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Re: Reverse factorial

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"Ed" <invalid@nospam.com> writes Re: Reverse factorial

> Marcel Hendrix wrote:
[..]
> I get these results using your algorithm

> Smallest number with a factorial of at least 10^0 digits: 1.
> Smallest number with a factorial of at least 10^1 digits: 10.
[..]
> Smallest number with a factorial of at least 10^6 digits: 205023.

> While the original (slow) routine gives

> Smallest number with a factorial of at least 1.E0 digits: 1.
> Smallest number with a factorial of at least 1.E1 digits: 13.
[..]
> Smallest number with a factorial of at least 1.E6 digits: 205022.
[..]

According to Wolfram Alpha, 

log10(13!) = 9.79428031638948
log10(14!) = 10.940408352067719

Therefore the result for 10^1 digits should be 14, not 13. My program
is wrong, but not because log(n!) is faulty (see below).

According to Wolfram Alpha, 

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.

The fix to my program is:

: FIND-n! ( F: #digits -- n )
...
	#digits F>S  3 2 */  1 LOCALS| low high |
...
	high ;

The result for 10^0 is wrong for both programs (0! = 1).
As should be obvious, I didn't test my code for 10^0 and 10^1 digits. 

-marcel

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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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