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6905046: More Dual-pivot quicksort improvements 

Summary: More improvements from the DPQ team
Reviewed-by: alanb
上级 399c52fb
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Showing with 627 addition and 403 deletion
src/share/classes/java/util/DualPivotQuicksort.java
浏览文件 @ 0ca86caf
...@@ -36,12 +36,12 @@ package java.util; ...@@ -36,12 +36,12 @@ package java.util;
* @author Jon Bentley * @author Jon Bentley
* @author Josh Bloch * @author Josh Bloch
* *
* @version 2009.11.16 m765.827.v12a * @version 2009.11.29 m765.827.12i
*/ */
final class DualPivotQuicksort { final class DualPivotQuicksort {
/** /**
* Suppresses default constructor. * Prevents instantiation.
*/ */
private DualPivotQuicksort() {} private DualPivotQuicksort() {}
...@@ -84,7 +84,7 @@ final class DualPivotQuicksort { ...@@ -84,7 +84,7 @@ final class DualPivotQuicksort {
* Sorts the specified range of the array into ascending order. The range * Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to * to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex}, * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty. * the range to be sorted is empty (and the call is a no-op).
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted * @param fromIndex the index of the first element, inclusive, to be sorted
...@@ -101,8 +101,8 @@ final class DualPivotQuicksort { ...@@ -101,8 +101,8 @@ final class DualPivotQuicksort {
/** /**
* Sorts the specified range of the array into ascending order. This * Sorts the specified range of the array into ascending order. This
* method differs from the public {@code sort} method in that the * method differs from the public {@code sort} method in that the
* {@code right} index is inclusive, and it does no range checking on * {@code right} index is inclusive, and it does no range checking
* {@code left} or {@code right}. * on {@code left} or {@code right}.
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted * @param left the index of the first element, inclusive, to be sorted
...@@ -111,13 +111,13 @@ final class DualPivotQuicksort { ...@@ -111,13 +111,13 @@ final class DualPivotQuicksort {
private static void doSort(int[] a, int left, int right) { private static void doSort(int[] a, int left, int right) {
// Use insertion sort on tiny arrays // Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) { if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) { for (int i = left + 1; i <= right; i++) {
int ak = a[k]; int ai = a[i];
int j; int j;
for (j = k - 1; j >= left && ak < a[j]; j--) { for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j]; a[j + 1] = a[j];
} }
a[j + 1] = ak; a[j + 1] = ai;
} }
} else { // Use Dual-Pivot Quicksort on large arrays } else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right); dualPivotQuicksort(a, left, right);
...@@ -162,7 +162,7 @@ final class DualPivotQuicksort { ...@@ -162,7 +162,7 @@ final class DualPivotQuicksort {
* second terciles of the array. Note that pivot1 <= pivot2. * second terciles of the array. Note that pivot1 <= pivot2.
* *
* The pivots are stored in local variables, and the first and * The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations * the last of the elements to be sorted are moved to the locations
* formerly occupied by the pivots. When partitioning is complete, * formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and * the pivots are swapped back into their final positions, and
* excluded from subsequent sorting. * excluded from subsequent sorting.
...@@ -170,27 +170,26 @@ final class DualPivotQuicksort { ...@@ -170,27 +170,26 @@ final class DualPivotQuicksort {
int pivot1 = ae2; a[e2] = a[left]; int pivot1 = ae2; a[e2] = a[left];
int pivot2 = ae4; a[e4] = a[right]; int pivot2 = ae4; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers // Pointers
int less = left + 1; // The index of first element of center part int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2; boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) { if (pivotsDiffer) {
/* /*
* Partitioning:
*
* left part center part right part
* +------------------------------------------------------------+
* | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 |
* +------------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants: * Invariants:
*
* all in (left, less) < pivot1 * all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2 * pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2 * all in (great, right) > pivot2
...@@ -200,37 +199,37 @@ final class DualPivotQuicksort { ...@@ -200,37 +199,37 @@ final class DualPivotQuicksort {
outer: outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
int ak = a[k]; int ak = a[k];
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else if (ak > pivot2) { } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) { while (a[great] > pivot2) {
if (k == great--) { if (great-- == k) {
break outer; break outer;
} }
} }
if (a[great] < pivot1) {
a[k] = a[less];
a[less++] = a[great];
a[great--] = ak;
} else { // pivot1 <= a[great] <= pivot2
a[k] = a[great]; a[k] = a[great];
a[great--] = ak; a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less];
a[less++] = ak;
} }
} }
} }
} else { // Pivots are equal } else { // Pivots are equal
/* /*
* Partition degenerates to the traditional 3-way * Partition degenerates to the traditional 3-way,
* (or "Dutch National Flag") partition: * or "Dutch National Flag", partition:
* *
* left part center part right part * left part center part right part
* ------------------------------------------------- * +----------------------------------------------+
* [ < pivot | == pivot | ? | > pivot ] * | < pivot | == pivot | ? | > pivot |
* ------------------------------------------------- * +----------------------------------------------+
*
* ^ ^ ^ * ^ ^ ^
* | | | * | | |
* less k great * less k great
...@@ -243,30 +242,34 @@ final class DualPivotQuicksort { ...@@ -243,30 +242,34 @@ final class DualPivotQuicksort {
* *
* Pointer k is the first index of ?-part * Pointer k is the first index of ?-part
*/ */
outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
int ak = a[k]; int ak = a[k];
if (ak == pivot1) { if (ak == pivot1) {
continue; continue;
} }
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else { // a[k] > pivot } else { // (a[k] > pivot1) - Move a[k] to right part
/*
* We know that pivot1 == a[e3] == pivot2. Thus, we know
* that great will still be >= k when the following loop
* terminates, even though we don't test for it explicitly.
* In other words, a[e3] acts as a sentinel for great.
