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 *
8 *  This program is free software; you can distribute it and/or modify it
9 *  under the terms of the GNU General Public License (Version 2) as
10 *  published by the Free Software Foundation.
11 *
12 *  This program is distributed in the hope it will be useful, but WITHOUT
13 *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 *  FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
15 *  for more details.
16 *
17 *  You should have received a copy of the GNU General Public License along
18 *  with this program; if not, write to the Free Software Foundation, Inc.,
19 *  51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA.
20 */
21
22#include "ieee754dp.h"
23
24static const unsigned table[] = {
25	0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
26	29598, 36145, 43202, 50740, 58733, 67158, 75992,
27	85215, 83599, 71378, 60428, 50647, 41945, 34246,
28	27478, 21581, 16499, 12183, 8588, 5674, 3403,
29	1742, 661, 130
30};
31
32union ieee754dp ieee754dp_sqrt(union ieee754dp x)
33{
34	struct _ieee754_csr oldcsr;
35	union ieee754dp y, z, t;
36	unsigned scalx, yh;
37	COMPXDP;
38
39	EXPLODEXDP;
40	ieee754_clearcx();
41	FLUSHXDP;
42
43	/* x == INF or NAN? */
44	switch (xc) {
45	case IEEE754_CLASS_SNAN:
46		return ieee754dp_nanxcpt(x);
47
48	case IEEE754_CLASS_QNAN:
49		/* sqrt(Nan) = Nan */
50		return x;
51
52	case IEEE754_CLASS_ZERO:
53		/* sqrt(0) = 0 */
54		return x;
55
56	case IEEE754_CLASS_INF:
57		if (xs) {
58			/* sqrt(-Inf) = Nan */
59			ieee754_setcx(IEEE754_INVALID_OPERATION);
60			return ieee754dp_indef();
61		}
62		/* sqrt(+Inf) = Inf */
63		return x;
64
65	case IEEE754_CLASS_DNORM:
66		DPDNORMX;
67		/* fall through */
68
69	case IEEE754_CLASS_NORM:
70		if (xs) {
71			/* sqrt(-x) = Nan */
72			ieee754_setcx(IEEE754_INVALID_OPERATION);
73			return ieee754dp_indef();
74		}
75		break;
76	}
77
78	/* save old csr; switch off INX enable & flag; set RN rounding */
79	oldcsr = ieee754_csr;
80	ieee754_csr.mx &= ~IEEE754_INEXACT;
81	ieee754_csr.sx &= ~IEEE754_INEXACT;
82	ieee754_csr.rm = FPU_CSR_RN;
83
84	/* adjust exponent to prevent overflow */
85	scalx = 0;
86	if (xe > 512) {		/* x > 2**-512? */
87		xe -= 512;	/* x = x / 2**512 */
88		scalx += 256;
89	} else if (xe < -512) { /* x < 2**-512? */
90		xe += 512;	/* x = x * 2**512 */
91		scalx -= 256;
92	}
93
94	y = x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
95
96	/* magic initial approximation to almost 8 sig. bits */
97	yh = y.bits >> 32;
98	yh = (yh >> 1) + 0x1ff80000;
99	yh = yh - table[(yh >> 15) & 31];
100	y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);
101
102	/* Heron's rule once with correction to improve to ~18 sig. bits */
103	/* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
104	t = ieee754dp_div(x, y);
105	y = ieee754dp_add(y, t);
106	y.bits -= 0x0010000600000000LL;
107	y.bits &= 0xffffffff00000000LL;
108
109	/* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
110	/* t=y*y; z=t;	pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
111	z = t = ieee754dp_mul(y, y);
112	t.bexp += 0x001;
113	t = ieee754dp_add(t, z);
114	z = ieee754dp_mul(ieee754dp_sub(x, z), y);
115
116	/* t=z/(t+x) ;	pt[n0]+=0x00100000; y+=t; */
117	t = ieee754dp_div(z, ieee754dp_add(t, x));
118	t.bexp += 0x001;
119	y = ieee754dp_add(y, t);
120
121	/* twiddle last bit to force y correctly rounded */
122
123	/* set RZ, clear INEX flag */
124	ieee754_csr.rm = FPU_CSR_RZ;
125	ieee754_csr.sx &= ~IEEE754_INEXACT;
126
127	/* t=x/y; ...chopped quotient, possibly inexact */
128	t = ieee754dp_div(x, y);
129
130	if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
131
132		if (!(ieee754_csr.sx & IEEE754_INEXACT))
133			/* t = t-ulp */
134			t.bits -= 1;
135
136		/* add inexact to result status */
137		oldcsr.cx |= IEEE754_INEXACT;
138		oldcsr.sx |= IEEE754_INEXACT;
139
140		switch (oldcsr.rm) {
141		case FPU_CSR_RU:
142			y.bits += 1;
143			/* drop through */
144		case FPU_CSR_RN:
145			t.bits += 1;
146			break;
147		}
148
149		/* y=y+t; ...chopped sum */
150		y = ieee754dp_add(y, t);
151
152		/* adjust scalx for correctly rounded sqrt(x) */
153		scalx -= 1;
154	}
155
156	/* py[n0]=py[n0]+scalx; ...scale back y */
157	y.bexp += scalx;
158
159	/* restore rounding mode, possibly set inexact */
160	ieee754_csr = oldcsr;
161
162	return y;
163}
164