this article the second representation mentioned above. We first recall the main properties of computable real numbers. We deduce from one definition, among the three definitions of this notion, a representation of these numbers as sequence of finite B-adic numbers and then we describe algorithms for rational operations and transcendental functions for this representation. Finally we describe briefly the prototype written in Caml. 2. Computable real numbers

Computers manipulate approximations of real numbers, called floating-point numbers. The calculations they make are accurate enough for most applications. Unfortunately, in some (catastrophic) situations, the floating-point operations lose so much precision that they quickly become irrelevant. In this article, we review some of the problems one can encounter, focussing on the IEEE754-1985 norm. We give a (sketch of a) semantics of its basic operations then abstract them (in the sense of abstract interpretation) to extract information about the possible loss of precision. The expected application is abstract debugging of software ranging from simple on-board systems (which use more and more on-the-shelf micro-processors with floating-point units) to scientific codes. The abstract analysis is demonstrated on simple examples and compared with related work. 1

A pass to the Cedar Fortran preprocessor, cftn, has been developed which allows the user to instrument his source code in a variety of ways. By specifying different command line options and linking with different libraries, one can automatically generate a report of the program's use of the Alliant FX/8's or Cedar's vector hardware, or apply several types of error analysis to obtain an indication of the numerical stability of the algorithm and its implementation. A library has been written with which the user can link to obtain a report of floating point operation counts, together with information regarding each type of operation or intrinsic function call, whether the operation is performed on scalar or array operands, and if so, the length and stride of the vector(s) involved. The package is called the op ct package, and has been integrated into the Faust programming environment under development at CSRD. A library for statistical roundoff error analysis has also been developed for ...