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36 /* -------------------------------------------------------------- */
37 /* PROLOG END TAG zYx */
38 #ifdef __SPU__
39 #ifndef _TANHD2_H_
40 #define _TANHD2_H_ 1
41
42 #include <spu_intrinsics.h>
43
44 #include "expd2.h"
45 #include "divd2.h"
46
47
48 /*
49 * Taylor coefficients for tanh
50 */
51 #define TANH_TAY01 1.000000000000000000000000000000E0
52 #define TANH_TAY02 -3.333333333333333333333333333333E-1
53 #define TANH_TAY03 1.333333333333333333333333333333E-1
54 #define TANH_TAY04 -5.396825396825396825396825396825E-2
55 #define TANH_TAY05 2.186948853615520282186948853616E-2
56 #define TANH_TAY06 -8.863235529902196568863235529902E-3
57 #define TANH_TAY07 3.592128036572481016925461369906E-3
58 #define TANH_TAY08 -1.455834387051318268249485180702E-3
59 #define TANH_TAY09 5.900274409455859813780759937000E-4
60 #define TANH_TAY10 -2.391291142435524814857314588851E-4
61 #define TANH_TAY11 9.691537956929450325595875000389E-5
62 #define TANH_TAY12 -3.927832388331683405337080809312E-5
63 #define TANH_TAY13 1.591890506932896474074427981657E-5
64 #define TANH_TAY14 -6.451689215655430763190842315303E-6
65 #define TANH_TAY15 2.614771151290754554263594256410E-6
66 #define TANH_TAY16 -1.059726832010465435091355394125E-6
67 #define TANH_TAY17 4.294911078273805854820351280397E-7
68
69
70 /*
71 * FUNCTION
72 * vector double _tanhd2(vector double x)
73 *
74 * DESCRIPTION
75 * The _tanhd2 function computes the hyperbolic tangent for each
76 * element of the input vector.
77 *
78 * We use the following to approximate tanh:
79 *
80 * |x| <= .25: Taylor Series
81 * |x| > .25: tanh(x) = (exp(2x) - 1)/(exp(2x) + 1)
82 *
83 *
84 * SPECIAL CASES:
85 * - tanh(+/- 0) = +/-0
86 * - tanh(+/- infinity) = +/- 1
87 * - tanh(NaN) = NaN
88 *
89 */
90
_tanhd2(vector double x)91 static __inline vector double _tanhd2(vector double x)
92 {
93 vector double signbit = spu_splats(-0.0);
94 vector double oned = spu_splats(1.0);
95 vector double twod = spu_splats(2.0);
96 vector double infd = (vector double)spu_splats(0x7FF0000000000000ull);
97 vector double xabs;
98 vector double x2;
99 vector unsigned long long gttaylor;
100 vector double e;
101 vector double tresult;
102 vector double eresult;
103 vector double result;
104
105 xabs = spu_andc(x, signbit);
106
107 /*
108 * This is where we switch from Taylor Series
109 * to exponential formula.
110 */
111 gttaylor = spu_cmpgt(xabs, spu_splats(0.25));
112
113
114 /*
115 * Taylor Series Approximation
116 */
117 x2 = spu_mul(x,x);
118 tresult = spu_madd(x2, spu_splats(TANH_TAY11), spu_splats(TANH_TAY10));
119 tresult = spu_madd(x2, tresult, spu_splats(TANH_TAY09));
120 tresult = spu_madd(x2, tresult, spu_splats(TANH_TAY08));
121 tresult = spu_madd(x2, tresult, spu_splats(TANH_TAY07));
122 tresult = spu_madd(x2, tresult, spu_splats(TANH_TAY06));
123 tresult = spu_madd(x2, tresult, spu_splats(TANH_TAY05));
124 tresult = spu_madd(x2, tresult, spu_splats(TANH_TAY04));
125 tresult = spu_madd(x2, tresult, spu_splats(TANH_TAY03));
126 tresult = spu_madd(x2, tresult, spu_splats(TANH_TAY02));
127 tresult = spu_madd(x2, tresult, spu_splats(TANH_TAY01));
128 tresult = spu_mul(xabs, tresult);
129
130
131 /*
132 * Exponential Formula
133 * Our expd2 function gives a more accurate result in general
134 * with xabs instead of x for x<0. We correct for sign later.
135 */
136 e = _expd2(spu_mul(xabs, twod));
137 eresult = _divd2(spu_sub(e, oned), spu_add(e, oned));
138
139
140 /*
141 * Select Taylor or exp result.
142 */
143 result = spu_sel(tresult, eresult, gttaylor);
144
145 /*
146 * Inf and NaN special cases. NaN is already in result
147 * for x = NaN.
148 */
149 result = spu_sel(result, oned, spu_cmpeq(xabs, infd));
150
151 /*
152 * Antisymmetric function - preserve sign bit of x
153 * in the result.
154 */
155 result = spu_sel(result, x, (vec_ullong2)signbit);
156
157 return result;
158 }
159
160 #endif /* _TANHD2_H_ */
161 #endif /* __SPU__ */
162
