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Optimal Constant Multiplication Using Integer Linear Programming
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DOI：10.1109/TCSII.2018.2823780.png)
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Abstract
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Constant multiplication circuits can be realized multiplierless by using additions, subtractions, and bit-shifts. The problem of finding a multiplication circuit with minimum adders and subtractors for a given constant (set of constants) is known as single (multiple) constant multiplication (SCM, MCM) problem. This brief proposes a novel integer linear programming (ILP) formulation to optimally solve SCM and MCM problems. In contrast to previous ILP approaches, none of the possible intermediate constants have to be pre-computed as all additions are directly evaluated. This leads to fewer ILP variables and more compact models. Due to the flexibility of ILP, the proposed model can be extended to several other (secondary) objectives. To demonstrate this, an extension for minimal SCM and MCM circuits using 3-input adders as well as an extension for minimizing the circuits' glitch path count for low power applications are provided. The experimental results show that the formulation is useful for practically relevant problem sizes.
Keywords:
Multiplying circuits
field programmable gate arrays
arithmetic
digital arithmetic
fixed-point arithmetic
Optimization methods
Circuit optimization
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