1//===-- Single-precision asinh 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/asinhf.h"
10#include "src/__support/FPUtil/FPBits.h"
11#include "src/__support/FPUtil/PolyEval.h"
12#include "src/__support/FPUtil/multiply_add.h"
13#include "src/__support/FPUtil/sqrt.h"
14#include "src/__support/macros/config.h"
15#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
16#include "src/math/generic/common_constants.h"
17#include "src/math/generic/explogxf.h"
18
19namespace LIBC_NAMESPACE_DECL {
20
21LLVM_LIBC_FUNCTION(float, asinhf, (float x)) {
22 using FPBits_t = typename fputil::FPBits<float>;
23 FPBits_t xbits(x);
24 uint32_t x_u = xbits.uintval();
25 uint32_t x_abs = xbits.abs().uintval();
26
27 // |x| <= 2^-3
28 if (LIBC_UNLIKELY(x_abs <= 0x3e80'0000U)) {
29 // |x| <= 2^-26
30 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
31 return static_cast<float>(LIBC_UNLIKELY(x_abs == 0)
32 ? x
33 : (x - 0x1.5555555555555p-3 * x * x * x));
34 }
35
36 double x_d = x;
37 double x_sq = x_d * x_d;
38 // Generated by Sollya with:
39 // > P = fpminimax(asinh(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16|], [|D...|],
40 // [0, 2^-2]);
41 double p = fputil::polyeval(
42 x_sq, 0.0, -0x1.555555555551ep-3, 0x1.3333333325495p-4,
43 -0x1.6db6db5a7622bp-5, 0x1.f1c70f82928c6p-6, -0x1.6e893934266b7p-6,
44 0x1.1c0b41d3fbe78p-6, -0x1.c0f47810b3c4fp-7, 0x1.2c8602690143dp-7);
45 return static_cast<float>(fputil::multiply_add(x_d, p, x_d));
46 }
47
48 const double SIGN[2] = {1.0, -1.0};
49 double x_sign = SIGN[x_u >> 31];
50 double x_d = x;
51
52#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
53 // Helper functions to set results for exceptional cases.
54 auto round_result_slightly_down = [x_sign](float r) -> float {
55 return fputil::multiply_add(static_cast<float>(x_sign), r,
56 static_cast<float>(x_sign) * (-0x1.0p-24f));
57 };
58 auto round_result_slightly_up = [x_sign](float r) -> float {
59 return fputil::multiply_add(static_cast<float>(x_sign), r,
60 static_cast<float>(x_sign) * 0x1.0p-24f);
61 };
62
63 if (LIBC_UNLIKELY(x_abs >= 0x4bdd'65a5U)) {
64 if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {
65 if (xbits.is_signaling_nan()) {
66 fputil::raise_except_if_required(FE_INVALID);
67 return FPBits_t::quiet_nan().get_val();
68 }
69
70 return x;
71 }
72
73 // Exceptional cases when x > 2^24.
74 switch (x_abs) {
75 case 0x4bdd65a5: // |x| = 0x1.bacb4ap24f
76 return round_result_slightly_down(0x1.1e0696p4f);
77 case 0x4c803f2c: // |x| = 0x1.007e58p26f
78 return round_result_slightly_down(0x1.2b786cp4f);
79 case 0x4f8ffb03: // |x| = 0x1.1ff606p32f
80 return round_result_slightly_up(0x1.6fdd34p4f);
81 case 0x5c569e88: // |x| = 0x1.ad3d1p57f
82 return round_result_slightly_up(0x1.45c146p5f);
83 case 0x5e68984e: // |x| = 0x1.d1309cp61f
84 return round_result_slightly_up(0x1.5c9442p5f);
85 case 0x655890d3: // |x| = 0x1.b121a6p75f
86 return round_result_slightly_down(0x1.a9a3f2p5f);
87 case 0x65de7ca6: // |x| = 0x1.bcf94cp76f
88 return round_result_slightly_up(0x1.af66cp5f);
89 case 0x6eb1a8ec: // |x| = 0x1.6351d8p94f
90 return round_result_slightly_down(0x1.08b512p6f);
91 case 0x7997f30a: // |x| = 0x1.2fe614p116f
92 return round_result_slightly_up(0x1.451436p6f);
93 }
94 } else {
95 // Exceptional cases when x < 2^24.
96 if (LIBC_UNLIKELY(x_abs == 0x45abaf26)) {
97 // |x| = 0x1.575e4cp12f
98 return round_result_slightly_down(0x1.29becap3f);
99 }
100 if (LIBC_UNLIKELY(x_abs == 0x49d29048)) {
101 // |x| = 0x1.a5209p20f
102 return round_result_slightly_down(0x1.e1b92p3f);
103 }
104 }
105#else
106 if (LIBC_UNLIKELY(xbits.is_inf_or_nan()))
107 return x;
108#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
109
110 // asinh(x) = log(x + sqrt(x^2 + 1))
111 return static_cast<float>(
112 x_sign * log_eval(fputil::multiply_add(
113 x_d, x_sign,
114 fputil::sqrt<double>(fputil::multiply_add(x_d, x_d, 1.0)))));
115}
116
117} // namespace LIBC_NAMESPACE_DECL
118

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