8012647: Add Arrays.parallelPrefix (prefix sum, scan, cumulative sum)
Reviewed-by: chegar, alanb, psandoz
Contributed-by: Doug Lea <dl@cs.oswego.edu>, Tristan Yan <tristan.yan@oracle.com>, Chris Hegarty <chris.hegarty@oracle.com>
/*
* Copyright (c) 2012, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. 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.
*/
package java.util;
/*
* 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/
*/
import java.util.concurrent.ForkJoinPool;
import java.util.concurrent.CountedCompleter;
import java.util.function.BinaryOperator;
import java.util.function.IntBinaryOperator;
import java.util.function.LongBinaryOperator;
import java.util.function.DoubleBinaryOperator;
/**
* 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 soley 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
if ((par = (CumulateTask<T>)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; 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
}
}
}
}
}
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
}
}
}
}
}
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
}
}
}
}
}
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
}
}
}
}
}
}