s_cexp.c revision 219359 
1/*-
2 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
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.
13 *
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
24 * SUCH DAMAGE.
25 */
26
27#include <sys/cdefs.h>
28__FBSDID("$FreeBSD: head/lib/msun/src/s_cexp.c 219359 2011-03-07 03:09:24Z das $");
29
30#include <complex.h>
31#include <math.h>
32
33#include "math_private.h"
34
35static const uint32_t
36exp_ovfl  = 0x40862e42,			/* high bits of MAX_EXP * ln2 ~= 710 */
37cexp_ovfl = 0x4096b8e4,			/* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
38k         = 1799;			/* constant for reduction */
39
40static const double
41kln2      =  1246.97177782734161156;	/* k * ln2 */
42
43double complex
44cexp(double complex z)
45{
46	double x, y, exp_x;
47	uint32_t hx, hy, lx, ly;
48	int scale;
49
50	x = creal(z);
51	y = cimag(z);
52
53	EXTRACT_WORDS(hy, ly, y);
54	hy &= 0x7fffffff;
55
56	/* cexp(x + I 0) = exp(x) + I 0 */
57	if ((hy | ly) == 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));
67		} else {
68			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
69			return (cpack(x, y - y));
70		}
71	}
72
73	GET_HIGH_WORD(hx, x);
74	if (hx >= exp_ovfl && hx <= cexp_ovfl) {
75		/*
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.
81		 */
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)));
88	} else {
89		/*
90		 * Cases covered here:
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)
95		 */
96		exp_x = exp(x);
97		return (cpack(exp_x * cos(y), exp_x * sin(y)));
98	}
99}
100