emul/compact/src/main/java/java/util/TimSort.java
branchmodel
changeset 878 ecbd252fd3a7
parent 877 3392f250c784
parent 871 6168fb585ab4
child 879 af170d42b5b3
     1.1 --- a/emul/compact/src/main/java/java/util/TimSort.java	Fri Mar 22 16:59:47 2013 +0100
     1.2 +++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.3 @@ -1,929 +0,0 @@
     1.4 -/*
     1.5 - * Copyright 2009 Google Inc.  All Rights Reserved.
     1.6 - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
     1.7 - *
     1.8 - * This code is free software; you can redistribute it and/or modify it
     1.9 - * under the terms of the GNU General Public License version 2 only, as
    1.10 - * published by the Free Software Foundation.  Oracle designates this
    1.11 - * particular file as subject to the "Classpath" exception as provided
    1.12 - * by Oracle in the LICENSE file that accompanied this code.
    1.13 - *
    1.14 - * This code is distributed in the hope that it will be useful, but WITHOUT
    1.15 - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    1.16 - * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    1.17 - * version 2 for more details (a copy is included in the LICENSE file that
    1.18 - * accompanied this code).
    1.19 - *
    1.20 - * You should have received a copy of the GNU General Public License version
    1.21 - * 2 along with this work; if not, write to the Free Software Foundation,
    1.22 - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
    1.23 - *
    1.24 - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
    1.25 - * or visit www.oracle.com if you need additional information or have any
    1.26 - * questions.
    1.27 - */
    1.28 -
    1.29 -package java.util;
    1.30 -
    1.31 -
    1.32 -/**
    1.33 - * A stable, adaptive, iterative mergesort that requires far fewer than
    1.34 - * n lg(n) comparisons when running on partially sorted arrays, while
    1.35 - * offering performance comparable to a traditional mergesort when run
    1.36 - * on random arrays.  Like all proper mergesorts, this sort is stable and
    1.37 - * runs O(n log n) time (worst case).  In the worst case, this sort requires
    1.38 - * temporary storage space for n/2 object references; in the best case,
    1.39 - * it requires only a small constant amount of space.
    1.40 - *
    1.41 - * This implementation was adapted from Tim Peters's list sort for
    1.42 - * Python, which is described in detail here:
    1.43 - *
    1.44 - *   http://svn.python.org/projects/python/trunk/Objects/listsort.txt
    1.45 - *
    1.46 - * Tim's C code may be found here:
    1.47 - *
    1.48 - *   http://svn.python.org/projects/python/trunk/Objects/listobject.c
    1.49 - *
    1.50 - * The underlying techniques are described in this paper (and may have
    1.51 - * even earlier origins):
    1.52 - *
    1.53 - *  "Optimistic Sorting and Information Theoretic Complexity"
    1.54 - *  Peter McIlroy
    1.55 - *  SODA (Fourth Annual ACM-SIAM Symposium on Discrete Algorithms),
    1.56 - *  pp 467-474, Austin, Texas, 25-27 January 1993.
    1.57 - *
    1.58 - * While the API to this class consists solely of static methods, it is
    1.59 - * (privately) instantiable; a TimSort instance holds the state of an ongoing
    1.60 - * sort, assuming the input array is large enough to warrant the full-blown
    1.61 - * TimSort. Small arrays are sorted in place, using a binary insertion sort.
    1.62 - *
    1.63 - * @author Josh Bloch
    1.64 - */
    1.65 -class TimSort<T> {
    1.66 -    /**
    1.67 -     * This is the minimum sized sequence that will be merged.  Shorter
    1.68 -     * sequences will be lengthened by calling binarySort.  If the entire
    1.69 -     * array is less than this length, no merges will be performed.
    1.70 -     *
    1.71 -     * This constant should be a power of two.  It was 64 in Tim Peter's C
    1.72 -     * implementation, but 32 was empirically determined to work better in
    1.73 -     * this implementation.  In the unlikely event that you set this constant
    1.74 -     * to be a number that's not a power of two, you'll need to change the
    1.75 -     * {@link #minRunLength} computation.
    1.76 -     *
    1.77 -     * If you decrease this constant, you must change the stackLen
    1.78 -     * computation in the TimSort constructor, or you risk an
    1.79 -     * ArrayOutOfBounds exception.  See listsort.txt for a discussion
    1.80 -     * of the minimum stack length required as a function of the length
    1.81 -     * of the array being sorted and the minimum merge sequence length.
    1.82 -     */
    1.83 -    private static final int MIN_MERGE = 32;
    1.84 -
    1.85 -    /**
    1.86 -     * The array being sorted.
    1.87 -     */
    1.88 -    private final T[] a;
    1.89 -
    1.90 -    /**
    1.91 -     * The comparator for this sort.
    1.92 -     */
    1.93 -    private final Comparator<? super T> c;
    1.94 -
    1.95 -    /**
    1.96 -     * When we get into galloping mode, we stay there until both runs win less
    1.97 -     * often than MIN_GALLOP consecutive times.
    1.98 -     */
    1.99 -    private static final int  MIN_GALLOP = 7;
   1.100 -
   1.101 -    /**
   1.102 -     * This controls when we get *into* galloping mode.  It is initialized
   1.103 -     * to MIN_GALLOP.  The mergeLo and mergeHi methods nudge it higher for
   1.104 -     * random data, and lower for highly structured data.
   1.105 -     */
   1.106 -    private int minGallop = MIN_GALLOP;
   1.107 -
   1.108 -    /**
   1.109 -     * Maximum initial size of tmp array, which is used for merging.  The array
   1.110 -     * can grow to accommodate demand.
   1.111 -     *
   1.112 -     * Unlike Tim's original C version, we do not allocate this much storage
   1.113 -     * when sorting smaller arrays.  This change was required for performance.
   1.114 -     */
   1.115 -    private static final int INITIAL_TMP_STORAGE_LENGTH = 256;
   1.116 -
   1.117 -    /**
   1.118 -     * Temp storage for merges.
