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Groups > comp.lang.forth > #13397

Re: Reverse factorial

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

> Here's a reverse factorial routine to wile away your free time.

> As the routine is highly f/p intensive it can double as a benchmark
> for testing relative performance between systems and implementation
> details such as separate/common/hardware f/p stacks.

Not this one.

[..]
> DX-Forth 3.98  2012-06-26

> Forth-94
> 80387 15-digit floating point (common stack)

> include n!

> Smallest number with a factorial of at least 1.E9 digits is ...
> 130202809.  ok

[..]

FORTH> runs
Smallest number with a factorial of at least 10^6 digits is 205023   \ 0.000 seconds elapsed.
Smallest number with a factorial of at least 10^7 digits is 1723508   \ 0.000 seconds elapsed.
Smallest number with a factorial of at least 10^8 digits is 14842907   \ 0.000 seconds elapsed.
Smallest number with a factorial of at least 10^9 digits is 130202809   \ 0.000 seconds elapsed.
Smallest number with a factorial of at least 10^10 digits is 1158787578   \ 0.000 seconds elapsed.
Smallest number with a factorial of at least 10^11 digits is 10433891464   \ 0.001 seconds elapsed.
Smallest number with a factorial of at least 10^12 digits is 94851898541   \ 0.000 seconds elapsed.
Smallest number with a factorial of at least 10^13 digits is 869200494600   \ 0.001 seconds elapsed.
Smallest number with a factorial of at least 10^14 digits is 8019346203786   \ 0.000 seconds elapsed.
Smallest number with a factorial of at least 10^15 digits is 74419210652836   \ 0.001 seconds elapsed.
Smallest number with a factorial of at least 10^16 digits is 694100859679692   \ 0.000 seconds elapsed.
Smallest number with a factorial of at least 10^17 digits is 6502464891216880   \ 0.001 seconds elapsed.
Smallest number with a factorial of at least 10^18 digits is 61154108320430276   \ 0.000 seconds elapsed. ok

-marcel

-- ----------------------------------------------------------
: LOG(N!) ( n -- ) ( F: -- log[n!] )
	S>F FLOCAL n
	PI*2 n F* 				FLOG F2/
	n 1e FEXP F/ 		 		FLOG n F* F+
	12e n F* 1/F F1+     
	288e n FSQR F* 1/F 		 	F+
	139e 512840e n F* n F* n F*  F/ 	F-
	571e 2488320e n FSQR FSQR F* F/  	F-  FLOG F+ ;

: FIND-n! ( F: #digits -- n )
	FLOCAL #digits
	#digits F>S 1 LOCALS| low high |
	BEGIN  
	  low high + 2/ LOG(N!) #digits 
	  F>= IF  low high + 2/  TO high  
	    ELSE  low high + 2/  TO low
	   ENDIF
	  low 1+ high >=
	UNTIL
	high ;

: run ( #digits -- )
	CR ." Smallest number with a factorial of at least 10^"
	DUP . ." digits is " timer-reset 10e S>F F** FIND-n! . ."   \ " .elapsed ;

: runs ( -- )  #19 6 DO  I run  LOOP ;

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Thread

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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