@article{zha-zha-zho-10-aa-accur,
  author = {Zhang, L. and Zhang, Y. and Zhou, W.},
  title = {Tradeoff between Approximation Accuracy and Complexity for Range Analysis using Affine Arithmetic},
  journal = {Journal of Signal Processing Systems},
  volume = {61},
  pages = {279--291},
  year = 2010,
  doi = {10.1007/s11265-010-0452-2},
  comment = {Faster AA with more relaxed approximation than Chebyshev},
  abstract = {Digital signal processing algorithms are usually developed in floating-point arithmetic. After that floating-point to fixed-point transformation is performed to implement them on fixed-point devices, for higher speed, smaller area and lower power. During this transformation, range analysis is to find the minimum integer bit-widths for signals to prevent overflow. Existing state-of-the-art analytical methods for range analysis are generally based on Affine Arithmetic, which presents two approximation methods for non-affine operations. The Chebyshev approximation provides the best approximation with prohibitive computation expense. The trivial range estimation, which is very efficient for computation, over-estimates the range four times at the worst case. This paper presents a novel approach to let user decide tradeoff between approximation accuracy and complexity of Affine Arithmetic. Case studies and experiments are carried out to demonstrate its efficiency.}
}