   1.119 -     */
   1.120 -    private T[] tmp; // Actual runtime type will be Object[], regardless of T
   1.121 -
   1.122 -    /**
   1.123 -     * A stack of pending runs yet to be merged.  Run i starts at
   1.124 -     * address base[i] and extends for len[i] elements.  It's always
   1.125 -     * true (so long as the indices are in bounds) that:
   1.126 -     *
   1.127 -     *     runBase[i] + runLen[i] == runBase[i + 1]
   1.128 -     *
   1.129 -     * so we could cut the storage for this, but it's a minor amount,
   1.130 -     * and keeping all the info explicit simplifies the code.
   1.131 -     */
   1.132 -    private int stackSize = 0;  // Number of pending runs on stack
   1.133 -    private final int[] runBase;
   1.134 -    private final int[] runLen;
   1.135 -
   1.136 -    /**
   1.137 -     * Creates a TimSort instance to maintain the state of an ongoing sort.
   1.138 -     *
   1.139 -     * @param a the array to be sorted
   1.140 -     * @param c the comparator to determine the order of the sort
   1.141 -     */
   1.142 -    private TimSort(T[] a, Comparator<? super T> c) {
   1.143 -        this.a = a;
   1.144 -        this.c = c;
   1.145 -
   1.146 -        // Allocate temp storage (which may be increased later if necessary)
   1.147 -        int len = a.length;
   1.148 -        @SuppressWarnings({"unchecked", "UnnecessaryLocalVariable"})
   1.149 -        T[] newArray = (T[]) new Object[len < 2 * INITIAL_TMP_STORAGE_LENGTH ?
   1.150 -                                        len >>> 1 : INITIAL_TMP_STORAGE_LENGTH];
   1.151 -        tmp = newArray;
   1.152 -
   1.153 -        /*
   1.154 -         * Allocate runs-to-be-merged stack (which cannot be expanded).  The
   1.155 -         * stack length requirements are described in listsort.txt.  The C
   1.156 -         * version always uses the same stack length (85), but this was
   1.157 -         * measured to be too expensive when sorting "mid-sized" arrays (e.g.,
   1.158 -         * 100 elements) in Java.  Therefore, we use smaller (but sufficiently
   1.159 -         * large) stack lengths for smaller arrays.  The "magic numbers" in the
   1.160 -         * computation below must be changed if MIN_MERGE is decreased.  See
   1.161 -         * the MIN_MERGE declaration above for more information.
   1.162 -         */
   1.163 -        int stackLen = (len <    120  ?  5 :
   1.164 -                        len <   1542  ? 10 :
   1.165 -                        len < 119151  ? 19 : 40);
   1.166 -        runBase = new int[stackLen];
   1.167 -        runLen = new int[stackLen];
   1.168 -    }
   1.169 -
   1.170 -    /*
   1.171 -     * The next two methods (which are package private and static) constitute
   1.172 -     * the entire API of this class.  Each of these methods obeys the contract
   1.173 -     * of the public method with the same signature in java.util.Arrays.
   1.174 -     */
   1.175 -
   1.176 -    static <T> void sort(T[] a, Comparator<? super T> c) {
   1.177 -        sort(a, 0, a.length, c);
   1.178 -    }
   1.179 -
   1.180 -    static <T> void sort(T[] a, int lo, int hi, Comparator<? super T> c) {
   1.181 -        if (c == null) {
   1.182 -            Arrays.sort(a, lo, hi);
   1.183 -            return;
   1.184 -        }
   1.185 -
   1.186 -        rangeCheck(a.length, lo, hi);
   1.187 -        int nRemaining  = hi - lo;
   1.188 -        if (nRemaining < 2)
   1.189 -            return;  // Arrays of size 0 and 1 are always sorted
   1.190 -
   1.191 -        // If array is small, do a "mini-TimSort" with no merges
   1.192 -        if (nRemaining < MIN_MERGE) {
   1.193 -            int initRunLen = countRunAndMakeAscending(a, lo, hi, c);
   1.194 -            binarySort(a, lo, hi, lo + initRunLen, c);
   1.195 -            return;
   1.196 -        }
   1.197 -
   1.198 -        /**
   1.199 -         * March over the array once, left to right, finding natural runs,
   1.200 -         * extending short natural runs to minRun elements, and merging runs
   1.201 -         * to maintain stack invariant.
   1.202 -         */
   1.203 -        TimSort<T> ts = new TimSort<>(a, c);
   1.204 -        int minRun = minRunLength(nRemaining);
   1.205 -        do {
   1.206 -            // Identify next run
   1.207 -            int runLen = countRunAndMakeAscending(a, lo, hi, c);
   1.208 -
   1.209 -            // If run is short, extend to min(minRun, nRemaining)
   1.210 -            if (runLen < minRun) {
   1.211 -                int force = nRemaining <= minRun ? nRemaining : minRun;
   1.212 -                binarySort(a, lo, lo + force, lo + runLen, c);
   1.213 -                runLen = force;
   1.214 -            }
   1.215 -
   1.216 -            // Push run onto pending-run stack, and maybe merge
   1.217 -            ts.pushRun(lo, runLen);
   1.218 -            ts.mergeCollapse();
   1.219 -
   1.220 -            // Advance to find next run
   1.221 -            lo += runLen;
   1.222 -            nRemaining -= runLen;
   1.223 -        } while (nRemaining != 0);
   1.224 -
   1.225 -        // Merge all remaining runs to complete sort
   1.226 -        assert lo == hi;
   1.227 -        ts.mergeForceCollapse();
   1.228 -        assert ts.stackSize == 1;
   1.229 -    }
   1.230 -
   1.231 -    /**
   1.232 -     * Sorts the specified portion of the specified array using a binary
   1.233 -     * insertion sort.  This is the best method for sorting small numbers
   1.234 -     * of elements.  It requires O(n log n) compares, but O(n^2) data
   1.235 -     * movement (worst case).
