Floating-point bitwidth analysis via automatic differentiation

Gaffar, A.A.; Mencer, Oskar; Luk, Wayne; Cheung, Peter Y. K.; Shirazi, N.

doi:10.1109/fpt.2002.1188677

Cited by 36 publications

(31 citation statements)

References 2 publications

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“…Accuracy guaranteed approaches employ static analysis and thus cannot always determine the number of iterations. Existing approaches [1,6] cover loops by simply unrolling them, however this technique is not practical for programs with large iteration spaces.…”

Section: Code Analysis and Instrumentationmentioning

confidence: 99%

“…Abdul Gaffer et al [1] use an approach called automatic differentiation which involves looking at the signals at different times and determining the width. Although this approach tends to be less time-consuming, neither approach is guaranteed to produce correct results for a given input.…”

Section: Related Workmentioning

confidence: 99%

“…They can be performed statically or dynamically. Static approaches [6,13] tend to be faster, but can over-estimate the result while dynamic analysis [1,4] does not usually guarantee the accuracy of results because it uses simulated inputs.…”

Section: Introductionmentioning

confidence: 99%

“…The first is a simulation-based approach [1,4,13] which involves optimizing the lengths for a specific training set. This has the obvious difficulty of choosing the training set, and the simulation is not guaranteed to produce results within the error requirement for every input.…”

Section: Introductionmentioning

confidence: 99%

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Instrumented Multi-Stage Word-Length Optimization

Osborne

Coutinho

Cheung

et al. 2007

2007 International Conference on Field-Programmable Technology

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In this paper we present a tool, LengthFinder, for optimizing word-lengths of hardware designs with fixed-point arithmetic based on analytical error models that guarantee accuracy. LengthFinder adopts a multi-stage approach, with four novel features. First, the code analysis stage selects loops to instrument, such that information about the number of iterations can be extracted to generate more accurate results. Second, aggressive heuristics are used to produce non-uniform word-lengths rapidly while meeting requirements from the guaranteed error functions. Third, a method capable of reducing the search space has been developed for data-partitioning with a variable word-length reduction. Fourth, a genetic algorithm with selective-crossover and high mutation probability is applied to obtain near-optimal results. The benefits of LengthFinder are illustrated with various case studies. We show that LengthFinder can run over 200 times faster than previous techniques [6], while producing more accurate results, relative to values obtained from integer linear programming.

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Section: Code Analysis and Instrumentationmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Instrumented Multi-Stage Word-Length Optimization

Osborne

Coutinho

Cheung

et al. 2007

2007 International Conference on Field-Programmable Technology

Self Cite

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“…The first is a simulation-based approach [2,3,4] and involves optimizing the widths given input data from a specific training set. This has the obvious difficulty of choosing the training set, and the simulation is not guaranteed to produce results within the error requirement for every input.…”

Section: Introductionmentioning

confidence: 99%

Automatic Accuracy-Guaranteed Bit-Width Optimization for Fixed and Floating-Point Systems

Osborne

Cheung

Coutinho

et al. 2007

2007 International Conference on Field Programmable Logic and Applications

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In this paper we present Minibit+, an approach that optimizes the bit-widths of fixed-point and floating-point designs, while guaranteeing accuracy. Our approach adopts different levels of analysis giving the designer the opportunity to terminate it at any stage to obtain a result. Range analysis is achieved using a combined affine and interval arithmetic approach to reduce the number of bits. Precision analysis involves a coarse-grain and fine-grain analysis. The best representation, in fixed-point or floating-point, for the numbers is then chosen based on the range, precision and latency. Three case studies are used: discrete cosine transform, B-Splines and RGB to YCbCr color conversion. Our analysis can run over 200 times faster than current approaches to this problem while producing more accurate results, on average within 2-3% of an exhaustive search.

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Accuracy-Aware Compilers

Misailovic

2022

Approximate Computing Techniques

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Floating-point bitwidth analysis via automatic differentiation

Cited by 36 publications

References 2 publications

Instrumented Multi-Stage Word-Length Optimization

Instrumented Multi-Stage Word-Length Optimization

Automatic Accuracy-Guaranteed Bit-Width Optimization for Fixed and Floating-Point Systems

Accuracy-Aware Compilers

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