/*

 * Copyright 2009 Google Inc.  All Rights Reserved.

 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

 *

 * This code is free software; you can redistribute it and/or modify it

 * under the terms of the GNU General Public License version 2 only, as

 * published by the Free Software Foundation.  Oracle designates this

 * particular file as subject to the "Classpath" exception as provided

 * by Oracle in the LICENSE file that accompanied this code.

 *

 * This code is distributed in the hope that it will be useful, but WITHOUT

 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

 *

 * You should have received a copy of the GNU General Public License version

 * 2 along with this work; if not, write to the Free Software Foundation,

 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

 *

 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

 * or visit www.oracle.com if you need additional information or have any

 * questions.

 */

package java.util;

/**

 * This is a near duplicate of {@link TimSort}, modified for use with

 * arrays of objects that implement {@link Comparable}, instead of using

 * explicit comparators.

 *

 * <p>If you are using an optimizing VM, you may find that ComparableTimSort

 * offers no performance benefit over TimSort in conjunction with a

 * comparator that simply returns {@code ((Comparable)first).compareTo(Second)}.

 * If this is the case, you are better off deleting ComparableTimSort to

 * eliminate the code duplication.  (See Arrays.java for details.)

 *

 * @author Josh Bloch

 */

class ComparableTimSort {

    /**

     * This is the minimum sized sequence that will be merged.  Shorter

     * sequences will be lengthened by calling binarySort.  If the entire

     * array is less than this length, no merges will be performed.

     *

     * This constant should be a power of two.  It was 64 in Tim Peter's C

     * implementation, but 32 was empirically determined to work better in

     * this implementation.  In the unlikely event that you set this constant

     * to be a number that's not a power of two, you'll need to change the

     * {@link #minRunLength} computation.

     *

     * If you decrease this constant, you must change the stackLen

     * computation in the TimSort constructor, or you risk an

     * ArrayOutOfBounds exception.  See listsort.txt for a discussion

     * of the minimum stack length required as a function of the length

     * of the array being sorted and the minimum merge sequence length.

     */

    private static final int MIN_MERGE = 32;

    /**

     * The array being sorted.

     */

    private final Object[] a;

    /**

     * When we get into galloping mode, we stay there until both runs win less

     * often than MIN_GALLOP consecutive times.

     */

    private static final int  MIN_GALLOP = 7;

    /**

     * This controls when we get *into* galloping mode.  It is initialized

     * to MIN_GALLOP.  The mergeLo and mergeHi methods nudge it higher for

     * random data, and lower for highly structured data.

     */

    private int minGallop = MIN_GALLOP;

    /**

     * Maximum initial size of tmp array, which is used for merging.  The array

     * can grow to accommodate demand.

     *

     * Unlike Tim's original C version, we do not allocate this much storage

     * when sorting smaller arrays.  This change was required for performance.

     */

    private static final int INITIAL_TMP_STORAGE_LENGTH = 256;

    /**

     * Temp storage for merges.

     */

    private Object[] tmp;

    /**

     * A stack of pending runs yet to be merged.  Run i starts at

     * address base[i] and extends for len[i] elements.  It's always

     * true (so long as the indices are in bounds) that:

     *

     *     runBase[i] + runLen[i] == runBase[i + 1]

     *

     * so we could cut the storage for this, but it's a minor amount,

     * and keeping all the info explicit simplifies the code.

     */

    private int stackSize = 0;  // Number of pending runs on stack

    private final int[] runBase;

    private final int[] runLen;

    /**

     * Creates a TimSort instance to maintain the state of an ongoing sort.

     *

     * @param a the array to be sorted

     */

    private ComparableTimSort(Object[] a) {

        this.a = a;

        // Allocate temp storage (which may be increased later if necessary)

        int len = a.length;

        @SuppressWarnings({"unchecked", "UnnecessaryLocalVariable"})

        Object[] newArray = new Object[len < 2 * INITIAL_TMP_STORAGE_LENGTH ?

