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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)

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)

teehniaue for the hi~h-level svnthesis of scalable 1 MCM-based architectures implementing ;nfinite-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 communications ,… (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)

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)