algorithm - What would be an efficient way of calculating ratio of two factorials with arbitrary precision? -


in research paper, read following statement

the computations of s (...) , c (...) involve computing ratios of factorials such (2n)!/(2k)!, 0 ≤k ≤ n. can done in time o(n^2(logn)^2) straightforward algorithm.

they have not mentioned straightforward algorithm talking about. if talking direct multiplication of integers, according this link, total time n! calculation alone o(n^2 log n) leaves around o(log n) time division, think not possible.

one approach can think of is:- 1.) choosing fast factorial algorithm here. 2.) dividing using schönhage–strassen algorithm combined newton’s reciprocal method.

it's initial idea though.

is there more specific efficient algorithm calculating ratio of 2 factorials arbitrary precision?

you not need divide, multiply numbers (2k+1) (2n), can done in limits specified;).


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