I suspect that if tanh 0.2+T is still not exactly 1 then the computation used in tanh is not the best.
To settle it, we can use http://www.jsoftware.com/jwiki/Essays/Extended_Precision_Functions#head-f43abe4b382ab35179da8c5ad8c8906158ae0a3e ----- Original Message ----- From: Zsbán Ambrus <[EMAIL PROTECTED]> Date: Sunday, March 2, 2008 9:03 Subject: Re: [Jprogramming] What is interesting about 27*^.2 ? To: Programming forum <[email protected]> > On Sun, Mar 2, 2008 at 7:45 AM, Roger Hui <[EMAIL PROTECTED]> wrote: > > T=: 27*^.2 > > > > (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]) > > I would rather defined tanh as > > tanh1 =: 7&o. > > If you use this definition, then the above statement is not > true. In > fact, (tanh1 0.2 + T) is still not exactly one. This is > similary to > what I get if I use the tanh function in the GNU libc, which is > supposed to be very precise, so I assume that for such large values, > tanh1 gives a more precise result than your tanh function (the > difference is minute of course). ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