*/
while (a[great] > pivot1) { while (a[great] > pivot1) {
if (k == great--) { great--;
break outer;
}
} }
a[k] = a[great]; if (a[great] < pivot1) {
a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less]; a[k] = a[less];
a[less++] = ak; a[less++] = a[great];
a[great--] = ak;
} else { // a[great] == pivot1
a[k] = pivot1;
a[great--] = ak;
} }
} }
} }
...@@ -289,26 +292,55 @@ final class DualPivotQuicksort { ...@@ -289,26 +292,55 @@ final class DualPivotQuicksort {
} }
/* /*
* If center part is too large (comprises > 5/6 of * If center part is too large (comprises > 2/3 of the array),
* the array), swap internal pivot values to ends * swap internal pivot values to ends
*/ */
if (less < e1 && e5 < great) { if (less < e1 && great > e5) {
while (a[less] == pivot1) { while (a[less] == pivot1) {
less++; less++;
} }
while (a[great] == pivot2) { while (a[great] == pivot2) {
great--; great--;
} }
for (int k = less + 1; k <= great; ) {
/*
* Partitioning:
*
* left part center part right part
* +----------------------------------------------------------+
* | == pivot1 | pivot1 < && < pivot2 | ? | == pivot2 |
* +----------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (*, less) == pivot1
* pivot1 < all in [less, k) < pivot2
* all in (great, *) == pivot2
*
* Pointer k is the first index of ?-part
*/
outer:
for (int k = less; k <= great; k++) {
int ak = a[k]; int ak = a[k];
if (ak == pivot1) { if (ak == pivot2) { // Move a[k] to right part
a[k++] = a[less]; while (a[great] == pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] == pivot1) {
a[k] = a[less];
a[less++] = pivot1; a[less++] = pivot1;
} else if (ak == pivot2) { } else { // pivot1 < a[great] < pivot2
a[k] = a[great]; a[k] = a[great];
}
a[great--] = pivot2; a[great--] = pivot2;
} else { } else if (ak == pivot1) { // Move a[k] to left part
k++; a[k] = a[less];
a[less++] = pivot1;
} }
} }
} }
...@@ -330,7 +362,7 @@ final class DualPivotQuicksort { ...@@ -330,7 +362,7 @@ final class DualPivotQuicksort {
* Sorts the specified range of the array into ascending order. The range * Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to * to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex}, * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty. * the range to be sorted is empty (and the call is a no-op).
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted * @param fromIndex the index of the first element, inclusive, to be sorted
...@@ -357,13 +389,13 @@ final class DualPivotQuicksort { ...@@ -357,13 +389,13 @@ final class DualPivotQuicksort {
private static void doSort(long[] a, int left, int right) { private static void doSort(long[] a, int left, int right) {
// Use insertion sort on tiny arrays // Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) { if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) { for (int i = left + 1; i <= right; i++) {
long ak = a[k]; long ai = a[i];
int j; int j;
for (j = k - 1; j >= left && ak < a[j]; j--) { for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j]; a[j + 1] = a[j];
} }
a[j + 1] = ak; a[j + 1] = ai;
} }
} else { // Use Dual-Pivot Quicksort on large arrays } else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right); dualPivotQuicksort(a, left, right);
...@@ -408,7 +440,7 @@ final class DualPivotQuicksort { ...@@ -408,7 +440,7 @@ final class DualPivotQuicksort {
* second terciles of the array. Note that pivot1 <= pivot2. * second terciles of the array. Note that pivot1 <= pivot2.
* *
* The pivots are stored in local variables, and the first and * The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations * the last of the elements to be sorted are moved to the locations
* formerly occupied by the pivots. When partitioning is complete, * formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and * the pivots are swapped back into their final positions, and
* excluded from subsequent sorting. * excluded from subsequent sorting.
...@@ -416,27 +448,26 @@ final class DualPivotQuicksort { ...@@ -416,27 +448,26 @@ final class DualPivotQuicksort {
long pivot1 = ae2; a[e2] = a[left]; long pivot1 = ae2; a[e2] = a[left];
long pivot2 = ae4; a[e4] = a[right]; long pivot2 = ae4; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers // Pointers
int less = left + 1; // The index of first element of center part int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2; boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) { if (pivotsDiffer) {
/* /*
* Partitioning:
*
* left part center part right part
* +------------------------------------------------------------+
* | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 |
* +------------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants: * Invariants:
*
* all in (left, less) < pivot1 * all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2 * pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2 * all in (great, right) > pivot2
...@@ -446,37 +477,37 @@ final class DualPivotQuicksort { ...@@ -446,37 +477,37 @@ final class DualPivotQuicksort {
outer: outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
long ak = a[k]; long ak = a[k];
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else if (ak > pivot2) { } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) { while (a[great] > pivot2) {
if (k == great--) { if (great-- == k) {
break outer; break outer;
} }
} }
if (a[great] < pivot1) {
a[k] = a[less];
a[less++] = a[great];
a[great--] = ak;
} else { // pivot1 <= a[great] <= pivot2
a[k] = a[great]; a[k] = a[great];
a[great--] = ak; a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less];
a[less++] = ak;
} }
} }
} }
} else { // Pivots are equal } else { // Pivots are equal
/* /*
* Partition degenerates to the traditional 3-way * Partition degenerates to the traditional 3-way,
* (or "Dutch National Flag") partition: * or "Dutch National Flag", partition:
* *
* left part center part right part * left part center part right part
* ------------------------------------------------- * +----------------------------------------------+
* [ < pivot | == pivot | ? | > pivot ] * | < pivot | == pivot | ? | > pivot |
* ------------------------------------------------- * +----------------------------------------------+
*
* ^ ^ ^ * ^ ^ ^
* | | | * | | |
* less k great * less k great
...@@ -489,30 +520,34 @@ final class DualPivotQuicksort { ...@@ -489,30 +520,34 @@ final class DualPivotQuicksort {
* *
* Pointer k is the first index of ?-part * Pointer k is the first index of ?-part
*/ */
outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
long ak = a[k]; long ak = a[k];
if (ak == pivot1) { if (ak == pivot1) {
continue; continue;
} }
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else { // a[k] > pivot } else { // (a[k] > pivot1) - Move a[k] to right part
/*
* We know that pivot1 == a[e3] == pivot2. Thus, we know
* that great will still be >= k when the following loop
* terminates, even though we don't test for it explicitly.
