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Made By Vatsal Agrawal

Karatsuba-multiplication-for-any-base-less-than-10-and-using-Big-Integer

Big Integer library for Addition and Karatsuba multiplication for any base less than 10 with exception raising

HOW TO MAKE EXECUTABLE AND RUN PROGRAMME****

  1. Run multiplication "564775447865215" "45522789553321555" 10 like function for Multiplication 10 is base passed here
  2. Run addition "564778954113512541" "455221555211225" 10 like function for addition 10 is base passed here
  3. Run main for prebuilt examples

Problem Statment

The goal in this problem is to create a big integer module in Haskell from scratch. Note that big integer arithmetic is widely used in multi-precision libraries in high-performance computing, as well as in cryptography (e.g., RSA). Your specific tasks include the implementation of addition and multiplication of two large integers. While the addition logic is the same as what is taugh in high school, the multiplication logic is going to be different. The multiplication of two n−digit numbers by the usual long multiplication algorithm (columnwise) that is taught in schools takes about O(n 2 ) single-digit multiplications. According to the Wikipedia, Karatsuba’s algorithm (discovered by Anatoly Karatsuba in 1960) reduces the complexity of multiplication of two n−digit numbers to at most n lg23 single-digit multiplications. Note that you may have to take special care for overflow. • Note that you are not allowed to use existing libraries for big integers. • Also, the input and output numbers to these functions are strings of digits. Therefore, define auxillary functions fromString: string -> [int] and toString: [int] -> string for purposes of input and output, respectively. • Your solution should be parametric in the base B in which the lists of digits have to be manipulated. • The Karatsuba multiplication function takes two numbers as input and returns the result of multiplication. The function to compute Karatsuba multiplication should have signature karatsuba: [int] -> [int] -> [int] • If the input string is not a valid number, your program should raise an exception of type exception string Invalid Input exception.