1 // SPDX-License-Identifier: GPL-2.0-only
2 /* IEEE754 floating point arithmetic
3  * double precision square root
4  */
5 /*
6  * MIPS floating point support
7  * Copyright (C) 1994-2000 Algorithmics Ltd.
8  */
9 
10 #include "ieee754dp.h"
11 
12 static const unsigned int table[] = {
13 	0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
14 	29598, 36145, 43202, 50740, 58733, 67158, 75992,
15 	85215, 83599, 71378, 60428, 50647, 41945, 34246,
16 	27478, 21581, 16499, 12183, 8588, 5674, 3403,
17 	1742, 661, 130
18 };
19 
ieee754dp_sqrt(union ieee754dp x)20 union ieee754dp ieee754dp_sqrt(union ieee754dp x)
21 {
22 	struct _ieee754_csr oldcsr;
23 	union ieee754dp y, z, t;
24 	unsigned int scalx, yh;
25 	COMPXDP;
26 
27 	EXPLODEXDP;
28 	ieee754_clearcx();
29 	FLUSHXDP;
30 
31 	/* x == INF or NAN? */
32 	switch (xc) {
33 	case IEEE754_CLASS_SNAN:
34 		return ieee754dp_nanxcpt(x);
35 
36 	case IEEE754_CLASS_QNAN:
37 		/* sqrt(Nan) = Nan */
38 		return x;
39 
40 	case IEEE754_CLASS_ZERO:
41 		/* sqrt(0) = 0 */
42 		return x;
43 
44 	case IEEE754_CLASS_INF:
45 		if (xs) {
46 			/* sqrt(-Inf) = Nan */
47 			ieee754_setcx(IEEE754_INVALID_OPERATION);
48 			return ieee754dp_indef();
49 		}
50 		/* sqrt(+Inf) = Inf */
51 		return x;
52 
53 	case IEEE754_CLASS_DNORM:
54 		DPDNORMX;
55 		fallthrough;
56 	case IEEE754_CLASS_NORM:
57 		if (xs) {
58 			/* sqrt(-x) = Nan */
59 			ieee754_setcx(IEEE754_INVALID_OPERATION);
60 			return ieee754dp_indef();
61 		}
62 		break;
63 	}
64 
65 	/* save old csr; switch off INX enable & flag; set RN rounding */
66 	oldcsr = ieee754_csr;
67 	ieee754_csr.mx &= ~IEEE754_INEXACT;
68 	ieee754_csr.sx &= ~IEEE754_INEXACT;
69 	ieee754_csr.rm = FPU_CSR_RN;
70 
71 	/* adjust exponent to prevent overflow */
72 	scalx = 0;
73 	if (xe > 512) {		/* x > 2**-512? */
74 		xe -= 512;	/* x = x / 2**512 */
75 		scalx += 256;
76 	} else if (xe < -512) { /* x < 2**-512? */
77 		xe += 512;	/* x = x * 2**512 */
78 		scalx -= 256;
79 	}
80 
81 	x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
82 	y = x;
83 
84 	/* magic initial approximation to almost 8 sig. bits */
85 	yh = y.bits >> 32;
86 	yh = (yh >> 1) + 0x1ff80000;
87 	yh = yh - table[(yh >> 15) & 31];
88 	y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);
89 
90 	/* Heron's rule once with correction to improve to ~18 sig. bits */
91 	/* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
92 	t = ieee754dp_div(x, y);
93 	y = ieee754dp_add(y, t);
94 	y.bits -= 0x0010000600000000LL;
95 	y.bits &= 0xffffffff00000000LL;
96 
97 	/* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
98 	/* t=y*y; z=t;	pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
99 	t = ieee754dp_mul(y, y);
100 	z = t;
101 	t.bexp += 0x001;
102 	t = ieee754dp_add(t, z);
103 	z = ieee754dp_mul(ieee754dp_sub(x, z), y);
104 
105 	/* t=z/(t+x) ;	pt[n0]+=0x00100000; y+=t; */
106 	t = ieee754dp_div(z, ieee754dp_add(t, x));
107 	t.bexp += 0x001;
108 	y = ieee754dp_add(y, t);
109 
110 	/* twiddle last bit to force y correctly rounded */
111 
112 	/* set RZ, clear INEX flag */
113 	ieee754_csr.rm = FPU_CSR_RZ;
114 	ieee754_csr.sx &= ~IEEE754_INEXACT;
115 
116 	/* t=x/y; ...chopped quotient, possibly inexact */
117 	t = ieee754dp_div(x, y);
118 
119 	if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
120 
121 		if (!(ieee754_csr.sx & IEEE754_INEXACT))
122 			/* t = t-ulp */
123 			t.bits -= 1;
124 
125 		/* add inexact to result status */
126 		oldcsr.cx |= IEEE754_INEXACT;
127 		oldcsr.sx |= IEEE754_INEXACT;
128 
129 		switch (oldcsr.rm) {
130 		case FPU_CSR_RU:
131 			y.bits += 1;
132 			fallthrough;
133 		case FPU_CSR_RN:
134 			t.bits += 1;
135 			break;
136 		}
137 
138 		/* y=y+t; ...chopped sum */
139 		y = ieee754dp_add(y, t);
140 
141 		/* adjust scalx for correctly rounded sqrt(x) */
142 		scalx -= 1;
143 	}
144 
145 	/* py[n0]=py[n0]+scalx; ...scale back y */
146 	y.bexp += scalx;
147 
148 	/* restore rounding mode, possibly set inexact */
149 	ieee754_csr = oldcsr;
150 
151 	return y;
152 }
153