References in raw/Page_56.html

• Instrumented multi-stage word-length optimization
  WG Osborne, JGF Coutinho... - ... Conference on Field ..., 2007 - ieeexplore.ieee.org
  ... The range analysis stage in our system involves both interval and affine arithmetic, because ... of x), whereas it does in affine arithmetic. Affine arithmetic has problems as well. When ...
  

• Optimizing Hardware Function Evaluation
  RCC Cheung, DJ Pearce, AA Gaffar - 2008 - pdfs.semanticscholar.org
  ... 4(a) MiniBit: design tool based on affine arithmetic 1. Introduction ... bit-width optimization: for fixed-point designs via affine arithmetic (AA) ... ∎ Analytical models based on affine arithmetic ...
  

• Robustness in soc design
  M Damm, K Waldschmidt - ... on Digital System Design (DSD'06), 2006 - ieeexplore.ieee.org
  ... Affine arithmetic and semi-symbolic simulation seems very promising for the approach [6, 18]. The affine expressions contain a central value and additional terms that formally describe ...
  

• Sound probabilistic numerical error analysis
  D Lohar, M Prokop, E Darulova - International Conference on Integrated ..., 2019 - Springer
  ... of interval arithmetic (IA) [23] or affine arithmetic (AA) [14]. Interval arithmetic computes a ...
  

• Automated abstraction of nonlinear analog circuits to reliable set-valued models with reduced overapproximation
  M Rechmal-Lesse, YG Adhisantoso, GA Koroa... - Microelectronics ..., 2021 - Elsevier
  ... Affine arithmetic represents intervals as symmetric sums, called affine forms,(4) x ̂ = x 0 + ∑ i ε i x i with ε i ∈ − 1 1 with x 0 as the center value, ε i as the noise symbols and x i ...
  

• Linear interval estimations for parametric objects theory and application
  K Bühler - Computer Graphics Forum, 2001 - Wiley Online Library
  ... For this purpose a short introduction into interval and affine arithmetic and the concept of ... section 3 taking the intrinsic structure of affine arithmetic and and Taylor Models of first degree ...
  

• Bit-width allocation for hardware accelerators for scientific computing using SAT-modulo theory
  AB Kinsman, N Nicolici - IEEE Transactions on Computer-Aided ..., 2010 - ieeexplore.ieee.org
  ... ranges obtained from simulation, affine arithmetic and the ... denominator contains zero,
  

• Powerbit-power aware arithmetic bit-width optimization
  AA Gaffar, JA Clarke... - 2006 IEEE International ..., 2006 - ieeexplore.ieee.org
  ... Affine arithmetic is used for both the range and precision analysis. In the precision analysis ... truncation in the signals on the output via affine arithmetic. In precision analysis it is possible ...
  

• Automated precision analysis: A polynomial algebraic approach
  D Boland, GA Constantinides - 2010 18th IEEE Annual ..., 2010 - ieeexplore.ieee.org
  ... It is argued in this paper that this method can achieve significantly tighter bounds than both interval and affine arithmetic, while running significantly faster, with better scalability, than the ...
  

• Fuzzy stability analysis of regenerative chatter in milling
  ND Sims, G Manson, B Mann - Journal of Sound and Vibration, 2010 - Elsevier
  ... of affine arithmetic. Affine arithmetic: Affine analysis attempts to allow for uncertainty in parameters whilst accounting for dependency between operands. Affine arithmetic provides a ...