* In other words, a[e3] acts as a sentinel for great.
*/
while (a[great] > pivot1) { while (a[great] > pivot1) {
if (k == great--) { great--;
break outer;
}
} }
a[k] = a[great]; if (a[great] < pivot1) {
a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less]; a[k] = a[less];
a[less++] = ak; a[less++] = a[great];
a[great--] = ak;
} else { // a[great] == pivot1
a[k] = pivot1;
a[great--] = ak;
} }
} }
} }
...@@ -535,26 +570,55 @@ final class DualPivotQuicksort { ...@@ -535,26 +570,55 @@ final class DualPivotQuicksort {
} }
/* /*
* If center part is too large (comprises > 5/6 of * If center part is too large (comprises > 2/3 of the array),
* the array), swap internal pivot values to ends * swap internal pivot values to ends
*/ */
if (less < e1 && e5 < great) { if (less < e1 && great > e5) {
while (a[less] == pivot1) { while (a[less] == pivot1) {
less++; less++;
} }
while (a[great] == pivot2) { while (a[great] == pivot2) {
great--; great--;
} }
for (int k = less + 1; k <= great; ) {
/*
* Partitioning:
*
* left part center part right part
* +----------------------------------------------------------+
* | == pivot1 | pivot1 < && < pivot2 | ? | == pivot2 |
* +----------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (*, less) == pivot1
* pivot1 < all in [less, k) < pivot2
* all in (great, *) == pivot2
*
* Pointer k is the first index of ?-part
*/
outer:
for (int k = less; k <= great; k++) {
long ak = a[k]; long ak = a[k];
if (ak == pivot1) { if (ak == pivot2) { // Move a[k] to right part
a[k++] = a[less]; while (a[great] == pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] == pivot1) {
a[k] = a[less];
a[less++] = pivot1; a[less++] = pivot1;
} else if (ak == pivot2) { } else { // pivot1 < a[great] < pivot2
a[k] = a[great]; a[k] = a[great];
}
a[great--] = pivot2; a[great--] = pivot2;
} else { } else if (ak == pivot1) { // Move a[k] to left part
k++; a[k] = a[less];
a[less++] = pivot1;
} }
} }
} }
...@@ -576,7 +640,7 @@ final class DualPivotQuicksort { ...@@ -576,7 +640,7 @@ final class DualPivotQuicksort {
* Sorts the specified range of the array into ascending order. The range * Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to * to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex}, * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty. * the range to be sorted is empty (and the call is a no-op).
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted * @param fromIndex the index of the first element, inclusive, to be sorted
...@@ -606,13 +670,13 @@ final class DualPivotQuicksort { ...@@ -606,13 +670,13 @@ final class DualPivotQuicksort {
private static void doSort(short[] a, int left, int right) { private static void doSort(short[] a, int left, int right) {
// Use insertion sort on tiny arrays // Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) { if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) { for (int i = left + 1; i <= right; i++) {
short ak = a[k]; short ai = a[i];
int j; int j;
for (j = k - 1; j >= left && ak < a[j]; j--) { for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j]; a[j + 1] = a[j];
} }
a[j + 1] = ak; a[j + 1] = ai;
} }
} else if (right-left+1 > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) { } else if (right-left+1 > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
// Use counting sort on huge arrays // Use counting sort on huge arrays
...@@ -671,7 +735,7 @@ final class DualPivotQuicksort { ...@@ -671,7 +735,7 @@ final class DualPivotQuicksort {
* second terciles of the array. Note that pivot1 <= pivot2. * second terciles of the array. Note that pivot1 <= pivot2.
* *
* The pivots are stored in local variables, and the first and * The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations * the last of the elements to be sorted are moved to the locations
* formerly occupied by the pivots. When partitioning is complete, * formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and * the pivots are swapped back into their final positions, and
* excluded from subsequent sorting. * excluded from subsequent sorting.
...@@ -679,27 +743,26 @@ final class DualPivotQuicksort { ...@@ -679,27 +743,26 @@ final class DualPivotQuicksort {
short pivot1 = ae2; a[e2] = a[left]; short pivot1 = ae2; a[e2] = a[left];
short pivot2 = ae4; a[e4] = a[right]; short pivot2 = ae4; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers // Pointers
int less = left + 1; // The index of first element of center part int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2; boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) { if (pivotsDiffer) {
/* /*
* Partitioning:
*
* left part center part right part
* +------------------------------------------------------------+
* | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 |
* +------------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants: * Invariants:
*
* all in (left, less) < pivot1 * all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2 * pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2 * all in (great, right) > pivot2
...@@ -709,37 +772,37 @@ final class DualPivotQuicksort { ...@@ -709,37 +772,37 @@ final class DualPivotQuicksort {
outer: outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
short ak = a[k]; short ak = a[k];
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else if (ak > pivot2) { } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) { while (a[great] > pivot2) {
if (k == great--) { if (great-- == k) {
break outer; break outer;
} }
} }
if (a[great] < pivot1) {
a[k] = a[less];
a[less++] = a[great];
a[great--] = ak;
} else { // pivot1 <= a[great] <= pivot2
a[k] = a[great]; a[k] = a[great];
a[great--] = ak; a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less];
a[less++] = ak;
} }
} }
} }
} else { // Pivots are equal } else { // Pivots are equal
/* /*
* Partition degenerates to the traditional 3-way * Partition degenerates to the traditional 3-way,
* (or "Dutch National Flag") partition: * or "Dutch National Flag", partition:
* *
* left part center part right part * left part center part right part
* ------------------------------------------------- * +----------------------------------------------+
* [ < pivot | == pivot | ? | > pivot ] * | < pivot | == pivot | ? | > pivot |
* ------------------------------------------------- * +----------------------------------------------+
*
* ^ ^ ^ * ^ ^ ^
* | | | * | | |
* less k great * less k great
...@@ -752,30 +815,34 @@ final class DualPivotQuicksort { ...@@ -752,30 +815,34 @@ final class DualPivotQuicksort {
* *
* Pointer k is the first index of ?-part * Pointer k is the first index of ?-part
*/ */
outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
short ak = a[k]; short ak = a[k];
if (ak == pivot1) { if (ak == pivot1) {
continue; continue;
} }
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else { // a[k] > pivot } else { // (a[k] > pivot1) - Move a[k] to right part
/*
* We know that pivot1 == a[e3] == pivot2. Thus, we know
* that great will still be >= k when the following loop
* terminates, even though we don't test for it explicitly.
