Results 1 
5 of
5
Arbitrary Precision Real Arithmetic: Design and Algorithms
, 1996
"... 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 Badic numbers and then we describe algorithms fo ..."
Abstract

Cited by 19 (0 self)
 Add to MetaCart
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 Badic 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
Static Analyses of FloatingPoint Operations
 In SAS’01, volume 2126 of LNCS
, 2001
"... Computers manipulate approximations of real numbers, called floatingpoint numbers. The calculations they make are accurate enough for most applications. Unfortunately, in some (catastrophic) situations, the floatingpoint operations lose so much precision that they quickly become irrelevant. In thi ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
Computers manipulate approximations of real numbers, called floatingpoint numbers. The calculations they make are accurate enough for most applications. Unfortunately, in some (catastrophic) situations, the floatingpoint 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 IEEE7541985 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 onboard systems (which use more and more ontheshelf microprocessors with floatingpoint units) to scientific codes. The abstract analysis is demonstrated on simple examples and compared with related work. 1
Instrumentation Of Fortran Programs For Automatic Roundoff Error Analysis And Performance Evaluation
, 1990
"... 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 ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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 ...
PROGRAM SUMMARY
"... The CADNA library enables one to estimate roundoff error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can b ..."
Abstract
 Add to MetaCart
The CADNA library enables one to estimate roundoff error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can be performed. CADNA provides new numerical types on which roundoff errors can be estimated. Slight modifications are required to control a code with CADNA, mainly changes in variable declarations, input and output. This paper describes the features of the CADNA library and shows how to interpret the information it provides concerning roundoff error propagation in a code.
Numerical ‘health check ’ for scientific codes: the CADNA approach
"... Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is roundoff error propagation which originates from the use of finite precision arithmetic. We propose that there is a need to perform regular nume ..."
Abstract
 Add to MetaCart
Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is roundoff error propagation which originates from the use of finite precision arithmetic. We propose that there is a need to perform regular numerical ‘health checks ’ on scientific codes in order to detect the cancerous effect of roundoff error propagation. This is particularly important in scientific codes that are built on legacy software. We advocate the use of the CADNA library as a suitable numerical screening tool. We present a case study to illustrate the practical use of CADNA in scientific codes that are of interest to the Computer Physics Communications readership. In doing so we hope to stimulate a greater awareness of roundoff error propagation and present a practical means by which it can be analyzed and managed.