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/** \file
* \brief Complex Data Type.
*
* See Copyright Notice in im_lib.h
*/
#ifndef __IM_COMPLEX_H
#define __IM_COMPLEX_H
#include "im_math.h"
/** \defgroup cpx Complex Numbers
* \par
* See \ref im_complex.h
* \ingroup util
*/
/** \brief Complex Float Data Type
*
* \par
* Complex class using two floats, one for real part, one for the imaginary part.
* \par
* It is not a complete complex class, we just implement constructors inside the class.
* All the other operators and functions are external to the class.
* \ingroup cpx */
class imcfloat
{
public:
float real; ///< Real part.
float imag; ///< Imaginary part.
/// Default Constructor (0,0).
imcfloat():real(0), imag(0) {}
/// Constructor from (real, imag)
imcfloat(const float& r, const float& i):real(r),imag(i) {}
/// Constructor from (real)
imcfloat(const float& r):real(r),imag(0) {}
};
/** \addtogroup cpx
* Complex numbers operators.
* @{
*/
inline int operator <= (const imcfloat& C1, const imcfloat& C2)
{
return ((C1.real <= C2.real) && (C1.imag <= C2.imag));
}
inline int operator <= (const imcfloat& C, const float& F)
{
return ((F <= C.real) && (0 <= C.imag));
}
inline int operator < (const imcfloat& C1, const imcfloat& C2)
{
return ((C1.real < C2.real) && (C1.imag < C2.imag));
}
inline int operator < (const imcfloat& C, const float& F)
{
return ((F < C.real) && (0 < C.imag));
}
inline int operator > (const imcfloat& C1, const imcfloat& C2)
{
return ((C1.real > C2.real) && (C1.imag > C2.imag));
}
inline int operator > (const imcfloat& C, const float& F)
{
return ((F > C.real) && (0 > C.imag));
}
inline imcfloat operator + (const imcfloat& C1, const imcfloat& C2)
{
return imcfloat(C1.real + C2.real, C1.imag + C2.imag);
}
inline imcfloat operator += (const imcfloat& C1, const imcfloat& C2)
{
return imcfloat(C1.real + C2.real, C1.imag + C2.imag);
}
inline imcfloat operator - (const imcfloat& C1, const imcfloat& C2)
{
return imcfloat(C1.real - C2.real, C1.imag - C2.imag);
}
inline imcfloat operator * (const imcfloat& C1, const imcfloat& C2)
{
return imcfloat(C1.real * C2.real - C1.imag * C2.imag,
C1.imag * C2.real + C1.real * C2.imag);
}
inline imcfloat operator / (const imcfloat& C1, const imcfloat& C2)
{
float den = C2.real * C2.real - C2.imag * C2.imag;
return imcfloat((C1.real * C2.real + C1.imag * C2.imag) / den,
(C1.imag * C2.real - C1.real * C2.imag) / den);
}
inline imcfloat operator / (const imcfloat& C, const float& R)
{
return imcfloat(C.real / R, C.imag / R);
}
inline imcfloat operator /= (const imcfloat& C, const float& R)
{
return imcfloat(C.real / R, C.imag / R);
}
inline imcfloat operator * (const imcfloat& C, const float& R)
{
return imcfloat(C.real * R, C.imag * R);
}
inline int operator == (const imcfloat& C1, const imcfloat& C2)
{
return ((C1.real == C2.real) && (C1.imag == C2.imag));
}
inline float cpxreal(const imcfloat& C)
{
return C.real;
}
inline float cpximag(const imcfloat& C)
{
return C.imag;
}
inline float cpxmag(const imcfloat& C)
{
return sqrtf(C.real*C.real + C.imag*C.imag);
}
inline float cpxphase(const imcfloat& C)
{
return atan2f(C.real, C.imag);
}
inline imcfloat cpxconj(const imcfloat& C)
{
return imcfloat(C.real, -C.imag);
}
inline imcfloat log(const imcfloat& C)
{
return imcfloat(logf(cpxmag(C)), atan2f(C.real, C.imag));
}
inline imcfloat exp(const imcfloat& C)
{
float mag = expf(C.real);
return imcfloat(mag * cosf(C.imag), mag * sinf(C.imag));
}
inline imcfloat pow(const imcfloat& C1, const imcfloat& C2)
{
return exp(C1 * log(C2));
}
inline imcfloat sqrt(const imcfloat& C)
{
float mag = sqrtf(sqrtf(C.real*C.real + C.imag*C.imag));
float phase = atan2f(C.real, C.imag) / 2;
return imcfloat(mag * cosf(phase), mag * sinf(phase));
}
inline imcfloat cpxpolar(const float& mag, const float& phase)
{
return imcfloat(mag * cosf(phase), mag * sinf(phase));
}
/** @} */
#endif
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