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Add asinf16() function
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+272
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11 files changed

+272
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‎libc/config/linux/x86_64/entrypoints.txt‎

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@@ -642,6 +642,7 @@ endif()
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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.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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@@ -256,7 +256,7 @@ Higher Math Functions
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| acospi | | | | | | 7.12.4.8 | F.10.1.8 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| asin | |check| | | | | | 7.12.4.2 | F.10.1.2 |
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| asin | |check| | | | |check| | | 7.12.4.2 | F.10.1.2 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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| asinh | |check| | | | | | 7.12.5.2 | F.10.2.2 |
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+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

‎libc/include/math.yaml‎

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@@ -32,6 +32,13 @@ functions:
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return_type: float
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arguments:
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- type: float
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- name: asinf16
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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: asinhf
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standards:
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- stdc

‎libc/src/math/CMakeLists.txt‎

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@@ -49,6 +49,7 @@ add_math_entrypoint_object(asin)
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add_math_entrypoint_object(asinf)
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add_math_entrypoint_object(asinh)
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add_math_entrypoint_object(asinhf)
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add_math_entrypoint_object(asinf16)
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add_math_entrypoint_object(atan)
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add_math_entrypoint_object(atanf)

‎libc/src/math/asinf16.h‎

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@@ -0,0 +1,21 @@
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//===-- Implementation header for asinf16 -----------------------*- 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_ASINF16_H
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#define LLVM_LIBC_SRC_MATH_ASINF16_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 asinf16(float16 x);
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LLVM_LIBC_SRC_MATH_ASINF16_H

‎libc/src/math/generic/CMakeLists.txt‎

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@@ -4598,6 +4598,25 @@ add_entrypoint_object(
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${libc_opt_high_flag}
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)
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add_entrypoint_object(
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asinf16
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SRCS
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asinf16.cpp
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HDRS
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../asinf16.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
4611+
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
4614+
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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acosf
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SRCS

‎libc/src/math/generic/asinf16.cpp‎

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//===-- Half-precision asinf16(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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#include "src/math/asinf16.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/cast.h"
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#include "src/__support/FPUtil/multiply_add.h"
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#include "src/__support/FPUtil/PolyEval.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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// Generated by Sollya using the following command:
23+
// > round(pi/2, D, RN);
24+
static constexpr float PI_2 = 0x1.921fb54442d18p0f;
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LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) {
27+
using FPBits = fputil::FPBits<float16>;
28+
FPBits xbits(x);
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uint16_t x_u = xbits.uintval();
31+
uint16_t x_abs = x_u & 0x7fff;
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float xf = x;
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float xsq = xf * xf;
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// |x| <= 0x1p-1, |x| <= 0.5
37+
if (x_abs <= 0x3800) {
38+
if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) {
39+
// asinf16(+/-0) = +/-0
40+
if (LIBC_UNLIKELY(x_abs == 0U)) {
41+
return x;
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}
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// Exhaustive tests show that, when:
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// x > 0, and rounding upward, then,
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// asin(x) = x * 2^-11 + x
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// else, in other rounding modes,
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// asin(x) = x
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int rounding = fputil::quick_get_round();
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if ((xbits.is_pos() && rounding == FE_UPWARD) ||
52+
(xbits.is_neg() && rounding == FE_DOWNWARD)) {
53+
return fputil::cast<float16>(fputil::multiply_add(xf, 0x1.0p-11f, xf));
54+
}
55+
return x;
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}
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// Degree-6 minimax odd polynomial of asin(x) generated by Sollya with:
59+
// > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
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float result = fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
61+
return fputil::cast<float16>(xf * result);
62+
}
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64+
// |x| > 1, asinf16(x) = NaN
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if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
66+
// |x| <= +/-inf
67+
if (LIBC_UNLIKELY(x_abs <= 0x7c00)) {
68+
fputil::set_errno_if_required(EDOM);
69+
fputil::raise_except_if_required(FE_INVALID);
70+
}
71+
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return FPBits::quiet_nan().get_val();
73+
}
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// When |x| > 0.5, assume that 0.5 < |x| <= 1,
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//
77+
// Step-by-step range-reduction proof:
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// 1: Let y = asin(x), such that, x = sin(y)
79+
// 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 - 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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// arcsin(sqrt(u)) = z/2
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// 2 * arcsin(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 * arcsin(sqrt(u))
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// 10: Recall [1], y = asin(x). Therefore:
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// arcsin(x) = pi/2 - 2 * arcsin(sqrt(u))
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//
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// WHY?
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// 11: Recall [7], u = (1 - x)/2
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// 12: 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 Step [10]
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// as `sqrt(u)` is in range.
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// 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0
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float xf_abs = (xf < 0 ? -xf : xf);
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float sign = ((xbits.uintval() >> 15) == 1 ? -1.0 : 1.0);
110+
float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
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float u_sqrt = fputil::sqrt<float>(u);
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// Degree-6 minimax odd polynomial of asin(x) generated by Sollya with:
114+
// > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
115+
float asin_sqrt_u = u_sqrt * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
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return fputil::cast<float16>(sign * fputil::multiply_add(-2.0f, asin_sqrt_u, PI_2));
118+
}
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120+
}

‎libc/test/src/math/CMakeLists.txt‎

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@@ -2186,6 +2186,17 @@ add_fp_unittest(
21862186
libc.src.__support.FPUtil.fp_bits
21872187
)
21882188

2189+
add_fp_unittest(
2190+
asinf16_test
2191+
NEED_MPFR
2192+
SUITE
2193+
libc-math-unittests
2194+
SRCS
2195+
asinf16_test.cpp
2196+
DEPENDS
2197+
libc.src.math.asinf16
2198+
)
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21892200
add_fp_unittest(
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acosf_test
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NEED_MPFR

‎libc/test/src/math/asinf16_test.cpp‎

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//===-- Exhaustive test for asinf16 ---------------------------------------===//
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//
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// 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/asinf16.h"
10+
#include "test/UnitTest/FPMatcher.h"
11+
#include "test/UnitTest/Test.h"
12+
#include "utils/MPFRWrapper/MPFRUtils.h"
13+
14+
using LlvmLibcAsinf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
15+
16+
namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
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18+
// Range: [0, Inf]
19+
static constexpr uint16_t POS_START = 0x0000U;
20+
static constexpr uint16_t POS_STOP = 0x7c00U;
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22+
// Range: [-Inf, 0]
23+
static constexpr uint16_t NEG_START = 0x8000U;
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static constexpr uint16_t NEG_STOP = 0xfc00U;
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TEST_F(LlvmLibcAsinf16Test, 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::Asin, x, LIBC_NAMESPACE::asinf16(x), 0.5);
31+
}
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}
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TEST_F(LlvmLibcAsinf16Test, NegativeRange) {
35+
for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
36+
float16 x = FPBits(v).get_val();
37+
38+
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Asin, x, LIBC_NAMESPACE::asinf16(x), 0.5);
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}
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}

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

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@@ -3954,6 +3954,17 @@ add_fp_unittest(
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libc.src.__support.FPUtil.fp_bits
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)
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3957+
add_fp_unittest(
3958+
asinf16_test
3959+
SUITE
3960+
libc-math-smoke-tests
3961+
SRCS
3962+
asinf16_test.cpp
3963+
DEPENDS
3964+
libc.src.errno.errno
3965+
libc.src.math.asinf16
3966+
)
3967+
39573968
add_fp_unittest(
39583969
acosf_test
39593970
SUITE

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