* In other words, a[e3] acts as a sentinel for great.
*/
while (a[great] > pivot1) { while (a[great] > pivot1) {
if (k == great--) { great--;
break outer;
}
} }
a[k] = a[great]; if (a[great] < pivot1) {
a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less]; a[k] = a[less];
a[less++] = ak; a[less++] = a[great];
a[great--] = ak;
} else { // a[great] == pivot1
a[k] = pivot1;
a[great--] = ak;
} }
} }
} }
...@@ -798,26 +865,55 @@ final class DualPivotQuicksort { ...@@ -798,26 +865,55 @@ final class DualPivotQuicksort {
} }
/* /*
* If center part is too large (comprises > 5/6 of * If center part is too large (comprises > 2/3 of the array),
* the array), swap internal pivot values to ends * swap internal pivot values to ends
*/ */
if (less < e1 && e5 < great) { if (less < e1 && great > e5) {
while (a[less] == pivot1) { while (a[less] == pivot1) {
less++; less++;
} }
while (a[great] == pivot2) { while (a[great] == pivot2) {
great--; great--;
} }
for (int k = less + 1; k <= great; ) {
/*
* Partitioning:
*
* left part center part right part
* +----------------------------------------------------------+
* | == pivot1 | pivot1 < && < pivot2 | ? | == pivot2 |
* +----------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (*, less) == pivot1
* pivot1 < all in [less, k) < pivot2
* all in (great, *) == pivot2
*
* Pointer k is the first index of ?-part
*/
outer:
for (int k = less; k <= great; k++) {
short ak = a[k]; short ak = a[k];
if (ak == pivot1) { if (ak == pivot2) { // Move a[k] to right part
a[k++] = a[less]; while (a[great] == pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] == pivot1) {
a[k] = a[less];
a[less++] = pivot1; a[less++] = pivot1;
} else if (ak == pivot2) { } else { // pivot1 < a[great] < pivot2
a[k] = a[great]; a[k] = a[great];
}
a[great--] = pivot2; a[great--] = pivot2;
} else { } else if (ak == pivot1) { // Move a[k] to left part
k++; a[k] = a[less];
a[less++] = pivot1;
} }
} }
} }
...@@ -839,7 +935,7 @@ final class DualPivotQuicksort { ...@@ -839,7 +935,7 @@ final class DualPivotQuicksort {
* Sorts the specified range of the array into ascending order. The range * Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to * to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex}, * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty. * the range to be sorted is empty (and the call is a no-op).
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted * @param fromIndex the index of the first element, inclusive, to be sorted
...@@ -869,13 +965,13 @@ final class DualPivotQuicksort { ...@@ -869,13 +965,13 @@ final class DualPivotQuicksort {
private static void doSort(char[] a, int left, int right) { private static void doSort(char[] a, int left, int right) {
// Use insertion sort on tiny arrays // Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) { if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) { for (int i = left + 1; i <= right; i++) {
char ak = a[k]; char ai = a[i];
int j; int j;
for (j = k - 1; j >= left && ak < a[j]; j--) { for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j]; a[j + 1] = a[j];
} }
a[j + 1] = ak; a[j + 1] = ai;
} }
} else if (right-left+1 > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) { } else if (right-left+1 > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
// Use counting sort on huge arrays // Use counting sort on huge arrays
...@@ -932,7 +1028,7 @@ final class DualPivotQuicksort { ...@@ -932,7 +1028,7 @@ final class DualPivotQuicksort {
* second terciles of the array. Note that pivot1 <= pivot2. * second terciles of the array. Note that pivot1 <= pivot2.
* *
* The pivots are stored in local variables, and the first and * The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations * the last of the elements to be sorted are moved to the locations
* formerly occupied by the pivots. When partitioning is complete, * formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and * the pivots are swapped back into their final positions, and
* excluded from subsequent sorting. * excluded from subsequent sorting.
