Adriano Ferreira wrote:
But the multiplication operator (*) is smarter and does an upgrade
from integer to floating point when needed, (possibly) increasing the
range of the correct results.
Adriano.
What JeeBee has stumbled across is a field of study called Numerical
Analysis. For a brief introduction see
http://en.wikipedia.org/wiki/Numerical_analysis
You are correct in that the multiplication operator automatically
converts from integer to float for large values of $p but JeeBee needs
an integer algorithm. For example, he uses ($p-1) % 3, which is only
defined for non-negative integers. The problem is for large values of
$p, $p == $p - 1. This is because floats only store a fixed number of
digits. For example, if it stores 3 digits and $p = 1_000_000, then $p-1
is 1.000e6 - 1 or 1.000e6. The one's column has dropped off the bottom;
it is too small to be recorded in the float.
I recommend that JeeBee takes his algorithm to a mailing list on
Numerical Analysis. They will have a lot more experience with the
foibles of computers doing simple arithmetic.
--
Just my 0.00000002 million dollars worth,
--- Shawn
"Probability is now one. Any problems that are left are your own."
SS Heart of Gold, _The Hitchhiker's Guide to the Galaxy_
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