From 9c6454fb3614d61a196de03a1eb7a3b06a9fa87e Mon Sep 17 00:00:00 2001 From: wldfngrs Date: Fri, 24 Jan 2025 00:54:08 +0100 Subject: [PATCH 1/9] Add asinf16() function --- libc/config/linux/x86_64/entrypoints.txt | 1 + libc/docs/headers/math/index.rst | 2 +- libc/include/math.yaml | 7 ++ libc/src/math/CMakeLists.txt | 1 + libc/src/math/asinf16.h | 21 ++++ libc/src/math/generic/CMakeLists.txt | 19 ++++ libc/src/math/generic/asinf16.cpp | 120 ++++++++++++++++++++++ libc/test/src/math/CMakeLists.txt | 11 ++ libc/test/src/math/asinf16_test.cpp | 40 ++++++++ libc/test/src/math/smoke/CMakeLists.txt | 11 ++ libc/test/src/math/smoke/asinf16_test.cpp | 40 ++++++++ 11 files changed, 272 insertions(+), 1 deletion(-) create mode 100644 libc/src/math/asinf16.h create mode 100644 libc/src/math/generic/asinf16.cpp create mode 100644 libc/test/src/math/asinf16_test.cpp create mode 100644 libc/test/src/math/smoke/asinf16_test.cpp diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt index 366e4d34294d1..bdf010876910b 100644 --- a/libc/config/linux/x86_64/entrypoints.txt +++ b/libc/config/linux/x86_64/entrypoints.txt @@ -642,6 +642,7 @@ endif() if(LIBC_TYPES_HAS_FLOAT16) list(APPEND TARGET_LIBM_ENTRYPOINTS # math.h C23 _Float16 entrypoints + libc.src.math.asinf16 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 8548e4a5773bc..3e45e3e618abb 100644 --- a/libc/docs/headers/math/index.rst +++ b/libc/docs/headers/math/index.rst @@ -256,7 +256,7 @@ Higher Math Functions +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | acospi | | | | | | 7.12.4.8 | F.10.1.8 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| asin | |check| | | | | | 7.12.4.2 | F.10.1.2 | +| asin | |check| | | | |check| | | 7.12.4.2 | F.10.1.2 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | asinh | |check| | | | | | 7.12.5.2 | F.10.2.2 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ diff --git a/libc/include/math.yaml b/libc/include/math.yaml index 3a660a59d3605..b98bc55f6cc53 100644 --- a/libc/include/math.yaml +++ b/libc/include/math.yaml @@ -32,6 +32,13 @@ functions: return_type: float arguments: - type: float + - name: asinf16 + standards: + - stdc + return_type: _Float16 + arguments: + - type: _Float16 + guard: LIBC_TYPES_HAS_FLOAT16 - name: asinhf standards: - stdc diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt index fe5ebd793b40a..87004bf6ddd0a 100644 --- a/libc/src/math/CMakeLists.txt +++ b/libc/src/math/CMakeLists.txt @@ -49,6 +49,7 @@ add_math_entrypoint_object(asin) add_math_entrypoint_object(asinf) add_math_entrypoint_object(asinh) add_math_entrypoint_object(asinhf) +add_math_entrypoint_object(asinf16) add_math_entrypoint_object(atan) add_math_entrypoint_object(atanf) diff --git a/libc/src/math/asinf16.h b/libc/src/math/asinf16.h new file mode 100644 index 0000000000000..f16647ec2a6f9 --- /dev/null +++ b/libc/src/math/asinf16.h @@ -0,0 +1,21 @@ +//===-- Implementation header for asinf16 -----------------------*- 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_ASINF16_H +#define LLVM_LIBC_SRC_MATH_ASINF16_H + +#include "src/__support/macros/config.h" +#include "src/__support/macros/properties/types.h" + +namespace LIBC_NAMESPACE_DECL { + +float16 asinf16(float16 x); + +} // namespace LIBC_NAMESPACE_DECL + +#endif // LLVM_LIBC_SRC_MATH_ASINF16_H diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index 0e57051807b33..cf77987ff3add 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -4598,6 +4598,25 @@ add_entrypoint_object( ${libc_opt_high_flag} ) +add_entrypoint_object( + asinf16 + SRCS + asinf16.cpp + HDRS + ../asinf16.