Technical Report an Enhanced Co-scheduling Method Using Reduced Ms-state Diagrams 1

Instruction scheduling methods based on the construction of state diagrams (or automatons) have been used for architectures involving deeply pipelined function units. However, the size of the state diagram is prohibitively large, resulting in high execution time and space requirement, which in turn, restrict the use of these methods. In this paper, we develop the underlying theory for reducing the size of state diagrams by identifying primary paths of a state diagram. We establish that a reduced state diagram consisting only primary paths is complete, i.e., it retains all the useful information represented by the original state diagram as far as scheduling of operations in the software pipelining method is concerned. Our experiments show that the number of paths in the reduced state diagram is signi cantly lower | by 1 to 3 orders of magnitude | compared to the number of paths in the original state diagram. Using the reduced MS-state diagrams, we develop an e cient software pipelining method. The proposed software pipelining algorithm produced e cient schedules when tested on a set of 1153 benchmark loops. Further our software pipelining method performs signi cantly better than the original Co-scheduling method as well as Hu 's Slack Scheduling method, in terms of both the initiation interval (II) and the time taken to construct a schedule. i