1//===-- Half-precision atanh(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/atanhf16.h"
10#include "explogxf.h"
11#include "hdr/errno_macros.h"
12#include "hdr/fenv_macros.h"
13#include "src/__support/FPUtil/FEnvImpl.h"
14#include "src/__support/FPUtil/FPBits.h"
15#include "src/__support/FPUtil/PolyEval.h"
16#include "src/__support/FPUtil/cast.h"
17#include "src/__support/FPUtil/except_value_utils.h"
18#include "src/__support/FPUtil/multiply_add.h"
19#include "src/__support/common.h"
20#include "src/__support/macros/config.h"
21#include "src/__support/macros/optimization.h"
22
23namespace LIBC_NAMESPACE_DECL {
24
25static constexpr size_t N_EXCEPTS = 1;
26static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ATANHF16_EXCEPTS{{
27 // (input, RZ output, RU offset, RD offset, RN offset)
28 // x = 0x1.a5cp-4, atanhf16(x) = 0x1.a74p-4 (RZ)
29 {0x2E97, 0x2E9D, 1, 0, 0},
30}};
31
32LLVM_LIBC_FUNCTION(float16, atanhf16, (float16 x)) {
33 using FPBits = fputil::FPBits<float16>;
34
35 FPBits xbits(x);
36 Sign sign = xbits.sign();
37 uint16_t x_abs = xbits.abs().uintval();
38
39 // |x| >= 1
40 if (LIBC_UNLIKELY(x_abs >= 0x3c00U)) {
41 if (xbits.is_nan()) {
42 if (xbits.is_signaling_nan()) {
43 fputil::raise_except_if_required(FE_INVALID);
44 return FPBits::quiet_nan().get_val();
45 }
46 return x;
47 }
48
49 // |x| == 1.0
50 if (x_abs == 0x3c00U) {
51 fputil::set_errno_if_required(ERANGE);
52 fputil::raise_except_if_required(FE_DIVBYZERO);
53 return FPBits::inf(sign).get_val();
54 }
55 // |x| > 1.0
56 fputil::set_errno_if_required(EDOM);
57 fputil::raise_except_if_required(FE_INVALID);
58 return FPBits::quiet_nan().get_val();
59 }
60
61 if (auto r = ATANHF16_EXCEPTS.lookup(xbits.uintval());
62 LIBC_UNLIKELY(r.has_value()))
63 return r.value();
64
65 // For |x| less than approximately 0.24
66 if (LIBC_UNLIKELY(x_abs <= 0x33f3U)) {
67 // atanh(+/-0) = +/-0
68 if (LIBC_UNLIKELY(x_abs == 0U))
69 return x;
70 // The Taylor expansion of atanh(x) is:
71 // atanh(x) = x + x^3/3 + x^5/5 + x^7/7 + x^9/9 + x^11/11
72 // = x * [1 + x^2/3 + x^4/5 + x^6/7 + x^8/9 + x^10/11]
73 // When |x| < 2^-5 (0x0800U), this can be approximated by:
74 // atanh(x) ≈ x + (1/3)*x^3
75 if (LIBC_UNLIKELY(x_abs < 0x0800U)) {
76 float xf = x;
77 return fputil::cast<float16>(xf + 0x1.555556p-2f * xf * xf * xf);
78 }
79
80 // For 2^-5 <= |x| <= 0x1.fccp-3 (~0.24):
81 // Let t = x^2.
82 // Define P(t) ≈ (1/3)*t + (1/5)*t^2 + (1/7)*t^3 + (1/9)*t^4 + (1/11)*t^5.
83 // Coefficients (from Sollya, RN, hexadecimal):
84 // 1/3 = 0x1.555556p-2, 1/5 = 0x1.99999ap-3, 1/7 = 0x1.24924ap-3,
85 // 1/9 = 0x1.c71c72p-4, 1/11 = 0x1.745d18p-4
86 // Thus, atanh(x) ≈ x * (1 + P(x^2)).
87 float xf = x;
88 float x2 = xf * xf;
89 float pe = fputil::polyeval(x2, 0.0f, 0x1.555556p-2f, 0x1.99999ap-3f,
90 0x1.24924ap-3f, 0x1.c71c72p-4f, 0x1.745d18p-4f);
91 return fputil::cast<float16>(fputil::multiply_add(xf, pe, xf));
92 }
93
94 float xf = x;
95 return fputil::cast<float16>(0.5 * log_eval_f((xf + 1.0f) / (xf - 1.0f)));
96}
97
98} // namespace LIBC_NAMESPACE_DECL
99

source code of libc/src/math/generic/atanhf16.cpp