use warnings; use strict; use 5.012;
use Scalar::Util; use Math::BigInt;

sub _make {
	my($o, @v) = @_;
	bless \@v, Scalar::Util::blessed($o) || $o;
}

sub zero {
	my($o) = @_;
	$o->_make();
}

sub one {
	my($o) = @_;
	$o->_make(1);
}

sub _comps {
	my($o, $b) = @_;
	my @v = @$o;
	my($u, $v) = (0, @v < 44 ? 1 : Math::BigInt->bone);
	for my $d (@v) {
		$v = $v + $u;
		$u = $v - $u;
		if ($d) {
			&$b($v);
		}
	}
}

sub str { # return the string representation showing terms
	my($o) = @_;
	my @r;
	$o->_comps(sub { push @r, $_[0] });
	@r ? "(" . join(" + ", @r) . ")" : "0";
}

sub val { # return the value as a perl number
	my($o) = @_;
	my $r = 0;
	$o->_comps(sub { $r += $_[0]; });
	$r;
}