Fast parallel arithmetic via modular representation
SIAM Journal on Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
A Novel Division Algorithm for the Residue Number System
IEEE Transactions on Computers - Special issue on computer arithmetic
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A New Euclidean Division Algorithm for Residue Number Systems
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
A Look-Up Scheme for Scaling in the RNS
IEEE Transactions on Computers
A Library for Parallel Modular Arithmetic
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Implementation of residue number systems on GPUs
ACM SIGGRAPH 2006 Research posters
Fast arithmetics using Chinese remaindering
Information Processing Letters
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This contribution to the ongoing discussion of division algorithms for residue number systems (RNS) is based on Newton iteration for computing the reciprocal. An extended RNS with twice the number of moduli provides the range required for multiplication and scaling. Separation of the algorithm description from its RNS implementation achieves a high level of modularity, and makes the complexity analysis more transparent. The number of iterations needed is logarithmic in the size of the quotient for a fixed start value. With preconditioning it becomes the logarithm of the input bit size. An implementation of the conversion to mixed radix representation is outlined in the appendix.