xref: /illumos-gate/usr/src/lib/libm/common/complex/ctanhl.c (revision 66582b606a8194f7f3ba5b3a3a6dca5b0d346361)
1 /*
2  * CDDL HEADER START
3  *
4  * The contents of this file are subject to the terms of the
5  * Common Development and Distribution License (the "License").
6  * You may not use this file except in compliance with the License.
7  *
8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9  * or http://www.opensolaris.org/os/licensing.
10  * See the License for the specific language governing permissions
11  * and limitations under the License.
12  *
13  * When distributing Covered Code, include this CDDL HEADER in each
14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15  * If applicable, add the following below this CDDL HEADER, with the
16  * fields enclosed by brackets "[]" replaced with your own identifying
17  * information: Portions Copyright [yyyy] [name of copyright owner]
18  *
19  * CDDL HEADER END
20  */
21 
22 /*
23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24  */
25 /*
26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27  * Use is subject to license terms.
28  */
29 
30 #pragma weak __ctanhl = ctanhl
31 
32 #include "libm.h"	/* expl/expm1l/fabsl/isinfl/isnanl/sincosl/sinl/tanhl */
33 #include "complex_wrapper.h"
34 #include "longdouble.h"
35 
36 /* INDENT OFF */
37 static const long double four = 4.0L, two = 2.0L, one = 1.0L, zero = 0.0L;
38 /* INDENT ON */
39 
40 ldcomplex
41 ctanhl(ldcomplex z) {
42 	long double r, u, v, t, x, y, S, C;
43 	int hx, ix, hy, iy;
44 	ldcomplex ans;
45 
46 	x = LD_RE(z);
47 	y = LD_IM(z);
48 	hx = HI_XWORD(x);
49 	ix = hx & 0x7fffffff;
50 	hy = HI_XWORD(y);
51 	iy = hy & 0x7fffffff;
52 	x = fabsl(x);
53 	y = fabsl(y);
54 
55 	if (y == zero) {	/* ctanh(x,0) = (x,0) for x = 0 or NaN */
56 		LD_RE(ans) = tanhl(x);
57 		LD_IM(ans) = zero;
58 	} else if (iy >= 0x7fff0000) {	/* y is inf or NaN */
59 		if (ix < 0x7fff0000)	/* catanh(finite x,inf/nan) is nan */
60 			LD_RE(ans) = LD_IM(ans) = y - y;
61 		else if (isinfl(x)) {	/* x is inf */
62 			LD_RE(ans) = one;
63 			LD_IM(ans) = zero;
64 		} else {
65 			LD_RE(ans) = x + y;
66 			LD_IM(ans) = y - y;
67 		}
68 	} else if (ix >= 0x4004e000) {
69 		/* INDENT OFF */
70 		/*
71 		 * |x| > 60 = prec/2 (14,28,34,60)
72 		 * ctanh z ~ 1 + i (sin2y)/(exp(2x))
73 		 */
74 		/* INDENT ON */
75 		LD_RE(ans) = one;
76 		if (iy < 0x7ffe0000)	/* t = sin(2y) */
77 			S = sinl(y + y);
78 		else {
79 			(void) sincosl(y, &S, &C);
80 			S = (S + S) * C;
81 		}
82 		if (ix >= 0x7ffe0000) {	/* |x| > max/2 */
83 			if (ix >= 0x7fff0000) {	/* |x| is inf or NaN */
84 				if (isnanl(x))	/* x is NaN */
85 					LD_RE(ans) = LD_IM(ans) = x + y;
86 				else
87 					LD_IM(ans) = zero * S;	/* x is inf */
88 			} else
89 				LD_IM(ans) = S * expl(-x);	/* underflow */
90 		} else
91 			LD_IM(ans) = (S + S) * expl(-(x + x));
92 							/* 2 sin 2y / exp(2x) */
93 	} else {
94 		/* INDENT OFF */
95 		/*
96 		 *                        t*t+2t
97 		 *    ctanh z = ---------------------------
98 		 *               t*t+[4(t+1)(cos y)](cos y)
99 		 *
100 		 *                  [4(t+1)(cos y)]*(sin y)
101 		 *              i --------------------------
102 		 *                t*t+[4(t+1)(cos y)](cos y)
103 		 */
104 		/* INDENT ON */
105 		sincosl(y, &S, &C);
106 		t = expm1l(x + x);
107 		r = (four * C) * (t + one);
108 		u = t * t;
109 		v = one / (u + r * C);
110 		LD_RE(ans) = (u + two * t) * v;
111 		LD_IM(ans) = (r * S) * v;
112 	}
113 	if (hx < 0)
114 		LD_RE(ans) = -LD_RE(ans);
115 	if (hy < 0)
116 		LD_IM(ans) = -LD_IM(ans);
117 	return (ans);
118 }
119