2 * SPDX-License-Identifier: BSD-2-Clause
4 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
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.
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
29 #include <sys/cdefs.h>
34 #include "math_private.h"
37 exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */
38 cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
41 cexp(double complex z)
43 double c, exp_x, s, x, y;
44 uint32_t hx, hy, lx, ly;
49 EXTRACT_WORDS(hy, ly, y);
52 /* cexp(x + I 0) = exp(x) + I 0 */
54 return (CMPLX(exp(x), y));
55 EXTRACT_WORDS(hx, lx, x);
56 /* cexp(0 + I y) = cos(y) + I sin(y) */
57 if (((hx & 0x7fffffff) | lx) == 0) {
62 if (hy >= 0x7ff00000) {
63 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
64 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
65 return (CMPLX(y - y, y - y));
66 } else if (hx & 0x80000000) {
67 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
68 return (CMPLX(0.0, 0.0));
70 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
71 return (CMPLX(x, y - y));
75 if (hx >= exp_ovfl && hx <= cexp_ovfl) {
77 * x is between 709.7 and 1454.3, so we must scale to avoid
80 return (__ldexp_cexp(z, 0));
84 * - x < exp_ovfl and exp(x) won't overflow (common case)
85 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
86 * - x = +-Inf (generated by exp())
87 * - x = NaN (spurious inexact exception from y)
91 return (CMPLX(exp_x * c, exp_x * s));
95 #if (LDBL_MANT_DIG == 53)
96 __weak_reference(cexp, cexpl);