We propose a Domain-Specific Architecture for elementary function computation to improve throughput while reducing power consumption as a model for more general applications: support fine-grained parallelism by eliminating branches, eliminate the duplication required by co-processors by decomposing computation into instructions which fit existing pipelined execution models and standard register...

A paper by Bruno Salvy and the author introduced measured multiseries and gave an algorithm to compute these for a large class of elementary functions, modulo a zeroequivalence method for constants. This gave a theoretical background for the Maple c © implementation that Salvy was developing at that time. The main result of the present article is an algorithm to calculate measured multiseries f...

We describe here a representation of computable real numbers and a set of algorithms for the elementary functions associated to this representation. A real number is represented as a sequence of nite B-adic numbers and for each classical function (rational, algebraic or transcendental), we describe how to produce a sequence representing the result of the application of this function to its argu...

We give the results of our search for the worst cases for correct rounding of themajor elementary functions in double precision floating-point arithmetic. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to ...

We construct multimonopole solutions containing N−1 distinct fundamental monopoles in SU(N) gauge theory. When the gauge symmetry is spontaneously broken to U(1)N−1, the monopoles are all massive, and we show that the fields can be written in terms of elementary function for all values of the monopole positions and phases. In the limit of unbroken U(1) × SU(N − 2) × U(1) symmetry, the configura...

We have recently explored the Elementary Function method, previously presented by Wald et al (Proc. SPIE 59621G, 2005), and we have demonstrated under what circumstances this method can be used to reduce the propagation calculations of partially coherent light to two dimensions. In this paper, we examine the methods used to measure the spatial coherence of a light source in the literature. We p...

A commonly used argument reduction technique in elementary function computations begins with two positive floating point numbers α and γ that approximate (usually irrational but not necessarily) numbers 1/C and C, e.g., C = 2π for trigonometric functions and ln 2 for e. Given an argument to the function of interest it extracts z as defined by xα = z + ς with z = k2−N and |ς| ≤ 2−N−1, where k,N ...

Exact rounding of numbers and functions is a fundamental computational problem. This paper introduces the mathematical and computational foundations for exact rounding. We show that all the elementary functions in ISO standard (ISO/IEC 10967) for Language Independent Arithmetic can be exactly rounded, in any format, and to any precision. Moreover, a priori complexity bounds can be given for the...

The literature of these classical isoperimetric inequalities is very extensive (comprehensive presentations may be found in Blaschke [l] and Bonnesen [l](1)). In most instances, only convex curves and convex surfaces are considered, or else it is assumed that the curves and surfaces involved are sufficiently regular to permit the use of the classical formulas for the quantities a(C), 1(C), A(S)...

As p—► » we get the space E„ with the distance function max,-=i,... ,m | x< — as/ |. Let, furthermore, lp stand for the space of real sequences with the series of pth powers of the absolute values convergent. Similarly let Lp denote the space of real measurable functions in the interval (0, 1) which are oummable to the ^»th power, while C shall mean the space of real continuous functions in the...