Overloading issue

Question

I'm trying to create a set of classes in order to handle complex numbers. I've seen that there is already a set of classes for the complex numbers, but because I'm learning C++ I thought it was a good idea to create a basic implementation. The problem comes up when I tried to overload the operator "/". I got a segfault and I can't understand if the problem is my implementation of the division:

complex.hpp :

#include <iostream>
#include <cstdlib>

class Complex {
  float real;
  float imm;
public:
  Complex(float new_real = 0,float new_imm = 0) {this->real = new_real;this->imm = new_imm;}
  void set(float new_real,float new_imm) {this->real = new_real; this->imm = new_imm;}
  float get_real(void) const { return this->real;}
  float get_imm(void) const { return this->imm;}
  Complex conj(void) const {Complex tmp; tmp.set(this->real,-1.0 * this->imm); return tmp;}
  friend std::ostream& operator<<(std::ostream& os, const Complex& cpx) {os << "Real: " << cpx.real << " Imm: " << cpx.imm << std::endl; return os; }
  friend Complex operator*(const Complex& lhs,const Complex& rhs);
  friend Complex operator+(const Complex& lhs,const Complex& rhs);
  friend Complex operator+(const Complex& lhs,const float& rhs);
};

complex.cpp:

#include "complex.hpp"


Complex operator*(const Complex& lhs,const Complex& rhs)
{
  float real_part = (lhs.real * rhs.real) - ( lhs.imm * rhs.imm);
  float imm_part = (lhs.real * rhs.imm) + ( lhs.imm * rhs.real);
  Complex result;
  result.set(real_part,imm_part);
  return result;
}

Complex operator+(const Complex& lhs,const Complex& rhs)
{
  float real_part = lhs.real + rhs.real;
  float imm_part = lhs.imm + rhs.imm;
  Complex result;
  result.set(real_part,imm_part);
  return result;
}

Complex operator+(const Complex& lhs,const float& rhs)
{
  float real_part = lhs.real + rhs;
  float imm_part = lhs.imm;
  Complex result;
  result.set(real_part,imm_part);
  return result;
}

Complex operator/(const Complex& lhs,const Complex& rhs)
{
  Complex numerator(0,0);
  numerator = rhs * rhs.conj();

  Complex denominator(0,0);
  denominator = lhs * rhs.conj();

  Complex result;
  float real_numerator = numerator.get_real();
  result = denominator / real_numerator;
  return result;
}

Complex operator/(const Complex& lhs,const float& rhs)
{
  float real_part = lhs.get_real() / rhs;
  float imm_part = lhs.get_imm() / rhs;
  Complex result;
  result.set(real_part,imm_part);
  return result;
}

The whole idea of the division between 2 complex is to multiply the numerator and denominator for the conjugate of the numerator in order to have only a real number on the numerator. Just to make it clear :

(a + ib) / (c + id) = ((a + ib) / (c + id)) * ((c - id) / (c - id)) = ((a + ib) * (c - id)) / (c^2 + d^2)

Now when I try to do this:

main.cpp :

int main(int argc, char *argv[])
{
  Complex x(4,8);
  Complex y(3,7);
  Complex result = x / y;
  result = x / 6;
  return 0;
}

I got this segfault, which I don't understand:

(gdb) break main
Breakpoint 2 at 0x401c56: file equalization_main.cpp, line 49.
(gdb) r
The program being debugged has been started already.
Start it from the beginning? (y or n) y
`/home/campiets/workspace/frontend/dfe_equalizer_fe/dev/view/src_c/test' has changed; re-reading symbols.
Starting program: /home/campiets/workspace/frontend/dfe_equalizer_fe/dev/view/src_c/test 

Breakpoint 2, main (argc=1, argv=0x7fffffffbf08) at equalization_main.cpp:49
49    Complex x(4,8);
(gdb) n
50    Complex y(3,7);
(gdb) n
51    Complex result = x / y;
(gdb) n

Program received signal SIGSEGV, Segmentation fault.
0x0000000000401e64 in Complex::Complex (this=<error reading variable: Cannot access memory at address 0x7fffff3feff8>, new_real=<error reading variable: Cannot access memory at address 0x7fffff3feff4>, 
    new_imm=<error reading variable: Cannot access memory at address 0x7fffff3feff0>) at complex.hpp:38
38    Complex(float new_real = 0,float new_imm = 0) {this->real = new_real; this->imm = new_imm;}

Any ideas ?

Answer 1

Complex operator/(const Complex& lhs,const Complex& rhs)
{
  ...
  Complex denominator...;
  ...
  float real_numerator = ...;
  result = denominator / real_numerator;
  ...
}

That's infinite recursion.

Since the compiler hasn't seen operator/(const Complex &lhs, const float &rhs), it converts the float argument to Complex and hence you get recursion.

The simplest solution is to declare or define operator/(const Complex &lhs, const float &rhs) before operator/(const Complex &lhs, const Complex &rhs).

My preference would be to implement the operators as class members, though. That yields simpler source code and solves the problem too.

Answer 2

The function

Complex operator/(const Complex& lhs,const Complex& rhs) { ... }

causes stack overflow since the line

result = denominator / real_numerator;

ends up being interpreted as:

result = denominator / Complex(real_numerator);

You can resolve that problem by defining or declaring

Complex operator/(const Complex& lhs, const float& rhs)

before it.

If you change your code to use:

Complex operator/(const Complex& lhs,const float& rhs)
{
   return Complex(lhs.get_real()/rhs, lhs.get_imm()/rhs);
}

Complex operator/(const Complex& lhs,const Complex& rhs)
{
   ...
}

your program will work ok.

---

A suggestion for simplifying the above operator/ function.

If you add the following member function

float magnitude_square() const { return (real*real + imm*imm); }

then you can use

Complex operator/(const Complex& lhs,const Complex& rhs)
{
   return (lhs * rhs.conj())/rhs.magnitude_square());
}