Byte to Number conversion, LUT and Alchemy

after trying to faster convert an integer to a Number, lets explore some new conversions tricks..
By reading this Blog about “Understanding fast float/integer conversions”, lets try some of the techniques !

this time, I want to convert a byte or an integer [0;255] to a Number, and normalize the result [0;1]

const oo255:Number = 1/255;

and the code:

var n:Number = byteValue * oo255;


can we go faster?

//first, lets fill a lookup table when our program starts:
for(var i:int=0;i<256;i++)
{
  fastMem.fastSetDouble( i*oo255 , i<<3);
}

and our conversion code becomes:

var n:Number = fastMem.fastGetDouble(i<<3);

Which version is faster ? Lets find-out...



okay, lookup table is slower, but its not far from being at the same speed, so doing a LUT of a formula with more maths than just a multiply will quickly become faster !

so here, lets assume we want to add a simple ease-in ease-out function, a very simple sigmoid:
n = n*n*(3-2*n)


which method is the best ?

1)direct computation

a = val*oo255;a=a*a*(3-a-a);


2)LUT and alchemy:

//first, initialize our LUT:
for(i= 0;i<256;i++)
{	
var n:Number = i*oo255;
n =n*n*(3-n-n);
fastmem.fastSetDouble(n,i<<3);	
}

now, the only call we need to profile:

a = fastmem.fastGetDouble(val<<3);

which method is the best?



LUT is just a tiny better, so lessons learned:
* flash can be pretty good at doing brute force maths if carefully coded.
* LUT lookup table are not always faster

Next time... we coud try a slower function.. such as:

What do you get ?

the code:

	protected function byteto01():void
		{
		
			// initialize alchemy
			var ba:ByteArray= new ByteArray();
			ba.endian = Endian.LITTLE_ENDIAN;
			ba.length = 4096;
			fastmem.fastSelectMem(ba); //azoth
	
			var i:int = 0;
			var a:Number;			
			var val:int;
			var oo255:Number = 1.0/255.0;

			//Fill our look-up-table:
			for(i= 0;i<256;i++)
			{				
				fastmem.fastSetDouble(i*oo255,i<<3);	
			}

			
			var time1:uint = getTimer();
			
			for(i= 0;i<50000000;i++)
			{
				val = i&255;
				a = val*oo255;	
				a = val*oo255;	
				a = val*oo255;	
				a = val*oo255;	
				a = val*oo255;	
				a = val*oo255;	
				a = val*oo255;	
				a = val*oo255;	
				a = val*oo255;	
				a = val*oo255;	
			}
	
			var time2:uint = getTimer();

			for(i= 0;i<50000000;i++)
			{
				val = i&255;
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
			}
			var time3:uint = getTimer();
			
			
			//with a simple sigmoid - lookup table
			//y=x*x*(3−2x).
			for(i= 0;i<256;i++)
			{	
				var n:Number = i*oo255;
				n =n*n*(3-n-n);
				fastmem.fastSetDouble(n,i<<3);	
			}
			
			var time4:uint = getTimer();
			
			for(i= 0;i<50000000;i++)
			{
				val = i&255;
				a = val*oo255;a=a*a*(3-a-a);	
				a = val*oo255;a=a*a*(3-a-a);	
				a = val*oo255;a=a*a*(3-a-a);
				a = val*oo255;a=a*a*(3-a-a);
				a = val*oo255;a=a*a*(3-a-a);
				a = val*oo255;a=a*a*(3-a-a);
				a = val*oo255;a=a*a*(3-a-a);
				a = val*oo255;a=a*a*(3-a-a);
				a = val*oo255;a=a*a*(3-a-a);
				a = val*oo255;a=a*a*(3-a-a);
			}
			
			var time5:uint = getTimer();
			
			for(i= 0;i<50000000;i++)
			{
				val = i&255;
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
				a = fastmem.fastGetDouble(val<<3);
			}

			var time6:uint = getTimer();
			
			startTest();
			setTest( "n=i*oo255"    , "byteTo01", time2-time1 );
			setTest( "n=alchemyLookupTable"   	  , "byteTo01", time3-time2  );
			setTest( "n=i*oo255;n=n*n*(3-n-n)"    , "byteTo01_sigmoid", time5-time4 );
			setTest( "n=alchemyLookupTable"   	  , "byteTo01_sigmoid", time6-time5  );

			endTest();					
			
		}