xref: /freebsd/lib/msun/ld80/s_cexpl.c (revision ba3c1f5972d7b90feb6e6da47905ff2757e0fe57)
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  * src/s_cexp.c converted to long double complex by Steven G. Kargl
29  */
30 
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
33 
34 #include <complex.h>
35 #include <float.h>
36 #ifdef __i386__
37 #include <ieeefp.h>
38 #endif
39 
40 #include "fpmath.h"
41 #include "math.h"
42 #include "math_private.h"
43 #include "k_expl.h"
44 
45 long double complex
46 cexpl (long double complex z)
47 {
48 	long double c, exp_x, s, x, y;
49 	uint64_t lx, ly;
50 	uint16_t hx, hy;
51 
52 	ENTERI();
53 
54 	x = creall(z);
55 	y = cimagl(z);
56 
57 	EXTRACT_LDBL80_WORDS(hy, ly, y);
58 	hy &= 0x7fff;
59 
60 	/* cexp(x + I 0) = exp(x) + I 0 */
61 	if ((hy | ly) == 0)
62 		RETURNI(CMPLXL(expl(x), y));
63 	EXTRACT_LDBL80_WORDS(hx, lx, x);
64 	/* cexp(0 + I y) = cos(y) + I sin(y) */
65 	if (((hx & 0x7fff) | lx) == 0) {
66 		sincosl(y, &s, &c);
67 		RETURNI(CMPLXL(c, s));
68 	}
69 
70 	if (hy >= 0x7fff) {
71 		if ((hx & 0x7fff) < 0x7fff || ((hx & 0x7fff) == 0x7fff &&
72 		    (lx & 0x7fffffffffffffffULL) != 0)) {
73 			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
74 			RETURNI(CMPLXL(y - y, y - y));
75 		} else if (hx & 0x8000) {
76 			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
77 			RETURNI(CMPLXL(0.0, 0.0));
78 		} else {
79 			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
80 			RETURNI(CMPLXL(x, y - y));
81 		}
82 	}
83 
84 	/*
85 	 *  exp_ovfl = 11356.5234062941439497
86 	 * cexp_ovfl = 22755.3287906024445633
87 	 */
88 	if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
89 	    (hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
90 		/*
91 		 * x is between exp_ovfl and cexp_ovfl, so we must scale to
92 		 * avoid overflow in exp(x).
93 		 */
94 		RETURNI(__ldexp_cexpl(z, 0));
95 	} else {
96 		/*
97 		 * Cases covered here:
98 		 *  -  x < exp_ovfl and exp(x) won't overflow (common case)
99 		 *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
100 		 *  -  x = +-Inf (generated by exp())
101 		 *  -  x = NaN (spurious inexact exception from y)
102 		 */
103 		exp_x = expl(x);
104 		sincosl(y, &s, &c);
105 		RETURNI(CMPLXL(exp_x * c, exp_x * s));
106 	}
107 }
108