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	/*
	* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
	*
	* This code is free software; you can redistribute it and/or modify it
	* under the terms of the GNU General Public License version 2 only, as
	* published by the Free Software Foundation. Oracle designates this
	* particular file as subject to the "Classpath" exception as provided
	* by Oracle in the LICENSE file that accompanied this code.
	*
	* This code is distributed in the hope that it will be useful, but WITHOUT
	* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
	* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
	* version 2 for more details (a copy is included in the LICENSE file that
	* accompanied this code).
	*
	* You should have received a copy of the GNU General Public License version
	* 2 along with this work; if not, write to the Free Software Foundation,
	* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
	*
	* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
	* or visit www.oracle.com if you need additional information or have any
	* questions.
	*/

	/*
	* This file is available under and governed by the GNU General Public
	* License version 2 only, as published by the Free Software Foundation.
	* However, the following notice accompanied the original version of this
	* file:
	*
	* Written by Doug Lea with assistance from members of JCP JSR-166
	* Expert Group and released to the public domain, as explained at
	* http://creativecommons.org/publicdomain/zero/1.0/
	*/

	package java.util;

	import java.util.concurrent.CountedCompleter;
	import java.util.concurrent.ForkJoinPool;
	import java.util.function.BinaryOperator;
	import java.util.function.DoubleBinaryOperator;
	import java.util.function.IntBinaryOperator;
	import java.util.function.LongBinaryOperator;

	/**
	* ForkJoin tasks to perform Arrays.parallelPrefix operations.
	*
	* @author Doug Lea
	* @since 1.8
	*/
	class ArrayPrefixHelpers {
	private ArrayPrefixHelpers() {} // non-instantiable

	/*
	* Parallel prefix (aka cumulate, scan) task classes
	* are based loosely on Guy Blelloch's original
	* algorithm (http://www.cs.cmu.edu/~scandal/alg/scan.html):
	* Keep dividing by two to threshold segment size, and then:
	* Pass 1: Create tree of partial sums for each segment
	* Pass 2: For each segment, cumulate with offset of left sibling
	*
	* This version improves performance within FJ framework mainly by
	* allowing the second pass of ready left-hand sides to proceed
	* even if some right-hand side first passes are still executing.
	* It also combines first and second pass for leftmost segment,
	* and skips the first pass for rightmost segment (whose result is
	* not needed for second pass). It similarly manages to avoid
	* requiring that users supply an identity basis for accumulations
	* by tracking those segments/subtasks for which the first
	* existing element is used as base.
	*
	* Managing this relies on ORing some bits in the pendingCount for
	* phases/states: CUMULATE, SUMMED, and FINISHED. CUMULATE is the
	* main phase bit. When false, segments compute only their sum.
	* When true, they cumulate array elements. CUMULATE is set at
	* root at beginning of second pass and then propagated down. But
	* it may also be set earlier for subtrees with lo==0 (the left
	* spine of tree). SUMMED is a one bit join count. For leafs, it
	* is set when summed. For internal nodes, it becomes true when
	* one child is summed. When the second child finishes summing,
	* we then moves up tree to trigger the cumulate phase. FINISHED
	* is also a one bit join count. For leafs, it is set when
	* cumulated. For internal nodes, it becomes true when one child
	* is cumulated. When the second child finishes cumulating, it
	* then moves up tree, completing at the root.
	*
	* To better exploit locality and reduce overhead, the compute
	* method loops starting with the current task, moving if possible
	* to one of its subtasks rather than forking.
	*
	* As usual for this sort of utility, there are 4 versions, that
	* are simple copy/paste/adapt variants of each other. (The
	* double and int versions differ from long version solely by
	* replacing "long" (with case-matching)).
	*/

	// see above
	static final int CUMULATE = 1;
	static final int SUMMED = 2;
	static final int FINISHED = 4;

