IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Improved use of the carry-save representation for the synthesis of complex arithmetic circuits
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
An exact algorithm for the maximal sharing of partial terms in multiple constant multiplications
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Optimizing high speed arithmetic circuits using three-term extraction
Proceedings of the conference on Design, automation and test in Europe: Proceedings
Multiplierless multiple constant multiplication
ACM Transactions on Algorithms (TALG)
Circuit optimization using carry-save-adder cells
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A new algorithm for elimination of common subexpressions
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
| Hi-index | 0.00 |
In the last decade, efficient algorithms have been proposed for the multiplication of one data sample with multiple constants using addition/subtraction and shift operations, i.e., the multiple constant multiplications (MCM) problem. However, in these algorithms, an addition/subtraction operation is assumed to be a two-input operation that is generally implemented with ripple carry adders increasing the delay of the computation. On the other hand, carry-save adders (CSAs) are commonly used for high-speed implementation of multi-operand additions. The previously proposed algorithms designed for the optimization of the number of CSA blocks obtain good results, but they have been heuristics and cannot guarantee the minimum solution. In this work, we introduce an exact common subexpression elimination (CSE) algorithm that finds the minimum number of CSA blocks in the implementation of MCM. Furthermore, we present an approximate algorithm based on the exact CSE algorithm that can also handle general number representation of constants. It is shown by the experimental results that the algorithms introduced in this paper obtain competitive and better results than the previously proposed heuristics.