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/*******************************************************************************
* ___ _ ____ ____
* / _ \ _ _ ___ ___| |_| _ \| __ )
* | | | | | | |/ _ \/ __| __| | | | _ \
* | |_| | |_| | __/\__ \ |_| |_| | |_) |
* \__\_\\__,_|\___||___/\__|____/|____/
*
* Copyright (c) 2014-2019 Appsicle
* Copyright (c) 2019-2020 QuestDB
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
******************************************************************************/
package io.questdb.std;
public class LongSort {
/**
* If the length of an array to be sorted is less than this
* constant, Quicksort is used in preference to merge sort.
*/
private static final int QUICKSORT_THRESHOLD = 286;
/**
* The maximum length of run in merge sort.
*/
private static final int MAX_RUN_LENGTH = 33;
/**
* The maximum number of runs in merge sort.
*/
private static final int MAX_RUN_COUNT = 67;
/**
* If the length of an array to be sorted is less than this
* constant, insertion sort is used in preference to Quicksort.
*/
private static final int INSERTION_SORT_THRESHOLD = 47;
/**
* Sorts the specified range of the array.
*
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
public static void sort(LongVec vec, int left, int right) {
// Use Quicksort on small arrays
if (right - left < QUICKSORT_THRESHOLD) {
sort(vec, left, right, true);
return;
}
/*
* Index run[i] is the start of i-th run
* (ascending or descending sequence).
*/
int[] run = new int[MAX_RUN_COUNT + 1];
int count = 0;
run[0] = left;
// Check if the array is nearly sorted
for (int k = left; k < right; run[count] = k) {
if (vec.getQuick(k) < vec.getQuick(k + 1)) { // ascending
//noinspection StatementWithEmptyBody
while (++k <= right && vec.getQuick(k - 1) <= vec.getQuick(k)) ;
} else if (vec.getQuick(k) > vec.getQuick(k + 1)) { // descending
//noinspection StatementWithEmptyBody
while (++k <= right && vec.getQuick(k - 1) >= vec.getQuick(k)) ;
for (int lo = run[count] - 1, hi = k; ++lo < --hi; ) {
swap(vec, lo, hi);
}
} else { // equal
for (int m = MAX_RUN_LENGTH; ++k <= right && vec.getQuick(k - 1) == vec.getQuick(k); ) {
if (--m == 0) {
sort(vec, left, right, true);
return;
}
}
}
/*
* The array is not highly structured,
* use Quicksort instead of merge sort.
*/
if (++count == MAX_RUN_COUNT) {
sort(vec, left, right, true);
return;
}
}
// Check special cases
if (run[count] == right++) { // The last run contains one element
run[++count] = right;
} else if (count == 1) { // The array is already sorted
return;
}
/*
* Create temporary array, which is used for merging.
* Implementation note: variable "right" is increased by 1.
*/
LongVec a;
LongVec b;
byte odd = 0;
//noinspection StatementWithEmptyBody
for (int n = 1; (n <<= 1) < count; odd ^= 1) ;
if (odd == 0) {
b = vec;
a = vec.newInstance();
//noinspection StatementWithEmptyBody
for (int i = left - 1; ++i < right; a.setQuick(i, b.getQuick(i))) ;
} else {
a = vec;
b = vec.newInstance();
}
// Merging
for (int last; count > 1; count = last) {
for (int k = (last = 0) + 2; k <= count; k += 2) {
int hi = run[k], mi = run[k - 1];
for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
if (q >= hi || p < mi && vec.getQuick(p) <= vec.getQuick(q)) {
b.setQuick(i, a.getQuick(p++));
} else {
b.setQuick(i, a.getQuick(q++));
}
}
run[++last] = hi;
}
if ((count & 1) != 0) {
//noinspection StatementWithEmptyBody
for (int i = right, lo = run[count - 1]; --i >= lo; b.setQuick(i, a.getQuick(i))) ;
run[++last] = right;
}
LongVec t = a;
a = b;
b = t;
}
}
/**
* Sorts the specified range of the array by Dual-Pivot Quicksort.
*
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
* @param leftmost indicates if this part is the leftmost in the range
*/
private static void sort(LongVec vec, int left, int right, boolean leftmost) {
int length = right - left + 1;
// Use insertion sort on tiny arrays
if (length < INSERTION_SORT_THRESHOLD) {
if (leftmost) {
/*
* Traditional (without sentinel) insertion sort,
* optimized for server VM, is used in case of
* the leftmost part.
