1/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrtf.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 */
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16#include "libm.h"
17
18static const float tiny = 1.0e-30;
19
20float sqrtf(float x)
21{
22	float z;
23	int32_t sign = (int)0x80000000;
24	int32_t ix,s,q,m,t,i;
25	uint32_t r;
26
27	GET_FLOAT_WORD(ix, x);
28
29	/* take care of Inf and NaN */
30	if ((ix&0x7f800000) == 0x7f800000)
31		return x*x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
32
33	/* take care of zero */
34	if (ix <= 0) {
35		if ((ix&~sign) == 0)
36			return x;  /* sqrt(+-0) = +-0 */
37		if (ix < 0)
38			return (x-x)/(x-x);  /* sqrt(-ve) = sNaN */
39	}
40	/* normalize x */
41	m = ix>>23;
42	if (m == 0) {  /* subnormal x */
43		for (i = 0; (ix&0x00800000) == 0; i++)
44			ix<<=1;
45		m -= i - 1;
46	}
47	m -= 127;  /* unbias exponent */
48	ix = (ix&0x007fffff)|0x00800000;
49	if (m&1)  /* odd m, double x to make it even */
50		ix += ix;
51	m >>= 1;  /* m = [m/2] */
52
53	/* generate sqrt(x) bit by bit */
54	ix += ix;
55	q = s = 0;       /* q = sqrt(x) */
56	r = 0x01000000;  /* r = moving bit from right to left */
57
58	while (r != 0) {
59		t = s + r;
60		if (t <= ix) {
61			s = t+r;
62			ix -= t;
63			q += r;
64		}
65		ix += ix;
66		r >>= 1;
67	}
68
69	/* use floating add to find out rounding direction */
70	if (ix != 0) {
71		z = 1.0f - tiny; /* raise inexact flag */
72		if (z >= 1.0f) {
73			z = 1.0f + tiny;
74			if (z > 1.0f)
75				q += 2;
76			else
77				q += q & 1;
78		}
79	}
80	ix = (q>>1) + 0x3f000000;
81	ix += m << 23;
82	SET_FLOAT_WORD(z, ix);
83	return z;
84}
85