Arcfactorial ( product ; numberOfFactors )

returns the inverse factorial of a given integer

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Jeff Drake - Show more from this author
Drakeling Technologies

Sample input:

Arcfactorial ( 120 , 3 )

Sample output:

Function definition: (Copy & paste into FileMaker's Edit Custom Function window)

/*
=======================================================
    Arcfactorial ©2012 Drakeling Technologies
    Creation: 5 April 2012 by Jeff Drake

    Purpose: performs the reverse of the Factorial function.

    Note: Custom functions do not allow for optional parameters.
     The numberOfFactors parameter may be left blank.

    Examples:
    • Arcfactorial ( 120 ; 5 ) = 5
    • Arcfactorial ( 720 ; 3 ) = 10

    Dependencies: none
=======================================================
*/ 


Let ( [
         $ƒArcfactorial = $ƒArcfactorial + 1 ; //AUGMENT THE COUNTER.

         //CREATE THE TEXT FOR TESTING THE FACTORIAL.
         #testFactorialText = "Factorial ( " & $ƒArcfactorial &
                                            If ( numberOfFactors > 0 ; "; " & numberOfFactors ) & " )" ;

         //EVALUATE THE FACTORIAL.
         #testFactorial = Evaluate ( #testFactorialText )

] ; //end define Let

   Case (

      //IF THE TEST FACTORIAL IS INVALID, RECURSE THE FUNCTION AND TRY AGAIN.
      EvaluationError ( Evaluate ( #testFactorialText ) ) > 0 ;

         Arcfactorial ( product ; numberOfFactors ) ;


      /*IF THE TEST FACTORIAL IS LESS THAN THE SPECIFIED
         PRODUCT, RECURSE THE FUNCTION AND TRY AGAIN.*/
      #testFactorial < product;

         Arcfactorial ( product ; numberOfFactors ) ;


      /*IF THE TEST FACTORIAL IS GREATER THAN THE SPECIFIED
         PRODUCT, THERE IS NO VALID SOLUTION. RETURN AN ERROR.*/
      #testFactorial > product;

         Let ( $ƒArcfactorial = "" ; 1/0 ) ;


      /*IF NONE OF THE ABOVE BE TRUE, WE’VE FOUND OUR SOLUTION.*/
      Let ( [ #solution = $ƒArcfactorial ; $ƒArcfactorial = "" ] ; #solution )

   ) //end Case

) //end Let

The Factorial function is great, if you want to know the value of 5!. But what if the value you’re given is 120, and you want to know which factorial would give you that product? Enter Arcfactorial.

This function has been tested to FileMaker’s indexable limits of Factorial ( 212 ), but like FileMaker’s own Factorial function, does not handle half-factorials.

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Note: these functions are not guaranteed or supported by BrianDunning.com. Please contact the individual developer with any questions or problems.

Arcfactorial ( product ; numberOfFactors )

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