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From z..@apache.org
Subject [25/50] [abbrv] hadoop git commit: HADOOP-11542. Raw Reed-Solomon coder in pure Java. Contributed by Kai Zheng
Date Thu, 02 Apr 2015 18:10:03 GMT
HADOOP-11542. Raw Reed-Solomon coder in pure Java. Contributed by Kai Zheng


Project: http://git-wip-us.apache.org/repos/asf/hadoop/repo
Commit: http://git-wip-us.apache.org/repos/asf/hadoop/commit/aac0254e
Tree: http://git-wip-us.apache.org/repos/asf/hadoop/tree/aac0254e
Diff: http://git-wip-us.apache.org/repos/asf/hadoop/diff/aac0254e

Branch: refs/heads/HDFS-7285
Commit: aac0254e30a46323ae652d014ba8a19d41d12dcf
Parents: 626b4c5
Author: drankye <drankye@gmail.com>
Authored: Thu Feb 12 21:12:44 2015 +0800
Committer: Zhe Zhang <zhz@apache.org>
Committed: Thu Apr 2 11:06:05 2015 -0700

----------------------------------------------------------------------
 .../hadoop-common/CHANGES-HDFS-EC-7285.txt      |   4 +
 .../io/erasurecode/rawcoder/JRSRawDecoder.java  |  69 +++
 .../io/erasurecode/rawcoder/JRSRawEncoder.java  |  78 +++
 .../erasurecode/rawcoder/RawErasureCoder.java   |   2 +-
 .../erasurecode/rawcoder/util/GaloisField.java  | 497 +++++++++++++++++++
 .../io/erasurecode/rawcoder/util/RSUtil.java    |  22 +
 .../hadoop/io/erasurecode/TestCoderBase.java    |  28 +-
 .../erasurecode/rawcoder/TestJRSRawCoder.java   |  93 ++++
 .../erasurecode/rawcoder/TestRawCoderBase.java  |   5 +-
 .../erasurecode/rawcoder/TestXorRawCoder.java   |   1 -
 10 files changed, 786 insertions(+), 13 deletions(-)
----------------------------------------------------------------------


http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/CHANGES-HDFS-EC-7285.txt
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/CHANGES-HDFS-EC-7285.txt b/hadoop-common-project/hadoop-common/CHANGES-HDFS-EC-7285.txt
index 9728f97..7bbacf7 100644
--- a/hadoop-common-project/hadoop-common/CHANGES-HDFS-EC-7285.txt
+++ b/hadoop-common-project/hadoop-common/CHANGES-HDFS-EC-7285.txt
@@ -8,3 +8,7 @@
 
     HADOOP-11541. Raw XOR coder
     ( Kai Zheng )
+
+    HADOOP-11542. Raw Reed-Solomon coder in pure Java. Contributed by Kai Zheng
+    ( Kai Zheng )
+

http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/JRSRawDecoder.java
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/JRSRawDecoder.java
b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/JRSRawDecoder.java
new file mode 100644
index 0000000..dbb689e
--- /dev/null
+++ b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/JRSRawDecoder.java
@@ -0,0 +1,69 @@
+/**
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you 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 org.apache.hadoop.io.erasurecode.rawcoder;
+
+import org.apache.hadoop.io.erasurecode.rawcoder.util.RSUtil;
+
+import java.nio.ByteBuffer;
+
+/**
+ * A raw erasure decoder in RS code scheme in pure Java in case native one
+ * isn't available in some environment. Please always use native implementations
+ * when possible.
+ */
+public class JRSRawDecoder extends AbstractRawErasureDecoder {
+  // To describe and calculate the needed Vandermonde matrix
+  private int[] errSignature;
+  private int[] primitivePower;
+
+  @Override
+  public void initialize(int numDataUnits, int numParityUnits, int chunkSize) {
+    super.initialize(numDataUnits, numParityUnits, chunkSize);
+    assert (getNumDataUnits() + getNumParityUnits() < RSUtil.GF.getFieldSize());
+
+    this.errSignature = new int[getNumParityUnits()];
+    this.primitivePower = RSUtil.getPrimitivePower(getNumDataUnits(),
+        getNumParityUnits());
+  }
+
+  @Override
+  protected void doDecode(ByteBuffer[] inputs, int[] erasedIndexes,
+                          ByteBuffer[] outputs) {
+    for (int i = 0; i < erasedIndexes.length; i++) {
+      errSignature[i] = primitivePower[erasedIndexes[i]];
+      RSUtil.GF.substitute(inputs, outputs[i], primitivePower[i]);
+    }
+
+    int dataLen = inputs[0].remaining();
+    RSUtil.GF.solveVandermondeSystem(errSignature, outputs,
+        erasedIndexes.length, dataLen);
+  }
+
+  @Override
+  protected void doDecode(byte[][] inputs, int[] erasedIndexes,
+                          byte[][] outputs) {
+    for (int i = 0; i < erasedIndexes.length; i++) {
+      errSignature[i] = primitivePower[erasedIndexes[i]];
+      RSUtil.GF.substitute(inputs, outputs[i], primitivePower[i]);
+    }
+
+    int dataLen = inputs[0].length;
+    RSUtil.GF.solveVandermondeSystem(errSignature, outputs,
+        erasedIndexes.length, dataLen);
+  }
+}

