SPARK-5984: Fix TimSort bug causes ArrayOutOfBoundsException

Fix TimSort bug which causes a ArrayOutOfBoundsException.

Using the proposed fix here
http://envisage-project.eu/proving-android-java-and-python-sorting-algorithm-is-broken-and-how-to-fix-it/

Author: Evan Yu <ehotou@gmail.com>

Closes #4804 from hotou/SPARK-5984 and squashes the following commits:

3421b6c [Evan Yu] SPARK-5984: Add info to LICENSE
e61c6b8 [Evan Yu] SPARK-5984: Fix license and document
6ccc280 [Evan Yu] SPARK-5984: Add License header to file
e06c0d2 [Evan Yu] SPARK-5984: Add License header to file
4d95f75 [Evan Yu] SPARK-5984: Fix TimSort bug causes ArrayOutOfBoundsException
479a106 [Evan Yu] SPARK-5984: Fix TimSort bug causes ArrayOutOfBoundsException

LICENSE

@@ -771,6 +771,22 @@ 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.
 
+========================================================================
+For TestTimSort (core/src/test/java/org/apache/spark/util/collection/TestTimSort.java):
+========================================================================
+Copyright (C) 2015 Stijn de Gouw
+
+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.
 
 ========================================================================
 For LimitedInputStream

core/src/main/java/org/apache/spark/util/collection/TimSort.java

@@ -425,15 +425,14 @@ private void pushRun(int runBase, int runLen) {
     private void mergeCollapse() {
       while (stackSize > 1) {
         int n = stackSize - 2;
-        if (n > 0 && runLen[n-1] <= runLen[n] + runLen[n+1]) {
+        if ( (n >= 1 && runLen[n-1] <= runLen[n] + runLen[n+1])
+          || (n >= 2 && runLen[n-2] <= runLen[n] + runLen[n-1])) {
           if (runLen[n - 1] < runLen[n + 1])
             n--;
-          mergeAt(n);
-        } else if (runLen[n] <= runLen[n + 1]) {
-          mergeAt(n);
-        } else {
+        } else if (runLen[n] > runLen[n + 1]) {
           break; // Invariant is established
         }
+        mergeAt(n);
       }
     }
 