                                       len >>> 1 : INITIAL_TMP_STORAGE_LENGTH];

        tmp = newArray;

        /*

         * Allocate runs-to-be-merged stack (which cannot be expanded).  The

         * stack length requirements are described in listsort.txt.  The C

         * version always uses the same stack length (85), but this was

         * measured to be too expensive when sorting "mid-sized" arrays (e.g.,

         * 100 elements) in Java.  Therefore, we use smaller (but sufficiently

         * large) stack lengths for smaller arrays.  The "magic numbers" in the

         * computation below must be changed if MIN_MERGE is decreased.  See

         * the MIN_MERGE declaration above for more information.

         */

        int stackLen = (len <    120  ?  5 :

                        len <   1542  ? 10 :

                        len < 119151  ? 19 : 40);

        runBase = new int[stackLen];

        runLen = new int[stackLen];

    }

    /*

     * The next two methods (which are package private and static) constitute

     * the entire API of this class.  Each of these methods obeys the contract

     * of the public method with the same signature in java.util.Arrays.

     */

    static void sort(Object[] a) {

          sort(a, 0, a.length);

    }

    static void sort(Object[] a, int lo, int hi) {

        rangeCheck(a.length, lo, hi);

        int nRemaining  = hi - lo;

        if (nRemaining < 2)

            return;  // Arrays of size 0 and 1 are always sorted

        // If array is small, do a "mini-TimSort" with no merges

        if (nRemaining < MIN_MERGE) {

            int initRunLen = countRunAndMakeAscending(a, lo, hi);

            binarySort(a, lo, hi, lo + initRunLen);

            return;

        }

        /**

         * March over the array once, left to right, finding natural runs,

         * extending short natural runs to minRun elements, and merging runs

         * to maintain stack invariant.

         */

        ComparableTimSort ts = new ComparableTimSort(a);

        int minRun = minRunLength(nRemaining);

        do {

            // Identify next run

            int runLen = countRunAndMakeAscending(a, lo, hi);

            // If run is short, extend to min(minRun, nRemaining)

            if (runLen < minRun) {

                int force = nRemaining <= minRun ? nRemaining : minRun;

                binarySort(a, lo, lo + force, lo + runLen);

                runLen = force;

            }

            // Push run onto pending-run stack, and maybe merge

            ts.pushRun(lo, runLen);

            ts.mergeCollapse();

            // Advance to find next run

            lo += runLen;

            nRemaining -= runLen;

        } while (nRemaining != 0);

        // Merge all remaining runs to complete sort

        assert lo == hi;

        ts.mergeForceCollapse();

        assert ts.stackSize == 1;

    }

    /**

     * Sorts the specified portion of the specified array using a binary

     * insertion sort.  This is the best method for sorting small numbers

     * of elements.  It requires O(n log n) compares, but O(n^2) data

     * movement (worst case).

     *

     * If the initial part of the specified range is already sorted,

     * this method can take advantage of it: the method assumes that the

     * elements from index {@code lo}, inclusive, to {@code start},

     * exclusive are already sorted.

     *

     * @param a the array in which a range is to be sorted

     * @param lo the index of the first element in the range to be sorted

     * @param hi the index after the last element in the range to be sorted

     * @param start the index of the first element in the range that is

     *        not already known to be sorted ({@code lo <= start <= hi})

     */

    @SuppressWarnings("fallthrough")

    private static void binarySort(Object[] a, int lo, int hi, int start) {

        assert lo <= start && start <= hi;

        if (start == lo)

            start++;

        for ( ; start < hi; start++) {

            @SuppressWarnings("unchecked")

            Comparable<Object> pivot = (Comparable) a[start];

            // Set left (and right) to the index where a[start] (pivot) belongs

            int left = lo;

            int right = start;

            assert left <= right;

            /*

             * Invariants:

             *   pivot >= all in [lo, left).

             *   pivot <  all in [right, start).

