Fast and Correct SIMD Algorithms for Interval Arithmetic

Abstract. SIMD instructions on floating-point numbers have been read-ily available on ix86 computers for the past ten years or so. Almost from the start, they have been considered to compute the two bounds of inter-vals in parallel. Some authors reported marginal improvements over pure sequential computation, and those who reported otherwise had made choices that relinquished reliability. We discuss these works, pointing out their achievements and shortcomings, and then present data storage and SIMD algorithms that are both correct and much faster than the fastest routines in standard interval libraries.