PASCAL-XSC

This manual describes a PASCAL extension for scientific computation with the short title PASCAL-XSC (PASCAL eXtension for Scientific Computation). The language is the result of a long term effort of members of the Institute for Applied Mathematics of Karlsruhe University and several associated scientists. PASCAL XSC is intended to make the computer more powerful arithmetically than usual. It makes the computer look like a vector processor to the programmer by providing the vector/matrix operations in a natural form with array data types and the usual operator symbols. Programming of algorithms is thus brought considerably closer to the usual mathematical notation. As an additional feature in PASCAL-XSC, all predefined operators for real and complex numbers and intervals, vectors, matrices, and so on, deliver an answer that differs from the exact result by at most one rounding. Numerical mathematics has devised algorithms that deliver highly accurate and automatically verified results by applying mathematical fixed point theorems. That is, these computations carry their own accuracy control. However, their imple mentation requires arithmetic and programming tools that have not been available previously. The development of PASCAL-XSC has been aimed at providing these tools within the PASCAL setting. Work on the subject began during the 1960's with the development of a general theory of computer arithmetic. At first, new algorithms for the realization of the arithmetic operations had to be developed and implemented.

Auteur
Prof. Dr. Ulrich Kulisch (Karlsruhe) ist auf dem Gebiet der Numerischen Mathematik tätig.

Texte du rabat

The programming language PASCAL-XSC (PASCAL eXtension forScientific Computation) significantly simplifies programmingin the area of scientific and technical computing.PASCAL-XSC provides a large number of predefined data typeswith arithmetic operators and predefined functions ofhighestaccuracy for real and complex numbers, for real andcomplex intervals, and for the corresponding vectors andmatrices. Thus PASCAL-XSC makes the computer more powerfulconcerning the arithmetic. Through an implementation in C,compilers for PASCAL-XSC are available for a large varietyof computers such as personal computers, workstations,mainframes, and supercomputers. PASCAL-XSC provides a moduleconcept, an operator concept, functions and operators withgeneral result type, overloading of functions, procedures,and operators, dynamic arrays, access to subarrays, roundingcontrol by the user, and accurate evaluation of expressions.The language is particularly suited for the development ofnumerical algorithms that deliver highly accurate andautomatically verified results. A number of problem-solvingroutines with automatic resultverification have alreadybeen implemented. PASCAL-XSC contains Standard PASCAL. It isimmediately usable by PASCAL programmers. PASCAL-XSC is easyto learn and ideal for programming education. The book canbe used as a textbook for lectures on computer programming.It contains a major chapter with sample programs, exercises,and solutions. A complete set of syntax diagrams, detailedtables, and indices complete the book.

Contenu
1 Introduction.- 1.1 Typography.- 1.2 Historical Remarks and Motivation.- 1.3 Advanced Computer Arithmetic.- 1.4 Connection with Programming Languages.- 1.5 Survey of PASCAL-XSC.- 2 Language Reference.- 2.1 Basic Symbols.- 2.2 Identifiers.- 2.3 Constants, Types, and Variables.- 2.4 Expressions.- 2.5 Statements.- 2.6 Program Structure.- 2.7 Subroutines.- 2.8 Modules.- 2.9 String Handling and Text Processing.- 2.10 How to Use Dynamic Arrays.- 3 The Arithmetic Modules.- 3.1 The Module C_ARI.- 3.2 The Module I_ARI.- 3.3 The Module CI_ARI.- 3.4 The Module MV_ARI.- 3.5 The Module MVC_ARI.- 3.6 The Module MVI_ARI.- 3.7 The Module MVCI_ARI.- 3.8 The Hierarchy of the Arithmetic Modules.- 3.9 A Complete Sample Program.- 4 Problem-Solving Routines.- 5 Exercises with Solutions.- 5.1 Test of Representability.- 5.2 Summation of Exponential Series.- 5.3 Influence of Rounding Errors.- 5.4 Scalar Product.- 5.5 Boothroyd/Dekker Matrices.- 5.6 Complex Functions.- 5.7 Surface Area of a Parallelepiped.- 5.8 Parallelism and Intersection of Lines.- 5.9 Transposed Matrix, Symmetry.- 5.10 Rail Route Map.- 5.11 Inventory Lists.- 5.12 Complex Numbers and Polar Representation.- 5.13 Complex Division.- 5.14 Electric Circuit.- 5.15 Alternating Current Measuring Bridge.- 5.16 Optical Lens.- 5.17 Interval Evaluation of a Polynomial.- 5.18 Calculations for Interval Matrices.- 5.19 Differentiation Arithmetic.- 5.20 Newton's Method with Automatic Differentiation.- 5.21 Measurement of Time.- 5.22 Iterative Method.- 5.23 Trace of a Product Matrix.- 5.24 Calculator for Polynomials.- 5.25 Interval Newton Method.- 5.26 Runge-Kutta Method.- 5.27 Rational Arithmetic.- 5.28 Evaluation of Polynomials.- A Syntax Diagrams.- B Indices and Lists.- B.1 Syntax Diagrams.- B.2 Reserved Words.- B.3 PredefinedIdentifiers.- B.4 Operators.- B.4.1 Basic Operators.- B.4.2 Arithmetic Operators.- B.4.3 Relational Operators for the Arithmetic Types.- B.4.4 Assignment Operators.- B.5 Predefined Functions.- B.6 Transfer Functions.- B.7 Predefined Procedures.- B.8 #-Expressions.- B.8.1 Real and Complex #-Expressions.- B.8.2 Real and Complex Interval #-Expressions.