xref: /openbmc/linux/arch/mips/math-emu/dp_sqrt.c (revision 22246614)
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 
30 static 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 
38 ieee754dp 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