New submission from benrg <[email protected]>:
math.prod is slow at multiplying arbitrary-precision numbers. E.g., compare the
run time of factorial(50000) to prod(range(2, 50001)).
factorial has some special-case optimizations, but the bulk of the difference
is due to prod evaluating an expression tree of depth n. If you re-parenthesize
the product so that the tree has depth log n, as factorial does, it's much
faster. The evaluation order of prod isn't documented, so I think the change
would be safe.
factorial uses recursion to build the tree, but it can be done iteratively with
no advance knowledge of the total number of nodes.
This trick is widely useful for turning a way of combining two things into a
way of combining many things, so I wouldn't mind seeing a generic version of it
in the standard library, e.g. reduce(..., order='mid'). For many specific cases
there are more efficient alternatives (''.join, itertools.chain, set.unions,
heapq.merge), but it's nice to have a recipe that saves you the trouble of
writing special-case algorithms at the cost of a log factor that's often
ignorable.
----------
components: Library (Lib)
messages: 414126
nosy: benrg
priority: normal
severity: normal
status: open
title: Improve performance of math.prod with bignums (and functools.reduce?)
type: enhancement
versions: Python 3.11
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<https://bugs.python.org/issue46868>
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