src/main/java/de/uniks/networkparser/bytes/qr/GenericGFPoly.java
package de.uniks.networkparser.bytes.qr;
/**
* <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
*/
public final class GenericGFPoly {
private GenericGF field;
private int[] coefficients;
public GenericGFPoly() {
}
/**
* @param field the {@link GenericGF} instance representing the field to
* use to perform computations
* @param coefficients coefficients as ints representing elements of GF(size),
* arranged from most significant (highest-power term)
* coefficient to least significant
*/
GenericGFPoly(GenericGF field, int[] coefficients) {
if (coefficients == null || coefficients.length == 0) {
return;
}
this.field = field;
int coefficientsLength = coefficients.length;
if (coefficientsLength > 1 && coefficients[0] == 0) {
/*
* Leading term must be non-zero for anything except the constant polynomial "0"
*/
int firstNonZero = 1;
while (firstNonZero < coefficientsLength && coefficients[firstNonZero] == 0) {
firstNonZero++;
}
if (firstNonZero == coefficientsLength) {
this.coefficients = new int[] { 0 };
} else {
this.coefficients = new int[coefficientsLength - firstNonZero];
System.arraycopy(coefficients, firstNonZero, this.coefficients, 0, this.coefficients.length);
}
} else {
this.coefficients = coefficients;
}
}
int[] getCoefficients() {
return coefficients;
}
/**
* @return degree of this polynomial
*/
int getDegree() {
if (coefficients == null) {
return 0;
}
return coefficients.length - 1;
}
/**
* @return true iff this polynomial is the monomial "0"
*/
boolean isZero() {
return coefficients != null && coefficients[0] == 0;
}
/**
* @return coefficient of x^degree term in this polynomial
*/
int getCoefficient(int degree) {
if (coefficients == null) {
return 0;
}
return coefficients[coefficients.length - 1 - degree];
}
/**
* @return evaluation of this polynomial at a given point
*/
int evaluateAt(int a) {
if (a == 0 || coefficients == null) {
/* Just return the x^0 coefficient */
return getCoefficient(0);
}
int size = coefficients.length;
if (a == 1) {
/* Just the sum of the coefficients */
int result = 0;
for (int coefficient : coefficients) {
result = GenericGF.addOrSubtract(result, coefficient);
}
return result;
}
int result = coefficients[0];
for (int i = 1; i < size; i++) {
result = GenericGF.addOrSubtract(field.multiply(a, result), coefficients[i]);
}
return result;
}
GenericGFPoly addOrSubtract(GenericGFPoly other) {
if (field == null || field.equals(other.field) == false) {
return null;
}
if (isZero()) {
return other;
}
if (other.isZero()) {
return this;
}
int[] smallerCoefficients = this.coefficients;
int[] largerCoefficients = other.coefficients;
if (smallerCoefficients.length > largerCoefficients.length) {
int[] temp = smallerCoefficients;
smallerCoefficients = largerCoefficients;
largerCoefficients = temp;
}
int[] sumDiff = new int[largerCoefficients.length];
int lengthDiff = largerCoefficients.length - smallerCoefficients.length;
/*
* Copy high-order terms only found in higher-degree polynomial's coefficients
*/
System.arraycopy(largerCoefficients, 0, sumDiff, 0, lengthDiff);
for (int i = lengthDiff; i < largerCoefficients.length; i++) {
sumDiff[i] = GenericGF.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return new GenericGFPoly(field, sumDiff);
}
GenericGFPoly multiply(GenericGFPoly other) {
if (field == null || field.equals(other.field) == false) {
return null;
}
if (isZero() || other.isZero()) {
return field.getZero();
}
int[] aCoefficients = this.coefficients;
int aLength = aCoefficients.length;
int[] bCoefficients = other.coefficients;
int bLength = bCoefficients.length;
int[] product = new int[aLength + bLength - 1];
for (int i = 0; i < aLength; i++) {
int aCoeff = aCoefficients[i];
for (int j = 0; j < bLength; j++) {
product[i + j] = GenericGF.addOrSubtract(product[i + j], field.multiply(aCoeff, bCoefficients[j]));
}
}
return new GenericGFPoly(field, product);
}
GenericGFPoly multiply(int scalar) {
if (field == null) {
return this;
}
if (scalar == 0) {
return field.getZero();
}
if (scalar == 1) {
return this;
}
int size = coefficients.length;
int[] product = new int[size];
for (int i = 0; i < size; i++) {
product[i] = field.multiply(coefficients[i], scalar);
}
return new GenericGFPoly(field, product);
}
GenericGFPoly multiplyByMonomial(int degree, int coefficient) {
if (degree < 0 || field == null) {
return null;
}
if (coefficient == 0) {
return field.getZero();
}
int size = coefficients.length;
int[] product = new int[size + degree];
for (int i = 0; i < size; i++) {
product[i] = field.multiply(coefficients[i], coefficient);
}
return new GenericGFPoly(field, product);
}
GenericGFPoly[] divide(GenericGFPoly other) {
if (field == null || field.equals(other.field) == false) {
return null;
}
if (other.isZero()) {
return null;
}
GenericGFPoly quotient = field.getZero();
GenericGFPoly remainder = this;
int denominatorLeadingTerm = other.getCoefficient(other.getDegree());
int inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm);
while (remainder.getDegree() >= other.getDegree() && !remainder.isZero()) {
int degreeDifference = remainder.getDegree() - other.getDegree();
int scale = field.multiply(remainder.getCoefficient(remainder.getDegree()), inverseDenominatorLeadingTerm);
GenericGFPoly term = other.multiplyByMonomial(degreeDifference, scale);
GenericGFPoly iterationQuotient = field.buildMonomial(degreeDifference, scale);
quotient = quotient.addOrSubtract(iterationQuotient);
remainder = remainder.addOrSubtract(term);
}
return new GenericGFPoly[] { quotient, remainder };
}
@Override
public String toString() {
StringBuilder result = new StringBuilder(8 * getDegree());
for (int degree = getDegree(); degree >= 0; degree--) {
int coefficient = getCoefficient(degree);
if (coefficient != 0) {
if (coefficient < 0) {
result.append(" - ");
coefficient = -coefficient;
} else {
if (result.length() > 0) {
result.append(" + ");
}
}
if (degree == 0 || coefficient != 1) {
int alphaPower = field.log(coefficient);
if (alphaPower == 0) {
result.append('1');
} else if (alphaPower == 1) {
result.append('a');
} else {
result.append("a^");
result.append(alphaPower);
}
}
if (degree != 0) {
if (degree == 1) {
result.append('x');
} else {
result.append("x^");
result.append(degree);
}
}
}
}
return result.toString();
}
}