Bignum

CS177/457 C++ Programming
Spring 1998
An abstract data type for large integers

Introduction

Your task is to write a class for very large integers, i.e. ones that do not have a size limitation, and can be any number of digits long. Your program will consist of a single class, and a main function that tests its capabilities.

Requirements

Your class must:

be capable of representing integers of any length
have constructors to initialize numbers with standard integers (type long int), and from an string of digits (e.g. "1234567890")
have overloaded operators for addition (+) and multiplication (*)
have an overloaded operator for assignment (=)
have overloaded operators for equality (==) and comparsion (<)
have friend declarations for overloaded stream insertion (<<) operators--these functions will be global functions. (No need to write the extraction operator >>).

Hints and notes

use a vector of unsigned char to hold the digits of the number--use push_back and pop_back to add and remove digits--store them in reverse order, e.g. the number 12345 is stored as digits 5, 4, 3, 2, 1

use const reference parameters in the member functions to avoid copying of the vector

use *new to create new objects of the class

return *this in the assignment operator

use bool for the return type of the relational operators

use for loops, either forward or backward to process elements

Testing

Your program should be able to succesfully compile and execute the following main function (assuming the name of the class is Bignum):

int main() {
  Bignum t1, t2(111), t3("1234567890"); // three different constructors
  Bignum t4 = t2; // default copy constructor

  cout << "t1 is " << t1 << endl;
  cout << "t2 is " << t2 << endl;
  cout << "t3 is " << t3 << endl;
  cout << "t4 is " << t4 << endl;

  t1 = t4 * t3 + t3 * t2; // arithmetic operators, and assignment
  
  cout << "t1 is " << t1 << endl;

  if (t1 < t2) // comparison
    cout << "t1 is less than t2" << endl;
  else
    cout << "t1 is not less than t2" << endl;

  if (t4 == t2) // equality
    cout << "t4 equals t2" << endl;
  else
    cout << "t4 does not equal t2" << endl;
}

Due date

Hand in a print of your completed source code file, with output of running with the above main function, by 5pm on Friday 27^th. March.