core/src/test/java/org/apache/spark/util/collection/TestTimSort.java

@@ -0,0 +1,134 @@
+/**
+ * Copyright 2015 Stijn de Gouw
+ *
+ * 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 org.apache.spark.util.collection;
+
+import java.util.*;
+
+/**
+ * This codes generates a int array which fails the standard TimSort.
+ *
+ * The blog that reported the bug
+ * http://www.envisage-project.eu/timsort-specification-and-verification/
+ *
+ * This codes was originally wrote by Stijn de Gouw, modified by Evan Yu to adapt to
+ * our test suite.
+ *
+ * https://github.com/abstools/java-timsort-bug
+ * https://github.com/abstools/java-timsort-bug/blob/master/LICENSE
+ */
+public class TestTimSort {
+
+  private static final int MIN_MERGE = 32;
+
+  /**
+   * Returns an array of integers that demonstrate the bug in TimSort
+   */
+  public static int[] getTimSortBugTestSet(int length) {
+    int minRun = minRunLength(length);
+    List<Long> runs = runsJDKWorstCase(minRun, length);
+    return createArray(runs, length);
+  }
+
+  private static int minRunLength(int n) {
+    int r = 0; // Becomes 1 if any 1 bits are shifted off
+    while (n >= MIN_MERGE) {
+      r |= (n & 1);
+      n >>= 1;
+    }
+    return n + r;
+  }
+
+  private static int[] createArray(List<Long> runs, int length) {
+    int[] a = new int[length];
+    Arrays.fill(a, 0);
+    int endRun = -1;
+    for (long len : runs) {
+      a[endRun += len] = 1;
+    }
+    a[length - 1] = 0;
+    return a;
+  }
+
+  /**
+   * Fills <code>runs</code> with a sequence of run lengths of the form<br>
+   * Y_n     x_{n,1}   x_{n,2}   ... x_{n,l_n} <br>
+   * Y_{n-1} x_{n-1,1} x_{n-1,2} ... x_{n-1,l_{n-1}} <br>
+   * ... <br>
+   * Y_1     x_{1,1}   x_{1,2}   ... x_{1,l_1}<br>
+   * The Y_i's are chosen to satisfy the invariant throughout execution,
+   * but the x_{i,j}'s are merged (by <code>TimSort.mergeCollapse</code>)
+   * into an X_i that violates the invariant.
+   *
+   * @param length The sum of all run lengths that will be added to <code>runs</code>.
+   */
+  private static List<Long> runsJDKWorstCase(int minRun, int length) {
+    List<Long> runs = new ArrayList<Long>();
+
+    long runningTotal = 0, Y = minRun + 4, X = minRun;
+
+    while (runningTotal + Y + X <= length) {
+      runningTotal += X + Y;
+      generateJDKWrongElem(runs, minRun, X);
+      runs.add(0, Y);
+      // X_{i+1} = Y_i + x_{i,1} + 1, since runs.get(1) = x_{i,1}
+      X = Y + runs.get(1) + 1;
+      // Y_{i+1} = X_{i+1} + Y_i + 1
+      Y += X + 1;
+    }
+
+    if (runningTotal + X <= length) {
+      runningTotal += X;
+      generateJDKWrongElem(runs, minRun, X);
+    }
+
+    runs.add(length - runningTotal);
+    return runs;
+  }
+
+  /**
+   * Adds a sequence x_1, ..., x_n of run lengths to <code>runs</code> such that:<br>
+   * 1. X = x_1 + ... + x_n <br>
+   * 2. x_j >= minRun for all j <br>
+   * 3. x_1 + ... + x_{j-2}  <  x_j  <  x_1 + ... + x_{j-1} for all j <br>
+   * These conditions guarantee that TimSort merges all x_j's one by one
+   * (resulting in X) using only merges on the second-to-last element.
+   *
+   * @param X The sum of the sequence that should be added to runs.
+   */
+  private static void generateJDKWrongElem(List<Long> runs, int minRun, long X) {
+    for (long newTotal; X >= 2 * minRun + 1; X = newTotal) {
+      //Default strategy
+      newTotal = X / 2 + 1;
+      //Specialized strategies
+      if (3 * minRun + 3 <= X && X <= 4 * minRun + 1) {
+        // add x_1=MIN+1, x_2=MIN, x_3=X-newTotal  to runs
+        newTotal = 2 * minRun + 1;
+      } else if (5 * minRun + 5 <= X && X <= 6 * minRun + 5) {
+        // add x_1=MIN+1, x_2=MIN, x_3=MIN+2, x_4=X-newTotal  to runs
+        newTotal = 3 * minRun + 3;
+      } else if (8 * minRun + 9 <= X && X <= 10 * minRun + 9) {
+        // add x_1=MIN+1, x_2=MIN, x_3=MIN+2, x_4=2MIN+2, x_5=X-newTotal  to runs
+        newTotal = 5 * minRun + 5;
+      } else if (13 * minRun + 15 <= X && X <= 16 * minRun + 17) {
+        // add x_1=MIN+1, x_2=MIN, x_3=MIN+2, x_4=2MIN+2, x_5=3MIN+4, x_6=X-newTotal to runs
+        newTotal = 8 * minRun + 9;
+      }
+      runs.add(0, X - newTotal);
+    }
+    runs.add(0, X);
+  }
+}

core/src/test/scala/org/apache/spark/util/collection/SorterSuite.scala

@@ -65,6 +65,13 @@ class SorterSuite extends FunSuite {
     }
   }
 
+  // http://www.envisage-project.eu/timsort-specification-and-verification/
+  test("SPARK-5984 TimSort bug") {
+    val data = TestTimSort.getTimSortBugTestSet(67108864)
+    new Sorter(new IntArraySortDataFormat).sort(data, 0, data.length, Ordering.Int)
+    (0 to data.length - 2).foreach(i => assert(data(i) <= data(i + 1)))
+  }
+
   /** Runs an experiment several times. */
   def runExperiment(name: String, skip: Boolean = false)(f: => Unit, prepare: () => Unit): Unit = {
     if (skip) {