ETH_Informatik/Informatik_I/Exercise_9/Task_1

Task 1: Complex Numbers

• Task
• Solution
  • complex.h
  • complex.cpp

Task

Create your own data type for complex numbers that can be used as a drop-in replacement for double. The definition of the data type and the forward declarations of operators must be in file complex.h, while the implementation of operators must be in file complex.cpp.

1. Define a struct named Complex that represents a complex number in the cartesian form. As data type use floating point numbers with double precision.
2. Implement input and output (>>, <<) operators for reading and writing of complex numbers.

A complex number \((x pm yi)\) is represented in the format [x,y], where x and y follows the format of floating point numbers with double precision.

E.g., [-2,5] represents \((-2 + 5i)\) . Important: No spaces.

Note: You can assume that your input value is a well-formatted complex number.

3. Implement arithmetic operators for addition, subtraction, multiplication, and division \((+,-,*,/)\) of complex numbers. For the division, you may assume that the squared modulus of the divisor is not zero, even after rounding it to a floating point number. Finally, you do not need to treat the case of division by zero.
4. Implement the negation operator \((-)\) of complex numbers.
5. Implement comparison operators for equality and inequality \((==,!=)\) of complex numbers.

Hint: recall from Exercise 5 how to correctly compare floating point numbers.

Solution

complex.h

#pragma once

#include <cmath>
#include <iostream>

struct Complex {
  double a;
  double b;
};

// arithmetic operators
Complex operator+(const Complex &cn1, const Complex &cn2);
Complex operator-(const Complex &cn1, const Complex &cn2);
Complex operator*(const Complex &cn1, const Complex &cn2);
Complex operator/(const Complex &cn1, const Complex &cn2);

// negation operator

Complex operator-(const Complex &cn1);

// equality and inequality operators

bool operator==(const Complex &cn1, const Complex &cn2);
bool operator!=(const Complex &cn1, const Complex &cn2);

// reads a complex number from input
std::istream &operator>>(std::istream &in, Complex &a);
std::ostream &operator<<(std::ostream &out, const Complex &a);

complex.cpp

#include "complex.h"
#include <cstdlib>

std::istream &operator>>(std::istream &in, Complex &a) {
  char open;
  char comma;
  char close;
  double aa;
  double ab;
  in >> open;
  if (open == '[') {
    in >> aa >> comma >> ab >> close;
    if (comma == ',' && close == ']') {
      a.a = aa;
      a.b = ab;
    } else {
      std::cerr << "Invalid Input!";
  }
  } else {
    std::cerr << "Invalid Input!";
  }
  return in;
}

std::ostream &operator<<(std::ostream &out, const Complex &a) {
  return out << "[" << a.a << "," << a.b << "]";
}

Complex operator+(const Complex &cn1, const Complex &cn2) {
  Complex res;
  double a = cn1.a + cn2.a;
  double b = cn1.b + cn2.b;
  res.a = a;
  res.b = b;
  return res;
}

Complex operator-(const Complex &cn1, const Complex &cn2) {
  Complex res;
  double a = cn1.a - cn2.a;
  double b = cn1.b - cn2.b;
  res.a = a;
  res.b = b;
  return res;
}

Complex operator*(const Complex &cn1, const Complex &cn2) {
  Complex res;
  double a = (cn1.a * cn2.a) - (cn1.b * cn2.b);
  double b = (cn1.a * cn2.b) + (cn1.b * cn2.a);
  res.a = a;
  res.b = b;
  return res;
}

Complex operator/(const Complex &cn1, const Complex &cn2) {
  Complex res;
  double a = (cn1.a * cn2.a + cn1.b * cn2.b) / (cn2.a * cn2.a + cn2.b * cn2.b);
  double b = (cn1.b * cn2.a - cn1.a * cn2.b) / (cn2.a * cn2.a + cn2.b * cn2.b);
  res.a = a;
  res.b = b;
  return res;
}

Complex operator-(const Complex &cn1) {
  Complex res;
  double a = -cn1.a;
  double b = -cn1.b;
  res.a = a;
  res.b = b;
  return res;
}

bool operator==(const Complex &cn1, const Complex &cn2) {
  double epsilon = 0.1;
  return (std::abs(cn1.a - cn2.a) < epsilon) &&
  (std::abs(cn1.b - cn2.b) < epsilon);
}

bool operator!=(const Complex &cn1, const Complex &cn2) {
  double epsilon = 0.1;
  return (std::abs(cn1.a - cn2.a) > epsilon) ||
  (std::abs(cn1.b - cn2.b) > epsilon);
}

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