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	return __PACKAGE__->make(@_);
}

#
# cplxe
#
# Creates a complex number from a (rho, theta) tuple.
# This avoids the burden of writing Math::Complex->emake(rho, theta).
#
sub cplxe {
	return __PACKAGE__->emake(@_);
}

#
# pi
#
# The number defined as pi = 180 degrees
#
sub pi () { 4 * CORE::atan2(1, 1) }

#
# pi2
#
# The full circle
#
sub pi2 () { 2 * pi }

#
# pi4
#
# The full circle twice.
#
sub pi4 () { 4 * pi }

#
# pip2
#
# The quarter circle
#
sub pip2 () { pi / 2 }

#
# pip4
#
# The eighth circle.
#
sub pip4 () { pi / 4 }

#
# _uplog10
#
# Used in log10().
#
sub _uplog10 () { 1 / CORE::log(10) }

#
# i
#
# The number defined as i*i = -1;
#
sub i () {
        return $i if ($i);
	$i = bless {};
	$i->{'cartesian'} = [0, 1];
	$i->{'polar'}     = [1, pip2];
	$i->{c_dirty} = 0;
	$i->{p_dirty} = 0;
	return $i;
}

#
# _ip2
#
# Half of i.
#
sub _ip2 () { i / 2 }

#
# Attribute access/set routines
#

sub _cartesian {$_[0]->{c_dirty} ?
		   $_[0]->_update_cartesian : $_[0]->{'cartesian'}}
sub _polar     {$_[0]->{p_dirty} ?
		   $_[0]->_update_polar : $_[0]->{'polar'}}

sub _set_cartesian { $_[0]->{p_dirty}++; $_[0]->{c_dirty} = 0;
		     $_[0]->{'cartesian'} = $_[1] }
sub _set_polar     { $_[0]->{c_dirty}++; $_[0]->{p_dirty} = 0;
		     $_[0]->{'polar'} = $_[1] }

#
# ->_update_cartesian
#
# Recompute and return the cartesian form, given accurate polar form.
#
sub _update_cartesian {
	my $self = shift;
	my ($r, $t) = @{$self->{'polar'}};
	$self->{c_dirty} = 0;
	return $self->{'cartesian'} = [$r * CORE::cos($t), $r * CORE::sin($t)];
}

#
#
# ->_update_polar
#
# Recompute and return the polar form, given accurate cartesian form.
#
sub _update_polar {
	my $self = shift;
	my ($x, $y) = @{$self->{'cartesian'}};
	$self->{p_dirty} = 0;
	return $self->{'polar'} = [0, 0] if $x == 0 && $y == 0;
	return $self->{'polar'} = [CORE::sqrt($x*$x + $y*$y),
				   CORE::atan2($y, $x)];
}

#
# (_plus)
#