   1.236 -     *
   1.237 -     * If the initial part of the specified range is already sorted,
   1.238 -     * this method can take advantage of it: the method assumes that the
   1.239 -     * elements from index {@code lo}, inclusive, to {@code start},
   1.240 -     * exclusive are already sorted.
   1.241 -     *
   1.242 -     * @param a the array in which a range is to be sorted
   1.243 -     * @param lo the index of the first element in the range to be sorted
   1.244 -     * @param hi the index after the last element in the range to be sorted
   1.245 -     * @param start the index of the first element in the range that is
   1.246 -     *        not already known to be sorted ({@code lo <= start <= hi})
   1.247 -     * @param c comparator to used for the sort
   1.248 -     */
   1.249 -    @SuppressWarnings("fallthrough")
   1.250 -    private static <T> void binarySort(T[] a, int lo, int hi, int start,
   1.251 -                                       Comparator<? super T> c) {
   1.252 -        assert lo <= start && start <= hi;
   1.253 -        if (start == lo)
   1.254 -            start++;
   1.255 -        for ( ; start < hi; start++) {
   1.256 -            T pivot = a[start];
   1.257 -
   1.258 -            // Set left (and right) to the index where a[start] (pivot) belongs
   1.259 -            int left = lo;
   1.260 -            int right = start;
   1.261 -            assert left <= right;
   1.262 -            /*
   1.263 -             * Invariants:
   1.264 -             *   pivot >= all in [lo, left).
   1.265 -             *   pivot <  all in [right, start).
   1.266 -             */
   1.267 -            while (left < right) {
   1.268 -                int mid = (left + right) >>> 1;
   1.269 -                if (c.compare(pivot, a[mid]) < 0)
   1.270 -                    right = mid;
   1.271 -                else
   1.272 -                    left = mid + 1;
   1.273 -            }
   1.274 -            assert left == right;
   1.275 -
   1.276 -            /*
   1.277 -             * The invariants still hold: pivot >= all in [lo, left) and
   1.278 -             * pivot < all in [left, start), so pivot belongs at left.  Note
   1.279 -             * that if there are elements equal to pivot, left points to the
   1.280 -             * first slot after them -- that's why this sort is stable.
   1.281 -             * Slide elements over to make room for pivot.
   1.282 -             */
   1.283 -            int n = start - left;  // The number of elements to move
   1.284 -            // Switch is just an optimization for arraycopy in default case
   1.285 -            switch (n) {
   1.286 -                case 2:  a[left + 2] = a[left + 1];
   1.287 -                case 1:  a[left + 1] = a[left];
   1.288 -                         break;
   1.289 -                default: System.arraycopy(a, left, a, left + 1, n);
   1.290 -            }
   1.291 -            a[left] = pivot;
   1.292 -        }
   1.293 -    }
   1.294 -
   1.295 -    /**
   1.296 -     * Returns the length of the run beginning at the specified position in
   1.297 -     * the specified array and reverses the run if it is descending (ensuring
   1.298 -     * that the run will always be ascending when the method returns).
   1.299 -     *
   1.300 -     * A run is the longest ascending sequence with:
   1.301 -     *
   1.302 -     *    a[lo] <= a[lo + 1] <= a[lo + 2] <= ...
   1.303 -     *
   1.304 -     * or the longest descending sequence with:
   1.305 -     *
   1.306 -     *    a[lo] >  a[lo + 1] >  a[lo + 2] >  ...
   1.307 -     *
   1.308 -     * For its intended use in a stable mergesort, the strictness of the
   1.309 -     * definition of "descending" is needed so that the call can safely
   1.310 -     * reverse a descending sequence without violating stability.
   1.311 -     *
   1.312 -     * @param a the array in which a run is to be counted and possibly reversed
   1.313 -     * @param lo index of the first element in the run
   1.314 -     * @param hi index after the last element that may be contained in the run.
   1.315 -              It is required that {@code lo < hi}.
   1.316 -     * @param c the comparator to used for the sort
   1.317 -     * @return  the length of the run beginning at the specified position in
   1.318 -     *          the specified array
   1.319 -     */
   1.320 -    private static <T> int countRunAndMakeAscending(T[] a, int lo, int hi,
   1.321 -                                                    Comparator<? super T> c) {
   1.322 -        assert lo < hi;
   1.323 -        int runHi = lo + 1;
   1.324 -        if (runHi == hi)
   1.325 -            return 1;
   1.326 -
   1.327 -        // Find end of run, and reverse range if descending
   1.328 -        if (c.compare(a[runHi++], a[lo]) < 0) { // Descending
   1.329 -            while (runHi < hi && c.compare(a[runHi], a[runHi - 1]) < 0)
   1.330 -                runHi++;
   1.331 -            reverseRange(a, lo, runHi);
   1.332 -        } else {                              // Ascending
   1.333 -            while (runHi < hi && c.compare(a[runHi], a[runHi - 1]) >= 0)
   1.334 -                runHi++;
   1.335 -        }
   1.336 -
   1.337 -        return runHi - lo;
   1.338 -    }
   1.339 -
   1.340 -    /**
   1.341 -     * Reverse the specified range of the specified array.
   1.342 -     *
   1.343 -     * @param a the array in which a range is to be reversed
   1.344 -     * @param lo the index of the first element in the range to be reversed
   1.345 -     * @param hi the index after the last element in the range to be reversed
   1.346 -     */
   1.347 -    private static void reverseRange(Object[] a, int lo, int hi) {
   1.348 -        hi--;
   1.349 -        while (lo < hi) {
   1.350 -            Object t = a[lo];
   1.351 -            a[lo++] = a[hi];
   1.352 -            a[hi--] = t;
   1.353 -        }
   1.354 -    }
   1.355 -
   1.356 -    /**
   1.357 -     * Returns the minimum acceptable run length for an array of the specified
   1.358 -     * length. Natural runs shorter than this will be extended with
   1.359 -     * {@link #binarySort}.
