=head1 NAME

BigInteger - Arbitrary length integer extension module for Perl

=head1 SYNOPSIS

 use Math::BigInteger;

=head1 DESCRIPTION

The BigInteger extension module gives access to Eric Young's bignum library.
This provides a faster alternative to the Math::BigInt library.

The basic object in this library is a BigInteger.
It is used to hold a single large integer.

It is not intended that this package be used directly,
but instead be used by a wrapper package, such as the Math::BigInteger class.

=head1 FUNCTIONS

Many of the following functions can be used in two styles,
by calling the function on an object, or by calling
the function explicitly; for example, here are two ways
of assigning to $a the sum of $b and $c:

	$a->add($b, $c);
or

	BigInteger::add($a, $b, $c);


=head2 Creation/Destruction routines.

=over 4

=item new

	my $bi = new BigInteger;	# Create a new BigInteger object.

=item clone

	my $b = $a->clone();

Create a new BigInteger object from another BigInteger object.

=item copy

	copy($a, $b);

Copy one BigInteger object to another.

=item save

	my $data = $bi->save();

Save a BigInteger object as a MSB-first string.

=item restore

	my $bi = restore BigInteger $data;

Create a new BigInteger object from a MSB-first string.

=back


=head2 Comparison functions

=over 4

=item ucmp

	ucmp($a, $b);

Return -1 if $a is less than $b, 0 if $a and $b are the same
and 1 is $a is greater than $b.  This is an I<unsigned> comparison.

=item cmp

	cmp($a, $b);

Return -1 if $a is less than $b, 0 if $a and $b are the same
and 1 is $a is greater than $b.  This is a I<signed> comparison.

=back


=head2 Arithmetic Functions

=over 4

=item inc
	$bi->inc();

Increment $bi by one:

=item dec
	$bi->dec();

Decrement $bi by one:

=item add

	$r->add($a, $b);

Add $a and $b and return the result in $r.

=item mul

	$r->mul($a, $b);

Multiply $a by $b and return the result in $r.
Note that $r must not be the same object as $a or $b.

=item div

	div($dv, $rem, $m, $d);

Divide $m by $d and return the result in $dv and the remainder
in $rem.  Either of $dv or $rem can be C<undef>, in which case
that value is not returned.

=item mod

	$rem->mod($m, $d);

Find the remainder of $m divided by $d and return it in $rem.
This function is more efficient than C<div>.


=item lshift

	$r->lshift($a, $n);

Shift $a left by $n bits.

=item lshift1

	$r->lshift1($a);

Shift $a left by 1 bit.  This form is more efficient than C<lshift($r, $a, 1)>.

=item rshift

	$r->rshift($a, $n);

Shift $a right by $n bits.

=item rshift1

	$r->rshift1($a);

Shift $a right by 1 bit.  This form is more efficient than C<rshift($r, $a, 1)>.

=item mod_exp

	$r->mod_exp($a, $p, $mod);

Raise $a to the $p power and return the remainder into $r when divided by $m.

=item modmul_recip

	modmul_recip($r, $x, $y, $m, $i, $nb);

This function is used to perform an efficient C<mod_mul> operation.
If one is going to repeatedly perform C<mod_mul> with the same modulus
is worth calculating the reciprocal of the modulus and then using this
function.  This operation uses the fact that a/b == a*r where r is the
reciprocal of b.  On modern computers multiplication is very fast and
big number division is very slow.  $x is multiplied by $y and then
divided by $m and the remainder is returned in $r.  $i is the reciprocal
of $m and $nb is the number of bits as returned from C<reciprocal>.
This function is used in C<mod_exp>.

=item mul_mod

	$r->mul_mod($a, $b, $m);

Multiply $a by $b and return the remainder into $r when divided by $m.

=item reciprical

	$r->reciprical($m);

Return the reciprocal of $m into $r.

=back

=head2 Miscellaneous Routines

=over 4

=item num_bits

	my $size = $bi->numbits();

Return the size (in bits) of the BigInteger.

=item gcd

	$r->gcd($a, $b);

$r has the greatest common divisor of $a and $b.

=item inverse_modn

	$r->inverse_modn($a, $n);

This function creates a new BigInteger and returns it in $r.  This number
is the inverse mod $n of $a.  By this it is meant that the returned value
$r satisfies (a*r)%n == 1.  This function is used in the generation of RSA keys.

=back

=head1 BUGS

Negative numbers cannot be saved or restored.
To fix this requires modification of Eric Young's library.

The documentation.

=head1 COPYRIGHT

Systemics Ltd ( http://www.systemics.com/ ).

Portions copyright Eric Young (eay@mincom.oz.au).
