Tight Timing Estimation With the Newton-Gregory Formulae∗

Parametric worst-case execution time (WCET) bounds are critical in removing restrictions, such as known loop bounds, on algorithms for important applications such as scheduling for real-time embedded systems. Current parametric approaches have difficulties with loop nests that include non-rectangular loops, zero-trip loops, and/or loops with non-unit strides. This paper presents a novel approach to parametric WCET estimation based on numeric/symbolic manipulation of polynomial representations for the timing of rectangular and non-rectangular loop nests including those with zero-trip loops, non-unit strides, and multiple critical paths.