#!perl
use warnings; use strict; use 5.010;
use Math::BigFloat try => "GMP";

my $digits = int($ARGV[0] // 0) || 60;

{
	say "Newton iteration, using Taylor series of sine and cosine.";
	my $b = Math::BigFloat->new(0, undef, -$digits);
	my $x = $b + 0.5;
	my %x;
	while (!$x{$x}++) {
		my $m = 1;
		my $s = 0;
		my $c = 1;
		my $k = 0;
		while (0 != $m) {
			$s += $m = $m * $x / ++$k;
			$c += $m = -$m * $x / ++$k;
		}
		$x += (0.5 - $s) / $c;
	}
	say "pi = ", 6*$x, ";";
}

{ 
	say "Using Taylor series of arctangent.";
	my $b = Math::BigFloat->new(0, undef, -$digits);
	my $x = 2 - sqrt($b + 3);
	my $f = -$x * $x;
	my $m = $x * ($b + 12);
	my $a = $m;
	my $k = 1;
	while (0 != $m) {
		$m *= $f;
		$k += 2;
		$a += $m / $k;
	}
	say "pi = ", $a, ";";
}

__END__