Depth-size trade-offs for parallel prefix computation
Journal of Algorithms
Compiling techniques for first-order linear recurrences on a vector computer
The Journal of Supercomputing
Automatic recognition of induction variables and recurrence relations by abstract interpretation
PLDI '90 Proceedings of the ACM SIGPLAN 1990 conference on Programming language design and implementation
Program optimization and parallelization using idioms
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Optimal schedules for parallel prefix computation with bounded resources
PPOPP '91 Proceedings of the third ACM SIGPLAN symposium on Principles and practice of parallel programming
Time Optimal Linear Schedules for Algorithms with Uniform Dependencies
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Independent Partitioning of Algorithms with Uniform Dependencies
IEEE Transactions on Computers
Speedup of band linear recurrences in the presence of resource constraints
ICS '92 Proceedings of the 6th international conference on Supercomputing
The Organization of Computations for Uniform Recurrence Equations
Journal of the ACM (JACM)
The Complexity of Parallel Evaluation of Linear Recurrences
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Practical Parallel Band Triangular System Solvers
ACM Transactions on Mathematical Software (TOMS)
Structure of Computers and Computations
Structure of Computers and Computations
On Time Mapping of Uniform Dependence Algorithms into Lower Dimensional Processor Arrays
IEEE Transactions on Parallel and Distributed Systems
Recognizing and Parallelizing Bounded Recurrences
Proceedings of the Fourth International Workshop on Languages and Compilers for Parallel Computing
New bounds for parallel prefix circuits
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Derivation, extensions and parallel implementation of regular iterative algorithms
Derivation, extensions and parallel implementation of regular iterative algorithms
Parallel Processing of First Order Linear Recurrence on SMP Machines
The Journal of Supercomputing
Optimizing techniques for saturated arithmetic with first-order linear recurrence
Proceedings of the 2009 ACM symposium on Applied Computing
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Many large-scale scientific 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 (BLRs). Conventional compiler parallelization techniques[4] cannot generate scalable parallel code for this type of computation because they respect loop-carried dependences (LCDs) in programs, and there is a limited amount of parallelism in a BLR with respect to LCDs. For many applications, using library routines to replace the core BLR requires the separation of BLR from its dependent computation, which usually incurs significant overhead. In this paper, we present a new scalable algorithm, called the Regular Schedule, for parallel evaluation of BLRs. We describe our implementation of the Regular Schedule and discuss how to obtain maximum memory throughput in implementing the schedule on vector supercomputers. We also illustrate our approach, based on our Regular Schedule, to parallelizing programs containing BLR and other kinds of code. Significant improvements in CPU performance for a range of programs containing BLR implemented using the Regular Schedule in C over the same programs implemented using highly optimized coded-in-assembly BLAS routines [11] are demonstrated on Convex C240. Our approach can be used both at the user level in parallel programming code containing BLRs, and in compiler parallelization of such programs combined with recurrence recognition techniques for vector supercomputers.