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36 /* -------------------------------------------------------------- */
37 /* PROLOG END TAG zYx */
38 #ifdef __SPU__
39 #ifndef _ASINHF4_H_
40 #define _ASINHF4_H_ 1
41
42 #include <spu_intrinsics.h>
43
44 #include "logf4.h"
45 #include "sqrtf4.h"
46
47 /*
48 * FUNCTION
49 * vector float _asinhf4(vector float x)
50 *
51 * DESCRIPTION
52 * The asinhf4 function returns a vector containing the hyperbolic
53 * arcsines of the corresponding elements of the input vector.
54 *
55 * We are using the formula:
56 * asinh = ln(|x| + sqrt(x^2 + 1))
57 * and the anti-symmetry of asinh.
58 *
59 * For x near zero, we use the Taylor series:
60 *
61 * infinity
62 * ------
63 * - ' P (0)
64 * - k-1 k
65 * asinh x = - ----- x
66 * - k
67 * - ,
68 * ------
69 * k = 1
70 *
71 * Special Cases:
72 * - asinh(+0) returns +0
73 * - asinh(-0) returns -0
74 * - Normally, asinh(+/- infinity) returns +/- infinity,
75 * but on the SPU, single-precision infinity is not supported,
76 * so it is treated as a normal number here.
77 *
78 */
79
80 /*
81 * Maclaurin Series Coefficients
82 * for x near 0.
83 */
84 #define ASINH_MAC01 1.0000000000000000000000000000000000000000000000000000000000000000000000E0
85 #define ASINH_MAC03 -1.6666666666666666666666666666666666666666666666666666666666666666666667E-1
86 #define ASINH_MAC05 7.5000000000000000000000000000000000000000000000000000000000000000000000E-2
87 #define ASINH_MAC07 -4.4642857142857142857142857142857142857142857142857142857142857142857143E-2
88 #define ASINH_MAC09 3.0381944444444444444444444444444444444444444444444444444444444444444444E-2
89 #define ASINH_MAC11 -2.2372159090909090909090909090909090909090909090909090909090909090909091E-2
90 #define ASINH_MAC13 1.7352764423076923076923076923076923076923076923076923076923076923076923E-2
91 #define ASINH_MAC15 -1.3964843750000000000000000000000000000000000000000000000000000000000000E-2
92 #define ASINH_MAC17 1.1551800896139705882352941176470588235294117647058823529411764705882353E-2
93 #define ASINH_MAC19 -9.7616095291940789473684210526315789473684210526315789473684210526315789E-3
94 #define ASINH_MAC21 8.3903358096168154761904761904761904761904761904761904761904761904761905E-3
95 #define ASINH_MAC23 -7.3125258735988451086956521739130434782608695652173913043478260869565217E-3
96 #define ASINH_MAC25 6.4472103118896484375000000000000000000000000000000000000000000000000000E-3
97 #define ASINH_MAC27 -5.7400376708419234664351851851851851851851851851851851851851851851851852E-3
98 #define ASINH_MAC29 5.1533096823199041958512931034482758620689655172413793103448275862068966E-3
99 #define ASINH_MAC31 -4.6601434869150961599042338709677419354838709677419354838709677419354839E-3
100 #if 0
101 #define ASINH_MAC33 4.2409070936793630773370916193181818181818181818181818181818181818181818E-3
102 #define ASINH_MAC35 -3.8809645588376692363194056919642857142857142857142857142857142857142857E-3
103 #define ASINH_MAC37 3.5692053938259345454138678473395270270270270270270270270270270270270270E-3
104 #define ASINH_MAC39 -3.2970595034734847453924325796274038461538461538461538461538461538461538E-3
105 #define ASINH_MAC41 3.0578216492580306693548109473251714939024390243902439024390243902439024E-3
106 #define ASINH_MAC43 -2.8461784011089421678767647854117460029069767441860465116279069767441860E-3
107 #endif
108
109
_asinhf4(vector float x)110 static __inline vector float _asinhf4(vector float x)
111 {
112 vec_float4 sign_mask = spu_splats(-0.0f);
113 vec_float4 onef = spu_splats(1.0f);
114 vec_uint4 oneu = spu_splats(1u);
115 vec_uint4 twou = spu_splats(2u);
116 vec_uint4 threeu = spu_splats(3u);
117 vec_float4 ln2 = spu_splats(6.931471805599453094172321E-1f);
118 vec_float4 largef = spu_splats(9.21e18f);
119 vec_float4 result, fresult, mresult;
120 vec_float4 xabs, xsqu;
121 /* Where we switch from maclaurin to formula */
122 vec_float4 switch_approx = spu_splats(0.74f);
123 vec_float4 trunc_part2 = spu_splats(20.0f);
124 vec_uint4 truncadd;
125 vec_uint4 islarge;
126 vec_uint4 use_form;
127
128 xabs = spu_andc(x, sign_mask);
129 xsqu = spu_mul(x, x);
130 islarge = spu_cmpgt(xabs, largef);
131
132 /*
133 * Formula:
134 * asinh = ln(|x| + sqrt(x^2 + 1))
135 */
136
137 vec_float4 logarg = spu_add(xabs, _sqrtf4(spu_madd(xabs, xabs, onef)));
138 logarg = spu_sel(logarg, xabs, islarge);
139 fresult = _logf4(logarg);
140 fresult = spu_sel(fresult, spu_add(fresult, ln2), islarge);
141
142 /*
143 * Maclaurin Series
144 */
145 mresult = spu_madd(xsqu, spu_splats((float)ASINH_MAC31), spu_splats((float)ASINH_MAC29));
146 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC27));
147 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC25));
148 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC23));
149 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC21));
150 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC19));
151 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC17));
152 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC15));
153 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC13));
154 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC11));
155 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC09));
156 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC07));
157 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC05));
158 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC03));
159 mresult = spu_madd(xsqu, mresult, spu_splats((float)ASINH_MAC01));
160 mresult = spu_mul(xabs, mresult);
161
162 /*
163 * Choose between series and formula
164 */
165 use_form = spu_cmpgt(xabs, switch_approx);
166 result = spu_sel(mresult, fresult, use_form);
167
168 /*
169 * Truncation correction on spu
170 */
171 truncadd = spu_sel(oneu, threeu, use_form);
172 truncadd = spu_sel(truncadd, twou, spu_cmpgt(xabs, trunc_part2));
173 result = (vec_float4)spu_add((vec_uint4)result, truncadd);
174
175 /* Preserve sign - asinh is anti-symmetric */
176 result = spu_sel(result, x, (vec_uint4)sign_mask);
177
178 return result;
179 }
180
181 #endif /* _ASINHF4_H_ */
182 #endif /* __SPU__ */
183
