Re: Reverse factorial

From	"Ed" <invalid@nospam.com>
Newsgroups	comp.lang.forth
Subject	Re: Reverse factorial
Date	2012-07-03 17:02 +1000
Organization	Aioe.org NNTP Server
Message-ID	<jsu5d6$bs7$1@speranza.aioe.org> (permalink)
References	<jspim5$hcn$1@speranza.aioe.org> <92841902968435@frunobulax.edu><jsq93l$983$1@speranza.aioe.org> <7xhatpig84.fsf@ruckus.brouhaha.com>

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Paul Rubin wrote:
> "Ed" <invalid@nospam.com> writes:

That was Marcel.  Maths is beyond me.

> >> log10(205022!) = 999999.08681421082059069559626773741428638233100481270
> >> log10(205023!) = 1.00000439861679486551512255600216645545545382220e6
> >>
> >> Therefore 205023 as the "Smallest number with a factorial of at least 10^6
> >> digits" is correct.
>
> Of course 10**999999.08 has 1e6 digits just like 10^9 has 10 digits.
>
> I calculated 205022! exactly with GHC (uses GMP underneath).  This took
> about 8 seconds including the output conversion (which used around 300MB
> of memory, doesn't seem good).  The first digits are:
>
>  1221277091680869925277501633213930559467939034445151838141073953...
>
> I think for inverse factorial of large numbers, it probably is pretty
> accurate to use a numerical rootfinder on the first few terms of the
> Stirling series:
>
> http://en.wikipedia.org/wiki/Stirling%27s_approximation#Speed_of_convergence_and_error_estimates
>
> Even just the first (1/12n) correction term makes Stirling's
> approximation pretty accurate.

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Reverse factorial "Ed" <invalid@nospam.com> - 2012-06-29 11:51 +1000
  Re: Reverse factorial mhx@iae.nl (Marcel Hendrix) - 2012-06-30 02:05 +0200
    Re: Reverse factorial "Ed" <invalid@nospam.com> - 2012-06-30 12:26 +1000
    Re: Reverse factorial "Ed" <invalid@nospam.com> - 2012-07-01 23:17 +1000
      Re: Reverse factorial mhx@iae.nl (Marcel Hendrix) - 2012-07-01 16:51 +0200
        Re: Reverse factorial "Ed" <invalid@nospam.com> - 2012-07-02 05:40 +1000
          Re: Reverse factorial Paul Rubin <no.email@nospam.invalid> - 2012-07-02 22:08 -0700
            Re: Reverse factorial "Ed" <invalid@nospam.com> - 2012-07-03 17:02 +1000
            Re: Reverse factorial mhx@iae.nl (Marcel Hendrix) - 2012-07-03 21:14 +0200
              Re: Reverse factorial Paul Rubin <no.email@nospam.invalid> - 2012-07-03 12:44 -0700
                Re: Reverse factorial mhx@iae.nl (Marcel Hendrix) - 2012-07-03 22:37 +0200
                Re: Reverse factorial "Ed" <invalid@nospam.com> - 2012-07-05 23:14 +1000

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