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 <complex.h>
30 #include <float.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 c, exp_x, s, x, y;
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 (CMPLX(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 sincos(y, &s, &c);
58 return (CMPLX(c, s));
59 }
60
61 if (hy >= 0x7ff00000) {
62 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
63 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
64 return (CMPLX(y - y, y - y));
65 } else if (hx & 0x80000000) {
66 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
67 return (CMPLX(0.0, 0.0));
68 } else {
69 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
70 return (CMPLX(x, y - y));
71 }
72 }
73
74 if (hx >= exp_ovfl && hx <= cexp_ovfl) {
75 /*
76 * x is between 709.7 and 1454.3, so we must scale to avoid
77 * overflow in exp(x).
78 */
79 return (__ldexp_cexp(z, 0));
80 } else {
81 /*
82 * Cases covered here:
83 * - x < exp_ovfl and exp(x) won't overflow (common case)
84 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
85 * - x = +-Inf (generated by exp())
86 * - x = NaN (spurious inexact exception from y)
87 */
88 exp_x = exp(x);
89 sincos(y, &s, &c);
90 return (CMPLX(exp_x * c, exp_x * s));
91 }
92 }
93
94 #if (LDBL_MANT_DIG == 53)
95 __weak_reference(cexp, cexpl);
96 #endif
97