http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/JRSRawEncoder.java
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/JRSRawEncoder.java
b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/JRSRawEncoder.java
new file mode 100644
index 0000000..6ea7551
--- /dev/null
+++ b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/JRSRawEncoder.java
@@ -0,0 +1,78 @@
+/**
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you 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 org.apache.hadoop.io.erasurecode.rawcoder;
+
+import org.apache.hadoop.io.erasurecode.rawcoder.util.RSUtil;
+
+import java.nio.ByteBuffer;
+
+/**
+ * A raw erasure encoder in RS code scheme in pure Java in case native one
+ * isn't available in some environment. Please always use native implementations
+ * when possible.
+ */
+public class JRSRawEncoder extends AbstractRawErasureEncoder {
+  private int[] generatingPolynomial;
+
+  @Override
+  public void initialize(int numDataUnits, int numParityUnits, int chunkSize) {
+    super.initialize(numDataUnits, numParityUnits, chunkSize);
+    assert (getNumDataUnits() + getNumParityUnits() < RSUtil.GF.getFieldSize());
+
+    int[] primitivePower = RSUtil.getPrimitivePower(getNumDataUnits(),
+        getNumParityUnits());
+    // compute generating polynomial
+    int[] gen = {1};
+    int[] poly = new int[2];
+    for (int i = 0; i < getNumParityUnits(); i++) {
+      poly[0] = primitivePower[i];
+      poly[1] = 1;
+      gen = RSUtil.GF.multiply(gen, poly);
+    }
+    // generating polynomial has all generating roots
+    generatingPolynomial = gen;
+  }
+
+  @Override
+  protected void doEncode(ByteBuffer[] inputs, ByteBuffer[] outputs) {
+    ByteBuffer[] data = new ByteBuffer[getNumDataUnits() + getNumParityUnits()];
+    for (int i = 0; i < getNumParityUnits(); i++) {
+      data[i] = outputs[i];
+    }
+    for (int i = 0; i < getNumDataUnits(); i++) {
+      data[i + getNumParityUnits()] = inputs[i];
+    }
+
+    // Compute the remainder
+    RSUtil.GF.remainder(data, generatingPolynomial);
+  }
+
+  @Override
+  protected void doEncode(byte[][] inputs, byte[][] outputs) {
+    byte[][] data = new byte[getNumDataUnits() + getNumParityUnits()][];
+    for (int i = 0; i < getNumParityUnits(); i++) {
+      data[i] = outputs[i];
+    }
+    for (int i = 0; i < getNumDataUnits(); i++) {
+      data[i + getNumParityUnits()] = inputs[i];
+    }
+
+    // Compute the remainder
+    RSUtil.GF.remainder(data, generatingPolynomial);
+  }
+}

http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/RawErasureCoder.java
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/RawErasureCoder.java
b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/RawErasureCoder.java
index 91a9abf..6e07cf1 100644
--- a/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/RawErasureCoder.java
+++ b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/RawErasureCoder.java
@@ -71,7 +71,7 @@ public interface RawErasureCoder {
   public boolean preferNativeBuffer();
 
