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
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
|
/* -------------------------------------------------------------- */
/* (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 _ASINHD2_H_
#define _ASINHD2_H_ 1
#include <spu_intrinsics.h>
#include "logd2.h"
#include "sqrtd2.h"
/*
* FUNCTION
* vector double _asinhd2(vector double x)
*
* DESCRIPTION
* The asinhd2 function returns a vector containing the hyperbolic
* arcsines of the corresponding elements of the input vector.
*
* We are using the formula:
* asinh = ln(|x| + sqrt(x^2 + 1))
* and the anti-symmetry of asinh.
*
* For x near zero, we use the Taylor series:
*
* infinity
* ------
* - ' P (0)
* - k-1 k
* asinh x = - ----- x
* - k
* - ,
* ------
* k = 1
*
* Special Cases:
* asinh(+0) returns +0
* asinh(-0) returns -0
* asinh(+infinity) returns +infinity
* asinh(-infinity) returns -infinity
* asinh(NaN) returns NaN
*
*/
/*
* Maclaurin Series Coefficients
* for x near 0.
*/
#define SDM_ASINHD2_MAC01 1.000000000000000000000000000000000000000000E0
#define SDM_ASINHD2_MAC03 -1.666666666666666666666666666666666666666667E-1
#define SDM_ASINHD2_MAC05 7.500000000000000000000000000000000000000000E-2
#define SDM_ASINHD2_MAC07 -4.464285714285714285714285714285714285714286E-2
#define SDM_ASINHD2_MAC09 3.038194444444444444444444444444444444444444E-2
#define SDM_ASINHD2_MAC11 -2.237215909090909090909090909090909090909091E-2
#define SDM_ASINHD2_MAC13 1.735276442307692307692307692307692307692308E-2
#define SDM_ASINHD2_MAC15 -1.396484375000000000000000000000000000000000E-2
#define SDM_ASINHD2_MAC17 1.155180089613970588235294117647058823529412E-2
static __inline vector double _asinhd2(vector double x)
{
vec_double2 sign_mask = spu_splats(-0.0);
vec_double2 oned = spu_splats(1.0);
vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 });
vec_uint4 infminus1 = spu_splats(0x7FEFFFFFU);
vec_uint4 isinfnan;
vec_double2 xabs, xsqu;
vec_uint4 xabshigh;
vec_float4 switch_approx = spu_splats(0.165f); /* Where we switch from maclaurin to formula */
vec_uint4 use_form;
vec_float4 xf;
vec_double2 result, fresult, mresult;
xabs = spu_andc(x, sign_mask);
xsqu = spu_mul(x, x);
xf = spu_roundtf(xabs);
xf = spu_shuffle(xf, xf, dup_even);
/*
* Formula:
* asinh = ln(|x| + sqrt(x^2 + 1))
*/
fresult = _sqrtd2(spu_add(xsqu, oned));
fresult = spu_add(xabs, fresult);
fresult = _logd2(fresult);
/*
* Maclaurin Series approximation
*/
mresult = spu_splats(SDM_ASINHD2_MAC17);
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC15));
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC13));
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC11));
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC09));
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC07));
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC05));
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC03));
mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC01));
mresult = spu_mul(xabs, mresult);
/*
* Choose between series and formula
*/
use_form = spu_cmpgt(xf, switch_approx);
result = spu_sel(mresult, fresult, (vec_ullong2)use_form);
/* Special Cases */
/* Infinity and NaN */
xabshigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even);
isinfnan = spu_cmpgt(xabshigh, infminus1);
result = spu_sel(result, x, (vec_ullong2)isinfnan);
/* Restore sign - asinh is an anti-symmetric */
result = spu_sel(result, x, (vec_ullong2)sign_mask);
return result;
}
#endif /* _ASINHD2_H_ */
#endif /* __SPU__ */
|