   1.360 -     *
   1.361 -     * Roughly speaking, the computation is:
   1.362 -     *
   1.363 -     *  If n < MIN_MERGE, return n (it's too small to bother with fancy stuff).
   1.364 -     *  Else if n is an exact power of 2, return MIN_MERGE/2.
   1.365 -     *  Else return an int k, MIN_MERGE/2 <= k <= MIN_MERGE, such that n/k
   1.366 -     *   is close to, but strictly less than, an exact power of 2.
   1.367 -     *
   1.368 -     * For the rationale, see listsort.txt.
   1.369 -     *
   1.370 -     * @param n the length of the array to be sorted
   1.371 -     * @return the length of the minimum run to be merged
   1.372 -     */
   1.373 -    private static int minRunLength(int n) {
   1.374 -        assert n >= 0;
   1.375 -        int r = 0;      // Becomes 1 if any 1 bits are shifted off
   1.376 -        while (n >= MIN_MERGE) {
   1.377 -            r |= (n & 1);
   1.378 -            n >>= 1;
   1.379 -        }
   1.380 -        return n + r;
   1.381 -    }
   1.382 -
   1.383 -    /**
   1.384 -     * Pushes the specified run onto the pending-run stack.
   1.385 -     *
   1.386 -     * @param runBase index of the first element in the run
   1.387 -     * @param runLen  the number of elements in the run
   1.388 -     */
   1.389 -    private void pushRun(int runBase, int runLen) {
   1.390 -        this.runBase[stackSize] = runBase;
   1.391 -        this.runLen[stackSize] = runLen;
   1.392 -        stackSize++;
   1.393 -    }
   1.394 -
   1.395 -    /**
   1.396 -     * Examines the stack of runs waiting to be merged and merges adjacent runs
   1.397 -     * until the stack invariants are reestablished:
   1.398 -     *
   1.399 -     *     1. runLen[i - 3] > runLen[i - 2] + runLen[i - 1]
   1.400 -     *     2. runLen[i - 2] > runLen[i - 1]
   1.401 -     *
   1.402 -     * This method is called each time a new run is pushed onto the stack,
   1.403 -     * so the invariants are guaranteed to hold for i < stackSize upon
   1.404 -     * entry to the method.
   1.405 -     */
   1.406 -    private void mergeCollapse() {
   1.407 -        while (stackSize > 1) {
   1.408 -            int n = stackSize - 2;
   1.409 -            if (n > 0 && runLen[n-1] <= runLen[n] + runLen[n+1]) {
   1.410 -                if (runLen[n - 1] < runLen[n + 1])
   1.411 -                    n--;
   1.412 -                mergeAt(n);
   1.413 -            } else if (runLen[n] <= runLen[n + 1]) {
   1.414 -                mergeAt(n);
   1.415 -            } else {
   1.416 -                break; // Invariant is established
   1.417 -            }
   1.418 -        }
   1.419 -    }
   1.420 -
   1.421 -    /**
   1.422 -     * Merges all runs on the stack until only one remains.  This method is
   1.423 -     * called once, to complete the sort.
   1.424 -     */
   1.425 -    private void mergeForceCollapse() {
   1.426 -        while (stackSize > 1) {
   1.427 -            int n = stackSize - 2;
   1.428 -            if (n > 0 && runLen[n - 1] < runLen[n + 1])
   1.429 -                n--;
   1.430 -            mergeAt(n);
   1.431 -        }
   1.432 -    }
   1.433 -
   1.434 -    /**
   1.435 -     * Merges the two runs at stack indices i and i+1.  Run i must be
   1.436 -     * the penultimate or antepenultimate run on the stack.  In other words,
   1.437 -     * i must be equal to stackSize-2 or stackSize-3.
   1.438 -     *
   1.439 -     * @param i stack index of the first of the two runs to merge
   1.440 -     */
   1.441 -    private void mergeAt(int i) {
   1.442 -        assert stackSize >= 2;
   1.443 -        assert i >= 0;
   1.444 -        assert i == stackSize - 2 || i == stackSize - 3;
   1.445 -
   1.446 -        int base1 = runBase[i];
   1.447 -        int len1 = runLen[i];
   1.448 -        int base2 = runBase[i + 1];
   1.449 -        int len2 = runLen[i + 1];
   1.450 -        assert len1 > 0 && len2 > 0;
   1.451 -        assert base1 + len1 == base2;
   1.452 -
   1.453 -        /*
   1.454 -         * Record the length of the combined runs; if i is the 3rd-last
   1.455 -         * run now, also slide over the last run (which isn't involved
   1.456 -         * in this merge).  The current run (i+1) goes away in any case.
   1.457 -         */
   1.458 -        runLen[i] = len1 + len2;
   1.459 -        if (i == stackSize - 3) {
   1.460 -            runBase[i + 1] = runBase[i + 2];
   1.461 -            runLen[i + 1] = runLen[i + 2];
   1.462 -        }
   1.463 -        stackSize--;
   1.464 -
   1.465 -        /*
   1.466 -         * Find where the first element of run2 goes in run1. Prior elements
   1.467 -         * in run1 can be ignored (because they're already in place).
   1.468 -         */
   1.469 -        int k = gallopRight(a[base2], a, base1, len1, 0, c);
   1.470 -        assert k >= 0;
   1.471 -        base1 += k;
   1.472 -        len1 -= k;
   1.473 -        if (len1 == 0)
   1.474 -            return;
   1.475 -
   1.476 -        /*
   1.477 -         * Find where the last element of run1 goes in run2. Subsequent elements
   1.478 -         * in run2 can be ignored (because they're already in place).
