Estimating PI through simple geometry and statistics

pi.adb

with Ada.Text_IO;
with Ada.Float_Text_IO;
with Ada.Numerics.Float_Random;

use Ada.Text_IO;
use Ada.Float_Text_IO;
use Ada.Numerics.Float_Random;

procedure Pi is
	N: constant Integer := 500000; -- Number of iterations.
	Counter_Square, Counter_Circle: Integer := 0;
	Point_X, Point_Y: Float;
	Pi: Float;
	G: Generator;
	
	function Belongs_To_Circle (X, Y: Float) return Boolean is
	begin
		return X*X + Y*Y <= 0.25;
	end Belongs_To_Circle;
	
begin
	for I in 1 .. N loop
		-- Generate a random point inside the square.
		Point_X := Random(G) - 0.5;
		Point_Y := Random(G) - 0.5;
	
		-- Verify if the points is inside the circle.
		if Belongs_To_Circle(Point_X, Point_Y) then
			-- The point belongs to the circle AND the square.
			Counter_Circle := Counter_Circle + 1;
			Counter_Square := Counter_Square + 1;
		else
			-- In this case, the point is outside the circle.
			Counter_Square := Counter_Square + 1;
		end if;
	end loop;
	
	-- Area of square / area of circle = pi/4.
	Pi := 4.0 * (Float(Counter_Circle) / Float(Counter_Square));
	
	Put ("The estimated value of PI is: ");
	Put (Pi);
end Pi;