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