1/* origin: FreeBSD /usr/src/lib/msun/src/s_cexpf.c */
2/*-
3 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27
28#include "libm.h"
29
30static const uint32_t
31exp_ovfl  = 0x42b17218,  /* MAX_EXP * ln2 ~= 88.722839355 */
32cexp_ovfl = 0x43400074;  /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
33
34float complex cexpf(float complex z)
35{
36	float x, y, exp_x;
37	uint32_t hx, hy;
38
39	x = crealf(z);
40	y = cimagf(z);
41
42	GET_FLOAT_WORD(hy, y);
43	hy &= 0x7fffffff;
44
45	/* cexp(x + I 0) = exp(x) + I 0 */
46	if (hy == 0)
47		return CMPLXF(expf(x), y);
48	GET_FLOAT_WORD(hx, x);
49	/* cexp(0 + I y) = cos(y) + I sin(y) */
50	if ((hx & 0x7fffffff) == 0)
51		return CMPLXF(cosf(y), sinf(y));
52
53	if (hy >= 0x7f800000) {
54		if ((hx & 0x7fffffff) != 0x7f800000) {
55			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
56			return CMPLXF(y - y, y - y);
57		} else if (hx & 0x80000000) {
58			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
59			return CMPLXF(0.0, 0.0);
60		} else {
61			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
62			return CMPLXF(x, y - y);
63		}
64	}
65
66	if (hx >= exp_ovfl && hx <= cexp_ovfl) {
67		/*
68		 * x is between 88.7 and 192, so we must scale to avoid
69		 * overflow in expf(x).
70		 */
71		return __ldexp_cexpf(z, 0);
72	} else {
73		/*
74		 * Cases covered here:
75		 *  -  x < exp_ovfl and exp(x) won't overflow (common case)
76		 *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
77		 *  -  x = +-Inf (generated by exp())
78		 *  -  x = NaN (spurious inexact exception from y)
79		 */
80		exp_x = expf(x);
81		return CMPLXF(exp_x * cosf(y), exp_x * sinf(y));
82	}
83}
84