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: head/lib/msun/src/s_cexpf.c 275819 2014-12-16 09:21:56Z ed $");
29 
30 #include <complex.h>
31 #include <math.h>
32 
33 #include "math_private.h"
34 
35 static const uint32_t
36 exp_ovfl  = 0x42b17218,		/* MAX_EXP * ln2 ~= 88.722839355 */
37 cexp_ovfl = 0x43400074;		/* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
38 
39 float complex
cexpf(float complex z)40 cexpf(float complex z)
41 {
42 	float x, y, exp_x;
43 	uint32_t hx, hy;
44 
45 	x = crealf(z);
46 	y = cimagf(z);
47 
48 	GET_FLOAT_WORD(hy, y);
49 	hy &= 0x7fffffff;
50 
51 	/* cexp(x + I 0) = exp(x) + I 0 */
52 	if (hy == 0)
53 		return (CMPLXF(expf(x), y));
54 	GET_FLOAT_WORD(hx, x);
55 	/* cexp(0 + I y) = cos(y) + I sin(y) */
56 	if ((hx & 0x7fffffff) == 0)
57 		return (CMPLXF(cosf(y), sinf(y)));
58 
59 	if (hy >= 0x7f800000) {
60 		if ((hx & 0x7fffffff) != 0x7f800000) {
61 			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
62 			return (CMPLXF(y - y, y - y));
63 		} else if (hx & 0x80000000) {
64 			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
65 			return (CMPLXF(0.0, 0.0));
66 		} else {
67 			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
68 			return (CMPLXF(x, y - y));
69 		}
70 	}
71 
72 	if (hx >= exp_ovfl && hx <= cexp_ovfl) {
73 		/*
74 		 * x is between 88.7 and 192, so we must scale to avoid
75 		 * overflow in expf(x).
76 		 */
77 		return (__ldexp_cexpf(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 = expf(x);
87 		return (CMPLXF(exp_x * cosf(y), exp_x * sinf(y)));
88 	}
89 }
90