   /**
-   * Should be called when release this coder. Good chance to release encoding
+   * Should be called when release this blockcoder. Good chance to release encoding
    * or decoding buffers
    */
   public void release();

http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/util/GaloisField.java
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/util/GaloisField.java
b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/util/GaloisField.java
new file mode 100644
index 0000000..77544c6
--- /dev/null
+++ b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/util/GaloisField.java
@@ -0,0 +1,497 @@
+/**
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you 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 org.apache.hadoop.io.erasurecode.rawcoder.util;
+
+import java.nio.ByteBuffer;
+import java.util.HashMap;
+import java.util.Map;
+
+/**
+ * Implementation of Galois field arithmetic with 2^p elements. The input must
+ * be unsigned integers. It's ported from HDFS-RAID, slightly adapted.
+ */
+public class GaloisField {
+
+  // Field size 256 is good for byte based system
+  private static final int DEFAULT_FIELD_SIZE = 256;
+  // primitive polynomial 1 + X^2 + X^3 + X^4 + X^8 (substitute 2)
+  private static final int DEFAULT_PRIMITIVE_POLYNOMIAL = 285;
+  static private final Map<Integer, GaloisField> instances =
+      new HashMap<Integer, GaloisField>();
+  private final int[] logTable;
+  private final int[] powTable;
+  private final int[][] mulTable;
+  private final int[][] divTable;
+  private final int fieldSize;
+  private final int primitivePeriod;
+  private final int primitivePolynomial;
+
+  private GaloisField(int fieldSize, int primitivePolynomial) {
+    assert fieldSize > 0;
+    assert primitivePolynomial > 0;
+
+    this.fieldSize = fieldSize;
+    this.primitivePeriod = fieldSize - 1;
+    this.primitivePolynomial = primitivePolynomial;
+    logTable = new int[fieldSize];
+    powTable = new int[fieldSize];
+    mulTable = new int[fieldSize][fieldSize];
+    divTable = new int[fieldSize][fieldSize];
+    int value = 1;
+    for (int pow = 0; pow < fieldSize - 1; pow++) {
+      powTable[pow] = value;
+      logTable[value] = pow;
+      value = value * 2;
+      if (value >= fieldSize) {
+        value = value ^ primitivePolynomial;
+      }
+    }
+    // building multiplication table
+    for (int i = 0; i < fieldSize; i++) {
+      for (int j = 0; j < fieldSize; j++) {
+        if (i == 0 || j == 0) {
+          mulTable[i][j] = 0;
+          continue;
+        }
+        int z = logTable[i] + logTable[j];
+        z = z >= primitivePeriod ? z - primitivePeriod : z;
+        z = powTable[z];
+        mulTable[i][j] = z;
+      }
+    }
+    // building division table
+    for (int i = 0; i < fieldSize; i++) {
+      for (int j = 1; j < fieldSize; j++) {
+        if (i == 0) {
+          divTable[i][j] = 0;
+          continue;
+        }
+        int z = logTable[i] - logTable[j];
+        z = z < 0 ? z + primitivePeriod : z;
+        z = powTable[z];
+        divTable[i][j] = z;
+      }
+    }
+  }
+
+  /**
+   * Get the object performs Galois field arithmetics
+   *
+   * @param fieldSize           size of the field
+   * @param primitivePolynomial a primitive polynomial corresponds to the size
+   */
+  public static GaloisField getInstance(int fieldSize,
+                                        int primitivePolynomial) {
+    int key = ((fieldSize << 16) & 0xFFFF0000)
+        + (primitivePolynomial & 0x0000FFFF);
+    GaloisField gf;
+    synchronized (instances) {
+      gf = instances.get(key);
+      if (gf == null) {
+        gf = new GaloisField(fieldSize, primitivePolynomial);
+        instances.put(key, gf);
+      }
+    }
+    return gf;
+  }
+
+  /**
+   * Get the object performs Galois field arithmetic with default setting
+   */
+  public static GaloisField getInstance() {
+    return getInstance(DEFAULT_FIELD_SIZE, DEFAULT_PRIMITIVE_POLYNOMIAL);
+  }
+
+  /**
+   * Return number of elements in the field
+   *
+   * @return number of elements in the field
+   */
+  public int getFieldSize() {
+    return fieldSize;
+  }
+
+  /**
+   * Return the primitive polynomial in GF(2)
+   *
+   * @return primitive polynomial as a integer
+   */
+  public int getPrimitivePolynomial() {
+    return primitivePolynomial;
+  }
+
+  /**
+   * Compute the sum of two fields
+   *
+   * @param x input field
+   * @param y input field
+   * @return result of addition
+   */
+  public int add(int x, int y) {
+    assert (x >= 0 && x < getFieldSize() && y >= 0 && y
< getFieldSize());
+    return x ^ y;
+  }
+
+  /**
+   * Compute the multiplication of two fields
+   *
+   * @param x input field
+   * @param y input field
+   * @return result of multiplication
+   */
+  public int multiply(int x, int y) {
+    assert (x >= 0 && x < getFieldSize() && y >= 0 && y
< getFieldSize());
+    return mulTable[x][y];
+  }
+
+  /**
+   * Compute the division of two fields
+   *
+   * @param x input field
+   * @param y input field
+   * @return x/y
+   */