	/** The smallest subtask array partition size to use as threshold */
	static final int MIN_PARTITION = 16;

	static final class CumulateTask<T> extends CountedCompleter<Void> {
	final T[] array;
	final BinaryOperator<T> function;
	CumulateTask<T> left, right;
	T in, out;
	final int lo, hi, origin, fence, threshold;

	/** Root task constructor */
	public CumulateTask(CumulateTask<T> parent,
	BinaryOperator<T> function,
	T[] array, int lo, int hi) {
	super(parent);
	this.function = function; this.array = array;
	this.lo = this.origin = lo; this.hi = this.fence = hi;
	int p;
	this.threshold =
	(p = (hi - lo) / (ForkJoinPool.getCommonPoolParallelism() << 3))
	<= MIN_PARTITION ? MIN_PARTITION : p;
	}

	/** Subtask constructor */
	CumulateTask(CumulateTask<T> parent, BinaryOperator<T> function,
	T[] array, int origin, int fence, int threshold,
	int lo, int hi) {
	super(parent);
	this.function = function; this.array = array;
	this.origin = origin; this.fence = fence;
	this.threshold = threshold;
	this.lo = lo; this.hi = hi;
	}

	public final void compute() {
	final BinaryOperator<T> fn;
	final T[] a;
	if ((fn = this.function) == null \|\| (a = this.array) == null)
	throw new NullPointerException(); // hoist checks
	int th = threshold, org = origin, fnc = fence, l, h;
	CumulateTask<T> t = this;
	outer: while ((l = t.lo) >= 0 && (h = t.hi) <= a.length) {
	if (h - l > th) {
	CumulateTask<T> lt = t.left, rt = t.right, f;
	if (lt == null) { // first pass
	int mid = (l + h) >>> 1;
	f = rt = t.right =
	new CumulateTask<T>(t, fn, a, org, fnc, th, mid, h);
	t = lt = t.left =
	new CumulateTask<T>(t, fn, a, org, fnc, th, l, mid);
	}
	else { // possibly refork
	T pin = t.in;
	lt.in = pin;
	f = t = null;
	if (rt != null) {
	T lout = lt.out;
	rt.in = (l == org ? lout :
	fn.apply(pin, lout));
	for (int c;;) {
	if (((c = rt.getPendingCount()) & CUMULATE) != 0)
	break;
	if (rt.compareAndSetPendingCount(c, c\|CUMULATE)){
	t = rt;
	break;
	}
	}
	}
	for (int c;;) {
	if (((c = lt.getPendingCount()) & CUMULATE) != 0)
	break;
	if (lt.compareAndSetPendingCount(c, c\|CUMULATE)) {
	if (t != null)
	f = t;
	t = lt;
	break;
	}
	}
	if (t == null)
	break;
	}
	if (f != null)
	f.fork();
	}
	else {
	int state; // Transition to sum, cumulate, or both
	for (int b;;) {
	if (((b = t.getPendingCount()) & FINISHED) != 0)
	break outer; // already done
	state = ((b & CUMULATE) != 0 ? FINISHED :
	(l > org) ? SUMMED : (SUMMED\|FINISHED));
	if (t.compareAndSetPendingCount(b, b\|state))
	break;
	}

