Optimizing imprecise fixed-point arithmetic circuits specified by Taylor Series through arithmetic transform

  • Authors:
  • Yu Pang;Katarzyna Radecka

  • Affiliations:
  • Mcgill University, Montreal, Quebec, Canada;Mcgill University, Montreal, Quebec, Canada

  • Venue:
  • Proceedings of the 45th annual Design Automation Conference
  • Year:
  • 2008

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Abstract

We consider synthesis of arithmetic DSP circuits with finite precision fixed-point operations. The aim is to choose the lowest cost implementation that matches a real-valued specification within the allowed imprecision. Starting from Taylor Series or real-valued polynomials, we demonstrate first a method to obtain satisfying implementations that uses intermediate Arithmetic Transform polynomials as an analytical apparatus suitable to precision analysis for both the quantization (bit-width) and approximation sources of imprecision. We then derive the precision optimization algorithm that explores multiple precision parameters in a branch-and-bound search.