             */

            while (left < right) {

                int mid = (left + right) >>> 1;

                if (pivot.compareTo(a[mid]) < 0)

                    right = mid;

                else

                    left = mid + 1;

            }

            assert left == right;

            /*

             * The invariants still hold: pivot >= all in [lo, left) and

             * pivot < all in [left, start), so pivot belongs at left.  Note

             * that if there are elements equal to pivot, left points to the

             * first slot after them -- that's why this sort is stable.

             * Slide elements over to make room for pivot.

             */

            int n = start - left;  // The number of elements to move

            // Switch is just an optimization for arraycopy in default case

            switch (n) {

                case 2:  a[left + 2] = a[left + 1];

                case 1:  a[left + 1] = a[left];

                         break;

                default: System.arraycopy(a, left, a, left + 1, n);

            }

            a[left] = pivot;

        }

    }

    /**

     * Returns the length of the run beginning at the specified position in

     * the specified array and reverses the run if it is descending (ensuring

     * that the run will always be ascending when the method returns).

     *

     * A run is the longest ascending sequence with:

     *

     *    a[lo] <= a[lo + 1] <= a[lo + 2] <= ...

     *

     * or the longest descending sequence with:

     *

     *    a[lo] >  a[lo + 1] >  a[lo + 2] >  ...

     *

     * For its intended use in a stable mergesort, the strictness of the

     * definition of "descending" is needed so that the call can safely

     * reverse a descending sequence without violating stability.

     *

     * @param a the array in which a run is to be counted and possibly reversed

     * @param lo index of the first element in the run

     * @param hi index after the last element that may be contained in the run.

              It is required that {@code lo < hi}.

     * @return  the length of the run beginning at the specified position in

     *          the specified array

     */

    @SuppressWarnings("unchecked")

    private static int countRunAndMakeAscending(Object[] a, int lo, int hi) {

        assert lo < hi;

        int runHi = lo + 1;

        if (runHi == hi)

            return 1;

        // Find end of run, and reverse range if descending

        if (((Comparable) a[runHi++]).compareTo(a[lo]) < 0) { // Descending

            while (runHi < hi && ((Comparable) a[runHi]).compareTo(a[runHi - 1]) < 0)

                runHi++;

            reverseRange(a, lo, runHi);

        } else {                              // Ascending

            while (runHi < hi && ((Comparable) a[runHi]).compareTo(a[runHi - 1]) >= 0)

                runHi++;

        }

        return runHi - lo;

    }

    /**

     * Reverse the specified range of the specified array.

     *

     * @param a the array in which a range is to be reversed

     * @param lo the index of the first element in the range to be reversed

     * @param hi the index after the last element in the range to be reversed

     */

    private static void reverseRange(Object[] a, int lo, int hi) {

        hi--;

        while (lo < hi) {

            Object t = a[lo];

            a[lo++] = a[hi];

            a[hi--] = t;

        }

    }

    /**

     * Returns the minimum acceptable run length for an array of the specified

     * length. Natural runs shorter than this will be extended with

     * {@link #binarySort}.

     *

     * Roughly speaking, the computation is:

     *

     *  If n < MIN_MERGE, return n (it's too small to bother with fancy stuff).

     *  Else if n is an exact power of 2, return MIN_MERGE/2.

     *  Else return an int k, MIN_MERGE/2 <= k <= MIN_MERGE, such that n/k

     *   is close to, but strictly less than, an exact power of 2.

     *

     * For the rationale, see listsort.txt.

     *

     * @param n the length of the array to be sorted

     * @return the length of the minimum run to be merged

     */

    private static int minRunLength(int n) {

        assert n >= 0;

        int r = 0;      // Becomes 1 if any 1 bits are shifted off

        while (n >= MIN_MERGE) {

            r |= (n & 1);

            n >>= 1;

        }

        return n + r;

    }

    /**

     * Pushes the specified run onto the pending-run stack.

