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,...
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 ...
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...
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 ...
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 ...