1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26 * SUCH DAMAGE.
27 */
28
29 #include <sys/cdefs.h>
30 __FBSDID("$FreeBSD$");
31
32 #include <complex.h>
33 #include <float.h>
34 #include <math.h>
35
36 #include "math_private.h"
37
38 static const uint32_t
39 exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */
40 cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
41
42 double complex
cexp(double complex z)43 cexp(double complex z)
44 {
45 double c, exp_x, s, x, y;
46 uint32_t hx, hy, lx, ly;
47
48 x = creal(z);
49 y = cimag(z);
50
51 EXTRACT_WORDS(hy, ly, y);
52 hy &= 0x7fffffff;
53
54 /* cexp(x + I 0) = exp(x) + I 0 */
55 if ((hy | ly) == 0)
56 return (CMPLX(exp(x), y));
57 EXTRACT_WORDS(hx, lx, x);
58 /* cexp(0 + I y) = cos(y) + I sin(y) */
59 if (((hx & 0x7fffffff) | lx) == 0) {
60 sincos(y, &s, &c);
61 return (CMPLX(c, s));
62 }
63
64 if (hy >= 0x7ff00000) {
65 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
66 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
67 return (CMPLX(y - y, y - y));
68 } else if (hx & 0x80000000) {
69 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
70 return (CMPLX(0.0, 0.0));
71 } else {
72 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
73 return (CMPLX(x, y - y));
74 }
75 }
76
77 if (hx >= exp_ovfl && hx <= cexp_ovfl) {
78 /*
79 * x is between 709.7 and 1454.3, so we must scale to avoid
80 * overflow in exp(x).
81 */
82 return (__ldexp_cexp(z, 0));
83 } else {
84 /*
85 * Cases covered here:
86 * - x < exp_ovfl and exp(x) won't overflow (common case)
87 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
88 * - x = +-Inf (generated by exp())
89 * - x = NaN (spurious inexact exception from y)
90 */
91 exp_x = exp(x);
92 sincos(y, &s, &c);
93 return (CMPLX(exp_x * c, exp_x * s));
94 }
95 }
96
97 #if (LDBL_MANT_DIG == 53)
98 __weak_reference(cexp, cexpl);
99 #endif
100