	T sum;
	if (state != SUMMED) {
	int first;
	if (l == org) { // leftmost; no in
	sum = a[org];
	first = org + 1;
	}
	else {
	sum = t.in;
	first = l;
	}
	for (int i = first; i < h; ++i) // cumulate
	a[i] = sum = fn.apply(sum, a[i]);
	}
	else if (h < fnc) { // skip rightmost
	sum = a[l];
	for (int i = l + 1; i < h; ++i) // sum only
	sum = fn.apply(sum, a[i]);
	}
	else
	sum = t.in;
	t.out = sum;
	for (CumulateTask<T> par;;) { // propagate
	@SuppressWarnings("unchecked") CumulateTask<T> partmp
	= (CumulateTask<T>)t.getCompleter();
	if ((par = partmp) == null) {
	if ((state & FINISHED) != 0) // enable join
	t.quietlyComplete();
	break outer;
	}
	int b = par.getPendingCount();
	if ((b & state & FINISHED) != 0)
	t = par; // both done
	else if ((b & state & SUMMED) != 0) { // both summed
	int nextState; CumulateTask<T> lt, rt;
	if ((lt = par.left) != null &&
	(rt = par.right) != null) {
	T lout = lt.out;
	par.out = (rt.hi == fnc ? lout :
	fn.apply(lout, rt.out));
	}
	int refork = (((b & CUMULATE) == 0 &&
	par.lo == org) ? CUMULATE : 0);
	if ((nextState = b\|state\|refork) == b \|\|
	par.compareAndSetPendingCount(b, nextState)) {
	state = SUMMED; // drop finished
	t = par;
	if (refork != 0)
	par.fork();
	}
	}
	else if (par.compareAndSetPendingCount(b, b\|state))
	break outer; // sib not ready
	}
	}
	}
	}
	private static final long serialVersionUID = 5293554502939613543L;
	}

	static final class LongCumulateTask extends CountedCompleter<Void> {
	final long[] array;
	final LongBinaryOperator function;
	LongCumulateTask left, right;
	long in, out;
	final int lo, hi, origin, fence, threshold;

	/** Root task constructor */
	public LongCumulateTask(LongCumulateTask parent,
	LongBinaryOperator function,
	long[] array, int lo, int hi) {
	super(parent);
	this.function = function; this.array = array;
	this.lo = this.origin = lo; this.hi = this.fence = hi;
	int p;
	this.threshold =
	(p = (hi - lo) / (ForkJoinPool.getCommonPoolParallelism() << 3))
	<= MIN_PARTITION ? MIN_PARTITION : p;
	}

	/** Subtask constructor */
	LongCumulateTask(LongCumulateTask parent, LongBinaryOperator function,
	long[] array, int origin, int fence, int threshold,
	int lo, int hi) {
	super(parent);
	this.function = function; this.array = array;
	this.origin = origin; this.fence = fence;
	this.threshold = threshold;
	this.lo = lo; this.hi = hi;
	}

	public final void compute() {
	final LongBinaryOperator fn;
	final long[] a;
	if ((fn = this.function) == null \|\| (a = this.array) == null)
	throw new NullPointerException(); // hoist checks
	int th = threshold, org = origin, fnc = fence, l, h;
	LongCumulateTask t = this;
	outer: while ((l = t.lo) >= 0 && (h = t.hi) <= a.length) {
	if (h - l > th) {
	LongCumulateTask lt = t.left, rt = t.right, f;
	if (lt == null) { // first pass
	int mid = (l + h) >>> 1;
	f = rt = t.right =
	new LongCumulateTask(t, fn, a, org, fnc, th, mid, h);
	t = lt = t.left =
	new LongCumulateTask(t, fn, a, org, fnc, th, l, mid);
	}
	else { // possibly refork
	long pin = t.in;
	lt.in = pin;
	f = t = null;
	if (rt != null) {
	long lout = lt.out;
	rt.in = (l == org ? lout :
	fn.applyAsLong(pin, lout));
	for (int c;;) {
	if (((c = rt.getPendingCount()) & CUMULATE) != 0)
	break;
	if (rt.compareAndSetPendingCount(c, c\|CUMULATE)){
	t = rt;
	break;
	}
	}
	}
	for (int c;;) {
	if (((c = lt.getPendingCount()) & CUMULATE) != 0)
	break;
	if (lt.compareAndSetPendingCount(c, c\|CUMULATE)) {
	if (t != null)
	f = t;
	t = lt;
	break;
	}
	}
	if (t == null)
	break;
	}
	if (f != null)
	f.fork();
	}
	else {
	int state; // Transition to sum, cumulate, or both
	for (int b;;) {
	if (((b = t.getPendingCount()) & FINISHED) != 0)
	break outer; // already done
	state = ((b & CUMULATE) != 0 ? FINISHED :
	(l > org) ? SUMMED : (SUMMED\|FINISHED));
	if (t.compareAndSetPendingCount(b, b\|state))
	break;
	}

