Automatic propagated and round-off error analysis

Abstract

The routine described below is a modification of the Carnegie Tech (IT) Compiler system for the IBM-650, which will provide automatic empirical analysis of propagated and round-off errors in computation. In the modified system, three kinds of variables are admissable: fixed-point integers called I-variables; floating-point numbers called C-variables, which are considered to be exact values; and 2-word variables called Y-variables, in which one word is a floating-point number which represents the value of the variable and the other word represents a bound upon the propagated and round-off error present in that value. Statements written in the IT language may refer to any or all of these classes of variables. During the execution phase of a program, computation proceeds in typical fashion, except that each time a Y-variable is operated upon by the program, its error term is modified so as to represent a valid bound upon propagated and round-off error in the variable.