$field
$field :
<p>Represents a polynomial whose coefficients are elements of a GF.
Instances of this class are immutable.
Much credit is due to William Rucklidge since portions of this code are an indirect port of his C++ Reed-Solomon implementation.
<?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>Represents a polynomial whose coefficients are elements of a GF.
* Instances of this class are immutable.</p>
*
* <p>Much credit is due to William Rucklidge since portions of this code are an indirect
* port of his C++ Reed-Solomon implementation.</p>
*
* @author Sean Owen
*/
final class GenericGFPoly {
private $field;
private $coefficients;
/**
* @param field the {@link GenericGF} instance representing the field to use
* to perform computations
* @param coefficients array coefficients as ints representing elements of GF(size), arranged
* from most significant (highest-power term) coefficient to least significant
* @throws IllegalArgumentException if argument is null or empty,
* or if leading coefficient is 0 and this is not a
* constant polynomial (that is, it is not the monomial "0")
*/
function __construct($field, $coefficients) {
if (count($coefficients) == 0) {
throw new \InvalidArgumentException();
}
$this->field = $field;
$coefficientsLength = count($coefficients);
if ($coefficientsLength > 1 && $coefficients[0] == 0) {
// Leading term must be non-zero for anything except the constant polynomial "0"
$firstNonZero = 1;
while ($firstNonZero < $coefficientsLength && $coefficients[$firstNonZero] == 0) {
$firstNonZero++;
}
if ($firstNonZero == $coefficientsLength) {
$this->coefficients = array(0);
} else {
$this->coefficients = fill_array(0,$coefficientsLength - $firstNonZero,0);
$this->coefficients = arraycopy($coefficients,
$firstNonZero,
$this->coefficients,
0,
count($this->coefficients));
}
} else {
$this->coefficients = $coefficients;
}
}
function getCoefficients() {
return $this->coefficients;
}
/**
* @return degree of this polynomial
*/
function getDegree() {
return count($this->coefficients) - 1;
}
/**
* @return true iff this polynomial is the monomial "0"
*/
function isZero() {
return $this->coefficients[0] == 0;
}
/**
* @return coefficient of x^degree term in this polynomial
*/
function getCoefficient($degree) {
return $this->coefficients[count($this->coefficients) - 1 - $degree];
}
/**
* @return evaluation of this polynomial at a given point
*/
function evaluateAt($a) {
if ($a == 0) {
// Just return the x^0 coefficient
return $this->getCoefficient(0);
}
$size = count($this->coefficients);
if ($a == 1) {
// Just the sum of the coefficients
$result = 0;
foreach ($this->coefficients as $coefficient ) {
$result = GenericGF::addOrSubtract($result, $coefficient);
}
return $result;
}
$result = $this->coefficients[0];
for ($i = 1; $i < $size; $i++) {
$result = GenericGF::addOrSubtract($this->field->multiply($a, $result), $this->coefficients[$i]);
}
return $result;
}
function addOrSubtract($other) {
if ($this->field !== $other->field) {
throw new \InvalidArgumentException("GenericGFPolys do not have same GenericGF field");
}
if ($this->isZero()) {
return $other;
}
if ($other->isZero()) {
return $this;
}
$smallerCoefficients = $this->coefficients;
$largerCoefficients = $other->coefficients;
if (count($smallerCoefficients) > count($largerCoefficients)) {
$temp = $smallerCoefficients;
$smallerCoefficients = $largerCoefficients;
$largerCoefficients = $temp;
}
$sumDiff = fill_array(0,count($largerCoefficients),0);
$lengthDiff = count($largerCoefficients) - count($smallerCoefficients);
