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
12static 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
20union 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