@article{bel-lam-bel-tag-bel-19-aa-polyev,
  author = {Bellal, Rima and Lamini, El-sedik and Belbachir, Hacène and Tagzout, Samir and Belouchrani, Adel},
  journal = {IEEE Transactions on Computers}, 
  title = {Improved Affine Arithmetic-Based Precision Analysis for Polynomial Function Evaluation}, 
  year = 2019,
  volume = {68},
  number = {5},
  pages = {702-712},
  doi = {10.1109/TC.2018.2882537},
  comment = {Optimizing bit width for polynomial evaluation. Up to 70{\%} reduction in circuit area},
  abstract = {Word-length allocation is the most important design phase to optimize hardware resources while guaranteeing a determined accuracy for circuits with fixed-point numbers. This paper presents an enhanced precision analysis for degree-n polynomial Horner's rule. It is based on affine arithmetic and introduces an error propagating formula for a degree-n polynomial Horner's rule. It takes into account quantization error of all the circuit's connections including the inputs. Furthermore, a tighter upper bound error is defined, exploiting the dependencies between intermediate connections. Hardware implementations show that the proposed upper bound results in an area reduction that reaches 70 percent.}
}