An arithmetic is described that can replace floating-point arithmetic for programming tasks requiring assured accuracy. A general explanation is given of how the arithmetic is constructed with C++, and a programming example in this language is supplied. Times for solving representative problems are presented.

When a high-level programming language is used for scientific computation, usually one must use standard floating point and choose the precision-single, double, or higher-before one's program executes. This paper describes a modified Basic that accommodates the advanced computation techniques of dynamic adjustable precision and interval arithmetic. This language-Precision Basic or Pbasic-allows a user to routinely obtain his n decimal place answers accurate to the last decimal place. An interpreter for this modified Basic was recently completed that runs on a Z-80 microprocessor. Some features of the interpreter are described.

A system of memory sharing is proposed as a means for computer communication.

It is well known that real variable analysis is nonconstructive. For example, although it is asserted that every bounded monotone sequence converges to a limit, there is no algorithm for obtaining this limit. This paper presents a constructive analysis which is restricted to a countable set of numbers, the field of computable numbers. These numbers are defined in a new way by employing the concept of “programmable functions.” The resultant analysis differs from real analysis in many important respects.