/**
 * @author tjgurwara99
 * @file
 *
 * \brief An implementation of Complex Number as Objects
 * \details A basic implementation of Complex Number field as a class with
 * operators overloaded to accommodate (mathematical) field operations.
 */

#include <cassert>
#include <cmath>
#include <complex>
#include <ctime>
#include <iostream>
#include <stdexcept>

/**
 * \brief Class Complex to represent complex numbers as a field.
 */
class Complex {
 // The real value of the complex number
 double re;
 // The imaginary value of the complex number
 double im;

 public:
 /**
 * \brief Complex Constructor which initialises our complex number.
 * \details
 * Complex Constructor which initialises the complex number which takes
 * three arguments.
 * @param x If the third parameter is 'true' then this x is the absolute
 * value of the complex number, if the third parameter is 'false' then this
 * x is the real value of the complex number (optional).
 * @param y If the third parameter is 'true' then this y is the argument of
 * the complex number, if the third parameter is 'false' then this y is the
 * imaginary value of the complex number (optional).
 * @param is_polar 'false' by default. If we want to initialise our complex
 * number using polar form then set this to true, otherwise set it to false
 * to use initialiser which initialises real and imaginary values using the
 * first two parameters (optional).
 */
 explicit Complex(double x = 0.f, double y = 0.f, bool is_polar = false) {
 if (!is_polar) {
 re = x;
 im = y;
 return;
 }

 re = x * std::cos(y);
 im = x * std::sin(y);
 }

 /**
 * \brief Copy Constructor
 * @param other The other number to equate our number to.
 */
 Complex(const Complex &other) : re(other.real()), im(other.imag()) {}

 /**
 * \brief Member function to get real value of our complex number.
 * Member function (getter) to access the class' re value.
 */
 double real() const { return this->re; }

 /**
 * \brief Member function to get imaginary value of our complex number.
 * Member function (getter) to access the class' im value.
 */
 double imag() const { return this->im; }

 /**
 * \brief Member function to give the modulus of our complex number.
 * Member function to which gives the absolute value (modulus) of our
 * complex number
 * @return \f$ \sqrt{z \bar{z}} \f$ where \f$ z \f$ is our complex
 * number.
 */
 double abs() const {
 return std::sqrt(this->re * this->re + this->im * this->im);
 }

 /**
 * \brief Member function to give the argument of our complex number.
 * @return Argument of our Complex number in radians.
 */
 double arg() const { return std::atan2(this->im, this->re); }

 /**
 * \brief Operator overload of '+' on Complex class.
 * Operator overload to be able to add two complex numbers.
 * @param other The other number that is added to the current number.
 * @return result current number plus other number
 */
 Complex operator+(const Complex &other) {
 Complex result(this->re + other.re, this->im + other.im);
 return result;
 }

 /**
 * \brief Operator overload of '-' on Complex class.
 * Operator overload to be able to subtract two complex numbers.
 * @param other The other number being subtracted from the current number.
 * @return result current number subtract other number
 */
 Complex operator-(const Complex &other) {
 Complex result(this->re - other.re, this->im - other.im);
 return result;
 }

 /**
 * \brief Operator overload of '*' on Complex class.
 * Operator overload to be able to multiple two complex numbers.
 * @param other The other number to multiply the current number to.
 * @return result current number times other number.
 */
 Complex operator*(const Complex &other) {
 Complex result(this->re * other.re - this->im * other.im,
 this->re * other.im + this->im * other.re);
 return result;
 }

 /**
 * \brief Operator overload of '~' on Complex class.
 * Operator overload of the BITWISE NOT which gives us the conjugate of our
 * complex number. NOTE: This is overloading the BITWISE operator but its
 * not a BITWISE operation in this definition.
 * @return result The conjugate of our complex number.
 */
 Complex operator~() const {
 Complex result(this->re, -(this->im));
 return result;
 }

 /**
 * \brief Operator overload of '/' on Complex class.
 * Operator overload to be able to divide two complex numbers. This function
 * would throw an exception if the other number is zero.
 * @param other The other number we divide our number by.
 * @return result Current number divided by other number.
 */
 Complex operator/(const Complex &other) {
 Complex result = *this * ~other;
 double denominator =
 other.real() * other.real() + other.imag() * other.imag();
 if (denominator != 0) {
 result = Complex(result.real() / denominator,
 result.imag() / denominator);
 return result;
 } else {
 throw std::invalid_argument("Undefined Value");
 }
 }

