#!/usr/bin/env perl

use strict;
use warnings;

use Math::BigRat;
use Math::Trig;

my $x = abs(Math::BigRat->new(-1/3));

print "$x\n";

for my $s(0..6) {
  my $pi = ratFromFloatSteps($s, pi);

  print "$s -> $pi\n";
}

my $pi = ratFromFloatEpsilon(0.000001, pi);
print "  $pi\n";

sub ratFromFloatEpsilon {
  my ($epsilon, $inp) = @_;
  my $steps = 0;
  my $old = ratFromFloatSteps($steps, $inp);
  for(;;) {
    $steps++;
    my $n = ratFromFloatSteps($steps, $inp);
    if(abs($old-$n) < $epsilon) {
      return $n
    } else {
      $old = $n
    }
  }
}

sub ratFromFloatSteps {
  my ($steps, $inp) = @_;
  #print "  [[ $steps $inp ]]\n";
  if($inp < 0) { return ratFromFloatSteps($steps, -$inp) }
  if(0 == $inp) { return Math::BigRat->new(0) }
  if($steps <= 0) {
    return Math::BigRat->new(int $inp);
  }
  my $prop = int $inp;
  my $rem = $inp - $prop;
  $prop = Math::BigRat->new($prop);
  $rem = 1/ratFromFloatSteps($steps-1, 1/$rem);
  return $prop + $rem;
}