On a divide-and-correct method for variable precision division

:: The aberration in this generator was (}bvious on('.e we k n e w where to look. In a g e n e r a t o r whose parameters are : k~ss transparent, its may be much more difticult to know ": whePe to look, and ihe aberration nnay be znu( 'h nlore ('on~plex in nature; but. there is no a priori reason to suppose that a silnilar aberration does not exist;. The corrective procedure that La('h adopted was to switch back and fort,h among tive variations of the generator , using the following five multipliers: 2186277, t86285, 186293, 186301 and 186309. Each of these mul t i pliers approximates %/2 at' and each of them is (:ongruent; to ± 3 modulo 8, t)ut none of them equals (2 ]s + 3). ~_w~tehlng among some such set. of generators may intui t ively seem to resolve the problem, particularly if ;he switching is done "at random." Recalling yon Neu]~ann's observation, however, the user would be well advised to heed the customary warning and construct his own tests.