On May 5, 12:44 am, "Dr. David Kirkby" <david.kir...@onetel.net>
wrote:
> mabshoff wrote:
<SNIP>
Hi Dave,
> > We are talking about two different limits here.
>
> No, we were not - just a confusing way I wrote it. A memory alloction
> issue is completely different to limiting an algorithm due to concerns
> about it.
Well, I certainly am. To recap:
(a) prime_pi() used to use to be trivially implemented as len
(prime_range())
(b) len(prime_range()) sucks memory and performance wise, i.e. eats
in excess of 124GB for input n=2^35 and plainly segfaults for n=2^50.
(c) we have known failures of the new prime_pi() for some inputs,
i.e. n=2^47
So what I am doing is:
(a) cap the new prime_pi() to 2^40 since that is the upper bound we
can verify via doctests in reasonable time. Given the wide testing I
have done this seems to work.
(c) cap prime_range() to a reasonable value and/or rewrite it sanely
- this has not happened yet.
> As a matter of interested, what does Sage give for
> primepi(249999999999999)? Is it the same as Mathematica (7783516108362)?
Sage.math, i.e. 64 bit, gives me:
sage: time prime_pi(249999999999999)
CPU times: user 1241.60 s, sys: 1.07 s, total: 1242.67 s
Wall time: 1243.69 s
7783516108362
Since this is 20 minutes CPU time on a fast box we cannot make this a
doctest, even a long one. I guess we need to implement a better
algorithm :p
> It would be interesting if it gave the same result as Mathematica on any
> of the computers.
>
> In[95]:= PrimePi[249999999999999]
> Out[95]= 7783516108362
>
> Dave
Cheers,
Michael
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