Testing for palindromes (Matev)
Matevž Markovič
ivwcorporation.matevz at gmail.com
Wed Feb 8 10:15:33 CET 2012
2012/2/8 Jim White <mathimagics at yahoo.co.uk>
> > If I understand these things right, this is a good idea, but only to a
> > certain point (some numbers have more than 20 x 10^6 digits). And yes, it
> > is safe to assume that 99.999% of those numbers are non-palindromic.
>
> Not sure what you mean by "only to a certain point". Given that you are
> testing for base 10 palindromes, the method suggested by TG seems to me
> to be the only way to attack this problem.
>
> To recap, for each target integer A, with known size N digits (or N-1), we
> look at the
> leading and trailing digits, K digits at a time. TG suggests K = 30, it
> might be worth
> testing a sample of your A's to see what value of K is optimal for you.
>
> Forming the required divisors 10 ^ (N - K) might best be done with the
> traditional binary
> mask approach, ie using a table of precomputed values 10, 10^2, 10^4 etc
> (ie. 10^2^x).
>
> Jim White
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I wrote "only to a certain point" due to the fact that I experienced a
drastic slowdown after numbers got bigger. Fortunately, those slowdowns
were not caused by gmp but were only a consequence of another software
problem (one of my test server applications decided to allocate little too
much memory from time to time).
About Torbjorn`s decission to use k=30, I thought that there was already
some research done. Thank you for your answers.
Yours,
Matevž
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