xref: /illumos-gate/usr/src/lib/libm/common/complex/cexp.c (revision 0250bb16937dff6249965f46ef0ff3927359e704)
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 __cexp = cexp
31 
32 /* INDENT OFF */
33 /*
34  * dcomplex cexp(dcomplex z);
35  *
36  *  x+iy    x
37  * e     = e  (cos(y)+i*sin(y))
38  *
39  * Over/underflow issue
40  * --------------------
41  * exp(x) may be huge but cos(y) or sin(y) may be tiny. So we use
42  * function __k_cexp(x,&n) to return exp(x) = __k_cexp(x,&n)*2**n.
43  * Thus if exp(x+iy) = A + Bi and t = __k_cexp(x,&n), then
44  *         A = t*cos(y)*2**n,   B = t*sin(y)*2**n
45  *
46  * Purge off all exceptional arguments:
47  *	(x,0) --> (exp(x),0)         for all x, include inf and NaN
48  *	(+inf, y) --> (+inf, NaN)    for inf, nan
49  *	(-inf, y) --> (+-0, +-0)     for y = inf, nan
50  *	(x,+-inf/NaN) --> (NaN,NaN)  for finite x
51  * For all other cases, return
52  *	(x,y) --> exp(x)*cos(y)+i*exp(x)*sin(y))
53  *
54  * Algorithm for out of range x and finite y
55  *	1. compute exp(x) in factor form (t=__k_cexp(x,&n))*2**n
56  *	2. compute sincos(y,&s,&c)
57  *	3. compute t*s+i*(t*c), then scale back to 2**n and return.
58  */
59 /* INDENT ON */
60 
61 #include "libm.h"		/* exp/scalbn/sincos/__k_cexp */
62 #include "complex_wrapper.h"
63 
64 static const double zero = 0.0;
65 
66 dcomplex
67 cexp(dcomplex z) {
68 	dcomplex ans;
69 	double x, y, t, c, s;
70 	int n, ix, iy, hx, hy, lx, ly;
71 
72 	x = D_RE(z);
73 	y = D_IM(z);
74 	hx = HI_WORD(x);
75 	lx = LO_WORD(x);
76 	hy = HI_WORD(y);
77 	ly = LO_WORD(y);
78 	ix = hx & 0x7fffffff;
79 	iy = hy & 0x7fffffff;
80 	if ((iy | ly) == 0) {	/* y = 0 */
81 		D_RE(ans) = exp(x);
82 		D_IM(ans) = y;
83 	} else if (ISINF(ix, lx)) {	/* x is +-inf */
84 		if (hx < 0) {
85 			if (iy >= 0x7ff00000) {
86 				D_RE(ans) = zero;
87 				D_IM(ans) = zero;
88 			} else {
89 				sincos(y, &s, &c);
90 				D_RE(ans) = zero * c;
91 				D_IM(ans) = zero * s;
92 			}
93 		} else {
94 			if (iy >= 0x7ff00000) {
95 				D_RE(ans) = x;
96 				D_IM(ans) = y - y;
97 			} else {
98 				(void) sincos(y, &s, &c);
99 				D_RE(ans) = x * c;
100 				D_IM(ans) = x * s;
101 			}
102 		}
103 	} else {
104 		(void) sincos(y, &s, &c);
105 		if (ix >= 0x40862E42) {	/* |x| > 709.78... ~ log(2**1024) */
106 			t = __k_cexp(x, &n);
107 			D_RE(ans) = scalbn(t * c, n);
108 			D_IM(ans) = scalbn(t * s, n);
109 		} else {
110 			t = exp(x);
111 			D_RE(ans) = t * c;
112 			D_IM(ans) = t * s;
113 		}
114 	}
115 	return (ans);
116 }
117