TimSort

Some of you many know I have a bit of an obesstion with sorting algorithms ^_^

Anyway their is a revolutionary algorithm come to greater light, developed in 2002 by Tim Peters and called the TimSort 😛 which is a adaptive, stable, natural mergesort. It has supernatural performance on many kinds of partially ordered arrays (less than lg(N!) comparisons needed, andas few as N-1), yet as fast as Python’s previous highly tuned samplesort hybrid on random arrays.

and for us Java nerds it will be replacing java collections sort() as of Java 7

Anyway its sexy as hell check it out:

/*
* 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. Sun designates this
* particular file as subject to the “Classpath” exception as provided
* by Sun 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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
* CA 95054 USA or visit www.sun.com if you need additional information or
* have any questions.
*/

package java.util;

/**
* A stable, adaptive, iterative mergesort that requires far fewer than
* n lg(n) comparisons when running on partially sorted arrays, while
* offering performance comparable to a traditional mergesort when run
* on random arrays. Like all proper mergesorts, this sort is stable and
* runs O(n log n) time (worst case). In the worst case, this sort requires
* temporary storage space for n/2 object references; in the best case,
* it requires only a small constant amount of space.
*
* This implementation was adapted from Tim Peters’s list sort for
* Python, which is described in detail here:
*
* http://svn.python.org/projects/python/trunk/Objects/listsort.txt
*
* Tim’s C code may be found here:
*
* http://svn.python.org/projects/python/trunk/Objects/listobject.c
*
* The underlying techniques are described in this paper (and may have
* even earlier origins):
*
* “Optimistic Sorting and Information Theoretic Complexity”
* Peter McIlroy
* SODA (Fourth Annual ACM-SIAM Symposium on Discrete Algorithms),
* pp 467-474, Austin, Texas, 25-27 January 1993.
*
* While the API to this class consists solely of static methods, it is
* (privately) instantiable; a TimSort instance holds the state of an ongoing
* sort, assuming the input array is large enough to warrant the full-blown
* TimSort. Small arrays are sorted in place, using a binary insertion sort.
*
* @author Josh Bloch
*/
class TimSort {
/**
* 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 T[] a;

/**
* The comparator for this sort.
*/
private final Comparator c;

/**
* 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 T[] tmp; // Actual runtime type will be Object[], regardless of T

/**
* 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
* @param c the comparator to determine the order of the sort
*/
private TimSort(T[] a, Comparator c) {
this.a = a;
this.c = c;

// Allocate temp storage (which may be increased later if necessary)
int len = a.length;
@SuppressWarnings({“unchecked”, “UnnecessaryLocalVariable”})
T[] newArray = (T[]) 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(T[] a, Comparator c) {
sort(a, 0, a.length, c);
}

static void sort(T[] a, int lo, int hi, Comparator c) {
if (c == null) {
Arrays.sort(a, lo, hi);
return;
}

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, c);
binarySort(a, lo, hi, lo + initRunLen, c);
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.
*/
TimSort ts = new TimSort(a, c);
int minRun = minRunLength(nRemaining);
do {
// Identify next run
int runLen = countRunAndMakeAscending(a, lo, hi, c);

// 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, c);
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}
* @param c comparator to used for the sort
*/
@SuppressWarnings(“fallthrough”)
private static void binarySort(T[] a, int lo, int hi, int start,
Comparator c) {
assert lo <= start && start <= hi;
if (start == lo)
start++;
for ( ; start < hi; start++) {
T pivot = 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 (c.compare(pivot, 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 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}.
* @param c the comparator to used for the sort
* @return the length of the run beginning at the specified position in
* the specified array
*/
private static int countRunAndMakeAscending(T[] a, int lo, int hi,
Comparator c) {
assert lo < hi;
int runHi = lo + 1;
if (runHi == hi)
return 1;

// Find end of run, and reverse range if descending
if (c.compare(a[runHi++], a[lo]) < 0) { // Descending
while(runHi < hi && c.compare(a[runHi], a[runHi – 1]) < 0)
runHi++;
reverseRange(a, lo, runHi);
} else { // Ascending
while (runHi < hi && c.compare(a[runHi], 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 */ 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(a[base2], a, base1, len1, 0, c);
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(a[base1 + len1 – 1], a, base2, len2, len2 – 1, c);
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.
* @param c the comparator used to order the range, and to search
* @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(T key, T[] a, int base, int len, int hint,
Comparator c) {
assert len > 0 && hint >= 0 && hint < len; int lastOfs = 0; int ofs = 1; if (c.compare(key, a[base + hint]) > 0) {
// Gallop right until a[base+hint+lastOfs] < key <= a[base+hint+ofs]
int maxOfs = len – hint;
while (ofs < maxOfs && c.compare(key, 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 && c.compare(key, 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 (c.compare(key, 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.
* @param c the comparator used to order the range, and to search
* @return the int k, 0 <= k <= n such that a[b + k – 1] <= key < a[b + k]
*/
private static int gallopRight(T key, T[] a, int base, int len,
int hint, Comparator c) {
assert len > 0 && hint >= 0 && hint < len;

int ofs = 1;
int lastOfs = 0;
if (c.compare(key, a[base + hint]) < 0) {
// Gallop left until a[b+hint – ofs] <= key < a[b+hint – lastOfs]
int maxOfs = hint + 1;
while (ofs < maxOfs && c.compare(key, 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 && c.compare(key, 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 (c.compare(key, 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)
*/
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
T[] a = this.a; // For performance
T[] 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;
}

Comparator c = this.c; // Use local variable for performance
int minGallop = this.minGallop; // ” ” ” ” ”
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 (c.compare(a[cursor2], 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(a[cursor2], tmp, cursor1, len1, 0, c);
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(tmp[cursor1], a, cursor2, len2, 0, c); 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)
*/
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
T[] a = this.a; // For performance
T[] 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;
}

Comparator c = this.c; // Use local variable for performance
int minGallop = this.minGallop; // ” ” ” ” ”
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 (c.compare(tmp[cursor2], 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(tmp[cursor2], a, base1, len1, len1 – 1, c);
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(a[cursor1], tmp, 0, len2, len2 – 1, c);
if (count2 != 0) {
dest -= count2;
cursor2 -= count2;
len2 -= count2;
System.arraycopy(tmp, cursor2 + 1, a, dest + 1, count2);
if (len2 <= 1) // len2 == 1 || len2 == 0 break outer; } 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 T[] 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”})
T[] newArray = (T[]) 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);
}
}

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