2 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
27 #include <sys/cdefs.h>
28 __FBSDID("$FreeBSD$");
33 #include "math_private.h"
36 exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */
37 cexp_ovfl = 0x4096b8e4, /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
38 k = 1799; /* constant for reduction */
41 kln2 = 1246.97177782734161156; /* k * ln2 */
44 cexp(double complex z)
47 uint32_t hx, hy, lx, ly;
53 EXTRACT_WORDS(hy, ly, y);
56 /* cexp(x + I 0) = exp(x) + I 0 */
58 return (cpack(exp(x), y));
59 if (hy >= 0x7ff00000) {
60 EXTRACT_WORDS(hx, lx, x);
61 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
62 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
63 return (cpack(y - y, y - y));
64 } else if (hx & 0x80000000) {
65 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
66 return (cpack(0.0, 0.0));
68 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
69 return (cpack(x, y - y));
74 if (hx >= exp_ovfl && hx <= cexp_ovfl) {
76 * x is between 709.7 and 1454.3, so we must scale to avoid
77 * overflow in exp(x). We use exp(x) = exp(x - kln2) * 2**k,
78 * carefully chosen to minimize |exp(kln2) - 2**k|. We also
79 * scale the exponent of exp(x) to MANT_DIG to avoid loss of
80 * accuracy due to underflow if sin(y) is tiny.
82 exp_x = exp(x - kln2);
83 GET_HIGH_WORD(hx, exp_x);
84 SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 52) << 20));
85 scale = (hx >> 20) - (0x3ff + 52) + k;
86 return (cpack(scalbn(cos(y) * exp_x, scale),
87 scalbn(sin(y) * exp_x, scale)));
91 * - x < exp_ovfl and exp(x) won't overflow (common case)
92 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
93 * - x = +-Inf (generated by exp())
94 * - x = NaN (spurious inexact exception from y)
97 return (cpack(exp_x * cos(y), exp_x * sin(y)));