Simplification and optimization transformations of chains of recurrences
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
How fast can we compute products?
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Space-efficient evaluation of hypergeometric series
ACM SIGSAM Bulletin
Space-efficient evaluation of hypergeometric series
ACM SIGSAM Bulletin
Time-and space-efficient evaluation of some hypergeometric constants
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
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In this paper we consider the problem of fast computation of sums of n-ary products of rational numbers, for large n. We present improvements to the standard binary splitting algorithm which are due to numerous factors, including changing the standard arbitrary precision integer representation to one that is more suitable for such computations, unrolling, and chains of recurrences techniques. For the computation of &zgr;(3) to 640000 decimal digits, we achieve a speedup factor of 2.65 over the standard binary splitting algorithm, which compares favorably to the ideal case in which the numerator and the denominator can be reduced by their greatest common divisor at no cost. If asymptotically fast multiplication is not available (as in the Java Development Kit), a speedup of an order of magnitude is easily obtained.