/*
* Copyright 2012 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.
*/
package com.google.zxing.pdf417.decoder.ec;
/**
* @author Sean Owen
* @see com.google.zxing.common.reedsolomon.GenericGFPoly
*/
final class ModulusPoly {
private final ModulusGF field;
private final int[] coefficients;
ModulusPoly(ModulusGF field, int[] coefficients) {
if (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 coefficient : coefficients) {
result = field.add(result, coefficient);
}
return result;
}
int result = coefficients[0];
for (int i = 1; i < size; i++) {
result = field.add(field.multiply(a, result), coefficients[i]);
}
return result;
}
ModulusPoly add(ModulusPoly other) {
if (!field.equals(other.field)) {
throw new IllegalArgumentException("ModulusPolys do not have same ModulusGF 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] = field.add(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return new ModulusPoly(field, sumDiff);
}
ModulusPoly subtract(ModulusPoly other) {
if (!field.equals(other.field)) {
throw new IllegalArgumentException("ModulusPolys do not have same ModulusGF field");
}
if (other.isZero()) {
return this;
}
return add(other.negative());
}
ModulusPoly multiply(ModulusPoly other) {
if (!field.equals(other.field)) {
throw new IllegalArgumentException("ModulusPolys do not have same ModulusGF 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] = field.add(product[i + j], field.multiply(aCoeff, bCoefficients[j]));
}
}
return new ModulusPoly(field, product);
}
ModulusPoly negative() {
int size = coefficients.length;
int[] negativeCoefficients = new int[size];
for (int i = 0; i < size; i++) {
negativeCoefficients[i] = field.subtract(0, coefficients[i]);
}
return new ModulusPoly(field, negativeCoefficients);
}
ModulusPoly 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 ModulusPoly(field, product);
}
ModulusPoly 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 ModulusPoly(field, product);
}
ModulusPoly[] divide(ModulusPoly other) {
if (!field.equals(other.field)) {
throw new IllegalArgumentException("ModulusPolys do not have same ModulusGF field");
}
if (other.isZero()) {
throw new IllegalArgumentException("Divide by 0");
}
ModulusPoly quotient = field.getZero();
ModulusPoly 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);
ModulusPoly term = other.multiplyByMonomial(degreeDifference, scale);
ModulusPoly iterationQuotient = field.buildMonomial(degreeDifference, scale);
quotient = quotient.add(iterationQuotient);
remainder = remainder.subtract(term);
}
return new ModulusPoly[] { 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) {
result.append(coefficient);
}
if (degree != 0) {
if (degree == 1) {
result.append('x');
} else {
result.append("x^");
result.append(degree);
}
}
}
}
return result.toString();
}
}