src/core/common/reedsolomon/GenericGFPoly.ts
/*
* 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 com.google.zxing.common.reedsolomon {*/
import AbstractGenericGF from './AbstractGenericGF';
import System from '../../util/System';
import IllegalArgumentException from '../../IllegalArgumentException';
/**
* <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
*/
export default class GenericGFPoly {
private field: AbstractGenericGF;
private coefficients: Int32Array;
/**
* @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
* @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")
*/
public constructor(field: AbstractGenericGF, coefficients: Int32Array) {
if (coefficients.length === 0) {
throw new IllegalArgumentException();
}
this.field = field;
const coefficientsLength = coefficients.length;
if (coefficientsLength > 1 && coefficients[0] === 0) {
// Leading term must be non-zero for anything except the constant polynomial "0"
let firstNonZero = 1;
while (firstNonZero < coefficientsLength && coefficients[firstNonZero] === 0) {
firstNonZero++;
}
if (firstNonZero === coefficientsLength) {
this.coefficients = Int32Array.from([0]);
} else {
this.coefficients = new Int32Array(coefficientsLength - firstNonZero);
System.arraycopy(coefficients,
firstNonZero,
this.coefficients,
0,
this.coefficients.length);
}
} else {
this.coefficients = coefficients;
}
}
public getCoefficients(): Int32Array {
return this.coefficients;
}
/**
* @return degree of this polynomial
*/
public getDegree(): number {
return this.coefficients.length - 1;
}
/**
* @return true iff this polynomial is the monomial "0"
*/
public isZero(): boolean {
return this.coefficients[0] === 0;
}
/**
* @return coefficient of x^degree term in this polynomial
*/
public getCoefficient(degree: number /*int*/): number {
return this.coefficients[this.coefficients.length - 1 - degree];
}
/**
* @return evaluation of this polynomial at a given point
*/
public evaluateAt(a: number /*int*/): number {
if (a === 0) {
// Just return the x^0 coefficient
return this.getCoefficient(0);
}
const coefficients = this.coefficients;
let result: number;
if (a === 1) {
// Just the sum of the coefficients
result = 0;
for (let i = 0, length = coefficients.length; i !== length; i++) {
const coefficient = coefficients[i];
result = AbstractGenericGF.addOrSubtract(result, coefficient);
}
return result;
}
result = coefficients[0];
const size = coefficients.length;
const field = this.field;
for (let i = 1; i < size; i++) {
result = AbstractGenericGF.addOrSubtract(field.multiply(a, result), coefficients[i]);
}
return result;
}
public addOrSubtract(other: GenericGFPoly): GenericGFPoly {
if (!this.field.equals(other.field)) {
throw new IllegalArgumentException('GenericGFPolys do not have same GenericGF field');
}
if (this.isZero()) {
return other;
}
if (other.isZero()) {
return this;
}
let smallerCoefficients = this.coefficients;
let largerCoefficients = other.coefficients;
if (smallerCoefficients.length > largerCoefficients.length) {
const temp = smallerCoefficients;
smallerCoefficients = largerCoefficients;
largerCoefficients = temp;
}
let sumDiff = new Int32Array(largerCoefficients.length);
const 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 (let i = lengthDiff; i < largerCoefficients.length; i++) {
sumDiff[i] = AbstractGenericGF.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return new GenericGFPoly(this.field, sumDiff);
}
public multiply(other: GenericGFPoly): GenericGFPoly {
if (!this.field.equals(other.field)) {
throw new IllegalArgumentException('GenericGFPolys do not have same GenericGF field');
}
if (this.isZero() || other.isZero()) {
return this.field.getZero();
}
const aCoefficients = this.coefficients;
const aLength = aCoefficients.length;
const bCoefficients = other.coefficients;
const bLength = bCoefficients.length;
const product = new Int32Array(aLength + bLength - 1);
const field = this.field;
for (let i = 0; i < aLength; i++) {
const aCoeff = aCoefficients[i];
for (let j = 0; j < bLength; j++) {
product[i + j] = AbstractGenericGF.addOrSubtract(product[i + j],
field.multiply(aCoeff, bCoefficients[j]));
}
}
return new GenericGFPoly(field, product);
}
public multiplyScalar(scalar: number /*int*/): GenericGFPoly {
if (scalar === 0) {
return this.field.getZero();
}
if (scalar === 1) {
return this;
}
const size = this.coefficients.length;
const field = this.field;
const product = new Int32Array(size);
const coefficients = this.coefficients;
for (let i = 0; i < size; i++) {
product[i] = field.multiply(coefficients[i], scalar);
}
return new GenericGFPoly(field, product);
}
public multiplyByMonomial(degree: number /*int*/, coefficient: number /*int*/): GenericGFPoly {
if (degree < 0) {
throw new IllegalArgumentException();
}
if (coefficient === 0) {
return this.field.getZero();
}
const coefficients = this.coefficients;
const size = coefficients.length;
const product = new Int32Array(size + degree);
const field = this.field;
for (let i = 0; i < size; i++) {
product[i] = field.multiply(coefficients[i], coefficient);
}
return new GenericGFPoly(field, product);
}
public divide(other: GenericGFPoly): GenericGFPoly[] {
if (!this.field.equals(other.field)) {
throw new IllegalArgumentException('GenericGFPolys do not have same GenericGF field');
}
if (other.isZero()) {
throw new IllegalArgumentException('Divide by 0');
}
const field = this.field;
let quotient: GenericGFPoly = field.getZero();
let remainder: GenericGFPoly = this;
const denominatorLeadingTerm = other.getCoefficient(other.getDegree());
const inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm);
while (remainder.getDegree() >= other.getDegree() && !remainder.isZero()) {
const degreeDifference = remainder.getDegree() - other.getDegree();
const scale = field.multiply(remainder.getCoefficient(remainder.getDegree()), inverseDenominatorLeadingTerm);
const term = other.multiplyByMonomial(degreeDifference, scale);
const iterationQuotient = field.buildMonomial(degreeDifference, scale);
quotient = quotient.addOrSubtract(iterationQuotient);
remainder = remainder.addOrSubtract(term);
}
return [quotient, remainder];
}
/*@Override*/
public toString(): string {
let result = '';
for (let degree = this.getDegree(); degree >= 0; degree--) {
let coefficient = this.getCoefficient(degree);
if (coefficient !== 0) {
if (coefficient < 0) {
result += ' - ';
coefficient = -coefficient;
} else {
if (result.length > 0) {
result += ' + ';
}
}
if (degree === 0 || coefficient !== 1) {
const 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;
}
}