*/
for (int i = left, j = i; i < right; j = ++i) {
long ai = vec.getQuick(i + 1);
while (ai < vec.getQuick(j)) {
let(vec, j + 1, j);
if (j-- == left) {
break;
}
}
vec.setQuick(j + 1, ai);
}
} else {
/*
* Skip the longest ascending sequence.
*/
do {
if (left >= right) {
return;
}
} while (vec.getQuick(++left) >= vec.getQuick(left - 1));
/*
* Every element from adjoining part plays the role
* of sentinel, therefore this allows us to avoid the
* left range check on each iteration. Moreover, we use
* the more optimized algorithm, so called pair insertion
* sort, which is faster (in the context of Quicksort)
* than traditional implementation of insertion sort.
*/
for (int k = left; ++left <= right; k = ++left) {
long a1 = vec.getQuick(k), a2 = vec.getQuick(left);
if (a1 < a2) {
a2 = a1;
a1 = vec.getQuick(left);
}
while (a1 < vec.getQuick(--k)) {
let(vec, k + 2, k);
}
vec.setQuick(++k + 1, a1);
while (a2 < vec.getQuick(--k)) {
let(vec, k + 1, k);
}
vec.setQuick(k + 1, a2);
}
long last = vec.getQuick(right);
while (last < vec.getQuick(--right)) {
let(vec, right + 1, right);
}
vec.setQuick(right + 1, last);
}
return;
}
// Inexpensive approximation of length / 7
int seventh = (length >> 3) + (length >> 6) + 1;
/*
* Sort five evenly spaced elements around (and including) the
* center element in the range. These elements will be used for
* pivot selection as described below. The choice for spacing
* these elements was empirically determined to work well on
* a wide variety of inputs.
*/
int e3 = (left + right) >>> 1; // The midpoint
int e2 = e3 - seventh;
int e1 = e2 - seventh;
int e4 = e3 + seventh;
int e5 = e4 + seventh;
// Sort these elements using insertion sort
if (vec.getQuick(e2) < vec.getQuick(e1)) {
swap(vec, e2, e1);
}
if (vec.getQuick(e3) < vec.getQuick(e2)) {
long t = vec.getQuick(e3);
let(vec, e3, e2);
vec.setQuick(e2, t);
if (t < vec.getQuick(e1)) {
let(vec, e2, e1);
vec.setQuick(e1, t);
}
}
if (vec.getQuick(e4) < vec.getQuick(e3)) {
long t = vec.getQuick(e4);
let(vec, e4, e3);
vec.setQuick(e3, t);
if (t < vec.getQuick(e2)) {
let(vec, e3, e2);
vec.setQuick(e2, t);
if (t < vec.getQuick(e1)) {
let(vec, e2, e1);
vec.setQuick(e1, t);
}
}
}
if (vec.getQuick(e5) < vec.getQuick(e4)) {
long t = vec.getQuick(e5);
let(vec, e5, e4);
vec.setQuick(e4, t);
if (t < vec.getQuick(e3)) {
let(vec, e4, e3);
vec.setQuick(e3, t);
if (t < vec.getQuick(e2)) {
let(vec, e3, e2);
vec.setQuick(e2, t);
if (t < vec.getQuick(e1)) {
let(vec, e2, e1);
vec.setQuick(e1, t);
}
}
}
}
// Pointers
int less = left; // The index of the first element of center part
int great = right; // The index before the first element of right part
if (vec.getQuick(e1) != vec.getQuick(e2) && vec.getQuick(e2) != vec.getQuick(e3) && vec.getQuick(e3) != vec.getQuick(e4) && vec.getQuick(e4) != vec.getQuick(e5)) {
/*
* Use the second and fourth of the five sorted elements as pivots.
* These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*/
long pivot1 = vec.getQuick(e2);
long pivot2 = vec.getQuick(e4);
/*
* The first and the last elements to be sorted are moved to the
* locations formerly occupied by the pivots. When partitioning
* is complete, the pivots are swapped back into their final
* positions, and excluded from subsequent sorting.
*/
let(vec, e2, left);
let(vec, e4, right);
/*
* Skip elements, which are less or greater than pivot values.
*/
//noinspection StatementWithEmptyBody
while (vec.getQuick(++less) < pivot1) ;
//noinspection StatementWithEmptyBody
while (vec.getQuick(--great) > pivot2) ;
/*
* Partitioning:
*
* left part center part right part
* +--------------------------------------------------------------+
* | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 |
* +--------------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2
*
* Pointer k is the first index of ?-part.
