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<?php
/*
* Copyright 2007 ZXing authors
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
namespace Zxing\Common\Reedsolomon;
/**
* <p>This class contains utility methods for performing mathematical operations over
* the Galois Fields. Operations use a given primitive polynomial in calculations.</p>
*
* <p>Throughout this package, elements of the GF are represented as an {@code int}
* for convenience and speed (but at the cost of memory).
* </p>
*
* @author Sean Owen
* @author David Olivier
*/
final class GenericGF
{
public static $AZTEC_DATA_12;
public static $AZTEC_DATA_10;
public static $AZTEC_DATA_6;
public static $AZTEC_PARAM;
public static $QR_CODE_FIELD_256;
public static $DATA_MATRIX_FIELD_256;
public static $AZTEC_DATA_8;
public static $MAXICODE_FIELD_64;
private $expTable;
private $logTable;
private $zero;
private $one;
private $size;
private $primitive;
private $generatorBase;
/**
* Create a representation of GF(size) using the given primitive polynomial.
*
* @param primitive irreducible polynomial whose coefficients are represented by
* the bits of an int, where the least-significant bit represents the constant
* coefficient
* @param size the size of the field
* @param b the factor b in the generator polynomial can be 0- or 1-based
* (g(x) = (x+a^b)(x+a^(b+1))...(x+a^(b+2t-1))).
* In most cases it should be 1, but for QR code it is 0.
*/
public function __construct($primitive, $size, $b)
{
$this->primitive = $primitive;
$this->size = $size;
$this->generatorBase = $b;
$this->expTable = [];
$this->logTable = [];
$x = 1;
for ($i = 0; $i < $size; $i++) {
$this->expTable[$i] = $x;
$x *= 2; // we're assuming the generator alpha is 2
if ($x >= $size) {
$x ^= $primitive;
$x &= $size - 1;
}
}
for ($i = 0; $i < $size - 1; $i++) {
$this->logTable[$this->expTable[$i]] = $i;
}
// logTable[0] == 0 but this should never be used
$this->zero = new GenericGFPoly($this, [0]);
$this->one = new GenericGFPoly($this, [1]);
}
public static function Init()
{
self::$AZTEC_DATA_12 = new GenericGF(0x1069, 4096, 1); // x^12 + x^6 + x^5 + x^3 + 1
self::$AZTEC_DATA_10 = new GenericGF(0x409, 1024, 1); // x^10 + x^3 + 1
self::$AZTEC_DATA_6 = new GenericGF(0x43, 64, 1); // x^6 + x + 1
self::$AZTEC_PARAM = new GenericGF(0x13, 16, 1); // x^4 + x + 1
self::$QR_CODE_FIELD_256 = new GenericGF(0x011D, 256, 0); // x^8 + x^4 + x^3 + x^2 + 1
self::$DATA_MATRIX_FIELD_256 = new GenericGF(0x012D, 256, 1); // x^8 + x^5 + x^3 + x^2 + 1
self::$AZTEC_DATA_8 = self::$DATA_MATRIX_FIELD_256;
self::$MAXICODE_FIELD_64 = self::$AZTEC_DATA_6;
}
/**
* Implements both addition and subtraction -- they are the same in GF(size).
*
* @return sum/difference of a and b
*/
public static function addOrSubtract($a, $b)
{
return $a ^ $b;
}
public function getZero()
{
return $this->zero;
}
public function getOne()
{
return $this->one;
}
/**
* @return the monomial representing coefficient * x^degree
*/
public function buildMonomial($degree, $coefficient)
{
if ($degree < 0) {
throw new \InvalidArgumentException();
}
if ($coefficient == 0) {
return $this->zero;
}
$coefficients = fill_array(0, $degree + 1, 0);//new int[degree + 1];
$coefficients[0] = $coefficient;
return new GenericGFPoly($this, $coefficients);
}
/**
* @return 2 to the power of a in GF(size)
*/
public function exp($a)
{
return $this->expTable[$a];
}
/**
* @return base 2 log of a in GF(size)
*/
public function log($a)
{
if ($a == 0) {
throw new \InvalidArgumentException();
}
return $this->logTable[$a];
}
/**
* @return multiplicative inverse of a
*/
public function inverse($a)
{
if ($a == 0) {
throw new \Exception();
}
return $this->expTable[$this->size - $this->logTable[$a] - 1];
}
/**
* @return int product of a and b in GF(size)
*/
public function multiply($a, $b)
{
if ($a == 0 || $b == 0) {
return 0;
}
return $this->expTable[($this->logTable[$a] + $this->logTable[$b]) % ($this->size - 1)];
}
public function getSize()
{
return $this->size;
}
public function getGeneratorBase()
{
return $this->generatorBase;
}
// @Override
public function toString()
{
return "GF(0x" . dechex((int)($this->primitive)) . ',' . $this->size . ')';
}
}
GenericGF::Init();
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