xref: /freebsd/lib/msun/ld80/s_cexpl.c (revision 4543ef516683042d46f3bd3bb8a4f3f746e00499)
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 <complex.h>
32 #include <float.h>
33 #ifdef __i386__
34 #include <ieeefp.h>
35 #endif
36 
37 #include "fpmath.h"
38 #include "math.h"
39 #include "math_private.h"
40 #include "k_expl.h"
41 
42 long double complex
43 cexpl (long double complex z)
44 {
45 	long double c, exp_x, s, x, y;
46 	uint64_t lx, ly;
47 	uint16_t hx, hy;
48 
49 	ENTERI();
50 
51 	x = creall(z);
52 	y = cimagl(z);
53 
54 	EXTRACT_LDBL80_WORDS(hy, ly, y);
55 	hy &= 0x7fff;
56 
57 	/* cexp(x + I 0) = exp(x) + I 0 */
58 	if ((hy | ly) == 0)
59 		RETURNI(CMPLXL(expl(x), y));
60 	EXTRACT_LDBL80_WORDS(hx, lx, x);
61 	/* cexp(0 + I y) = cos(y) + I sin(y) */
62 	if (((hx & 0x7fff) | lx) == 0) {
63 		sincosl(y, &s, &c);
64 		RETURNI(CMPLXL(c, s));
65 	}
66 
67 	if (hy >= 0x7fff) {
68 		if ((hx & 0x7fff) < 0x7fff || ((hx & 0x7fff) == 0x7fff &&
69 		    (lx & 0x7fffffffffffffffULL) != 0)) {
70 			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
71 			RETURNI(CMPLXL(y - y, y - y));
72 		} else if (hx & 0x8000) {
73 			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
74 			RETURNI(CMPLXL(0.0, 0.0));
75 		} else {
76 			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
77 			RETURNI(CMPLXL(x, y - y));
78 		}
79 	}
80 
81 	/*
82 	 *  exp_ovfl = 11356.5234062941439497
83 	 * cexp_ovfl = 22755.3287906024445633
84 	 */
85 	if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
86 	    (hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
87 		/*
88 		 * x is between exp_ovfl and cexp_ovfl, so we must scale to
89 		 * avoid overflow in exp(x).
90 		 */
91 		RETURNI(__ldexp_cexpl(z, 0));
92 	} else {
93 		/*
94 		 * Cases covered here:
95 		 *  -  x < exp_ovfl and exp(x) won't overflow (common case)
96 		 *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
97 		 *  -  x = +-Inf (generated by exp())
98 		 *  -  x = NaN (spurious inexact exception from y)
99 		 */
100 		exp_x = expl(x);
101 		sincosl(y, &s, &c);
102 		RETURNI(CMPLXL(exp_x * c, exp_x * s));
103 	}
104 }
105