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The main language features and numerical tools of ACRITH-XSC are presented and illustrated by some typical examples. Differences to Fortran 90 are noted where appropriate. A complete sample program for computing continuous bounds on the solution of an initial value problem is given at the end. 1 Development of ACRITH-XSC The expressive and functional power of algorithmic programming languages has been continually enhanced since the 1950's. New powerful languages such as Ada, C++,and Fortran 90 have evolved over the past decade or so.

Ratz 30 It is necessary to frame only the original main program by a procedure (here: main), which is refered to with the dimension of the dynamic arrays as a transfer parameter. 6 The implementation of enclosure algorithms with automatic result verification or validation (see [17],[24],[28],[33]) makes extensive use of the accurate evaluation of dot products with the property (see [25]) To evaluate this kind of expression the new datatype dotprecision was introduced. Based upon this type, so-called accurate ezpressions (#-expressions), can be formulated by an accurate symbol (#, #*, #<, #>, or ##) followed by an ezact ezpression enclosed in parentheses.

This has become quite apparent in numerical programming and scientific computing. Even though programming has become more convenient through the use of more modern language concepts, numerical programs have not necessarily become more reliable. Scientific Computing with Automatic Result Verification 45 Copyright @ 1993 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-044210-8 46 Wolfgang V. Walter The development of programming languages suited for the particular needs of numerical programming has been a long-term commitment of the Institute of Applied Mathematics a t the University of Karlsruhe.

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