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/*
* Copyright (c) 2009 Samit Basu
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#ifndef __Complex_hpp__
#define __Complex_hpp__
#include "IEEEFP.hpp"
template <typename T>
static inline void complex_divide(const T& ar, const T& ai,
const T& br, const T& bi,
T& c0, T& c1) {
double ratio, den;
double abr, abi, cr;
if ((ai == 0) && (bi == 0)) {
c1 = 0;
c0 = ar/br;
return;
}
if (bi == 0) {
c0 = ar/br;
c1 = ai/br;
return;
}
if ((ar == 0) && (bi == 0)) {
c0 = 0;
c1 = ai/br;
return;
}
if ((ai == 0) && (br == 0)) {
c0 = 0;
c1 = -ar/bi;
return;
}
// if (ar == 0) {
// c0 = (ai*bi)/(br*br + bi*bi);
// c1 = (ai*br)/(br*br + bi*bi);
// return;
// }
if ((ar == br) && (ai == bi)) {
c0 = 1; c1 = 0;
return;
}
if( (abr = br) < 0.)
abr = - abr;
if( (abi = bi) < 0.)
abi = - abi;
if( abr <= abi )
{
if(abi == 0) {
if (ai != 0 || ar != 0)
abi = 1.;
c1 = c0 = abi / abr;
return;
}
ratio = br / bi ;
den = bi * (1 + ratio*ratio);
cr = (ar*ratio + ai) / den;
c1 = (ai*ratio - ar) / den;
}
else
{
ratio = bi / br ;
den = br * (1 + ratio*ratio);
cr = (ar + ai*ratio) / den;
c1 = (ai - ar*ratio) / den;
}
c0 = cr;
}
template <typename T>
static inline void complex_recip(const T& ar, const T& ai, T& cr, T& ci) {
if (ai == 0) {
ci = 0;
cr = 1/ar;
return;
}
complex_divide<T>(1,0,ar,ai,cr,ci);
}
template <class T>
inline T complex_abs(T real, T imag) {
T swap;
if(real < 0)
real = -real;
if(imag < 0)
imag = -imag;
if(imag > real){
swap = real;
real = imag;
imag = swap;
}
if((real+imag) == real)
return(real);
double temp = double(imag)/double(real);
temp = real*sqrt(1.0 + temp*temp); /*overflow!!*/
return(T(temp));
}
template <typename T>
inline T complex_phase(const T &ar, const T &ai) {
return T(atan2(double(ai),double(ar)));
}
template <typename T>
inline void complex_multiply(const T &ar, const T &ai,
const T &br, const T &bi,
T &cr, T &ci) {
if ((ai == 0) && (bi == 0)) {
cr = ar * br;
ci = 0;
} else if (ai == 0) {
cr = ar * br;
ci = ar * bi;
} else if (bi == 0) {
cr = br * ar;
ci = br * ai;
} else {
cr = ar * br - ai * bi;
ci = ar * bi + ai * br;
}
}
template <typename T>
inline bool complex_lt(const T &ar, const T &ai,
const T &br, const T &bi) {
T mag_a = complex_abs(ar,ai);
T mag_b = complex_abs(br,bi);
if ((mag_b-mag_a) > feps(mag_a)*4) return true;
if ((mag_a-mag_b) > feps(mag_b)*4) return false;
return (complex_phase(ar,ai) < complex_phase(br,bi));
}
template <typename T>
inline bool complex_gt(const T &ar, const T &ai,
const T &br, const T &bi) {
T mag_a = complex_abs(ar,ai);
T mag_b = complex_abs(br,bi);
if ((mag_b-mag_a) > feps(mag_a)*4) return false;
if ((mag_a-mag_b) > feps(mag_b)*4) return true;
return (complex_phase(ar,ai) > complex_phase(br,bi));
}
template <typename T>
inline bool complex_eq(const T & ar, const T & ai,
const T & br, const T & bi) {
return ((ar == br) && (ai == bi));
}
template <typename T>
inline bool complex_ne(const T & ar, const T & ai,
const T & br, const T & bi) {
return ((ar != br) || (ai != bi));
}
template <typename T>
inline bool complex_le(const T & ar, const T & ai,
const T & br, const T & bi) {
return complex_eq(ar,ai,br,bi) || complex_lt(ar,ai,br,bi);
}
template <typename T>
inline bool complex_ge(const T & ar, const T & ai,
const T & br, const T & bi) {
return complex_eq(ar,ai,br,bi) || complex_gt(ar,ai,br,bi);
}
template <typename T>
inline void complex_log(T xr, T xi, T &yr, T &yi) {
yr = log(complex_abs(xr,xi));
yi = atan2(xi,xr);
}
template <typename T>
inline void complex_exp(T xr, T xi, T &yr, T &yi) {
yr = exp(xr)*cos(xi);
yi = exp(xr)*sin(xi);
}
template <typename T>
inline void complex_sqrt(T xr, T xi, T &yr, T &yi) {
T tr, ti;
if ((xr >= 0) && (xi == 0)) {
yr = sqrt(xr);
yi = 0;
return;
}
if ((xr < 0) && (xi == 0)) {
yi = sqrt(-xr);
yr = 0;
return;
}
complex_log(xr,xi,tr,ti);
tr /= 2.0;
ti /= 2.0;
complex_exp(tr,ti,yr,yi);
}
template <typename T>
inline void complex_square(T xr, T xi, T &yr, T &yi) {
yr = xr*xr - xi*xi;
yi = 2*xr*xi;
}
#endif
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