bigInt.h

/**
    @author Gatea David
    @brief  Big Integer header in CPP

    source: https://www.geeksforgeeks.org/bigint-big-integers-in-c-with-example/
    other approaches/implementations (using strings or 64bit blocks):
     -C/C++ Math Library - 4 - Big Integer Basics: https://www.youtube.com/watch?v=CEIrT3rl9QA
     -Really Big Numbers in C for Cryptography: https://www.youtube.com/watch?v=k-Y9vEqB-xQ


    gains:
    -cpp class implementation and bp's

    changelog:
    -2023.02:	-initial draft

    @version 2023.02
*/



////////////////// LIBS

#include <bits/stdc++.h>
using namespace std;


class BigInt{
    string digits;
public:

    //Constructors:
    BigInt(unsigned long long n = 0);
    BigInt(string &);
    BigInt(const char *);
    BigInt(BigInt &);

    //Helper Functions:
    friend void divide_by_2(BigInt &a);
    friend bool Null(const BigInt &);
    friend int Length(const BigInt &);
    int operator[](const int)const;

               /* * * * Operator Overloading * * * */

    //Direct assignment
    BigInt &operator=(const BigInt &);

    //Post/Pre - Incrementation
    BigInt &operator++();
    BigInt operator++(int temp);
    BigInt &operator--();
    BigInt operator--(int temp);

    //Addition and Subtraction
    friend BigInt &operator+=(BigInt &, const BigInt &);
    friend BigInt operator+(const BigInt &, const BigInt &);
    friend BigInt operator-(const BigInt &, const BigInt &);
    friend BigInt &operator-=(BigInt &, const BigInt &);

    //Comparison operators
    friend bool operator==(const BigInt &, const BigInt &);
    friend bool operator!=(const BigInt &, const BigInt &);

    friend bool operator>(const BigInt &, const BigInt &);
    friend bool operator>=(const BigInt &, const BigInt &);
    friend bool operator<(const BigInt &, const BigInt &);
    friend bool operator<=(const BigInt &, const BigInt &);

    //Multiplication and Division
    friend BigInt &operator*=(BigInt &, const BigInt &);
    friend BigInt operator*(const BigInt &, const BigInt &);
    friend BigInt &operator/=(BigInt &, const BigInt &);
    friend BigInt operator/(const BigInt &, const BigInt &);

    //Modulo
    friend BigInt operator%(const BigInt &, const BigInt &);
    friend BigInt &operator%=(BigInt &, const BigInt &);

    //Power Function
    friend BigInt &operator^=(BigInt &,const BigInt &);
    friend BigInt operator^(BigInt &, const BigInt &);

    //Square Root Function
    friend BigInt sqrt(BigInt &a);

    //Read and Write
    friend ostream &operator<<(ostream &,const BigInt &);
    friend istream &operator>>(istream &, BigInt &);

    //Others
    friend BigInt NthCatalan(int n);
    friend BigInt NthFibonacci(int n);
    friend BigInt Factorial(int n);
};