diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt index 1ac3a781d5279..394452e916d33 100644 --- a/libc/config/linux/x86_64/entrypoints.txt +++ b/libc/config/linux/x86_64/entrypoints.txt @@ -658,6 +658,7 @@ if(LIBC_TYPES_HAS_FLOAT16) # math.h C23 _Float16 entrypoints libc.src.math.acosf16 libc.src.math.acoshf16 + libc.src.math.acospif16 libc.src.math.asinf16 libc.src.math.asinhf16 libc.src.math.canonicalizef16 diff --git a/libc/docs/headers/math/index.rst b/libc/docs/headers/math/index.rst index 947bd4b60b391..cf88e6237d1e3 100644 --- a/libc/docs/headers/math/index.rst +++ b/libc/docs/headers/math/index.rst @@ -253,7 +253,7 @@ Higher Math Functions +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | acosh | |check| | | | |check| | | 7.12.5.1 | F.10.2.1 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| acospi | | | | | | 7.12.4.8 | F.10.1.8 | +| acospi | | | | |check| | | 7.12.4.8 | F.10.1.8 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | asin | |check| | | | |check| | | 7.12.4.2 | F.10.1.2 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ diff --git a/libc/include/math.yaml b/libc/include/math.yaml index fef829422244d..b725c33c0bb06 100644 --- a/libc/include/math.yaml +++ b/libc/include/math.yaml @@ -34,6 +34,13 @@ functions: arguments: - type: _Float16 guard: LIBC_TYPES_HAS_FLOAT16 + name: acospif16 + standards: + - stdc + return_type: _Float16 + arguments: + - type: _Float16 + guard: LIBC_TYPES_HAS_FLOAT16 - name: asin standards: - stdc diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt index d177ff79141c0..5161b2b61aa94 100644 --- a/libc/src/math/CMakeLists.txt +++ b/libc/src/math/CMakeLists.txt @@ -48,6 +48,8 @@ add_math_entrypoint_object(acosh) add_math_entrypoint_object(acoshf) add_math_entrypoint_object(acoshf16) +add_math_entrypoint_object(acospif16) + add_math_entrypoint_object(asin) add_math_entrypoint_object(asinf) add_math_entrypoint_object(asinf16) diff --git a/libc/src/math/acospif16.h b/libc/src/math/acospif16.h new file mode 100644 index 0000000000000..e94a35bdf6fb7 --- /dev/null +++ b/libc/src/math/acospif16.h @@ -0,0 +1,21 @@ +//===-- Implementation header for acospif16 ---------------------*- 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_ACOSPIF16_H +#define LLVM_LIBC_SRC_MATH_ACOSPIF16_H + +#include "src/__support/macros/config.h" +#include "src/__support/macros/properties/types.h" + +namespace LIBC_NAMESPACE_DECL { + +float16 acospif16(float16 x); + +} // namespace LIBC_NAMESPACE_DECL + +#endif // LLVM_LIBC_SRC_MATH_ACOSPIF16_H diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index f7c36aab77b7d..e7e5efa475816 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -4112,6 +4112,25 @@ add_entrypoint_object( libc.src.__support.macros.properties.types ) +add_entrypoint_object( + acospif16 + SRCS + acospif16.cpp + HDRS + ../acospif16.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_header_library( atan_utils HDRS diff --git a/libc/src/math/generic/acospif16.cpp b/libc/src/math/generic/acospif16.cpp new file mode 100644 index 0000000000000..bfdf1694e3ba6 --- /dev/null +++ b/libc/src/math/generic/acospif16.cpp @@ -0,0 +1,134 @@ +//===-- Half-precision acospi 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/acospif16.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/multiply_add.h" +#include "src/__support/FPUtil/sqrt.h" +#include "src/__support/macros/optimization.h" + +namespace LIBC_NAMESPACE_DECL { + +LLVM_LIBC_FUNCTION(float16, acospif16, (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)) { + // acospif16(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(); + } + + // |x| == 0x1p0, x is 1 or -1 + // if x is (-)1, return 1 + // if x is (+)1, return 0 + if (LIBC_UNLIKELY(x_abs == 0x3c00)) + return fputil::cast(x_sign ? 