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
23 static inline float
eval_poly(float m)24 eval_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
43 static inline float
log1pf_inline(float x)44 log1pf_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. */
61 float
atanhf(float x)62 atanhf (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
82 PL_SIG (S, F, 1, atanh, -1.0, 1.0)
83 PL_TEST_ULP (atanhf, 2.59)
84 PL_TEST_SYM_INTERVAL (atanhf, 0, 0x1p-12, 500)
85 PL_TEST_SYM_INTERVAL (atanhf, 0x1p-12, 1, 200000)
86 PL_TEST_SYM_INTERVAL (atanhf, 1, inf, 1000)
87