ArraysParallelSortHelpers.java

/*
 * Copyright (c) 2012, 2013, 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;

import java.util.concurrent.RecursiveAction;
import java.util.concurrent.CountedCompleter;

/**
 * Helper utilities for the parallel sort methods in Arrays.parallelSort.
 *
 * For each primitive type, plus Object, we define a static class to
 * contain the Sorter and Merger implementations for that type:
 *
 * Sorter classes based mainly on CilkSort
 * <A href="http://supertech.lcs.mit.edu/cilk/"> Cilk</A>:
 * Basic algorithm:
 * if array size is small, just use a sequential quicksort (via Arrays.sort)
 *         Otherwise:
 *         1. Break array in half.
 *         2. For each half,
 *             a. break the half in half (i.e., quarters),
 *             b. sort the quarters
 *             c. merge them together
 *         3. merge together the two halves.
 *
 * One reason for splitting in quarters is that this guarantees that
 * the final sort is in the main array, not the workspace array.
 * (workspace and main swap roles on each subsort step.)  Leaf-level
 * sorts use the associated sequential sort.
 *
 * Merger classes perform merging for Sorter.  They are structured
 * such that if the underlying sort is stable (as is true for
 * TimSort), then so is the full sort.  If big enough, they split the
 * largest of the two partitions in half, find the greatest point in
 * smaller partition less than the beginning of the second half of
 * larger via binary search; and then merge in parallel the two
 * partitions.  In part to ensure tasks are triggered in
 * stability-preserving order, the current CountedCompleter design
 * requires some little tasks to serve as place holders for triggering
 * completion tasks.  These classes (EmptyCompleter and Relay) don't
 * need to keep track of the arrays, and are never themselves forked,
 * so don't hold any task state.
 *
 * The primitive class versions (FJByte... FJDouble) are
 * identical to each other except for type declarations.
 *
 * The base sequential sorts rely on non-public versions of TimSort,
 * ComparableTimSort, and DualPivotQuicksort sort methods that accept
 * temp workspace array slices that we will have already allocated, so
 * avoids redundant allocation. (Except for DualPivotQuicksort byte[]
 * sort, that does not ever use a workspace array.)
 */
/*package*/ class ArraysParallelSortHelpers {

    /*
     * Style note: The task classes have a lot of parameters, that are
     * stored as task fields and copied to local variables and used in
     * compute() methods, We pack these into as few lines as possible,
     * and hoist consistency checks among them before main loops, to
     * reduce distraction.
     */

    /**
     * A placeholder task for Sorters, used for the lowest
     * quartile task, that does not need to maintain array state.
     */
    static final class EmptyCompleter extends CountedCompleter<Void> {
        static final long serialVersionUID = 2446542900576103244L;
        EmptyCompleter(CountedCompleter<?> p) { super(p); }
        public final void compute() { }
    }

    /**
     * A trigger for secondary merge of two merges
     */
    static final class Relay extends CountedCompleter<Void> {
        static final long serialVersionUID = 2446542900576103244L;
        final CountedCompleter<?> task;
        Relay(CountedCompleter<?> task) {
            super(null, 1);
            this.task = task;
        }
        public final void compute() { }
        public final void onCompletion(CountedCompleter<?> t) {
            task.compute();
        }
    }

    /** Object + Comparator support class */
    static final class FJObject {
        static final class Sorter<T> extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final T[] a, w;
            final int base, size, wbase, gran;
            Comparator<? super T> comparator;
            Sorter(CountedCompleter<?> par, T[] a, T[] w, int base, int size,
                   int wbase, int gran,
                   Comparator<? super T> comparator) {
                super(par);
                this.a = a; this.w = w; this.base = base; this.size = size;
                this.wbase = wbase; this.gran = gran;
                this.comparator = comparator;
            }
            public final void compute() {
                CountedCompleter<?> s = this;
                Comparator<? super T> c = this.comparator;
                T[] a = this.a, w = this.w; // localize all params
                int b = this.base, n = this.size, wb = this.wbase, g = this.gran;
                while (n > g) {
                    int h = n >>> 1, q = h >>> 1, u = h + q; // quartiles
                    Relay fc = new Relay(new Merger<>(s, w, a, wb, h,
                                                      wb+h, n-h, b, g, c));
                    Relay rc = new Relay(new Merger<>(fc, a, w, b+h, q,
                                                      b+u, n-u, wb+h, g, c));
                    new Sorter<>(rc, a, w, b+u, n-u, wb+u, g, c).fork();
                    new Sorter<>(rc, a, w, b+h, q, wb+h, g, c).fork();;
                    Relay bc = new Relay(new Merger<>(fc, a, w, b, q,
                                                      b+q, h-q, wb, g, c));
                    new Sorter<>(bc, a, w, b+q, h-q, wb+q, g, c).fork();
                    s = new EmptyCompleter(bc);
                    n = q;
                }
                TimSort.sort(a, b, b + n, c, w, wb, n);
                s.tryComplete();
            }
        }

