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/*
Ported to JavaScript by Lazar Laszlo 2011
lazarsoft@gmail.com, www.lazarsoft.info
*/
/*
*
* 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.
*/
function ReedSolomonDecoder(field)
{
this.field = field;
this.decode=function(received, twoS)
{
var poly = new GF256Poly(this.field, received);
var syndromeCoefficients = new Array(twoS);
for(var i=0;i<syndromeCoefficients.length;i++)syndromeCoefficients[i]=0;
var dataMatrix = false;//this.field.Equals(GF256.DATA_MATRIX_FIELD);
var noError = true;
for (var i = 0; i < twoS; i++)
{
// Thanks to sanfordsquires for this fix:
var eval = poly.evaluateAt(this.field.exp(dataMatrix?i + 1:i));
syndromeCoefficients[syndromeCoefficients.length - 1 - i] = eval;
if (eval != 0)
{
noError = false;
}
}
if (noError)
{
return ;
}
var syndrome = new GF256Poly(this.field, syndromeCoefficients);
var sigmaOmega = this.runEuclideanAlgorithm(this.field.buildMonomial(twoS, 1), syndrome, twoS);
var sigma = sigmaOmega[0];
var omega = sigmaOmega[1];
var errorLocations = this.findErrorLocations(sigma);
var errorMagnitudes = this.findErrorMagnitudes(omega, errorLocations, dataMatrix);
for (var i = 0; i < errorLocations.length; i++)
{
var position = received.length - 1 - this.field.log(errorLocations[i]);
if (position < 0)
{
throw "ReedSolomonException Bad error location";
}
received[position] = GF256.addOrSubtract(received[position], errorMagnitudes[i]);
}
}
this.runEuclideanAlgorithm=function( a, b, R)
{
// Assume a's degree is >= b's
if (a.Degree < b.Degree)
{
var temp = a;
a = b;
b = temp;
}
var rLast = a;
var r = b;
var sLast = this.field.One;
var s = this.field.Zero;
var tLast = this.field.Zero;
var t = this.field.One;
// Run Euclidean algorithm until r's degree is less than R/2
while (r.Degree >= Math.floor(R / 2))
{
var rLastLast = rLast;
var sLastLast = sLast;
var tLastLast = tLast;
rLast = r;
sLast = s;
tLast = t;
// Divide rLastLast by rLast, with quotient in q and remainder in r
if (rLast.Zero)
{
// Oops, Euclidean algorithm already terminated?
throw "r_{i-1} was zero";
}
r = rLastLast;
var q = this.field.Zero;
var denominatorLeadingTerm = rLast.getCoefficient(rLast.Degree);
var dltInverse = this.field.inverse(denominatorLeadingTerm);
while (r.Degree >= rLast.Degree && !r.Zero)
{
var degreeDiff = r.Degree - rLast.Degree;
var scale = this.field.multiply(r.getCoefficient(r.Degree), dltInverse);
q = q.addOrSubtract(this.field.buildMonomial(degreeDiff, scale));
r = r.addOrSubtract(rLast.multiplyByMonomial(degreeDiff, scale));
//r.EXE();
}
s = q.multiply1(sLast).addOrSubtract(sLastLast);
t = q.multiply1(tLast).addOrSubtract(tLastLast);
}
var sigmaTildeAtZero = t.getCoefficient(0);
if (sigmaTildeAtZero == 0)
{
throw "ReedSolomonException sigmaTilde(0) was zero";
}
var inverse = this.field.inverse(sigmaTildeAtZero);
var sigma = t.multiply2(inverse);
var omega = r.multiply2(inverse);
return new Array(sigma, omega);
}
this.findErrorLocations=function( errorLocator)
{
// This is a direct application of Chien's search
var numErrors = errorLocator.Degree;
if (numErrors == 1)
{
// shortcut
return new Array(errorLocator.getCoefficient(1));
}
var result = new Array(numErrors);
var e = 0;
for (var i = 1; i < 256 && e < numErrors; i++)
{
if (errorLocator.evaluateAt(i) == 0)
{
result[e] = this.field.inverse(i);
e++;
}
}
if (e != numErrors)
{
throw "Error locator degree does not match number of roots";
}
return result;
}
this.findErrorMagnitudes=function( errorEvaluator, errorLocations, dataMatrix)
{
// This is directly applying Forney's Formula
var s = errorLocations.length;
var result = new Array(s);
for (var i = 0; i < s; i++)
{
var xiInverse = this.field.inverse(errorLocations[i]);
var denominator = 1;
for (var j = 0; j < s; j++)
{
if (i != j)
{
denominator = this.field.multiply(denominator, GF256.addOrSubtract(1, this.field.multiply(errorLocations[j], xiInverse)));
}
}
result[i] = this.field.multiply(errorEvaluator.evaluateAt(xiInverse), this.field.inverse(denominator));
// Thanks to sanfordsquires for this fix:
if (dataMatrix)
{
result[i] = this.field.multiply(result[i], xiInverse);
}
}
return result;
}
}