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( acosf SRCS diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp new file mode 100644 index 0000000000000..0a0bdc0e28c3d --- /dev/null +++ b/libc/src/math/generic/asinf16.cpp @@ -0,0 +1,120 @@ +//===-- Half-precision asinf16(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/asinf16.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/cast.h" +#include "src/__support/FPUtil/multiply_add.h" +#include "src/__support/FPUtil/PolyEval.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); +static constexpr float PI_2 = 0x1.921fb54442d18p0f; + +LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { + using FPBits = fputil::FPBits; + FPBits xbits(x); + + uint16_t x_u = xbits.uintval(); + uint16_t x_abs = x_u & 0x7fff; + float xf = x; + + float xsq = xf * xf; + + // |x| <= 0x1p-1, |x| <= 0.5 + if (x_abs <= 0x3800) { + if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) { + // asinf16(+/-0) = +/-0 + if (LIBC_UNLIKELY(x_abs == 0U)) { + return x; + } + + // Exhaustive tests show that, when: + // x > 0, and rounding upward, then, + // asin(x) = x * 2^-11 + x + // else, in other rounding modes, + // asin(x) = x + int rounding = fputil::quick_get_round(); + + if ((xbits.is_pos() && rounding == FE_UPWARD) || + (xbits.is_neg() && rounding == FE_DOWNWARD)) { + return fputil::cast(fputil::multiply_add(xf, 0x1.0p-11f, xf)); + } + return x; + } + + // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with: + // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]); + float result = fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); + return fputil::cast(xf * result); + } + + // |x| > 1, asinf16(x) = NaN + if (LIBC_UNLIKELY(x_abs > 0x3c00)) { + // |x| <= +/-inf + if (LIBC_UNLIKELY(x_abs <= 0x7c00)) { + fputil::set_errno_if_required(EDOM); + fputil::raise_except_if_required(FE_INVALID); + } + + return FPBits::quiet_nan().get_val(); + } + + // 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: + // arcsin(sqrt(u)) = z/2 + // 2 * arcsin(sqrt(u)) = z + // 9: Recall [3], z = pi/2 - y. Therefore: + // y = pi/2 - z + // y = pi/2 - 2 * arcsin(sqrt(u)) + // 10: Recall [1], y = asin(x). Therefore: + // arcsin(x) = pi/2 - 2 * arcsin(sqrt(u)) + // + // WHY? + // 11: Recall [7], u = (1 - x)/2 + // 12: 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 [10] + // as `sqrt(u)` is in range. + + // 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0 + float xf_abs = (xf < 0 ? -xf : xf); + float sign = ((xbits.uintval() >> 15) == 1 ? -1.0 : 1.0); + float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f); + float u_sqrt = fputil::sqrt(u); + + // Degree-6 minimax odd 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 = u_sqrt * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); + + return fputil::cast(sign * fputil::multiply_add(-2.0f, asin_sqrt_u, PI_2)); +} + +} diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt index bbcdf2363c1e2..7af20dcaab4bd 100644 --- a/libc/test/src/math/CMakeLists.txt +++ b/libc/test/src/math/CMakeLists.txt @@ -2186,6 +2186,17 @@ add_fp_unittest( libc.src.