1/*
2 * Single-precision atanh(x) function.
3 *
4 * Copyright (c) 2022-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include "math_config.h"
9#include "mathlib.h"
10#include "pl_sig.h"
11#include "pl_test.h"
12
13#define AbsMask 0x7fffffff
14#define Half 0x3f000000
15#define One 0x3f800000
16#define Four 0x40800000
17#define Ln2 0x1.62e43p-1f
18/* asuint(0x1p-12), below which atanhf(x) rounds to x.  */
19#define TinyBound 0x39800000
20
21#define C(i) __log1pf_data.coeffs[i]
22
23static inline float
24eval_poly (float m)
25{
26  /* Approximate log(1+m) on [-0.25, 0.5] using Estrin scheme.  */
27  float p_12 = fmaf (m, C (1), C (0));
28  float p_34 = fmaf (m, C (3), C (2));
29  float p_56 = fmaf (m, C (5), C (4));
30  float p_78 = fmaf (m, C (7), C (6));
31
32  float m2 = m * m;
33  float p_02 = fmaf (m2, p_12, m);
34  float p_36 = fmaf (m2, p_56, p_34);
35  float p_79 = fmaf (m2, C (8), p_78);
36
37  float m4 = m2 * m2;
38  float p_06 = fmaf (m4, p_36, p_02);
39
40  return fmaf (m4 * p_79, m4, p_06);
41}
42
43static inline float
44log1pf_inline (float x)
45{
46  /* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no
47     special-case handling. See that file for details of the algorithm.  */
48  float m = x + 1.0f;
49  int k = (asuint (m) - 0x3f400000) & 0xff800000;
50  float s = asfloat (Four - k);
51  float m_scale = asfloat (asuint (x) - k) + fmaf (0.25f, s, -1.0f);
52  float p = eval_poly (m_scale);
53  float scale_back = (float) k * 0x1.0p-23f;
54  return fmaf (scale_back, Ln2, p);
55}
56
57/* Approximation for single-precision inverse tanh(x), using a simplified
58   version of log1p. Maximum error is 3.08 ULP:
59   atanhf(0x1.ff0d5p-5) got 0x1.ffb768p-5
60		       want 0x1.ffb76ep-5.  */
61float
62atanhf (float x)
63{
64  uint32_t ix = asuint (x);
65  uint32_t iax = ix & AbsMask;
66  uint32_t sign = ix & ~AbsMask;
67
68  if (unlikely (iax < TinyBound))
69    return x;
70
71  if (iax == One)
72    return __math_divzero (sign);
73
74  if (unlikely (iax > One))
75    return __math_invalidf (x);
76
77  float halfsign = asfloat (Half | sign);
78  float ax = asfloat (iax);
79  return halfsign * log1pf_inline ((2 * ax) / (1 - ax));
80}
81
82PL_SIG (S, F, 1, atanh, -1.0, 1.0)
83PL_TEST_ULP (atanhf, 2.59)
84PL_TEST_SYM_INTERVAL (atanhf, 0, 0x1p-12, 500)
85PL_TEST_SYM_INTERVAL (atanhf, 0x1p-12, 1, 200000)
86PL_TEST_SYM_INTERVAL (atanhf, 1, inf, 1000)
87