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39 /* -------------------------------------------------------------- */
40 /* PROLOG END TAG zYx */
41 #ifdef __SPU__
42
43 #ifndef _RECIPD2_H_
44 #define _RECIPD2_H_ 1
45
46 #include <spu_intrinsics.h>
47
48
49 /*
50 * FUNCTION
51 * vector double _recipd2(vector double value)
52 *
53 * DESCRIPTION
54 * The _recipd2 function inverts "value" and returns the result.
55 * Computation is performed using the single precision reciprocal
56 * estimate and interpolate instructions to produce a 12 accurate
57 * estimate.
58 *
59 * One (1) iteration of a Newton-Raphson is performed to improve
60 * accuracy to single precision floating point. Two additional double
61 * precision iterations are needed to achieve a full double
62 * preicision result.
63 *
64 * The Newton-Raphson iteration is of the form:
65 * a) X[i+1] = X[i] * (2.0 - b*X[i])
66 * or
67 * b) X[i+1] = X[i] + X[i]*(1.0 - X[i]*b)
68 * where b is the input value to be inverted
69 *
70 * The later (b) form improves the accuracy to 99.95% correctly rounded.
71 */
_recipd2(vector double value_in)72 static __inline vector double _recipd2(vector double value_in)
73 {
74 vec_float4 x0;
75 vec_float4 value;
76 vec_float4 one = spu_splats(1.0f);
77 vec_double2 one_d = spu_splats(1.0);
78 vec_double2 x1, x2, x3;
79 vec_double2 scale;
80 vec_double2 exp, value_d;
81 vec_ullong2 expmask = spu_splats(0x7FF0000000000000ULL);
82 vec_ullong2 is0inf;
83
84 #ifdef __SPU_EDP__
85 vec_ullong2 isdenorm;
86 vec_ullong2 expmask_minus1 = spu_splats(0x7FE0000000000000ULL);
87
88 /* Determine special input values. For example, if the input is a denorm, infinity or 0 */
89
90 isdenorm = spu_testsv(value_in, (SPU_SV_POS_DENORM | SPU_SV_NEG_DENORM));
91 is0inf = spu_testsv(value_in, (SPU_SV_NEG_ZERO | SPU_SV_POS_ZERO |
92 SPU_SV_NEG_INFINITY | SPU_SV_POS_INFINITY));
93
94 /* Scale the divisor to correct for double precision floating
95 * point exponents that are out of single precision range.
96 */
97 exp = spu_and(value_in, (vec_double2)expmask);
98 scale = spu_xor(exp, (vec_double2)spu_sel(expmask, expmask_minus1, isdenorm));
99 value_d = spu_mul(value_in, scale);
100 value = spu_roundtf(value_d);
101
102 /* Perform reciprocal with 1 single precision and 2 double precision
103 * Newton-Raphson iterations.
104 */
105 x0 = spu_re(value);
106 x1 = spu_extend(spu_madd(spu_nmsub(value, x0, one), x0, x0));
107 x2 = spu_madd(spu_nmsub(value_d, x1, one_d), x1, x1);
108 x3 = spu_madd(spu_nmsub(value_d, x2, one_d), x2, x2);
109 x3 = spu_sel(spu_mul(x3, scale), spu_xor(value_in, (vector double)expmask), is0inf);
110
111 #else /* !__SPU_EDP__ */
112
113 vec_uint4 isinf, iszero, isdenorm0;
114 vec_double2 value_abs;
115 vec_double2 sign = spu_splats(-0.0);
116 vec_double2 denorm_scale = (vec_double2)spu_splats(0x4330000000000000ULL);
117 vec_double2 exp_53 = (vec_double2)spu_splats(0x0350000000000000ULL);
118 vec_uchar16 splat_hi = (vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11};
119 vec_uchar16 swap = (vec_uchar16){4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11};
120
121 value_abs = spu_andc(value_in, sign);
122 exp = spu_and(value_in, (vec_double2)expmask);
123
124 /* Determine if the input is a special value. These include:
125 * denorm - then we must coerce it to a normal value.
126 * zero - then we must return an infinity
127 * infinity - then we must return a zero.
128 */
129 isdenorm0 = spu_cmpeq(spu_shuffle((vec_uint4)exp, (vec_uint4)exp, splat_hi), 0);
130
131 isinf = spu_cmpeq((vec_uint4)value_abs, (vec_uint4)expmask);
132 iszero = spu_cmpeq((vec_uint4)value_abs, 0);
133 isinf = spu_and(isinf, spu_shuffle(isinf, isinf, swap));
134 iszero = spu_and(iszero, spu_shuffle(iszero, iszero, swap));
135 is0inf = (vec_ullong2)spu_or(isinf, iszero);
136
137 /* If the inputs is a denorm, we must first convert it to a normal number since
138 * arithmetic operations on denormals produces 0 on Cell/B.E.
139 */
140 value_d = spu_sub(spu_or(value_abs, exp_53), exp_53);
141 value_d = spu_sel(value_abs, value_d, (vec_ullong2)isdenorm0);
142
143 /* Scale the divisor to correct for double precision floating
144 * point exponents that are out of single precision range.
145 */
146 scale = spu_xor(spu_and(value_d, (vec_double2)expmask), (vec_double2)expmask);
147 value_d = spu_mul(value_d, scale);
148 value = spu_roundtf(value_d);
149
150 /* Perform reciprocal with 1 single precision and 2 double precision
151 * Newton-Raphson iterations. The bias is removed after the single
152 * precision iteration.
153 */
154 x0 = spu_re(value);
155 x1 = spu_extend(spu_madd(spu_nmsub(value, x0, one), x0, x0));
156 x2 = spu_madd(spu_nmsub(value_d, x1, one_d), x1, x1);
157 x3 = spu_madd(spu_nmsub(value_d, x2, one_d), x2, x2);
158 x3 = spu_mul(x3, spu_sel(scale, value_in, (vec_ullong2)sign));
159 x3 = spu_sel(x3, spu_mul(x3, denorm_scale), (vec_ullong2)isdenorm0);
160 x3 = spu_sel(x3, spu_xor(value_in, (vector double)expmask), is0inf);
161
162 #endif /* __SPU_EDP__ */
163
164 return (x3);
165 }
166
167 #endif /* _RECIPD2_H_ */
168 #endif /* __SPU__ */
169
