use strict;
use bignum;

iter_fib(0);

sub iter_fib {
    my @buffer      = ( 1, 1, 2 );
    my $phi         = 0;
    my $convergence = -1;
    my $iter        = 3;

    while ( !$convergence->is_zero() ) {

        # calculate next fibbonacci number
        $buffer[2] = $buffer[0] + $buffer[1];

        # calculate phi
        ( $phi, $convergence ) = 
        calcPhi( $buffer[0], $buffer[1], $buffer[2] );

        # report
        my $pad = ( $iter < 10 ) ? '0' : '';

        print "Iter: $pad$iter\tPHI=$phi\t".
        "DELTA$convergence\tBuffer:($buffer[0],".
        " $buffer[1],"." $buffer[2])\n";

        ++$iter;

        # shift the buffer
        $buffer[0] = $buffer[1];
        $buffer[1] = $buffer[2];
    }
}

sub calcPhi {
    my $argPrevPrev = shift;
    my $argPrev     = shift;
    my $argCurr     = shift;

    my @ratio = ( $argPrev / $argPrevPrev, 
                  $argCurr / $argPrev );

    my $phi         = $ratio[1];
    my $convergence = $ratio[1] - $ratio[0];

    return ( $phi, $convergence );

}

__END__

=pod

=head1 NAME

  phi.pl - find phi using the fibonacci sequence

=head1 SYNOPSIS

  Iterates through the fibbonacci numbers, 
  keeping a buffer of three numbers.  Then it uses the 
  ratio of the current and previous fibonacci numbers to 
  calculate the golden ratio, a constant named phi.  
  Convergence is also calculated as a difference in 
  ratios.  The program stops when it determines no 
  changes have occurred in successive steps (aka. it has 
  converged on PHI as far as the datatypes will allow).

=head1 QUESTIONS

   What was I thinking when I wrote this ? 

=cut
[download]

Iter: 96    PHI=1.61803398874989484820458683436563811772    DELTA-0.00
+0000000000000000000000000000000000001    Buffer:(19740274219868223167
+, 31940434634990099905, 51680708854858323072)
Iter: 97    PHI=1.61803398874989484820458683436563811772    DELTA0    
+Buffer:(31940434634990099905, 51680708854858323072, 83621143489848422
+977)
[download]