BigInteger 1.0

BigInteger is an arbitrary length integer extension module for Perl.

SYNOPSIS

use Math::BigInteger;

The BigInteger extension module gives access to Eric Youngs 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.

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);

Creation/Destruction routines.

new
my $bi = new BigInteger; # Create a new BigInteger object.
clone
my $b = $a->clone();

Create a new BigInteger object from another BigInteger object.

copy
copy($a, $b);

Copy one BigInteger object to another.

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

Save a BigInteger object as a MSB-first string.

restore
my $bi = restore BigInteger $data;

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

Comparison functions

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 unsigned comparison.

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 signed comparison.

Arithmetic Functions

inc $bi->inc();

Increment $bi by one:

dec $bi->dec();

Decrement $bi by one:

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

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

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.

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 undef, in which case that value is not returned.

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

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

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

Shift $a left by $n bits.

lshift1
$r->lshift1($a);

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

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

Shift $a right by $n bits.

rshift1
$r->rshift1($a);

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

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

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

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

This function is used to perform an efficient mod_mul operation. If one is going to repeatedly perform 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 reciprocal. This function is used in mod_exp.

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

Multiply $a by $b and return the remainder into $r when divided by $m.
reciprical
$r->reciprical($m);

Return the reciprocal of $m into $r.

Miscellaneous Routines

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

Return the size (in bits) of the BigInteger.

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

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

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.