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The result of a simple oating-point computation can be in great error, even though no error is signaled, no coding mistakes are in the program, and the computer hardware is functioning correctly. This paper proposes a set of instructions appropriate for a general purpose microprocessor that can be used to improve the credibility and accuracy of numerical computations. Such instructions provide direct hardware support for monitoring events which may threaten computational integrity, implementing oating-point data types of arbitrary precision, and repeating calculations with greater precision. These useful features are obtained by the e cient implementation of high radix on-line arithmetic. The prevalence of super-scalar and VLIW processors makes this approach especially attractive.

A High Radix On-line Arithmetic for Credible and Accurate Computing