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 <sys/cdefs.h>
30 __FBSDID("$FreeBSD$");
31
32 #include <complex.h>
33 #include <math.h>
34
35 #include "math_private.h"
36
37 static const uint32_t
38 exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */
39 cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
40
41 float complex
cexpf(float complex z)42 cexpf(float complex z)
43 {
44 float c, exp_x, s, x, y;
45 uint32_t hx, hy;
46
47 x = crealf(z);
48 y = cimagf(z);
49
50 GET_FLOAT_WORD(hy, y);
51 hy &= 0x7fffffff;
52
53 /* cexp(x + I 0) = exp(x) + I 0 */
54 if (hy == 0)
55 return (CMPLXF(expf(x), y));
56 GET_FLOAT_WORD(hx, x);
57 /* cexp(0 + I y) = cos(y) + I sin(y) */
58 if ((hx & 0x7fffffff) == 0) {
59 sincosf(y, &s, &c);
60 return (CMPLXF(c, s));
61 }
62
63 if (hy >= 0x7f800000) {
64 if ((hx & 0x7fffffff) != 0x7f800000) {
65 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
66 return (CMPLXF(y - y, y - y));
67 } else if (hx & 0x80000000) {
68 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
69 return (CMPLXF(0.0, 0.0));
70 } else {
71 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
72 return (CMPLXF(x, y - y));
73 }
74 }
75
76 if (hx >= exp_ovfl && hx <= cexp_ovfl) {
77 /*
78 * x is between 88.7 and 192, so we must scale to avoid
79 * overflow in expf(x).
80 */
81 return (__ldexp_cexpf(z, 0));
82 } else {
83 /*
84 * Cases covered here:
85 * - x < exp_ovfl and exp(x) won't overflow (common case)
86 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
87 * - x = +-Inf (generated by exp())
88 * - x = NaN (spurious inexact exception from y)
89 */
90 exp_x = expf(x);
91 sincosf(y, &s, &c);
92 return (CMPLXF(exp_x * c, exp_x * s));
93 }
94 }
95