Symbolic noise analysis approach to computational hardware optimization

This paper addresses the problem of computational error modeling and analysis. Choosing different word-lengths for each functional unit in hardware implementations of numerical algorithms always results in an optimization problem of trading computational error with implementation costs. In this study, a symbolic noise analysis method is introduced for high-level synthesis, which is based on symbolic modeling of the error bounds where the error symbols are considered to be specified with a probability distribution function over a known range. The ability to combine word-length optimization with high-level synthesis parameters and costs to minimize the overall design cost is demonstrated using case studies.

[1]  Robert W. Brodersen,et al.  A perturbation theory on statistical quantization effects in fixed-point DSP with non-stationary inputs , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[2]  Brian L. Evans,et al.  Optimum Wordlength Search Using Sensitivity Information , 2006, EURASIP J. Adv. Signal Process..

[3]  R. Cmar,et al.  A methodology and design environment for DSP ASIC fixed point refinement , 1999, Design, Automation and Test in Europe Conference and Exhibition, 1999. Proceedings (Cat. No. PR00078).

[4]  Rob A. Rutenbar,et al.  Fast, Accurate Static Analysis for Fixed-Point Finite-Precision Effects in DSP Designs , 2003, ICCAD.

[5]  Bertrand Le Gal,et al.  Bit-Width Aware High-Level Synthesis for Digital Signal Processing Systems , 2006, SoCC.

[6]  Takashi Horiyama,et al.  Bit-Length Optimization Method for High-Level Synthesis Based on Non-linear Programming Technique , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[7]  Yajun Ha,et al.  An automated, efficient and static bit-width optimization methodology towards maximum bit-width-to-error tradeoff with affine arithmetic model , 2006, Asia and South Pacific Conference on Design Automation, 2006..

[8]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[9]  Mark Zwolinski,et al.  Multiple-Width Bus Partitioning Approach to Datapath Synthesis , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[10]  Vladik Kreinovich,et al.  Interval Arithmetic, Affine Arithmetic, Taylor Series Methods: Why, What Next? , 2004, Numerical Algorithms.

[11]  George A. Constantinides,et al.  Word-length optimization for differentiable nonlinear systems , 2006, TODE.

[12]  Heinrich Meyr,et al.  FRIDGE: a fixed-point design and simulation environment , 1998, Proceedings Design, Automation and Test in Europe.

[13]  Wonyong Sung,et al.  Combined word-length optimization and high-level synthesis ofdigital signal processing systems , 2001, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[14]  Sanghamitra Roy,et al.  An Algorithm for Trading Off Quantization Error with Hardware Resources for MATLAB-Based FPGA Design , 2005, IEEE Trans. Computers.

[15]  M. Zwolinski,et al.  A Symbolic Noise Analysis Approach to Word-Length Optimization in DSP Hardware , 2007, 2007 International Symposium on Integrated Circuits.

[16]  Octavio Nieto-Taladriz,et al.  Improved Interval-Based Characterization of Fixed-Point LTI Systems With Feedback Loops , 2007, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[17]  Wayne Luk,et al.  Ieee Transactions on Computer-aided Design of Integrated Circuits and Systems Accuracy Guaranteed Bit-width Optimization Abstract— We Present Minibit, an Automated Static Approach for Optimizing Bit-widths of Fixed-point Feedforward Designs with Guaranteed Accuracy. Methods to Minimize Both the In- , 2022 .

[18]  Alan V. Oppenheim,et al.  Discrete-time signal processing (2nd ed.) , 1999 .

[19]  Alok N. Choudhary,et al.  Precision and error analysis of MATLAB applications during automated hardware synthesis for FPGAs , 2001, Proceedings Design, Automation and Test in Europe. Conference and Exhibition 2001.

[20]  Wayne Luk,et al.  Synthesis and optimization of DSP algorithms , 2004 .