Fast, accurate static analysis for fixed-point finite-precision effects in DSP designs

Fang, Claire Fang; Rutenbar, Rob A.; Chen, Tsuhan

doi:10.1109/iccad.2003.159701

Cited by 62 publications

(54 citation statements)

References 17 publications

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“…This mistake appears in many AAbased precision analysis or bitwidth optimization papers in literature [3]- [5]. )…”

Section: B Application Of Affine Arithmetic In Precision Analysismentioning

confidence: 99%

“…AA can often achieve tighter bounds than IA with better estimation of error cancelation. The work in [3] gives statistical interpretations of affine arithmetic.…”

Section: Introductionmentioning

confidence: 99%

“…The approach is a dynamic analysis, but when the number of the samples is large, it can serve as a reference for static analysis techniques. Affine arithmetic (AA) [6], as an improved static analysis technique over the traditional interval arithmetic (IA) [7], is used in [3]- [5] for precision analysis. AA can often achieve tighter bounds than IA with better estimation of error cancelation.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of Static Analysis Techniques for Fixed-Point Precision Optimization

Cong

Gururaj

Liu

et al. 2009

2009 17th IEEE Symposium on Field Programmable Custom Computing Machines

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Abstract-Precision analysis and optimization is very important when transforming a floating-point algorithm into fixedpoint hardware implementations. The core analysis techniques are either based on dynamic analysis or static analysis. We believe in static error analysis, as it is the only technique that can guarantee the desired worst-case accuracy. In this paper we study various underlying arithmetic candidates that can be used in static error analysis and compare their computed sensitivities. The approaches studied include Affine Arithmetic (AA), General Interval Arithmetic (GIA) and Automatic Differentiation (Symbolic Arithmetic). Our study shows that symbolic method is preferred for expressions with higher order cancelation. For programs without strong cancelation, any method works fairly well and GIA slightly outperforms others. We also study the impact of program transformations on these arithmetics.

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“…This mistake appears in many AAbased precision analysis or bitwidth optimization papers in literature [3]- [5]. )…”

Section: B Application Of Affine Arithmetic In Precision Analysismentioning

confidence: 99%

“…AA can often achieve tighter bounds than IA with better estimation of error cancelation. The work in [3] gives statistical interpretations of affine arithmetic.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Evaluation of Static Analysis Techniques for Fixed-Point Precision Optimization

Cong

Gururaj

Liu

et al. 2009

2009 17th IEEE Symposium on Field Programmable Custom Computing Machines

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“…and it is formed by a collection of affine forms at each time step n. This expression of the error can be used to estimate the error peak-value, using the traditional interpretation of AA [20,10], and, also, to obtain the PDF of the error [5,20]. However, in the next subsection we focus on obtaining the value of the power of the error considering the actual PDF of each error term (i.e.…”

Section: Affine Arithmetic Applied To Error Propagation Analysismentioning

confidence: 99%

“…(18) are developed in (19) and (20). The former makes use of the fact that it can be assumed that error terms i,k are uncorrelated to each other [12].…”

Section: Analytical Sqnr Estimationmentioning

confidence: 99%

Fast Fixed-Point Optimization of DSP Algorithms

Caffarena

Carreras

López

et al. 2012

VLSI-SoC: Forward-Looking Trends in IC and Systems Design

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Abstract. In this chapter, the fast fixed-point optimization of Digital Signal Processing (DSP) algorithms is addressed. A fast quantization noise estimator is presented. The estimator enables a significant reduction in the computation time required to perform complex fixed-point optimizations, while providing a high accuracy. Also, a methodology to perform fixed-point optimization is developed.Affine Arithmetic (AA) is used to provide a fast Signal-to-Quantization Noise-Ratio (SQNR) estimation that can be used during the fixed-point optimization stage. The fast estimator covers differentiable non-linear algorithms with and without feedbacks. The estimation is based on the parameterization of the statistical properties of the noise at the output of fixed-point algorithms. This parameterization allows relating the fixedpoint formats of the signals to the output noise distribution by means of fast matrix operations. Thus, a fast estimation is achieved and the computation time of the fixed-point optimization process is significantly reduced.The proposed estimator and the fixed-point optimization methodology are tested using a subset of non-linear algorithms, such as vector operations, IIR filter for mean power computation, adaptive filters -for both linear and non-linear system identification -and a channel equalizer. The computation time of fixed-point optimization is boosted by three orders of magnitude while keeping the average estimation error down to 6% in most cases.

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