1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cexp.c */
2 /*-
3 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27 28 #include "complex_impl.h"
29 30 static const uint32_t
31 exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */
32 cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
33 34 double complex cexp(double complex z)
35 {
36 double x, y, exp_x;
37 uint32_t hx, hy, lx, ly;
38 39 x = creal(z);
40 y = cimag(z);
41 42 EXTRACT_WORDS(hy, ly, y);
43 hy &= 0x7fffffff;
44 45 /* cexp(x + I 0) = exp(x) + I 0 */
46 if ((hy | ly) == 0)
47 return CMPLX(exp(x), y);
48 EXTRACT_WORDS(hx, lx, x);
49 /* cexp(0 + I y) = cos(y) + I sin(y) */
50 if (((hx & 0x7fffffff) | lx) == 0)
51 return CMPLX(cos(y), sin(y));
52 53 if (hy >= 0x7ff00000) {
54 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
55 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
56 return CMPLX(y - y, y - y);
57 } else if (hx & 0x80000000) {
58 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
59 return CMPLX(0.0, 0.0);
60 } else {
61 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
62 return CMPLX(x, y - y);
63 }
64 }
65 66 if (hx >= exp_ovfl && hx <= cexp_ovfl) {
67 /*
68 * x is between 709.7 and 1454.3, so we must scale to avoid
69 * overflow in exp(x).
70 */
71 return __ldexp_cexp(z, 0);
72 } else {
73 /*
74 * Cases covered here:
75 * - x < exp_ovfl and exp(x) won't overflow (common case)
76 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
77 * - x = +-Inf (generated by exp())
78 * - x = NaN (spurious inexact exception from y)
79 */
80 exp_x = exp(x);
81 return CMPLX(exp_x * cos(y), exp_x * sin(y));
82 }
83 }
84