1 /* origin: OpenBSD /usr/src/lib/libm/src/s_catanl.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
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15 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
18 * Complex circular arc tangent
23 * long double complex catanl();
24 * long double complex z, w;
36 * Re w = - arctan(-----------) + k PI
42 * Im w = - log(------------)
46 * Where k is an arbitrary integer.
52 * arithmetic domain # trials peak rms
53 * DEC -10,+10 5900 1.3e-16 7.8e-18
54 * IEEE -10,+10 30000 2.3e-15 8.5e-17
55 * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
56 * had peak relative error 1.5e-16, rms relative error
57 * 2.9e-17. See also clog().
64 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
65 long double complex catanl(long double complex z)
70 static const long double PIL = 3.141592653589793238462643383279502884197169L;
71 static const long double DP1 = 3.14159265358979323829596852490908531763125L;
72 static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
73 static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
75 static long double redupil(long double x)
86 i = t; /* the multiple */
88 t = ((x - t * DP1) - t * DP2) - t * DP3;
92 long double complex catanl(long double complex z)
94 long double complex w;
95 long double a, t, x, x2, y;
100 if ((x == 0.0L) && (y > 1.0L))
104 a = 1.0L - x2 - (y * y);
108 t = atan2l(2.0L * x, a) * 0.5L;
117 a = (x2 + (t * t)) / a;
118 w = w + (0.25L * logl(a)) * I;
123 w = LDBL_MAX + LDBL_MAX * I;