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
95 static const double four = 4.0, two = 2.0, one = 1.0, zero = 0.0;
96
97 dcomplex
98 ctanh(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 }