...@@ -940,27 +1036,26 @@ final class DualPivotQuicksort { ...@@ -940,27 +1036,26 @@ final class DualPivotQuicksort {
char pivot1 = ae2; a[e2] = a[left]; char pivot1 = ae2; a[e2] = a[left];
char pivot2 = ae4; a[e4] = a[right]; char pivot2 = ae4; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers // Pointers
int less = left + 1; // The index of first element of center part int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2; boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) { if (pivotsDiffer) {
/* /*
* Partitioning:
*
* left part center part right part
* +------------------------------------------------------------+
* | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 |
* +------------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants: * Invariants:
*
* all in (left, less) < pivot1 * all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2 * pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2 * all in (great, right) > pivot2
...@@ -970,37 +1065,37 @@ final class DualPivotQuicksort { ...@@ -970,37 +1065,37 @@ final class DualPivotQuicksort {
outer: outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
char ak = a[k]; char ak = a[k];
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else if (ak > pivot2) { } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) { while (a[great] > pivot2) {
if (k == great--) { if (great-- == k) {
break outer; break outer;
} }
} }
if (a[great] < pivot1) {
a[k] = a[less];
a[less++] = a[great];
a[great--] = ak;
} else { // pivot1 <= a[great] <= pivot2
a[k] = a[great]; a[k] = a[great];
a[great--] = ak; a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less];
a[less++] = ak;
} }
} }
} }
} else { // Pivots are equal } else { // Pivots are equal
/* /*
* Partition degenerates to the traditional 3-way * Partition degenerates to the traditional 3-way,
* (or "Dutch National Flag") partition: * or "Dutch National Flag", partition:
* *
* left part center part right part * left part center part right part
* ------------------------------------------------- * +----------------------------------------------+
* [ < pivot | == pivot | ? | > pivot ] * | < pivot | == pivot | ? | > pivot |
* ------------------------------------------------- * +----------------------------------------------+
*
* ^ ^ ^ * ^ ^ ^
* | | | * | | |
* less k great * less k great
...@@ -1013,30 +1108,34 @@ final class DualPivotQuicksort { ...@@ -1013,30 +1108,34 @@ final class DualPivotQuicksort {
* *
* Pointer k is the first index of ?-part * Pointer k is the first index of ?-part
*/ */
outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
char ak = a[k]; char ak = a[k];
if (ak == pivot1) { if (ak == pivot1) {
continue; continue;
} }
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else { // a[k] > pivot } else { // (a[k] > pivot1) - Move a[k] to right part
/*
* We know that pivot1 == a[e3] == pivot2. Thus, we know
* that great will still be >= k when the following loop
* terminates, even though we don't test for it explicitly.
* In other words, a[e3] acts as a sentinel for great.
*/
while (a[great] > pivot1) { while (a[great] > pivot1) {
if (k == great--) { great--;
break outer;
}
} }
a[k] = a[great]; if (a[great] < pivot1) {
a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less]; a[k] = a[less];
a[less++] = ak; a[less++] = a[great];
a[great--] = ak;
} else { // a[great] == pivot1
a[k] = pivot1;
a[great--] = ak;
} }
} }
} }
...@@ -1059,26 +1158,55 @@ final class DualPivotQuicksort { ...@@ -1059,26 +1158,55 @@ final class DualPivotQuicksort {
} }
/* /*
* If center part is too large (comprises > 5/6 of * If center part is too large (comprises > 2/3 of the array),
* the array), swap internal pivot values to ends * swap internal pivot values to ends
*/ */
if (less < e1 && e5 < great) { if (less < e1 && great > e5) {
while (a[less] == pivot1) { while (a[less] == pivot1) {
less++; less++;
} }
while (a[great] == pivot2) { while (a[great] == pivot2) {
great--; great--;
} }
for (int k = less + 1; k <= great; ) {
/*
* Partitioning:
*
* left part center part right part
* +----------------------------------------------------------+
* | == pivot1 | pivot1 < && < pivot2 | ? | == pivot2 |
* +----------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (*, less) == pivot1
* pivot1 < all in [less, k) < pivot2
* all in (great, *) == pivot2
*
* Pointer k is the first index of ?-part
*/
outer:
for (int k = less; k <= great; k++) {
char ak = a[k]; char ak = a[k];
if (ak == pivot1) { if (ak == pivot2) { // Move a[k] to right part
a[k++] = a[less]; while (a[great] == pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] == pivot1) {
a[k] = a[less];
a[less++] = pivot1; a[less++] = pivot1;
} else if (ak == pivot2) { } else { // pivot1 < a[great] < pivot2
a[k] = a[great]; a[k] = a[great];
}
a[great--] = pivot2; a[great--] = pivot2;
} else { } else if (ak == pivot1) { // Move a[k] to left part
k++; a[k] = a[less];
a[less++] = pivot1;
} }
} }
} }
...@@ -1100,7 +1228,7 @@ final class DualPivotQuicksort { ...@@ -1100,7 +1228,7 @@ final class DualPivotQuicksort {
* Sorts the specified range of the array into ascending order. The range * Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to * to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex}, * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty. * the range to be sorted is empty (and the call is a no-op).
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted * @param fromIndex the index of the first element, inclusive, to be sorted
...@@ -1130,13 +1258,13 @@ final class DualPivotQuicksort { ...@@ -1130,13 +1258,13 @@ final class DualPivotQuicksort {
private static void doSort(byte[] a, int left, int right) { private static void doSort(byte[] a, int left, int right) {
// Use insertion sort on tiny arrays // Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) { if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) { for (int i = left + 1; i <= right; i++) {
byte ak = a[k]; byte ai = a[i];
int j; int j;
for (j = k - 1; j >= left && ak < a[j]; j--) { for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j]; a[j + 1] = a[j];
} }
a[j + 1] = ak; a[j + 1] = ai;
} }
} else if (right - left + 1 > COUNTING_SORT_THRESHOLD_FOR_BYTE) { } else if (right - left + 1 > COUNTING_SORT_THRESHOLD_FOR_BYTE) {
// Use counting sort on huge arrays // Use counting sort on huge arrays
...@@ -1195,7 +1323,7 @@ final class DualPivotQuicksort { ...@@ -1195,7 +1323,7 @@ final class DualPivotQuicksort {
* second terciles of the array. Note that pivot1 <= pivot2. * second terciles of the array. Note that pivot1 <= pivot2.
* *
* The pivots are stored in local variables, and the first and * The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations * the last of the elements to be sorted are moved to the locations
* formerly occupied by the pivots. When partitioning is complete, * formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and * the pivots are swapped back into their final positions, and
* excluded from subsequent sorting. * excluded from subsequent sorting.
