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 * src/s_cexp.c converted to long double complex by Steven G. Kargl
29 */
30
31 #include <sys/cdefs.h>
32 #include <complex.h>
33 #include <float.h>
34
35 #include "fpmath.h"
36 #include "math.h"
37 #include "math_private.h"
38 #include "k_expl.h"
39
40 long double complex
cexpl(long double complex z)41 cexpl (long double complex z)
42 {
43 long double c, exp_x, s, x, y;
44 uint64_t lx, ly;
45 uint16_t hx, hy;
46
47 ENTERI();
48
49 x = creall(z);
50 y = cimagl(z);
51
52 EXTRACT_LDBL80_WORDS(hy, ly, y);
53 hy &= 0x7fff;
54
55 /* cexp(x + I 0) = exp(x) + I 0 */
56 if ((hy | ly) == 0)
57 RETURNI(CMPLXL(expl(x), y));
58 EXTRACT_LDBL80_WORDS(hx, lx, x);
59 /* cexp(0 + I y) = cos(y) + I sin(y) */
60 if (((hx & 0x7fff) | lx) == 0) {
61 sincosl(y, &s, &c);
62 RETURNI(CMPLXL(c, s));
63 }
64
65 if (hy >= 0x7fff) {
66 if ((hx & 0x7fff) < 0x7fff || ((hx & 0x7fff) == 0x7fff &&
67 (lx & 0x7fffffffffffffffULL) != 0)) {
68 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
69 RETURNI(CMPLXL(y - y, y - y));
70 } else if (hx & 0x8000) {
71 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
72 RETURNI(CMPLXL(0.0, 0.0));
73 } else {
74 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
75 RETURNI(CMPLXL(x, y - y));
76 }
77 }
78
79 /*
80 * exp_ovfl = 11356.5234062941439497
81 * cexp_ovfl = 22755.3287906024445633
82 */
83 if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
84 (hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
85 /*
86 * x is between exp_ovfl and cexp_ovfl, so we must scale to
87 * avoid overflow in exp(x).
88 */
89 RETURNI(__ldexp_cexpl(z, 0));
90 } else {
91 /*
92 * Cases covered here:
93 * - x < exp_ovfl and exp(x) won't overflow (common case)
94 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
95 * - x = +-Inf (generated by exp())
96 * - x = NaN (spurious inexact exception from y)
97 */
98 exp_x = expl(x);
99 sincosl(y, &s, &c);
100 RETURNI(CMPLXL(exp_x * c, exp_x * s));
101 }
102 }
103