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 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | | (float) | (double) | (long double) | (float16) | (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..3114289bad486 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -4034,6 +4034,26 @@ 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.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_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..858da3bfaa918 --- /dev/null +++ b/libc/src/math/generic/acosf16.cpp @@ -0,0 +1,147 @@ +//===-- 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, SG, RN); +// > round(pi, SG, RN); +static constexpr float PI_OVER_2 = 0x1.921fb6p0f; +static constexpr float PI = 0x1.921fb6p1f; + +static constexpr size_t N_EXCEPTS = 2; + +static constexpr fputil::ExceptValues 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; + 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; + + // 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(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(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(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(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( + 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; + +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; + +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); +}