Floating Point Square Root under HUB Format

Unit-Biased (HUB) is an emerging format based on shifting the representation line of the binary numbers by half unit in the last place. The HUB format is specially relevant for computers where rounding to nearest is required because it is performed simply by truncation. From a hardware point of view, the circuits implementing this representation save both area and time since rounding does not involve any carry propagation. Designs to perform the four basic operations have been proposed under HUB format recently. Nevertheless, the square root operation has not been confronted yet. In this paper we present an architecture to carry out the square root operation under HUB format for floating point numbers. The results of this work keep supporting the fact that the HUB representation involves simpler hardware than its conventional counterpart for computers requiring round-to-nearest mode.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Portable random number generators

Computers are deterministic devices, and a computer-generated random number is a contradiction in terms. As a result, computer-generated pseudorandom numbers are fraught with peril for the unwary. We summarize much that is known about the most well-known pseudorandom number generators: congruential generators. We also provide machine-independent programs to implement the generators in any language that has 32-bit signed integers-for example C, C++, and FORTRAN. Based on an extensive search, we provide parameter values better than those previously available.Programming (Mathematics) ; Computers

Quantum Computing with Very Noisy Devices

In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices called ``gates'' that tend to destroy the fragile quantum states needed for computation. The goal of fault-tolerant quantum computing is to compute accurately even when gates have a high probability of error each time they are used. Here we give evidence that accurate quantum computing is possible with error probabilities above 3% per gate, which is significantly higher than what was previously thought possible. However, the resources required for computing at such high error probabilities are excessive. Fortunately, they decrease rapidly with decreasing error probabilities. If we had quantum resources comparable to the considerable resources available in today's digital computers, we could implement non-trivial quantum computations at error probabilities as high as 1% per gate.Comment: 47 page