I want to implement this square root method in Pascal using recursion. However, I have some problems understanding how to transfer iterative method into recursive method:
Program NewtonRaphsonRecursive(output);
{$mode objFPC}
function newton_raphson_rec(a: real; p: real; eps: real; max_i: integer) : real;
var
x: real;
i: integer;
begin
x := a / 2.0;
i := 0;
if abs(x - a / x) < eps then
begin
result := x;
end
else
begin
x := (x + a / x) / 2.0;
i := i + 1;
result := newton_raphson_rec(x, p, eps, max_i);
end;
end;
var
sqroot: real;
begin
sqroot := newton_raphson_rec(25, 0.001, 0.000001, 100);
writeln(sqroot);
end.
The code: https://onlinegdb.com/OvDBfHzLf
If you look at the start of the Newton-Raphson iterative solution in the other question, you will see that the first calculation (x := num / 2.0) is merely a first guess of the solution. You must remove that line in your recursive solution and enter a best guess into the function parameter.
function newton_raphson_recurse(num: real; new_guess: real; eps: real; max_i: integer) : real;
begin
Dec(max_i); // Decrement counter
new_guess := (new_guess + num / new_guess) / 2.0;
if (Abs(new_guess - num) < eps) or (max_i < 1)
then Result := new_guess
else Result := newton_raphson_recurse(num,new_guess,eps,max_I);
end;
...
sqroot := newton_raphson_recurse(9, 9/2.0, 0.0000001, 10);
Note how the new_guess
is reused during the recursion with a more accurate value each time.
As always when testing a routine, single stepping into the program is a very good skill to learn when debugging.