xref: /openbmc/linux/arch/mips/math-emu/dp_sqrt.c (revision e23feb16)
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 
29 static 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 
37 ieee754dp 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