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[libc][math][c23] Add acospif16() function (llvm#134664)
Addresses llvm#132211 llvm#132754 Part of llvm#95250
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‎libc/config/linux/x86_64/entrypoints.txt‎

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@@ -662,6 +662,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
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# math.h C23 _Float16 entrypoints
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libc.src.math.acosf16
664664
libc.src.math.acoshf16
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libc.src.math.acospif16
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libc.src.math.asinf16
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libc.src.math.asinhf16
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libc.src.math.canonicalizef16

‎libc/docs/headers/math/index.rst‎

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@@ -253,7 +253,7 @@ Higher Math Functions
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| acosh | |check| | | | |check| | | 7.12.5.1 | F.10.2.1 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| acospi | | | | | | 7.12.4.8 | F.10.1.8 |
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| acospi | | | | |check| | | 7.12.4.8 | F.10.1.8 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| asin | |check| | | | |check| | | 7.12.4.2 | F.10.1.2 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

‎libc/include/math.yaml‎

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@@ -34,6 +34,13 @@ functions:
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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: acospif16
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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: asin
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standards:
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- stdc

‎libc/src/math/CMakeLists.txt‎

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@@ -48,6 +48,8 @@ add_math_entrypoint_object(acosh)
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add_math_entrypoint_object(acoshf)
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add_math_entrypoint_object(acoshf16)
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add_math_entrypoint_object(acospif16)
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add_math_entrypoint_object(asin)
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add_math_entrypoint_object(asinf)
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add_math_entrypoint_object(asinf16)

‎libc/src/math/acospif16.h‎

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@@ -0,0 +1,21 @@
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//===-- Implementation header for acospif16 ---------------------*- 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_ACOSPIF16_H
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#define LLVM_LIBC_SRC_MATH_ACOSPIF16_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 acospif16(float16 x);
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LLVM_LIBC_SRC_MATH_ACOSPIF16_H

‎libc/src/math/generic/CMakeLists.txt‎

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@@ -4112,6 +4112,25 @@ add_entrypoint_object(
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libc.src.__support.macros.properties.types
41134113
)
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add_entrypoint_object(
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acospif16
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SRCS
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acospif16.cpp
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HDRS
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../acospif16.h
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DEPENDS
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libc.hdr.errno_macros
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libc.hdr.fenv_macros
4124+
libc.src.__support.FPUtil.cast
4125+
libc.src.__support.FPUtil.fenv_impl
4126+
libc.src.__support.FPUtil.fp_bits
4127+
libc.src.__support.FPUtil.multiply_add
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libc.src.__support.FPUtil.polyeval
4129+
libc.src.__support.FPUtil.sqrt
4130+
libc.src.__support.macros.optimization
4131+
libc.src.__support.macros.properties.types
4132+
)
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41154134
add_header_library(
41164135
atan_utils
41174136
HDRS

‎libc/src/math/generic/acospif16.cpp‎

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//===-- Half-precision acospi 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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#include "src/math/acospif16.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/multiply_add.h"
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#include "src/__support/FPUtil/sqrt.h"
18+
#include "src/__support/macros/optimization.h"
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namespace LIBC_NAMESPACE_DECL {
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LLVM_LIBC_FUNCTION(float16, acospif16, (float16 x)) {
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using FPBits = fputil::FPBits<float16>;
24+
FPBits xbits(x);
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uint16_t x_u = xbits.uintval();
27+
uint16_t x_abs = x_u & 0x7fff;
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uint16_t x_sign = x_u >> 15;
29+
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// |x| > 0x1p0, |x| > 1, or x is NaN.
31+
if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
32+
// acospif16(NaN) = NaN
33+
if (xbits.is_nan()) {
34+
if (xbits.is_signaling_nan()) {
35+
fputil::raise_except_if_required(FE_INVALID);
36+
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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// |x| == 0x1p0, x is 1 or -1
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// if x is (-)1, return 1
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// if x is (+)1, return 0
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if (LIBC_UNLIKELY(x_abs == 0x3c00))
53+
return fputil::cast<float16>(x_sign ? 1.0f : 0.0f);
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float xf = x;
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float xsq = xf * xf;
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// Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya
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// with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0,
60+
// 0.5]);
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constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f,
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0x1.897e36p-6f, 0x1.9efafcp-7f,
63+
0x1.06d884p-6f};
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// |x| <= 0x1p-1, |x| <= 0.5
65+
if (x_abs <= 0x3800) {
66+
// if x is 0, return 0.5
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if (LIBC_UNLIKELY(x_abs == 0))
68+
return fputil::cast<float16>(0.5f);
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// Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x), then
71+
// acospi(x) = 0.5 - asin(x)/pi
72+
float interm =
73+
fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2],
74+
POLY_COEFFS[3], POLY_COEFFS[4]);
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return fputil::cast<float16>(fputil::multiply_add(-xf, interm, 0.5f));
77+
}
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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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// acospi(x) = 2 * (asin(sqrt(u)) / pi)
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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
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// 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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// acospi(x) = 1 - acos(-x)/pi
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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);
122+
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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125+
float asin_sqrt_u =
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sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1],
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POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]);
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// Same as acos(x), but devided the expression with pi
130+
return fputil::cast<float16>(
131+
x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f)
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: 2.0f * 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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@@ -2269,6 +2269,17 @@ add_fp_unittest(
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libc.src.math.acosf16
22702270
)
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add_fp_unittest(
2273+
acospif16_test
2274+
NEED_MPFR
2275+
SUITE
2276+
libc-math-unittests
2277+
SRCS
2278+
acospif16_test.cpp
2279+
DEPENDS
2280+
libc.src.math.acospif16
2281+
)
2282+
22722283
add_fp_unittest(
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atanf_test
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NEED_MPFR

‎libc/test/src/math/acospif16_test.cpp‎

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//===-- Exhaustive test for acospif16 -------------------------------------===//
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//
3+
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4+
// See https://llvm.org/LICENSE.txt for license information.
5+
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6+
//
7+
//===----------------------------------------------------------------------===//
8+
9+
#include "src/math/acospif16.h"
10+
#include "test/UnitTest/FPMatcher.h"
11+
#include "test/UnitTest/Test.h"
12+
#include "utils/MPFRWrapper/MPFRUtils.h"
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using LlvmLibcAcospif16Test = 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(LlvmLibcAcospif16Test, PositiveRange) {
27+
for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
28+
float16 x = FPBits(v).get_val();
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30+
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acospi, x,
31+
LIBC_NAMESPACE::acospif16(x), 0.5);
32+
}
33+
}
34+
35+
TEST_F(LlvmLibcAcospif16Test, NegativeRange) {
36+
for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
37+
float16 x = FPBits(v).get_val();
38+
39+
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acospi, x,
40+
LIBC_NAMESPACE::acospif16(x), 0.5);
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}
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}

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

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@@ -4040,6 +4040,17 @@ add_fp_unittest(
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libc.src.math.acosf16
40414041
)
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4043+
add_fp_unittest(
4044+
acospif16_test
4045+
SUITE
4046+
libc-math-smoke-tests
4047+
SRCS
4048+
acospif16_test.cpp
4049+
DEPENDS
4050+
libc.src.errno.errno
4051+
libc.src.math.acospif16
4052+
)
4053+
40434054
add_fp_unittest(
40444055
atanf_test
40454056
SUITE

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