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 __ccosh = ccosh
32
33
34 /*
35 * dcomplex ccosh(dcomplex z);
36 *
37 * z -z x -x
38 * e + e e (cos(y)+i*sin(y)) + e (cos(-y)+i*sin(-y))
39 * cosh z = -------------- = ---------------------------------------------
40 * 2 2
41 * x -x x -x
42 * cos(y) ( e + e ) + i*sin(y) (e - e )
43 * = --------------------------------------------
44 * 2
45 *
46 * = cos(y) cosh(x) + i sin(y) sinh(x)
47 *
48 * Implementation Note
49 * -------------------
50 *
51 * |x| -|x| |x| -2|x| -2|x| -P-4
52 * Note that e +- e = e ( 1 +- e ). If e < 2 , where
53 *
54 * P stands for the number of significant bits of the machine precision,
55 * |x|
56 * then the result will be rounded to e . Therefore, we have
57 *
58 * z
59 * e
60 * cosh z = ----- if |x| >= (P/2 + 2)*ln2
61 * 2
62 *
63 * EXCEPTION (conform to ISO/IEC 9899:1999(E)):
64 * ccosh(0,0)=(1,0)
65 * ccosh(0,inf)=(NaN,+-0)
66 * ccosh(0,NaN)=(NaN,+-0)
67 * ccosh(x,inf) = (NaN,NaN) for finite non-zero x
68 * ccosh(x,NaN) = (NaN,NaN) for finite non-zero x
69 * ccosh(inf,0) = (inf, 0)
70 * ccosh(inf,y) = (inf*cos(y),inf*sin(y)) for finite non-zero y
71 * ccosh(inf,inf) = (+-inf,NaN)
72 * ccosh(inf,NaN) = (+inf,NaN)
73 * ccosh(NaN,0) = (NaN,+-0)
74 * ccosh(NaN,y) = (NaN,NaN) for non-zero y
75 * ccosh(NaN,NaN) = (NaN,NaN)
76 */
77
78 #include "libm.h" /* cosh/exp/fabs/scalbn/sinh/sincos/__k_cexp */
79 #include "complex_wrapper.h"
80
81 dcomplex
82 ccosh(dcomplex z)
83 {
84 double t, x, y, S, C;
85 int hx, ix, lx, hy, iy, ly, n;
86 dcomplex ans;
87
88 x = D_RE(z);
89 y = D_IM(z);
90 hx = HI_WORD(x);
91 lx = LO_WORD(x);
92 ix = hx & 0x7fffffff;
93 hy = HI_WORD(y);
94 ly = LO_WORD(y);
95 iy = hy & 0x7fffffff;
96 x = fabs(x);
97 y = fabs(y);
98
99 (void) sincos(y, &S, &C);
100
101 if (ix >= 0x403c0000) { /* |x| > 28 = prec/2 (14,28,34,60) */
102 if (ix >= 0x40862E42) { /* |x| > 709.78... ~ log(2**1024) */
103 if (ix >= 0x7ff00000) { /* |x| is inf or NaN */
104 if ((iy | ly) == 0) {
105 D_RE(ans) = x;
106 D_IM(ans) = y;
107 } else if (iy >= 0x7ff00000) {
108 D_RE(ans) = x;
109 D_IM(ans) = x - y;
110 } else {
111 D_RE(ans) = C * x;
112 D_IM(ans) = S * x;
113 }
114 } else {
115 t = __k_cexp(x, &n);
116 /* return exp(x)=t*2**n */
117 D_RE(ans) = scalbn(C * t, n - 1);
118 D_IM(ans) = scalbn(S * t, n - 1);
119 }
120 } else {
121 t = exp(x) * 0.5;
122 D_RE(ans) = C * t;
123 D_IM(ans) = S * t;
124 }
125 } else {
126 if ((ix | lx) == 0) { /* x = 0, return (C,0) */
127 D_RE(ans) = C;
128 D_IM(ans) = 0.0;
129 } else {
130 D_RE(ans) = C * cosh(x);
131 D_IM(ans) = S * sinh(x);
132 }
133 }
134
135 if ((hx ^ hy) < 0)
136 D_IM(ans) = -D_IM(ans);
137
138 return (ans);
139 }