At 11:14 -0600 2009/08/07, DIETER ENSSLEN wrote:
>thanks
>
>my reaction: "ouch" re the funny numbers. I really don't like
>funny numbers. i love numbers that are right on to the last listed
>digit, or maybe out by one there. how is a person supposed to
>generate pi or e or gamma=Euler-Mascheroni and such to 16, 32 or
>more or many more accurate digits as hobbyists do?
>
>Incidentally, I watched my pc download J602 into my smart phone over
>a while, then afterwards i have been unable to find any trace of it
>on the smart phone yet.
>
The hazards of floating point representation are well known -
sacrifice precision for speed. For most practical purposes,
"engineering precision" works well enough. As a hobby (when I was 11
years old) I memorized pi thusly -
Pi 50
3.14159265358979323846264338327950288419716939937510
Pi
(2: + j.~) ": [: (<....@o. % ]) 10"_ ^ x:
(760+i.15) { Pi 800 NB. a part of pi commented on by Richard Feynman
134999999837297
See, for example: http://en.wikipedia.org/wiki/Feynman_point
But, as you can see, the presentation is formatted, not a number that
can be used in further calculations - depends on your objective...
The Hilbert matrix is a famous case difficult to deal with in
floating point. A nice article about that can be seen at:
http://www.jsoftware.com/jwiki/Essays/Hilbert%20Matrix
There is a more general article about extended precision techniques found at:
http://www.jsoftware.com/jwiki/Essays/Extended%20Precision%20Functions
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
