arXiv subjects
Publications and source records attributed to Peter Kornerup.
It has been pointed out by counterexamples in a 2013 paper in the IEEE Transactions on Computers [1], that there is an error in the previously ibid.\ in 2005 published paper [2] on the construction of valid digit selection tables for SRT type division and square root algorithms. The error has been corrected, and new results found on selection constants for maximally redundant digit sets.
Recently we introduced a class of number representations denoted RN-representations, allowing an un-biased rounding-to-nearest to take place by a simple truncation. In this paper we briefly review the binary fixed-point representation in an encoding which is essentially an ordinary 2's complement representation with an appended round-bit. Not only is this rounding a constant time operation, so is also sign inversion, both of which are at best log-time operations on ordinary 2's complement representations. Addition, multiplication and division is defined in such a way that rounding information can be carried along in a meaningful way, at minimal cost. Based on the fixed-point encoding we here define a floating point representation, and describe to some detail a possible implementation of a floating point arithmetic unit employing this representation, including also the directed roundings.
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).