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[libc][math][c23] Add acosf16() function (#127731)
- Implementation of acosf16 (inverse cosine) function for 16-bit inputs. - Exhaustive tests across the 16-bit input range.
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-1
lines changed

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‎libc/config/linux/x86_64/entrypoints.txt

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@@ -649,6 +649,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
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list(APPEND TARGET_LIBM_ENTRYPOINTS
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# math.h C23 _Float16 entrypoints
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libc.src.math.asinf16
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libc.src.math.acosf16
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libc.src.math.canonicalizef16
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libc.src.math.ceilf16
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libc.src.math.copysignf16

‎libc/docs/headers/math/index.rst

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@@ -250,7 +250,7 @@ Higher Math Functions
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| <Func> | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | C23 Definition Section | C23 Error Handling Section |
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+===========+==================+=================+========================+======================+========================+========================+============================+
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| acos | |check| | | | | | 7.12.4.1 | F.10.1.1 |
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| acos | |check| | | | |check| | | 7.12.4.1 | F.10.1.1 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| acosh | |check| | | | | | 7.12.5.1 | F.10.2.1 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

‎libc/include/math.yaml

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@@ -14,6 +14,13 @@ functions:
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return_type: float
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arguments:
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- type: float
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- name: acosf16
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standards:
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- stdc
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return_type: _Float16
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arguments:
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- type: _Float16
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guard: LIBC_TYPES_HAS_FLOAT16
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- name: acoshf
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standards:
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- stdc

‎libc/src/math/CMakeLists.txt

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@@ -42,6 +42,8 @@ endfunction()
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add_math_entrypoint_object(acos)
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add_math_entrypoint_object(acosf)
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add_math_entrypoint_object(acosf16)
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add_math_entrypoint_object(acosh)
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add_math_entrypoint_object(acoshf)
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‎libc/src/math/acosf16.h

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//===-- Implementation header for acosf16 -----------------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception.
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//
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_SRC_MATH_ACOSF16_H
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#define LLVM_LIBC_SRC_MATH_ACOSF16_H
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#include "src/__support/macros/config.h"
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#include "src/__support/macros/properties/types.h"
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namespace LIBC_NAMESPACE_DECL {
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float16 acosf16(float16 x);
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LLVM_LIBC_SRC_MATH_ACOSF16_H

‎libc/src/math/generic/CMakeLists.txt

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@@ -4034,6 +4034,26 @@ add_entrypoint_object(
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.inv_trigf_utils
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)
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add_entrypoint_object(
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acosf16
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SRCS
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acosf16.cpp
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HDRS
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../acosf16.h
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DEPENDS
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libc.hdr.errno_macros
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libc.hdr.fenv_macros
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libc.src.__support.FPUtil.cast
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libc.src.__support.FPUtil.except_value_utils
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libc.src.__support.FPUtil.fenv_impl
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libc.src.__support.FPUtil.fp_bits
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libc.src.__support.FPUtil.multiply_add
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libc.src.__support.FPUtil.polyeval
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libc.src.__support.FPUtil.sqrt
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libc.src.__support.macros.optimization
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libc.src.__support.macros.properties.types
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)
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add_entrypoint_object(
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atanf
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SRCS

