Parametric worst case execution time (WCET) bounds are useful in removing restrictions, such as known loop bounds, on algorithms for important applications such as scheduling for real-time embedded systems. However, current parametric approaches have difficulties with multiple loop nests that include non-rectangular loops, zero-trip loops, and/or loops with non-unit strides. These difficulties may result in the increased looseness of the upper bound, increased complexity in determining the bound, or loss of the upper bound property of the estimate. In this paper, we propose a new framework to compute tight parameterized WCET bounds for multiple loop nests that may include nonrectangular loops, zero-trip loops, and loops with non-unit strides. The framework requires only very simple symbolic manipulation capabilities and is restricted only by certain monotonic properties required of the iteration spaces of the inner loops.
展开▼
