Python supports extremely long integers; so how does it implement the multiplication of two really long integers?
CPython uses a divide-and-conquer algorithm called the Karatsuba Algorithm to implement the multiplication of massive numbers efficiently. It works by recursively dividing the input numbers into smaller subproblems and then combining them to obtain the final product.
The time complexity of the Karatsuba algorithm is O(n^log₂ 3), which is asymptotically faster than the naive multiplication algorithm, which has a time complexity of O(n²).
When I was going through the implementation, I could see a familiar name “Knuth Vol 2”. This was one book that our teachers always told us to read, but we neglected.
The more I go through the source code of languages and databases, I see myself going back to my graduation days and referring to the same books that I once skipped.
You can find the implementation of this algorithm in the CPython codebase here. ref: https://lnkd.in/giiE8SiH
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