xref: /freebsd/lib/msun/src/s_ctanhf.c (revision 1c05a6ea6b849ff95e539c31adea887c644a6a01)
1 /*-
2  * Copyright (c) 2011 David Schultz
3  * All rights reserved.
4  *
5  * Redistribution and use in source and binary forms, with or without
6  * modification, are permitted provided that the following conditions
7  * are met:
8  * 1. Redistributions of source code must retain the above copyright
9  *    notice unmodified, this list of conditions, and the following
10  *    disclaimer.
11  * 2. Redistributions in binary form must reproduce the above copyright
12  *    notice, this list of conditions and the following disclaimer in the
13  *    documentation and/or other materials provided with the distribution.
14  *
15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25  */
26 
27 /*
28  * Hyperbolic tangent of a complex argument z.  See s_ctanh.c for details.
29  */
30 
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
33 
34 #include <complex.h>
35 #include <math.h>
36 
37 #include "math_private.h"
38 
39 float complex
40 ctanhf(float complex z)
41 {
42 	float x, y;
43 	float t, beta, s, rho, denom;
44 	uint32_t hx, ix;
45 
46 	x = crealf(z);
47 	y = cimagf(z);
48 
49 	GET_FLOAT_WORD(hx, x);
50 	ix = hx & 0x7fffffff;
51 
52 	if (ix >= 0x7f800000) {
53 		if (ix & 0x7fffff)
54 			return (CMPLXF((x + 0) * (y + 0),
55 			    y == 0 ? y : (x + 0) * (y + 0)));
56 		SET_FLOAT_WORD(x, hx - 0x40000000);
57 		return (CMPLXF(x,
58 		    copysignf(0, isinf(y) ? y : sinf(y) * cosf(y))));
59 	}
60 
61 	if (!isfinite(y))
62 		return (CMPLXF(y - y, y - y));
63 
64 	if (ix >= 0x41300000) {	/* |x| >= 11 */
65 		float exp_mx = expf(-fabsf(x));
66 		return (CMPLXF(copysignf(1, x),
67 		    4 * sinf(y) * cosf(y) * exp_mx * exp_mx));
68 	}
69 
70 	t = tanf(y);
71 	beta = 1.0 + t * t;
72 	s = sinhf(x);
73 	rho = sqrtf(1 + s * s);
74 	denom = 1 + beta * s * s;
75 	return (CMPLXF((beta * rho * s) / denom, t / denom));
76 }
77 
78 float complex
79 ctanf(float complex z)
80 {
81 
82 	z = ctanhf(CMPLXF(cimagf(z), crealf(z)));
83 	return (CMPLXF(cimagf(z), crealf(z)));
84 }
85 
86