Binary splitting

In mathematics, binary splitting is a technique for speeding up numerical evaluation of series with rational terms.

The advantage of binary splitting comes from moving the bulk of the computation into the domain of multiplication using fast algorithms like Schönhage-Strassen. If a slower multiplication algorithm is used, binary splitting does not provide the same benefit.

Binary splitting is used by the fastest existing software for computing constants such as π and e to high accuracy.

References

• Xavier Gourdon & Pascal Sebah. Binary splitting method
• Bruno Haible & Thomas Papanikolaou. Fast multiprecision evaluation of series of rational numbers. Technical Report No. TI-7/97, Darmstadt University of Technology, 1997