It is in fact right on the edge: T=: 2^_34 2=!.T 2+T+T 1
hex=: 5 }. 2: 3!:3 , hex 2+T+T 4000000000040000 X=: }: 2 (3!:3) 2*1+t X e200000000000000 0000000000000008 0000000000000001 0000000000000000 unhex=: 3!:2 @ (X&,) 2 =!.T unhex '4000000000040000' 1 2 =!.T unhex '4000000000040001' 0 A difference in the last bit. On Wed, Feb 19, 2014 at 5:35 PM, Henry Rich <henryhr...@nc.rr.com> wrote: > Yes, the test is very close to the edge: > > T=: 2^_34 > 2 =!.T 2+T+T > 1 > 2 =!.T 2+T+T+2^_50 > 0 > > Henry Rich > > On 2/19/2014 8:33 PM, Roger Hui wrote: > >> You have to consider the definition of tolerant equality carefully. It is >> the _relative_ difference that matters, not the absolute difference. The >> absolute difference between 2 and 2+T+T is 2*T, but the relative >> difference >> is (2*T)%2+T+T, and this relative difference is less than T. >> >> >> >> >> >> On Wed, Feb 19, 2014 at 5:24 PM, Ian Clark <earthspo...@gmail.com> wrote: >> >> Okay, I was reading that as *less* than 2^_34 >>> >>> All is not as it seems however... >>> >>> ] T=: 2^_34 >>> 5.82077e_11 >>> 2 =!.T 2+T >>> 1 >>> 2 =!.T 2+T+T NB. I'd expect 0 here >>> 1 >>> 2 =!.T 2+T+T+T >>> 0 >>> NB. at last! >>> >>> >>> >>> On Thu, Feb 20, 2014 at 12:37 AM, Henry Rich <henryhr...@nc.rr.com> >>> wrote: >>> >>> Comparison tolerance cannot be more than 2^_34. >>>> >>>> (So that integer comparisons on 32-bit machines do not have to worry >>>> >>> about >>> >>>> tolerance) >>>> >>>> Henry Rich >>>> >>>> >>>> >>>> On 2/19/2014 7:03 PM, Ian Clark wrote: >>>> >>>> I'm trying to construct an example using Fit (!.) to customize a given >>>>> primitive (e.g. =) to set its tolerance. >>>>> Try as I might I cannot get variants of this to work: >>>>> >>>>> T=: 0.001 >>>>> 2 =!.T 2.0001 >>>>> |domain error >>>>> | 2 =!.T 2.0001 >>>>> >>>>> What am I doing wrong? >>>>> ---------------------------------------------------------------------- >>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>>> >>>>> ------------------------------------------------------------ >>>>> ---------- >>>>> >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >>> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
