Abstract. Formal verification of numerical programs is notoriously difficult. On the one hand, there exist automatic tools specialized in floatingpoint arithmetic, such as Gappa...
Abstract— Floating-point arithmetic is notoriously nonassociative due to the limited precision representation which demands intermediate values be rounded to fit in the availabl...
Abstract—Some processors designed for consumer applications, such as Graphics Processing Units (GPUs) and the CELL processor, promise outstanding floating-point performance for ...
Abstract. A so called staggered precision arithmetic is a special kind of a multiple precision arithmetic based on the underlying floating point data format (typically IEEE double ...
Frithjof Blomquist, Werner Hofschuster, Walter Kr&...
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit ...
Marc Baboulin, Alfredo Buttari, Jack Dongarra, Jak...