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