1 | /* -------------------------------------------------------------- */ |
---|
2 | /* (C)Copyright 2007,2008, */ |
---|
3 | /* International Business Machines Corporation */ |
---|
4 | /* All Rights Reserved. */ |
---|
5 | /* */ |
---|
6 | /* Redistribution and use in source and binary forms, with or */ |
---|
7 | /* without modification, are permitted provided that the */ |
---|
8 | /* following conditions are met: */ |
---|
9 | /* */ |
---|
10 | /* - Redistributions of source code must retain the above copyright*/ |
---|
11 | /* notice, this list of conditions and the following disclaimer. */ |
---|
12 | /* */ |
---|
13 | /* - Redistributions in binary form must reproduce the above */ |
---|
14 | /* copyright notice, this list of conditions and the following */ |
---|
15 | /* disclaimer in the documentation and/or other materials */ |
---|
16 | /* provided with the distribution. */ |
---|
17 | /* */ |
---|
18 | /* - Neither the name of IBM Corporation nor the names of its */ |
---|
19 | /* contributors may be used to endorse or promote products */ |
---|
20 | /* derived from this software without specific prior written */ |
---|
21 | /* permission. */ |
---|
22 | /* */ |
---|
23 | /* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */ |
---|
24 | /* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */ |
---|
25 | /* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */ |
---|
26 | /* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */ |
---|
27 | /* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */ |
---|
28 | /* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */ |
---|
29 | /* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */ |
---|
30 | /* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */ |
---|
31 | /* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */ |
---|
32 | /* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */ |
---|
33 | /* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */ |
---|
34 | /* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */ |
---|
35 | /* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
---|
36 | /* -------------------------------------------------------------- */ |
---|
37 | /* PROLOG END TAG zYx */ |
---|
38 | #ifdef __SPU__ |
---|
39 | #ifndef _ACOSHF4_H_ |
---|
40 | #define _ACOSHF4_H_ 1 |
---|
41 | |
---|
42 | #include <spu_intrinsics.h> |
---|
43 | #include "logf4.h" |
---|
44 | #include "sqrtf4.h" |
---|
45 | |
---|
46 | /* |
---|
47 | * FUNCTION |
---|
48 | * vector float _acoshf4(vector float x) |
---|
49 | * |
---|
50 | * DESCRIPTION |
---|
51 | * The acoshf4 function returns a vector containing the hyperbolic |
---|
52 | * arccosines of the corresponding elements of the input vector. |
---|
53 | * |
---|
54 | * We are using the formula: |
---|
55 | * acosh = ln(x + sqrt(x^2 - 1)) |
---|
56 | * |
---|
57 | * For x near one, we use the Taylor series: |
---|
58 | * |
---|
59 | * infinity |
---|
60 | * ------ |
---|
61 | * - ' |
---|
62 | * - k |
---|
63 | * acosh x = - C (x - 1) |
---|
64 | * - k |
---|
65 | * - , |
---|
66 | * ------ |
---|
67 | * k = 0 |
---|
68 | * |
---|
69 | * |
---|
70 | * Special Cases: |
---|
71 | * - acosh(1) = +0 |
---|
72 | * - NaNs and Infinity aren't supported for single-precision on SPU. |
---|
73 | * |
---|
74 | */ |
---|
75 | |
---|
76 | /* |
---|
77 | * Taylor Series Coefficients |
---|
78 | * for x around 1. |
---|
79 | */ |
---|
80 | #define SDM_ACOSHF4_TAY01 1.00000000000000000000000000000000000E0f /* 1 / 1 */ |
---|
81 | #define SDM_ACOSHF4_TAY02 -8.33333333333333333333333333333333333E-2f /* 1 / 12 */ |
---|
82 | #define SDM_ACOSHF4_TAY03 1.87500000000000000000000000000000000E-2f /* 3 / 160 */ |
---|
83 | #define SDM_ACOSHF4_TAY04 -5.58035714285714285714285714285714286E-3f /* 5 / 896 */ |
---|
84 | #define SDM_ACOSHF4_TAY05 1.89887152777777777777777777777777778E-3f /* 35 / 18432 */ |
---|
85 | #define SDM_ACOSHF4_TAY06 -6.99129971590909090909090909090909091E-4f /* 63 / 90112 */ |
---|
