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/*-
* Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
static const uint32_t
exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */
cexp_ovfl = 0x4096b8e4, /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
k = 1799; /* constant for reduction */
static const double
kln2 = 1246.97177782734161156; /* k * ln2 */
double complex
cexp(double complex z)
{
double x, y, exp_x;
uint32_t hx, hy, lx, ly;
int scale;
x = creal(z);
y = cimag(z);
EXTRACT_WORDS(hy, ly, y);
hy &= 0x7fffffff;
/* cexp(x + I 0) = exp(x) + I 0 */
if ((hy | ly) == 0)
return (cpack(exp(x), y));
if (hy >= 0x7ff00000) {
EXTRACT_WORDS(hx, lx, x);
if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
return (cpack(y - y, y - y));
} else if (hx & 0x80000000) {
/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
return (cpack(0.0, 0.0));
} else {
/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
return (cpack(x, y - y));
}
}
GET_HIGH_WORD(hx, x);
if (hx >= exp_ovfl && hx <= cexp_ovfl) {
/*
* x is between 709.7 and 1454.3, so we must scale to avoid
* overflow in exp(x). We use exp(x) = exp(x - kln2) * 2**k,
* carefully chosen to minimize |exp(kln2) - 2**k|. We also
* scale the exponent of exp(x) to MANT_DIG to avoid loss of
* accuracy due to underflow if sin(y) is tiny.
*/
exp_x = exp(x - kln2);
GET_HIGH_WORD(hx, exp_x);
SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 52) << 20));
scale = (hx >> 20) - (0x3ff + 52) + k;
return (cpack(scalbn(cos(y) * exp_x, scale),
scalbn(sin(y) * exp_x, scale)));
} else {
/*
* Cases covered here:
* - x < exp_ovfl and exp(x) won't overflow (common case)
* - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
* - x = +-Inf (generated by exp())
* - x = NaN (spurious inexact exception from y)
*/
exp_x = exp(x);
return (cpack(exp_x * cos(y), exp_x * sin(y)));
}
}
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