Project 1: Big Integer Arithmetic

For this project I would like you to create a bigInt class which overloads all of the basic arithmetic operations *, +, - and never faces an overflow.

All integers in C++ have finite size (yours will too at any particular moment) but I want you to manage the growth of your integers as users act on them.

By the way, this task, if done right, can lead to a successful career. Many great minds have thought about how to make the basics really fast. You guys don't have to worry about speed or read papers, but if you would like to ding the world you can explore how researchers are doing this.

Your tasks

• Decide how to get data into an instance of your class.
• Overload +, *, - to combine two bigInts into another bigInt. (Or make a different choice and defend it.)
• Allow division of bigInts which returns a double, and a different division which returns the integer quotient as a bigInt.
• Overload << so that cout displays the bigInt well. Do >> for cin to.
• Give an indication of your performance at various sizes.

Extra Credit Tasks

• Create a matrix of bigInts which can also be added and multiplied both by a scalar and another matrix.
• Report the complexity of your matrix multiplication algorithm, and your integer multiplication algorithm.

Resources

Check out this set of tutorials on overloading (pretty simple).

Check out https://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic

https://en.wikipedia.org/wiki/List_of_arbitrary-precision_arithmetic_software