xref: /freebsd/lib/msun/src/s_cexpf.c (revision 3fb8f1272b50cb87cb624b321f7b81e76627c437)
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 
29 #include <complex.h>
30 #include <math.h>
31 
32 #include "math_private.h"
33 
34 static const uint32_t
35 exp_ovfl  = 0x42b17218,		/* MAX_EXP * ln2 ~= 88.722839355 */
36 cexp_ovfl = 0x43400074;		/* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
37 
38 float complex
39 cexpf(float complex z)
40 {
41 	float c, exp_x, s, x, y;
42 	uint32_t hx, hy;
43 
44 	x = crealf(z);
45 	y = cimagf(z);
46 
47 	GET_FLOAT_WORD(hy, y);
48 	hy &= 0x7fffffff;
49 
50 	/* cexp(x + I 0) = exp(x) + I 0 */
51 	if (hy == 0)
52 		return (CMPLXF(expf(x), y));
53 	GET_FLOAT_WORD(hx, x);
54 	/* cexp(0 + I y) = cos(y) + I sin(y) */
55 	if ((hx & 0x7fffffff) == 0) {
56 		sincosf(y, &s, &c);
57 		return (CMPLXF(c, s));
58 	}
59 
60 	if (hy >= 0x7f800000) {
61 		if ((hx & 0x7fffffff) != 0x7f800000) {
62 			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
63 			return (CMPLXF(y - y, y - y));
64 		} else if (hx & 0x80000000) {
65 			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
66 			return (CMPLXF(0.0, 0.0));
67 		} else {
68 			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
69 			return (CMPLXF(x, y - y));
70 		}
71 	}
72 
73 	if (hx >= exp_ovfl && hx <= cexp_ovfl) {
74 		/*
75 		 * x is between 88.7 and 192, so we must scale to avoid
76 		 * overflow in expf(x).
77 		 */
78 		return (__ldexp_cexpf(z, 0));
79 	} else {
80 		/*
81 		 * Cases covered here:
82 		 *  -  x < exp_ovfl and exp(x) won't overflow (common case)
83 		 *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
84 		 *  -  x = +-Inf (generated by exp())
85 		 *  -  x = NaN (spurious inexact exception from y)
86 		 */
87 		exp_x = expf(x);
88 		sincosf(y, &s, &c);
89 		return (CMPLXF(exp_x * c, exp_x * s));
90 	}
91 }
92