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
42long double complex
43cexpl (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