Double rounding is a phenomenon that may occur when different floatingpoint precisions are available on the same system. Although double rounding is, in general, innocuous, it may change the behavior of some useful small floating-point algorithms. We analyze the potential influence of double rounding on the Fast2Sum and 2Sum algorithms, on some summation algorithms, and Veltkamp’s splitting.

A set of abstract operations is given that allows the uniform analysis of integer and floating point arithmetic in the abstract domain of convex polyhedra. We show how to implement rounding faithfully and show that the modelling of rounding is necessary even for the analysis of integer variables. Different rounding modes occurring in floating point implementations are discussed and their implem...

We present a design of an IEEE oating-point multiplier capable of performing either a double-precision multiplication or a single-precision multiplication. In single-precision the la-tency is two clock cycles and in double-precision the latency is three clock cycles, where each pipeline stage contains roughly fteen logic levels. A single-precision multiplication can be followed immediately by a...

Often, the edge weights of graphs are given in implicitly infinite or overly high precision (think of Euclidean lengths) which leads to both theoretical as well as practical challenges. In this paper we investigate how to round edge weights of a given graph G(V,E,w) such that the rounded weights of paths satisfy certain consistency criteria. Natural consistency criteria are, for example, preser...

In this paper, we propose a new one-dimensional (1D) integer discrete cosine transform (Int-DCT) for unified lossless/lossy image compression. The proposed 1D Int-DCT is newly designed to reduce rounding effects by minimizing number of rounding operations. The proposed Int-DCT can be operated not only lossless coding for a high quality decoded image but also lossy coding for a compatibility wit...