...@@ -1203,27 +1331,26 @@ final class DualPivotQuicksort { ...@@ -1203,27 +1331,26 @@ final class DualPivotQuicksort {
byte pivot1 = ae2; a[e2] = a[left]; byte pivot1 = ae2; a[e2] = a[left];
byte pivot2 = ae4; a[e4] = a[right]; byte pivot2 = ae4; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers // Pointers
int less = left + 1; // The index of first element of center part int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2; boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) { if (pivotsDiffer) {
/* /*
* Partitioning:
*
* left part center part right part
* +------------------------------------------------------------+
* | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 |
* +------------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants: * Invariants:
*
* all in (left, less) < pivot1 * all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2 * pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2 * all in (great, right) > pivot2
...@@ -1233,37 +1360,37 @@ final class DualPivotQuicksort { ...@@ -1233,37 +1360,37 @@ final class DualPivotQuicksort {
outer: outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
byte ak = a[k]; byte ak = a[k];
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else if (ak > pivot2) { } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) { while (a[great] > pivot2) {
if (k == great--) { if (great-- == k) {
break outer; break outer;
} }
} }
if (a[great] < pivot1) {
a[k] = a[less];
a[less++] = a[great];
a[great--] = ak;
} else { // pivot1 <= a[great] <= pivot2
a[k] = a[great]; a[k] = a[great];
a[great--] = ak; a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less];
a[less++] = ak;
} }
} }
} }
} else { // Pivots are equal } else { // Pivots are equal
/* /*
* Partition degenerates to the traditional 3-way * Partition degenerates to the traditional 3-way,
* (or "Dutch National Flag") partition: * or "Dutch National Flag", partition:
* *
* left part center part right part * left part center part right part
* ------------------------------------------------- * +----------------------------------------------+
* [ < pivot | == pivot | ? | > pivot ] * | < pivot | == pivot | ? | > pivot |
* ------------------------------------------------- * +----------------------------------------------+
*
* ^ ^ ^ * ^ ^ ^
* | | | * | | |
* less k great * less k great
...@@ -1276,30 +1403,34 @@ final class DualPivotQuicksort { ...@@ -1276,30 +1403,34 @@ final class DualPivotQuicksort {
* *
* Pointer k is the first index of ?-part * Pointer k is the first index of ?-part
*/ */
outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
byte ak = a[k]; byte ak = a[k];
if (ak == pivot1) { if (ak == pivot1) {
continue; continue;
} }
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else { // a[k] > pivot } else { // (a[k] > pivot1) - Move a[k] to right part
/*
* We know that pivot1 == a[e3] == pivot2. Thus, we know
* that great will still be >= k when the following loop
* terminates, even though we don't test for it explicitly.
* In other words, a[e3] acts as a sentinel for great.
*/
while (a[great] > pivot1) { while (a[great] > pivot1) {
if (k == great--) { great--;
break outer;
}
} }
a[k] = a[great]; if (a[great] < pivot1) {
a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less]; a[k] = a[less];
a[less++] = ak; a[less++] = a[great];
a[great--] = ak;
} else { // a[great] == pivot1
a[k] = pivot1;
a[great--] = ak;
} }
} }
} }
...@@ -1322,26 +1453,55 @@ final class DualPivotQuicksort { ...@@ -1322,26 +1453,55 @@ final class DualPivotQuicksort {
} }
/* /*
* If center part is too large (comprises > 5/6 of * If center part is too large (comprises > 2/3 of the array),
* the array), swap internal pivot values to ends * swap internal pivot values to ends
*/ */
if (less < e1 && e5 < great) { if (less < e1 && great > e5) {
while (a[less] == pivot1) { while (a[less] == pivot1) {
less++; less++;
} }
while (a[great] == pivot2) { while (a[great] == pivot2) {
great--; great--;
} }
for (int k = less + 1; k <= great; ) {
/*
* Partitioning:
*
* left part center part right part
* +----------------------------------------------------------+
* | == pivot1 | pivot1 < && < pivot2 | ? | == pivot2 |
* +----------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (*, less) == pivot1
* pivot1 < all in [less, k) < pivot2
* all in (great, *) == pivot2
*
* Pointer k is the first index of ?-part
*/
outer:
for (int k = less; k <= great; k++) {
byte ak = a[k]; byte ak = a[k];
if (ak == pivot1) { if (ak == pivot2) { // Move a[k] to right part
a[k++] = a[less]; while (a[great] == pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] == pivot1) {
a[k] = a[less];
a[less++] = pivot1; a[less++] = pivot1;
} else if (ak == pivot2) { } else { // pivot1 < a[great] < pivot2
a[k] = a[great]; a[k] = a[great];
}
a[great--] = pivot2; a[great--] = pivot2;
} else { } else if (ak == pivot1) { // Move a[k] to left part
k++; a[k] = a[less];
a[less++] = pivot1;
} }
} }
} }
...@@ -1371,7 +1531,7 @@ final class DualPivotQuicksort { ...@@ -1371,7 +1531,7 @@ final class DualPivotQuicksort {
* Sorts the specified range of the array into ascending order. The range * Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to * to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex}, * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty. * the range to be sorted is empty and the call is a no-op).
* *
* <p>The {@code <} relation does not provide a total order on all float * <p>The {@code <} relation does not provide a total order on all float
* values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN} * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
...@@ -1485,13 +1645,13 @@ final class DualPivotQuicksort { ...@@ -1485,13 +1645,13 @@ final class DualPivotQuicksort {
private static void doSort(float[] a, int left, int right) { private static void doSort(float[] a, int left, int right) {
// Use insertion sort on tiny arrays // Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) { if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) { for (int i = left + 1; i <= right; i++) {
float ak = a[k]; float ai = a[i];
int j; int j;
for (j = k - 1; j >= left && ak < a[j]; j--) { for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j]; a[j + 1] = a[j];
} }
a[j + 1] = ak; a[j + 1] = ai;
} }
} else { // Use Dual-Pivot Quicksort on large arrays } else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right); dualPivotQuicksort(a, left, right);
...@@ -1536,7 +1696,7 @@ final class DualPivotQuicksort { ...@@ -1536,7 +1696,7 @@ final class DualPivotQuicksort {
* second terciles of the array. Note that pivot1 <= pivot2. * second terciles of the array. Note that pivot1 <= pivot2.
* *
* The pivots are stored in local variables, and the first and * The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations * the last of the elements to be sorted are moved to the locations
* formerly occupied by the pivots. When partitioning is complete, * formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and * the pivots are swapped back into their final positions, and
* excluded from subsequent sorting. * excluded from subsequent sorting.
