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 2006,2007, */
/* International Business Machines Corporation, */
/* Sony Computer Entertainment, Incorporated, */
/* Toshiba 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. */
/* 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 _EXP2F4_H_
#define _EXP2F4_H_ 1
#include <spu_intrinsics.h>
#include "simdmath.h"
/*
* FUNCTION
* vector float _exp2f4(vector float x)
*
* DESCRIPTION
* The _exp2f4 function computes 2 raised to the input vector x.
* Computation is performed by observing the 2^(a+b) = 2^a * 2^b.
* We decompose x into a and b (above) by letting.
* a = ceil(x), b = x - a;
*
* 2^a is easilty computed by placing a into the exponent
* or a floating point number whose mantissa is all zeros.
*
* 2^b is computed using the following polynomial approximation.
* (C. Hastings, Jr, 1955).
*
* __7__
* \
* \
* 2^(-x) = / Ci*x^i
* /____
* i=1
*
* for x in the range 0.0 to 1.0
*
* C0 = 1.0
* C1 = -0.9999999995
* C2 = 0.4999999206
* C3 = -0.1666653019
* C4 = 0.0416573475
* C5 = -0.0083013598
* C6 = 0.0013298820
* C7 = -0.0001413161
*
*/
static __inline vector float _exp2f4(vector float x)
{
vector signed int ix;
vector unsigned int overflow, underflow;
vector float frac, frac2, frac4;
vector float exp_int, exp_frac;
vector float result;
vector float hi, lo;
vector float bias;
/* Break in the input x into two parts ceil(x), x - ceil(x).
*/
bias = (vector float)(spu_rlmaska((vector signed int)(x), -31));
bias = (vector float)(spu_andc(spu_splats((unsigned int)0x3F7FFFFF), (vector unsigned int)bias));
ix = spu_convts(spu_add(x, bias), 0);
frac = spu_sub(spu_convtf(ix, 0), x);
frac = spu_mul(frac, spu_splats((float)SM_LN2));
overflow = spu_rlmask(spu_cmpgt(ix, 128), -1);
underflow = spu_cmpgt(ix, -128);
exp_int = (vector float)spu_and((vector unsigned int)spu_sl(spu_add(ix, 127), 23), underflow);
/* Instruction counts can be reduced if the polynomial was
* computed entirely from nested (dependent) fma's. However,
* to reduce the number of pipeline stalls, the polygon is evaluated
* in two halves (hi amd lo).
*/
frac2 = spu_mul(frac, frac);
frac4 = spu_mul(frac2, frac2);
hi = spu_madd(frac, spu_splats(-0.0001413161f), spu_splats(0.0013298820f));
hi = spu_madd(frac, hi, spu_splats(-0.0083013598f));
hi = spu_madd(frac, hi, spu_splats(0.0416573475f));
lo = spu_madd(frac, spu_splats(-0.1666653019f), spu_splats(0.4999999206f));
lo = spu_madd(frac, lo, spu_splats(-0.9999999995f));
lo = spu_madd(frac, lo, spu_splats(1.0f));
exp_frac = spu_madd(frac4, hi, lo);
ix = spu_add(ix, spu_rlmask((vector signed int)(exp_frac), -23));
result = spu_mul(exp_frac, exp_int);
/* Handle overflow */
result = spu_or(result, (vector float)overflow);
return (result);
}
#endif /* _EXP2F4_H_ */
#endif /* __SPU__ */
|
