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2 /* (C)Copyright 2007,2008, */
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36 /* -------------------------------------------------------------- */
37 /* PROLOG END TAG zYx */
38 #ifdef __SPU__
39 #ifndef _ACOSHD2_H_
40 #define _ACOSHD2_H_ 1
41
42 #include <spu_intrinsics.h>
43 #include "logd2.h"
44 #include "sqrtd2.h"
45
46 /*
47 * FUNCTION
48 * vector double _acoshd2(vector double x)
49 *
50 * DESCRIPTION
51 * The acoshd2 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 * - acosh(NaN) = NaN
73 * - acosh(Infinity) = Infinity
74 * - acosh(x < 1) = NaN
75 *
76 */
77
78 /*
79 * Taylor Series Coefficients
80 * for x around 1.
81 */
82 #define SDM_ACOSHD2_TAY01 1.000000000000000000000000000000000E0 /* 1 / 1 */
83 #define SDM_ACOSHD2_TAY02 -8.333333333333333333333333333333333E-2 /* 1 / 12 */
84 #define SDM_ACOSHD2_TAY03 1.875000000000000000000000000000000E-2 /* 3 / 160 */
85 #define SDM_ACOSHD2_TAY04 -5.580357142857142857142857142857142E-3 /* 5 / 896 */
86 #define SDM_ACOSHD2_TAY05 1.898871527777777777777777777777777E-3 /* 35 / 18432 */
87 #define SDM_ACOSHD2_TAY06 -6.991299715909090909090909090909090E-4 /* 63 / 90112 */
88 #define SDM_ACOSHD2_TAY07 2.711369441105769230769230769230769E-4 /* 231 / 851968 */
89 #define SDM_ACOSHD2_TAY08 -1.091003417968750000000000000000000E-4 /* 143 / 1310720 */
90 #define SDM_ACOSHD2_TAY09 4.512422225054572610294117647058823E-5 /* 6435 / 142606336 */
91 #define SDM_ACOSHD2_TAY10 -1.906564361170718544407894736842105E-5 /* 12155 / 637534208 */
92 #define SDM_ACOSHD2_TAY11 8.193687314078921363467261904761904E-6 /* 46189 / 5637144576 */
93 #define SDM_ACOSHD2_TAY12 -3.570569274218186088230298913043478E-6 /* 88179 / 24696061952 */
94 #define SDM_ACOSHD2_TAY13 1.574025955051183700561523437500000E-6 /* 676039 / 429496729600 */
95 #define SDM_ACOSHD2_TAY14 -7.006881922414457356488263165509259E-7 /* 1300075 / 1855425871872 */
96 #define SDM_ACOSHD2_TAY15 3.145330616650332150788142763335129E-7 /* 5014575 / 15942918602752 */
97
_acoshd2(vector double x)98 static __inline vector double _acoshd2(vector double x)
99 {
100 vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 });
101 vec_double2 minus_oned = spu_splats(-1.0);
102 vec_double2 twod = spu_splats(2.0);
103 /* Where we switch from taylor to formula */
104 vec_float4 switch_approx = spu_splats(1.15f);
105 vec_double2 result, fresult, mresult;;
106
107
108 vec_double2 xminus1 = spu_add(x, minus_oned);
109 vec_float4 xf = spu_roundtf(x);
110 xf = spu_shuffle(xf, xf, dup_even);
111
112 vec_ullong2 use_form = (vec_ullong2)spu_cmpgt(xf, switch_approx);
113
114 vec_double2 sqrtargformula = spu_madd(x, x, minus_oned);
115 vec_double2 sqrtargtaylor = spu_mul(xminus1, twod);
116 vec_double2 sqrtarg = spu_sel(sqrtargtaylor, sqrtargformula, use_form);
117
118 vec_double2 sqrtresult = _sqrtd2(sqrtarg);
119
120 /*
121 * Formula:
122 * acosh = ln(x + sqrt(x^2 - 1))
123 */
124 fresult = spu_add(x, sqrtresult);
125 fresult = _logd2(fresult);
126
127 /*
128 * Taylor Series
129 */
130 mresult = spu_splats(SDM_ACOSHD2_TAY15);
131 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY14));
132 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY13));
133 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY12));
134 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY11));
135 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY10));
136 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY09));
137 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY08));
138 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY07));
139 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY06));
140 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY05));
141 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY04));
142 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY03));
143 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY02));
144 mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY01));
145
146
147 mresult = spu_mul(mresult, sqrtresult);
148
149
150 /*
151 * Select series or formula
152 */
153 result = spu_sel(mresult, fresult, use_form);
154
155 return result;
156 }
157
158 #endif /* _ACOSHD2_H_ */
159 #endif /* __SPU__ */
160
