Nth digit of PI

[david_ullrich at my-deja.com]

In article <FvuAy4.51q at cwi.nl>,
  "Dik T. Winter" <Dik.Winter at cwi.nl> wrote:
> In article <bivnjsoq0amb8qjmqtgkbfjsl2df2n2tta at 4ax.com>
urner at alumni.princeton.edu writes:
>  > Recent number theory breakthrough:  you can get the
>  > nth digit of PI without doing all the work needed
>  > to compute all the digits up to the nth digit (same
>  > with some other numbers -- not sure if we know all
>  > the relevant criteria as to which).
>
> I checked the pages and have to make a correction here.  There is no
such
> claim.  The only claim is that it can be done without using much
memory.
> As one of the referred pages says:
>   "we have not found a faster algorithm, nor have we proven that one
does
>   not exist."
> Se essentially the amount of work is still the same, but the memory
> requirents are smaller.

    ??? In one of the references cited the authors say

"The computation can
be achieved without having to compute the preceeding digits. We claim
that the algorithm has a more theoretical rather
than practical interest, we have not found a faster algorithm, nor have
we proven that one does not exist."

The statement "The computation can be achieved without having to
compute the preceeding digits." could be a lie, I suppose, but
it's certainly at least a _claim_ that they can calculate the
n-th digit without finding the preceding ones.

    Regarding the "have not found a faster algorithm": Are
you certain they're saying that none of this is any faster
than finding the first n digits, or do they mean that they
have not found a faster "digit-extraction" algorithm than
the original Bailey-Borwein-Plouffe algorithm?

    The other reference begins

"David Bailey, Peter Borwein and Simon Plouffe have recently computed
the ten billionth digit in the hexadecimal
 expansion of pi. They utilized an astonishing formula:

[astonishing formula goes here]

 which enables one to calculate the dth digit of pi without being forced
to calculate all the preceding d-1 digits."

    If these algorithms _really_ take as much time as finding
all the digits, as you seem to be saying, it's hard to see why
they'd have everybody so excited (or rather why they _did_ have
everybody so excited back when this was news). It's also hard to
see why people would suggest that one point to the digit-extraction
algorithms would be to be able to check the accuracy of calculations
of _all_ the digits.

> --
> dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland,
+31205924131
> home: bovenover 215, 1025 jn  amsterdam, nederland;
http://www.cwi.nl/~dik/
>


Sent via Deja.com http://www.deja.com/
Before you buy.