Dyadic digit swell

The problem of the size of the dyadic digit representations swelling during the course of a computation (see section 7.1 can be a serious problem. Experimentation shows that if we were to perform a series of computations involving dyadic stream multiplication such as computing iterations of the logistic map, for example, the problem can cause calculation to slow down very quickly. It is easy to see why by examining the first digit of output when computing ten iterations of the logistic map with the input $\frac{1}{2}$, which is the following large number.

388724570240705552142776682659458947805233224971859047752053338671439429888249069717757239313788490855334773356668182913613076126
552062213403564490610115613879629448773326009906579395235728097731596429190636911575213790785968204525040785029732203576471005350
951634165803606107538538116079472135738129467210780105351961615961185396421655274104732599578476551971538700680019225274588464976
895373596656654737071019377572902620812208450390621338292169853029681069459203464648330292157739569298813293253272386475249342402
851477594014885182650701889533684366050366443636678080968237909546976725623467384695888847956243028042083901779843462335576089740
37211232428948182312068910977382409530734339520634770286168280173816752977514667057983730439270328511795464461041623322625/2^2558

This problem is one of the reasons the dyadic stream representation is not the main representation used by the calculator.