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Large Integer Multiplication

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IT University of Copenhagen
Last Update: 2008-07-31 22:40:22
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2008
Mathematical operations are central part of many algorithms. In order to achieve faster computational speeds, these operations need to be efficient. Integer multiplication is one of those operations. Classrooms everywhere teach the classic method of multiplying each digit on one number with a digit of the other resulting in a complexity of O(n squared). Karatsuba introduced a method that required O(n power 1.54). His method used Divide & Conquer. In this project, a similar algorithm is introduced. The algorithm uses the intuition of using Divide and Conquer as in the Karatsuba, but this time, squares of differences are utilized instead. Various optimizations are then discussed and implemented to improve its computational efficiency.