/**
* Performs Karatsuba "squaring" on two BigIntegers
*
* See {@link http://en.wikipedia.org/wiki/Karatsuba_algorithm Karatsuba algorithm} and
* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=151 MPM 5.3.4}.
*
* @param Math_BigInteger $y
* @return Math_BigInteger
* @access private
*/
function _karatsubaSquare()
{
$m = count($this->value) >> 1;
if ($m < MATH_BIGINTEGER_KARATSUBA_CUTOFF) {
return $this->_square();
}
$x1 = new Math_BigInteger();
$x0 = new Math_BigInteger();
$x1->value = array_slice($this->value, $m);
$x0->value = array_slice($this->value, 0, $m);
$z2 = $x1->_karatsubaSquare();
$z0 = $x0->_karatsubaSquare();
$z1 = $x1->add($x0);
$z1 = $z1->_karatsubaSquare();
$z1 = $z1->subtract($z2->add($z0));
$z2->value = array_merge(array_fill(0, 2 * $m, 0), $z2->value);
$z1->value = array_merge(array_fill(0, $m, 0), $z1->value);
$xx = $z2->add($z1);
$xx = $xx->add($z0);
return $xx;
}
