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
30static const uint32_t
31exp_ovfl  = 0x40862e42,  /* high bits of MAX_EXP * ln2 ~= 710 */
32cexp_ovfl = 0x4096b8e4;  /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
33
34double 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}