1 /*
2 (C) Copyright 2001,2006,
3 International Business Machines Corporation,
4 Sony Computer Entertainment, Incorporated,
5 Toshiba Corporation,
6
7 All rights reserved.
8
9 Redistribution and use in source and binary forms, with or without
10 modification, are permitted provided that the following conditions are met:
11
12 * Redistributions of source code must retain the above copyright notice,
13 this list of conditions and the following disclaimer.
14 * Redistributions in binary form must reproduce the above copyright
15 notice, this list of conditions and the following disclaimer in the
16 documentation and/or other materials provided with the distribution.
17 * Neither the names of the copyright holders nor the names of their
18 contributors may be used to endorse or promote products derived from this
19 software without specific prior written permission.
20
21 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
22 IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
23 TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
24 PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
25 OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
26 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
27 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
28 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
29 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
30 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
31 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
32 */
33 #ifndef _SQRT_H_
34 #define _SQRT_H_ 1
35
36 /*
37 * FUNCTION
38 * double _sqrt(double in)
39 *
40 * DESCRIPTION
41 * _sqrt computes the square root of the input "in" and returns the
42 * result.
43 */
44 #include <spu_intrinsics.h>
45 #include "headers/vec_literal.h"
46 #include "headers/dom_chkd_less_than.h"
47
_sqrt(double in)48 static __inline double _sqrt(double in)
49 {
50 vec_int4 bias_exp;
51 vec_uint4 exp;
52 vec_float4 fx, fg, fy, fd, fe, fy2, fhalf;
53 vec_ullong2 nochange;
54 vec_ullong2 mask = VEC_SPLAT_U64(0x7FE0000000000000ULL);
55 vec_double2 x, dx, de, dd, dy, dg, dy2, dhalf;
56 vec_double2 denorm, neg;
57 vec_double2 vc = { 0.0, 0.0 };
58
59 fhalf = VEC_SPLAT_F32(0.5f);
60 dhalf = VEC_SPLAT_F64(0.5);
61
62 /* Coerce the input, in, into the argument reduced space [0.5, 2.0).
63 */
64 x = spu_promote(in, 0);
65 dx = spu_sel(x, dhalf, mask);
66
67 /* Compute an initial single precision guess for the square root (fg)
68 * and half reciprocal (fy2).
69 */
70 fx = spu_roundtf(dx);
71
72 fy2 = spu_rsqrte(fx);
73 fy = spu_mul(fy2, fhalf);
74 fg = spu_mul(fy2, fx); /* 12-bit approximation to sqrt(cx) */
75
76 /* Perform one single precision Newton-Raphson iteration to improve
77 * accuracy to about 22 bits.
78 */
79 fe = spu_nmsub(fy, fg, fhalf);
80 fd = spu_nmsub(fg, fg, fx);
81
82 fy = spu_madd(fy2, fe, fy);
83 fg = spu_madd(fy, fd, fg); /* 22-bit approximation */
84
85 dy = spu_extend(fy);
86 dg = spu_extend(fg);
87
88 /* Perform two double precision Newton-Raphson iteration to improve
89 * accuracy to about 44 and 88 bits repectively.
90 */
91 dy2 = spu_add(dy, dy);
92 de = spu_nmsub(dy, dg, dhalf);
93 dd = spu_nmsub(dg, dg, dx);
94 dy = spu_madd(dy2, de, dy);
95 dg = spu_madd(dy, dd, dg); /* 44 bit approximation */
96
97 dd = spu_nmsub(dg, dg, dx);
98 dg = spu_madd(dy, dd, dg); /* full double precision approximation */
99
100
101 /* Compute the expected exponent assuming that it is not a special value.
102 * See special value handling below.
103 */
104 bias_exp = spu_rlmaska(spu_sub((vec_int4)spu_and((vec_ullong2)x, mask),
105 (vec_int4)VEC_SPLAT_U64(0x3FE0000000000000ULL)), -1);
106 dg = (vec_double2)spu_add((vec_int4)dg, bias_exp);
107
108
109 /* Handle special inputs. These include:
110 *
111 * input output
112 * ========= =========
113 * -0 -0
114 * +infinity +infinity
115 * NaN NaN
116 * <0 NaN
117 * denorm zero
118 */
119 exp = (vec_uint4)spu_and((vec_ullong2)x, VEC_SPLAT_U64(0xFFF0000000000000ULL));
120 exp = spu_shuffle(exp, exp, VEC_LITERAL(vec_uchar16, 0,1,2,3,0,1,2,3, 8,9,10,11,8,9,10,11));
121
122 neg = (vec_double2)spu_rlmaska((vec_int4)exp, -31);
123 denorm = (vec_double2)spu_rlmask(spu_cmpeq(spu_sl(exp, 1), 0), VEC_LITERAL(vec_int4, -1,0,-1,0));
124
125 nochange = (vec_ullong2)spu_cmpeq(exp, 0x7FF00000);
126
127 dg = spu_sel(spu_andc(spu_or(dg, neg), denorm), x, nochange);
128
129 #ifndef _IEEE_LIBM
130 dom_chkd_less_than(spu_splats(in), vc);
131 #endif
132 return (spu_extract(dg, 0));
133 }
134 #endif /* _SQRT_H_ */
135