DAC '96 Proceedings of the 33rd annual Design Automation Conference
Digital filter synthesis based on minimal signed digit representation
Proceedings of the 38th annual Design Automation Conference
Multiplierless multiple constant multiplication
ACM Transactions on Algorithms (TALG)
Search algorithms for the multiple constant multiplications problem: Exact and approximate
Microprocessors & Microsystems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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The multiple constant multiplications (MCM) problem, that is defined as finding the minimum number of addition and subtraction operations required for the multiplication of multiple constants by an input variable, has been the subject of great interest since the complexity of many digital signal processing (DSP) systems is dominated by an MCM operation. This paper introduces a variant of the MCM problem, called multiple tunable constant multiplications (MTCM) problem, where each constant is not fixed as in the MCM problem, but can be selected from a set of possible constants. We present an exact algorithm that formalizes the MTCM problem as a 0--1 integer linear programming (ILP) problem when constants are defined under a number representation. We also introduce a local search method for the MTCM problem that includes an efficient MCM algorithm. Furthermore, we show that these techniques can be used to solve various optimization problems in finite impulse response (FIR) filter design and we apply them to one of these problems. Experimental results clearly show the efficiency of the proposed methods when compared to prominent algorithms designed for the MCM problem.