1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision atanh(x) function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited.
5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*f3087befSAndrew Turner */
7*f3087befSAndrew Turner
8*f3087befSAndrew Turner #include "math_config.h"
9*f3087befSAndrew Turner #include "mathlib.h"
10*f3087befSAndrew Turner #include "test_sig.h"
11*f3087befSAndrew Turner #include "test_defs.h"
12*f3087befSAndrew Turner
13*f3087befSAndrew Turner #define AbsMask 0x7fffffff
14*f3087befSAndrew Turner #define Half 0x3f000000
15*f3087befSAndrew Turner #define One 0x3f800000
16*f3087befSAndrew Turner #define Four 0x40800000
17*f3087befSAndrew Turner #define Ln2 0x1.62e43p-1f
18*f3087befSAndrew Turner /* asuint(0x1p-12), below which atanhf(x) rounds to x. */
19*f3087befSAndrew Turner #define TinyBound 0x39800000
20*f3087befSAndrew Turner
21*f3087befSAndrew Turner #define C(i) __log1pf_data.coeffs[i]
22*f3087befSAndrew Turner
23*f3087befSAndrew Turner static inline float
eval_poly(float m)24*f3087befSAndrew Turner eval_poly (float m)
25*f3087befSAndrew Turner {
26*f3087befSAndrew Turner /* Approximate log(1+m) on [-0.25, 0.5] using Estrin scheme. */
27*f3087befSAndrew Turner float p_12 = fmaf (m, C (1), C (0));
28*f3087befSAndrew Turner float p_34 = fmaf (m, C (3), C (2));
29*f3087befSAndrew Turner float p_56 = fmaf (m, C (5), C (4));
30*f3087befSAndrew Turner float p_78 = fmaf (m, C (7), C (6));
31*f3087befSAndrew Turner
32*f3087befSAndrew Turner float m2 = m * m;
33*f3087befSAndrew Turner float p_02 = fmaf (m2, p_12, m);
34*f3087befSAndrew Turner float p_36 = fmaf (m2, p_56, p_34);
35*f3087befSAndrew Turner float p_79 = fmaf (m2, C (8), p_78);
36*f3087befSAndrew Turner
37*f3087befSAndrew Turner float m4 = m2 * m2;
38*f3087befSAndrew Turner float p_06 = fmaf (m4, p_36, p_02);
39*f3087befSAndrew Turner
40*f3087befSAndrew Turner return fmaf (m4 * p_79, m4, p_06);
41*f3087befSAndrew Turner }
42*f3087befSAndrew Turner
43*f3087befSAndrew Turner static inline float
log1pf_inline(float x)44*f3087befSAndrew Turner log1pf_inline (float x)
45*f3087befSAndrew Turner {
46*f3087befSAndrew Turner /* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no
47*f3087befSAndrew Turner special-case handling. See that file for details of the algorithm. */
48*f3087befSAndrew Turner float m = x + 1.0f;
49*f3087befSAndrew Turner int k = (asuint (m) - 0x3f400000) & 0xff800000;
50*f3087befSAndrew Turner float s = asfloat (Four - k);
51*f3087befSAndrew Turner float m_scale = asfloat (asuint (x) - k) + fmaf (0.25f, s, -1.0f);
52*f3087befSAndrew Turner float p = eval_poly (m_scale);
53*f3087befSAndrew Turner float scale_back = (float) k * 0x1.0p-23f;
54*f3087befSAndrew Turner return fmaf (scale_back, Ln2, p);
55*f3087befSAndrew Turner }
56*f3087befSAndrew Turner
57*f3087befSAndrew Turner /* Approximation for single-precision inverse tanh(x), using a simplified
58*f3087befSAndrew Turner version of log1p. Maximum error is 3.08 ULP:
59*f3087befSAndrew Turner atanhf(0x1.ff0d5p-5) got 0x1.ffb768p-5
60*f3087befSAndrew Turner want 0x1.ffb76ep-5. */
61*f3087befSAndrew Turner float
atanhf(float x)62*f3087befSAndrew Turner atanhf (float x)
63*f3087befSAndrew Turner {
64*f3087befSAndrew Turner uint32_t ix = asuint (x);
65*f3087befSAndrew Turner uint32_t iax = ix & AbsMask;
66*f3087befSAndrew Turner uint32_t sign = ix & ~AbsMask;
67*f3087befSAndrew Turner
68*f3087befSAndrew Turner if (unlikely (iax < TinyBound))
69*f3087befSAndrew Turner return x;
70*f3087befSAndrew Turner
71*f3087befSAndrew Turner if (iax == One)
72*f3087befSAndrew Turner return __math_divzero (sign);
73*f3087befSAndrew Turner
74*f3087befSAndrew Turner if (unlikely (iax > One))
75*f3087befSAndrew Turner return __math_invalidf (x);
76*f3087befSAndrew Turner
77*f3087befSAndrew Turner float halfsign = asfloat (Half | sign);
78*f3087befSAndrew Turner float ax = asfloat (iax);
79*f3087befSAndrew Turner return halfsign * log1pf_inline ((2 * ax) / (1 - ax));
80*f3087befSAndrew Turner }
81*f3087befSAndrew Turner
82*f3087befSAndrew Turner TEST_SIG (S, F, 1, atanh, -1.0, 1.0)
83*f3087befSAndrew Turner TEST_ULP (atanhf, 2.59)
84*f3087befSAndrew Turner TEST_SYM_INTERVAL (atanhf, 0, 0x1p-12, 500)
85*f3087befSAndrew Turner TEST_SYM_INTERVAL (atanhf, 0x1p-12, 1, 200000)
86*f3087befSAndrew Turner TEST_SYM_INTERVAL (atanhf, 1, inf, 1000)
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