The Generic Multiple-Precision Floating-Point Addition With Exact Rounding (as in the MPFR Library)

We study the multiple-precision addition of two positive floating-point numbers in base 2, with exact rounding, as specified in the MPFR library, i.e. where each number has its own precision. We show how the best possible complexity (up to a constant factor that depends on the implementation) can be obtain.Comment: Conference website at http://cca-net.de/rnc6

Correctly Rounded Arbitrary-Precision Floating-Point Summation

International audienceWe present a fast algorithm together with its low-level implementation of correctly rounded arbitrary-precision floating-point summation. The arithmetic is the one used by the GNU MPFR library: radix 2; no subnormals; each variable (each input and the output) has its own precision. We also describe how the implementation is tested

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

A propos d'une célèbre toile peinte (kalamkari) de la collection Riboud au musée Guimet

Un des chefs-d'œuvre de la collection Riboud, offert au musée Guimet en 1990, est un grand kalamkari, c'est-à-dire une toile de coton peinte à la main, à l'aide de mordants et de teintures naturelles, représentant une scène de cour, de toute évidence en Inde du Sud. Très rare par sa qualité, ses dimensions, son ancienneté et surtout son iconographie, cette œuvre est relativement bien connue. Exposée à plusieurs reprises, elle a donné lieu à plusieurs publications, portant essentiellement sur sa datation. L'idée initiale de cet article est de reprendre les grands éléments du débat. Jusqu'alors, tous les arguments avancés étaient d'ordre purement stylistique. Après avoir rappelé les différentes hypothèses, on signale celles qui nous semblaient les plus convaincantes. Mais, d'une manière générale, les facteurs stylistiques paraissent insuffisants et c'est pourquoi on s'est proposé d'étudier plus avant ce qui fait la véritable originalité du kalamkari : son iconographie. En décrivant le mode de représentation et en mettant en parallèle la thématique de la scène de cour avec ce que l'on connaît de la littérature d'Inde du Sud à l'époque pré-coloniale, il est donc possible de proposer une datation et une provenance de l'œuvre qui, en même temps, en éclaire le contexte de création

An efficient rounding boundary test for pow(x,y) in double precision

18 pagesThe correct rounding of the function pow: (x,y) -> x^y is currently based on Ziv's iterative approximation process. In order to ensure its termination, cases when x^y falls on a rounding boundary must be filtered out. Such rounding boundaries are floating-point numbers and midpoints between two consecutive floating-point numbers. Detecting rounding boundaries for pow is a difficult problem. Previous approaches use repeated square root extraction followed by repeated square and multiply. This article presents a new rounding boundary test for pow in double precision which resumes to a few comparisons with pre-computed constants. These constants are deduced from worst cases for the Table Maker's Dilemma, searched over a small subset of the input domain. This is a novel use of such worst-case bounds. The resulting algorithm has been designed for a fast-on-average correctly rounded implementation of pow, considering the scarcity of rounding boundary cases. It does not stall average computations for rounding boundary detection. The article includes its correction proof and experimental results

Topic segmentation of TV-streams by watershed transform and vectorization

International audienceA fine-grained segmentation of Radio or TV broadcasts is an essential step for most multimedia processing tasks. Applying segmentation algorithms to the speech transcripts seems straightforward. Yet, most of these algorithms are not suited when dealing with short segments or noisy data. In this paper, we present a new segmentation technique inspired from the image analysis field and relying on a new way to compute similarities between candidate segments called Vectorization. Vectorization makes it possible to match text segments that do not share common words; this property is shown to be particularly useful when dealing with transcripts in which transcription errors and short segments makes the segmentation difficult. This new topic segmen-tation technique is evaluated on two corpora of transcripts from French TV broadcasts on which it largely outperforms other existing approaches from the state-of-the-art

Some notes on the possible under/overflow of the most common elementary functions

The purpose of this short note is not to describe when underflow or overflow must be signalled (it is quite clear that the rules are the same as for the basic arithmetic operations). We just want to show that for some of the most common functions and floating-point formats, in many cases, we can know in advance that the results will always lie in the range of the numbers that are representable by normal floating-point numbers, so that in these cases there is no need to worry about underflow or overflow. Note that when it is not the case, an implementation is still possible using a run-time test

On-The-Fly Range Reduction

In several cases, the input argument of an elementary function evaluation is given bit-serially, most significant bit first. We suggest a solution for performing the first step of the evaluation (namely, the range reduction) on the fly: the computation is overlapped with the reception of the input bits. This algorithm can be used for the trigonometric functions sin, cos, tan as well as for the exponential function.Il arrive que l’oprande dont on doit calculer une fonction élémentaire soit disponible chiffre après chiffre, en série, en commençant par les poids forts. Nous proposons une solution permettant d’effectuer la première phase de l’évaluation(la réduction d’argument)au vol: le calcul et la réception des chiffres d’entré se recouvrent. Cet algorithme peut être utilisé pour les fonctions trigonométriques sin, cos, tan ainsi que pour l'exponentiell