Listing 4 A rudimentary class for complex numbers using "lazy" evaluation and caching for polar form

// z2.cpp

#include <iostream.h>
#include <iomanip.h>
#include <math.h>

class complex
   {
public:
   complex(double r, double i);
   complex(const complex &z);
   complex &operator=(const complex &z);
   ~complex();
   double real() const;
   double imag() const;
   double rho() const;
   double theta() const;
private:
   double re, im;
   struct polar;
   polar *p;
   };

struct complex::polar
   {
   polar(double r, double t);
   double rho, theta;
   };

inline complex::polar::polar(double r, double t)
   : rho(r), theta(t)
   {
   }

inline complex::complex(double r, double i)
   : re(r), im(i), p(0)
   {
   }

inline complex::complex(const complex &z)
   : re(z.re), im(z.im), p(0)
   {
   }

inline complex &complex::operator=(const complex &z)
   {
   re =  z.re;
   im = z.im;
   p = 0;
   return *this;
   }

inline complex::~complex()
   {
   delete p;
   }

inline double complex::real() const
   {
   return re;
   }

inline double complex::imag() const
   {
   return im;
   }

double complex::rho() const
   {
   if (p == 0)
      {
      complex *This = const_cast<complex *>(this);
      This->p =
         new polar(sqrt(re*re + im*im), atan2(im, re));
      }
   return p->rho;
   }

double complex::theta() const
   {
   if (p == 0)
      (polar *&)p =
         new polar(sqrt(re*re + im*im), atan2(im, re));
   return p->theta;
   }

complex operator+(const complex &z1, const complex &z2)
   {
   return complex
      (z1.real() + z2.real(), z1.imag() + z2.imag());
   }

int main()
   {
   // same as Listing 3
   }
// End of File