__support.FPUtil.fp_bits ) +add_fp_unittest( + asinf16_test + NEED_MPFR + SUITE + libc-math-unittests + SRCS + asinf16_test.cpp + DEPENDS + libc.src.math.asinf16 +) + add_fp_unittest( acosf_test NEED_MPFR diff --git a/libc/test/src/math/asinf16_test.cpp b/libc/test/src/math/asinf16_test.cpp new file mode 100644 index 0000000000000..43b3aeccd6636 --- /dev/null +++ b/libc/test/src/math/asinf16_test.cpp @@ -0,0 +1,40 @@ +//===-- Exhaustive test for asinf16 ---------------------------------------===// +// +// 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/asinf16.h" +#include "test/UnitTest/FPMatcher.h" +#include "test/UnitTest/Test.h" +#include "utils/MPFRWrapper/MPFRUtils.h" + +using LlvmLibcAsinf16Test = 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(LlvmLibcAsinf16Test, PositiveRange) { + for (uint16_t v = POS_START; v <= POS_STOP; ++v) { + float16 x = FPBits(v).get_val(); + + EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asin, x, LIBC_NAMESPACE::asinf16(x), 0.5); + } +} + +TEST_F(LlvmLibcAsinf16Test, NegativeRange) { + for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) { + float16 x = FPBits(v).get_val(); + + EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asin, x, LIBC_NAMESPACE::asinf16(x), 0.5); + } +} diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt index e4501eb75fa48..43a580ac6b894 100644 --- a/libc/test/src/math/smoke/CMakeLists.txt +++ b/libc/test/src/math/smoke/CMakeLists.txt @@ -3954,6 +3954,17 @@ add_fp_unittest( libc.src.__support.FPUtil.fp_bits ) +add_fp_unittest( + asinf16_test + SUITE + libc-math-smoke-tests + SRCS + asinf16_test.cpp + DEPENDS + libc.src.errno.errno + libc.src.math.asinf16 +) + add_fp_unittest( acosf_test SUITE diff --git a/libc/test/src/math/smoke/asinf16_test.cpp b/libc/test/src/math/smoke/asinf16_test.cpp new file mode 100644 index 0000000000000..303a3a302c2d5 --- /dev/null +++ b/libc/test/src/math/smoke/asinf16_test.cpp @@ -0,0 +1,40 @@ +//===-- Unittests for asinf16 ---------------------------------------------===// +// +// +// 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/asinf16.h" +#include "test/UnitTest/FPMatcher.h" +#include "test/UnitTest/Test.h" + +using LlvmLibcAsinf16Test = LIBC_NAMESPACE::testing::FPTest; + +TEST_F(LlvmLibcAsinf16Test, SpecialNumbers) { + LIBC_NAMESPACE::libc_errno = 0; + + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(aNaN)); + EXPECT_MATH_ERRNO(0); + + EXPECT_FP_EQ(zero, LIBC_NAMESPACE::asinf16(zero)); + EXPECT_MATH_ERRNO(0); + + EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::asinf16(neg_zero)); + EXPECT_MATH_ERRNO(0); + + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(inf)); + EXPECT_MATH_ERRNO(EDOM); + + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(neg_inf)); + EXPECT_MATH_ERRNO(EDOM); + + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(2.0f)); + EXPECT_MATH_ERRNO(EDOM); + + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(-2.0f)); + EXPECT_MATH_ERRNO(EDOM); +} From d8fa4dddfd88f0bbac407410d77a0edd426a26fc Mon Sep 17 00:00:00 2001 From: wldfngrs Date: Fri, 24 Jan 2025 00:55:47 +0100 Subject: [PATCH 2/9] clang-format --- libc/src/math/generic/asinf16.cpp | 42 ++++++++++++++++------------- libc/test/src/math/asinf16_test.cpp | 6 +++-- 2 files changed, 28 insertions(+), 20 deletions(-) diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp index 0a0bdc0e28c3d..d340a7244cf34 100644 --- a/libc/src/math/generic/asinf16.cpp +++ b/libc/src/math/generic/asinf16.cpp @@ -11,9 +11,9 @@ #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/PolyEval.h" #include "src/__support/FPUtil/sqrt.h" #include "src/__support/macros/optimization.h" @@ -32,17 +32,18 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { float xf = x; float xsq = xf * xf; - + // |x| <= 0x1p-1, |x| <= 0.5 - if (x_abs <= 0x3800) { + if (x_abs <= 0x3800) { if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) { // asinf16(+/-0) = +/-0 if (LIBC_UNLIKELY(x_abs == 0U)) { return x; } - + // Exhaustive tests show that, when: - // x > 0, and rounding upward, then, + // x > 0, and rounding upward, or + // x < 0, and rounding downward, then, // asin(x) = x * 2^-11 + x // else, in other rounding modes, // asin(x) = x @@ -57,10 +58,12 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with: // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]); - float result = fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); + float result = + fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, + 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); return fputil::cast(xf * result); } - + // |x| > 1, asinf16(x) = NaN if (LIBC_UNLIKELY(x_abs > 0x3c00)) { // |x| <= +/-inf @@ -72,7 +75,7 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { return FPBits::quiet_nan().get_val(); } - // When |x| > 0.5, assume that 0.5 < |x| <= 1, + // 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) @@ -95,26 +98,29 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // y = pi/2 - 2 * arcsin(sqrt(u)) // 10: Recall [1], y = asin(x). Therefore: // arcsin(x) = pi/2 - 2 * arcsin(sqrt(u)) - // + // // WHY? // 11: Recall [7], u = (1 - x)/2 // 12: 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 [10] - // as `sqrt(u)` is in range. - + // + // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for + // Step [10] as `sqrt(u)` is in range. + // 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0 float xf_abs = (xf < 0 ? -xf : xf); float sign = ((xbits.uintval() >> 15) == 1 ? -1.0 : 1.0); float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f); float u_sqrt = fputil::sqrt(u); - + // Degree-6 minimax odd 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 = u_sqrt * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); - - return fputil::cast(sign * fputil::multiply_add(-2.0f, asin_sqrt_u, PI_2)); -} + float asin_sqrt_u = + u_sqrt * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f, + 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); + return fputil::cast(sign * + fputil::multiply_add(-2.0f, asin_sqrt_u, PI_2)); } + +} // namespace LIBC_NAMESPACE_DECL diff --git a/libc/test/src/math/asinf16_test.cpp b/libc/test/src/math/asinf16_test.cpp index 43b3aeccd6636..9593cad16ac77 100644 --- a/libc/test/src/math/asinf16_test.cpp +++ b/libc/test/src/math/asinf16_test.cpp @@ -27,7 +27,8 @@ TEST_F(LlvmLibcAsinf16Test, PositiveRange) { for (uint16_t v = POS_START; v <= POS_STOP; ++v) { float16 x = FPBits(v).get_val(); - EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asin, x, LIBC_NAMESPACE::asinf16(x), 0.5); + EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asin, x, + LIBC_NAMESPACE::asinf16(x), 0.5); } } @@ -35,6 +36,7 @@ TEST_F(LlvmLibcAsinf16Test, NegativeRange) { for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) { float16 x = FPBits(v).get_val(); - EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asin, x, LIBC_NAMESPACE::asinf16(x), 