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 _ASINHD2_H_
40 #define _ASINHD2_H_ 1
41
42 #include <spu_intrinsics.h>
43
44 #include "logd2.h"
45 #include "sqrtd2.h"
46
47 /*
48 * FUNCTION
49 * vector double _asinhd2(vector double x)
50 *
51 * DESCRIPTION
52 * The asinhd2 function returns a vector containing the hyperbolic
53 * arcsines of the corresponding elements of the input vector.
54 *
55 * We are using the formula:
56 * asinh = ln(|x| + sqrt(x^2 + 1))
57 * and the anti-symmetry of asinh.
58 *
59 * For x near zero, we use the Taylor series:
60 *
61 * infinity
62 * ------
63 * - ' P (0)
64 * - k-1 k
65 * asinh x = - ----- x
66 * - k
67 * - ,
68 * ------
69 * k = 1
70 *
71 * Special Cases:
72 * asinh(+0) returns +0
73 * asinh(-0) returns -0
74 * asinh(+infinity) returns +infinity
75 * asinh(-infinity) returns -infinity
76 * asinh(NaN) returns NaN
77 *
78 */
79
80 /*
81 * Maclaurin Series Coefficients
82 * for x near 0.
83 */
84 #define SDM_ASINHD2_MAC01 1.000000000000000000000000000000000000000000E0
85 #define SDM_ASINHD2_MAC03 -1.666666666666666666666666666666666666666667E-1
86 #define SDM_ASINHD2_MAC05 7.500000000000000000000000000000000000000000E-2
87 #define SDM_ASINHD2_MAC07 -4.464285714285714285714285714285714285714286E-2
88 #define SDM_ASINHD2_MAC09 3.038194444444444444444444444444444444444444E-2
89 #define SDM_ASINHD2_MAC11 -2.237215909090909090909090909090909090909091E-2
90 #define SDM_ASINHD2_MAC13 1.735276442307692307692307692307692307692308E-2
91 #define SDM_ASINHD2_MAC15 -1.396484375000000000000000000000000000000000E-2
92 #define SDM_ASINHD2_MAC17 1.155180089613970588235294117647058823529412E-2
93
94
_asinhd2(vector double x)95 static __inline vector double _asinhd2(vector double x)
96 {
97 vec_double2 sign_mask = spu_splats(-0.0);
98 vec_double2 oned = spu_splats(1.0);
99 vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 });
100 vec_uint4 infminus1 = spu_splats(0x7FEFFFFFU);
101 vec_uint4 isinfnan;
102 vec_double2 xabs, xsqu;
103 vec_uint4 xabshigh;
104 vec_float4 switch_approx = spu_splats(0.165f); /* Where we switch from maclaurin to formula */
105 vec_uint4 use_form;
106 vec_float4 xf;
107 vec_double2 result, fresult, mresult;
108
109
110 xabs = spu_andc(x, sign_mask);
111 xsqu = spu_mul(x, x);
112
113 xf = spu_roundtf(xabs);
114 xf = spu_shuffle(xf, xf, dup_even);
115
116 /*
117 * Formula:
118 * asinh = ln(|x| + sqrt(x^2 + 1))
119 */
120 fresult = _sqrtd2(spu_add(xsqu, oned));
121 fresult = spu_add(xabs, fresult);
122 fresult = _logd2(fresult);
123
124
125 /*
126 * Maclaurin Series approximation
127 */
128
129 mresult = spu_splats(SDM_ASINHD2_MAC17);
130 mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC15));
131 mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC13));
132 mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC11));
133 mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC09));
134 mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC07));
135 mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC05));
136 mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC03));
137 mresult = spu_madd(xsqu, mresult, spu_splats(SDM_ASINHD2_MAC01));
138 mresult = spu_mul(xabs, mresult);
139
140
141 /*
142 * Choose between series and formula
143 */
144 use_form = spu_cmpgt(xf, switch_approx);
145 result = spu_sel(mresult, fresult, (vec_ullong2)use_form);
146
147
148 /* Special Cases */
149
150 /* Infinity and NaN */
151 xabshigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even);
152 isinfnan = spu_cmpgt(xabshigh, infminus1);
153 result = spu_sel(result, x, (vec_ullong2)isinfnan);
154
155
156 /* Restore sign - asinh is an anti-symmetric */
157 result = spu_sel(result, x, (vec_ullong2)sign_mask);
158
159 return result;
160 }
161
162 #endif /* _ASINHD2_H_ */
163 #endif /* __SPU__ */
164
