antibase2 has an inverse only for nonnegative numbers, given by #. twoscomplement's inverse is [:#. (* _1^0=i.@#)"1 signwithbits has inverse #.
Marshall On Wed, Dec 14, 2011 at 11:10 PM, Kip Murray <k...@math.uh.edu> wrote: > Thank you, Raul. May we have inverses? > > On 12/14/2011 9:13 AM, Raul Miller wrote: > > The subject line of this thread is arguably wrong -- there are a > > variety of "good ways" of decomposing integers to binary. > > > > That said, it's interesting to think about the various proposals > > expressed in terms similar to those which could be used to implement > > monadic #: > > > > antibase2=: #:~ 2 #~ 1 + 2<.@^. 1>.>./@,@:|@:<. > > twoscomplement=: #:~ 2 #~ 1 + 2<.@^. 1 +>./@,@:|@:<. > > signwithbits=: #:~ 0, 2 #~ 1 + 2<.@^. 1>.>./@,@:|@:<. > > > > (In all cases the #: here is dyadic, so these definitions are > > independent of the definition of monadic #:) > > > > antibase2 i: 3 > > 0 1 > > 1 0 > > 1 1 > > 0 0 > > 0 1 > > 1 0 > > 1 1 > > twoscomplement i: 3 > > 1 0 1 > > 1 1 0 > > 1 1 1 > > 0 0 0 > > 0 0 1 > > 0 1 0 > > 0 1 1 > > signwithbits i: 3 > > _1 0 1 > > _1 1 0 > > _1 1 1 > > 0 0 0 > > 0 0 1 > > 0 1 0 > > 0 1 1 > > > > There's also (* * #:) but that one assumes the antibase2 > implementation... > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
