1 /* origin: OpenBSD /usr/src/lib/libm/src/s_catan.c */
3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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.
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.
18 * Complex circular arc tangent
23 * double complex catan();
24 * double complex z, w;
36 * Re w = - arctan(-----------) + k PI
42 * Im w = - log(------------)
46 * Where k is an arbitrary integer.
48 * catan(z) = -i catanh(iz).
53 * arithmetic domain # trials peak rms
54 * DEC -10,+10 5900 1.3e-16 7.8e-18
55 * IEEE -10,+10 30000 2.3e-15 8.5e-17
56 * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
57 * had peak relative error 1.5e-16, rms relative error
58 * 2.9e-17. See also clog().
63 #define MAXNUM 1.0e308
65 static const double DP1 = 3.14159265160560607910E0;
66 static const double DP2 = 1.98418714791870343106E-9;
67 static const double DP3 = 1.14423774522196636802E-17;
69 static double _redupi(double x)
80 i = t; /* the multiple */
82 t = ((x - t * DP1) - t * DP2) - t * DP3;
86 double complex catan(double complex z)
89 double a, t, x, x2, y;
94 if (x == 0.0 && y > 1.0)
98 a = 1.0 - x2 - (y * y);
102 t = 0.5 * atan2(2.0 * x, a);
112 w = w + (0.25 * log(a)) * I;
117 w = MAXNUM + MAXNUM * I;