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 __ctanh = ctanh
31
32/* INDENT OFF */
33/*
34 * dcomplex ctanh(dcomplex z);
35 *
36 *            tanh x  + i tan y      sinh 2x  +  i sin 2y
37 * ctanh z = --------------------- = --------------------
38 *           1 + i tanh(x)tan(y)       cosh 2x + cos 2y
39 *
40 * For |x| >= prec/2 (14,28,34,60 for single, double, double extended, quad),
41 * we use
42 *
43 *                         1   2x                              2 sin 2y
44 *    cosh 2x = sinh 2x = --- e    and hence  ctanh z = 1 + i -----------;
45 *                         2                                       2x
46 *                                                                e
47 *
48 * otherwise, to avoid cancellation, for |x| < prec/2,
49 *                              2x     2
50 *                            (e   - 1)        2       2
51 *    cosh 2x + cos 2y = 1 + ------------ + cos y - sin y
52 *                                 2x
53 *                              2 e
54 *
55 *                        1    2x     2  -2x         2
56 *                     = --- (e   - 1)  e     + 2 cos y
57 *                        2
58 * and
59 *
60 *                  [            2x      ]
61 *               1  [  2x       e   - 1  ]
62 *    sinh 2x = --- [ e  - 1 + --------- ]
63 *               2  [               2x   ]
64 *                  [              e     ]
65 *                                             2x
66 * Implementation notes:  let t = expm1(2x) = e   - 1, then
67 *
68 *                     1    [  t*t         2  ]              1    [      t  ]
69 * cosh 2x + cos 2y = --- * [ ----- + 4 cos y ];  sinh 2x = --- * [ t + --- ]
70 *                     2    [  t+1            ]              2    [     t+1 ]
71 *
72 * Hence,
73 *
74 *
75 *                        t*t+2t                  [4(t+1)(cos y)]*(sin y)
76 *    ctanh z = --------------------------- + i --------------------------
77 *               t*t+[4(t+1)(cos y)](cos y)     t*t+[4(t+1)(cos y)](cos y)
78 *
79 * EXCEPTION (conform to ISO/IEC 9899:1999(E)):
80 *      ctanh(0,0)=(0,0)
81 *      ctanh(x,inf) = (NaN,NaN) for finite x
82 *      ctanh(x,NaN) = (NaN,NaN) for finite x
83 *      ctanh(inf,y) = 1+ i*0*sin(2y) for positive-signed finite y
84 *      ctanh(inf,inf) = (1, +-0)
85 *      ctanh(inf,NaN) = (1, +-0)
86 *      ctanh(NaN,0) = (NaN,0)
87 *      ctanh(NaN,y) = (NaN,NaN) for non-zero y
88 *      ctanh(NaN,NaN) = (NaN,NaN)
89 */
90/* INDENT ON */
91
92#include "libm.h"		/* exp/expm1/fabs/sin/tanh/sincos */
93#include "complex_wrapper.h"
94
95static const double four = 4.0, two = 2.0, one = 1.0, zero = 0.0;
96
97dcomplex
98ctanh(dcomplex z) {
99	double t, r, v, u, x, y, S, C;
100	int hx, ix, lx, hy, iy, ly;
101	dcomplex ans;
102
103	x = D_RE(z);
104	y = D_IM(z);
105	hx = HI_WORD(x);
106	lx = LO_WORD(x);
107	ix = hx & 0x7fffffff;
108	hy = HI_WORD(y);
109	ly = LO_WORD(y);
110	iy = hy & 0x7fffffff;
111	x = fabs(x);
112	y = fabs(y);
113
114	if ((iy | ly) == 0) {	/* ctanh(x,0) = (x,0) for x = 0 or NaN */
115		D_RE(ans) = tanh(x);
116		D_IM(ans) = zero;
117	} else if (iy >= 0x7ff00000) {	/* y is inf or NaN */
118		if (ix < 0x7ff00000)	/* catanh(finite x,inf/nan) is nan */
119			D_RE(ans) = D_IM(ans) = y - y;
120		else if (((ix - 0x7ff00000) | lx) == 0) {	/* x is inf */
121			D_RE(ans) = one;
122			D_IM(ans) = zero;
123		} else {
124			D_RE(ans) = x + y;
125			D_IM(ans) = y - y;
126		}
127	} else if (ix >= 0x403c0000) {
128		/*
129		 * |x| > 28 = prec/2 (14,28,34,60)
130		 * ctanh z ~ 1 + i (sin2y)/(exp(2x))
131		 */
132		D_RE(ans) = one;
133		if (iy < 0x7fe00000)	/* t = sin(2y) */
134			S = sin(y + y);
135		else {
136			(void) sincos(y, &S, &C);
137			S = (S + S) * C;
138		}
139		if (ix >= 0x7fe00000) {	/* |x| > max/2 */
140			if (ix >= 0x7ff00000) {	/* |x| is inf or NaN */
141				if (((ix - 0x7ff00000) | lx) != 0)
142					D_RE(ans) = D_IM(ans) = x + y;
143								/* x is NaN */
144				else
145					D_IM(ans) = zero * S;	/* x is inf */
146			} else
147				D_IM(ans) = S * exp(-x);	/* underflow */
148		} else
149			D_IM(ans) = (S + S) * exp(-(x + x));
150							/* 2 sin 2y / exp(2x) */
151	} else {
152		/* INDENT OFF */
153		/*
154		 *                        t*t+2t
155		 *    ctanh z = --------------------------- +
156		 *               t*t+[4(t+1)(cos y)](cos y)
157		 *
158		 *                  [4(t+1)(cos y)]*(sin y)
159		 *              i --------------------------
160		 *                t*t+[4(t+1)(cos y)](cos y)
161		 */
162		/* INDENT ON */
163		(void) sincos(y, &S, &C);
164		t = expm1(x + x);
165		r = (four * C) * (t + one);
166		u = t * t;
167		v = one / (u + r * C);
168		D_RE(ans) = (u + two * t) * v;
169		D_IM(ans) = (r * S) * v;
170	}
171	if (hx < 0)
172		D_RE(ans) = -D_RE(ans);
173	if (hy < 0)
174		D_IM(ans) = -D_IM(ans);
175	return (ans);
176}
177