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 #define TinyBound 0x39800000 /* 0x1p-12, below which atanhf(x) rounds to x. */
19
20 #define C(i) __log1pf_data.coeffs[i]
21
22 static inline float
eval_poly(float m)23 eval_poly (float m)
24 {
25 /* Approximate log(1+m) on [-0.25, 0.5] using Estrin scheme. */
26 float p_12 = fmaf (m, C (1), C (0));
27 float p_34 = fmaf (m, C (3), C (2));
28 float p_56 = fmaf (m, C (5), C (4));
29 float p_78 = fmaf (m, C (7), C (6));
30
31 float m2 = m * m;
32 float p_02 = fmaf (m2, p_12, m);
33 float p_36 = fmaf (m2, p_56, p_34);
34 float p_79 = fmaf (m2, C (8), p_78);
35
36 float m4 = m2 * m2;
37 float p_06 = fmaf (m4, p_36, p_02);
38
39 return fmaf (m4 * p_79, m4, p_06);
40 }
41
42 static inline float
log1pf_inline(float x)43 log1pf_inline (float x)
44 {
45 /* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no
46 special-case handling. See that file for details of the algorithm. */
47 float m = x + 1.0f;
48 int k = (asuint (m) - 0x3f400000) & 0xff800000;
49 float s = asfloat (Four - k);
50 float m_scale = asfloat (asuint (x) - k) + fmaf (0.25f, s, -1.0f);
51 float p = eval_poly (m_scale);
52 float scale_back = (float) k * 0x1.0p-23f;
53 return fmaf (scale_back, Ln2, p);
54 }
55
56 /* Approximation for single-precision inverse tanh(x), using a simplified
57 version of log1p. Maximum error is 3.08 ULP:
58 atanhf(0x1.ff0d5p-5) got 0x1.ffb768p-5
59 want 0x1.ffb76ep-5. */
60 float
atanhf(float x)61 atanhf (float x)
62 {
63 uint32_t ix = asuint (x);
64 uint32_t iax = ix & AbsMask;
65 uint32_t sign = ix & ~AbsMask;
66
67 if (unlikely (iax < TinyBound))
68 return x;
69
70 if (iax == One)
71 return __math_divzero (sign);
72
73 if (unlikely (iax > One))
74 return __math_invalidf (x);
75
76 float halfsign = asfloat (Half | sign);
77 float ax = asfloat (iax);
78 return halfsign * log1pf_inline ((2 * ax) / (1 - ax));
79 }
80
81 PL_SIG (S, F, 1, atanh, -1.0, 1.0)
82 PL_TEST_ULP (atanhf, 2.59)
83 PL_TEST_INTERVAL (atanhf, 0, 0x1p-12, 500)
84 PL_TEST_INTERVAL (atanhf, 0x1p-12, 1, 200000)
85 PL_TEST_INTERVAL (atanhf, 1, inf, 1000)
86 PL_TEST_INTERVAL (atanhf, -0, -0x1p-12, 500)
87 PL_TEST_INTERVAL (atanhf, -0x1p-12, -1, 200000)
88 PL_TEST_INTERVAL (atanhf, -1, -inf, 1000)
89