An enhanced Co-scheduling method using reduced MS-state diagrams
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. 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 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 efficient software pipelining method. The proposed software pipelining algorithm produced efficient schedules and performed better than R.A. Huff's (1993) 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.

title: A theory for software-hardware co-scheduling for ASIPs and embedded processors
abstract: Exploiting instruction-level parallelism (ILP) is extremely important for achieving high performance in application specific instruction set processors (ASIPs) and embedded processors. Existing techniques deal with either scheduling hardware pipelines to obtain higher throughput or software pipeline-an instruction scheduling technique for iterative computation-loops for exploiting greater ILP. We integrate these techniques to co-schedule hardware and software pipelines to achieve greater instruction throughput. In this paper, we develop the underlying theory of co-scheduling, called the Modulo-Scheduled Pipeline (or MS-Pipeline) theory. More specifically, we establish the necessary and sufficient condition for achieving the maximum throughput in a given pipeline operating under module scheduling. Further, we establish a sufficient condition to achieve a specified throughput, based on which we also develop a methodology for designing the hardware pipelines that achieve such a throughput.

title: A Framework for Resource-Constrained Rate-Optimal Software Pipelining
abstract: The rapid advances in high-performance computer architecture and compilation techniques provide both challenges and opportunities to exploit the rich solution space of software pipelined loop schedules. In this paper, we develop a framework to construct a software pipelined loop schedule which runs on the given architecture (with a fixed number of processor resources) at the maximum possible iteration rate (a la rate-optimal) while minimizing the number of buffers-a close approximation to minimizing the number of registers. The main contributions of this paper are: First, we demonstrate that such problem can be described by a simple mathematical formulation with precise optimization objectives under a periodic linear scheduling framework. The mathematical formulation provides a clear picture which permits one to visualize the overall solution space (for rate-optimal schedules) under different sets of constraints. Secondly, we show that a precise mathematical formulation and its solution does make a significant performance difference. We evaluated the performance of our method against three leading contemporary heuristic methods. Experimental results show that the method described in this paper performed significantly better than these methods. The techniques proposed in this paper are useful in two different ways: 1) As a compiler option which can be used in generating faster schedules for performance-critical loops (if the interested users are willing to trade the cost of longer compile time with faster runtime). 2) As a framework for compiler writers to evaluate and improve other heuristics-based approaches by providing quantitative information as to where and how much their heuristic methods could be further improved.

title: Co-scheduling hardware and software pipelines
abstract: In this paper we propose co-scheduling, a framework for simultaneous design of hardware pipelines structures and software-pipelined schedules. Two important components of the co-scheduling framework are: (1) An extension to the analysis of hardware pipeline design that meets the needs of periodic (or software pipelined) schedules. Reservation tables, forbidden latencies, collision vectors, and state diagrams from classical pipeline theory are revisited and extended to solve the new problems. (2) An efficient method, based on the above extension of pipeline analysis, to perform (a) software pipeline scheduling and (b) hardware pipeline reconfiguration which are mutually "compatible". The proposed method has been implemented and preliminary experimental results for 1008 kernel loops are reported. Co-scheduling successfully obtains a schedule for 95% of these loops. The median time to obtain these schedules is 0.25 seconds on a Sparc-20.

title: A Framework for Resource-Constrained Rate-Optimal Software Pipelining
abstract: The rapid advances in high-performance computer architecture and compilation techniques provide both challenges and opportunities to exploit the rich solution space of software pipelined loop schedules. In this paper, we develop a framework to construct a software pipelined loop schedule which runs on the given architecture (with a fixed number of processor resources) at the maximum possible iteration rate (a la rate-optimal) while minimizing the number of buffers-a close approximation to minimizing the number of registers. The main contributions of this paper are: First, we demonstrate that such problem can be described by a simple mathematical formulation with precise optimization objectives under a periodic linear scheduling framework. The mathematical formulation provides a clear picture which permits one to visualize the overall solution space (for rate-optimal schedules) under different sets of constraints. Secondly, we show that a precise mathematical formulation and its solution does make a significant performance difference. We evaluated the performance of our method against three leading contemporary heuristic methods. Experimental results show that the method described in this paper performed significantly better than these methods. The techniques proposed in this paper are useful in two different ways: 1) As a compiler option which can be used in generating faster schedules for performance-critical loops (if the interested users are willing to trade the cost of longer compile time with faster runtime). 2) As a framework for compiler writers to evaluate and improve other heuristics-based approaches by providing quantitative information as to where and how much their heuristic methods could be further improved.

