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.
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.
Power reduction is becoming more important as circuit size increases. This paper presents a tool called PowerCutter which employs accuracy-guaranteed word-length optimization to reduce power consumption of circuits. We adapt circuit word-lengths at run time to decrease power consumption, with optimizations based on branch statistics. Our tool uses a technique based on Automatic Differentiation to analyze library cores specified as black box functions, which do not include implementation information. We use this technique to analyze benchmarks containing library functions such as square root. Our approach shows that power savings of up to 32% can be achieved on benchmarks which cannot be analyzed by previous approaches, because library cores with an unknown implementation are used.
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