	long sum;
	if (state != SUMMED) {
	int first;
	if (l == org) { // leftmost; no in
	sum = a[org];
	first = org + 1;
	}
	else {
	sum = t.in;
	first = l;
	}
	for (int i = first; i < h; ++i) // cumulate
	a[i] = sum = fn.applyAsLong(sum, a[i]);
	}
	else if (h < fnc) { // skip rightmost
	sum = a[l];
	for (int i = l + 1; i < h; ++i) // sum only
	sum = fn.applyAsLong(sum, a[i]);
	}
	else
	sum = t.in;
	t.out = sum;
	for (LongCumulateTask par;;) { // propagate
	if ((par = (LongCumulateTask)t.getCompleter()) == null) {
	if ((state & FINISHED) != 0) // enable join
	t.quietlyComplete();
	break outer;
	}
	int b = par.getPendingCount();
	if ((b & state & FINISHED) != 0)
	t = par; // both done
	else if ((b & state & SUMMED) != 0) { // both summed
	int nextState; LongCumulateTask lt, rt;
	if ((lt = par.left) != null &&
	(rt = par.right) != null) {
	long lout = lt.out;
	par.out = (rt.hi == fnc ? lout :
	fn.applyAsLong(lout, rt.out));
	}
	int refork = (((b & CUMULATE) == 0 &&
	par.lo == org) ? CUMULATE : 0);
	if ((nextState = b\|state\|refork) == b \|\|
	par.compareAndSetPendingCount(b, nextState)) {
	state = SUMMED; // drop finished
	t = par;
	if (refork != 0)
	par.fork();
	}
	}
	else if (par.compareAndSetPendingCount(b, b\|state))
	break outer; // sib not ready
	}
	}
	}
	}
	private static final long serialVersionUID = -5074099945909284273L;
	}

	static final class DoubleCumulateTask extends CountedCompleter<Void> {
	final double[] array;
	final DoubleBinaryOperator function;
	DoubleCumulateTask left, right;
	double in, out;
	final int lo, hi, origin, fence, threshold;

	/** Root task constructor */
	public DoubleCumulateTask(DoubleCumulateTask parent,
	DoubleBinaryOperator function,
	double[] array, int lo, int hi) {
	super(parent);
	this.function = function; this.array = array;
	this.lo = this.origin = lo; this.hi = this.fence = hi;
	int p;
	this.threshold =
	(p = (hi - lo) / (ForkJoinPool.getCommonPoolParallelism() << 3))
	<= MIN_PARTITION ? MIN_PARTITION : p;
	}

	/** Subtask constructor */
	DoubleCumulateTask(DoubleCumulateTask parent, DoubleBinaryOperator function,
	double[] array, int origin, int fence, int threshold,
	int lo, int hi) {
	super(parent);
	this.function = function; this.array = array;
	this.origin = origin; this.fence = fence;
	this.threshold = threshold;
	this.lo = lo; this.hi = hi;
	}

