Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
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Floating-point arithmetic[1] is the design almost universally accepted for computers dealing with so-called scientific computations. It was present in some of the earliest machines and successfully survived the controversies that followed its first implementations. Since then, it has been consistently available in the hardware of many systems and it has been extensively used by high-level programming languages. The description of a numerical algorithm is truly accurate if and only if it includes pertinent statements on the precision of the computation. Therefore, it is most desirable that an algorithmic language such as APL give the designer the ability to express such statements. Accordingly, if this language is also used for programming, it is essential that the programmer be allowed to access the full range of available hardware precisions. These considerations are the basis for the proposal to add to APL a system variable and a system function, @@@@CP and @@@@FP, described in this paper.