C-Xsc : A C++ Class Library for Extended Scientific Computing

1 Introduction.- 1.1 Typography.- 1.2 C-XSC: A Class Library in the Programming Language C++.- 1.3 C-XSC: A Programming Environment for Scientific Computing with Result Verification.- 1.4 Survey of C-XSC.- 2 The Programming Languages C and C++.- 2.1 A Short Introduction to C.- 2.1.1 Overview.- 2.1.2 Data Types, Operators, and Expressions.- 2.1.3 Control Flow.- 2.1.4 Functions.- 2.1.5 The Structure of a C Program.- 2.1.6 External Variables.- 2.1.7 The Scope of Variables and Functions.- 2.1.8 The C Preprocessor.- 2.1.9 Pointers.- 2.1.10 Pointers and Function Arguments.- 2.1.11 Arithmetic with Pointers and Arrays.- 2.1.12 Structures.- 2.1.13 The C Standard Library.- 2.2 Additional Features in C++.- 2.2.1 Overview.- 2.2.2 A Sample Program.- 2.2.3 Comments.- 2.2.4 Classes.- 2.2.5 Member Functions.- 2.2.6 Friend Functions.- 2.2.7 Reference Variables.- 2.2.8 Constructors and Destructors.- 2.2.9 The Structure of a C++ Program.- 2.2.10 Inline Functions.- 2.2.11 Overloaded Operators and Functions.- 2.2.12 Input and Output with Streams.- 2.2.13 Memory Management Operators.- 2.2.14 Type Casting.- 2.2.15 Additional Features of C++.- 3 C-XSC Reference.- 3.1 Constants, Data Types, and Variables.- 3.1.1 Constants.- 3.1.2 Variables.- 3.1.3 Scalar Data Types.- 3.1.4 Vector Data Types.- 3.1.5 Matrix Data Types.- 3.1.6 Dot precision Data Types.- 3.1.7 Multiple-Precision Data Types.- 3.1.8 User-Defined Data Types.- 3.2 Expressions.- 3.2.1 Implicit Type Casting.- 3.2.2 Explicit Type Casting.- 3.2.3 Arithmetic Operators.- 3.2.4 Relational Operators.- 3.2.5 Standard Functions.- 3.3 Statements.- 3.3.1 Assignments.- 3.3.2 Manipulation of Index Bounds.- 3.3.3 Resize of Vectors and Matrices.- 3.3.4 Addition of a Product to a Dotprecision Accumulator.- 3.3.5 Rounding of Dotprecision Accumulators.- 3.3.6 Input and Output.- 3.4 Error Handling.- 3.5 Pitfalls for Programming with C - XSC.- A Syntax Diagrams.- A.1 Data Types.- A.2 Management of Vectors and Matrices.- A.3 Definition of Variables.- A.4 Expressions.- A.5 Logical Expressions.- A.6 Type Castings.- A.7 Assignments.- A.8 Arithmetic Standard Functions.- A.9 Other Functions.- A.10 Input and Output.- A.11 Extension of a Syntax Diagram of C++.- B The Structure of the C - XSC Package.- B.1 Header Files.- B.2 Module Libraries.- C Error List.- D Sample Programs.- D.1 Rounding Control of Arithmetic Operations.- D.2 Rounding Control of Input and Output.- D.3 Scalar Product.- D.4 Transpose of a Matrix.- D.5 Trace of a Product Matrix.- D.6 Inverse of a Matrix.- D.7 Multiple-Precision Arithmetic.- D.8 Interval Newton Method.- D.9 Runge-Kutta Method.- D.10 Complex Polynomial Arithmetic.- D.11 Automatic Differentiation.- E Scientific Computation with Verified Results.- E.1 Evaluation of Polynomials.- E.2 Matrix Inversion.- E.3 Linear Systems of Equations.- E.4 Eigenvalues of Symmetric Matrices.- E.5 Fast Fourier Transform.- E.6 Zeros of a Nonlinear Equation.- E.7 System of Nonlinear Equations.- E.8 Ordinary Differential Equations.