Hello;
Something interesting happens when the exponent is an actual number:
27*^0.2
32.9779
This suggests:
27 ^ (^. 2)
Which takes me back to the documentation....
Roger Hui wrote:
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
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