// Copy high-order terms only found in higher-degree polynomial's coefficients
$sumDiff = arraycopy($largerCoefficients, 0, $sumDiff, 0, $lengthDiff);
for ($i = $lengthDiff; $i < count($largerCoefficients); $i++) {
$sumDiff[$i] = GenericGF::addOrSubtract($smallerCoefficients[$i - $lengthDiff], $largerCoefficients[$i]);
}
return new GenericGFPoly($this->field, $sumDiff);
}
function multiply($other) {
if(is_int($other)){
return $this->multiply_($other);
}
if ($this->field !== $other->field) {
throw new \InvalidArgumentException("GenericGFPolys do not have same GenericGF field");
}
if ($this->isZero() || $other->isZero()) {
return $this->field->getZero();
}
$aCoefficients = $this->coefficients;
$aLength = count($aCoefficients);
$bCoefficients = $other->coefficients;
$bLength = count($bCoefficients);
$product = fill_array(0,$aLength + $bLength - 1,0);
for ($i = 0; $i < $aLength; $i++) {
$aCoeff = $aCoefficients[$i];
for ($j = 0; $j < $bLength; $j++) {
$product[$i + $j] = GenericGF::addOrSubtract($product[$i + $j],
$this->field->multiply($aCoeff, $bCoefficients[$j]));
}
}
return new GenericGFPoly($this->field, $product);
}
function multiply_($scalar) {
if ($scalar == 0) {
return $this->field->getZero();
}
if ($scalar == 1) {
return $this;
}
$size = count($this->coefficients);
$product = fill_array(0,$size,0);
for ($i = 0; $i < $size; $i++) {
$product[$i] = $this->field->multiply($this->coefficients[$i], $scalar);
}
return new GenericGFPoly($this->field, $product);
}
function multiplyByMonomial($degree, $coefficient) {
if ($degree < 0) {
throw new \InvalidArgumentException();
}
if ($coefficient == 0) {
return $this->field->getZero();
}
$size = count($this->coefficients);
$product = fill_array(0,$size + $degree,0);
for ($i = 0; $i < $size; $i++) {
$product[$i] = $this->field->multiply($this->coefficients[$i], $coefficient);
}
return new GenericGFPoly($this->field, $product);
}
function divide($other) {
if ($this->field !==$other->field) {
throw new \InvalidArgumentException("GenericGFPolys do not have same GenericGF field");
}
if ($other->isZero()) {
throw new \InvalidArgumentException("Divide by 0");
}
$quotient = $this->field->getZero();
$remainder = $this;
$denominatorLeadingTerm = $other->getCoefficient($other->getDegree());
$inverseDenominatorLeadingTerm = $this->field->inverse($denominatorLeadingTerm);
while ($remainder->getDegree() >= $other->getDegree() && !$remainder->isZero()) {
$degreeDifference = $remainder->getDegree() - $other->getDegree();
$scale = $this->field->multiply($remainder->getCoefficient($remainder->getDegree()), $inverseDenominatorLeadingTerm);
$term = $other->multiplyByMonomial($degreeDifference, $scale);
$iterationQuotient = $this->field->buildMonomial($degreeDifference, $scale);
$quotient = $quotient->addOrSubtract($iterationQuotient);
$remainder = $remainder->addOrSubtract($term);
}
return array($quotient, $remainder );
}
//@Override
public function toString() {
$result = '';
for ($degree = $this->getDegree(); $degree >= 0; $degree--) {
$coefficient = $this->getCoefficient($degree);
if ($coefficient != 0) {
if ($coefficient < 0) {
$result.=" - ";
$coefficient = -$coefficient;
} else {
if (strlen($result) > 0) {
$result .= " + ";
}
}
if ($degree == 0 || $coefficient != 1) {
$alphaPower = $this->field->log($coefficient);
if ($alphaPower == 0) {
$result.='1';
} else if ($alphaPower == 1) {
$result.='a';
} else {
$result.="a^";
$result.=($alphaPower);
}
}
if ($degree != 0) {
if ($degree == 1) {
$result.='x';
} else {
$result.="x^";
$result.= $degree;
}
}
}
}
return $result;
}
}