Computing Integer Powers in Floating-Point Arithmetic

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 show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).Comment: Laboratoire LIP : CNRS/ENS Lyon/INRIA/Universit\'e Lyon

Leading Guard Digits in Finite-Precision Redundant Representations

Redundant number representations are generally used to allow constant time additions, based on the fact that only bounded carry-ripples take place. But, carries may ripple out into positions which may not be needed to represent the final value of the result and, thus, a certain amount of leading guard digits are needed to correctly determine the result. Also, when cancellation during subtractions occurs, there may be nonzero digits in positions not needed to represent the result of the calculation. It is shown here that, for normal redundant digit sets with radix greater than two, a single guard digit is sufficient to determine the value of such an arbitrary length prefix of leading nonzero digits. This is also the case for the unsigned carry-save representation, whereas two guard digits are sufficient, and may be necessary, for additions in the binary signed-digit and 2's complement carry-save representations. Thus, only the guard digits need to be retained during sequences of additions and subtractions. At suitable points, the guard digits may then be converted into a single digit, representing the complete prefix

Guest Editors' Introduction: Special Section on Computer Arithmetic

International audienceCOMPUTER arithmetic is the mother of all computer research and application topics, like mathematics (as the title of a famous book by E.T. Bell) is the queen and servant of sciences and arithmetic the queen of mathematics. The etymology itself of the word computer is intrinsically related to the concept of arithmetic and mathematics. Interesting to note is that the origin of the word computer comes from the Latin word computare, which is defined as count, evaluate, calculate the result. In all cases, the connection between computers and computer arithmetic goes beyond simple etymology reasons. Computers are designed either to perform a specific calculation or to have extensive programmability for many changing tasks. In either case, at a certain level this translates into doing computations and arithmetic evaluations

Implementation of Bus Rapid Transit in Copenhagen: A Mesoscopic Model Approach

Bus Rapid Transit (BRT) has shown to be an efficient and cost-effective mode of public transport, and has gained popularity in many cities around the world. To optimise the operations and infrastructure it is advantageous to deploy transport models. However, microscopic models are very inefficient for large scale corridors due to the vast amount of data and resources required. Hence, it is relevant to investigate how to model and evaluate BRT efficiently. In this paper the effects of implementing BRT in Copenhagen is discussed including how to evaluate and model bus operations. For this purpose, a mesoscopic simulation model is developed. In the model bus operations are modelled on a microscopic level whereas the interactions with other traffic are modelled macroscopically. This makes it possible to model high-frequency bus services such as BRT lines in more details without the time consumption of micro-simulation models. The developed model is capable of modelling bus operations in terms of travel time and reliability including important mode-specific issues such as bus bunching. The model is applied to a BRT project proposal with different combinations of BRT elements. The model results show that infrastructure upgrades (busways and enhanced stations) ensure a reduction to travel time whereas no improvements to reliability occur. Upgrades to technology and service planning (pre-paid fare collection, boarding and alighting from all doors, special BRT vehicles, ITS, and active bus control) ensure an increase in service reliability whereas only small reductions to travel time are observed. By combining all BRT elements it is possible to obtain synergies where the improved reliability due to planning and technology elements makes it possible to utilise the infrastructure optimally. Hence, it is possible to increase commercial speed from 14.8 to 19.9 km/h and service reliability in terms of headway time regularity from 46% to 84% aggregated on both directions for the morning peak period making the implementation of BRT feasible from a pure financial point of view

Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic

23 pagesWe introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We aim at always obtaining correctly-rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number that is nearest the exact value

Analysing improvements to on-street public transport systems: a mesoscopic model approach

Light rail transit and bus rapid transit have shown to be efficient and cost-effective in improving public transport systems in cities around the world. As these systems comprise various elements, which can be tailored to any given setting, e.g. pre-board fare-collection, holding strategies and other advanced public transport systems (APTS), the attractiveness of such systems depends heavily on their implementation. In the early planning stage it is advantageous to deploy simple and transparent models to evaluate possible ways of implementation. For this purpose, the present study develops a mesoscopic model which makes it possible to evaluate public transport operations in details, including dwell times, intelligent traffic signal timings and holding strategies while modelling impacts from other traffic using statistical distributional data thereby ensuring simplicity in use and fast computational times. This makes it appropriate for analysing the impacts of improvements to public transport operations, individually or in combination, in early planning stages. The paper presents a joint measure of reliability for such evaluations based on passengers’ perceived travel time by considering headway time regularity and running time variability, i.e. taking into account waiting time and in-vehicle time. The approach was applied on a case study by assessing the effects of implementing segregated infrastructure and APTS elements, individually and in combination. The results showed that the reliability of on-street public transport operations mainly depends on APTS elements, and especially holding strategies, whereas pure infrastructure improvements induced travel time reductions. The results further suggested that synergy effects can be obtained by planning on-street public transport coherently in terms of reduced travel times and increased reliability

Immunological effects of reduced mucosal integrity in the early life of BALB/c mice

Certain stimuli at the gut barrier may be necessary in early life to establish a proper balance of immune tolerance. We evaluated a compromised barrier in juvenile mice in relation to microbiota and local and systemic immunity. BALB/c mice were treated with a low dose of dextran sulfate sodium (DSS) with or without ampicillin and lipopolysaccharide (LPS) to clarify the importance of microbial antigens and interaction between microbial-associated patterns and toll-like receptors. The barrier breach resulted in increased plasma LPS, which was highest in mice treated simultaneously with ampicillin. Adding LPS in the food reduced its levels in plasma. Regulatory T cells were acutely increased in mesenteric lymph nodes (MLN) and spleen during DSS treatment regardless of simultaneous ampicillin treatment. In contrast, NK T and NK cells decreased in MLN and in spleen. This acute DSS effect was reflected in fold changes of haptoglobin and Il1a in colon, and this was also more pronounced in mice simultaneously treated with ampicillin. On day 1 post-treatment, major upregulations of Ifng, Foxp3, Il1b, Il2, and Il6 genes in colon were only observed in the mice simultaneously treated with ampicillin. A two-fold upregulation of colonic Foxp3 and Il1a was evident 25 days post-treatment. DSS skewed the microbiota in favor of Gram negative phyla. Therefore, increased permeability induced tolerogenic immunity independent of microbiota, and this was enhanced by LPS stimulation