Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-p base $$\beta $$

Abstract

Abstract There are simple algorithms to compute the predecessor, successor, unit in the first place, unit in the last place etc. in binary arithmetic. In this note equally simple algorithms for computing the unit in the first place and the unit in the last place in precision- p base- $$\beta $$ β arithmetic with $$p \geqslant 1$$ p ⩾ 1 and with $$\beta \geqslant 2$$ β ⩾ 2 are presented. The algorithms work in the underflow range, and numbers close to overflow are treated by scaling. The algorithms use only the basic operations with directed rounding. If the successor (or predecessor) of a floating-point number is available, an algorithm in rounding to nearest is presented as well.