	public final void compute() {
	final DoubleBinaryOperator fn;
	final double[] a;
	if ((fn = this.function) == null \|\| (a = this.array) == null)
	throw new NullPointerException(); // hoist checks
	int th = threshold, org = origin, fnc = fence, l, h;
	DoubleCumulateTask t = this;
	outer: while ((l = t.lo) >= 0 && (h = t.hi) <= a.length) {
	if (h - l > th) {
	DoubleCumulateTask lt = t.left, rt = t.right, f;
	if (lt == null) { // first pass
	int mid = (l + h) >>> 1;
	f = rt = t.right =
	new DoubleCumulateTask(t, fn, a, org, fnc, th, mid, h);
	t = lt = t.left =
	new DoubleCumulateTask(t, fn, a, org, fnc, th, l, mid);
	}
	else { // possibly refork
	double pin = t.in;
	lt.in = pin;
	f = t = null;
	if (rt != null) {
	double lout = lt.out;
	rt.in = (l == org ? lout :
	fn.applyAsDouble(pin, lout));
	for (int c;;) {
	if (((c = rt.getPendingCount()) & CUMULATE) != 0)
	break;
	if (rt.compareAndSetPendingCount(c, c\|CUMULATE)){
	t = rt;
	break;
	}
	}
	}
	for (int c;;) {
	if (((c = lt.getPendingCount()) & CUMULATE) != 0)
	break;
	if (lt.compareAndSetPendingCount(c, c\|CUMULATE)) {
	if (t != null)
	f = t;
	t = lt;
	break;
	}
	}
	if (t == null)
	break;
	}
	if (f != null)
	f.fork();
	}
	else {
	int state; // Transition to sum, cumulate, or both
	for (int b;;) {
	if (((b = t.getPendingCount()) & FINISHED) != 0)
	break outer; // already done
	state = ((b & CUMULATE) != 0 ? FINISHED :
	(l > org) ? SUMMED : (SUMMED\|FINISHED));
	if (t.compareAndSetPendingCount(b, b\|state))
	break;
	}

	double sum;
	if (state != SUMMED) {
	int first;
	if (l == org) { // leftmost; no in
	sum = a[org];
	first = org + 1;
	}
	else {
	sum = t.in;
	first = l;
	}
	for (int i = first; i < h; ++i) // cumulate
	a[i] = sum = fn.applyAsDouble(sum, a[i]);
	}
	else if (h < fnc) { // skip rightmost
	sum = a[l];
	for (int i = l + 1; i < h; ++i) // sum only
	sum = fn.applyAsDouble(sum, a[i]);
	}
	else
	sum = t.in;
	t.out = sum;
	for (DoubleCumulateTask par;;) { // propagate
	if ((par = (DoubleCumulateTask)t.getCompleter()) == null) {
	if ((state & FINISHED) != 0) // enable join
	t.quietlyComplete();
	break outer;
	}
	int b = par.getPendingCount();
	if ((b & state & FINISHED) != 0)
	t = par; // both done
	else if ((b & state & SUMMED) != 0) { // both summed
	int nextState; DoubleCumulateTask lt, rt;
	if ((lt = par.left) != null &&
	(rt = par.right) != null) {
	double lout = lt.out;
	par.out = (rt.hi == fnc ? lout :
	fn.applyAsDouble(lout, rt.out));
	}
	int refork = (((b & CUMULATE) == 0 &&
	par.lo == org) ? CUMULATE : 0);
	if ((nextState = b\|state\|refork) == b \|\|
	par.compareAndSetPendingCount(b, nextState)) {
	state = SUMMED; // drop finished
	t = par;
	if (refork != 0)
	par.fork();
	}
	}
	else if (par.compareAndSetPendingCount(b, b\|state))
	break outer; // sib not ready
	}
	}
	}
	}
	private static final long serialVersionUID = -586947823794232033L;
	}

	static final class IntCumulateTask extends CountedCompleter<Void> {
	final int[] array;
	final IntBinaryOperator function;
	IntCumulateTask left, right;
	int in, out;
	final int lo, hi, origin, fence, threshold;

	/** Root task constructor */
	public IntCumulateTask(IntCumulateTask parent,
	IntBinaryOperator function,
	int[] array, int lo, int hi) {
	super(parent);
	this.function = function; this.array = array;
	this.lo = this.origin = lo; this.hi = this.fence = hi;
	int p;
	this.threshold =
	(p = (hi - lo) / (ForkJoinPool.getCommonPoolParallelism() << 3))
	<= MIN_PARTITION ? MIN_PARTITION : p;
	}

