Circuit retiming applied to decomposed software pipelining

Abstract

International audienceThis paper elaborates on a new view on software pipelining, called decomposed software pipelining. The approach is to decouple the problem into resource constraints and dependence constraints. Resource constraints management amounts to scheduling an acyclic graph subject to resource constraints for which an efficiency bound is known, resulting in a bound for loop scheduling. The acyclic graph is obtained by cutting some particular edges of the (cyclic) dependence graph. In this paper, we cut edges in a different way, using circuit retiming algorithms, so as to minimize both the longest dependence path in the acyclic graph, and the number of edges in the acyclic graph. With this technique, we improve the efficiency bound given for Gasperoni and Schwlegelshohn algorithm, and we reduce the constraints that remain for the acyclic problem. We believe this framework to be of interest because it brings a new insight into the software problem by establishing its deep link with the circuit retiming proble

Predicate-aware, makespan-preserving software pipelining of scheduling tables

“…Closest to our work are previous results on decomposed software pipelining [Wang and Eisenbeis 1993;Gasperoni and Schwiegelshohn 1994;Calland et al 1998]. In these papers, the software pipelining of a sequential loop is realized using two-phase heuristic approaches with good practical results.…”

“…As noted in Calland et al [1998], existing decomposed software pipelining approaches solve this loop scheduling problem by using retiming algorithms. Retiming [Leiserson and Saxe 1991] can therefore be seen as a very specialized form of pipelining targeted at cyclic (synchronous) systems where each operation has its own execution unit.…”

“…To (heuristically) solve this optimization problem, we use a two-phase scheduling flow that can be seen as a form of decomposed software pipelining [Wang and Eisenbeis 1993;Gasperoni and Schwiegelshohn 1994;Calland et al 1998]. As pictured in Figure 1, the first phase of this flow consists in applying one of the previously mentioned makespan-optimizing tools.…”

Combining Extended Retiming and Unfolding for Rate-Optimal Graph Transformation

“…If no copy of v is split, then there exists an integer i 0 such that M , Sv;i, 1 Proof: The equivalence of (1) and (2) is given by Lemma 2.3 (Lemma 3.1 of [4]). The equivalence of (2) and (3) is Theorem 6.3 above.…”

“…This technique was introduced in [10] to optimize the throughput of synchronous circuits, and has since been used extensively in such diverse areas as software pipelining [1,16] and hardware-software codesign [6,17]. We have shown previously that this traditional form of retiming [12] cannot produce optimal results when applied individually.…”