Approximates the distance between 0,0 and x,y 30% faster than euclidean squares method because no square root calculation (approximation) is needed

Also includes the formula for 3D point distance calculation, but it doesn't work well. Deviation is around 60%.

                                    ` This code was downloaded from The Game Creators
                                    ` It is reproduced here with full permission
                                    ` http://www.thegamecreators.com
                                    
                                    `The approx_distance(x,y) function is a linear calculation for distance.
`It is around 30% faster than the pythagorean squares method and has around 2% deviation.

`-------------------------------------------Test Drivers---------------------------------------------
`uncomment the sections you'd like to use for testing

// 	`---Declarations needed for any test driver---
// 	#constant iter = 100
// 	set text font "Courier"
// 	randomize timer()
// 
// 	`---Deviation Test---
// 		for n = 0 to iter
// 			x# = (rnd(100) - 50.0)/3
// 			y# = (rnd(100) - 50.0)/3
// 			z# = (rnd(100) - 50.0)/3
// 			//sum_diff# = sum_diff# + abs(approx_distance(x#,y#) - true_distance(x#,y#)) / true_distance(x#,y#)
// 			sum_diff# = sum_diff# + abs(approx3d_distance(x#,y#,z#) - true3d_distance(x#,y#,z#)) / true3d_distance(x#,y#,z#)
//  			print "approx = ",approx3d_distance(x#,y#,z#)
//  			print "true   = ",true3d_distance(x#,y#,z#)			
// 		next n	
// 		avg# = sum_diff# / iter
// 		print "Error rate:"
// 		print "    Average deviation = ", avg#
// 		print 
// 
// 	`---Computing Time Test---
// 		print "Computing Time comparison:"
// 		 
// 		t0 = timer()
// 		for n = 0 to iter
// 			x# = (rnd(100000) - 50000.0)/3
// 			y# = (rnd(100000) - 50000.0)/3
// 			z# = (rnd(100000) - 50000.0)/3
// 			//approx_distance(x#,y#)
// 			approx3d_distance(x#,y#,z#)
// 		next n
// 		t1 = timer()
// 		time# = (t1 - t0)/1000.0
// 		print "    Approx Distance function time: ", time#, " seconds"
// 		print
// 		
// 		t0 = timer()
// 		for n = 0 to iter
// 			x# = (rnd(100000) - 50000.0)/3
// 			y# = (rnd(100000) - 50000.0)/3
// 			z# = (rnd(100000) - 50000.0)/3
// 			//true_distance(x#,y#)
// 			true3d_distance(x#,y#,z#)
// 		next n
// 		t1 = timer()
// 		time2# = (t1 - t0)/1000.0
// 		print "    True Distance function time: ", time2#, " seconds"
// 		print 
// 		print "    Time Difference = ", time2# - time#, " seconds ";
// 		print "over ", iter," iterations"
// 		print "    Time per calculation = ", (time2# - time#)/iter, " seconds "
// 		print "    Percent time saved = ", (100*(time2# - time#)/time2#),"%"
// 
//  
// 
// wait key : end


function approx_distance(x as float,y as float)

	if x < 0 then x = -x
	if y < 0 then y = -y
	
	if x < y
		min = x
		max = y
	else
		min = y
		max = x
	endif
	
	approx = ( max * 1007 ) + ( min * 441 )
	
	if ( max < ( min << 4 ) )
		approx = approx - ( max * 40 )
	endif
	
	result = ( ( approx + 512 ) >> 10 )
	// actual calculation is [1007 * max(|x|,|y|) + 441 * min(|x|,|y|)]/1024
	//  or 0.5 * [1 + 1/(4 - 2 * 2^0.5)] * min [ (|X|+|Y|) / 2^0.5 , max(|X|,|Y|) ]
endfunction result

// function true_distance(x as float,y as float)
// 	result = ( x^2 + y^2 )^0.5
// endfunction result

// function true3d_distance(x as float,y as float, z as float)
// 	result = ( x^2 + y^2 + z^2 )^0.5
// endfunction result

// 3D distance approximation formula
// 0.5 * [1 + (1 / (3^.25))] * min[ (|X|+|Y|+|Z|)/3^0.5 , max (|X|,|Y|,|Z|) ]
// 0.57216878364870322056364359756274 * min[ (|X|+|Y|+|Z|)/1.7320508075688772935274463415059 , max (|X|,|Y|,|Z|) ]
// should give about 16% error
// meh this doesn't work very well i'm getting 30+ % deviation

// function approx3d_distance(x as float,y as float, z as float)
// 	if x < 0 then x = -x
// 	if y < 0 then y = -y
// 	if z < 0 then z = -z
// 	
// 	if x >= y and x >= z then max# = x
// 	if y >= x and y >= z then max# = y
// 	if z >= y and z >= x then max# = z
// 	
// 	sumXYZoverQ = (x + y + z)/1.7320508075688772935274463415059
// 	if sumXYZoverQ < max#
// 		min# = sumXYZoverQ
// 	else
// 		min# = max#
// 	endif
// 	
// 	result = 0.87991784282579627366559387532727 * min#
// 	
// endfunction result