     *

     * @param runBase index of the first element in the run

     * @param runLen  the number of elements in the run

     */

    private void pushRun(int runBase, int runLen) {

        this.runBase[stackSize] = runBase;

        this.runLen[stackSize] = runLen;

        stackSize++;

    }

    /**

     * Examines the stack of runs waiting to be merged and merges adjacent runs

     * until the stack invariants are reestablished:

     *

     *     1. runLen[i - 3] > runLen[i - 2] + runLen[i - 1]

     *     2. runLen[i - 2] > runLen[i - 1]

     *

     * This method is called each time a new run is pushed onto the stack,

     * so the invariants are guaranteed to hold for i < stackSize upon

     * entry to the method.

     */

    private void mergeCollapse() {

        while (stackSize > 1) {

            int n = stackSize - 2;

            if (n > 0 && runLen[n-1] <= 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 {

                break; // Invariant is established

            }

        }

    }

    /**

     * Merges all runs on the stack until only one remains.  This method is

     * called once, to complete the sort.

     */

    private void mergeForceCollapse() {

        while (stackSize > 1) {

            int n = stackSize - 2;

            if (n > 0 && runLen[n - 1] < runLen[n + 1])

                n--;

            mergeAt(n);

        }

    }

    /**

     * Merges the two runs at stack indices i and i+1.  Run i must be

     * the penultimate or antepenultimate run on the stack.  In other words,

     * i must be equal to stackSize-2 or stackSize-3.

     *

     * @param i stack index of the first of the two runs to merge

     */

    @SuppressWarnings("unchecked")

    private void mergeAt(int i) {

        assert stackSize >= 2;

        assert i >= 0;

        assert i == stackSize - 2 || i == stackSize - 3;

        int base1 = runBase[i];

        int len1 = runLen[i];

        int base2 = runBase[i + 1];

        int len2 = runLen[i + 1];

        assert len1 > 0 && len2 > 0;

        assert base1 + len1 == base2;

        /*

         * Record the length of the combined runs; if i is the 3rd-last

         * run now, also slide over the last run (which isn't involved

         * in this merge).  The current run (i+1) goes away in any case.

         */

        runLen[i] = len1 + len2;

        if (i == stackSize - 3) {

            runBase[i + 1] = runBase[i + 2];

            runLen[i + 1] = runLen[i + 2];

        }

        stackSize--;

        /*

         * Find where the first element of run2 goes in run1. Prior elements

         * in run1 can be ignored (because they're already in place).

         */

        int k = gallopRight((Comparable<Object>) a[base2], a, base1, len1, 0);

        assert k >= 0;

        base1 += k;

        len1 -= k;

        if (len1 == 0)

            return;

        /*

         * Find where the last element of run1 goes in run2. Subsequent elements

         * in run2 can be ignored (because they're already in place).

         */

        len2 = gallopLeft((Comparable<Object>) a[base1 + len1 - 1], a,

                base2, len2, len2 - 1);

        assert len2 >= 0;

        if (len2 == 0)

            return;

        // Merge remaining runs, using tmp array with min(len1, len2) elements

        if (len1 <= len2)

            mergeLo(base1, len1, base2, len2);

        else

            mergeHi(base1, len1, base2, len2);

    }

    /**

     * Locates the position at which to insert the specified key into the

     * specified sorted range; if the range contains an element equal to key,

     * returns the index of the leftmost equal element.

     *

     * @param key the key whose insertion point to search for

     * @param a the array in which to search

     * @param base the index of the first element in the range

     * @param len the length of the range; must be > 0

     * @param hint the index at which to begin the search, 0 <= hint < n.

     *     The closer hint is to the result, the faster this method will run.

     * @return the int k,  0 <= k <= n such that a[b + k - 1] < key <= a[b + k],

     *    pretending that a[b - 1] is minus infinity and a[b + n] is infinity.

     *    In other words, key belongs at index b + k; or in other words,

     *    the first k elements of a should precede key, and the last n - k

     *    should follow it.

