1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
|
/*
* Copyright (c) 2014 Advanced Micro Devices, Inc.
*
* Copyright (c) 2017 Michal Babej / Tampere University of Technology
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
_CL_OVERLOADABLE vtype tanh(vtype x)
{
// The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent
// to the following three formulae:
// 1. (exp(x) - exp(-x))/(exp(x) + exp(-x))
// 2. (1 - (2/(exp(2*x) + 1 )))
// 3. (exp(2*x) - 1)/(exp(2*x) + 1)
// but computationally, some formulae are better on some ranges.
// The point at which e^-x is insignificant compared to e^x = ln(2^27)
const vtype large_threshold = (vtype)0x1.2b708872320e2p+4;
utype ux = as_utype(x);
utype ax = ux & (utype)EXSIGNBIT_DP64;
utype sx = ux ^ ax;
vtype y = as_vtype(ax);
vtype y2 = y * y;
// y < 0.9
vtype znl = pocl_fma(y2,
pocl_fma(y2,
pocl_fma(y2,
(vtype)-0.142077926378834722618091e-7,
(vtype)-0.200047621071909498730453e-3),
(vtype)-0.176016349003044679402273e-1),
(vtype)-0.274030424656179760118928e0);
vtype zdl = pocl_fma(y2,
pocl_fma(y2,
pocl_fma(y2,
(vtype)0.2091140262529164482568557e-3,
(vtype)0.201562166026937652780575e-1),
(vtype)0.381641414288328849317962e0),
(vtype)0.822091273968539282568011e0);
// 0.9 <= y <= 1
vtype znm = pocl_fma(y2,
pocl_fma(y2,
pocl_fma(y2,
(vtype)-0.115475878996143396378318e-7,
(vtype)-0.165597043903549960486816e-3),
(vtype)-0.146173047288731678404066e-1),
(vtype)-0.227793870659088295252442e0);
vtype zdm = pocl_fma(y2,
pocl_fma(y2,
pocl_fma(y2,
(vtype)0.173076050126225961768710e-3,
(vtype)0.167358775461896562588695e-1),
(vtype)0.317204558977294374244770e0),
(vtype)0.683381611977295894959554e0);
itype c = (y < (vtype)0.9);
vtype zn = c ? znl : znm;
vtype zd = c ? zdl : zdm;
vtype z = y + y*y2 * MATH_DIVIDE(zn, zd);
// y > 1
vtype p = exp(2.0 * y) + (vtype)1.0;
vtype zg = (vtype)1.0 - ((vtype)2.0 / p);
z = (y > (vtype)1.0) ? zg : z;
// Other cases
z = (y < (vtype)0x1.0p-28) ? x : z;
z = (ax > (utype)PINFBITPATT_DP64) ? x : z;
z = (y > large_threshold) ? (vtype)1.0 : z;
return as_vtype(sx | as_utype(z));
}
|
