In mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms.
When a and b are sufficiently close, P(a, b) and Q(a, b) can be computed directly from pa...pb and qa...qb.
Binary splitting requires more memory than direct term-by-term summation, but is asymptotically faster since the sizes of all occurring subproducts are reduced.
Additionally, whereas the most naive evaluation scheme for a rational series uses a full-precision division for each term in the series, binary splitting requires only one final division at the target precision; this is not only faster, but conveniently eliminates rounding errors.
Since all subdivisions of the series can be computed independently of each other, binary splitting lends well to parallelization and checkpointing.