0.5); + EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asin, x, + LIBC_NAMESPACE::asinf16(x), 0.5); } } From c6002ffd3a652d8ba3cb1f04a0e6c1ed819f8921 Mon Sep 17 00:00:00 2001 From: wldfngrs Date: Mon, 27 Jan 2025 17:23:48 +0100 Subject: [PATCH 3/9] nit --- libc/src/math/generic/asinf16.cpp | 40 ++++++++++------------- libc/test/src/math/smoke/asinf16_test.cpp | 3 -- 2 files changed, 18 insertions(+), 25 deletions(-) diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp index d340a7244cf34..df1d7ec1cd1ed 100644 --- a/libc/src/math/generic/asinf16.cpp +++ b/libc/src/math/generic/asinf16.cpp @@ -35,24 +35,23 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // |x| <= 0x1p-1, |x| <= 0.5 if (x_abs <= 0x3800) { + // asinf16(+/-0) = +/-0 + if (LIBC_UNLIKELY(x_abs == 0)) + return x; + + // Exhaustive tests show that, + // for |x| <= 0x1.878p-9, when: + // x > 0, and rounding upward, or + // x < 0, and rounding downward, then, + // asin(x) = x * 2^-11 + x + // else, in other rounding modes, + // asin(x) = x if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) { - // asinf16(+/-0) = +/-0 - if (LIBC_UNLIKELY(x_abs == 0U)) { - return x; - } - - // Exhaustive tests show that, when: - // x > 0, and rounding upward, or - // x < 0, and rounding downward, then, - // asin(x) = x * 2^-11 + x - // else, in other rounding modes, - // asin(x) = x int rounding = fputil::quick_get_round(); if ((xbits.is_pos() && rounding == FE_UPWARD) || - (xbits.is_neg() && rounding == FE_DOWNWARD)) { + (xbits.is_neg() && rounding == FE_DOWNWARD)) return fputil::cast(fputil::multiply_add(xf, 0x1.0p-11f, xf)); - } return x; } @@ -66,11 +65,8 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // |x| > 1, asinf16(x) = NaN if (LIBC_UNLIKELY(x_abs > 0x3c00)) { - // |x| <= +/-inf - if (LIBC_UNLIKELY(x_abs <= 0x7c00)) { - fputil::set_errno_if_required(EDOM); - fputil::raise_except_if_required(FE_INVALID); - } + fputil::set_errno_if_required(EDOM); + fputil::raise_except_if_required(FE_INVALID); return FPBits::quiet_nan().get_val(); } @@ -91,13 +87,13 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // sin(z/2) = sqrt((1 - x)/2) // 7: Let u = (1 - x)/2 // 8: Therefore: - // arcsin(sqrt(u)) = z/2 - // 2 * arcsin(sqrt(u)) = z + // 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 * arcsin(sqrt(u)) // 10: Recall [1], y = asin(x). Therefore: - // arcsin(x) = pi/2 - 2 * arcsin(sqrt(u)) + // asin(x) = pi/2 - 2 * asin(sqrt(u)) // // WHY? // 11: Recall [7], u = (1 - x)/2 @@ -109,7 +105,7 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0 float xf_abs = (xf < 0 ? -xf : xf); - float sign = ((xbits.uintval() >> 15) == 1 ? -1.0 : 1.0); + float sign = (xbits.uintval() >> 15 == 1 ? -1.0 : 1.0); float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f); float u_sqrt = fputil::sqrt(u); diff --git a/libc/test/src/math/smoke/asinf16_test.cpp b/libc/test/src/math/smoke/asinf16_test.cpp index 303a3a302c2d5..76ce36f673a8a 100644 --- a/libc/test/src/math/smoke/asinf16_test.cpp +++ b/libc/test/src/math/smoke/asinf16_test.cpp @@ -17,9 +17,6 @@ using LlvmLibcAsinf16Test = LIBC_NAMESPACE::testing::FPTest; TEST_F(LlvmLibcAsinf16Test, SpecialNumbers) { LIBC_NAMESPACE::libc_errno = 0; - EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(aNaN)); - EXPECT_MATH_ERRNO(0); - EXPECT_FP_EQ(zero, LIBC_NAMESPACE::asinf16(zero)); EXPECT_MATH_ERRNO(0); From 299a753074882b5d0689802e1cf6d043e14afa85 Mon