...@@ -1544,27 +1704,26 @@ final class DualPivotQuicksort { ...@@ -1544,27 +1704,26 @@ final class DualPivotQuicksort {
float pivot1 = ae2; a[e2] = a[left]; float pivot1 = ae2; a[e2] = a[left];
float pivot2 = ae4; a[e4] = a[right]; float pivot2 = ae4; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers // Pointers
int less = left + 1; // The index of first element of center part int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2; boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) { if (pivotsDiffer) {
/* /*
* Partitioning:
*
* left part center part right part
* +------------------------------------------------------------+
* | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 |
* +------------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants: * Invariants:
*
* all in (left, less) < pivot1 * all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2 * pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2 * all in (great, right) > pivot2
...@@ -1574,37 +1733,37 @@ final class DualPivotQuicksort { ...@@ -1574,37 +1733,37 @@ final class DualPivotQuicksort {
outer: outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
float ak = a[k]; float ak = a[k];
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else if (ak > pivot2) { } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) { while (a[great] > pivot2) {
if (k == great--) { if (great-- == k) {
break outer; break outer;
} }
} }
if (a[great] < pivot1) {
a[k] = a[less];
a[less++] = a[great];
a[great--] = ak;
} else { // pivot1 <= a[great] <= pivot2
a[k] = a[great]; a[k] = a[great];
a[great--] = ak; a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less];
a[less++] = ak;
} }
} }
} }
} else { // Pivots are equal } else { // Pivots are equal
/* /*
* Partition degenerates to the traditional 3-way * Partition degenerates to the traditional 3-way,
* (or "Dutch National Flag") partition: * or "Dutch National Flag", partition:
* *
* left part center part right part * left part center part right part
* ------------------------------------------------- * +----------------------------------------------+
* [ < pivot | == pivot | ? | > pivot ] * | < pivot | == pivot | ? | > pivot |
* ------------------------------------------------- * +----------------------------------------------+
*
* ^ ^ ^ * ^ ^ ^
* | | | * | | |
* less k great * less k great
...@@ -1617,30 +1776,34 @@ final class DualPivotQuicksort { ...@@ -1617,30 +1776,34 @@ final class DualPivotQuicksort {
* *
* Pointer k is the first index of ?-part * Pointer k is the first index of ?-part
*/ */
outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
float ak = a[k]; float ak = a[k];
if (ak == pivot1) { if (ak == pivot1) {
continue; continue;
} }
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else { // a[k] > pivot } else { // (a[k] > pivot1) - Move a[k] to right part
/*
* We know that pivot1 == a[e3] == pivot2. Thus, we know
* that great will still be >= k when the following loop
* terminates, even though we don't test for it explicitly.
* In other words, a[e3] acts as a sentinel for great.
*/
while (a[great] > pivot1) { while (a[great] > pivot1) {
if (k == great--) { great--;
break outer;
}
} }
a[k] = a[great]; if (a[great] < pivot1) {
a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less]; a[k] = a[less];
a[less++] = ak; a[less++] = a[great];
a[great--] = ak;
} else { // a[great] == pivot1
a[k] = pivot1;
a[great--] = ak;
} }
} }
} }
...@@ -1663,26 +1826,55 @@ final class DualPivotQuicksort { ...@@ -1663,26 +1826,55 @@ final class DualPivotQuicksort {
} }
/* /*
* If center part is too large (comprises > 5/6 of * If center part is too large (comprises > 2/3 of the array),
* the array), swap internal pivot values to ends * swap internal pivot values to ends
*/ */
if (less < e1 && e5 < great) { if (less < e1 && great > e5) {
while (a[less] == pivot1) { while (a[less] == pivot1) {
less++; less++;
} }
while (a[great] == pivot2) { while (a[great] == pivot2) {
great--; great--;
} }
for (int k = less + 1; k <= great; ) {
/*
* Partitioning:
*
* left part center part right part
* +----------------------------------------------------------+
* | == pivot1 | pivot1 < && < pivot2 | ? | == pivot2 |
* +----------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (*, less) == pivot1
* pivot1 < all in [less, k) < pivot2
* all in (great, *) == pivot2
*
* Pointer k is the first index of ?-part
*/
outer:
for (int k = less; k <= great; k++) {
float ak = a[k]; float ak = a[k];
if (ak == pivot1) { if (ak == pivot2) { // Move a[k] to right part
a[k++] = a[less]; while (a[great] == pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] == pivot1) {
a[k] = a[less];
a[less++] = pivot1; a[less++] = pivot1;
} else if (ak == pivot2) { } else { // pivot1 < a[great] < pivot2
a[k] = a[great]; a[k] = a[great];
}
a[great--] = pivot2; a[great--] = pivot2;
} else { } else if (ak == pivot1) { // Move a[k] to left part
k++; a[k] = a[less];
a[less++] = pivot1;
} }
} }
} }
...@@ -1712,7 +1904,7 @@ final class DualPivotQuicksort { ...@@ -1712,7 +1904,7 @@ final class DualPivotQuicksort {
* Sorts the specified range of the array into ascending order. The range * Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to * to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex}, * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty. * the range to be sorted is empty (and the call is a no-op).
* *
* <p>The {@code <} relation does not provide a total order on all double * <p>The {@code <} relation does not provide a total order on all double
* values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN} * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
...@@ -1826,13 +2018,13 @@ final class DualPivotQuicksort { ...@@ -1826,13 +2018,13 @@ final class DualPivotQuicksort {
private static void doSort(double[] a, int left, int right) { private static void doSort(double[] a, int left, int right) {
// Use insertion sort on tiny arrays // Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) { if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) { for (int i = left + 1; i <= right; i++) {
double ak = a[k]; double ai = a[i];
int j; int j;
for (j = k - 1; j >= left && ak < a[j]; j--) { for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j]; a[j + 1] = a[j];
} }
a[j + 1] = ak; a[j + 1] = ai;
} }
} else { // Use Dual-Pivot Quicksort on large arrays } else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right); dualPivotQuicksort(a, left, right);
...@@ -1877,7 +2069,7 @@ final class DualPivotQuicksort { ...@@ -1877,7 +2069,7 @@ final class DualPivotQuicksort {
* second terciles of the array. Note that pivot1 <= pivot2. * second terciles of the array. Note that pivot1 <= pivot2.