 /**
 * \brief Operator overload of '=' on Complex class.
 * Operator overload to be able to copy RHS instance of Complex to LHS
 * instance of Complex
 */
 const Complex &operator=(const Complex &other) {
 this->re = other.real();
 this->im = other.imag();
 return *this;
 }
};

/**
 * \brief Operator overload of '==' on Complex class.
 * Logical Equal overload for our Complex class.
 * @param a Left hand side of our expression
 * @param b Right hand side of our expression
 * @return 'True' If real and imaginary parts of a and b are same
 * @return 'False' Otherwise.
 */
bool operator==(const Complex &a, const Complex &b) {
 return a.real() == b.real() && a.imag() == b.imag();
}

/**
 * \brief Operator overload of '<<' of ostream for Complex class.
 * Overloaded insersion operator to accommodate the printing of our complex
 * number in their standard form.
 * @param os The console stream
 * @param num The complex number.
 */
std::ostream &operator<<(std::ostream &os, const Complex &num) {
 os << "(" << num.real();
 if (num.imag() < 0) {
 os << " - " << -num.imag();
 } else {
 os << " + " << num.imag();
 }
 os << "i)";
 return os;
}

/**
 * \brief Function to get random numbers to generate our complex numbers for
 * test
 */
double get_rand() { return (std::rand() % 100 - 50) / 100.f; }

/**
 * Tests Function
 */
void tests() {
 std::srand(std::time(nullptr));
 double x1 = get_rand(), y1 = get_rand(), x2 = get_rand(), y2 = get_rand();
 Complex num1(x1, y1), num2(x2, y2);
 std::complex<double> cnum1(x1, y1), cnum2(x2, y2);
 Complex result;
 std::complex<double> expected;
 // Test for addition
 result = num1 + num2;
 expected = cnum1 + cnum2;
 assert(((void)"1 + 1i + 1 + 1i is equal to 2 + 2i but the addition doesn't "
 "add up \n",
 (result.real() == expected.real() &&
 result.imag() == expected.imag())));
 std::cout << "First test passes." << std::endl;
 // Test for subtraction
 result = num1 - num2;
 expected = cnum1 - cnum2;
 assert(((void)"1 + 1i - 1 - 1i is equal to 0 but the program says "
 "otherwise. \n",
 (result.real() == expected.real() &&
 result.imag() == expected.imag())));
 std::cout << "Second test passes." << std::endl;
 // Test for multiplication
 result = num1 * num2;
 expected = cnum1 * cnum2;
 assert(((void)"(1 + 1i) * (1 + 1i) is equal to 2i but the program says "
 "otherwise. \n",
 (result.real() == expected.real() &&
 result.imag() == expected.imag())));
 std::cout << "Third test passes." << std::endl;
 // Test for division
 result = num1 / num2;
 expected = cnum1 / cnum2;
 assert(((void)"(1 + 1i) / (1 + 1i) is equal to 1 but the program says "
 "otherwise.\n",
 (result.real() == expected.real() &&
 result.imag() == expected.imag())));
 std::cout << "Fourth test passes." << std::endl;
 // Test for conjugates
 result = ~num1;
 expected = std::conj(cnum1);
 assert(((void)"(1 + 1i) has a conjugate which is equal to (1 - 1i) but the "
 "program says otherwise.\n",
 (result.real() == expected.real() &&
 result.imag() == expected.imag())));
 std::cout << "Fifth test passes.\n";
 // Test for Argument of our complex number
 assert(((void)"(1 + 1i) has argument PI / 4 but the program differs from "
 "the std::complex result.\n",
 (num1.arg() == std::arg(cnum1))));
 std::cout << "Sixth test passes.\n";
 // Test for absolute value of our complex number
 assert(((void)"(1 + 1i) has absolute value sqrt(2) but the program differs "
 "from the std::complex result. \n",
 (num1.abs() == std::abs(cnum1))));
 std::cout << "Seventh test passes.\n";
}

/**
 * Main function
 */
int main() {
 tests();
 return 0;
}