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39 /* -------------------------------------------------------------- */
40 /* PROLOG END TAG zYx */
41 #ifdef __SPU__
42 #ifndef _EXPF4_H_
43 #define _EXPF4_H_ 1
44
45
46 #include "floorf4.h"
47 #include "ldexpf4.h"
48
49 /*
50 * FUNCTION
51 * vector float _expf4(vector float x)
52 *
53 * DESCRIPTION
54 * The _expf4 function computes e raised to the input x for
55 * each of the element of the float vector.
56 *
57 */
_expf4(vector float x)58 static __inline vector float _expf4(vector float x)
59 {
60
61 // log2(e)
62 vec_float4 log2e = spu_splats(1.4426950408889634074f);
63
64 // Extra precision for the ln2 multiply
65 vec_float4 ln2_hi = spu_splats(0.693359375f);
66 vec_float4 ln2_lo = spu_splats(-2.12194440E-4f);
67
68 // Coefficents for the Taylor series
69 vec_float4 f02 = spu_splats(5.0000000000000000E-1f); // 1/2!
70 vec_float4 f03 = spu_splats(1.6666666666666667E-1f); // 1/3!
71 vec_float4 f04 = spu_splats(4.1666666666666667E-2f); // 1/4!
72 vec_float4 f05 = spu_splats(8.3333333333333333E-3f); // 1/5!
73 vec_float4 f06 = spu_splats(1.3888888888888889E-3f); // 1/6!
74 vec_float4 f07 = spu_splats(1.9841269841269841E-4f); // 1/7!
75
76 // Range reduce input, so that:
77 // e^x = e^z * 2^n
78 // e^x = e^z * e^(n * ln(2))
79 // e^x = e^(z + (n * ln(2)))
80
81 vec_int4 n; // exponent of reduction
82 vec_float4 q; // range reduced result
83
84 vec_float4 z;
85 vec_float4 r;
86
87 z = spu_madd(x,log2e,spu_splats(0.5f));
88 z = _floorf4(z);
89 r = spu_nmsub(z,ln2_hi,x);
90 r = spu_nmsub(z,ln2_lo,r);
91 n = spu_convts(z,0);
92 z = spu_mul(r,r);
93
94 // Use Horner's method on the Taylor series
95 q = spu_madd(r,f07,f06);
96 q = spu_madd(q,r,f05);
97 q = spu_madd(q,r,f04);
98 q = spu_madd(q,r,f03);
99 q = spu_madd(q,r,f02);
100 q = spu_madd(q,z,r);
101 q = spu_add(q,spu_splats(1.0f));
102
103 // Adjust the result by the range reduction
104 r = _ldexpf4( q, n );
105
106 return(r);
107
108 }
109
110 #endif /* _EXPF4_H_ */
111 #endif /* __SPU__ */
112
113
