1 /* origin: OpenBSD /usr/src/lib/libm/src/s_catanl.c */
2 /*
3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4 *
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.
8 *
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.
16 */
17 /*
18 * Complex circular arc tangent
19 *
20 *
21 * SYNOPSIS:
22 *
23 * long double complex catanl();
24 * long double complex z, w;
25 *
26 * w = catanl( z );
27 *
28 *
29 * DESCRIPTION:
30 *
31 * If
32 * z = x + iy,
33 *
34 * then
35 * 1 ( 2x )
36 * Re w = - arctan(-----------) + k PI
37 * 2 ( 2 2)
38 * (1 - x - y )
39 *
40 * ( 2 2)
41 * 1 (x + (y+1) )
42 * Im w = - log(------------)
43 * 4 ( 2 2)
44 * (x + (y-1) )
45 *
46 * Where k is an arbitrary integer.
47 *
48 *
49 * ACCURACY:
50 *
51 * Relative error:
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().
58 */
59 60 #include <complex.h>
61 #include <float.h>
62 #include "complex_impl.h"
63 64 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
65 long double complex catanl(long double complex z)
66 {
67 return catan(z);
68 }
69 #else
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;
74 75 static long double redupil(long double x)
76 {
77 long double t;
78 long i;
79 80 t = x / PIL;
81 if (t >= 0.0L)
82 t += 0.5L;
83 else
84 t -= 0.5L;
85 86 i = t; /* the multiple */
87 t = i;
88 t = ((x - t * DP1) - t * DP2) - t * DP3;
89 return t;
90 }
91 92 long double complex catanl(long double complex z)
93 {
94 long double complex w;
95 long double a, t, x, x2, y;
96 97 x = creall(z);
98 y = cimagl(z);
99 100 x2 = x * x;
101 a = 1.0L - x2 - (y * y);
102 103 t = atan2l(2.0L * x, a) * 0.5L;
104 w = redupil(t);
105 106 t = y - 1.0L;
107 a = x2 + (t * t);
108 109 t = y + 1.0L;
110 a = (x2 + (t * t)) / a;
111 w = CMPLXF(w, 0.25L * logl(a));
112 return w;
113 }
114 #endif
115