1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
|
//===-- Half-precision atanh(x) function ----------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/math/atanhf16.h"
#include "explogxf.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/cast.h"
#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
static constexpr size_t N_EXCEPTS = 1;
static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ATANHF16_EXCEPTS{{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.a5cp-4, atanhf16(x) = 0x1.a74p-4 (RZ)
{0x2E97, 0x2E9D, 1, 0, 0},
}};
LLVM_LIBC_FUNCTION(float16, atanhf16, (float16 x)) {
using FPBits = fputil::FPBits<float16>;
FPBits xbits(x);
Sign sign = xbits.sign();
uint16_t x_abs = xbits.abs().uintval();
// |x| >= 1
if (LIBC_UNLIKELY(x_abs >= 0x3c00U)) {
if (xbits.is_nan()) {
if (xbits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
return x;
}
// |x| == 1.0
if (x_abs == 0x3c00U) {
fputil::set_errno_if_required(ERANGE);
fputil::raise_except_if_required(FE_DIVBYZERO);
return FPBits::inf(sign).get_val();
}
// |x| > 1.0
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
if (auto r = ATANHF16_EXCEPTS.lookup(xbits.uintval());
LIBC_UNLIKELY(r.has_value()))
return r.value();
// For |x| less than approximately 0.24
if (LIBC_UNLIKELY(x_abs <= 0x33f3U)) {
// atanh(+/-0) = +/-0
if (LIBC_UNLIKELY(x_abs == 0U))
return x;
// The Taylor expansion of atanh(x) is:
// atanh(x) = x + x^3/3 + x^5/5 + x^7/7 + x^9/9 + x^11/11
// = x * [1 + x^2/3 + x^4/5 + x^6/7 + x^8/9 + x^10/11]
// When |x| < 2^-5 (0x0800U), this can be approximated by:
// atanh(x) ≈ x + (1/3)*x^3
if (LIBC_UNLIKELY(x_abs < 0x0800U)) {
float xf = x;
return fputil::cast<float16>(xf + 0x1.555556p-2f * xf * xf * xf);
}
// For 2^-5 <= |x| <= 0x1.fccp-3 (~0.24):
// Let t = x^2.
// Define P(t) ≈ (1/3)*t + (1/5)*t^2 + (1/7)*t^3 + (1/9)*t^4 + (1/11)*t^5.
// Coefficients (from Sollya, RN, hexadecimal):
// 1/3 = 0x1.555556p-2, 1/5 = 0x1.99999ap-3, 1/7 = 0x1.24924ap-3,
// 1/9 = 0x1.c71c72p-4, 1/11 = 0x1.745d18p-4
// Thus, atanh(x) ≈ x * (1 + P(x^2)).
float xf = x;
float x2 = xf * xf;
float pe = fputil::polyeval(x2, 0.0f, 0x1.555556p-2f, 0x1.99999ap-3f,
0x1.24924ap-3f, 0x1.c71c72p-4f, 0x1.745d18p-4f);
return fputil::cast<float16>(fputil::multiply_add(xf, pe, xf));
}
float xf = x;
return fputil::cast<float16>(0.5 * log_eval_f((xf + 1.0f) / (xf - 1.0f)));
}
} // namespace LIBC_NAMESPACE_DECL
|
