Title
A variable RADIX-2<sup>r</sup> algorithm for single constant multiplication
Abstract
In previous work, a fully predictable sub-linear runtime heuristic for the multiplication by a constant based on Radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> arithmetic using a fixed radix was developed, called RADIX-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> . In this paper, we introduce a new constant multiplication algorithm based also on Radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> arithmetic but considering a variable radix. The new version is named RADIX-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> -VAR. Using a variable radix allows to optimize the average number of additions in the constant multiplication since a larger search space is explored. The new RADIX-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> -VAR recoding requires an average of 4.4% and 2.2% less additions than RADIX-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> for 24 and 32 bits, respectively. The RADIX-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> -VAR algorithm is combined with RADIX-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> for more improvements of the average number of additions. An overall saving of 6.7% and 5.5% is obtained over RADIX-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> for 24 and 32 bits, respectively.
Year
DOI
Venue
2017
10.1109/NEWCAS.2017.8010156
2017 15th IEEE International New Circuits and Systems Conference (NEWCAS)
Keywords
Field
DocType
High-Speed and Low-Power Design,Linear-Time-Invariant (LTI) Systems,Multiplierless Single/Multiple Constant Multiplication (SCM/MCM),Radix-2r Arithmetic
Heuristic,Multiplication algorithm,Algorithm design,Adder,Algorithm,Arithmetic,Radix,Prediction algorithms,Multiplication,Matrix multiplication,Mathematics
Conference
ISSN
ISBN
Citations 
2472-467X
978-1-5090-4992-9
1
PageRank 
References 
Authors
0.35
10
5
Name
Order
Citations
PageRank
Ahmed Liacha1174.54
Abdelkrim Kamel Oudjida2316.05
Farid Ferguene370.94
Jose Monteiro4660128.33
Paulo Flores527025.28