+  public int divide(int x, int y) {
+    assert (x >= 0 && x < getFieldSize() && y > 0 && y <
getFieldSize());
+    return divTable[x][y];
+  }
+
+  /**
+   * Compute power n of a field
+   *
+   * @param x input field
+   * @param n power
+   * @return x^n
+   */
+  public int power(int x, int n) {
+    assert (x >= 0 && x < getFieldSize());
+    if (n == 0) {
+      return 1;
+    }
+    if (x == 0) {
+      return 0;
+    }
+    x = logTable[x] * n;
+    if (x < primitivePeriod) {
+      return powTable[x];
+    }
+    x = x % primitivePeriod;
+    return powTable[x];
+  }
+
+  /**
+   * Given a Vandermonde matrix V[i][j]=x[j]^i and vector y, solve for z such
+   * that Vz=y. The output z will be placed in y.
+   *
+   * @param x the vector which describe the Vandermonde matrix
+   * @param y right-hand side of the Vandermonde system equation. will be
+   *          replaced the output in this vector
+   */
+  public void solveVandermondeSystem(int[] x, int[] y) {
+    solveVandermondeSystem(x, y, x.length);
+  }
+
+  /**
+   * Given a Vandermonde matrix V[i][j]=x[j]^i and vector y, solve for z such
+   * that Vz=y. The output z will be placed in y.
+   *
+   * @param x   the vector which describe the Vandermonde matrix
+   * @param y   right-hand side of the Vandermonde system equation. will be
+   *            replaced the output in this vector
+   * @param len consider x and y only from 0...len-1
+   */
+  public void solveVandermondeSystem(int[] x, int[] y, int len) {
+    assert (x.length <= len && y.length <= len);
+    for (int i = 0; i < len - 1; i++) {
+      for (int j = len - 1; j > i; j--) {
+        y[j] = y[j] ^ mulTable[x[i]][y[j - 1]];
+      }
+    }
+    for (int i = len - 1; i >= 0; i--) {
+      for (int j = i + 1; j < len; j++) {
+        y[j] = divTable[y[j]][x[j] ^ x[j - i - 1]];
+      }
+      for (int j = i; j < len - 1; j++) {
+        y[j] = y[j] ^ y[j + 1];
+      }
+    }
+  }
+
+  /**
+   * A "bulk" version to the solving of Vandermonde System
+   */
+  public void solveVandermondeSystem(int[] x, byte[][] y,
+                                     int len, int dataLen) {
+    for (int i = 0; i < len - 1; i++) {
+      for (int j = len - 1; j > i; j--) {
+        for (int k = 0; k < dataLen; k++) {
+          y[j][k] = (byte) (y[j][k] ^ mulTable[x[i]][y[j - 1][k] &
+              0x000000FF]);
+        }
+      }
+    }
+    for (int i = len - 1; i >= 0; i--) {
+      for (int j = i + 1; j < len; j++) {
+        for (int k = 0; k < dataLen; k++) {
+          y[j][k] = (byte) (divTable[y[j][k] & 0x000000FF][x[j] ^
+              x[j - i - 1]]);
+        }
+      }
+      for (int j = i; j < len - 1; j++) {
+        for (int k = 0; k < dataLen; k++) {
+          y[j][k] = (byte) (y[j][k] ^ y[j + 1][k]);
+        }
+      }
+    }
+  }
+
+  /**
+   * A "bulk" version of the solveVandermondeSystem, using ByteBuffer.
+   */
+  public void solveVandermondeSystem(int[] x, ByteBuffer[] y,
+                                     int len, int dataLen) {
+    for (int i = 0; i < len - 1; i++) {
+      for (int j = len - 1; j > i; j--) {
+        for (int k = 0; k < dataLen; k++) {
+          y[j].put(k, (byte) (y[j].get(k) ^ mulTable[x[i]][y[j - 1].get(k) &
+              0x000000FF]));
+        }
+      }
+    }
+    for (int i = len - 1; i >= 0; i--) {
+      for (int j = i + 1; j < len; j++) {
+        for (int k = 0; k < dataLen; k++) {
+          y[j].put(k, (byte) (divTable[y[j].get(k) & 0x000000FF][x[j] ^
+              x[j - i - 1]]));
+        }
+      }
+      for (int j = i; j < len - 1; j++) {
+        for (int k = 0; k < dataLen; k++) {
+          y[j].put(k, (byte) (y[j].get(k) ^ y[j + 1].get(k)));
+        }
+      }
+    }
+  }
+
+  /**
+   * Compute the multiplication of two polynomials. The index in the array
+   * corresponds to the power of the entry. For example p[0] is the constant
+   * term of the polynomial p.
+   *
+   * @param p input polynomial
+   * @param q input polynomial
+   * @return polynomial represents p*q
+   */
+  public int[] multiply(int[] p, int[] q) {
+    int len = p.length + q.length - 1;
+    int[] result = new int[len];
+    for (int i = 0; i < len; i++) {
+      result[i] = 0;
+    }
+    for (int i = 0; i < p.length; i++) {
+
+      for (int j = 0; j < q.length; j++) {
+        result[i + j] = add(result[i + j], multiply(p[i], q[j]));
+      }
+    }
+    return result;
+  }
+
+  /**
+   * Compute the remainder of a dividend and divisor pair. The index in the
+   * array corresponds to the power of the entry. For example p[0] is the
+   * constant term of the polynomial p.
+   *
+   * @param dividend dividend polynomial, the remainder will be placed
+   *                 here when return
+   * @param divisor  divisor polynomial
+   */
+  public void remainder(int[] dividend, int[] divisor) {
+    for (int i = dividend.length - divisor.length; i >= 0; i--) {
+      int ratio = divTable[dividend[i +
+          divisor.length - 1]][divisor[divisor.length - 1]];
+      for (int j = 0; j < divisor.length; j++) {
+        int k = j + i;
