An enhanced Co-scheduling method using reduced MS-state diagrams

Abstract

Instruction scheduling methods based on the construction of state diagrams (or automata) 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. In this paper, we present a simple method for reducing the size of the state diagram by recognizing unique paths of a state diagram. Our experiments show that the number of paths in the reduced state diagram is significantly lowerby 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 efficient software pipelining method. The proposed software pipelining algorithm produced efficient schedules and performed better than Huff's Slack Scheduling method, and the original Co-scheduling method, in terms of both the initiation interval (II) and the time taken to construct the schedule.

Efficient State-Diagram Construction Methods for Software Pipelining

“…The state diagram for the above reservation table is shown in Figure 2. For more detailed information on related concepts and the construction of state diagrams see [6,7,8]. …”

“…Their approach was based on [12] and subsequently improved and applied to production compilers in [2]. This approach was extended to software pipelining methods in [6,7]. This paper focuses on the efficient construction of finite state automata for software pipelining methods.…”

“…This paper focuses on the efficient construction of finite state automata for software pipelining methods. In the above methods [2,6,7,12,14], processor resources are modeled using a finite state automata (or state diagram) which is constructed from the resource usage table for each instruction (class). Each path in the state diagram represents a legal latency sequence which could be directly used by the scheduler for modeling resource contention.…”

“…The construction of the state diagram is typically done off-line and stored in some form so that the instruction scheduler, at the schedule time, only need to read this information. This has effectively reduced the problem of checking structural hazards in the scheduling method to a fast table lookup, resulting in several fold speedup [2,7,12]. In particular, the enhanced Co-Scheduling method, a state diagram based modulo scheduling method, reports a 2-fold speedup in the scheduling time (time to construct the software pipelined schedule) [7].…”

“…This obviously makes the Co-Scheduling approach impractical. The previous effort on reduced state diagram [7,8] has met with only very limited success.…”