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DAGSTUHL
2008
14 years 1 months ago
Interval Arithmetic and Standardization
Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of real numbers with floating-point bounds. Operations for intervals can be efficient...
Jürgen Wolff von Gudenberg
DAGSTUHL
2010
14 years 1 months ago
CSG Operations of Arbitrary Primitives with Interval Arithmetic and Real-Time Ray Casting
We apply Knoll et al.'s algorithm [9] to interactively ray-cast constructive solid geometry (CSG) objects of arbitrary primitives represented as implicit functions. Whereas m...
Younis Hijazi, Aaron Knoll, Mathias Schott, Andrew...
DFG
2007
Springer
14 years 4 months ago
Why Interval Arithmetic is so Useful
: Interval arithmetic was introduced by Ramon Moore [Moo66] in the 1960s as an approach to bound rounding errors in mathematical computation. The theory of interval analysis emerge...
Younis Hijazi, Hans Hagen, Charles D. Hansen, Kenn...
GLVLSI
1998
IEEE
119views VLSI» more  GLVLSI 1998»
14 years 4 months ago
A Combined Interval and Floating Point Multiplier
Interval arithmetic provides an e cient method for monitoring and controlling errors in numerical calculations. However, existing software packages for interval arithmetic are oft...
James E. Stine, Michael J. Schulte
SIBGRAPI
1999
IEEE
14 years 4 months ago
Interval Methods for Ray Casting Implicit Surfaces with Affine Arithmetic
We study the performance of affine arithmetic as a replacement for interval arithmetic in interval methods for ray casting implicit surfaces. Affine arithmetic is a variant of inte...
Affonso de Cusatis Junior, Luiz Henrique de Figuei...
FDL
2003
IEEE
14 years 5 months ago
A New Method for Modeling and Analysis of Accuracy and Tolerances in Mixed-Signal Systems
Tolerances are a very important property of a design. This paper presents a method for simulating tolerances in signal processing and control systems on the system level using aï¬...
Wilhelm Heupke, Christoph Grimm, Klaus Waldschmidt
ARITH
2005
IEEE
14 years 6 months ago
Guaranteed Proofs Using Interval Arithmetic
This paper presents a set of tools for mechanical reasoning of numerical bounds using interval arithmetic. The tools implement two techniques for reducing decorrelation: interval ...
Marc Daumas, Guillaume Melquiond, César Mu&...