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39 /* -------------------------------------------------------------- */
40 /* PROLOG END TAG zYx */
41 #ifdef __SPU__
42 #ifndef _SQRTD2_H_
43 #define _SQRTD2_H_ 1
44
45 #include <spu_intrinsics.h>
46
47 /*
48 * FUNCTION
49 * vector double _sqrtd2(vector double in)
50 *
51 * DESCRIPTION
52 * The _sqrtd2 function computes the square root of the vector input "in"
53 * and returns the result.
54 *
55 */
_sqrtd2(vector double in)56 static __inline vector double _sqrtd2(vector double in)
57 {
58 vec_int4 bias_exp;
59 vec_uint4 exp;
60 vec_float4 fx, fg, fy, fd, fe, fy2, fhalf;
61 vec_ullong2 nochange, denorm;
62 vec_ullong2 mask = spu_splats(0x7FE0000000000000ULL);
63 vec_double2 dx, de, dd, dy, dg, dy2, dhalf;
64 vec_double2 neg;
65 vec_double2 one = spu_splats(1.0);
66 vec_double2 two_pow_52 = (vec_double2)spu_splats(0x4330000000000000ULL);
67
68 /* If the input is a denorm, then multiply it by 2^52 so that the input is no
69 * longer denormal.
70 */
71 exp = (vec_uint4)spu_and((vec_ullong2)in, spu_splats(0xFFF0000000000000ULL));
72 denorm = (vec_ullong2)spu_cmpeq(exp,0);
73
74 in = spu_mul(in, spu_sel(one, two_pow_52, denorm));
75
76 fhalf = spu_splats(0.5f);
77 dhalf = spu_splats(0.5);
78
79 /* Coerce the input, in, into the argument reduced space [0.5, 2.0).
80 */
81 dx = spu_sel(in, dhalf, mask);
82
83 /* Compute an initial single precision guess for the square root (fg)
84 * and half reciprocal (fy2).
85 */
86 fx = spu_roundtf(dx);
87
88 fy2 = spu_rsqrte(fx);
89 fy = spu_mul(fy2, fhalf);
90 fg = spu_mul(fy2, fx); /* 12-bit approximation to sqrt(cx) */
91
92 /* Perform one single precision Newton-Raphson iteration to improve
93 * accuracy to about 22 bits.
94 */
95 fe = spu_nmsub(fy, fg, fhalf);
96 fd = spu_nmsub(fg, fg, fx);
97
98 fy = spu_madd(fy2, fe, fy);
99 fg = spu_madd(fy, fd, fg); /* 22-bit approximation */
100
101 dy = spu_extend(fy);
102 dg = spu_extend(fg);
103
104 /* Perform two double precision Newton-Raphson iteration to improve
105 * accuracy to about 44 and 88 bits repectively.
106 */
107 dy2 = spu_add(dy, dy);
108 de = spu_nmsub(dy, dg, dhalf);
109 dd = spu_nmsub(dg, dg, dx);
110 dy = spu_madd(dy2, de, dy);
111 dg = spu_madd(dy, dd, dg); /* 44 bit approximation */
112
113 dd = spu_nmsub(dg, dg, dx);
114 dg = spu_madd(dy, dd, dg); /* full double precision approximation */
115
116
117 /* Compute the expected exponent assuming that it is not a special value.
118 * See special value handling below.
119 */
120 bias_exp = spu_rlmaska(spu_sub((vec_int4)spu_and((vec_ullong2)in, mask),
121 (vec_int4)spu_splats(0x3FE0000000000000ULL)),
122 -1);
123
124 /* Adjust the exponent bias if the input was denormalized */
125 bias_exp = spu_sub(bias_exp, (vec_int4)spu_and(spu_splats(0x01A0000000000000ULL), denorm));
126
127 dg = (vec_double2)spu_add((vec_int4)dg, bias_exp);
128
129 /* Handle special inputs. These include:
130 *
131 * input output
132 * ========= =========
133 * -0 -0
134 * 0 0
135 * +infinity +infinity
136 * NaN NaN
137 * <0 NaN
138 */
139 exp = spu_shuffle(exp, exp, ((vec_uchar16) { 0,1,2,3,0,1,2,3, 8,9,10,11,8,9,10,11 }));
140
141 neg = (vec_double2)spu_rlmaska((vec_int4)exp, -31);
142 nochange = spu_or((vec_ullong2)spu_cmpeq(exp, 0x7FF00000),
143 spu_cmpeq(in, spu_splats(0.0)));
144
145 dg = spu_sel(spu_or(dg, neg), in, nochange);
146
147 return (dg);
148 }
149 #endif /* _SQRTD2_H_ */
150 #endif /* __SPU__ */
151