   1.479 -         */
   1.480 -        len2 = gallopLeft(a[base1 + len1 - 1], a, base2, len2, len2 - 1, c);
   1.481 -        assert len2 >= 0;
   1.482 -        if (len2 == 0)
   1.483 -            return;
   1.484 -
   1.485 -        // Merge remaining runs, using tmp array with min(len1, len2) elements
   1.486 -        if (len1 <= len2)
   1.487 -            mergeLo(base1, len1, base2, len2);
   1.488 -        else
   1.489 -            mergeHi(base1, len1, base2, len2);
   1.490 -    }
   1.491 -
   1.492 -    /**
   1.493 -     * Locates the position at which to insert the specified key into the
   1.494 -     * specified sorted range; if the range contains an element equal to key,
   1.495 -     * returns the index of the leftmost equal element.
   1.496 -     *
   1.497 -     * @param key the key whose insertion point to search for
   1.498 -     * @param a the array in which to search
   1.499 -     * @param base the index of the first element in the range
   1.500 -     * @param len the length of the range; must be > 0
   1.501 -     * @param hint the index at which to begin the search, 0 <= hint < n.
   1.502 -     *     The closer hint is to the result, the faster this method will run.
   1.503 -     * @param c the comparator used to order the range, and to search
   1.504 -     * @return the int k,  0 <= k <= n such that a[b + k - 1] < key <= a[b + k],
   1.505 -     *    pretending that a[b - 1] is minus infinity and a[b + n] is infinity.
   1.506 -     *    In other words, key belongs at index b + k; or in other words,
   1.507 -     *    the first k elements of a should precede key, and the last n - k
   1.508 -     *    should follow it.
   1.509 -     */
   1.510 -    private static <T> int gallopLeft(T key, T[] a, int base, int len, int hint,
   1.511 -                                      Comparator<? super T> c) {
   1.512 -        assert len > 0 && hint >= 0 && hint < len;
   1.513 -        int lastOfs = 0;
   1.514 -        int ofs = 1;
   1.515 -        if (c.compare(key, a[base + hint]) > 0) {
   1.516 -            // Gallop right until a[base+hint+lastOfs] < key <= a[base+hint+ofs]
   1.517 -            int maxOfs = len - hint;
   1.518 -            while (ofs < maxOfs && c.compare(key, a[base + hint + ofs]) > 0) {
   1.519 -                lastOfs = ofs;
   1.520 -                ofs = (ofs << 1) + 1;
   1.521 -                if (ofs <= 0)   // int overflow
   1.522 -                    ofs = maxOfs;
   1.523 -            }
   1.524 -            if (ofs > maxOfs)
   1.525 -                ofs = maxOfs;
   1.526 -
   1.527 -            // Make offsets relative to base
   1.528 -            lastOfs += hint;
   1.529 -            ofs += hint;
   1.530 -        } else { // key <= a[base + hint]
   1.531 -            // Gallop left until a[base+hint-ofs] < key <= a[base+hint-lastOfs]
   1.532 -            final int maxOfs = hint + 1;
   1.533 -            while (ofs < maxOfs && c.compare(key, a[base + hint - ofs]) <= 0) {
   1.534 -                lastOfs = ofs;
   1.535 -                ofs = (ofs << 1) + 1;
   1.536 -                if (ofs <= 0)   // int overflow
   1.537 -                    ofs = maxOfs;
   1.538 -            }
   1.539 -            if (ofs > maxOfs)
   1.540 -                ofs = maxOfs;
   1.541 -
   1.542 -            // Make offsets relative to base
   1.543 -            int tmp = lastOfs;
   1.544 -            lastOfs = hint - ofs;
   1.545 -            ofs = hint - tmp;
   1.546 -        }
   1.547 -        assert -1 <= lastOfs && lastOfs < ofs && ofs <= len;
   1.548 -
   1.549 -        /*
   1.550 -         * Now a[base+lastOfs] < key <= a[base+ofs], so key belongs somewhere
   1.551 -         * to the right of lastOfs but no farther right than ofs.  Do a binary
   1.552 -         * search, with invariant a[base + lastOfs - 1] < key <= a[base + ofs].
   1.553 -         */
   1.554 -        lastOfs++;
   1.555 -        while (lastOfs < ofs) {
   1.556 -            int m = lastOfs + ((ofs - lastOfs) >>> 1);
   1.557 -
   1.558 -            if (c.compare(key, a[base + m]) > 0)
   1.559 -                lastOfs = m + 1;  // a[base + m] < key
   1.560 -            else
   1.561 -                ofs = m;          // key <= a[base + m]
   1.562 -        }
   1.563 -        assert lastOfs == ofs;    // so a[base + ofs - 1] < key <= a[base + ofs]
   1.564 -        return ofs;
   1.565 -    }
   1.566 -
   1.567 -    /**
   1.568 -     * Like gallopLeft, except that if the range contains an element equal to
   1.569 -     * key, gallopRight returns the index after the rightmost equal element.
   1.570 -     *
   1.571 -     * @param key the key whose insertion point to search for
   1.572 -     * @param a the array in which to search
   1.573 -     * @param base the index of the first element in the range
   1.574 -     * @param len the length of the range; must be > 0
   1.575 -     * @param hint the index at which to begin the search, 0 <= hint < n.
   1.576 -     *     The closer hint is to the result, the faster this method will run.
