A Dynamic Dual Fixed-Point Arithmetic Architecture for FPGAs

In FPGA embedded systems, designers usually have to make a compromise between numerical precision and logical resources. Scientific computations in particular, usually require highly accurate calculations and are computing intensive. In this context, a designer is left with the task of implementing several arithmetic cores for parallel processing while supporting high numerical precision with finite logical resources. This paper introduces an arithmetic architecture that uses runtime partial reconfiguration to dynamically adapt its numerical precision, without requiring significant additional logical resources. The paper also quantifies the relationship between reduced logical resources and savings in power consumption, which is particularly important for FPGA implementations. Finally, our results show performance benefits when this approach is compared to alternative static solutions within bounds on the reconfiguration rate.

[1]  Brad L. Hutchings,et al.  A dynamic instruction set computer , 1995, Proceedings IEEE Symposium on FPGAs for Custom Computing Machines.

[2]  Wayne Luk,et al.  Optimum and heuristic synthesis of multiple word-length architectures , 2005, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[3]  Gilbert Strang,et al.  Computational Science and Engineering , 2007 .

[4]  Reiner W. Hartenstein,et al.  A decade of reconfigurable computing: a visionary retrospective , 2001, Proceedings Design, Automation and Test in Europe. Conference and Exhibition 2001.

[5]  George A. Constantinides,et al.  Automated Precision Analysis: A Polynomial Algebraic Approach , 2010, 2010 18th IEEE Annual International Symposium on Field-Programmable Custom Computing Machines.

[6]  Scott Hauck,et al.  Reconfigurable computing: a survey of systems and software , 2002, CSUR.

[7]  Yvon Savaria,et al.  A comparison of automatic word length optimization procedures , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[8]  Y. Savaria,et al.  Variable-precision multiplier for equalizer with adaptive modulation , 2004, The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS '04..

[9]  Peter Y. K. Cheung,et al.  Dual Fixed-Point: An Efficient Alternative to Floating-Point Computation , 2004, FPL.

[10]  Eric C. Kerrigan,et al.  More Flops or More Precision? Accuracy Parameterizable Linear Equation Solvers for Model Predictive Control , 2009, 2009 17th IEEE Symposium on Field Programmable Custom Computing Machines.

[11]  Shahram Shirani,et al.  Run-Time Reconfigurable Systems for Digital Signal Processing Applications: A Survey , 2005, J. VLSI Signal Process..

[12]  Peter Y. K. Cheung,et al.  Error modelling of dual fixed-point arithmetic and its application in field programmable logic , 2005, International Conference on Field Programmable Logic and Applications, 2005..

[13]  Viktor K. Prasanna,et al.  Dynamic precision management for loop computations on reconfigurable architectures , 1999, Seventh Annual IEEE Symposium on Field-Programmable Custom Computing Machines (Cat. No.PR00375).

[14]  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 .

[15]  Gerhard J. Woeginger,et al.  The complexity of multiple wordlength assignment , 2002, Appl. Math. Lett..

[16]  Wayne Luk,et al.  Reconfigurable computing: architectures and design methods , 2005 .

[17]  Russell Tessier,et al.  c ○ 2001 Kluwer Academic Publishers. Manufactured in The Netherlands. Reconfigurable Computing for Digital Signal Processing: A Survey ∗ , 1999 .

[18]  Diederik Verkest,et al.  A reconfigurable manager for dynamically reconfigurable hardware , 2005, IEEE Design & Test of Computers.

[19]  Philip I. Davies,et al.  Numerically Stable Generation of Correlation Matrices and Their Factors , 2000 .

[20]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[21]  Sanghamitra Roy,et al.  An algorithm for trading off quantization error with hardware resources for MATLAB-based FPGA design , 2005, IEEE Transactions on Computers.

[22]  Wayne Luk,et al.  Wordlength optimization for linear digital signal processing , 2003, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[23]  D. Handelman Representing polynomials by positive linear functions on compact convex polyhedra. , 1988 .

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

[25]  Henry Stark,et al.  Probability, Random Processes, and Estimation Theory for Engineers , 1995 .

[26]  R. Dembo,et al.  INEXACT NEWTON METHODS , 1982 .

[27]  Gregory D. Peterson,et al.  High-Performance Mixed-Precision Linear Solver for FPGAs , 2008, IEEE Transactions on Computers.

[28]  André DeHon,et al.  Reconfigurable architectures for general-purpose computing , 1996 .

[29]  Jeff Mason,et al.  Invited Paper: Enhanced Architectures, Design Methodologies and CAD Tools for Dynamic Reconfiguration of Xilinx FPGAs , 2006, 2006 International Conference on Field Programmable Logic and Applications.

[30]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[31]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[32]  Jorge Stolfi,et al.  Affine Arithmetic: Concepts and Applications , 2004, Numerical Algorithms.

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

[34]  Implementation of CORDIC-Based QRD-RLS Algorithm on Altera Stratix FPGA with Embedded Nios Soft Processor Technology , 2004 .