Back-port more proper PDF417 R-S error correction

git-svn-id: https://zxing.googlecode.com/svn/trunk@2275 59b500cc-1b3d-0410-9834-0bbf25fbcc57

core/src/com/google/zxing/pdf417/decoder/ec/ErrorCorrection.java

@@ -19,7 +19,10 @@ package com.google.zxing.pdf417.decoder.ec;
 import com.google.zxing.ChecksumException;
 
 /**
- * <p>Incomplete implementation of PDF417 error correction. For now, only detects errors.</p>
+ * <p>PDF417 error correction implementation.</p>
+ *
+ * <p>This <a href="http://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction#Example">example</a>
+ * is quite useful in understanding the algorithm.</p>
  *
  * @author Sean Owen
  * @see com.google.zxing.common.reedsolomon.ReedSolomonDecoder
@@ -34,19 +37,127 @@ public final class ErrorCorrection {
 
   public void decode(int[] received, int numECCodewords) throws ChecksumException {
     ModulusPoly poly = new ModulusPoly(field, received);
-    int[] syndromeCoefficients = new int[numECCodewords];
-    boolean noError = true;
-    for (int i = 0; i < numECCodewords; i++) {
-      int eval = poly.evaluateAt(field.exp(i + 1));
-      syndromeCoefficients[syndromeCoefficients.length - 1 - i] = eval;
+    int[] S = new int[numECCodewords];
+    boolean error = false;
+    for (int i = numECCodewords; i > 0; i--) {
+      int eval = poly.evaluateAt(field.exp(i));
+      S[numECCodewords - i] = eval;
       if (eval != 0) {
-        noError = false;
+        error = true;
       }
     }
-    if (!noError) {
-      throw ChecksumException.getChecksumInstance();
+    if (error) {
+      ModulusPoly syndrome = new ModulusPoly(field, S);
+      ErrorCorrection ec = new ErrorCorrection();
+      ModulusPoly[] sigmaOmega =
+          ec.runEuclideanAlgorithm(field.buildMonomial(numECCodewords, 1), syndrome, numECCodewords);
+      ModulusPoly sigma = sigmaOmega[0];
+      ModulusPoly omega = sigmaOmega[1];
+      int[] errorLocations = ec.findErrorLocations(sigma);
+      int[] errorMagnitudes = ec.findErrorMagnitudes(omega, sigma, errorLocations);
+      for (int i = 0; i < errorLocations.length; i++) {
+        int position = received.length - 1 - field.log(errorLocations[i]);
+        if (position < 0) {
+          throw ChecksumException.getChecksumInstance();
+        }
+        received[position] = field.subtract(received[position], errorMagnitudes[i]);
+      }
     }
-    // TODO actually correct errors!
   }
 
+  private ModulusPoly[] runEuclideanAlgorithm(ModulusPoly a, ModulusPoly b, int R)
+      throws ChecksumException {
+    // Assume a's degree is >= b's
+    if (a.getDegree() < b.getDegree()) {
+      ModulusPoly temp = a;
+      a = b;
+      b = temp;
+    }
+
+    ModulusPoly rLast = a;
+    ModulusPoly r = b;
+    ModulusPoly sLast = field.getOne();
+    ModulusPoly s = field.getZero();
+    ModulusPoly tLast = field.getZero();
+    ModulusPoly t = field.getOne();
+
+    // Run Euclidean algorithm until r's degree is less than R/2
+    while (r.getDegree() >= R / 2) {
+      ModulusPoly rLastLast = rLast;
+      ModulusPoly sLastLast = sLast;
+      ModulusPoly tLastLast = tLast;
+      rLast = r;
+      sLast = s;
+      tLast = t;
+
+      // Divide rLastLast by rLast, with quotient in q and remainder in r
+      if (rLast.isZero()) {
+        // Oops, Euclidean algorithm already terminated?
+        throw ChecksumException.getChecksumInstance();
+      }
+      r = rLastLast;
+      ModulusPoly q = field.getZero();
+      int denominatorLeadingTerm = rLast.getCoefficient(rLast.getDegree());
+      int dltInverse = field.inverse(denominatorLeadingTerm);
+      while (r.getDegree() >= rLast.getDegree() && !r.isZero()) {
+        int degreeDiff = r.getDegree() - rLast.getDegree();
+        int scale = field.multiply(r.getCoefficient(r.getDegree()), dltInverse);
+        q = q.add(field.buildMonomial(degreeDiff, scale));
+        r = r.subtract(rLast.multiplyByMonomial(degreeDiff, scale));
+      }
+
+      s = q.multiply(sLast).subtract(sLastLast).negative();
+      t = q.multiply(tLast).subtract(tLastLast).negative();
+    }
+
+    int sigmaTildeAtZero = t.getCoefficient(0);
+    if (sigmaTildeAtZero == 0) {
+      throw ChecksumException.getChecksumInstance();
+    }
+
+    int inverse = field.inverse(sigmaTildeAtZero);
+    ModulusPoly sigma = t.multiply(inverse);
+    ModulusPoly omega = r.multiply(inverse);
+    return new ModulusPoly[]{sigma, omega};
+  }
+
+  private int[] findErrorLocations(ModulusPoly errorLocator) throws ChecksumException {
+    // This is a direct application of Chien's search
+    int numErrors = errorLocator.getDegree();
+    int[] result = new int[numErrors];
+    int e = 0;
+    for (int i = 1; i < field.getSize() && e < numErrors; i++) {
+      if (errorLocator.evaluateAt(i) == 0) {
+        result[e] = field.inverse(i);
+        e++;
+      }
+    }
+    if (e != numErrors) {
+      throw ChecksumException.getChecksumInstance();
+    }
+    return result;
+  }
+
+  private int[] findErrorMagnitudes(ModulusPoly errorEvaluator,
+                                    ModulusPoly errorLocator,
+                                    int[] errorLocations) {
+    int errorLocatorDegree = errorLocator.getDegree();
+    int[] formalDerivativeCoefficients = new int[errorLocatorDegree];
+    for (int i = 1; i <= errorLocatorDegree; i++) {
+      formalDerivativeCoefficients[errorLocatorDegree - i] =
+          field.multiply(i, errorLocator.getCoefficient(i));
+    }
+    ModulusPoly formalDerivative = new ModulusPoly(field, formalDerivativeCoefficients);
+
+    // This is directly applying Forney's Formula
+    int s = errorLocations.length;
+    int[] result = new int[s];
+    for (int i = 0; i < s; i++) {
+      int xiInverse = field.inverse(errorLocations[i]);
+      int numerator = field.subtract(0, errorEvaluator.evaluateAt(xiInverse));
+      int denominator = field.inverse(formalDerivative.evaluateAt(xiInverse));
+      result[i] = field.multiply(numerator, denominator);
+    }
+    return result;
+  }
 }