   1.577 -     * @param c the comparator used to order the range, and to search
   1.578 -     * @return the int k,  0 <= k <= n such that a[b + k - 1] <= key < a[b + k]
   1.579 -     */
   1.580 -    private static <T> int gallopRight(T key, T[] a, int base, int len,
   1.581 -                                       int hint, Comparator<? super T> c) {
   1.582 -        assert len > 0 && hint >= 0 && hint < len;
   1.583 -
   1.584 -        int ofs = 1;
   1.585 -        int lastOfs = 0;
   1.586 -        if (c.compare(key, a[base + hint]) < 0) {
   1.587 -            // Gallop left until a[b+hint - ofs] <= key < a[b+hint - lastOfs]
   1.588 -            int maxOfs = hint + 1;
   1.589 -            while (ofs < maxOfs && c.compare(key, a[base + hint - ofs]) < 0) {
   1.590 -                lastOfs = ofs;
   1.591 -                ofs = (ofs << 1) + 1;
   1.592 -                if (ofs <= 0)   // int overflow
   1.593 -                    ofs = maxOfs;
   1.594 -            }
   1.595 -            if (ofs > maxOfs)
   1.596 -                ofs = maxOfs;
   1.597 -
   1.598 -            // Make offsets relative to b
   1.599 -            int tmp = lastOfs;
   1.600 -            lastOfs = hint - ofs;
   1.601 -            ofs = hint - tmp;
   1.602 -        } else { // a[b + hint] <= key
   1.603 -            // Gallop right until a[b+hint + lastOfs] <= key < a[b+hint + ofs]
   1.604 -            int maxOfs = len - hint;
   1.605 -            while (ofs < maxOfs && c.compare(key, a[base + hint + ofs]) >= 0) {
   1.606 -                lastOfs = ofs;
   1.607 -                ofs = (ofs << 1) + 1;
   1.608 -                if (ofs <= 0)   // int overflow
   1.609 -                    ofs = maxOfs;
   1.610 -            }
   1.611 -            if (ofs > maxOfs)
   1.612 -                ofs = maxOfs;
   1.613 -
   1.614 -            // Make offsets relative to b
   1.615 -            lastOfs += hint;
   1.616 -            ofs += hint;
   1.617 -        }
   1.618 -        assert -1 <= lastOfs && lastOfs < ofs && ofs <= len;
   1.619 -
   1.620 -        /*
   1.621 -         * Now a[b + lastOfs] <= key < a[b + ofs], so key belongs somewhere to
   1.622 -         * the right of lastOfs but no farther right than ofs.  Do a binary
   1.623 -         * search, with invariant a[b + lastOfs - 1] <= key < a[b + ofs].
   1.624 -         */
   1.625 -        lastOfs++;
   1.626 -        while (lastOfs < ofs) {
   1.627 -            int m = lastOfs + ((ofs - lastOfs) >>> 1);
   1.628 -
   1.629 -            if (c.compare(key, a[base + m]) < 0)
   1.630 -                ofs = m;          // key < a[b + m]
   1.631 -            else
   1.632 -                lastOfs = m + 1;  // a[b + m] <= key
   1.633 -        }
   1.634 -        assert lastOfs == ofs;    // so a[b + ofs - 1] <= key < a[b + ofs]
   1.635 -        return ofs;
   1.636 -    }
   1.637 -
   1.638 -    /**
   1.639 -     * Merges two adjacent runs in place, in a stable fashion.  The first
   1.640 -     * element of the first run must be greater than the first element of the
   1.641 -     * second run (a[base1] > a[base2]), and the last element of the first run
   1.642 -     * (a[base1 + len1-1]) must be greater than all elements of the second run.
   1.643 -     *
   1.644 -     * For performance, this method should be called only when len1 <= len2;
   1.645 -     * its twin, mergeHi should be called if len1 >= len2.  (Either method
   1.646 -     * may be called if len1 == len2.)
   1.647 -     *
   1.648 -     * @param base1 index of first element in first run to be merged
   1.649 -     * @param len1  length of first run to be merged (must be > 0)
   1.650 -     * @param base2 index of first element in second run to be merged
   1.651 -     *        (must be aBase + aLen)
   1.652 -     * @param len2  length of second run to be merged (must be > 0)
   1.653 -     */
   1.654 -    private void mergeLo(int base1, int len1, int base2, int len2) {
   1.655 -        assert len1 > 0 && len2 > 0 && base1 + len1 == base2;
   1.656 -
   1.657 -        // Copy first run into temp array
   1.658 -        T[] a = this.a; // For performance
   1.659 -        T[] tmp = ensureCapacity(len1);
   1.660 -        System.arraycopy(a, base1, tmp, 0, len1);
   1.661 -
   1.662 -        int cursor1 = 0;       // Indexes into tmp array
   1.663 -        int cursor2 = base2;   // Indexes int a
   1.664 -        int dest = base1;      // Indexes int a
   1.665 -
   1.666 -        // Move first element of second run and deal with degenerate cases
   1.667 -        a[dest++] = a[cursor2++];
   1.668 -        if (--len2 == 0) {
   1.669 -            System.arraycopy(tmp, cursor1, a, dest, len1);
   1.670 -            return;
   1.671 -        }
   1.672 -        if (len1 == 1) {
   1.673 -            System.arraycopy(a, cursor2, a, dest, len2);
   1.674 -            a[dest + len2] = tmp[cursor1]; // Last elt of run 1 to end of merge
   1.675 -            return;
   1.676 -        }
   1.677 -
   1.678 -        Comparator<? super T> c = this.c;  // Use local variable for performance
   1.679 -        int minGallop = this.minGallop;    //  "    "       "     "      "
   1.680 -    outer:
   1.681 -        while (true) {
   1.682 -            int count1 = 0; // Number of times in a row that first run won
   1.683 -            int count2 = 0; // Number of times in a row that second run won
   1.684 -
   1.685 -            /*
   1.686 -             * Do the straightforward thing until (if ever) one run starts
   1.687 -             * winning consistently.
   1.688 -             */
   1.689 -            do {
   1.690 -                assert len1 > 1 && len2 > 0;
   1.691 -                if (c.compare(a[cursor2], tmp[cursor1]) < 0) {
   1.692 -                    a[dest++] = a[cursor2++];
   1.693 -                    count2++;
   1.694 -                    count1 = 0;
   1.695 -                    if (--len2 == 0)
   1.696 -                        break outer;
   1.697 -                } else {
   1.698 -                    a[dest++] = tmp[cursor1++];
   1.699 -                    count1++;
   1.700 -                    count2 = 0;
   1.701 -                    if (--len1 == 1)
   1.702 -                        break outer;
   1.703 -                }
   1.704 -            } while ((count1 | count2) < minGallop);
   1.705 -
   1.706 -            /*
   1.707 -             * One run is winning so consistently that galloping may be a
   1.708 -             * huge win. So try that, and continue galloping until (if ever)
   1.709 -             * neither run appears to be winning consistently anymore.
