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 <complex.h>
32 #include <float.h>
33 #ifdef __i386__
34 #include <ieeefp.h>
35 #endif
36
37 #include "fpmath.h"
38 #include "math.h"
39 #include "math_private.h"
40 #include "k_expl.h"
41
42 long double complex
cexpl(long double complex z)43 cexpl (long double complex z)
44 {
45 long double c, exp_x, s, x, y;
46 uint64_t lx, ly;
47 uint16_t hx, hy;
48
49 ENTERI();
50
51 x = creall(z);
52 y = cimagl(z);
53
54 EXTRACT_LDBL80_WORDS(hy, ly, y);
55 hy &= 0x7fff;
56
57 /* cexp(x + I 0) = exp(x) + I 0 */
58 if ((hy | ly) == 0)
59 RETURNI(CMPLXL(expl(x), y));
60 EXTRACT_LDBL80_WORDS(hx, lx, x);
61 /* cexp(0 + I y) = cos(y) + I sin(y) */
62 if (((hx & 0x7fff) | lx) == 0) {
63 sincosl(y, &s, &c);
64 RETURNI(CMPLXL(c, s));
65 }
66
67 if (hy >= 0x7fff) {
68 if ((hx & 0x7fff) < 0x7fff || ((hx & 0x7fff) == 0x7fff &&
69 (lx & 0x7fffffffffffffffULL) != 0)) {
70 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
71 RETURNI(CMPLXL(y - y, y - y));
72 } else if (hx & 0x8000) {
73 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
74 RETURNI(CMPLXL(0.0, 0.0));
75 } else {
76 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
77 RETURNI(CMPLXL(x, y - y));
78 }
79 }
80
81 /*
82 * exp_ovfl = 11356.5234062941439497
83 * cexp_ovfl = 22755.3287906024445633
84 */
85 if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
86 (hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
87 /*
88 * x is between exp_ovfl and cexp_ovfl, so we must scale to
89 * avoid overflow in exp(x).
90 */
91 RETURNI(__ldexp_cexpl(z, 0));
92 } else {
93 /*
94 * Cases covered here:
95 * - x < exp_ovfl and exp(x) won't overflow (common case)
96 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
97 * - x = +-Inf (generated by exp())
98 * - x = NaN (spurious inexact exception from y)
99 */
100 exp_x = expl(x);
101 sincosl(y, &s, &c);
102 RETURNI(CMPLXL(exp_x * c, exp_x * s));
103 }
104 }
105