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{
40	struct _ieee754_csr oldcsr;
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}
166