+        dividend[k] = dividend[k] ^ mulTable[ratio][divisor[j]];
+      }
+    }
+  }
+
+  /**
+   * Compute the sum of two polynomials. The index in the array corresponds to
+   * the power of the entry. For example p[0] is the constant term of the
+   * polynomial p.
+   *
+   * @param p input polynomial
+   * @param q input polynomial
+   * @return polynomial represents p+q
+   */
+  public int[] add(int[] p, int[] q) {
+    int len = Math.max(p.length, q.length);
+    int[] result = new int[len];
+    for (int i = 0; i < len; i++) {
+      if (i < p.length && i < q.length) {
+        result[i] = add(p[i], q[i]);
+      } else if (i < p.length) {
+        result[i] = p[i];
+      } else {
+        result[i] = q[i];
+      }
+    }
+    return result;
+  }
+
+  /**
+   * Substitute x into polynomial p(x).
+   *
+   * @param p input polynomial
+   * @param x input field
+   * @return p(x)
+   */
+  public int substitute(int[] p, int x) {
+    int result = 0;
+    int y = 1;
+    for (int i = 0; i < p.length; i++) {
+      result = result ^ mulTable[p[i]][y];
+      y = mulTable[x][y];
+    }
+    return result;
+  }
+
+  /**
+   * A "bulk" version of the substitute.
+   * Tends to be 2X faster than the "int" substitute in a loop.
+   *
+   * @param p input polynomial
+   * @param q store the return result
+   * @param x input field
+   */
+  public void substitute(byte[][] p, byte[] q, int x) {
+    int y = 1;
+    for (int i = 0; i < p.length; i++) {
+      byte[] pi = p[i];
+      for (int j = 0; j < pi.length; j++) {
+        int pij = pi[j] & 0x000000FF;
+        q[j] = (byte) (q[j] ^ mulTable[pij][y]);
+      }
+      y = mulTable[x][y];
+    }
+  }
+
+  /**
+   * A "bulk" version of the substitute, using ByteBuffer.
+   * Tends to be 2X faster than the "int" substitute in a loop.
+   *
+   * @param p input polynomial
+   * @param q store the return result
+   * @param x input field
+   */
+  public void substitute(ByteBuffer[] p, ByteBuffer q, int x) {
+    int y = 1;
+    for (int i = 0; i < p.length; i++) {
+      ByteBuffer pi = p[i];
+      int len = pi.remaining();
+      for (int j = 0; j < len; j++) {
+        int pij = pi.get(j) & 0x000000FF;
+        q.put(j, (byte) (q.get(j) ^ mulTable[pij][y]));
+      }
+      y = mulTable[x][y];
+    }
+  }
+
+  /**
+   * The "bulk" version of the remainder.
+   * Warning: This function will modify the "dividend" inputs.
+   */
+  public void remainder(byte[][] dividend, int[] divisor) {
+    for (int i = dividend.length - divisor.length; i >= 0; i--) {
+      for (int j = 0; j < divisor.length; j++) {
+        for (int k = 0; k < dividend[i].length; k++) {
+          int ratio = divTable[dividend[i + divisor.length - 1][k] &
+              0x00FF][divisor[divisor.length - 1]];
+          dividend[j + i][k] = (byte) ((dividend[j + i][k] & 0x00FF) ^
+              mulTable[ratio][divisor[j]]);
+        }
+      }
+    }
+  }
+
+  /**
+   * The "bulk" version of the remainder, using ByteBuffer.
+   * Warning: This function will modify the "dividend" inputs.
+   */
+  public void remainder(ByteBuffer[] dividend, int[] divisor) {
+    for (int i = dividend.length - divisor.length; i >= 0; i--) {
+      int width = dividend[i].remaining();
+      for (int j = 0; j < divisor.length; j++) {
+        for (int k = 0; k < width; k++) {
+          int ratio = divTable[dividend[i + divisor.length - 1].get(k) &
+              0x00FF][divisor[divisor.length - 1]];
+          dividend[j + i].put(k, (byte) ((dividend[j + i].get(k) & 0x00FF) ^
+              mulTable[ratio][divisor[j]]));
+        }
+      }
+    }
+  }
+
+  /**
+   * Perform Gaussian elimination on the given matrix. This matrix has to be a
+   * fat matrix (number of rows > number of columns).
+   */
+  public void gaussianElimination(int[][] matrix) {
+    assert(matrix != null && matrix.length > 0 && matrix[0].length >
0
+        && matrix.length < matrix[0].length);
+    int height = matrix.length;
+    int width = matrix[0].length;
+    for (int i = 0; i < height; i++) {
+      boolean pivotFound = false;
+      // scan the column for a nonzero pivot and swap it to the diagonal
+      for (int j = i; j < height; j++) {
+        if (matrix[i][j] != 0) {
+          int[] tmp = matrix[i];
+          matrix[i] = matrix[j];
+          matrix[j] = tmp;
+          pivotFound = true;
+          break;
+        }
+      }
+      if (!pivotFound) {
+        continue;
+      }
+      int pivot = matrix[i][i];
+      for (int j = i; j < width; j++) {
+        matrix[i][j] = divide(matrix[i][j], pivot);
+      }
+      for (int j = i + 1; j < height; j++) {
+        int lead = matrix[j][i];
+        for (int k = i; k < width; k++) {
+          matrix[j][k] = add(matrix[j][k], multiply(lead, matrix[i][k]));
+        }
+      }
+    }
+    for (int i = height - 1; i >=0; i--) {
+      for (int j = 0; j < i; j++) {
+        int lead = matrix[j][i];
+        for (int k = i; k < width; k++) {
+          matrix[j][k] = add(matrix[j][k], multiply(lead, matrix[i][k]));
+        }
+      }
+    }
+  }
+
+}

