1/*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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 <math.h>
34
35#include "math_private.h"
36
37static const uint32_t
38exp_ovfl  = 0x40862e42,			/* high bits of MAX_EXP * ln2 ~= 710 */
39cexp_ovfl = 0x4096b8e4;			/* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
40
41double complex
42cexp(double complex z)
43{
44	double x, y, exp_x;
45	uint32_t hx, hy, lx, ly;
46
47	x = creal(z);
48	y = cimag(z);
49
50	EXTRACT_WORDS(hy, ly, y);
51	hy &= 0x7fffffff;
52
53	/* cexp(x + I 0) = exp(x) + I 0 */
54	if ((hy | ly) == 0)
55		return (CMPLX(exp(x), y));
56	EXTRACT_WORDS(hx, lx, x);
57	/* cexp(0 + I y) = cos(y) + I sin(y) */
58	if (((hx & 0x7fffffff) | lx) == 0)
59		return (CMPLX(cos(y), sin(y)));
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		return (CMPLX(exp_x * cos(y), exp_x * sin(y)));
90	}
91}
92