header for SPIE use Theoretical Constraints on Multi-Dimensional Retiming Design Techniques

Image signal processing depends on computation intensive programs, which include the repetition of sequences of operations coded as nested loops. An effective technique in increasing the computing performance of such applications is the design and use of Application Specific Integrated Circuits using loop transformation techniques, and in particular, multidimensional (MD) retiming. The MD-retiming method improves the instruction-level parallelism of uniform loops. While many have written about the multi-dimensional retiming technique, no results have been published on the possible limitations of its application. This paper presents an analysis of that technique and its constraints when applied to nested loops with known index bounds, such as those found in two and three dimensional image processing

Loop Pipelining for Scheduling Multi-Dimensional Systems via Rotation

Abstract Multi-dimensional (MD) systems are widely used in scienti c applications such as image processing, geophysical signal processing and uid dynamics. Earlier scheduling methods in synthesizing MD systems do not explore loop pipelining across di erent dimensions. This paper explores the basic properties of MD loop pipelining and presents an algorithm, called multi-dimensional rotation scheduling, to nd an e cient schedule based on the multi-dimensional retiming technique we developed. The description and the correctness of our algorithm are presented in the paper. The experiments show that our algorithm can achieve optimal results e ciently. I

Loop Pipelining for Scheduling Multi-dimensional Systems via Rotation

Multi-dimensional (MD) systems are widely used in scientific applications such as image processing, geophysical signal processing and fluid dynamics. Earlier scheduling methods in synthesizing MD systems do not explore loop pipelining across different dimensions. This paper explores the basic properties of MD loop pipelining and presents an algorithm, called multi-dimensional rotation scheduling, to find an efficient schedule based on the multidimensional retiming technique we developed. The description and the correctness of our algorithm are presented in the paper. The experiments show that our algorithm can achieve optimal results efficiently. 1 Introduction Computation intensive applications usually depend on time-critical sections consisting of a loop of instructions. To optimize the execution rate of such applications, the designer needs to explore the parallelism embedded in repetitive patterns of a loop. However, the existence of resource constraints makes the problem of sche..