1 /* origin: OpenBSD /usr/src/lib/libm/src/s_catanf.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 * float complex catanf();
36 * Re w = - arctan(-----------) + k PI
42 * Im w = - log(------------)
46 * Where k is an arbitrary integer.
52 * arithmetic domain # trials peak rms
53 * IEEE -10,+10 30000 2.3e-6 5.2e-8
58 #define MAXNUMF 1.0e38F
60 static const double DP1 = 3.140625;
61 static const double DP2 = 9.67502593994140625E-4;
62 static const double DP3 = 1.509957990978376432E-7;
64 static float _redupif(float xx)
76 i = t; /* the multiple */
78 t = ((x - t * DP1) - t * DP2) - t * DP3;
82 float complex catanf(float complex z)
90 if ((x == 0.0f) && (y > 1.0f))
94 a = 1.0f - x2 - (y * y);
98 t = 0.5f * atan2f(2.0f * x, a);
107 a = (x2 + (t * t))/a;
108 w = w + (0.25f * logf (a)) * I;
113 w = MAXNUMF + MAXNUMF * I;