1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2019 Steven G. Kargl <kargl@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 "fpmath.h"
34 #include "math_private.h"
35 #include "k_expl.h"
36
37 /* XXX cexpl() should be converted to use bits likeo src/s_cexp.c. */
38
39 static const long double
40 cexp_ovfl = 2.27892930024498818830197576893019292e+04L,
41 exp_ovfl = 1.13565234062941439494919310779707649e+04L;
42
43 long double complex
cexpl(long double complex z)44 cexpl(long double complex z)
45 {
46 long double c, exp_x, s, x, y;
47
48 x = creall(z);
49 y = cimagl(z);
50
51 /* cexp(x + I 0) = exp(x) + I 0 */
52 if (y == 0)
53 return (CMPLXL(expl(x), y));
54 /* cexp(0 + I y) = cos(y) + I sin(y) */
55 if (x == 0) {
56 sincosl(y, &s, &c);
57 return (CMPLXL(c, s));
58 }
59
60 if (!isfinite(y)) {
61 if (isfinite(x) || isnan(x)) {
62 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
63 return (CMPLXL(y - y, y - y));
64 } else if (isinf(x) && copysignl(1.L, x) < 0) {
65 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
66 return (CMPLXL(0.0, 0.0));
67 } else {
68 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
69 return (CMPLXL(x, y - y));
70 }
71 }
72
73 if (x > exp_ovfl && x < cexp_ovfl) {
74 /*
75 * x is between exp_ovfl and cexp_ovfl, so we must scale to
76 * avoid overflow in exp(x).
77 */
78 return (__ldexp_cexpl(z, 0));
79 } else {
80 /*
81 * Cases covered here:
82 * - x < exp_ovfl and exp(x) won't overflow (common case)
83 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
84 * - x = +-Inf (generated by exp())
85 * - x = NaN (spurious inexact exception from y)
86 */
87 exp_x = expl(x);
88 sincosl(y, &s, &c);
89 return (CMPLXL(exp_x * c, exp_x * s));
90 }
91 }
92