http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/util/RSUtil.java
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/util/RSUtil.java
b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/util/RSUtil.java
new file mode 100644
index 0000000..33ba561
--- /dev/null
+++ b/hadoop-common-project/hadoop-common/src/main/java/org/apache/hadoop/io/erasurecode/rawcoder/util/RSUtil.java
@@ -0,0 +1,22 @@
+package org.apache.hadoop.io.erasurecode.rawcoder.util;
+
+/**
+ * Some utilities for Reed-Solomon coding.
+ */
+public class RSUtil {
+
+  // We always use the byte system (with symbol size 8, field size 256,
+  // primitive polynomial 285, and primitive root 2).
+  public static GaloisField GF = GaloisField.getInstance();
+  public static final int PRIMITIVE_ROOT = 2;
+
+  public static int[] getPrimitivePower(int numDataUnits, int numParityUnits) {
+    int[] primitivePower = new int[numDataUnits + numParityUnits];
+    // compute powers of the primitive root
+    for (int i = 0; i < numDataUnits + numParityUnits; i++) {
+      primitivePower[i] = GF.power(PRIMITIVE_ROOT, i);
+    }
+    return primitivePower;
+  }
+
+}

http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/TestCoderBase.java
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/TestCoderBase.java
b/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/TestCoderBase.java
index 9482b43..3c4288c 100644
--- a/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/TestCoderBase.java
+++ b/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/TestCoderBase.java
@@ -18,9 +18,11 @@
 package org.apache.hadoop.io.erasurecode;
 
 import java.nio.ByteBuffer;
+import java.util.Arrays;
 import java.util.Random;
 
 import static org.junit.Assert.assertArrayEquals;
+import static org.junit.Assert.assertTrue;
 
