1*412f47f9SXin Li /*
2*412f47f9SXin Li * Single-precision atanh(x) function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2022-2023, Arm Limited.
5*412f47f9SXin Li * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*412f47f9SXin Li */
7*412f47f9SXin Li
8*412f47f9SXin Li #include "math_config.h"
9*412f47f9SXin Li #include "mathlib.h"
10*412f47f9SXin Li #include "pl_sig.h"
11*412f47f9SXin Li #include "pl_test.h"
12*412f47f9SXin Li
13*412f47f9SXin Li #define AbsMask 0x7fffffff
14*412f47f9SXin Li #define Half 0x3f000000
15*412f47f9SXin Li #define One 0x3f800000
16*412f47f9SXin Li #define Four 0x40800000
17*412f47f9SXin Li #define Ln2 0x1.62e43p-1f
18*412f47f9SXin Li /* asuint(0x1p-12), below which atanhf(x) rounds to x. */
19*412f47f9SXin Li #define TinyBound 0x39800000
20*412f47f9SXin Li
21*412f47f9SXin Li #define C(i) __log1pf_data.coeffs[i]
22*412f47f9SXin Li
23*412f47f9SXin Li static inline float
eval_poly(float m)24*412f47f9SXin Li eval_poly (float m)
25*412f47f9SXin Li {
26*412f47f9SXin Li /* Approximate log(1+m) on [-0.25, 0.5] using Estrin scheme. */
27*412f47f9SXin Li float p_12 = fmaf (m, C (1), C (0));
28*412f47f9SXin Li float p_34 = fmaf (m, C (3), C (2));
29*412f47f9SXin Li float p_56 = fmaf (m, C (5), C (4));
30*412f47f9SXin Li float p_78 = fmaf (m, C (7), C (6));
31*412f47f9SXin Li
32*412f47f9SXin Li float m2 = m * m;
33*412f47f9SXin Li float p_02 = fmaf (m2, p_12, m);
34*412f47f9SXin Li float p_36 = fmaf (m2, p_56, p_34);
35*412f47f9SXin Li float p_79 = fmaf (m2, C (8), p_78);
36*412f47f9SXin Li
37*412f47f9SXin Li float m4 = m2 * m2;
38*412f47f9SXin Li float p_06 = fmaf (m4, p_36, p_02);
39*412f47f9SXin Li
40*412f47f9SXin Li return fmaf (m4 * p_79, m4, p_06);
41*412f47f9SXin Li }
42*412f47f9SXin Li
43*412f47f9SXin Li static inline float
log1pf_inline(float x)44*412f47f9SXin Li log1pf_inline (float x)
45*412f47f9SXin Li {
46*412f47f9SXin Li /* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no
47*412f47f9SXin Li special-case handling. See that file for details of the algorithm. */
48*412f47f9SXin Li float m = x + 1.0f;
49*412f47f9SXin Li int k = (asuint (m) - 0x3f400000) & 0xff800000;
50*412f47f9SXin Li float s = asfloat (Four - k);
51*412f47f9SXin Li float m_scale = asfloat (asuint (x) - k) + fmaf (0.25f, s, -1.0f);
52*412f47f9SXin Li float p = eval_poly (m_scale);
53*412f47f9SXin Li float scale_back = (float) k * 0x1.0p-23f;
54*412f47f9SXin Li return fmaf (scale_back, Ln2, p);
55*412f47f9SXin Li }
56*412f47f9SXin Li
57*412f47f9SXin Li /* Approximation for single-precision inverse tanh(x), using a simplified
58*412f47f9SXin Li version of log1p. Maximum error is 3.08 ULP:
59*412f47f9SXin Li atanhf(0x1.ff0d5p-5) got 0x1.ffb768p-5
60*412f47f9SXin Li want 0x1.ffb76ep-5. */
61*412f47f9SXin Li float
atanhf(float x)62*412f47f9SXin Li atanhf (float x)
63*412f47f9SXin Li {
64*412f47f9SXin Li uint32_t ix = asuint (x);
65*412f47f9SXin Li uint32_t iax = ix & AbsMask;
66*412f47f9SXin Li uint32_t sign = ix & ~AbsMask;
67*412f47f9SXin Li
68*412f47f9SXin Li if (unlikely (iax < TinyBound))
69*412f47f9SXin Li return x;
70*412f47f9SXin Li
71*412f47f9SXin Li if (iax == One)
72*412f47f9SXin Li return __math_divzero (sign);
73*412f47f9SXin Li
74*412f47f9SXin Li if (unlikely (iax > One))
75*412f47f9SXin Li return __math_invalidf (x);
76*412f47f9SXin Li
77*412f47f9SXin Li float halfsign = asfloat (Half | sign);
78*412f47f9SXin Li float ax = asfloat (iax);
79*412f47f9SXin Li return halfsign * log1pf_inline ((2 * ax) / (1 - ax));
80*412f47f9SXin Li }
81*412f47f9SXin Li
82*412f47f9SXin Li PL_SIG (S, F, 1, atanh, -1.0, 1.0)
83*412f47f9SXin Li PL_TEST_ULP (atanhf, 2.59)
84*412f47f9SXin Li PL_TEST_SYM_INTERVAL (atanhf, 0, 0x1p-12, 500)
85*412f47f9SXin Li PL_TEST_SYM_INTERVAL (atanhf, 0x1p-12, 1, 200000)
86*412f47f9SXin Li PL_TEST_SYM_INTERVAL (atanhf, 1, inf, 1000)
87