1 /*-
2 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26
27 #include <sys/cdefs.h>
28 __FBSDID("$FreeBSD$");
29
30 #include <complex.h>
31 #include <math.h>
32
33 #include "math_private.h"
34
35 static const uint32_t
36 exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */
37 cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
38
39 double complex
cexp(double complex z)40 cexp(double complex z)
41 {
42 double x, y, exp_x;
43 uint32_t hx, hy, lx, ly;
44
45 x = creal(z);
46 y = cimag(z);
47
48 EXTRACT_WORDS(hy, ly, y);
49 hy &= 0x7fffffff;
50
51 /* cexp(x + I 0) = exp(x) + I 0 */
52 if ((hy | ly) == 0)
53 return (cpack(exp(x), y));
54 EXTRACT_WORDS(hx, lx, x);
55 /* cexp(0 + I y) = cos(y) + I sin(y) */
56 if (((hx & 0x7fffffff) | lx) == 0)
57 return (cpack(cos(y), sin(y)));
58
59 if (hy >= 0x7ff00000) {
60 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
61 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
62 return (cpack(y - y, y - y));
63 } else if (hx & 0x80000000) {
64 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
65 return (cpack(0.0, 0.0));
66 } else {
67 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
68 return (cpack(x, y - y));
69 }
70 }
71
72 if (hx >= exp_ovfl && hx <= cexp_ovfl) {
73 /*
74 * x is between 709.7 and 1454.3, so we must scale to avoid
75 * overflow in exp(x).
76 */
77 return (__ldexp_cexp(z, 0));
78 } else {
79 /*
80 * Cases covered here:
81 * - x < exp_ovfl and exp(x) won't overflow (common case)
82 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
83 * - x = +-Inf (generated by exp())
84 * - x = NaN (spurious inexact exception from y)
85 */
86 exp_x = exp(x);
87 return (cpack(exp_x * cos(y), exp_x * sin(y)));
88 }
89 }
90