     */

    private static int gallopLeft(Comparable<Object> key, Object[] a,

            int base, int len, int hint) {

        assert len > 0 && hint >= 0 && hint < len;

        int lastOfs = 0;

        int ofs = 1;

        if (key.compareTo(a[base + hint]) > 0) {

            // Gallop right until a[base+hint+lastOfs] < key <= a[base+hint+ofs]

            int maxOfs = len - hint;

            while (ofs < maxOfs && key.compareTo(a[base + hint + ofs]) > 0) {

                lastOfs = ofs;

                ofs = (ofs << 1) + 1;

                if (ofs <= 0)   // int overflow

                    ofs = maxOfs;

            }

            if (ofs > maxOfs)

                ofs = maxOfs;

            // Make offsets relative to base

            lastOfs += hint;

            ofs += hint;

        } else { // key <= a[base + hint]

            // Gallop left until a[base+hint-ofs] < key <= a[base+hint-lastOfs]

            final int maxOfs = hint + 1;

            while (ofs < maxOfs && key.compareTo(a[base + hint - ofs]) <= 0) {

                lastOfs = ofs;

                ofs = (ofs << 1) + 1;

                if (ofs <= 0)   // int overflow

                    ofs = maxOfs;

            }

            if (ofs > maxOfs)

                ofs = maxOfs;

            // Make offsets relative to base

            int tmp = lastOfs;

            lastOfs = hint - ofs;

            ofs = hint - tmp;

        }

        assert -1 <= lastOfs && lastOfs < ofs && ofs <= len;

        /*

         * Now a[base+lastOfs] < key <= a[base+ofs], so key belongs somewhere

         * to the right of lastOfs but no farther right than ofs.  Do a binary

         * search, with invariant a[base + lastOfs - 1] < key <= a[base + ofs].

         */

        lastOfs++;

        while (lastOfs < ofs) {

            int m = lastOfs + ((ofs - lastOfs) >>> 1);

            if (key.compareTo(a[base + m]) > 0)

                lastOfs = m + 1;  // a[base + m] < key

            else

                ofs = m;          // key <= a[base + m]

        }

        assert lastOfs == ofs;    // so a[base + ofs - 1] < key <= a[base + ofs]

        return ofs;

    }

    /**

     * Like gallopLeft, except that if the range contains an element equal to

     * key, gallopRight returns the index after the rightmost equal element.

     *

     * @param key the key whose insertion point to search for

     * @param a the array in which to search

     * @param base the index of the first element in the range

     * @param len the length of the range; must be > 0

     * @param hint the index at which to begin the search, 0 <= hint < n.

     *     The closer hint is to the result, the faster this method will run.

     * @return the int k,  0 <= k <= n such that a[b + k - 1] <= key < a[b + k]

     */

    private static int gallopRight(Comparable<Object> key, Object[] a,

            int base, int len, int hint) {

        assert len > 0 && hint >= 0 && hint < len;

        int ofs = 1;

        int lastOfs = 0;

        if (key.compareTo(a[base + hint]) < 0) {

            // Gallop left until a[b+hint - ofs] <= key < a[b+hint - lastOfs]

            int maxOfs = hint + 1;

            while (ofs < maxOfs && key.compareTo(a[base + hint - ofs]) < 0) {

                lastOfs = ofs;

                ofs = (ofs << 1) + 1;

                if (ofs <= 0)   // int overflow

                    ofs = maxOfs;

            }

            if (ofs > maxOfs)

                ofs = maxOfs;

            // Make offsets relative to b

            int tmp = lastOfs;

            lastOfs = hint - ofs;

            ofs = hint - tmp;

        } else { // a[b + hint] <= key

            // Gallop right until a[b+hint + lastOfs] <= key < a[b+hint + ofs]

            int maxOfs = len - hint;

            while (ofs < maxOfs && key.compareTo(a[base + hint + ofs]) >= 0) {

                lastOfs = ofs;

                ofs = (ofs << 1) + 1;

                if (ofs <= 0)   // int overflow

                    ofs = maxOfs;

