1/*	$OpenBSD: s_csqrtl.c,v 1.4 2016/09/12 19:47:02 guenther Exp $	*/
2
3/*
4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5 *
6 * Permission to use, copy, modify, and distribute this software for any
7 * purpose with or without fee is hereby granted, provided that the above
8 * copyright notice and this permission notice appear in all copies.
9 *
10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17 */
18
19/*							csqrtl()
20 *
21 *	Complex square root
22 *
23 *
24 *
25 * SYNOPSIS:
26 *
27 * long double complex csqrtl();
28 * long double complex z, w;
29 *
30 * w = csqrtl( z );
31 *
32 *
33 *
34 * DESCRIPTION:
35 *
36 *
37 * If z = x + iy,  r = |z|, then
38 *
39 *                       1/2
40 * Re w  =  [ (r + x)/2 ]   ,
41 *
42 *                       1/2
43 * Im w  =  [ (r - x)/2 ]   .
44 *
45 * Cancellation error in r-x or r+x is avoided by using the
46 * identity  2 Re w Im w  =  y.
47 *
48 * Note that -w is also a square root of z.  The root chosen
49 * is always in the right half plane and Im w has the same sign as y.
50 *
51 *
52 *
53 * ACCURACY:
54 *
55 *                      Relative error:
56 * arithmetic   domain     # trials      peak         rms
57 *    IEEE      -10,+10     500000      1.1e-19     3.0e-20
58 *
59 */
60
61#include <complex.h>
62#include <math.h>
63
64long double complex
65csqrtl(long double complex z)
66{
67	long double complex w;
68	long double x, y, r, t, scale;
69
70	x = creall(z);
71	y = cimagl(z);
72
73	if (y == 0.0L) {
74		if (x < 0.0L) {
75			w = 0.0L + copysign(sqrtl(-x), y) * I;
76			return (w);
77		}
78		else {
79			w = sqrtl(x) + 0.0L * I;
80			return (w);
81		}
82	}
83
84	if (x == 0.0L) {
85		r = fabsl(y);
86		r = sqrtl(0.5L * r);
87		if (y > 0.0L)
88			w = r + r * I;
89		else
90			w = r - r * I;
91		return (w);
92	}
93
94	/* Rescale to avoid internal overflow or underflow.  */
95	if ((fabsl(x) > 4.0L) || (fabsl(y) > 4.0L)) {
96		x *= 0.25L;
97		y *= 0.25L;
98		scale = 2.0L;
99	}
100	else {
101#if 1
102		x *= 7.3786976294838206464e19;  /* 2^66 */
103		y *= 7.3786976294838206464e19;
104		scale = 1.16415321826934814453125e-10;  /* 2^-33 */
105#else
106		x *= 4.0L;
107		y *= 4.0L;
108		scale = 0.5L;
109#endif
110	}
111	w = x + y * I;
112	r = cabsl(w);
113	if (x > 0) {
114		t = sqrtl(0.5L * r + 0.5L * x);
115		r = scale * fabsl((0.5L * y) / t);
116		t *= scale;
117	}
118	else {
119		r = sqrtl(0.5L * r - 0.5L * x);
120		t = scale * fabsl((0.5L * y) / r);
121		r *= scale;
122	}
123	if (y < 0)
124		w = t - r * I;
125	else
126		w = t + r * I;
127	return (w);
128}
129DEF_STD(csqrtl);
130