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most bignum libraries do not use base 10, as far as I can tell (why should they? it would be ridiculous) |
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The major improvement in this algorithm arises because the number of operations required is O(log y) rather than O(y). For numbers which can be represented directly as computer words a further benefit is that multiplying by 2 is equivalent to an arithmetic shift left, while division by 2 is equivalent to an arithmetic shift right. Clearly the major benefits arise when y is very large in which case it will not be possible to represent it as a single computer word.
This may not help so much for multiplcation by [[real number|real]] or [[complex number|complex]] values, but is useful for multiplication of very large integers which are supported in some programming languages such as [[Haskell]].
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