86 | #define SDM_ACOSHF4_TAY07 2.71136944110576923076923076923076923E-4f /* 231 / 851968 */ |
---|
87 | #define SDM_ACOSHF4_TAY08 -1.09100341796875000000000000000000000E-4f /* 143 / 1310720 */ |
---|
88 | #define SDM_ACOSHF4_TAY09 4.51242222505457261029411764705882353E-5f /* 6435 / 142606336 */ |
---|
89 | #define SDM_ACOSHF4_TAY10 -1.90656436117071854440789473684210526E-5f /* 12155 / 637534208 */ |
---|
90 | #define SDM_ACOSHF4_TAY11 8.19368731407892136346726190476190476E-6f /* 46189 / 5637144576 */ |
---|
91 | #define SDM_ACOSHF4_TAY12 -3.57056927421818608823029891304347826E-6f /* 88179 / 24696061952 */ |
---|
92 | #define SDM_ACOSHF4_TAY13 1.57402595505118370056152343750000000E-6f /* 676039 / 429496729600 */ |
---|
93 | #define SDM_ACOSHF4_TAY14 -7.00688192241445735648826316550925926E-7f /* 1300075 / 1855425871872 */ |
---|
94 | #define SDM_ACOSHF4_TAY15 3.14533061665033215078814276333512931E-7f /* 5014575 / 15942918602752 */ |
---|
95 | #if 0 |
---|
96 | #define SDM_ACOSHF4_TAY16 -1.42216292935641362301764949675529234E-7f /* 9694845 / 68169720922112 */ |
---|
97 | #define SDM_ACOSHF4_TAY17 6.47111067761133282064375552264126864E-8f /* 100180065 / 1548112371908608 */ |
---|
98 | #define SDM_ACOSHF4_TAY18 -2.96094097811711825280716376645224435E-8f /* 116680311 / 3940649673949184 */ |
---|
99 | #define SDM_ACOSHF4_TAY19 1.36154380562817937676005090612011987E-8f /* 2268783825 / 166633186212708352 */ |
---|
100 | #endif |
---|
101 | |
---|
102 | |
---|
103 | |
---|
104 | static __inline vector float _acoshf4(vector float x) |
---|
105 | { |
---|
106 | vec_float4 minus_onef = spu_splats(-1.0f); |
---|
107 | vec_float4 twof = spu_splats(2.0f); |
---|
108 | vec_float4 largef = spu_splats(2.5e19f); |
---|
109 | vec_float4 xminus1; |
---|
110 | /* Where we switch from taylor to formula */ |
---|
111 | vec_float4 switch_approx = spu_splats(2.0f); |
---|
112 | vec_uint4 use_form; |
---|
113 | vec_float4 result, fresult, mresult;; |
---|
114 | |
---|
115 | |
---|
116 | /* |
---|
117 | * Formula: |
---|
118 | * acosh = ln(x + sqrt(x^2 - 1)) |
---|
119 | */ |
---|
120 | fresult = _sqrtf4(spu_madd(x, x, minus_onef)); |
---|
121 | fresult = spu_add(x, spu_sel(fresult, x, spu_cmpgt(x, largef))); |
---|
122 | fresult = _logf4(fresult); |
---|
123 | fresult = (vec_float4)spu_add((vec_uint4)fresult, spu_splats(2u)); |
---|
124 | |
---|
125 | /* |
---|
126 | * Taylor Series |
---|
127 | */ |
---|
128 | xminus1 = spu_add(x, minus_onef); |
---|
129 | |
---|
130 | mresult = spu_splats(SDM_ACOSHF4_TAY15); |
---|
131 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY14)); |
---|
132 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY13)); |
---|
133 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY12)); |
---|
134 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY11)); |
---|
135 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY10)); |
---|
136 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY09)); |
---|
137 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY08)); |
---|
138 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY07)); |
---|
139 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY06)); |
---|
140 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY05)); |
---|
141 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY04)); |
---|
142 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY03)); |
---|
143 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY02)); |
---|
144 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHF4_TAY01)); |
---|
145 | |
---|
146 | mresult = spu_mul(mresult, _sqrtf4(spu_mul(xminus1, twof))); |
---|
147 | mresult = (vec_float4)spu_add((vec_uint4)mresult, spu_splats(1u)); |
---|
148 | |
---|
149 | /* |
---|
150 | * Select series or formula |
---|
151 | */ |
---|
152 | use_form = spu_cmpgt(x, switch_approx); |
---|
153 | result = spu_sel(mresult, fresult, use_form); |
---|
154 | |
---|
155 | |
---|
156 | return result; |
---|
157 | } |
---|
158 | |
---|
159 | #endif /* _ACOSHF4_H_ */ |
---|
160 | #endif /* __SPU__ */ |
---|