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review.evervolv.com / android_kernel_htc_msm8960 / 18eb0893c12898253c18ba23b51a6ea9a07ba4c7 / . / arch / mips / math-emu / dp_sqrt.c
blob: 032328c49888b21ec343341e6954f4d1d1317dd4 [file] [log] [blame]
Linus Torvalds1da177e2005-04-16 15:20:36 -0700[diff] [blame]1/* IEEE754 floating point arithmetic
2 * double precision square root
3 */
4/*
5 * MIPS floating point support
6 * Copyright (C) 1994-2000 Algorithmics Ltd.
7 * http://www.algor.co.uk
8 *
9 * ########################################################################
10 *
11 * This program is free software; you can distribute it and/or modify it
12 * under the terms of the GNU General Public License (Version 2) as
13 * published by the Free Software Foundation.
14 *
15 * This program is distributed in the hope it will be useful, but WITHOUT
16 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
17 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
18 * for more details.
19 *
20 * You should have received a copy of the GNU General Public License along
21 * with this program; if not, write to the Free Software Foundation, Inc.,
22 * 59 Temple Place - Suite 330, Boston MA 02111-1307, USA.
23 *
24 * ########################################################################
25 */
26
27
28#include "ieee754dp.h"
29
30static const unsigned table[] = {
31 0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
32 29598, 36145, 43202, 50740, 58733, 67158, 75992,
33 85215, 83599, 71378, 60428, 50647, 41945, 34246,
34 27478, 21581, 16499, 12183, 8588, 5674, 3403,
35 1742, 661, 130
36};
37
38ieee754dp ieee754dp_sqrt(ieee754dp x)
39{
Ralf Baechlecd21dfc2005-04-28 13:39:10 +0000[diff] [blame]40 struct _ieee754_csr oldcsr;
Linus Torvalds1da177e2005-04-16 15:20:36 -0700[diff] [blame]41 ieee754dp y, z, t;
42 unsigned scalx, yh;
43 COMPXDP;
44
45 EXPLODEXDP;
46 CLEARCX;
47 FLUSHXDP;
48
49 /* x == INF or NAN? */
50 switch (xc) {
51 case IEEE754_CLASS_QNAN:
52 /* sqrt(Nan) = Nan */
53 return ieee754dp_nanxcpt(x, "sqrt");
54 case IEEE754_CLASS_SNAN:
55 SETCX(IEEE754_INVALID_OPERATION);
56 return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
57 case IEEE754_CLASS_ZERO:
58 /* sqrt(0) = 0 */
59 return x;
60 case IEEE754_CLASS_INF:
61 if (xs) {
62 /* sqrt(-Inf) = Nan */
63 SETCX(IEEE754_INVALID_OPERATION);
64 return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
65 }
66 /* sqrt(+Inf) = Inf */
67 return x;
68 case IEEE754_CLASS_DNORM:
69 DPDNORMX;
70 /* fall through */
71 case IEEE754_CLASS_NORM:
72 if (xs) {
73 /* sqrt(-x) = Nan */
74 SETCX(IEEE754_INVALID_OPERATION);
75 return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
76 }
77 break;
78 }
79
80 /* save old csr; switch off INX enable & flag; set RN rounding */
81 oldcsr = ieee754_csr;
82 ieee754_csr.mx &= ~IEEE754_INEXACT;
83 ieee754_csr.sx &= ~IEEE754_INEXACT;
84 ieee754_csr.rm = IEEE754_RN;
85
86 /* adjust exponent to prevent overflow */
87 scalx = 0;
88 if (xe > 512) { /* x > 2**-512? */
89 xe -= 512; /* x = x / 2**512 */
90 scalx += 256;
91 } else if (xe < -512) { /* x < 2**-512? */
92 xe += 512; /* x = x * 2**512 */
93 scalx -= 256;
94 }
95
96 y = x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
97
98 /* magic initial approximation to almost 8 sig. bits */
99 yh = y.bits >> 32;
100 yh = (yh >> 1) + 0x1ff80000;
101 yh = yh - table[(yh >> 15) & 31];
102 y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);
103
104 /* Heron's rule once with correction to improve to ~18 sig. bits */
105 /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
106 t = ieee754dp_div(x, y);
107 y = ieee754dp_add(y, t);
108 y.bits -= 0x0010000600000000LL;
109 y.bits &= 0xffffffff00000000LL;
110
111 /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
112 /* t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
113 z = t = ieee754dp_mul(y, y);
114 t.parts.bexp += 0x001;
115 t = ieee754dp_add(t, z);
116 z = ieee754dp_mul(ieee754dp_sub(x, z), y);
117
118 /* t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; */
119 t = ieee754dp_div(z, ieee754dp_add(t, x));
120 t.parts.bexp += 0x001;
121 y = ieee754dp_add(y, t);
122
123 /* twiddle last bit to force y correctly rounded */
124
125 /* set RZ, clear INEX flag */
126 ieee754_csr.rm = IEEE754_RZ;
127 ieee754_csr.sx &= ~IEEE754_INEXACT;
128
129 /* t=x/y; ...chopped quotient, possibly inexact */
130 t = ieee754dp_div(x, y);
131
132 if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
133
134 if (!(ieee754_csr.sx & IEEE754_INEXACT))
135 /* t = t-ulp */
136 t.bits -= 1;
137
138 /* add inexact to result status */
139 oldcsr.cx |= IEEE754_INEXACT;
140 oldcsr.sx |= IEEE754_INEXACT;
141
142 switch (oldcsr.rm) {
143 case IEEE754_RP:
144 y.bits += 1;
145 /* drop through */
146 case IEEE754_RN:
147 t.bits += 1;
148 break;
149 }
150
151 /* y=y+t; ...chopped sum */
152 y = ieee754dp_add(y, t);
153
154 /* adjust scalx for correctly rounded sqrt(x) */
155 scalx -= 1;
156 }
157
158 /* py[n0]=py[n0]+scalx; ...scale back y */
159 y.parts.bexp += scalx;
160
161 /* restore rounding mode, possibly set inexact */
162 ieee754_csr = oldcsr;
163
164 return y;
165}