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
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
|
/* -------------------------------------------------------------- */
/* (C)Copyright 2007,2008, */
/* International Business Machines Corporation */
/* All Rights Reserved. */
/* */
/* Redistribution and use in source and binary forms, with or */
/* without modification, are permitted provided that the */
/* following conditions are met: */
/* */
/* - Redistributions of source code must retain the above copyright*/
/* notice, this list of conditions and the following disclaimer. */
/* */
/* - Redistributions in binary form must reproduce the above */
/* copyright notice, this list of conditions and the following */
/* disclaimer in the documentation and/or other materials */
/* provided with the distribution. */
/* */
/* - Neither the name of IBM Corporation nor the names of its */
/* contributors may be used to endorse or promote products */
/* derived from this software without specific prior written */
/* permission. */
/* */
/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
/* -------------------------------------------------------------- */
/* PROLOG END TAG zYx */
#ifdef __SPU__
#ifndef _ATANHF4_H_
#define _ATANHF4_H_ 1
#include <spu_intrinsics.h>
#include <math.h>
#include "logf4.h"
/*
* FUNCTION
* vector float _atanhf4(vector float x)
*
* DESCRIPTION
* The atanhf4 function returns a vector containing the hyperbolic
* arctangents of the corresponding elements of the input vector.
*
* We are using the formula:
* atanh x = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)]
* and the anti-symmetry of atanh.
*
* For x near 0, we use the Taylor series:
* atanh x = x + x^3/3 + x^5/5 + x^7/7 + x^9/9 + ...
*
* Special Cases:
* - atanh(1) = HUGE_VALF
* - atanh(-1) = -HUGE_VALF
* - The result is undefined for x outside of the domain [-1,1].
*
*/
/*
* Maclaurin Series Coefficients
* for x near 0.
*/
#define SDM_SP_ATANH_MAC01 1.000000000000000000000000000000E0
#define SDM_SP_ATANH_MAC03 3.333333333333333333333333333333E-1
#define SDM_SP_ATANH_MAC05 2.000000000000000000000000000000E-1
#define SDM_SP_ATANH_MAC07 1.428571428571428571428571428571E-1
#if 0
#define SDM_SP_ATANH_MAC09 1.111111111111111111111111111111E-1
#define SDM_SP_ATANH_MAC11 9.090909090909090909090909090909E-2
#define SDM_SP_ATANH_MAC13 7.692307692307692307692307692308E-2
#define SDM_SP_ATANH_MAC15 6.666666666666666666666666666667E-2
#endif
static __inline vector float _atanhf4(vector float x)
{
vec_uint4 one = spu_splats(1u);
vec_float4 sign_mask = spu_splats(-0.0f);
vec_float4 onef = spu_splats(1.0f);
vec_float4 onehalff = spu_splats(0.5f);
vec_float4 huge = spu_splats(HUGE_VALF);
vec_float4 result, fresult, mresult;;
vec_float4 xabs, xsqu;
/* Where we switch from maclaurin to formula */
vec_float4 switch_approx = spu_splats(0.165f);
vec_uint4 use_form;
xabs = spu_andc(x, sign_mask);
xsqu = spu_mul(x, x);
/*
* Formula:
* atanh = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)]
*/
fresult = spu_sub(_logf4(spu_add(onef, xabs)), _logf4(spu_sub(onef, xabs)));
fresult = spu_mul(fresult, onehalff);
/*
* Taylor Series
*/
mresult = spu_madd(xsqu, spu_splats((float)SDM_SP_ATANH_MAC07), spu_splats((float)SDM_SP_ATANH_MAC05));
mresult = spu_madd(xsqu, mresult, spu_splats((float)SDM_SP_ATANH_MAC03));
mresult = spu_madd(xsqu, mresult, spu_splats((float)SDM_SP_ATANH_MAC01));
mresult = spu_mul(xabs, mresult);
/*
* Choose between series and formula
*/
use_form = spu_cmpgt(xabs, switch_approx);
result = spu_sel(mresult, fresult, use_form);
/*
* Correct for accumulated truncation error. Currently reduces rms of
* absolute error by about 50%
*/
result = (vec_float4)spu_add((vec_uint4)result, spu_and(one, spu_cmpgt(xabs, spu_splats(0.0f))));
result = (vec_float4)spu_add((vec_uint4)result, spu_and(one, spu_cmpgt(xabs, spu_splats(0.25f))));
/*
* Check Boundary Conditions
*/
result = spu_sel(result, huge, spu_cmpeq(xabs, onef));
/*
* Spec says |x| > 1, result is undefined, so no additional
* boundary checks needed.
*/
/* Preserve sign - atanh is anti-symmetric */
result = spu_sel(result, x, (vec_uint4)sign_mask);
return result;
}
#endif /* _ATANHF4_H_ */
#endif /* __SPU__ */
|
