How to Calculate pi

You can use the following series to calculate pi:

4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ...

I decided to try this out using PL/SQL. The example I created is shown below. It works OK but the series converges very slowly so you have to work out several million terms just to get pi accurate to 6 decimal places:

SQL> set timing on
SQL> declare
  2  pi          number  := 0;
  3  numerator   number  := 4;
  4  denominator number  := 1;
  5  dp          number  := 0;
  6  pi1         number;
  7  pi2         number;
  8  counter     number  := 0;
  9  finished    boolean := false;
 10  begin
 11  while not finished
 12  loop
 13   pi          := pi + (numerator / denominator);
 14   pi1         := round (pi,dp);
 15   denominator := denominator + 2;
 16   pi          := pi - (numerator / denominator);
 17   pi2         := round (pi,dp);
 18   denominator := denominator + 2;
 19   counter     := counter + 1;
 20   if pi1 = pi2 then
 21    dbms_output.put_line ('Counter = '||counter);
 22    if dp = 1 then
 23     dbms_output.put_line
 24     ('Accurate to 1 decimal place:');
 25    else
 26     dbms_output.put_line
 27     ('Accurate to '||dp||' decimal places:');
 28    end if;
 29    dbms_output.put_line ('Pi = '||pi1);
 30    dbms_output.put_line ('**********');
 31    dp := dp + 1;
 32    if dp > 6 then
 33     finished := true;
 34    end if;
 35   end if;
 36  end loop;
 37  end;
 38  /
Counter = 2
Accurate to 0 decimal places:
Pi = 3
**********
Counter = 60
Accurate to 1 decimal place:
Pi = 3.1
**********
Counter = 148
Accurate to 2 decimal places:
Pi = 3.14
**********
Counter = 5397
Accurate to 3 decimal places:
Pi = 3.142
**********
Counter = 11723
Accurate to 4 decimal places:
Pi = 3.1416
**********
Counter = 213092
Accurate to 5 decimal places:
Pi = 3.14159
**********
Counter = 3255425
Accurate to 6 decimal places:
Pi = 3.141593
**********

PL/SQL procedure successfully completed.

Elapsed: 00:00:34.53
SQL>