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The Design of a Function Subroutine
Introduction
General Considerations in Writing a Function Subroutine
Relation of the Function Subroutine to the Computer System
The Three Main Types of Function Subroutine
Special Programming Techniques
Subroutine Errors
Final Steps
General Methods of Computing Functions
Introduction
Application of Infinite Expansions
Recurrence and Difference Relations
Iterative Techniques
Integral Representations
Differential Equations
Tabular Data
Convergence Acceleration
Least Maximum Approximations
Introduction
Properties of Least Maximum Approximations
Nearly Least Maximum Approximations
Rational Approximation
Segmented Approximation
Computation of the Tables
The Choice and Application of Approximations
Introduction
Domain Considerations
Machine Considerations
Conditioning of Approximations
Polynomial Forms
Rational Forms
Transformation Algorithms
Description and Use of the Tables
Introduction
Funetion Notes
Accuracy of the Coefficients
How to Use the Tables
Preparation of the Tables
Function Notes
Square Root, Cube Root
Exponential and Hyperbolic Functions
The Logairithm Function
Trigonometrie Functions
The Inverse Trigonometric Functions
The Gamma Function and Its Logarithm
The Error Function
Bessel Functions
Complete Elliptic Integrals
Appendices:
Conversion Algorithms
Bibliography of Approximations
Decimai and Octal Constants
References
Tables of Coefficients