Sep 17 00:00:00 2001 From: wldfngrs Date: Fri, 31 Jan 2025 00:19:34 +0100 Subject: [PATCH 4/9] fix behaviour for 'signaling NaN'/'quiet nan' inputs --- libc/src/math/generic/asinf16.cpp | 11 ++++++++--- libc/test/src/math/smoke/asinf16_test.cpp | 2 ++ 2 files changed, 10 insertions(+), 3 deletions(-) diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp index df1d7ec1cd1ed..56e5b0905d957 100644 --- a/libc/src/math/generic/asinf16.cpp +++ b/libc/src/math/generic/asinf16.cpp @@ -65,8 +65,13 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // |x| > 1, asinf16(x) = NaN if (LIBC_UNLIKELY(x_abs > 0x3c00)) { - fputil::set_errno_if_required(EDOM); - fputil::raise_except_if_required(FE_INVALID); + // |x| <= +/-inf + if (LIBC_UNLIKELY(x_abs <= 0x7c00)) { + if (!xbits.is_signaling_nan()) + fputil::set_errno_if_required(EDOM); + + fputil::raise_except_if_required(FE_INVALID); + } return FPBits::quiet_nan().get_val(); } @@ -91,7 +96,7 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // 2 * asin(sqrt(u)) = z // 9: Recall [3], z = pi/2 - y. Therefore: // y = pi/2 - z - // y = pi/2 - 2 * arcsin(sqrt(u)) + // y = pi/2 - 2 * asin(sqrt(u)) // 10: Recall [1], y = asin(x). Therefore: // asin(x) = pi/2 - 2 * asin(sqrt(u)) // diff --git a/libc/test/src/math/smoke/asinf16_test.cpp b/libc/test/src/math/smoke/asinf16_test.cpp index 76ce36f673a8a..4b4836cc57958 100644 --- a/libc/test/src/math/smoke/asinf16_test.cpp +++ b/libc/test/src/math/smoke/asinf16_test.cpp @@ -16,6 +16,8 @@ using LlvmLibcAsinf16Test = LIBC_NAMESPACE::testing::FPTest; TEST_F(LlvmLibcAsinf16Test, SpecialNumbers) { LIBC_NAMESPACE::libc_errno = 0; + EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(aNaN)); + EXPECT_MATH_ERRNO(0); EXPECT_FP_EQ(zero, LIBC_NAMESPACE::asinf16(zero)); EXPECT_MATH_ERRNO(0); From dc173e35db3a16407c053cb444d2d4174c569c3f Mon Sep 17 00:00:00 2001 From: wldfngrs Date: Mon, 3 Feb 2025 15:31:51 +0100 Subject: [PATCH 5/9] convert signaling NaN (sNaN) to quiet NaN (qNaN) --- libc/src/math/generic/asinf16.cpp | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp index 56e5b0905d957..4c42624c2a674 100644 --- a/libc/src/math/generic/asinf16.cpp +++ b/libc/src/math/generic/asinf16.cpp @@ -35,6 +35,16 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // |x| <= 0x1p-1, |x| <= 0.5 if (x_abs <= 0x3800) { + //asinf16(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; + } + // asinf16(+/-0) = +/-0 if (LIBC_UNLIKELY(x_abs == 0)) return x; @@ -67,9 +77,7 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { if (LIBC_UNLIKELY(x_abs > 0x3c00)) { // |x| <= +/-inf if (LIBC_UNLIKELY(x_abs <= 0x7c00)) { - if (!xbits.is_signaling_nan()) - fputil::set_errno_if_required(EDOM); - + fputil::set_errno_if_required(EDOM); fputil::raise_except_if_required(FE_INVALID); } From 96ab6365395de2e7cf0954f30af2be24a5cc973a Mon Sep 17 00:00:00 2001 From: wldfngrs Date: Mon, 3 Feb 2025 15:40:31 +0100 Subject: [PATCH 6/9] clang-format --- libc/src/math/generic/asinf16.cpp | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp index 4c42624c2a674..f359f375e3596 100644 --- a/libc/src/math/generic/asinf16.cpp +++ b/libc/src/math/generic/asinf16.cpp @@ -35,16 +35,16 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { // |x| <= 0x1p-1, |x| <= 0.5 if (x_abs <= 0x3800) { - //asinf16(NaN) = NaN + // asinf16(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 FPBits::quiet_nan().get_val(); } return