‎libc/src/math/generic/acosf16.cpp

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//===-- Half-precision acosf16(x) function --------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception.
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//
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//
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//===----------------------------------------------------------------------===//
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#include "src/math/acosf16.h"
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#include "hdr/errno_macros.h"
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#include "hdr/fenv_macros.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FPBits.h"
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#include "src/__support/FPUtil/PolyEval.h"
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#include "src/__support/FPUtil/cast.h"
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#include "src/__support/FPUtil/except_value_utils.h"
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#include "src/__support/FPUtil/multiply_add.h"
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#include "src/__support/FPUtil/sqrt.h"
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#include "src/__support/macros/optimization.h"
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namespace LIBC_NAMESPACE_DECL {
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// Generated by Sollya using the following command:
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// > round(pi/2, SG, RN);
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// > round(pi, SG, RN);
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static constexpr float PI_OVER_2 = 0x1.921fb6p0f;
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static constexpr float PI = 0x1.921fb6p1f;
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static constexpr size_t N_EXCEPTS = 2;
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static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSF16_EXCEPTS{{
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// (input, RZ output, RU offset, RD offset, RN offset)
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{0xacaf, 0x3e93, 1, 0, 0},
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{0xb874, 0x4052, 1, 0, 1},
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}};
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LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) {
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using FPBits = fputil::FPBits<float16>;
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FPBits xbits(x);
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uint16_t x_u = xbits.uintval();
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uint16_t x_abs = x_u & 0x7fff;
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uint16_t x_sign = x_u >> 15;
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// |x| > 0x1p0, |x| > 1, or x is NaN.
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if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
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// acosf16(NaN) = NaN
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if (xbits.is_nan()) {
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if (xbits.is_signaling_nan()) {
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fputil::raise_except_if_required(FE_INVALID);
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return FPBits::quiet_nan().get_val();
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}
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return x;
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}
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// 1 < |x| <= +/-inf
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fputil::raise_except_if_required(FE_INVALID);
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fputil::set_errno_if_required(EDOM);
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return FPBits::quiet_nan().get_val();
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}
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float xf = x;
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// Handle exceptional values
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if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
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return r.value();
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// |x| == 0x1p0, x is 1 or -1
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// if x is (-)1, return pi, else
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// if x is (+)1, return 0
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if (LIBC_UNLIKELY(x_abs == 0x3c00))
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return fputil::cast<float16>(x_sign ? PI : 0.0f);
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float xsq = xf * xf;
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// |x| <= 0x1p-1, |x| <= 0.5
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if (x_abs <= 0x3800) {
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// if x is 0, return pi/2
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if (LIBC_UNLIKELY(x_abs == 0))
83+
return fputil::cast<float16>(PI_OVER_2);
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// Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
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// Degree-6 minimax polynomial of asin(x) generated by Sollya with:
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// > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
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float interm =
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fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
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0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
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return fputil::cast<float16>(fputil::multiply_add(-xf, interm, PI_OVER_2));
92+
}
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// When |x| > 0.5, assume that 0.5 < |x| <= 1
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//
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// Step-by-step range-reduction proof:
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// 1: Let y = asin(x), such that, x = sin(y)
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// 2: From complimentary angle identity:
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// x = sin(y) = cos(pi/2 - y)
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// 3: Let z = pi/2 - y, such that x = cos(z)
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// 4: From double angle formula; cos(2A) = 1 - 2 * sin^2(A):
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// z = 2A, z/2 = A
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// cos(z) = 1 - 2 * sin^2(z/2)
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// 5: Make sin(z/2) subject of the formula:
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// sin(z/2) = sqrt((1 - cos(z))/2)
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// 6: Recall [3]; x = cos(z). Therefore:
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// sin(z/2) = sqrt((1 - x)/2)
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// 7: Let u = (1 - x)/2
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// 8: Therefore:
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// asin(sqrt(u)) = z/2
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// 2 * asin(sqrt(u)) = z
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// 9: Recall [3]; z = pi/2 - y. Therefore:
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// y = pi/2 - z
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// y = pi/2 - 2 * asin(sqrt(u))
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// 10: Recall [1], y = asin(x). Therefore:
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// asin(x) = pi/2 - 2 * asin(sqrt(u))
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// 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
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// Therefore:
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// acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u)))
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// acos(x) = 2 * asin(sqrt(u))
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//
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// THE RANGE REDUCTION, HOW?
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// 12: Recall [7], u = (1 - x)/2
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// 13: Since 0.5 < x <= 1, therefore:
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// 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
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//
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// Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
128+
// Step [11] as `sqrt(u)` is in range.
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// When -1 < x <= -0.5, the identity:
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// acos(x) = pi - acos(-x)
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// allows us to compute for the negative x value (lhs)
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// with a positive x value instead (rhs).
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float xf_abs = (xf < 0 ? -xf : xf);
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float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
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float sqrt_u = fputil::sqrt<float>(u);
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// Degree-6 minimax polynomial of asin(x) generated by Sollya with:
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// > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
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float asin_sqrt_u =
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sqrt_u * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
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0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
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return fputil::cast<float16>(
145+
x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u);
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}
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} // namespace LIBC_NAMESPACE_DECL