1.0f : 0.0f); + + float xf = x; + float xsq = xf * xf; + + // Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya + // with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0, + // 0.5]); + constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f, + 0x1.897e36p-6f, 0x1.9efafcp-7f, + 0x1.06d884p-6f}; + // |x| <= 0x1p-1, |x| <= 0.5 + if (x_abs <= 0x3800) { + // if x is 0, return 0.5 + if (LIBC_UNLIKELY(x_abs == 0)) + return fputil::cast(0.5f); + + // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x), then + // acospi(x) = 0.5 - asin(x)/pi + float interm = + fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2], + POLY_COEFFS[3], POLY_COEFFS[4]); + + return fputil::cast(fputil::multiply_add(-xf, interm, 0.5f)); + } + + // 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)) + // acospi(x) = 2 * (asin(sqrt(u)) / pi) + // + // 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) + // acospi(x) = 1 - acos(-x)/pi + // 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); + + float asin_sqrt_u = + sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1], + POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]); + + // Same as acos(x), but devided the expression with pi + return fputil::cast( + x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f) + : 2.0f * asin_sqrt_u); +} +} // namespace LIBC_NAMESPACE_DECL diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt index 7ee8b86135557..ebf9f1c86cf15 100644 --- a/libc/test/src/math/CMakeLists.txt +++ b/libc/test/src/math/CMakeLists.txt @@ -2269,6 +2269,17 @@ add_fp_unittest( libc.src.math.acosf16 ) +add_fp_unittest( + acospif16_test + NEED_MPFR + SUITE + libc-math-unittests + SRCS + acospif16_test.cpp + DEPENDS + libc.src.math.acospif16 +) + add_fp_unittest( atanf_test NEED_MPFR diff --git a/libc/test/src/math/acospif16_test.cpp b/libc/test/src/math/acospif16_test.cpp new file mode 100644 index 0000000000000..1dd951f602c90 --- /dev/null +++ b/libc/test/src/math/acospif16_test.cpp @@ -0,0 +1,42 @@ +//===-- Exhaustive test for acospif16 -------------------------------------===// +// +// 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/acospif16.h" +#include "test/UnitTest/FPMatcher.h" +#include "test/UnitTest/Test.h" +#include "utils/MPFRWrapper/MPFRUtils.h" + +using LlvmLibcAcospif16Test = 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(LlvmLibcAcospif16Test, PositiveRange) { + for (uint16_t v = POS_START; v <= POS_STOP; ++v) { + float16 x = FPBits(v).get_val(); + + EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acospi, x, + LIBC_NAMESPACE::acospif16(x), 0.5); + } +} + +TEST_F(LlvmLibcAcospif16Test, NegativeRange) { + for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) { + float16 x = FPBits(v).get_val(); + + EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acospi, x, + LIBC_NAMESPACE::acospif16(x), 0.5); + } +} diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt index bf6999d5d5649..3579adfcc62ef 100644 --- a/libc/test/src/math/smoke/CMakeLists.txt +++ b/libc/test/src/math/smoke/CMakeLists.txt @@ -4040,6 +4040,17 @@ add_fp_unittest( libc.src.math.acosf16 ) +add_fp_unittest( + acospif16_test + SUITE + libc-math-smoke-tests + SRCS + acospif16_test.cpp + DEPENDS + libc.src.errno.errno + libc.src.math.acospif16 +) + add_fp_unittest( atanf_test SUITE diff --git a/libc/test/src/math/smoke/acospif16_test.cpp b/libc/test/src/math/smoke/acospif16_test.cpp new file mode 100644 index 0000000000000..66b94706eab94 --- /dev/null +++ b/libc/test/src/math/smoke/acospif16_test.cpp @@ -0,0 +1,38 @@ +//===-- Unittests for acospif16 -------------------------------------------===// +// +// 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/acospif16.h" +#include "test/UnitTest/FPMatcher.h" +#include "test/UnitTest/Test.h" + +using LlvmLibcAcospif16Test = LIBC_NAMESPACE::testing::FPTest; +TEST_F(LlvmLibcAcospif16Test, SpecialNumbers) { + LIBC_NAMESPACE::libc_errno = 0; + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(aNaN)); + EXPECT_MATH_ERRNO(0); + + EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::acospif16(sNaN), + FE_INVALID); + EXPECT_MATH_ERRNO(0); + + EXPECT_FP_EQ(zero, LIBC_NAMESPACE::acospif16(1.0f)); + EXPECT_MATH_ERRNO(0); + + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(inf)); + EXPECT_MATH_ERRNO(EDOM); + + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(neg_inf)); + EXPECT_MATH_ERRNO(EDOM); + + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(2.0f)); + EXPECT_MATH_ERRNO(EDOM); + + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acospif16(-2.0f)); + EXPECT_MATH_ERRNO(EDOM); +} diff --git a/libc/utils/MPFRWrapper/MPCommon.cpp b/libc/utils/MPFRWrapper/MPCommon.cpp index ac8cde2f97221..ccd4d2d01a4e2 100644 --- a/libc/utils/MPFRWrapper/MPCommon.cpp +++ b/libc/utils/MPFRWrapper/MPCommon.cpp @@ -70,6 +70,23 @@ MPFRNumber MPFRNumber::acosh() const { return result; } +MPFRNumber MPFRNumber::acospi() const { + MPFRNumber result(*this); + +#if MPFR_VERSION_MAJOR > 4 || \ + (MPFR_VERSION_MAJOR == 4 && MPFR_VERSION_MINOR >= 2) + mpfr_acospi(result.value, value, mpfr_rounding); + return result; +#else + MPFRNumber value_acos(0.0, 1280); + mpfr_acos(value_acos.value, value, MPFR_RNDN); + MPFRNumber value_pi(0.0, 1280); + mpfr_const_pi(value_pi.value, MPFR_RNDN); + mpfr_div(result.value, value_acos.value, value_pi.value, mpfr_rounding); + return result; +#endif +} + MPFRNumber MPFRNumber::add(const MPFRNumber &b) const { MPFRNumber result(*this); mpfr_add(result.value, value, b.value, mpfr_rounding); diff --git a/libc/utils/MPFRWrapper/MPCommon.h b/libc/utils/MPFRWrapper/MPCommon.h index eaa512e30bc86..99cb7ec66a2ca 100644 --- a/libc/utils/MPFRWrapper/MPCommon.h +++ b/libc/utils/MPFRWrapper/MPCommon.h @@ -181,6 +181,7 @@ class MPFRNumber { MPFRNumber abs() const; MPFRNumber acos() const; MPFRNumber acosh() const; + MPFRNumber acospi() const; MPFRNumber add(const MPFRNumber &b) const; MPFRNumber asin() const; MPFRNumber asinh() const; diff --git a/libc/utils/MPFRWrapper/MPFRUtils.cpp b/libc/utils/MPFRWrapper/MPFRUtils.cpp index 4a033dbc2049b..8853f96ef8f92 100644 --- a/libc/utils/MPFRWrapper/MPFRUtils.cpp +++ b/libc/utils/MPFRWrapper/MPFRUtils.cpp @@ -32,6 +32,8 @@ unary_operation(Operation op, InputType input, unsigned int precision, return mpfrInput.acos(); case Operation::Acosh: return mpfrInput.acosh(); + case Operation::Acospi: + return mpfrInput.acospi(); case Operation::Asin: return mpfrInput.asin(); case Operation::Asinh: diff --git a/libc/utils/MPFRWrapper/MPFRUtils.h b/libc/utils/MPFRWrapper/MPFRUtils.h index bc65f87c6b5ab..c77a6aa3adeae 100644 --- a/libc/utils/MPFRWrapper/MPFRUtils.h +++ b/libc/utils/MPFRWrapper/MPFRUtils.h @@ -28,6 +28,7 @@ enum class Operation : int { Abs, Acos, Acosh, + Acospi, Asin, Asinh, Atan,