 /**
  * Test base of common utilities for tests not only raw coders but also block
@@ -41,6 +43,14 @@ public abstract class TestCoderBase {
   // may go to different coding implementations.
   protected boolean usingDirectBuffer = true;
 
+  protected void prepare(int numDataUnits, int numParityUnits,
+                         int[] erasedIndexes) {
+    this.numDataUnits = numDataUnits;
+    this.numParityUnits = numParityUnits;
+    this.erasedDataIndexes = erasedIndexes != null ?
+        erasedIndexes : new int[] {0};
+  }
+
   /**
    * Compare and verify if erased chunks are equal to recovered chunks
    * @param erasedChunks
@@ -50,10 +60,8 @@ public abstract class TestCoderBase {
                                   ECChunk[] recoveredChunks) {
     byte[][] erased = ECChunk.toArray(erasedChunks);
     byte[][] recovered = ECChunk.toArray(recoveredChunks);
-    for (int i = 0; i < erasedChunks.length; ++i) {
-      assertArrayEquals("Decoding and comparing failed.", erased[i],
-          recovered[i]);
-    }
+    boolean result = Arrays.deepEquals(erased, recovered);
+    assertTrue("Decoding and comparing failed.", result);
   }
 
   /**
@@ -63,7 +71,7 @@ public abstract class TestCoderBase {
    */
   protected int[] getErasedIndexesForDecoding() {
     int[] erasedIndexesForDecoding = new int[erasedDataIndexes.length];
-    for (int i = 0; i < erasedDataIndexes.length; ++i) {
+    for (int i = 0; i < erasedDataIndexes.length; i++) {
       erasedIndexesForDecoding[i] = erasedDataIndexes[i] + numParityUnits;
     }
     return erasedIndexesForDecoding;
@@ -100,7 +108,7 @@ public abstract class TestCoderBase {
     ECChunk[] copiedChunks = new ECChunk[erasedDataIndexes.length];
 
     int j = 0;
-    for (int i = 0; i < erasedDataIndexes.length; ++i) {
+    for (int i = 0; i < erasedDataIndexes.length; i++) {
       copiedChunks[j ++] = cloneChunkWithData(dataChunks[erasedDataIndexes[i]]);
     }
 
@@ -112,7 +120,7 @@ public abstract class TestCoderBase {
    * @param dataChunks
    */
   protected void eraseSomeDataBlocks(ECChunk[] dataChunks) {
-    for (int i = 0; i < erasedDataIndexes.length; ++i) {
+    for (int i = 0; i < erasedDataIndexes.length; i++) {
       eraseDataFromChunk(dataChunks[erasedDataIndexes[i]]);
     }
   }
@@ -122,7 +130,7 @@ public abstract class TestCoderBase {
    * @param chunks
    */
   protected void eraseDataFromChunks(ECChunk[] chunks) {
-    for (int i = 0; i < chunks.length; ++i) {
+    for (int i = 0; i < chunks.length; i++) {
       eraseDataFromChunk(chunks[i]);
     }
   }
@@ -135,7 +143,7 @@ public abstract class TestCoderBase {
     ByteBuffer chunkBuffer = chunk.getBuffer();
     // erase the data
     chunkBuffer.position(0);
-    for (int i = 0; i < chunkSize; ++i) {
+    for (int i = 0; i < chunkSize; i++) {
       chunkBuffer.put((byte) 0);
     }
     chunkBuffer.flip();
@@ -150,7 +158,7 @@ public abstract class TestCoderBase {
    */
   protected static ECChunk[] cloneChunksWithData(ECChunk[] chunks) {
     ECChunk[] results = new ECChunk[chunks.length];
-    for (int i = 0; i < chunks.length; ++i) {
+    for (int i = 0; i < chunks.length; i++) {
       results[i] = cloneChunkWithData(chunks[i]);
     }
 

