LNS with Co-Transformation Competes with Floating-Point

Approximate Counting with a Floating-Point Counter

Memory becomes a limiting factor in contemporary applications, such as analyses of the Webgraph and molecular sequences, when many objects need to be counted simultaneously. Robert Morris [Communications of the ACM, 21:840–842, 1978] proposed a probabilistic technique for approximate counting that is extremely space-efficient. The basic idea is to increment a counter containing the value X with...

Segment LLL-Reduction with Floating Point Orthogonalization

Floating-Point Computation with Just Enough Accuracy

Most mathematical formulae are defined in terms of operations on real numbers, but computers can only operate on numeric values with finite precision and range. Using floating-point values as real numbers does not clearly identify the precision with which each value must be represented. Too little precision yields inaccurate results; too much wastes computational resources. The popularity of mu...

Floating-Point Numbers with Error Estimates (revised)

The original work [25] is here reconsidered, so many years after. The old text has been revised, plus several considerations have been added, in order to clarify some controversial aspects of the work, and to envision possible developments. A section has been added, to review the effects of the original paper. The study addresses the problem of precision in floating-point (FP) computations. A m...

The Unified Floating Point Vector Co-processor for Reconfigurable Hardware

There has been an increased interest recently in using embedded cores on FPGAs. Many of the applications that make use of these cores have floating point operations. Due to the complexity and expense of floating point hardware, these algorithms are usually converted to fixed point operations or implemented using floating-point emulation in software. As the technology advances, more and more hom...