            }

            if (ofs > maxOfs)

                ofs = maxOfs;

            // Make offsets relative to b

            lastOfs += hint;

            ofs += hint;

        }

        assert -1 <= lastOfs && lastOfs < ofs && ofs <= len;

        /*

         * Now a[b + lastOfs] <= key < a[b + ofs], so key belongs somewhere to

         * the right of lastOfs but no farther right than ofs.  Do a binary

         * search, with invariant a[b + lastOfs - 1] <= key < a[b + ofs].

         */

        lastOfs++;

        while (lastOfs < ofs) {

            int m = lastOfs + ((ofs - lastOfs) >>> 1);

            if (key.compareTo(a[base + m]) < 0)

                ofs = m;          // key < a[b + m]

            else

                lastOfs = m + 1;  // a[b + m] <= key

        }

        assert lastOfs == ofs;    // so a[b + ofs - 1] <= key < a[b + ofs]

        return ofs;

    }

    /**

     * Merges two adjacent runs in place, in a stable fashion.  The first

     * element of the first run must be greater than the first element of the

     * second run (a[base1] > a[base2]), and the last element of the first run

     * (a[base1 + len1-1]) must be greater than all elements of the second run.

     *

     * For performance, this method should be called only when len1 <= len2;

     * its twin, mergeHi should be called if len1 >= len2.  (Either method

     * may be called if len1 == len2.)

     *

     * @param base1 index of first element in first run to be merged

     * @param len1  length of first run to be merged (must be > 0)

     * @param base2 index of first element in second run to be merged

     *        (must be aBase + aLen)

     * @param len2  length of second run to be merged (must be > 0)

     */

    @SuppressWarnings("unchecked")

    private void mergeLo(int base1, int len1, int base2, int len2) {

        assert len1 > 0 && len2 > 0 && base1 + len1 == base2;

        // Copy first run into temp array

        Object[] a = this.a; // For performance

        Object[] tmp = ensureCapacity(len1);

        System.arraycopy(a, base1, tmp, 0, len1);

        int cursor1 = 0;       // Indexes into tmp array

        int cursor2 = base2;   // Indexes int a

        int dest = base1;      // Indexes int a

        // Move first element of second run and deal with degenerate cases

        a[dest++] = a[cursor2++];

        if (--len2 == 0) {

            System.arraycopy(tmp, cursor1, a, dest, len1);

            return;

        }

        if (len1 == 1) {

            System.arraycopy(a, cursor2, a, dest, len2);

            a[dest + len2] = tmp[cursor1]; // Last elt of run 1 to end of merge

            return;

        }

        int minGallop = this.minGallop;  // Use local variable for performance

    outer:

        while (true) {

            int count1 = 0; // Number of times in a row that first run won

            int count2 = 0; // Number of times in a row that second run won

            /*

             * Do the straightforward thing until (if ever) one run starts

             * winning consistently.

             */

            do {

                assert len1 > 1 && len2 > 0;

                if (((Comparable) a[cursor2]).compareTo(tmp[cursor1]) < 0) {

                    a[dest++] = a[cursor2++];

                    count2++;

                    count1 = 0;

                    if (--len2 == 0)

                        break outer;

                } else {

                    a[dest++] = tmp[cursor1++];

                    count1++;

                    count2 = 0;

                    if (--len1 == 1)

                        break outer;

                }

            } while ((count1 | count2) < minGallop);

            /*

             * One run is winning so consistently that galloping may be a

             * huge win. So try that, and continue galloping until (if ever)

             * neither run appears to be winning consistently anymore.