	/** Subtask constructor */
	IntCumulateTask(IntCumulateTask parent, IntBinaryOperator function,
	int[] array, int origin, int fence, int threshold,
	int lo, int hi) {
	super(parent);
	this.function = function; this.array = array;
	this.origin = origin; this.fence = fence;
	this.threshold = threshold;
	this.lo = lo; this.hi = hi;
	}

	public final void compute() {
	final IntBinaryOperator fn;
	final int[] a;
	if ((fn = this.function) == null \|\| (a = this.array) == null)
	throw new NullPointerException(); // hoist checks
	int th = threshold, org = origin, fnc = fence, l, h;
	IntCumulateTask t = this;
	outer: while ((l = t.lo) >= 0 && (h = t.hi) <= a.length) {
	if (h - l > th) {
	IntCumulateTask lt = t.left, rt = t.right, f;
	if (lt == null) { // first pass
	int mid = (l + h) >>> 1;
	f = rt = t.right =
	new IntCumulateTask(t, fn, a, org, fnc, th, mid, h);
	t = lt = t.left =
	new IntCumulateTask(t, fn, a, org, fnc, th, l, mid);
	}
	else { // possibly refork
	int pin = t.in;
	lt.in = pin;
	f = t = null;
	if (rt != null) {
	int lout = lt.out;
	rt.in = (l == org ? lout :
	fn.applyAsInt(pin, lout));
	for (int c;;) {
	if (((c = rt.getPendingCount()) & CUMULATE) != 0)
	break;
	if (rt.compareAndSetPendingCount(c, c\|CUMULATE)){
	t = rt;
	break;
	}
	}
	}
	for (int c;;) {
	if (((c = lt.getPendingCount()) & CUMULATE) != 0)
	break;
	if (lt.compareAndSetPendingCount(c, c\|CUMULATE)) {
	if (t != null)
	f = t;
	t = lt;
	break;
	}
	}
	if (t == null)
	break;
	}
	if (f != null)
	f.fork();
	}
	else {
	int state; // Transition to sum, cumulate, or both
	for (int b;;) {
	if (((b = t.getPendingCount()) & FINISHED) != 0)
	break outer; // already done
	state = ((b & CUMULATE) != 0 ? FINISHED :
	(l > org) ? SUMMED : (SUMMED\|FINISHED));
	if (t.compareAndSetPendingCount(b, b\|state))
	break;
	}

	int sum;
	if (state != SUMMED) {
	int first;
	if (l == org) { // leftmost; no in
	sum = a[org];
	first = org + 1;
	}
	else {
	sum = t.in;
	first = l;
	}
	for (int i = first; i < h; ++i) // cumulate
	a[i] = sum = fn.applyAsInt(sum, a[i]);
	}
	else if (h < fnc) { // skip rightmost
	sum = a[l];
	for (int i = l + 1; i < h; ++i) // sum only
	sum = fn.applyAsInt(sum, a[i]);
	}
	else
	sum = t.in;
	t.out = sum;
	for (IntCumulateTask par;;) { // propagate
	if ((par = (IntCumulateTask)t.getCompleter()) == null) {
	if ((state & FINISHED) != 0) // enable join
	t.quietlyComplete();
	break outer;
	}
	int b = par.getPendingCount();
	if ((b & state & FINISHED) != 0)
	t = par; // both done
	else if ((b & state & SUMMED) != 0) { // both summed
	int nextState; IntCumulateTask lt, rt;
	if ((lt = par.left) != null &&
	(rt = par.right) != null) {
	int lout = lt.out;
	par.out = (rt.hi == fnc ? lout :
	fn.applyAsInt(lout, rt.out));
	}
	int refork = (((b & CUMULATE) == 0 &&
	par.lo == org) ? CUMULATE : 0);
	if ((nextState = b\|state\|refork) == b \|\|
	par.compareAndSetPendingCount(b, nextState)) {
	state = SUMMED; // drop finished
	t = par;
	if (refork != 0)
	par.fork();
	}
	}
	else if (par.compareAndSetPendingCount(b, b\|state))
	break outer; // sib not ready
	}
	}
	}
	}
	private static final long serialVersionUID = 3731755594596840961L;
	}
	}

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