An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
C language algorithms for real-time DSP
C language algorithms for real-time DSP
MediaBench: a tool for evaluating and synthesizing multimedia and communicatons systems
MICRO 30 Proceedings of the 30th annual ACM/IEEE international symposium on Microarchitecture
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Advanced compiler design and implementation
Advanced compiler design and implementation
The Generation of Optimal Code for Arithmetic Expressions
Journal of the ACM (JACM)
Code Generation for Expressions with Common Subexpressions
Journal of the ACM (JACM)
Generation of optimal code for expressions via factorization
Communications of the ACM
Using symbolic algebra in algorithmic level DSP synthesis
Proceedings of the 38th annual Design Automation Conference
Low Power Embedded Software Optimization Using Symbolic Algebra
Proceedings of the conference on Design, automation and test in Europe
The impact of loop unrolling on controller delay in high level synthesis
Proceedings of the conference on Design, automation and test in Europe
Optimization of polynomial datapaths using finite ring algebra
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Algebraic Methods for Optimizing Constant Multiplications in Linear Systems
Journal of VLSI Signal Processing Systems
Finding linear building-blocks for RTL synthesis of polynomial datapaths with fixed-size bit-vectors
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Verification of arithmetic datapaths using polynomial function models and congruence solving
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Polynomial datapath optimization using partitioning and compensation heuristics
Proceedings of the 46th Annual Design Automation Conference
Improved heuristics for finite word-length polynomial datapath optimization
Proceedings of the 2009 International Conference on Computer-Aided Design
Modular datapath optimization and verification based on modular-HED
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient evaluation of large polynomials
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Polynomial datapath optimization using constraint solving and formal modelling
Proceedings of the International Conference on Computer-Aided Design
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Polynomial expressions are used to compute a wide variety of mathematical functions commonly found in signal processing and graphics applications, which provide good opportunities for optimization. However existing compiler techniques for reducing code complexity such as common subexpression elimination and value numbering are targeted towards general purpose applications and are unable to fully optimize these expressions. This work presents algorithms to reduce the number of operations to compute a set of polynomial expression by factoring and eliminating common subexpressions. These algorithms are based on the algebraic techniques for multi-level logic synthesis. Experimental results on a set of benchmark applications with polynomial expressions showed an average of 42.5% reduction in the number of multiplications and 39.6% reduction in the number of clock cycles for computation of these expressions on the ARM processor core, compared to common subexpression elimination.