Typos: all comparisons below should be with 0 tolerance, viz., =!.0 and >:!.0 .
----- Original Message ----- From: Roger Hui <[EMAIL PROTECTED]> Date: Saturday, March 1, 2008 22:45 Subject: [Jprogramming] What is interesting about 27*^.2 ? To: Programming forum <[email protected]> > What is interesting about 27*^.2 ? > > T=: 27*^.2 > T > 18.715 > ":!.18 T > 18.714973875118524 > > (spoiler alert.) > > > > > > > > > > > > > > > What is interesting about T=:27*^.2 ? In IEEE 64-bit > floating point calculation, for all y>:T, 1=tanh y > (and _1=tanh -y) and T is the smallest number with > this property. > > tanh=: (^ - [EMAIL PROTECTED]) % (^ + [EMAIL PROTECTED]) > > tanh T > 1 > 1 - tanh T > 0 > > hex =: ([EMAIL PROTECTED]) }. 2&(3!:3) > unhex=: (3!:2) @ ((}: 2 (3!:3) 0.5)&,) " 1 > > hex 1,tanh T > 3ff0000000000000 > 3ff0000000000000 > > hex T > 4032b708872320e2 > t=. unhex (}:,hex T),'1' NB. the next smaller > number hex t > 4032b708872320e1 > tanh t > 1 > 1 - tanh t > 2.22045e_16 > hex tanh t > 3feffffffffffffe ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
