The principal result of this paper answers a long-standing question in the model theory of arithmetic [KS, Question 7] by showing that there exists an uncountable arithmetically cl...
We give the results of our search for the worst cases for correct rounding of the major elementary functions in double precision floating-point arithmetic. These results allow the...
We design new feed-forward multi-layered neural networks which perform di erent elementary arithmetic operations, such as bit shifting, addition of N p-bit numbers, and multiplica...
Abstract. There is a very simple way in which the safe/normal variable discipline of Bellantoni-Cook recursion (1992) can be imposed on arithmetical theories like PA: quantify over...
Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of real numbers with floating-point bounds. Operations for intervals can be efficient...