Perhaps we shouldn't assume that the last binary digit is accurate. Previous calculations could reduce precision. And usually input is not accurate - especially to 16 significant digits. Often the input may not even be correct in the first digit.
On Thu, Apr 12, 2018 at 5:20 PM, Raul Miller <rauldmil...@gmail.com> wrote: > Conceptually, a floating point number does not represent a precise > value. Instead, it represents a value from an interval which extends > roughly half a bit lower and half a bit higher in the largest > fractional position which can't be represented in that floating point > format. > > But not only is that a mouthful, the "can't be represented" part makes > it hard to work with. > > One approach, though, would be to extend the range all the way into > the bit that can be represented. > > To illustrate: > > fmtexact=:3 :'5!:5<''y''' > ic=: 3!:4 > fc=: 3!:5 > > bump=:4 :0 > assert. IF64 > ($y)$_2 fc 3 ic x + _3 ic 2 fc,y > ) > > fmts=:3 :0 > _1 0 1 fmtexact@bump"0 _/ y > ) > > Using a recent example from this forum: > > fmts 11110171%100 > 111101.709999999992 > 111101.710000000006 > 111101.710000000021 > > What's interesting is that if there's a 00.. sequence which turns into > a 99.. sequence in a floating point neighbor, it's probably reasonable > to treat that sequence as an infinite stream of zeros (which can be > discarded). > > (Also perhaps interesting is that the verb 'bump' takes advantage of > an intentional design feature of floating point numbers: you can > compare them as integers to determine which of two floating point > numbers is larger.) > > Technically you don't even need to look for repetition - just a 0 that > turns into a 9 when you go smaller (or a 9 that turns into a 0 when > you go larger) could be sufficient to treat the digit sequence as > zeros from that point on. > > I am not sure if this would deal with all cases of complex number > fuzz, but it seems like an interesting idea to play with. > > -- > Raul > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
