
(********************************************************************)
(*                                                                  *)
(*  printpi1.sd7  PI with 1000 digits using John Machin's formula   *)
(*  Copyright (C) 2006  Thomas Mertes                               *)
(*                                                                  *)
(*  This program is free software; you can redistribute it and/or   *)
(*  modify it under the terms of the GNU General Public License as  *)
(*  published by the Free Software Foundation; either version 2 of  *)
(*  the License, or (at your option) any later version.             *)
(*                                                                  *)
(*  This program is distributed in the hope that it will be useful, *)
(*  but WITHOUT ANY WARRANTY; without even the implied warranty of  *)
(*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the   *)
(*  GNU General Public License for more details.                    *)
(*                                                                  *)
(*  You should have received a copy of the GNU General Public       *)
(*  License along with this program; if not, write to the           *)
(*  Free Software Foundation, Inc., 51 Franklin Street,             *)
(*  Fifth Floor, Boston, MA  02110-1301, USA.                       *)
(*                                                                  *)
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$ include "seed7_05.s7i";
  include "stdio.s7i";
  include "bigint.s7i";
  include "bigrat.s7i";

# John Machin's formula from 1706:
# PI = 16 * arctan(1 / 5) - 4 * arctan(1 / 239)

# Taylor series for arctan:
# arctan(x) = sum_n_from_0_to_inf((-1) ** n / succ(2 * n) * x ** succ(2 * n))

# Taylor series of John Machin's formula:
# PI = sum_n_from_0_to_inf(16 * (-1) ** n / (succ(2 * n) *   5 ** succ(2 * n)) -
#                           4 * (-1) ** n / (succ(2 * n) * 239 ** succ(2 * n)))

const func bigRational: compute_pi_machin is func
  result
    var bigRational: sum is 0_ / 1_;
  local
    var integer: n is 0;
  begin
    for n range 0 to 713 do
      sum +:= 16_ * (-1_) ** n / (bigInteger conv succ(2 * n) *   5_ ** succ(2 * n)) -
               4_ * (-1_) ** n / (bigInteger conv succ(2 * n) * 239_ ** succ(2 * n));
    end for;
  end func;

const proc: main is func
  begin
    writeln(compute_pi_machin digits 1000);
  end func;
