1//===-- Half-precision asinh(x) function ----------------------------------===//
2//
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/asinhf16.h"
10#include "explogxf.h"
11#include "hdr/fenv_macros.h"
12#include "src/__support/FPUtil/FEnvImpl.h"
13#include "src/__support/FPUtil/FPBits.h"
14#include "src/__support/FPUtil/PolyEval.h"
15#include "src/__support/FPUtil/cast.h"
16#include "src/__support/FPUtil/except_value_utils.h"
17#include "src/__support/FPUtil/multiply_add.h"
18#include "src/__support/FPUtil/rounding_mode.h"
19#include "src/__support/FPUtil/sqrt.h"
20#include "src/__support/common.h"
21#include "src/__support/macros/config.h"
22#include "src/__support/macros/optimization.h"
23
24namespace LIBC_NAMESPACE_DECL {
25
26#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
27static constexpr size_t N_EXCEPTS = 8;
28
29static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ASINHF16_EXCEPTS{{
30 // (input, RZ output, RU offset, RD offset, RN offset)
31
32 // x = 0x1.da4p-2, asinhf16(x) = 0x1.ca8p-2 (RZ)
33 {0x3769, 0x372a, 1, 0, 1},
34 // x = 0x1.d6cp-1, asinhf16(x) = 0x1.a58p-1 (RZ)
35 {0x3b5b, 0x3a96, 1, 0, 0},
36 // x = 0x1.c7cp+3, asinhf16(x) = 0x1.accp+1 (RZ)
37 {0x4b1f, 0x42b3, 1, 0, 0},
38 // x = 0x1.26cp+4, asinhf16(x) = 0x1.cd8p+1 (RZ)
39 {0x4c9b, 0x4336, 1, 0, 1},
40 // x = -0x1.da4p-2, asinhf16(x) = -0x1.ca8p-2 (RZ)
41 {0xb769, 0xb72a, 0, 1, 1},
42 // x = -0x1.d6cp-1, asinhf16(x) = -0x1.a58p-1 (RZ)
43 {0xbb5b, 0xba96, 0, 1, 0},
44 // x = -0x1.c7cp+3, asinhf16(x) = -0x1.accp+1 (RZ)
45 {0xcb1f, 0xc2b3, 0, 1, 0},
46 // x = -0x1.26cp+4, asinhf16(x) = -0x1.cd8p+1 (RZ)
47 {0xcc9b, 0xc336, 0, 1, 1},
48}};
49#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
50
51LLVM_LIBC_FUNCTION(float16, asinhf16, (float16 x)) {
52 using FPBits = fputil::FPBits<float16>;
53 FPBits xbits(x);
54
55 uint16_t x_u = xbits.uintval();
56 uint16_t x_abs = x_u & 0x7fff;
57
58 if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {
59 if (xbits.is_signaling_nan()) {
60 fputil::raise_except_if_required(FE_INVALID);
61 return FPBits::quiet_nan().get_val();
62 }
63
64 return x;
65 }
66
67#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
68 // Handle exceptional values
69 if (auto r = ASINHF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
70 return r.value();
71#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
72
73 float xf = x;
74 const float SIGN[2] = {1.0f, -1.0f};
75 float x_sign = SIGN[x_u >> 15];
76
77 // |x| <= 0.25
78 if (LIBC_UNLIKELY(x_abs <= 0x3400)) {
79 // when |x| < 0x1.718p-5, asinhf16(x) = x. Adjust by 1 ULP for certain
80 // rounding types.
81 if (LIBC_UNLIKELY(x_abs < 0x29c6)) {
82 int rounding = fputil::quick_get_round();
83 if ((rounding == FE_UPWARD || rounding == FE_TOWARDZERO) && xf < 0)
84 return fputil::cast<float16>(xf + 0x1p-24f);
85 if ((rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) && xf > 0)
86 return fputil::cast<float16>(xf - 0x1p-24f);
87 return fputil::cast<float16>(xf);
88 }
89
90 float x_sq = xf * xf;
91 // Generated by Sollya with:
92 // > P = fpminimax(asinh(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 2^-2]);
93 // The last coefficient 0x1.bd114ep-6f has been changed to 0x1.bd114ep-5f
94 // for better accuracy.
95 float p = fputil::polyeval(x_sq, 1.0f, -0x1.555552p-3f, 0x1.332f6ap-4f,
96 -0x1.6c53dep-5f, 0x1.bd114ep-5f);
97
98 return fputil::cast<float16>(xf * p);
99 }
100
101 // General case: asinh(x) = ln(x + sqrt(x^2 + 1))
102 float sqrt_term = fputil::sqrt<float>(fputil::multiply_add(xf, xf, 1.0f));
103 return fputil::cast<float16>(
104 x_sign * log_eval(fputil::multiply_add(xf, x_sign, sqrt_term)));
105}
106
107} // namespace LIBC_NAMESPACE_DECL
108

source code of libc/src/math/generic/asinhf16.cpp