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 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __ctanhl = ctanhl
32
33 #include "libm.h" /* expl/expm1l/fabsl/isinfl/isnanl/sincosl/sinl/tanhl */
34 #include "complex_wrapper.h"
35 #include "longdouble.h"
36
37 static const long double four = 4.0L, two = 2.0L, one = 1.0L, zero = 0.0L;
38
39
40 ldcomplex
41 ctanhl(ldcomplex z)
42 {
43 long double r, u, v, t, x, y, S, C;
44 int hx, ix, hy, iy;
45 ldcomplex ans;
46
47 x = LD_RE(z);
48 y = LD_IM(z);
49 hx = HI_XWORD(x);
50 ix = hx & 0x7fffffff;
51 hy = HI_XWORD(y);
52 iy = hy & 0x7fffffff;
53 x = fabsl(x);
54 y = fabsl(y);
55
56 if (y == zero) { /* ctanh(x,0) = (x,0) for x = 0 or NaN */
57 LD_RE(ans) = tanhl(x);
58 LD_IM(ans) = zero;
59 } else if (iy >= 0x7fff0000) { /* y is inf or NaN */
60 if (ix < 0x7fff0000) { /* catanh(finite x,inf/nan) is nan */
61 LD_RE(ans) = LD_IM(ans) = y - y;
62 } else if (isinfl(x)) { /* x is inf */
63 LD_RE(ans) = one;
64 LD_IM(ans) = zero;
65 } else {
66 LD_RE(ans) = x + y;
67 LD_IM(ans) = y - y;
68 }
69 } else if (ix >= 0x4004e000) {
70
71 /*
72 * |x| > 60 = prec/2 (14,28,34,60)
73 * ctanh z ~ 1 + i (sin2y)/(exp(2x))
74 */
75 LD_RE(ans) = one;
76
77 if (iy < 0x7ffe0000) { /* t = sin(2y) */
78 S = sinl(y + y);
79 } else {
80 (void) sincosl(y, &S, &C);
81 S = (S + S) * C;
82 }
83
84 if (ix >= 0x7ffe0000) { /* |x| > max/2 */
85 if (ix >= 0x7fff0000) { /* |x| is inf or NaN */
86 if (isnanl(x)) /* x is NaN */
87 LD_RE(ans) = LD_IM(ans) = x + y;
88 else
89 LD_IM(ans) = zero * S; /* x is inf */
90 } else {
91 LD_IM(ans) = S * expl(-x); /* underflow */
92 }
93 } else {
94 LD_IM(ans) = (S + S) * expl(-(x + x));
95 }
96
97 /* 2 sin 2y / exp(2x) */
98 } else {
99 /* BEGIN CSTYLED */
100 /*
101 * t*t+2t
102 * ctanh z = ---------------------------
103 * t*t+[4(t+1)(cos y)](cos y)
104 *
105 * [4(t+1)(cos y)]*(sin y)
106 * i --------------------------
107 * t*t+[4(t+1)(cos y)](cos y)
108 */
109 /* END CSTYLED */
110 sincosl(y, &S, &C);
111 t = expm1l(x + x);
112 r = (four * C) * (t + one);
113 u = t * t;
114 v = one / (u + r * C);
115 LD_RE(ans) = (u + two * t) * v;
116 LD_IM(ans) = (r * S) * v;
117 }
118
119 if (hx < 0)
120 LD_RE(ans) = -LD_RE(ans);
121
122 if (hy < 0)
123 LD_IM(ans) = -LD_IM(ans);
124
125 return (ans);
126 }