Arithmetic-geometric mean/Calculate Pi: Difference between revisions

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The purpose of this task is to demonstrate how to use this approximation in order to compute a large number of decimals of <math>\pi</math>.
The purpose of this task is to demonstrate how to use this approximation in order to compute a large number of decimals of <math>\pi</math>.

=={{header|Ada}}==
<syntaxhighlight lang="ada">
-- Use the Arithmetic-geometric mean to calculate Pi
-- J. Carter 2024 May

with Ada.Numerics.Generic_Elementary_Functions;
with Ada.Text_IO;
with System;

procedure AGM_Pi is
type Real is digits System.Max_Digits;

package Math is new Ada.Numerics.Generic_Elementary_Functions (Float_Type => Real);

A : Real := 1.0;
B : Real := Math.Sqrt (0.5);
T : Real := 0.25;
N : Real := 1.0;
Prev_A : Real;
Pi : Real;
Prev_Pi : Real := 0.0;
begin -- AGM_Pi
Calculate : loop
Prev_A := A;
A := (A + B) / 2.0;
B := Math.Sqrt (Prev_A * B);
T := T - N * (A - Prev_A) ** 2;
N := N + N;
Pi := (A + B) ** 2 / (4.0 * T);
Ada.Text_IO.Put_Line (Item => Pi'Image);

exit Calculate when abs (Prev_Pi - Pi) < 10.0 ** (-(Real'Digits - 1) );

Prev_Pi := Pi;
end loop Calculate;
end AGM_Pi;
</syntaxhighlight>
{{out}}
<pre>
3.14057925052216825E+00
3.14159264621354228E+00
3.14159265358979324E+00
3.14159265358979324E+00
</pre>


=={{header|BASIC}}==
=={{header|BASIC}}==
Retrieved from "https://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi"