Improved cotransformation for LNS subtraction

Two co-transformations have been proposed previously to avoid interpolation difficulties for logarithmic subtraction: Arnold's and Coleman's. We show these two are closely related, but that Arnold's is considerably more accurate in the worst case. Coleman's hardware is more convenient than Arnold's original method because it works with negative arguments. This paper gives a new variant of Arnold's co-transformation that works with negative arguments using hardware similar to Coleman's while maintaining superior accuracy. This reduces the need for input guard bits to an LNS interpolator, which in turn reduces the size of its multiplier(s).