Roger Hui <[EMAIL PROTECTED]> works:

> What is interesting about 27*^.2 ?
>
>    T=: 27*^.2

> 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])

This seems quit reasonable, since
  (tanh y) -: (p - %p) % (p + %p) NB. p=.^y
  (^T) -: 2^27
  p differs from %p by 2^54 (which is 2 * the double-precision accuracy).

It is possible that a library tanh function might attempt higher
accuracy by using extended precision internally, so smaller
values of T might be necessary for them.

In my own experiments (using J6.01 on XP), I found 27*^.2 to produce
inequality, while values around 27.5*^.2 and above produce equality.

-- Mark D. Niemiec <[EMAIL PROTECTED]>


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