             */

            do {

                assert len1 > 1 && len2 > 0;

                count1 = gallopRight((Comparable) a[cursor2], tmp, cursor1, len1, 0);

                if (count1 != 0) {

                    System.arraycopy(tmp, cursor1, a, dest, count1);

                    dest += count1;

                    cursor1 += count1;

                    len1 -= count1;

                    if (len1 <= 1)  // len1 == 1 || len1 == 0

                        break outer;

                }

                a[dest++] = a[cursor2++];

                if (--len2 == 0)

                    break outer;

                count2 = gallopLeft((Comparable) tmp[cursor1], a, cursor2, len2, 0);

                if (count2 != 0) {

                    System.arraycopy(a, cursor2, a, dest, count2);

                    dest += count2;

                    cursor2 += count2;

                    len2 -= count2;

                    if (len2 == 0)

                        break outer;

                }

                a[dest++] = tmp[cursor1++];

                if (--len1 == 1)

                    break outer;

                minGallop--;

            } while (count1 >= MIN_GALLOP | count2 >= MIN_GALLOP);

            if (minGallop < 0)

                minGallop = 0;

            minGallop += 2;  // Penalize for leaving gallop mode

        }  // End of "outer" loop

        this.minGallop = minGallop < 1 ? 1 : minGallop;  // Write back to field

        if (len1 == 1) {

            assert len2 > 0;

            System.arraycopy(a, cursor2, a, dest, len2);

            a[dest + len2] = tmp[cursor1]; //  Last elt of run 1 to end of merge

        } else if (len1 == 0) {

            throw new IllegalArgumentException(

                "Comparison method violates its general contract!");

        } else {

            assert len2 == 0;

            assert len1 > 1;

            System.arraycopy(tmp, cursor1, a, dest, len1);

        }

    }

    /**

     * Like mergeLo, except that this method should be called only if

     * len1 >= len2; mergeLo should be called if len1 <= len2.  (Either method

     * may be called if len1 == len2.)

     *

     * @param base1 index of first element in first run to be merged

     * @param len1  length of first run to be merged (must be > 0)

     * @param base2 index of first element in second run to be merged

     *        (must be aBase + aLen)

     * @param len2  length of second run to be merged (must be > 0)

     */

    @SuppressWarnings("unchecked")

    private void mergeHi(int base1, int len1, int base2, int len2) {

        assert len1 > 0 && len2 > 0 && base1 + len1 == base2;

        // Copy second run into temp array

        Object[] a = this.a; // For performance

        Object[] tmp = ensureCapacity(len2);

        System.arraycopy(a, base2, tmp, 0, len2);

        int cursor1 = base1 + len1 - 1;  // Indexes into a

        int cursor2 = len2 - 1;          // Indexes into tmp array

        int dest = base2 + len2 - 1;     // Indexes into a

        // Move last element of first run and deal with degenerate cases

        a[dest--] = a[cursor1--];

        if (--len1 == 0) {

            System.arraycopy(tmp, 0, a, dest - (len2 - 1), len2);

            return;

        }

        if (len2 == 1) {

            dest -= len1;

            cursor1 -= len1;

            System.arraycopy(a, cursor1 + 1, a, dest + 1, len1);

            a[dest] = tmp[cursor2];

            return;

        }

        int minGallop = this.minGallop;  // Use local variable for performance

    outer:

        while (true) {

            int count1 = 0; // Number of times in a row that first run won

            int count2 = 0; // Number of times in a row that second run won

            /*

             * Do the straightforward thing until (if ever) one run

             * appears to win consistently.

             */

            do {

                assert len1 > 0 && len2 > 1;

                if (((Comparable) tmp[cursor2]).compareTo(a[cursor1]) < 0) {

                    a[dest--] = a[cursor1--];

                    count1++;

                    count2 = 0;

                    if (--len1 == 0)

                        break outer;

                } else {

                    a[dest--] = tmp[cursor2--];

                    count2++;

                    count1 = 0;

                    if (--len2 == 1)

                        break outer;

                }

            } while ((count1 | count2) < minGallop);

            /*

             * One run is winning so consistently that galloping may be a

             * huge win. So try that, and continue galloping until (if ever)

             * neither run appears to be winning consistently anymore.

