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/*
* A handy, tested, small, stand-alone, double precision floating point
* complex number arithmetic library for C.
* Just include "complex.h" if you use this.
*
* Copyright (C) 1987-2012 George Gesslein II.
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
The chief copyright holder can be contacted at gesslein@mathomatic.org, or
George Gesslein II, P.O. Box 224, Lansing, NY 14882-0224 USA.
*/
#include "complex.h"
#include <math.h>
#define true 1
#define false 0
#define epsilon 0.00000000000005 /* a good value for doubles */
/*
* Zero out relatively very small real or imaginary parts of a complex number,
* because they probably are a result of accumulated floating point inaccuracies.
*
* Return true if something was zeroed out.
*/
int
complex_fixup(ap)
complexs *ap; /* complex number pointer */
{
if (fabs(ap->re * epsilon) > fabs(ap->im)) {
ap->im = 0.0;
return true;
}
if (fabs(ap->im * epsilon) > fabs(ap->re)) {
ap->re = 0.0;
return true;
}
return false;
}
/*
* Add two complex numbers (a + b)
* and return the complex number result.
*
* Complex number subtraction (a - b) is done by
* complex_add(a, complex_negate(b)).
*/
complexs
complex_add(a, b)
complexs a, b;
{
a.re += b.re;
a.im += b.im;
return(a);
}
/*
* Negate a complex number (-a)
* and return the complex number result.
*/
complexs
complex_negate(a)
complexs a;
{
a.re = -a.re;
a.im = -a.im;
return(a);
}
/*
* Multiply two complex numbers (a * b)
* and return the complex number result.
*/
complexs
complex_mult(a, b)
complexs a, b;
{
complexs r;
r.re = a.re * b.re - a.im * b.im;
r.im = a.re * b.im + a.im * b.re;
return(r);
}
/*
* Divide two complex numbers (a / b)
* and return the complex number result.
*/
complexs
complex_div(a, b)
complexs a; /* dividend */
complexs b; /* divisor */
{
complexs r, num;
double denom;
b.im = -b.im;
num = complex_mult(a, b);
denom = b.re * b.re + b.im * b.im;
r.re = num.re / denom;
r.im = num.im / denom;
return r;
}
/*
* Take the natural logarithm of a complex number
* and return the complex number result.
*/
complexs
complex_log(a)
complexs a;
{
complexs r;
r.re = log(a.re * a.re + a.im * a.im) / 2.0;
r.im = atan2(a.im, a.re);
return(r);
}
/*
* Raise the natural number (e) to the power of a complex number (e^a)
* and return the complex number result.
*/
complexs
complex_exp(a)
complexs a;
{
complexs r;
double m;
m = exp(a.re);
r.re = m * cos(a.im);
r.im = m * sin(a.im);
return(r);
}
/*
* Raise complex number "a" to the power of complex number "b" (a^b)
* and return the complex number result.
*/
complexs
complex_pow(a, b)
complexs a, b;
{
complexs r;
r = complex_log(a);
r = complex_mult(r, b);
r = complex_exp(r);
complex_fixup(&r);
return(r);
}
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