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 }