Interval Arithmetic Using SSE-2

We present an implementation of double precision interval arithmetic using the single-instruction-multiple-data SSE-2 instruction and register set extensions. The implementation is part of a package for exact real arithmetic, which defines the interval arithmetic variation that must be used: incorrect operations such as division by zero cause exceptions, loose evaluation of the operations is in effect, and performance is more important than tightness of the produced bounds. The SSE2 extensions are suitable for the job, because they can be used to operate on a pair of double precision numbers and include separate rounding mode control and detection of the exceptional conditions. The paper describes the ideas we use to fit interval arithmetic to this set of instructions, shows a performance comparison with other freely available interval arithmetic packages, and discusses possible very simple hardware extensions that can significantly increase the performance of interval arithmetic.