🚀 go-pugleaf

If you are able to spend some memory, you can improve the processing very much.


First Method:	There are only 2^16  square roots of a number, which is 32 Bits long.
		So generate a table of the squares of the numbers from
			 2		    2
			0   ... ( 2^16 - 1 )
		and find the square root with a binary search. You need only
		1 comparison, 1 addition, 1 shift and 1 assignment per search step.
		If you unroll the loop, you do not need any loop overhead.
		Disadvantage: the table consumes 256 KB.

		You can also use the same table to square your dx and dy, if
		your multiplication is slower than a table lookup.


Second Method:	Use Newton, but find the first approximation with a table lookup.
				
		Variant a:	Use a table of the square roots of  0 .. 255 (* 2^24)
				Perform the lookup with the first byte.
				You need 2 additional iterations with Newton.
				The table consumes 1 KB.

		Variant b:	Use a table of the square roots of 0 .. (2^16-1)
								             (* 2^16)
				Perform the lookup with teh first two bytes.
				You need 1  Newton iteration (onle`y 1 division!).
				Disadvantage: the table consumes 256 KB.

I think,  if you spend enwough memory (you have no PC?) you can calculate the
distance very fast with the second method, variant b!

Uli