   1.710 -             */
   1.711 -            do {
   1.712 -                assert len1 > 1 && len2 > 0;
   1.713 -                count1 = gallopRight(a[cursor2], tmp, cursor1, len1, 0, c);
   1.714 -                if (count1 != 0) {
   1.715 -                    System.arraycopy(tmp, cursor1, a, dest, count1);
   1.716 -                    dest += count1;
   1.717 -                    cursor1 += count1;
   1.718 -                    len1 -= count1;
   1.719 -                    if (len1 <= 1) // len1 == 1 || len1 == 0
   1.720 -                        break outer;
   1.721 -                }
   1.722 -                a[dest++] = a[cursor2++];
   1.723 -                if (--len2 == 0)
   1.724 -                    break outer;
   1.725 -
   1.726 -                count2 = gallopLeft(tmp[cursor1], a, cursor2, len2, 0, c);
   1.727 -                if (count2 != 0) {
   1.728 -                    System.arraycopy(a, cursor2, a, dest, count2);
   1.729 -                    dest += count2;
   1.730 -                    cursor2 += count2;
   1.731 -                    len2 -= count2;
   1.732 -                    if (len2 == 0)
   1.733 -                        break outer;
   1.734 -                }
   1.735 -                a[dest++] = tmp[cursor1++];
   1.736 -                if (--len1 == 1)
   1.737 -                    break outer;
   1.738 -                minGallop--;
   1.739 -            } while (count1 >= MIN_GALLOP | count2 >= MIN_GALLOP);
   1.740 -            if (minGallop < 0)
   1.741 -                minGallop = 0;
   1.742 -            minGallop += 2;  // Penalize for leaving gallop mode
   1.743 -        }  // End of "outer" loop
   1.744 -        this.minGallop = minGallop < 1 ? 1 : minGallop;  // Write back to field
   1.745 -
   1.746 -        if (len1 == 1) {
   1.747 -            assert len2 > 0;
   1.748 -            System.arraycopy(a, cursor2, a, dest, len2);
   1.749 -            a[dest + len2] = tmp[cursor1]; //  Last elt of run 1 to end of merge
   1.750 -        } else if (len1 == 0) {
   1.751 -            throw new IllegalArgumentException(
   1.752 -                "Comparison method violates its general contract!");
   1.753 -        } else {
   1.754 -            assert len2 == 0;
   1.755 -            assert len1 > 1;
   1.756 -            System.arraycopy(tmp, cursor1, a, dest, len1);
   1.757 -        }
   1.758 -    }
   1.759 -
   1.760 -    /**
   1.761 -     * Like mergeLo, except that this method should be called only if
   1.762 -     * len1 >= len2; mergeLo should be called if len1 <= len2.  (Either method
   1.763 -     * may be called if len1 == len2.)
   1.764 -     *
   1.765 -     * @param base1 index of first element in first run to be merged
   1.766 -     * @param len1  length of first run to be merged (must be > 0)
   1.767 -     * @param base2 index of first element in second run to be merged
   1.768 -     *        (must be aBase + aLen)
   1.769 -     * @param len2  length of second run to be merged (must be > 0)
   1.770 -     */
   1.771 -    private void mergeHi(int base1, int len1, int base2, int len2) {
   1.772 -        assert len1 > 0 && len2 > 0 && base1 + len1 == base2;
   1.773 -
   1.774 -        // Copy second run into temp array
   1.775 -        T[] a = this.a; // For performance
   1.776 -        T[] tmp = ensureCapacity(len2);
   1.777 -        System.arraycopy(a, base2, tmp, 0, len2);
   1.778 -
   1.779 -        int cursor1 = base1 + len1 - 1;  // Indexes into a
   1.780 -        int cursor2 = len2 - 1;          // Indexes into tmp array
   1.781 -        int dest = base2 + len2 - 1;     // Indexes into a
   1.782 -
   1.783 -        // Move last element of first run and deal with degenerate cases
   1.784 -        a[dest--] = a[cursor1--];
   1.785 -        if (--len1 == 0) {
   1.786 -            System.arraycopy(tmp, 0, a, dest - (len2 - 1), len2);
   1.787 -            return;
   1.788 -        }
   1.789 -        if (len2 == 1) {
   1.790 -            dest -= len1;
   1.791 -            cursor1 -= len1;
   1.792 -            System.arraycopy(a, cursor1 + 1, a, dest + 1, len1);
   1.793 -            a[dest] = tmp[cursor2];
   1.794 -            return;
   1.795 -        }
   1.796 -
   1.797 -        Comparator<? super T> c = this.c;  // Use local variable for performance
   1.798 -        int minGallop = this.minGallop;    //  "    "       "     "      "
   1.799 -    outer:
   1.800 -        while (true) {
   1.801 -            int count1 = 0; // Number of times in a row that first run won
   1.802 -            int count2 = 0; // Number of times in a row that second run won
   1.803 -
   1.804 -            /*
   1.805 -             * Do the straightforward thing until (if ever) one run
   1.806 -             * appears to win consistently.
