Multiplierless multiple constant multiplication
ACM Transactions on Algorithms (TALG)
Digital filter synthesis based on an algorithm to generate all minimal signed digit representations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A novel optimal single constant multiplication algorithm
Proceedings of the 47th Design Automation Conference
Optimization Algorithms for the Multiplierless Realization of Linear Transforms
ACM Transactions on Design Automation of Electronic Systems (TODAES)
CSD-RNS-based Single Constant Multipliers
Journal of Signal Processing Systems
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Common subexpression elimination (CSE) algorithms try to minimize the number of adders (or subtracters) required to implement constant multiplication by searching and substituting common patterns in the CSE representation of a constant. CSE algorithms, in general, cannot find certain patterns due to inherent restrictions in the CSE representation. We propose overlapping digit patterns (ODPs) to remove some of these restrictions. We integrate ODPs into H(k), the best existing heuristic algorithm for single constant multiplication (SCM). H(k) is not applicable to the multiple constant multiplication (MCM) problem, so we cannot consider this problem. Generally, H(k) finds solutions very close to optimal, so there is a strict limitation on any further improvement which applies to any new heuristic. Instead, by integrating ODPs within H(k), we can on average significantly improve the run time of the algorithm (typically by one order of magnitude) while still reducing the number of adders.