             */

            do {

                assert len1 > 0 && len2 > 1;

                count1 = len1 - gallopRight((Comparable) tmp[cursor2], a, base1, len1, len1 - 1);

                if (count1 != 0) {

                    dest -= count1;

                    cursor1 -= count1;

                    len1 -= count1;

                    System.arraycopy(a, cursor1 + 1, a, dest + 1, count1);

                    if (len1 == 0)

                        break outer;

                }

                a[dest--] = tmp[cursor2--];

                if (--len2 == 1)

                    break outer;

                count2 = len2 - gallopLeft((Comparable) a[cursor1], tmp, 0, len2, len2 - 1);

                if (count2 != 0) {

                    dest -= count2;

                    cursor2 -= count2;

                    len2 -= count2;

                    System.arraycopy(tmp, cursor2 + 1, a, dest + 1, count2);

                    if (len2 <= 1)

                        break outer; // len2 == 1 || len2 == 0

                }

                a[dest--] = a[cursor1--];

                if (--len1 == 0)

                    break outer;

                minGallop--;

            } while (count1 >= MIN_GALLOP | count2 >= MIN_GALLOP);

            if (minGallop < 0)

                minGallop = 0;

            minGallop += 2;  // Penalize for leaving gallop mode

        }  // End of "outer" loop

        this.minGallop = minGallop < 1 ? 1 : minGallop;  // Write back to field

        if (len2 == 1) {

            assert len1 > 0;

            dest -= len1;

            cursor1 -= len1;

            System.arraycopy(a, cursor1 + 1, a, dest + 1, len1);

            a[dest] = tmp[cursor2];  // Move first elt of run2 to front of merge

        } else if (len2 == 0) {

            throw new IllegalArgumentException(

                "Comparison method violates its general contract!");

        } else {

            assert len1 == 0;

            assert len2 > 0;

            System.arraycopy(tmp, 0, a, dest - (len2 - 1), len2);

        }

    }

    /**

     * Ensures that the external array tmp has at least the specified

     * number of elements, increasing its size if necessary.  The size

     * increases exponentially to ensure amortized linear time complexity.

     *

     * @param minCapacity the minimum required capacity of the tmp array

     * @return tmp, whether or not it grew

     */

    private Object[]  ensureCapacity(int minCapacity) {

        if (tmp.length < minCapacity) {

            // Compute smallest power of 2 > minCapacity

            int newSize = minCapacity;

            newSize |= newSize >> 1;

            newSize |= newSize >> 2;

            newSize |= newSize >> 4;

            newSize |= newSize >> 8;

            newSize |= newSize >> 16;

            newSize++;

            if (newSize < 0) // Not bloody likely!

                newSize = minCapacity;

            else

                newSize = Math.min(newSize, a.length >>> 1);

            @SuppressWarnings({"unchecked", "UnnecessaryLocalVariable"})

            Object[] newArray = new Object[newSize];

            tmp = newArray;

        }

        return tmp;

    }

    /**

     * Checks that fromIndex and toIndex are in range, and throws an

     * appropriate exception if they aren't.

     *

     * @param arrayLen the length of the array

     * @param fromIndex the index of the first element of the range

     * @param toIndex the index after the last element of the range

     * @throws IllegalArgumentException if fromIndex > toIndex

     * @throws ArrayIndexOutOfBoundsException if fromIndex < 0

     *         or toIndex > arrayLen

     */

    private static void rangeCheck(int arrayLen, int fromIndex, int toIndex) {

        if (fromIndex > toIndex)

            throw new IllegalArgumentException("fromIndex(" + fromIndex +

                       ") > toIndex(" + toIndex+")");

        if (fromIndex < 0)

            throw new ArrayIndexOutOfBoundsException(fromIndex);

        if (toIndex > arrayLen)

            throw new ArrayIndexOutOfBoundsException(toIndex);

    }

}