        static final class Merger<T> extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final T[] a, w; // main and workspace arrays
            final int lbase, lsize, rbase, rsize, wbase, gran;
            Comparator<? super T> comparator;
            Merger(CountedCompleter<?> par, T[] a, T[] w,
                   int lbase, int lsize, int rbase,
                   int rsize, int wbase, int gran,
                   Comparator<? super T> comparator) {
                super(par);
                this.a = a; this.w = w;
                this.lbase = lbase; this.lsize = lsize;
                this.rbase = rbase; this.rsize = rsize;
                this.wbase = wbase; this.gran = gran;
                this.comparator = comparator;
            }

            public final void compute() {
                Comparator<? super T> c = this.comparator;
                T[] a = this.a, w = this.w; // localize all params
                int lb = this.lbase, ln = this.lsize, rb = this.rbase,
                    rn = this.rsize, k = this.wbase, g = this.gran;
                if (a == null || w == null || lb < 0 || rb < 0 || k < 0 ||
                    c == null)
                    throw new IllegalStateException(); // hoist checks
                for (int lh, rh;;) {  // split larger, find point in smaller
                    if (ln >= rn) {
                        if (ln <= g)
                            break;
                        rh = rn;
                        T split = a[(lh = ln >>> 1) + lb];
                        for (int lo = 0; lo < rh; ) {
                            int rm = (lo + rh) >>> 1;
                            if (c.compare(split, a[rm + rb]) <= 0)
                                rh = rm;
                            else
                                lo = rm + 1;
                        }
                    }
                    else {
                        if (rn <= g)
                            break;
                        lh = ln;
                        T split = a[(rh = rn >>> 1) + rb];
                        for (int lo = 0; lo < lh; ) {
                            int lm = (lo + lh) >>> 1;
                            if (c.compare(split, a[lm + lb]) <= 0)
                                lh = lm;
                            else
                                lo = lm + 1;
                        }
                    }
                    Merger<T> m = new Merger<>(this, a, w, lb + lh, ln - lh,
                                               rb + rh, rn - rh,
                                               k + lh + rh, g, c);
                    rn = rh;
                    ln = lh;
                    addToPendingCount(1);
                    m.fork();
                }

                int lf = lb + ln, rf = rb + rn; // index bounds
                while (lb < lf && rb < rf) {
                    T t, al, ar;
                    if (c.compare((al = a[lb]), (ar = a[rb])) <= 0) {
                        lb++; t = al;
                    }
                    else {
                        rb++; t = ar;
                    }
                    w[k++] = t;
                }
                if (rb < rf)
                    System.arraycopy(a, rb, w, k, rf - rb);
                else if (lb < lf)
                    System.arraycopy(a, lb, w, k, lf - lb);