http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestJRSRawCoder.java
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestJRSRawCoder.java
b/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestJRSRawCoder.java
new file mode 100644
index 0000000..e54f647
--- /dev/null
+++ b/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestJRSRawCoder.java
@@ -0,0 +1,93 @@
+/**
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you 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 org.apache.hadoop.io.erasurecode.rawcoder;
+
+import org.apache.hadoop.io.erasurecode.ECChunk;
+import org.apache.hadoop.io.erasurecode.rawcoder.util.RSUtil;
+import org.junit.Before;
+import org.junit.Test;
+
+import java.nio.ByteBuffer;
+
+/**
+ * Test raw Reed-solomon encoding and decoding.
+ */
+public class TestJRSRawCoder extends TestRawCoderBase {
+
+  private static int symbolSize = 0;
+  private static int symbolMax = 0;
+
+  static {
+    symbolSize = (int) Math.round(Math.log(
+        RSUtil.GF.getFieldSize()) / Math.log(2));
+    symbolMax = (int) Math.pow(2, symbolSize);
+  }
+
+  @Before
+  public void setup() {
+    this.encoderClass = JRSRawEncoder.class;
+    this.decoderClass = JRSRawDecoder.class;
+  }
+
+  @Test
+  public void testCodingNoDirectBuffer_10x4() {
+    prepare(10, 4, null);
+    testCoding(false);
+  }
+
+  @Test
+  public void testCodingDirectBuffer_10x4() {
+    prepare(10, 4, null);
+    testCoding(true);
+  }
+
+  @Test
+  public void testCodingDirectBuffer_10x4_erasure_of_2_4() {
+    prepare(10, 4, new int[] {2, 4});
+    testCoding(true);
+  }
+
+  @Test
+  public void testCodingDirectBuffer_10x4_erasing_all() {
+    prepare(10, 4, new int[] {0, 1, 2, 3});
+    testCoding(true);
+  }
+
+  @Test
+  public void testCodingNoDirectBuffer_3x3() {
+    prepare(3, 3, null);
+    testCoding(false);
+  }
+
+  @Test
+  public void testCodingDirectBuffer_3x3() {
+    prepare(3, 3, null);
+    testCoding(true);
+  }
+
+  @Override
+  protected ECChunk generateDataChunk() {
+    ByteBuffer buffer = allocateOutputBuffer();
+    for (int i = 0; i < chunkSize; i++) {
+      buffer.put((byte) RAND.nextInt(symbolMax));
+    }
+    buffer.flip();
+
+    return new ECChunk(buffer);
+  }
+}

http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestRawCoderBase.java
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestRawCoderBase.java
b/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestRawCoderBase.java
index 9119211..5f6ccda 100644
--- a/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestRawCoderBase.java
+++ b/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestRawCoderBase.java
@@ -31,10 +31,13 @@ public abstract class TestRawCoderBase extends TestCoderBase {
    * Generating source data, encoding, recovering and then verifying.
    * RawErasureCoder mainly uses ECChunk to pass input and output data buffers,
    * it supports two kinds of ByteBuffers, one is array backed, the other is
-   * direct ByteBuffer. Have usingDirectBuffer to indicate which case to test.
+   * direct ByteBuffer. Use usingDirectBuffer indicate which case to test.
+   *
    * @param usingDirectBuffer
    */
   protected void testCoding(boolean usingDirectBuffer) {
+    this.usingDirectBuffer = usingDirectBuffer;
+
     // Generate data and encode
     ECChunk[] dataChunks = prepareDataChunksForEncoding();
     ECChunk[] parityChunks = prepareParityChunksForEncoding();

http://git-wip-us.apache.org/repos/asf/hadoop/blob/aac0254e/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestXorRawCoder.java
----------------------------------------------------------------------
diff --git a/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestXorRawCoder.java
b/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestXorRawCoder.java
index 8e59b8a..ff48586 100644
--- a/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestXorRawCoder.java
+++ b/hadoop-common-project/hadoop-common/src/test/java/org/apache/hadoop/io/erasurecode/rawcoder/TestXorRawCoder.java
@@ -26,7 +26,6 @@ import java.util.Random;
  * Test XOR encoding and decoding.
  */
 public class TestXorRawCoder extends TestRawCoderBase {
-  private static Random RAND = new Random();
 
   @Before
   public void setup() {


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