1/*	$OpenBSD: s_csqrt.c,v 1.8 2016/09/12 19:47:02 guenther Exp $	*/
2/*
3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4 *
5 * Permission to use, copy, modify, and distribute this software for any
6 * purpose with or without fee is hereby granted, provided that the above
7 * copyright notice and this permission notice appear in all copies.
8 *
9 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
16 */
17
18/*							csqrt()
19 *
20 *	Complex square root
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * double complex csqrt();
27 * double complex z, w;
28 *
29 * w = csqrt (z);
30 *
31 *
32 *
33 * DESCRIPTION:
34 *
35 *
36 * If z = x + iy,  r = |z|, then
37 *
38 *                       1/2
39 * Re w  =  [ (r + x)/2 ]   ,
40 *
41 *                       1/2
42 * Im w  =  [ (r - x)/2 ]   .
43 *
44 * Cancellation error in r-x or r+x is avoided by using the
45 * identity  2 Re w Im w  =  y.
46 *
47 * Note that -w is also a square root of z.  The root chosen
48 * is always in the right half plane and Im w has the same sign as y.
49 *
50 *
51 *
52 * ACCURACY:
53 *
54 *                      Relative error:
55 * arithmetic   domain     # trials      peak         rms
56 *    DEC       -10,+10     25000       3.2e-17     9.6e-18
57 *    IEEE      -10,+10   1,000,000     2.9e-16     6.1e-17
58 *
59 */
60
61#include <complex.h>
62#include <float.h>
63#include <math.h>
64
65double complex
66csqrt(double complex z)
67{
68	double complex w;
69	double x, y, r, t, scale;
70
71	x = creal (z);
72	y = cimag (z);
73
74	if (y == 0.0) {
75		if (x == 0.0) {
76			w = 0.0 + y * I;
77		}
78		else {
79			r = fabs (x);
80			r = sqrt (r);
81			if (x < 0.0) {
82				w = 0.0 + copysign(r, y) * I;
83			}
84			else {
85				w = r + y * I;
86			}
87		}
88		return (w);
89	}
90	if (x == 0.0) {
91		r = fabs (y);
92		r = sqrt (0.5*r);
93		if (y > 0)
94			w = r + r * I;
95		else
96			w = r - r * I;
97		return (w);
98	}
99	/* Rescale to avoid internal overflow or underflow.  */
100	if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) {
101		x *= 0.25;
102		y *= 0.25;
103		scale = 2.0;
104	}
105	else {
106		x *= 1.8014398509481984e16;  /* 2^54 */
107		y *= 1.8014398509481984e16;
108		scale = 7.450580596923828125e-9; /* 2^-27 */
109#if 0
110		x *= 4.0;
111		y *= 4.0;
112		scale = 0.5;
113#endif
114	}
115	w = x + y * I;
116	r = cabs(w);
117	if (x > 0) {
118		t = sqrt(0.5 * r + 0.5 * x);
119		r = scale * fabs((0.5 * y) / t);
120		t *= scale;
121	}
122	else {
123		r = sqrt( 0.5 * r - 0.5 * x );
124		t = scale * fabs( (0.5 * y) / r );
125		r *= scale;
126	}
127	if (y < 0)
128		w = t - r * I;
129	else
130		w = t + r * I;
131	return (w);
132}
133DEF_STD(csqrt);
134LDBL_MAYBE_CLONE(csqrt);
135