                tryComplete();
            }

        }
    } // FJObject

    /** byte support class */
    static final class FJByte {
        static final class Sorter extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final byte[] a, w;
            final int base, size, wbase, gran;
            Sorter(CountedCompleter<?> par, byte[] a, byte[] w, int base,
                   int size, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w; this.base = base; this.size = size;
                this.wbase = wbase; this.gran = gran;
            }
            public final void compute() {
                CountedCompleter<?> s = this;
                byte[] a = this.a, w = this.w; // localize all params
                int b = this.base, n = this.size, wb = this.wbase, g = this.gran;
                while (n > g) {
                    int h = n >>> 1, q = h >>> 1, u = h + q; // quartiles
                    Relay fc = new Relay(new Merger(s, w, a, wb, h,
                                                    wb+h, n-h, b, g));
                    Relay rc = new Relay(new Merger(fc, a, w, b+h, q,
                                                    b+u, n-u, wb+h, g));
                    new Sorter(rc, a, w, b+u, n-u, wb+u, g).fork();
                    new Sorter(rc, a, w, b+h, q, wb+h, g).fork();;
                    Relay bc = new Relay(new Merger(fc, a, w, b, q,
                                                    b+q, h-q, wb, g));
                    new Sorter(bc, a, w, b+q, h-q, wb+q, g).fork();
                    s = new EmptyCompleter(bc);
                    n = q;
                }
                DualPivotQuicksort.sort(a, b, b + n - 1);
                s.tryComplete();
            }
        }

        static final class Merger extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final byte[] a, w; // main and workspace arrays
            final int lbase, lsize, rbase, rsize, wbase, gran;
            Merger(CountedCompleter<?> par, byte[] a, byte[] w,
                   int lbase, int lsize, int rbase,
                   int rsize, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w;
                this.lbase = lbase; this.lsize = lsize;
                this.rbase = rbase; this.rsize = rsize;
                this.wbase = wbase; this.gran = gran;
            }

            public final void compute() {
                byte[] a = this.a, w = this.w; // localize all params
                int lb = this.lbase, ln = this.lsize, rb = this.rbase,
                    rn = this.rsize, k = this.wbase, g = this.gran;
                if (a == null || w == null || lb < 0 || rb < 0 || k < 0)
                    throw new IllegalStateException(); // hoist checks
                for (int lh, rh;;) {  // split larger, find point in smaller
                    if (ln >= rn) {
                        if (ln <= g)
                            break;
                        rh = rn;
                        byte split = a[(lh = ln >>> 1) + lb];
                        for (int lo = 0; lo < rh; ) {
                            int rm = (lo + rh) >>> 1;
                            if (split <= a[rm + rb])
                                rh = rm;
                            else
                                lo = rm + 1;
                        }
                    }
                    else {
                        if (rn <= g)
                            break;
                        lh = ln;
                        byte split = a[(rh = rn >>> 1) + rb];
                        for (int lo = 0; lo < lh; ) {
                            int lm = (lo + lh) >>> 1;
                            if (split <= a[lm + lb])
                                lh = lm;
                            else
                                lo = lm + 1;
                        }
                    }
                    Merger m = new Merger(this, a, w, lb + lh, ln - lh,
                                          rb + rh, rn - rh,
                                          k + lh + rh, g);
                    rn = rh;
                    ln = lh;
                    addToPendingCount(1);
                    m.fork();
                }

                int lf = lb + ln, rf = rb + rn; // index bounds
                while (lb < lf && rb < rf) {
                    byte t, al, ar;
                    if ((al = a[lb]) <= (ar = a[rb])) {
                        lb++; t = al;
                    }
                    else {
                        rb++; t = ar;
                    }
                    w[k++] = t;
                }
                if (rb < rf)
                    System.arraycopy(a, rb, w, k, rf - rb);
                else if (lb < lf)
                    System.arraycopy(a, lb, w, k, lf - lb);
                tryComplete();
            }
        }
    } // FJByte

    /** char support class */
    static final class FJChar {
        static final class Sorter extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final char[] a, w;
            final int base, size, wbase, gran;
            Sorter(CountedCompleter<?> par, char[] a, char[] w, int base,
                   int size, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w; this.base = base; this.size = size;
                this.wbase = wbase; this.gran = gran;
            }
            public final void compute() {
                CountedCompleter<?> s = this;
                char[] a = this.a, w = this.w; // localize all params
                int b = this.base, n = this.size, wb = this.wbase, g = this.gran;
                while (n > g) {
                    int h = n >>> 1, q = h >>> 1, u = h + q; // quartiles
                    Relay fc = new Relay(new Merger(s, w, a, wb, h,
                                                    wb+h, n-h, b, g));
                    Relay rc = new Relay(new Merger(fc, a, w, b+h, q,
                                                    b+u, n-u, wb+h, g));
                    new Sorter(rc, a, w, b+u, n-u, wb+u, g).fork();
                    new Sorter(rc, a, w, b+h, q, wb+h, g).fork();;
                    Relay bc = new Relay(new Merger(fc, a, w, b, q,
                                                    b+q, h-q, wb, g));
                    new Sorter(bc, a, w, b+q, h-q, wb+q, g).fork();
                    s = new EmptyCompleter(bc);
                    n = q;
                }
                DualPivotQuicksort.sort(a, b, b + n - 1, w, wb, n);
                s.tryComplete();
            }
        }

