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
64 long double complex
csqrtl(long double complex z)65 csqrtl(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 }
129 DEF_STD(csqrtl);
130