Dual procedure recursion

Sometimes have algorithms with multiple states

Example:

p(x) =	p(x-1) + q(x/2)	{x>1}
	2	{x<=1}
q(x) =	q(x-3) * p(x-5)	{x>3}
	x/3	{x<=3}

This involves two recursive functions

• directly recursive:
  • p calls itself
  • q calls itself
• also indirectly recursive
  • p calls q which call p again
  • q calls p which call q again

Ada requires that things must be declared before they can be used.

• You cannot both define p before q and define q before p.
• must predefine one or both of the functions

Code

	-- first declare q, so p can refer to it
	function q (x: in float) return float;

	-- now define p. Full definition is possible
	function p (x: in float) return float is
	begin
		if (x<=1) then 
		 	return 2;
		end if;
		return  p(x-1) + q(x/2);
        end p;

	-- now provide full definition of q
	function q(x: in float) return float is
 	begin
		if (x<=3) then
			return x/3;
		end if;
		return q(x-3) * p(x-5);
	end q;