   1.807 -             */
   1.808 -            do {
   1.809 -                assert len1 > 0 && len2 > 1;
   1.810 -                if (c.compare(tmp[cursor2], a[cursor1]) < 0) {
   1.811 -                    a[dest--] = a[cursor1--];
   1.812 -                    count1++;
   1.813 -                    count2 = 0;
   1.814 -                    if (--len1 == 0)
   1.815 -                        break outer;
   1.816 -                } else {
   1.817 -                    a[dest--] = tmp[cursor2--];
   1.818 -                    count2++;
   1.819 -                    count1 = 0;
   1.820 -                    if (--len2 == 1)
   1.821 -                        break outer;
   1.822 -                }
   1.823 -            } while ((count1 | count2) < minGallop);
   1.824 -
   1.825 -            /*
   1.826 -             * One run is winning so consistently that galloping may be a
   1.827 -             * huge win. So try that, and continue galloping until (if ever)
   1.828 -             * neither run appears to be winning consistently anymore.
   1.829 -             */
   1.830 -            do {
   1.831 -                assert len1 > 0 && len2 > 1;
   1.832 -                count1 = len1 - gallopRight(tmp[cursor2], a, base1, len1, len1 - 1, c);
   1.833 -                if (count1 != 0) {
   1.834 -                    dest -= count1;
   1.835 -                    cursor1 -= count1;
   1.836 -                    len1 -= count1;
   1.837 -                    System.arraycopy(a, cursor1 + 1, a, dest + 1, count1);
   1.838 -                    if (len1 == 0)
   1.839 -                        break outer;
   1.840 -                }
   1.841 -                a[dest--] = tmp[cursor2--];
   1.842 -                if (--len2 == 1)
   1.843 -                    break outer;
   1.844 -
   1.845 -                count2 = len2 - gallopLeft(a[cursor1], tmp, 0, len2, len2 - 1, c);
   1.846 -                if (count2 != 0) {
   1.847 -                    dest -= count2;
   1.848 -                    cursor2 -= count2;
   1.849 -                    len2 -= count2;
   1.850 -                    System.arraycopy(tmp, cursor2 + 1, a, dest + 1, count2);
   1.851 -                    if (len2 <= 1)  // len2 == 1 || len2 == 0
   1.852 -                        break outer;
   1.853 -                }
   1.854 -                a[dest--] = a[cursor1--];
   1.855 -                if (--len1 == 0)
   1.856 -                    break outer;
   1.857 -                minGallop--;
   1.858 -            } while (count1 >= MIN_GALLOP | count2 >= MIN_GALLOP);
   1.859 -            if (minGallop < 0)
   1.860 -                minGallop = 0;
   1.861 -            minGallop += 2;  // Penalize for leaving gallop mode
   1.862 -        }  // End of "outer" loop
   1.863 -        this.minGallop = minGallop < 1 ? 1 : minGallop;  // Write back to field
   1.864 -
   1.865 -        if (len2 == 1) {
   1.866 -            assert len1 > 0;
   1.867 -            dest -= len1;
   1.868 -            cursor1 -= len1;
   1.869 -            System.arraycopy(a, cursor1 + 1, a, dest + 1, len1);
   1.870 -            a[dest] = tmp[cursor2];  // Move first elt of run2 to front of merge
   1.871 -        } else if (len2 == 0) {
   1.872 -            throw new IllegalArgumentException(
   1.873 -                "Comparison method violates its general contract!");
   1.874 -        } else {
   1.875 -            assert len1 == 0;
   1.876 -            assert len2 > 0;
   1.877 -            System.arraycopy(tmp, 0, a, dest - (len2 - 1), len2);
   1.878 -        }
   1.879 -    }
   1.880 -
   1.881 -    /**
   1.882 -     * Ensures that the external array tmp has at least the specified
   1.883 -     * number of elements, increasing its size if necessary.  The size
   1.884 -     * increases exponentially to ensure amortized linear time complexity.
   1.885 -     *
   1.886 -     * @param minCapacity the minimum required capacity of the tmp array
   1.887 -     * @return tmp, whether or not it grew
   1.888 -     */
   1.889 -    private T[] ensureCapacity(int minCapacity) {
   1.890 -        if (tmp.length < minCapacity) {
   1.891 -            // Compute smallest power of 2 > minCapacity
   1.892 -            int newSize = minCapacity;
   1.893 -            newSize |= newSize >> 1;
   1.894 -            newSize |= newSize >> 2;
   1.895 -            newSize |= newSize >> 4;
   1.896 -            newSize |= newSize >> 8;
   1.897 -            newSize |= newSize >> 16;
   1.898 -            newSize++;
   1.899 -
   1.900 -            if (newSize < 0) // Not bloody likely!
   1.901 -                newSize = minCapacity;
   1.902 -            else
   1.903 -                newSize = Math.min(newSize, a.length >>> 1);
   1.904 -
   1.905 -            @SuppressWarnings({"unchecked", "UnnecessaryLocalVariable"})
   1.906 -            T[] newArray = (T[]) new Object[newSize];
   1.907 -            tmp = newArray;
   1.908 -        }
   1.909 -        return tmp;
   1.910 -    }
   1.911 -
   1.912 -    /**
   1.913 -     * Checks that fromIndex and toIndex are in range, and throws an
   1.914 -     * appropriate exception if they aren't.
   1.915 -     *
   1.916 -     * @param arrayLen the length of the array
   1.917 -     * @param fromIndex the index of the first element of the range
   1.918 -     * @param toIndex the index after the last element of the range
   1.919 -     * @throws IllegalArgumentException if fromIndex > toIndex
   1.920 -     * @throws ArrayIndexOutOfBoundsException if fromIndex < 0
   1.921 -     *         or toIndex > arrayLen
   1.922 -     */
   1.923 -    private static void rangeCheck(int arrayLen, int fromIndex, int toIndex) {
   1.924 -        if (fromIndex > toIndex)
   1.925 -            throw new IllegalArgumentException("fromIndex(" + fromIndex +
   1.926 -                       ") > toIndex(" + toIndex+")");
   1.927 -        if (fromIndex < 0)
   1.928 -            throw new ArrayIndexOutOfBoundsException(fromIndex);
   1.929 -        if (toIndex > arrayLen)
   1.930 -            throw new ArrayIndexOutOfBoundsException(toIndex);
   1.931 -    }
   1.932 -}