com.itextpdf.barcodes.qrcode.GF256Poly Maven / Gradle / Ivy
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* Much credit is due to William Rucklidge since portions of this code are an indirect
* port of his C++ Reed-Solomon implementation.
*
* @author Sean Owen
*/
final class GF256Poly {
private final GF256 field;
private final int[] coefficients;
/**
* @param field the {@link GF256} instance representing the field to use
* to perform computations
* @param coefficients coefficients as ints representing elements of GF(256), 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")
*/
GF256Poly(GF256 field, int[] coefficients) {
if (coefficients == null || coefficients.length == 0) {
throw new IllegalArgumentException();
}
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 = field.getZero().coefficients;
} 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() {
return coefficients.length - 1;
}
/**
* @return true iff this polynomial is the monomial "0"
*/
boolean isZero() {
return coefficients[0] == 0;
}
/**
* @return coefficient of x^degree term in this polynomial
*/
int getCoefficient(int degree) {
return coefficients[coefficients.length - 1 - degree];
}
/**
* @return evaluation of this polynomial at a given point
*/
int evaluateAt(int a) {
if (a == 0) {
// 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 i = 0; i < size; i++) {
result = GF256.addOrSubtract(result, coefficients[i]);
}
return result;
}
int result = coefficients[0];
for (int i = 1; i < size; i++) {
result = GF256.addOrSubtract(field.multiply(a, result), coefficients[i]);
}
return result;
}
/**
* GF addition or subtraction (they are identical for a GF(2^n)
* @param other the other GF-poly
* @return new GF256Poly obtained by summing this GF and other
*/
GF256Poly addOrSubtract(GF256Poly other) {
if (!field.equals(other.field)) {
throw new IllegalArgumentException("GF256Polys do not have same GF256 field");
}
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] = GF256.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return new GF256Poly(field, sumDiff);
}
/**
* GF multiplication
* @param other the other GF-poly
* @return new GF-poly obtained by multiplying this with other
*/
GF256Poly multiply(GF256Poly other) {
if (!field.equals(other.field)) {
throw new IllegalArgumentException("GF256Polys do not have same GF256 field");
}
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] = GF256.addOrSubtract(product[i + j],
field.multiply(aCoeff, bCoefficients[j]));
}
}
return new GF256Poly(field, product);
}
/**
* GF scalar multiplication
* @param scalar scalar
* @return new GF-poly obtained by multiplying every element of this with the scalar.
*/
GF256Poly multiply(int scalar) {
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 GF256Poly(field, product);
}
GF256Poly multiplyByMonomial(int degree, int coefficient) {
if (degree < 0) {
throw new IllegalArgumentException();
}
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 GF256Poly(field, product);
}
GF256Poly[] divide(GF256Poly other) {
if (!field.equals(other.field)) {
throw new IllegalArgumentException("GF256Polys do not have same GF256 field");
}
if (other.isZero()) {
throw new IllegalArgumentException("Divide by 0");
}
GF256Poly quotient = field.getZero();
GF256Poly 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);
GF256Poly term = other.multiplyByMonomial(degreeDifference, scale);
GF256Poly iterationQuotient = field.buildMonomial(degreeDifference, scale);
quotient = quotient.addOrSubtract(iterationQuotient);
remainder = remainder.addOrSubtract(term);
}
return new GF256Poly[] { quotient, remainder };
}
/**
* @return String representation of the Galois Field polynomial.
*/
public String toString() {
StringBuffer result = new StringBuffer(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();
}
}