APL comparison tolerance

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Abstract
An important aspect of the original implementation of APL\360 was the treatment of arithmetic functions as abstract functions defined on the continuous set of real numbers [1,2]. This had various consequences, including automatic conversion between different machine representations of numbers so that storage and other aspects of System/360 architecture could be used efficiently while suppressing its details. [2] “Fuzzy” comparisons were introduced so that the actual discrete, fixed-precision, hexadecimal representation could be partly disguised The technique used in the original implementation was to regard numbers whose difference was zero in the first twelve (of fourteen) hexadecimal digits to be equal. The definitions in [3] were developed by M. A. Jenkins and R. H. Lathwell in 1968 when it was found that, for some values, implications of relational functions such as B A←&rar;˜ B≤ A were violated. It was later discovered that these definitions did not completely correct the difficulty, and when APL system variables were introduced [4], the tolerant functions were rederived, resulting in the definitions given here.

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