1 /* -------------------------------------------------------------- */
2 /* (C)Copyright 2001,2008, */
3 /* International Business Machines Corporation, */
4 /* Sony Computer Entertainment, Incorporated, */
5 /* Toshiba Corporation, */
6 /* */
7 /* All Rights Reserved. */
8 /* */
9 /* Redistribution and use in source and binary forms, with or */
10 /* without modification, are permitted provided that the */
11 /* following conditions are met: */
12 /* */
13 /* - Redistributions of source code must retain the above copyright*/
14 /* notice, this list of conditions and the following disclaimer. */
15 /* */
16 /* - Redistributions in binary form must reproduce the above */
17 /* copyright notice, this list of conditions and the following */
18 /* disclaimer in the documentation and/or other materials */
19 /* provided with the distribution. */
20 /* */
21 /* - Neither the name of IBM Corporation nor the names of its */
22 /* contributors may be used to endorse or promote products */
23 /* derived from this software without specific prior written */
24 /* permission. */
25 /* */
26 /* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
27 /* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
28 /* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
29 /* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
30 /* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
31 /* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
32 /* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
33 /* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
34 /* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
35 /* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
36 /* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
37 /* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
38 /* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
39 /* -------------------------------------------------------------- */
40 /* PROLOG END TAG zYx */
41 #ifdef __SPU__
42
43 #ifndef _ASINF4_H_
44 #define _ASINF4_H_ 1
45
46 #include <spu_intrinsics.h>
47
48 #include "divf4.h"
49 #include "sqrtf4.h"
50
51 /*
52 * FUNCTION
53 * vector float _asinf4(vector float x)
54 *
55 * DESCRIPTION
56 * The _asinf4 function computes the arc sine for a vector of values x;
57 * that is the values whose sine is x. Results are undefined if x is
58 * outside the range [-1, 1].
59 *
60 */
_asinf4(vector float x)61 static __inline vector float _asinf4(vector float x)
62 {
63 /* The arcsin is computed using two different algorithms, depending
64 * upon the absolute value of the input. For inputs in the range
65 * [0, PI/4], it is computed as the ratio of two polynomials.
66 *
67 * asin(x) = p/q;
68 *
69 * where p = P11*x^11 + P09*x^9 + P07*x^7 + P05*x^5 + P03*x3 + x
70 * q = Q08*x^8 + Q06*x^6 + Q04*x^4 + Q02*x^2 + Q00
71 *
72 * For the range of value [PI/4, 1], the arcsin is computed using:
73 *
74 * asin = PI/2 - sqrt(1 - x) * r;
75 *
76 * where r = C07*x^7 + C06*x^6 + C05*x^5 + C04*x^4 + C03*x^3 + C02*x^2
77 * C01*x + C00;
78 */
79 vector float r, r1, r2, r_hi, r_lo;
80 vector float xabs, x2, x4, x6;
81 vector float p, p_hi, p_lo;
82 vector float q, q_hi, q_lo;
83 vector float pi_over_2 = spu_splats(1.5707963267949f);
84 vector float pi_over_4 = spu_splats(0.7853981633974f);
85 vector unsigned int msb = spu_splats(0x80000000);
86
87
88 x2 = spu_mul(x, x);
89 x4 = spu_mul(x2, x2);
90 x6 = spu_mul(x4, x2);
91
92 xabs = spu_andc(x, (vector float)msb);
93
94 /* Compute arc-sin for values in the range [0, PI/4]
95 */
96 p_hi = spu_madd(spu_splats(0.0000347933107596021167570f), x2,
97 spu_splats(0.000791534994289814532176f));
98 p_hi = spu_madd(p_hi, x2, spu_splats(-0.0400555345006794114027f));
99
100 p_lo = spu_madd(spu_splats(0.201212532134862925881f), x2,
101 spu_splats(-0.325565818622400915405f));
102 p_lo = spu_madd(p_lo, x2, spu_splats(0.166666666666666657415f));
103
104 p = spu_madd(p_hi, x6, p_lo);
105
106 q_hi = spu_madd(spu_splats(0.0770381505559019352791f), x2,
107 spu_splats(-0.688283971605453293030f));
108 q_hi = spu_madd(q_hi, x2, spu_splats(2.02094576023350569471f));
109
110 q_lo = spu_madd(spu_splats(-2.40339491173441421878f), x2,
111 spu_splats(1.0f));
112
113 q = spu_madd(q_hi, x4, q_lo);
114
115 r1 = spu_madd(_divf4(p, q), spu_mul(xabs, x2), xabs);
116
117 /* Compute arc-sin for values in the range [PI/4, 1]
118 */
119 r_hi = spu_madd(spu_splats(-0.0012624911f), xabs,
120 spu_splats(0.0066700901f));
121 r_hi = spu_madd(r_hi, xabs, spu_splats(-0.0170881256f));
122 r_hi = spu_madd(r_hi, xabs, spu_splats(0.0308918810f));
123
124 r_lo = spu_madd(spu_splats(-0.0501743046f), xabs,
125 spu_splats(0.0889789874f));
126 r_lo = spu_madd(r_lo, xabs, spu_splats(-0.2145988016f));
127 r_lo = spu_madd(r_lo, xabs, pi_over_2);
128
129 r = spu_madd(r_hi, x4, r_lo);
130
131 r2 = spu_nmsub(r, _sqrtf4(spu_sub(spu_splats(1.0f), xabs)),
132 pi_over_2);
133
134 /* Select the result depending upon the input value. Correct the
135 * sign of the result.
136 */
137 return (spu_sel(spu_sel(r1, r2, spu_cmpgt(xabs, pi_over_4)),
138 x, msb));
139 }
140
141 #endif /* _ASINF4_H_ */
142 #endif /* __SPU__ */
143
144
145
