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 <sys/cdefs.h>
30#include <complex.h>
31#include <float.h>
32#include <math.h>
33
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
39static const long double
40cexp_ovfl = 2.27892930024498818830197576893019292e+04L,
41exp_ovfl = 1.13565234062941439494919310779707649e+04L;
42
43long double complex
44cexpl(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