title: Minimum Register Instruction Sequencing to Reduce Register Spills in Out-of-Order Issue Superscalar Architectures
abstract: In this paper, we address the problem of generating an optimal instruction sequence S for a Directed Acyclic Graph (DAG), where S is optimal in terms of the number of registers used. We call this the Minimum Register Instruction Sequence (MRIS) problem. The motivation for revisiting the MRIS problem stems from several modern architecture innovations/requirements that has put the instruction sequencing problem in a new context. We develop an efficient heuristic solution for the MRIS problem. This solution is based on the notion of instruction lineage-a set of instructions that can definitely share a single register. The formation of lineages exploits the structure of the dependence graph to facilitate the sharing of registers not only among instructions within a lineage, but also across lineages. Our efficient heuristics to "fuse" lineages further reduce the register requirement. This reduced register requirement results in generating a code sequence with fewer register spills. We have implemented our solution in the MIPSpro production compiler and measured its performance on the SPEC95 floating point benchmark suite. Our experimental results demonstrate that the proposed instruction sequencing method significantly reduces the number of spill loads and stores inserted in the code, by more than 50 percent in each of the benchmarks. Our approach reduces the average number of dynamic loads and stores executed by 10.4 percent and 3.7 percent, respectively. Further, our approach improves the execution time of the benchmarks on an average by 3.2 percent. In order to evaluate how efficiently our heuristics find a near-optimal solution to the MRIS problem, we develop an elegant integer linear programming formulation for the MRIS problem. Using a commercial integer linear programming solver, we obtain the optimal solution for the MRIS problem. Comparing the optimal solution from the integer linear programming tool with our heuristic solution reveals that, in a very large majority (99.2 percent) of the cases, our heuristic solution is optimal. For this experiment, we used a set of 675 dependence graphs representing basic blocks extracted from scientific benchmark programs.

title: Information Technology and Product Variety: Evidence from Panel Data
abstract: This paper examines the relationship between information technology and product variety. Consistent with prior theoretical work, we argue that IT and product variety are complements. IT innovations such as computer-aided design and flexible manufacturing technology have enabled firms to offer greater product variety at a reasonable cost. Similarly, firms seeking to offer greater variety can facilitate this strategy through IT investment. Using a novel approach to measuring product variety at the firm level through trademark counts we examine the relationship between IT and variety in four ways: direct correlations, IT and variety demand estimation, productivity analyses, and market value analyses. We utilize an 11-year panel data set of information technology capital stock, trademark holdings, and other measures for 512 Fortune 1000 firms to test our hypotheses. Overall, we find that IT is found to be associated with increased product variety, and that increased product variety increases demand for IT investment. Complementarities between IT and product variety are not significant in the productivity analysis but appear strongly when we consider their influence on firm valuation.

title: Exploiting short-lived variables in superscalar processors
abstract: In this paper we present experimental evidence showing that a significant number of program variables are short-lived in the sense that their live ranges span only a few instructions. In dynamically scheduled superscalar processors using mechanisms like the reorder buffer, the live ranges for these short-lived variables may occur entirely within the reorder buffer. Therefore, there should be no need to retire (commit) the values produced by these live ranges to the register file. On the basis of this observation, we have proposed a scheme that includes a compiler analysis and a simple architecture extension to avoid the useless commits of the values generated for these short-lived variables. Moreover we have proposed an extension to the existing register allocation mechanism that does not assign these short-lived variables to locations in the register file. Analyses and results are presented.