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



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