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37 /* PROLOG END TAG zYx */
38
39 #ifdef __SPU__
40
41 #ifndef _ASIND2_H_
42 #define _ASIND2_H_ 1
43
44 #include "simdmath.h"
45 #include <spu_intrinsics.h>
46 #include "sqrtd2.h"
47 #include "divd2.h"
48
49
50
51 /*
52 * FUNCTION
53 * vector double _asind2(vector double x)
54 *
55 * DESCRIPTION
56 * Compute the arc sine of the vector of double precision elements
57 * specified by x, returning the resulting angles in radians. The input
58 * elements are to be in the closed interval [-1, 1]. Values outside
59 * this range result in a invalid operation execption being latched in
60 * the FPSCR register and a NAN is returned.
61 *
62 * The basic algorithm computes the arc sine using a rational polynomial
63 * of the form x + x^3 * P(x^2) / Q(x^2) for inputs |x| in the interval
64 * [0, 0.5]. Values outsize this range are transformed as by:
65 *
66 * asin(x) = PI/2 - 2*asin(sqrt((1-x)/2)) for x in the range (0.5, 1.0]
67 *
68 * asin(x) = -PI/2 + 2*asin(sqrt((1+x)/2)) for x in the range [-1.0, -0.5)
69 *
70 * This yields the basic algorithm of:
71 *
72 * absx = (x < 0.0) ? -x : x;
73 *
74 * if (absx > 0.5) {
75 * if (x < 0) {
76 * addend = -SM_PI_2;
77 * multiplier = -2.0;
78 * } else {
79 * addend = SM_PI_2;
80 * multiplier = 2.0;
81 * }
82 *
83 * x = sqrt(-0.5 * absx + 0.5);
84 * } else {
85 * addend = 0.0;
86 * multiplier = 1.0;
87 * }
88 *
89 * x2 = x * x;
90 * x3 = x2 * x;
91 *
92 * p = ((((P5 * x2 + P4)*x2 + P3)*x2 + P2)*x2 + P1)*x2 + P0;
93 *
94 * q = ((((Q5 * x2 + Q4)*x2 + Q3)*x2 + Q2)*x2 + Q1)*x2 + Q0;;
95 *
96 * pq = p / q;
97 *
98 * result = addend - (x3*pq + x)*multiplier;
99 *
100 * Where P5-P0 and Q5-Q0 are the polynomial coeficients.
101 */
_asind2(vector double x)102 static __inline vector double _asind2(vector double x)
103 {
104 vec_uint4 x_gt_half, x_eq_half;
105 vec_double2 x_abs; // absolute value of x
106 vec_double2 x_trans; // transformed x when |x| > 0.5
107 vec_double2 x2, x3; // x squared and x cubed, respectively.
108 vec_double2 result;
109 vec_double2 multiplier, addend;
110 vec_double2 p, q, pq;
111 vec_double2 half = spu_splats(0.5);
112 vec_double2 sign = (vec_double2)spu_splats(0x8000000000000000ULL);
113 vec_uchar16 splat_hi = ((vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11});
114
115 // Compute the absolute value of x
116 x_abs = spu_andc(x, sign);
117
118 // Perform transformation for the case where |x| > 0.5. We rely on
119 // sqrtd2 producing a NAN is |x| > 1.0.
120 x_trans = _sqrtd2(spu_nmsub(x_abs, half, half));
121
122 // Determine the correct addend and multiplier.
123 x_gt_half = spu_cmpgt((vec_uint4)x_abs, (vec_uint4)half);
124 x_eq_half = spu_cmpeq((vec_uint4)x_abs, (vec_uint4)half);
125 x_gt_half = spu_or(x_gt_half, spu_and(x_eq_half, spu_rlqwbyte(x_gt_half, 4)));
126 x_gt_half = spu_shuffle(x_gt_half, x_gt_half, splat_hi);
127
128 addend = spu_and(spu_sel(spu_splats((double)SM_PI_2), x, (vec_ullong2)sign), (vec_double2)x_gt_half);
129
130 multiplier = spu_sel(spu_splats(-1.0), spu_sel(spu_splats(2.0), x, (vec_ullong2)sign), (vec_ullong2)x_gt_half);
131
132 // Select whether to use the x or the transformed x for the polygon evaluation.
133 // if |x| > 0.5 use x_trans
134 // else use x
135
136 x = spu_sel(x, x_trans, (vec_ullong2)x_gt_half);
137
138 // Compute the polynomials.
139
140 x2 = spu_mul(x, x);
141 x3 = spu_mul(x2, x);
142
143 p = spu_madd(spu_splats(0.004253011369004428248960), x2, spu_splats(-0.6019598008014123785661));
144 p = spu_madd(p, x2, spu_splats(5.444622390564711410273));
145 p = spu_madd(p, x2, spu_splats(-16.26247967210700244449));
146 p = spu_madd(p, x2, spu_splats(19.56261983317594739197));
147 p = spu_madd(p, x2, spu_splats(-8.198089802484824371615));
148
149 q = spu_add(x2, spu_splats(-14.74091372988853791896));
150 q = spu_madd(q, x2, spu_splats(70.49610280856842141659));
151 q = spu_madd(q, x2, spu_splats(-147.1791292232726029859));
152 q = spu_madd(q, x2, spu_splats(139.5105614657485689735));
153 q = spu_madd(q, x2, spu_splats(-49.18853881490881290097));
154
155 // Compute the rational solution p/q and final multiplication and addend
156 // correction.
157 pq = _divd2(p, q);
158
159 result = spu_nmsub(spu_madd(x3, pq, x), multiplier, addend);
160
161 return (result);
162 }
163
164 #endif /* _ASIND2_H_ */
165 #endif /* __SPU__ */
166
