;
; Calculates the Wallis product to find an approximation of Pi:
; 
;	Pi/2 = 2  * 2  * 3  * 3  * 4  * 4  ...
;          /1   /3   /3   /4   /4   /5 ...
;
; As the terms get very large, rounding errors in dividing 
; large integers causes the approximation to drift away from the true 
; limiting value of the product. The rounding errors are due to limited 
; precision of the standard computer representation of real numbers. 
;
; See http://en.wikipedia.org/wiki/Wallis_product for more info about
; the Wallis product.
;
; Jacob, May 3, 2008
; Modified by Mark Dow May 4, 2008	(comments, output at a range of terms)
;


AppTitle( "Wallis Product" )
Graphics( 600, 600, 16, 2 )


Global nEven  = 2	; numerator
Global nOdd   = 3	; denominator component


Global flPi1# = 0  	; odd terms
Global flPi2# = 0	; even terms
Global flPi3# = 2	; two times the current product, so the result 
					; 	is an approximation of Pi

Global nRun   = 0

; Main loop:
While ( nRun <= 100000000 )

	nRun  = nRun  + 1
	
	; Find the next two terms each time through the main loop:
	flPi1# = 1.0 * nEven/( nOdd - 2 )	; multiply these by 1.0 so the result is a real number
	flPi2# = 1.0 * nEven/ nOdd         
	
	; Calculate product with the next two terms:
	flPi3# = flPi3# * flPi1# * flPi2#
	
	; Increment the numerator an denominator factors
	nOdd  = nOdd  + 2
	nEven = nEven + 2
	
	; Print the current approximation at every nth term, 
	;	where n is determined by the logarithm of n.
	If ( nRun <= 10  And  nRun Mod 2 = 0 )
		
		Print ( "The calculated value of Pi is " + flPi3# + ", at the " + 2*nRun + "th term" )
	EndIf
	If ( nRun <= 100  And  nRun Mod 20 = 0 )
		
		Print ( "The calculated value of Pi is " + flPi3# + ", at the " + 2*nRun + "th term" )
	EndIf
	If ( nRun <= 1000  And  nRun Mod 200 = 0 )
		
		Print ( "The calculated value of Pi is " + flPi3# + ", at the " + 2*nRun + "th term" )
	EndIf
	If ( nRun <= 10000  And  nRun Mod 2000 = 0 )
		
		Print ( "The calculated value of Pi is " + flPi3# + ", at the " + 2*nRun + "th term" )
	EndIf
	If ( nRun <= 100000  And  nRun Mod 20000 = 0 )
		
		Print ( "The calculated value of Pi is " + flPi3# + ", at the " + 2*nRun + "th term" )
	EndIf
	If ( nRun <= 1000000  And  nRun Mod 200000 = 0 )
		
		Print ( "The calculated value of Pi is " + flPi3# + ", at the " + 2*nRun + "th term" )
	EndIf
	If ( nRun <= 10000000  And  nRun Mod 2000000 = 0 )
		
		Print ( "The calculated value of Pi is " + flPi3# + ", at the " + 2*nRun + "th term" )
	EndIf
	If ( nRun <= 100000000  And  nRun Mod 20000000 = 0 )
		
		Print ( "The calculated value of Pi is " + flPi3# + ", at the " + 2*nRun + "th term" )
	EndIf
	;Stop
	
Wend	; end of main loop

Stop

End