s_cexp.c revision 331722 
1/*-
2 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 *    notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 *    notice, this list of conditions and the following disclaimer in the
12 *    documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26
27#include <sys/cdefs.h>
28__FBSDID("$FreeBSD: stable/11/lib/msun/src/s_cexp.c 331722 2018-03-29 02:50:57Z eadler $");
29
30#include <complex.h>
31#include <math.h>
32
33#include "math_private.h"
34
35static const uint32_t
36exp_ovfl  = 0x40862e42,			/* high bits of MAX_EXP * ln2 ~= 710 */
37cexp_ovfl = 0x4096b8e4;			/* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
38
39double complex
40cexp(double complex z)
41{
42	double x, y, exp_x;
43	uint32_t hx, hy, lx, ly;
44
45	x = creal(z);
46	y = cimag(z);
47
48	EXTRACT_WORDS(hy, ly, y);
49	hy &= 0x7fffffff;
50
51	/* cexp(x + I 0) = exp(x) + I 0 */
52	if ((hy | ly) == 0)
53		return (CMPLX(exp(x), y));
54	EXTRACT_WORDS(hx, lx, x);
55	/* cexp(0 + I y) = cos(y) + I sin(y) */
56	if (((hx & 0x7fffffff) | lx) == 0)
57		return (CMPLX(cos(y), sin(y)));
58
59	if (hy >= 0x7ff00000) {
60		if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
61			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
62			return (CMPLX(y - y, y - y));
63		} else if (hx & 0x80000000) {
64			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
65			return (CMPLX(0.0, 0.0));
66		} else {
67			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
68			return (CMPLX(x, y - y));
69		}
70	}
71
72	if (hx >= exp_ovfl && hx <= cexp_ovfl) {
73		/*
74		 * x is between 709.7 and 1454.3, so we must scale to avoid
75		 * overflow in exp(x).
76		 */
77		return (__ldexp_cexp(z, 0));
78	} else {
79		/*
80		 * Cases covered here:
81		 *  -  x < exp_ovfl and exp(x) won't overflow (common case)
82		 *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
83		 *  -  x = +-Inf (generated by exp())
84		 *  -  x = NaN (spurious inexact exception from y)
85		 */
86		exp_x = exp(x);
87		return (CMPLX(exp_x * cos(y), exp_x * sin(y)));
88	}
89}
90