), FE_INVALID);
+ EXPECT_MATH_ERRNO(0);
+
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::acosf16(1.0f));
+ EXPECT_MATH_ERRNO(0);
+
+ EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(inf));
+ EXPECT_MATH_ERRNO(EDOM);
+
+ EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(neg_inf));
+ EXPECT_MATH_ERRNO(EDOM);
+
+ EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(2.0f));
+ EXPECT_MATH_ERRNO(EDOM);
+
+ EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(-2.0f));
+ EXPECT_MATH_ERRNO(EDOM);
+}
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overmighty
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LLVM Buildbot has detected a new failure on builder Full details are available at: https://lab.llvm.org/buildbot/#/builders/153/builds/23676 Here is the relevant piece of the build log for the reference |
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