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 __ctanh = ctanh
32
33
34 /*
35 * dcomplex ctanh(dcomplex z);
36 *
37 * tanh x + i tan y sinh 2x + i sin 2y
38 * ctanh z = --------------------- = --------------------
39 * 1 + i tanh(x)tan(y) cosh 2x + cos 2y
40 *
41 * For |x| >= prec/2 (14,28,34,60 for single, double, double extended, quad),
42 * we use
43 *
44 * 1 2x 2 sin 2y
45 * cosh 2x = sinh 2x = --- e and hence ctanh z = 1 + i -----------;
46 * 2 2x
47 * e
48 *
49 * otherwise, to avoid cancellation, for |x| < prec/2,
50 * 2x 2
51 * (e - 1) 2 2
52 * cosh 2x + cos 2y = 1 + ------------ + cos y - sin y
53 * 2x
54 * 2 e
55 *
56 * 1 2x 2 -2x 2
57 * = --- (e - 1) e + 2 cos y
58 * 2
59 * and
60 *
61 * [ 2x ]
62 * 1 [ 2x e - 1 ]
63 * sinh 2x = --- [ e - 1 + --------- ]
64 * 2 [ 2x ]
65 * [ e ]
66 * 2x
67 * Implementation notes: let t = expm1(2x) = e - 1, then
68 *
69 * 1 [ t*t 2 ] 1 [ t ]
70 * cosh 2x + cos 2y = --- * [ ----- + 4 cos y ]; sinh 2x = --- * [ t + --- ]
71 * 2 [ t+1 ] 2 [ t+1 ]
72 *
73 * Hence,
74 *
75 *
76 * t*t+2t [4(t+1)(cos y)]*(sin y)
77 * ctanh z = --------------------------- + i --------------------------
78 * t*t+[4(t+1)(cos y)](cos y) t*t+[4(t+1)(cos y)](cos y)
79 *
80 * EXCEPTION (conform to ISO/IEC 9899:1999(E)):
81 * ctanh(0,0)=(0,0)
82 * ctanh(x,inf) = (NaN,NaN) for finite x
83 * ctanh(x,NaN) = (NaN,NaN) for finite x
84 * ctanh(inf,y) = 1+ i*0*sin(2y) for positive-signed finite y
85 * ctanh(inf,inf) = (1, +-0)
86 * ctanh(inf,NaN) = (1, +-0)
87 * ctanh(NaN,0) = (NaN,0)
88 * ctanh(NaN,y) = (NaN,NaN) for non-zero y
89 * ctanh(NaN,NaN) = (NaN,NaN)
90 */
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 {
100 double t, r, v, u, x, y, S, C;
101 int hx, ix, lx, hy, iy, ly;
102 dcomplex ans;
103
104 x = D_RE(z);
105 y = D_IM(z);
106 hx = HI_WORD(x);
107 lx = LO_WORD(x);
108 ix = hx & 0x7fffffff;
109 hy = HI_WORD(y);
110 ly = LO_WORD(y);
111 iy = hy & 0x7fffffff;
112 x = fabs(x);
113 y = fabs(y);
114
115 if ((iy | ly) == 0) { /* ctanh(x,0) = (x,0) for x = 0 or NaN */
116 D_RE(ans) = tanh(x);
117 D_IM(ans) = zero;
118 } else if (iy >= 0x7ff00000) { /* y is inf or NaN */
119 if (ix < 0x7ff00000) { /* catanh(finite x,inf/nan) is nan */
120 D_RE(ans) = D_IM(ans) = y - y;
121 } else if (((ix - 0x7ff00000) | lx) == 0) { /* x is inf */
122 D_RE(ans) = one;
123 D_IM(ans) = zero;
124 } else {
125 D_RE(ans) = x + y;
126 D_IM(ans) = y - y;
127 }
128 } else if (ix >= 0x403c0000) {
129 /*
130 * |x| > 28 = prec/2 (14,28,34,60)
131 * ctanh z ~ 1 + i (sin2y)/(exp(2x))
132 */
133 D_RE(ans) = one;
134
135 if (iy < 0x7fe00000) { /* t = sin(2y) */
136 S = sin(y + y);
137 } else {
138 (void) sincos(y, &S, &C);
139 S = (S + S) * C;
140 }
141
142 if (ix >= 0x7fe00000) { /* |x| > max/2 */
143 if (ix >= 0x7ff00000) { /* |x| is inf or NaN */
144 if (((ix - 0x7ff00000) | lx) != 0)
145 D_RE(ans) = D_IM(ans) = x + y;
146 /* x is NaN */
147 else
148 D_IM(ans) = zero * S; /* x is inf */
149 } else {
150 D_IM(ans) = S * exp(-x); /* underflow */
151 }
152 } else {
153 D_IM(ans) = (S + S) * exp(-(x + x));
154 }
155
156 /* 2 sin 2y / exp(2x) */
157 } else {
158 /* BEGIN CSTYLED */
159 /*
160 * t*t+2t
161 * ctanh z = --------------------------- +
162 * t*t+[4(t+1)(cos y)](cos y)
163 *
164 * [4(t+1)(cos y)]*(sin y)
165 * i --------------------------
166 * t*t+[4(t+1)(cos y)](cos y)
167 */
168 /* END CSTYLED */
169 (void) sincos(y, &S, &C);
170 t = expm1(x + x);
171 r = (four * C) * (t + one);
172 u = t * t;
173 v = one / (u + r * C);
174 D_RE(ans) = (u + two * t) * v;
175 D_IM(ans) = (r * S) * v;
176 }
177
178 if (hx < 0)
179 D_RE(ans) = -D_RE(ans);
180
181 if (hy < 0)
182 D_IM(ans) = -D_IM(ans);
183
184 return (ans);
185 }