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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