x; } - + // asinf16(+/-0) = +/-0 if (LIBC_UNLIKELY(x_abs == 0)) return x; From 5a5136cbffb67936778ba12891c969a4ba735c10 Mon Sep 17 00:00:00 2001 From: wldfngrs Date: Wed, 5 Feb 2025 19:05:32 +0100 Subject: [PATCH 7/9] minor changes --- libc/src/math/generic/asinf16.cpp | 28 +++++++++++------------ libc/test/src/math/smoke/asinf16_test.cpp | 3 +++ 2 files changed, 16 insertions(+), 15 deletions(-) diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp index f359f375e3596..bbcd133863e3e 100644 --- a/libc/src/math/generic/asinf16.cpp +++ b/libc/src/math/generic/asinf16.cpp @@ -31,10 +31,8 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { uint16_t x_abs = x_u & 0x7fff; float xf = x; - float xsq = xf * xf; - - // |x| <= 0x1p-1, |x| <= 0.5 - if (x_abs <= 0x3800) { + // |x| > 0x1p0, |x| > 1, or x is NaN. + if (LIBC_UNLIKELY(x_abs > 0x3c00)) { // asinf16(NaN) = NaN if (xbits.is_nan()) { if (xbits.is_signaling_nan()) { @@ -44,7 +42,18 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { 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) { // asinf16(+/-0) = +/-0 if (LIBC_UNLIKELY(x_abs == 0)) return x; @@ -73,17 +82,6 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { return fputil::cast(xf * result); } - // |x| > 1, asinf16(x) = NaN - if (LIBC_UNLIKELY(x_abs > 0x3c00)) { - // |x| <= +/-inf - if (LIBC_UNLIKELY(x_abs <= 0x7c00)) { - fputil::set_errno_if_required(EDOM); - fputil::raise_except_if_required(FE_INVALID); - } - - return FPBits::quiet_nan().get_val(); - } - // When |x| > 0.5, assume that 0.5 < |x| <= 1, // // Step-by-step range-reduction proof: diff --git a/libc/test/src/math/smoke/asinf16_test.cpp b/libc/test/src/math/smoke/asinf16_test.cpp index 4b4836cc57958..9f675b08319c0 100644 --- a/libc/test/src/math/smoke/asinf16_test.cpp +++ b/libc/test/src/math/smoke/asinf16_test.cpp @@ -19,6 +19,9 @@ TEST_F(LlvmLibcAsinf16Test, SpecialNumbers) { EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::asinf16(aNaN)); EXPECT_MATH_ERRNO(0); + EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::asinf16(sNaN), FE_INVALID); + EXPECT_MATH_ERRNO(0); + EXPECT_FP_EQ(zero, LIBC_NAMESPACE::asinf16(zero)); EXPECT_MATH_ERRNO(0); From cdf231a12979d68dc1933cc347ca42fe095fc9aa Mon Sep 17 00:00:00 2001 From: wldfngrs Date: Wed, 5 Feb 2025 23:33:14 +0100 Subject: [PATCH 8/9] clang formatt --- libc/src/math/generic/asinf16.cpp | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp index bbcd133863e3e..518c384a61530 100644 --- a/libc/src/math/generic/asinf16.cpp +++ b/libc/src/math/generic/asinf16.cpp @@ -42,14 +42,14 @@ LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { 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 From e3653bf88d1683af257274185af88911428ce65c Mon Sep 17 00:00:00 2001 From: OverMighty Date: Mon, 10 Feb 2025 10:59:57 +0100 Subject: [PATCH 9/9] Update libc/src/math/CMakeLists.txt --- libc/src/math/CMakeLists.txt | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt index 87004bf6ddd0a..82551a4b57f45 100644 --- a/libc/src/math/CMakeLists.txt +++ b/libc/src/math/CMakeLists.txt @@ -47,9 +47,10 @@ add_math_entrypoint_object(acoshf) add_math_entrypoint_object(asin) add_math_entrypoint_object(asinf) +add_math_entrypoint_object(asinf16) + add_math_entrypoint_object(asinh) add_math_entrypoint_object(asinhf) -add_math_entrypoint_object(asinf16) add_math_entrypoint_object(atan) add_math_entrypoint_object(atanf)