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40 /* PROLOG END TAG zYx */
41 #ifdef __SPU__
42
43 #ifndef _ATANF4_H_
44 #define _ATANF4_H_ 1
45
46 #include <spu_intrinsics.h>
47
48 #include "simdmath.h"
49 #include "recipf4.h"
50
51 /*
52 * FUNCTION
53 * vector float _atanf4(vector float x)
54 *
55 * DESCRIPTION
56 * The _atanf4 function computes the arc tangent of a vector of values x;
57 * that is the values whose tangent is x.
58 *
59 * The _atanf4 function returns the arc tangents in radians and the value
60 * is mathematically defined to be in the range -PI/2 to PI/2.
61 *
62 * The arc tangent function is computed using a polynomial approximation
63 * (B. Carlson, M. Goldstein, Los Alamos Scientific Laboratory, 1955).
64 * __8__
65 * \
66 * \
67 * atan(x) = / Ci*x^(2*i+1)
68 * /____
69 * i=0
70 *
71 * for x in the range -1 to 1. The remaining regions are defined to be:
72 *
73 * [1, infinity] : PI/2 + atanf(-1/x)
74 * [-infinity, -1] : -PI/2 + atanf(-1/x)
75 *
76 */
_atanf4(vector float x)77 static __inline vector float _atanf4(vector float x)
78 {
79 vector float bias;
80 vector float x2, x3, x4, x8, x9;
81 vector float hi, lo;
82 vector float result;
83 vector float inv_x;
84 vector unsigned int sign;
85 vector unsigned int select;
86
87 sign = spu_sl(spu_rlmask((vector unsigned int)x, -31), 31);
88 inv_x = _recipf4(x);
89 inv_x = (vector float)spu_xor((vector unsigned int)inv_x, spu_splats(0x80000000));
90
91 select = (vector unsigned int)spu_cmpabsgt(x, spu_splats(1.0f));
92 bias = (vector float)spu_or(sign, (vector unsigned int)(spu_splats((float)SM_PI_2)));
93 bias = (vector float)spu_and((vector unsigned int)bias, select);
94
95 x = spu_sel(x, inv_x, select);
96
97 /* Instruction counts can be reduced if the polynomial was
98 * computed entirely from nested (dependent) fma's. However,
99 * to reduce the number of pipeline stalls, the polygon is evaluated
100 * in two halves(hi and lo).
101 */
102 bias = spu_add(bias, x);
103 x2 = spu_mul(x, x);
104 x3 = spu_mul(x2, x);
105 x4 = spu_mul(x2, x2);
106 x8 = spu_mul(x4, x4);
107 x9 = spu_mul(x8, x);
108 hi = spu_madd(spu_splats(0.0028662257f), x2, spu_splats(-0.0161657367f));
109 hi = spu_madd(hi, x2, spu_splats(0.0429096138f));
110 hi = spu_madd(hi, x2, spu_splats(-0.0752896400f));
111 hi = spu_madd(hi, x2, spu_splats(0.1065626393f));
112 lo = spu_madd(spu_splats(-0.1420889944f), x2, spu_splats(0.1999355085f));
113 lo = spu_madd(lo, x2, spu_splats(-0.3333314528f));
114 lo = spu_madd(lo, x3, bias);
115
116 result = spu_madd(hi, x9, lo);
117
118 return (result);
119 }
120
121 #endif /* _ATANF4_H_ */
122 #endif /* __SPU__ */
123
124
125