* *
* The pivots are stored in local variables, and the first and * The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations * the last of the elements to be sorted are moved to the locations
* formerly occupied by the pivots. When partitioning is complete, * formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and * the pivots are swapped back into their final positions, and
* excluded from subsequent sorting. * excluded from subsequent sorting.
...@@ -1885,27 +2077,26 @@ final class DualPivotQuicksort { ...@@ -1885,27 +2077,26 @@ final class DualPivotQuicksort {
double pivot1 = ae2; a[e2] = a[left]; double pivot1 = ae2; a[e2] = a[left];
double pivot2 = ae4; a[e4] = a[right]; double pivot2 = ae4; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers // Pointers
int less = left + 1; // The index of first element of center part int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2; boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) { if (pivotsDiffer) {
/* /*
* Partitioning:
*
* left part center part right part
* +------------------------------------------------------------+
* | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 |
* +------------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants: * Invariants:
*
* all in (left, less) < pivot1 * all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2 * pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2 * all in (great, right) > pivot2
...@@ -1915,37 +2106,37 @@ final class DualPivotQuicksort { ...@@ -1915,37 +2106,37 @@ final class DualPivotQuicksort {
outer: outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
double ak = a[k]; double ak = a[k];
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else if (ak > pivot2) { } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) { while (a[great] > pivot2) {
if (k == great--) { if (great-- == k) {
break outer; break outer;
} }
} }
if (a[great] < pivot1) {
a[k] = a[less];
a[less++] = a[great];
a[great--] = ak;
} else { // pivot1 <= a[great] <= pivot2
a[k] = a[great]; a[k] = a[great];
a[great--] = ak; a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less];
a[less++] = ak;
} }
} }
} }
} else { // Pivots are equal } else { // Pivots are equal
/* /*
* Partition degenerates to the traditional 3-way * Partition degenerates to the traditional 3-way,
* (or "Dutch National Flag") partition: * or "Dutch National Flag", partition:
* *
* left part center part right part * left part center part right part
* ------------------------------------------------- * +----------------------------------------------+
* [ < pivot | == pivot | ? | > pivot ] * | < pivot | == pivot | ? | > pivot |
* ------------------------------------------------- * +----------------------------------------------+
*
* ^ ^ ^ * ^ ^ ^
* | | | * | | |
* less k great * less k great
...@@ -1958,30 +2149,34 @@ final class DualPivotQuicksort { ...@@ -1958,30 +2149,34 @@ final class DualPivotQuicksort {
* *
* Pointer k is the first index of ?-part * Pointer k is the first index of ?-part
*/ */
outer:
for (int k = less; k <= great; k++) { for (int k = less; k <= great; k++) {
double ak = a[k]; double ak = a[k];
if (ak == pivot1) { if (ak == pivot1) {
continue; continue;
} }
if (ak < pivot1) { if (ak < pivot1) { // Move a[k] to left part
if (k > less) { if (k != less) {
a[k] = a[less]; a[k] = a[less];
a[less] = ak; a[less] = ak;
} }
less++; less++;
} else { // a[k] > pivot } else { // (a[k] > pivot1) - Move a[k] to right part
/*
* We know that pivot1 == a[e3] == pivot2. Thus, we know
* that great will still be >= k when the following loop
* terminates, even though we don't test for it explicitly.
* In other words, a[e3] acts as a sentinel for great.
*/
while (a[great] > pivot1) { while (a[great] > pivot1) {
if (k == great--) { great--;
break outer;
}
} }
a[k] = a[great]; if (a[great] < pivot1) {
a[great--] = ak;
if ((ak = a[k]) < pivot1) {
a[k] = a[less]; a[k] = a[less];
a[less++] = ak; a[less++] = a[great];
a[great--] = ak;
} else { // a[great] == pivot1
a[k] = pivot1;
a[great--] = ak;
} }
} }
} }
...@@ -2004,26 +2199,55 @@ final class DualPivotQuicksort { ...@@ -2004,26 +2199,55 @@ final class DualPivotQuicksort {
} }
/* /*
* If center part is too large (comprises > 5/6 of * If center part is too large (comprises > 2/3 of the array),
* the array), swap internal pivot values to ends * swap internal pivot values to ends
*/ */
if (less < e1 && e5 < great) { if (less < e1 && great > e5) {
while (a[less] == pivot1) { while (a[less] == pivot1) {
less++; less++;
} }
while (a[great] == pivot2) { while (a[great] == pivot2) {
great--; great--;
} }
for (int k = less + 1; k <= great; ) {
/*
* Partitioning:
*
* left part center part right part
* +----------------------------------------------------------+
* | == pivot1 | pivot1 < && < pivot2 | ? | == pivot2 |
* +----------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (*, less) == pivot1
* pivot1 < all in [less, k) < pivot2
* all in (great, *) == pivot2
*
* Pointer k is the first index of ?-part
*/
outer:
for (int k = less; k <= great; k++) {
double ak = a[k]; double ak = a[k];
if (ak == pivot1) { if (ak == pivot2) { // Move a[k] to right part
a[k++] = a[less]; while (a[great] == pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] == pivot1) {
a[k] = a[less];
a[less++] = pivot1; a[less++] = pivot1;
} else if (ak == pivot2) { } else { // pivot1 < a[great] < pivot2
a[k] = a[great]; a[k] = a[great];
}
a[great--] = pivot2; a[great--] = pivot2;
} else { } else if (ak == pivot1) { // Move a[k] to left part
k++; a[k] = a[less];
a[less++] = pivot1;
} }
} }
} }
......
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