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37 /* PROLOG END TAG zYx */
38 #ifdef __SPU__
39
40 #ifndef _ACOSD2_H_
41 #define _ACOSD2_H_ 1
42
43 #include "simdmath.h"
44 #include <spu_intrinsics.h>
45 #include "sqrtd2.h"
46 #include "divd2.h"
47
48 /*
49 * FUNCTION
50 * vector double _acosd2(vector double x)
51 *
52 * DESCRIPTION
53 * Compute the arc cosine of the vector of double precision elements
54 * specified by x, returning the resulting angles in radians. The input
55 * elements are to be in the closed interval [-1, 1]. Values outside
56 * this range result in a invalid operation execption being latched in
57 * the FPSCR register and a NAN is returned.
58 *
59 * The basic algorithm computes the arc cosine using PI/2 - asind2(x).
60 * However, as |x| approaches 1, there is a cancellation error in
61 * subtracting asind2(x) from PI/2, so we simplify the evaluation
62 * instead of layering acosd2 on top of asind2.
63 *
64 * This yields the basic algorithm of:
65 *
66 * absx = (x < 0.0) ? -x : x;
67 *
68 * if (absx > 0.5) {
69 * if (x < 0) {
70 * addend = SM_PI;
71 * multiplier = -2.0;
72 * } else {
73 * addend = 0.0;
74 * multiplier = 2.0;
75 * }
76 *
77 * x = sqrt(-0.5 * absx + 0.5);
78 * } else {
79 * addend = SM_PI_2;
80 * multiplier = -1.0;
81 * }
82 *
83 * x2 = x * x;
84 * x3 = x2 * x;
85 *
86 * p = ((((P5 * x2 + P4)*x2 + P3)*x2 + P2)*x2 + P1)*x2 + P0;
87 *
88 * q = ((((Q5 * x2 + Q4)*x2 + Q3)*x2 + Q2)*x2 + Q1)*x2 + Q0;;
89 *
90 * pq = p / q;
91 *
92 * result = (x3*pq + x)*multiplier - addend;
93 *
94 * Where P5-P0 and Q5-Q0 are the polynomial coeficients. See asind2
95 * for additional details.
96 */
_acosd2(vector double x)97 static __inline vector double _acosd2(vector double x)
98 {
99 vec_uint4 x_gt_half, x_eq_half;
100 vec_double2 x_neg; // input x is negative
101 vec_double2 x_abs; // absolute value of x
102 vec_double2 x_trans; // transformed x when |x| > 0.5
103 vec_double2 x2, x3; // x squared and x cubed, respectively.
104 vec_double2 result;
105 vec_double2 multiplier, addend;
106 vec_double2 p, q, pq;
107 vec_double2 half = spu_splats(0.5);
108 vec_double2 sign = (vec_double2)spu_splats(0x8000000000000000ULL);
109 vec_uchar16 splat_hi = ((vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11});
110
111 // Compute the absolute value of x
112 x_abs = spu_andc(x, sign);
113
114 // Perform transformation for the case where |x| > 0.5. We rely on
115 // sqrtd2 producing a NAN is |x| > 1.0.
116 x_trans = _sqrtd2(spu_nmsub(x_abs, half, half));
117
118 // Determine the correct addend and multiplier.
119 x_neg = (vec_double2)spu_rlmaska((vec_int4)spu_shuffle(x, x, splat_hi), -31);
120
121 x_gt_half = spu_cmpgt((vec_uint4)x_abs, (vec_uint4)half);
122 x_eq_half = spu_cmpeq((vec_uint4)x_abs, (vec_uint4)half);
123 x_gt_half = spu_or(x_gt_half, spu_and(x_eq_half, spu_rlqwbyte(x_gt_half, 4)));
124 x_gt_half = spu_shuffle(x_gt_half, x_gt_half, splat_hi);
125
126 addend = spu_sel(spu_splats(SM_PI_2), spu_and(spu_splats(SM_PI), x_neg), (vec_ullong2)x_gt_half);
127
128 multiplier = spu_sel(spu_splats(-1.0), spu_sel(spu_splats(2.0), x, (vec_ullong2)sign), (vec_ullong2)x_gt_half);
129
130 // Select whether to use the x or the transformed x for the polygon evaluation.
131 // if |x| > 0.5 use x_trans
132 // else use x
133
134 x = spu_sel(x, x_trans, (vec_ullong2)x_gt_half);
135
136 // Compute the polynomials.
137
138 x2 = spu_mul(x, x);
139 x3 = spu_mul(x2, x);
140
141 p = spu_madd(spu_splats(0.004253011369004428248960), x2, spu_splats(-0.6019598008014123785661));
142 p = spu_madd(p, x2, spu_splats(5.444622390564711410273));
143 p = spu_madd(p, x2, spu_splats(-16.26247967210700244449));
144 p = spu_madd(p, x2, spu_splats(19.56261983317594739197));
145 p = spu_madd(p, x2, spu_splats(-8.198089802484824371615));
146
147 q = spu_add(x2, spu_splats(-14.74091372988853791896));
148 q = spu_madd(q, x2, spu_splats(70.49610280856842141659));
149 q = spu_madd(q, x2, spu_splats(-147.1791292232726029859));
150 q = spu_madd(q, x2, spu_splats(139.5105614657485689735));
151 q = spu_madd(q, x2, spu_splats(-49.18853881490881290097));
152
153 // Compute the rational solution p/q and final multiplication and addend
154 // correction.
155 pq = _divd2(p, q);
156
157 result = spu_madd(spu_madd(x3, pq, x), multiplier, addend);
158
159 return (result);
160 }
161
162 #endif /* _ACOSD2_H_ */
163 #endif /* __SPU__ */
164
165
