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 …

[PDF][PDF] 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 …
Affine arithmetic represents a range of possible values by an affine form: \( \hat{x} = x_0 + \…

[HTML][HTML] 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,
affine arithmetic cannot provide a … accuracy of bounds from affine arithmetic in the presence of …

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 …

[HTML][HTML] 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 …