1 // SPDX-License-Identifier: GPL-2.0-only
7  * Copyright (C) 1994-2000 Algorithmics Ltd.
20 union ieee754dp ieee754dp_sqrt(union ieee754dp x)  in ieee754dp_sqrt()  argument
23 	union ieee754dp y, z, t;  in ieee754dp_sqrt()  local
31 	/* x == INF or NAN? */  in ieee754dp_sqrt()
34 		return ieee754dp_nanxcpt(x);  in ieee754dp_sqrt()
38 		return x;  in ieee754dp_sqrt()
42 		return x;  in ieee754dp_sqrt()
46 			/* sqrt(-Inf) = Nan */  in ieee754dp_sqrt()
51 		return x;  in ieee754dp_sqrt()
58 			/* sqrt(-x) = Nan */  in ieee754dp_sqrt()
73 	if (xe > 512) {		/* x > 2**-512? */  in ieee754dp_sqrt()
74 		xe -= 512;	/* x = x / 2**512 */  in ieee754dp_sqrt()
76 	} else if (xe < -512) { /* x < 2**-512? */  in ieee754dp_sqrt()
77 		xe += 512;	/* x = x * 2**512 */  in ieee754dp_sqrt()
78 		scalx -= 256;  in ieee754dp_sqrt()
81 	x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);  in ieee754dp_sqrt()
82 	y = x;  in ieee754dp_sqrt()
85 	yh = y.bits >> 32;  in ieee754dp_sqrt()
87 	yh = yh - table[(yh >> 15) & 31];  in ieee754dp_sqrt()
88 	y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);  in ieee754dp_sqrt()
91 	/* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */  in ieee754dp_sqrt()
92 	t = ieee754dp_div(x, y);  in ieee754dp_sqrt()
93 	y = ieee754dp_add(y, t);  in ieee754dp_sqrt()
94 	y.bits -= 0x0010000600000000LL;  in ieee754dp_sqrt()
95 	y.bits &= 0xffffffff00000000LL;  in ieee754dp_sqrt()
97 	/* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */  in ieee754dp_sqrt()
98 	/* t=y*y; z=t;	pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */  in ieee754dp_sqrt()
99 	t = ieee754dp_mul(y, y);  in ieee754dp_sqrt()
103 	z = ieee754dp_mul(ieee754dp_sub(x, z), y);  in ieee754dp_sqrt()
105 	/* t=z/(t+x) ;	pt[n0]+=0x00100000; y+=t; */  in ieee754dp_sqrt()
106 	t = ieee754dp_div(z, ieee754dp_add(t, x));  in ieee754dp_sqrt()
108 	y = ieee754dp_add(y, t);  in ieee754dp_sqrt()
110 	/* twiddle last bit to force y correctly rounded */  in ieee754dp_sqrt()
116 	/* t=x/y; ...chopped quotient, possibly inexact */  in ieee754dp_sqrt()
117 	t = ieee754dp_div(x, y);  in ieee754dp_sqrt()
119 	if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {  in ieee754dp_sqrt()
122 			/* t = t-ulp */  in ieee754dp_sqrt()
123 			t.bits -= 1;  in ieee754dp_sqrt()
131 			y.bits += 1;  in ieee754dp_sqrt()
138 		/* y=y+t; ...chopped sum */  in ieee754dp_sqrt()
139 		y = ieee754dp_add(y, t);  in ieee754dp_sqrt()
141 		/* adjust scalx for correctly rounded sqrt(x) */  in ieee754dp_sqrt()
142 		scalx -= 1;  in ieee754dp_sqrt()
145 	/* py[n0]=py[n0]+scalx; ...scale back y */  in ieee754dp_sqrt()
146 	y.bexp += scalx;  in ieee754dp_sqrt()
151 	return y;  in ieee754dp_sqrt()