*/
outer:
for (int k = less - 1; ++k <= great; ) {
long ak = vec.getQuick(k);
if (ak < pivot1) { // Move a[k] to left part
let(vec, k, less);
/*
* Here and below we use "a[i] = b; i++;" instead
* of "a[i++] = b;" due to performance issue.
*/
vec.setQuick(less, ak);
++less;
} else if (ak > pivot2) { // Move a[k] to right part
while (vec.getQuick(great) > pivot2) {
if (great-- == k) {
break outer;
}
}
if (vec.getQuick(great) < pivot1) { // a[great] <= pivot2
let(vec, k, less);
let(vec, less, great);
++less;
} else { // pivot1 <= a[great] <= pivot2
let(vec, k, great);
}
/*
* Here and below we use "a[i] = b; i--;" instead
* of "a[i--] = b;" due to performance issue.
*/
vec.setQuick(great, ak);
--great;
}
}
// Swap pivots into their final positions
let(vec, left, less - 1);
vec.setQuick(less - 1, pivot1);
let(vec, right, great + 1);
vec.setQuick(great + 1, pivot2);
// Sort left and right parts recursively, excluding known pivots
sort(vec, left, less - 2, leftmost);
sort(vec, great + 2, right, false);
/*
* If center part is too large (comprises > 4/7 of the array),
* swap internal pivot values to ends.
*/
if (less < e1 && e5 < great) {
/*
* Skip elements, which are equal to pivot values.
*/
while (vec.getQuick(less) == pivot1) {
++less;
}
while (vec.getQuick(great) == pivot2) {
--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 - 1; ++k <= great; ) {
long ak = vec.getQuick(k);
if (ak == pivot1) { // Move a[k] to left part
let(vec, k, less);
vec.setQuick(less, ak);
++less;
} else if (ak == pivot2) { // Move a[k] to right part
while (vec.getQuick(great) == pivot2) {
if (great-- == k) {
break outer;
}
}
if (vec.getQuick(great) == pivot1) { // a[great] < pivot2
let(vec, k, less);
/*
* Even though a[great] equals to pivot1, the
* assignment a[less] = pivot1 may be incorrect,
* if a[great] and pivot1 are floating-point zeros
* of different signs. Therefore in float and
* double sorting methods we have to use more
* accurate assignment a[less] = a[great].
*/
vec.setQuick(less, pivot1);
++less;
} else { // pivot1 < a[great] < pivot2
let(vec, k, great);
}
vec.setQuick(great, ak);
--great;
}
}
}
// Sort center part recursively
sort(vec, less, great, false);
} else { // Partitioning with one pivot
/*
* Use the third of the five sorted elements as pivot.
* This value is inexpensive approximation of the median.
*/
long pivot = vec.getQuick(e3);
/*
* Partitioning degenerates to the traditional 3-way
* (or "Dutch National Flag") schema:
*
* left part center part right part
* +-------------------------------------------------+
* | < pivot | == pivot | ? | > pivot |
* +-------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot
* all in [less, k) == pivot
* all in (great, right) > pivot
*
* Pointer k is the first index of ?-part.
*/
for (int k = less; k <= great; ++k) {
if (vec.getQuick(k) == pivot) {
continue;
}
long ak = vec.getQuick(k);
if (ak < pivot) { // Move a[k] to left part
let(vec, k, less);
vec.setQuick(less, ak);
++less;
} else { // a[k] > pivot - Move a[k] to right part
while (vec.getQuick(great) > pivot) {
--great;
}
if (vec.getQuick(great) < pivot) { // a[great] <= pivot
let(vec, k, less);
let(vec, less, great);
++less;
} else { // a[great] == pivot
/*
* Even though a[great] equals to pivot, the
* assignment a[k] = pivot may be incorrect,
* if a[great] and pivot are floating-point
* zeros of different signs. Therefore in float
* and double sorting methods we have to use
* more accurate assignment a[k] = a[great].
*/
vec.setQuick(k, pivot);
}
vec.setQuick(great, ak);
--great;
}
}
/*
* Sort left and right parts recursively.
* All elements from center part are equal
* and, therefore, already sorted.
*/
sort(vec, left, less - 1, leftmost);
sort(vec, great + 1, right, false);
}
}
private static void swap(LongVec vec, int a, int b) {
long tmp = vec.getQuick(a);
vec.setQuick(a, vec.getQuick(b));
vec.setQuick(b, tmp);
}
private static void let(LongVec vec, int a, int b) {
vec.setQuick(a, vec.getQuick(b));
}
}
