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
cexp(dcomplex z)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