PASCAL-XSC : Language Reference with Examples

The programming language PASCAL-XSC (PASCAL eXtension for Scientific Computation) significantly simplifies programming in the area of scientific and technical computing. PASCAL-XSC provides a large number of predefined data types with arithmetic operators and predefined functions of highestaccuracy for real and complex numbers, for real and complex intervals, and for the corresponding vectors and matrices. Thus PASCAL-XSC makes the computer more powerful concerning the arithmetic. Through an implementation in C, compilers for PASCAL-XSC are available for a large variety of computers such as personal computers, workstations, mainframes, and supercomputers. PASCAL-XSC provides a module concept, an operator concept, functions and operators with general result type, overloading of functions, procedures, and operators, dynamic arrays, access to subarrays, rounding control by the user, and accurate evaluation of expressions. The language is particularly suited for the development of numerical algorithms that deliver highly accurate and automatically verified results. A number of problem-solving routines with automatic resultverification have already been implemented. PASCAL-XSC contains Standard PASCAL. It is immediately usable by PASCAL programmers. PASCAL-XSC is easy to learn and ideal for programming education. The book can be 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, detailed tables, and indices complete the book.

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.- 1.5.1 Universal Operator Concept and Arbitrary Result Type.- 1.5.2 Overloading of Procedures, Functions, and Operators.- 1.5.3 Module Concept.- 1.5.4 Dynamic Arrays and Subarrays.- 1.5.5 String Concept.- 1.5.6 Arithmetic and Rounding.- 1.5.7 Accurate Expressions.- 2 Language Reference.- 2.1 Basic Symbols.- 2.2 Identifiers.- 2.3 Constants, Types, and Variables.- 2.3.1 Simple Types.- 2.3.2 Structured Types.- 2.3.2.1 Arrays.- 2.3.2.2 Subarrays.- 2.3.2.3 Access to Index Bounds.- 2.3.2.4 Dynamic Arrays.- 2.3.2.5 Strings.- 2.3.2.6 Dynamic Strings.- 2.3.2.7 Records.- 2.3.2.8 Records with Variants.- 2.3.2.9 Sets.- 2.3.2.10 Files.- 2.3.2.11 Text Files.- 2.3.3 Structured Arithmetic Standard Types.- 2.3.3.1 The Type complex.- 2.3.3.2 The Type interval.- 2.3.3.3 The Type cinterval.- 2.3.3.4 Vector Types and Matrix Types.- 2.3.4 Pointers.- 2.3.5 Compatibility of Types.- 2.3.5.1 Compatibility of Array Types.- 2.3.5.2 Compatibility of Strings.- 2.4 Expressions.- 2.4.1 Standard Expressions.- 2.4.1.1 Integer Expressions.- 2.4.1.2 Real Expressions.- 2.4.1.3 Boolean Expressions.- 2.4.1.4 Character Expressions.- 2.4.1.5 Enumeration Expressions.- 2.4.2 Accurate Expressions (#-Expressions).- 2.4.3 Expressions for Structured Types and Pointer Expressions.- 2.4.3.1 Array Expressions.- 2.4.3.2 String Expressions.- 2.4.3.3 Record Expressions.- 2.4.3.4 Set Expressions.- 2.4.3.5 Pointer Expressions.- 2.4.4 Extended Accurate Expressions (#-Expressions).- 2.4.4.1 #-Expressions for the Arithmetic Types.- 2.4.4.2 #-Expressions for Vectors.- 2.4.4.3 #-Expressions for Matrices.- 2.4.4.4 List of the Operands in #-Expressions.- 2.4.4.5 Review of General #-Expressions.- 2.5 Statements.- 2.5.1 Assignment Statement.- 2.5.2 Input/Output Statements.- 2.5.3 Empty Statement.- 2.5.4 Procedure Statement.- 2.5.5 goto-Statement.- 2.5.6 Compound Statement.- 2.5.7 Conditional Statements.- 2.5.7.1 if-Statement.- 2.5.7.2 case-Statement.- 2.5.8 Repetitive Statements.- 2.5.8.1 while-Statement.- 2.5.8.2 repeat-Statement.- 2.5.8.3 for-Statement.- 2.5.9 with-Statement.- 2.6 Program Structure.- 2.7 Subroutines.- 2.7.1 Procedures.- 2.7.2 List of Predefined Procedures and Input/Output Statements.- 2.7.3 Functions.- 2.7.4 Functions with Arbitrary Result Type.- 2.7.5 List of Predefined Functions.- 2.7.6 Operators.- 2.7.7 Table of Predefined Operators.- 2.7.8 forward- and external-Declaration.- 2.7.9 Modified Call by Reference for Structured Types.- 2.7.10 Overloading of Procedures, Functions, and Operators.- 2.7.11 Overloading of read and write.- 2.7.12 Overloading of the Assignment Operator :=.- 2.8 Modules.- 2.9 String Handling and Text Processing.- 2.9.1 Input of Characters and Strings.- 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 Predefined Identifiers.- 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.