Replace Arrays.sort() with an efficient sort algorithm

This change reuses the existing insertion sort (which was previously what
Arrays.sort() executed) in a full intro sort pipeline.

The implementation is based on the Musser paper on intro sort (Musser,
David R. "Introspective sorting and selection algorithms." Softw., Pract.
Exper. 27.8 (1997): 983-993.) and Wikipedia's current description of the
heap sort: http://en.wikipedia.org/wiki/Heapsort.

Signed-off-by: Johannes Schindelin <johannes.schindelin@gmx.de>

classpath/java/util/Arrays.java

@@ -148,8 +148,100 @@ public class Arrays {
       });
   }
 
+  private final static int SORT_SIZE_THRESHOLD = 16;
+
   public static <T> void sort(T[] array, Comparator<? super T> comparator) {
-    // insertion sort
+    introSort(array, comparator, 0, array.length, array.length);
+    insertionSort(array, comparator);
+  }
+
+  private static <T > void introSort(T[] array,
+    Comparator<? super T> comparator, int begin, int end, int limit)
+  {
+    while (end - begin > SORT_SIZE_THRESHOLD) {
+      if (limit == 0) {
+        heapSort(array, comparator, begin, end);
+        return;
+      }
+      limit >>= 1;
+
+      // median of three
+      T a = array[begin];
+      T b = array[begin + (end - begin) / 2 + 1];
+      T c = array[end - 1];
+      T median;
+      if (comparator.compare(a, b) < 0) {
+        median = comparator.compare(b, c) < 0 ?
+          b : (comparator.compare(a, c) < 0 ? c : a);
+      } else {
+        median = comparator.compare(b, c) > 0 ?
+          b : (comparator.compare(a, c) > 0 ? c : a);
+      }
+
+      // partition
+      int pivot, i = begin, j = end;
+      for (;;) {
+        while (comparator.compare(array[i], median) < 0) {
+          ++i;
+        }
+        --j;
+        while (comparator.compare(median, array[j]) < 0) {
+          --j;
+        }
+        if (i >= j) {
+          pivot = i;
+          break;
+        }
+        T swap = array[i];
+        array[i] = array[j];
+        array[j] = swap;
+        ++i;
+      }
+
+      introSort(array, comparator, pivot, end, limit);
+      end = pivot;
+    }
+  }
+
+  private static <T> void heapSort(T[] array, Comparator<? super T> comparator,
+    int begin, int end)
+  {
+    int count = end - begin;
+    for (int i = count / 2 - 1; i >= 0; --i) {
+      siftDown(array, comparator, i, count, begin);
+    }
+    for (int i = count - 1; i > 0; --i) {
+      // swap begin and begin + i
+      T swap = array[begin + i];
+      array[begin + i] = array[begin];
+      array[begin] = swap;
+
+      siftDown(array, comparator, 0, i, begin);
+    }
+  }
+
+  private static <T> void siftDown(T[] array, Comparator<? super T> comparator,
+    int i, int count, int offset)
+  {
+    T value = array[offset + i];
+    while (i < count / 2) {
+      int child = 2 * i + 1;
+      if (child + 1 < count &&
+          comparator.compare(array[child], array[child + 1]) < 0) {
+        ++child;
+      }
+      if (comparator.compare(value, array[child]) >= 0) {
+        break;
+      }
+      array[offset + i] = array[offset + child];
+      i = child;
+    }
+    array[offset + i] = value;
+  }
+
+  private static <T> void insertionSort(T[] array,
+    Comparator<? super T> comparator)
+  {
     for (int j = 1; j < array.length; ++j) {
       T t = array[j];
       int i = j - 1;

test/Arrays.java

@@ -3,6 +3,41 @@ public class Arrays {
     if (! v) throw new RuntimeException();
   }
 
+  private static <T extends Comparable<T>> void expectSorted(T[] array) {
+    for (int i = 1; i < array.length; ++i) {
+      expect(array[i - 1].compareTo(array[i]) <= 0);
+    }
+  }
+
+  private static int pseudoRandom(int seed) {
+    return 3170425 * seed + 132102;
+  }
+
+  private static <T extends Comparable<T>> int shuffle(T[] array, int seed) {
+    for (int i = array.length; i > 1; --i) {
+      int i2 = (seed < 0 ? -seed : seed) % i;
+      T value = array[i - 1];
+      array[i - 1] = array[i2];
+      array[i2] = value;
+      seed = pseudoRandom(seed);
+    }
+    return seed;
+  }
+
+  public static void testSort() {
+    Integer[] array = new Integer[64];
+    for (int i = 0; i < array.length; ++i) {
+      array[i] = Integer.valueOf(i + 1);
+    }
+    ;
+    int random = 12345;
+    for (int i = 0; i < 32; ++i) {
+      random = shuffle(array, random);
+      java.util.Arrays.sort(array);
+      expectSorted(array);
+    }
+  }
+
   public static void main(String[] args) {
     { int[] array = new int[0];
       Exception exception = null;
@@ -94,5 +129,7 @@ public class Arrays {
       java.util.Arrays.hashCode(a);
       java.util.Arrays.hashCode((Object[])null);
     }
+
+    testSort();
   }
 }