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Preex computation is a fundamental operation at the core of many important applications, e.g., some of the Grand Challenge problems, circuit design, digital signal processing, graph optimizations, and computational geometry. Given a 0 ; : : :; a N?1 , preex computation evaluates a 0 a 1 : : : a k , for 0 k < N, with associative operation. In this paper, we… (More)

Given xl,. .. , XN, parallel prefix computes ~1 0 X2 0. .. 0 xk, for 1 < k ~ N, with associative operation o. We show optimal schedules for parallel prefix computation with a fixed number of resources p > 2 for a prefix of size N ~ p(p + 1)/2. The time of the opt imal schedules with p resources is [2N/(p + 1)1 for N ~ p(p + 1)/2, which we prove to be the… (More)

We present a new technique for the high-level synthesis of scalable MCM-based architectures implementing infinite-impulse response(IIR) filters. Our technique is based on the regular schedules, a class of parallel schedules for computing mth-order IIR filters. The simplicity of the regular schedules facilitates characterization of their inter-processor… (More)

Linear dierence equations involving recurrences are fundamental equations that describe many important signal processes, in particular, innite-duration impulse response (IIR) lters. Applying conventional dependence-preserving parallelization techniques such as software pipelining can only extract limited parallelism due to loop-carried dependences in the… (More)

Many large-scale scientic and engineering computations, e.g., some of the Grand Challenge problems [1], spend a major portion of execution time in their core loops computing band linear recurrences (BLR's). Conventional compiler parallelization techniques [4] cannot generate scalable parallel code for this type of computation because they respect… (More)

Linear difference equations involving recurrences are fundamental equations that describe many import ant signal processing applications. For many high sample rate digital filter applications , we need to effectively parallelize the linear difference equations used to describe digital tilt ers – a difficult task due to the recurrences inherent in the data… (More)

An m-th order linear recurrence system of N equations computes x i = c i + P j=i0m i01 a ij x j for 1 i N. Linear recurrences have a role of central importance in computer design, numerical analysis, program analysis, digital signal processing and many non-numerical algorithms. However, programs containing band linear recurrences are dicult to signicantly… (More)

In this paper, we present a new scalable algorithm, called the Regular Schedule, for parallel evaluation of band linear recurrences (BLR's, i.e., mth-order linear recurrences for m 1). Its scalability and simplicity make it well suited for vector su-percomputers and massively parallel computers. We describe our implementation of the Regular Schedule on two… (More)

Parallel prex is a fundamental common operation at the core of many important applications, 1 k N , with associative operation. For prex of N elements on p processors in N > p(p+1)=2, we derive Harmonic Schedules and show that the Harmonic Schedules achieve the strict optimal time (steps), d2(N 0 1)=(p + 1)e. We also derived Pipelined Schedules, optimal… (More)