‎libc/test/src/math/CMakeLists.txt

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@@ -2210,6 +2210,17 @@ add_fp_unittest(
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libc.src.__support.FPUtil.fp_bits
22112211
)
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add_fp_unittest(
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acosf16_test
2215+
NEED_MPFR
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SUITE
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libc-math-unittests
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SRCS
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acosf16_test.cpp
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DEPENDS
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libc.src.math.acosf16
2222+
)
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add_fp_unittest(
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atanf_test
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NEED_MPFR

‎libc/test/src/math/acosf16_test.cpp

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//===-- Exhaustive test for acosf16 ---------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#include "src/math/acosf16.h"
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#include "test/UnitTest/FPMatcher.h"
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#include "test/UnitTest/Test.h"
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#include "utils/MPFRWrapper/MPFRUtils.h"
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using LlvmLibcAcosf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
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16+
namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
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// Range: [0, Inf]
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static constexpr uint16_t POS_START = 0x0000U;
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static constexpr uint16_t POS_STOP = 0x7c00U;
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// Range: [-Inf, 0]
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static constexpr uint16_t NEG_START = 0x8000U;
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static constexpr uint16_t NEG_STOP = 0xfc00U;
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TEST_F(LlvmLibcAcosf16Test, PositiveRange) {
27+
for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
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float16 x = FPBits(v).get_val();
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EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
31+
LIBC_NAMESPACE::acosf16(x), 0.5);
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}
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}
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TEST_F(LlvmLibcAcosf16Test, NegativeRange) {
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for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
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float16 x = FPBits(v).get_val();
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EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
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LIBC_NAMESPACE::acosf16(x), 0.5);
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}
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}

‎libc/test/src/math/smoke/CMakeLists.txt

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@@ -3980,6 +3980,17 @@ add_fp_unittest(
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libc.src.__support.FPUtil.fp_bits
39813981
)
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add_fp_unittest(
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acosf16_test
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SUITE
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libc-math-smoke-tests
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SRCS
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acosf16_test.cpp
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DEPENDS
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libc.src.errno.errno
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libc.src.math.acosf16
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)
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add_fp_unittest(
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atanf_test
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SUITE

‎libc/test/src/math/smoke/acosf16_test.cpp

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//===-- Unittests for acosf16 ---------------------------------------------===//
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//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5+
// See https://llvm.org/LICENSE.txt for license information.
6+
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception.
7+
//
8+
//===----------------------------------------------------------------------===//
9+
10+
#include "src/errno/libc_errno.h"
11+
#include "src/math/acosf16.h"
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#include "test/UnitTest/FPMatcher.h"
13+
#include "test/UnitTest/Test.h"
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using LlvmLibcAcosf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
16+
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TEST_F(LlvmLibcAcosf16Test, SpecialNumbers) {
18+
LIBC_NAMESPACE::libc_errno = 0;
19+
EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(aNaN));
20+
EXPECT_MATH_ERRNO(0);
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EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::acosf16(sNaN), FE_INVALID);
23+
EXPECT_MATH_ERRNO(0);
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25+
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::acosf16(1.0f));
26+
EXPECT_MATH_ERRNO(0);
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EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(inf));
29+
EXPECT_MATH_ERRNO(EDOM);
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EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(neg_inf));
32+
EXPECT_MATH_ERRNO(EDOM);
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EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(2.0f));
35+
EXPECT_MATH_ERRNO(EDOM);
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EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::acosf16(-2.0f));
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EXPECT_MATH_ERRNO(EDOM);
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}

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