Abstract—Utility-directed transformations involve changing a design to optimize for given constraints while preserving behavior. These changes are often achieved by techniques such as linear programming or geometric programming. We present a systematic approach composing multiple utility-directed transformations for optimizing and mapping a sequential design onto a customizable parallel computing platform such as a Field-Programmable Gate Array (FPGA). Our aim is to enable automatic design optimization at compile time. Design goals specified by users drive the design transformations. Each utility-directed transformation achieves part of the overall goal, and multiple utility-directed transformations, connected by pattern-directed transformations, are composed to fulfil the overall design requirements. The utility-directed transformations in this work produce performance-optimized designs by exploiting data reuse, MapReduce and pipelining for the target parallel computing platform. Moreover, it is shown that performing transformations in different orders allows users to trade speed for resources, and design performance for compile time. Several applications are used to evaluate this approach on FPGAs. The system performance of a 64-bit matrix multiplication is shown to improve up to 98 times compared to the original design, in the target hardware platform. Index Terms—Design optimization, data reuse, MapReduce, pipelining, geometric programming. 1

Abstract The MapReduce pattern can be found in many important applications, and can be exploited to significantly improve system parallelism. Unlike previous work, in which designers explicitly specify how to exploit the pattern, we develop a compilation approach for mapping applications with the MapReduce pattern automatically onto Field-Programmable Gate Array (FPGA) based parallel computing platforms. We formulate the problem of mapping the MapReduce pattern to hardware as a geometric programming model; this model exploits loop-level parallelism and pipelining to give an optimal implementation on given hardware resources. The approach is capable of handling single and multiple nested MapReduce patterns. Furthermore, we explore important variations of MapReduce, such as using a linear structure rather than a tree structure for merging intermediate results generated in parallel. Results for six benchmarks show that our approach can find performance-optimal designs in the design space, improving system performance by up to 170 times compared to the initial designs on the target platform.