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» Algorithms for Ordinal Arithmetic
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FCCM
2009
IEEE
172views VLSI» more  FCCM 2009»
14 years 2 months ago
Evaluation of Static Analysis Techniques for Fixed-Point Precision Optimization
Abstract—Precision analysis and optimization is very important when transforming a floating-point algorithm into fixedpoint hardware implementations. The core analysis techniqu...
Jason Cong, Karthik Gururaj, Bin Liu, Chunyue Liu,...
COCO
2009
Springer
96views Algorithms» more  COCO 2009»
14 years 2 months ago
Reconstruction of Generalized Depth-3 Arithmetic Circuits with Bounded Top Fan-in
In this paper we give reconstruction algorithms for depth-3 arithmetic circuits with k multiplication gates (also known as ΣΠΣ(k) circuits), where k = O(1). Namely, we give an ...
Zohar Shay Karnin, Amir Shpilka
DCG
1998
59views more  DCG 1998»
13 years 7 months ago
A Probabilistic Analysis of the Power of Arithmetic Filters
The assumption of real-number arithmetic, which is at the basis of conventional geometric algorithms, has been seriously challenged in recent years, since digital computers do not...
Olivier Devillers, Franco P. Preparata
FLOPS
2008
Springer
13 years 9 months ago
Certified Exact Real Arithmetic Using Co-induction in Arbitrary Integer Base
In this paper we describe some certified algorithms for exact real arithmetic based on co-recursion. Our work is based on previous experiences using redundant digits of base 2 but ...
Nicolas Julien
CORR
2007
Springer
110views Education» more  CORR 2007»
13 years 7 months ago
Computing Integer Powers in Floating-Point Arithmetic
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We ...
Peter Kornerup, Vincent Lefèvre, Jean-Miche...