        static final class Merger extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final char[] a, w; // main and workspace arrays
            final int lbase, lsize, rbase, rsize, wbase, gran;
            Merger(CountedCompleter<?> par, char[] a, char[] w,
                   int lbase, int lsize, int rbase,
                   int rsize, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w;
                this.lbase = lbase; this.lsize = lsize;
                this.rbase = rbase; this.rsize = rsize;
                this.wbase = wbase; this.gran = gran;
            }

            public final void compute() {
                char[] a = this.a, w = this.w; // localize all params
                int lb = this.lbase, ln = this.lsize, rb = this.rbase,
                    rn = this.rsize, k = this.wbase, g = this.gran;
                if (a == null || w == null || lb < 0 || rb < 0 || k < 0)
                    throw new IllegalStateException(); // hoist checks
                for (int lh, rh;;) {  // split larger, find point in smaller
                    if (ln >= rn) {
                        if (ln <= g)
                            break;
                        rh = rn;
                        char split = a[(lh = ln >>> 1) + lb];
                        for (int lo = 0; lo < rh; ) {
                            int rm = (lo + rh) >>> 1;
                            if (split <= a[rm + rb])
                                rh = rm;
                            else
                                lo = rm + 1;
                        }
                    }
                    else {
                        if (rn <= g)
                            break;
                        lh = ln;
                        char split = a[(rh = rn >>> 1) + rb];
                        for (int lo = 0; lo < lh; ) {
                            int lm = (lo + lh) >>> 1;
                            if (split <= a[lm + lb])
                                lh = lm;
                            else
                                lo = lm + 1;
                        }
                    }
                    Merger m = new Merger(this, a, w, lb + lh, ln - lh,
                                          rb + rh, rn - rh,
                                          k + lh + rh, g);
                    rn = rh;
                    ln = lh;
                    addToPendingCount(1);
                    m.fork();
                }

                int lf = lb + ln, rf = rb + rn; // index bounds
                while (lb < lf && rb < rf) {
                    char t, al, ar;
                    if ((al = a[lb]) <= (ar = a[rb])) {
                        lb++; t = al;
                    }
                    else {
                        rb++; t = ar;
                    }
                    w[k++] = t;
                }
                if (rb < rf)
                    System.arraycopy(a, rb, w, k, rf - rb);
                else if (lb < lf)
                    System.arraycopy(a, lb, w, k, lf - lb);
                tryComplete();
            }
        }
    } // FJChar

    /** short support class */
    static final class FJShort {
        static final class Sorter extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final short[] a, w;
            final int base, size, wbase, gran;
            Sorter(CountedCompleter<?> par, short[] a, short[] w, int base,
                   int size, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w; this.base = base; this.size = size;
                this.wbase = wbase; this.gran = gran;
            }
            public final void compute() {
                CountedCompleter<?> s = this;
                short[] a = this.a, w = this.w; // localize all params
                int b = this.base, n = this.size, wb = this.wbase, g = this.gran;
                while (n > g) {
                    int h = n >>> 1, q = h >>> 1, u = h + q; // quartiles
                    Relay fc = new Relay(new Merger(s, w, a, wb, h,
                                                    wb+h, n-h, b, g));
                    Relay rc = new Relay(new Merger(fc, a, w, b+h, q,
                                                    b+u, n-u, wb+h, g));
                    new Sorter(rc, a, w, b+u, n-u, wb+u, g).fork();
                    new Sorter(rc, a, w, b+h, q, wb+h, g).fork();;
                    Relay bc = new Relay(new Merger(fc, a, w, b, q,
                                                    b+q, h-q, wb, g));
                    new Sorter(bc, a, w, b+q, h-q, wb+q, g).fork();
                    s = new EmptyCompleter(bc);
                    n = q;
                }
                DualPivotQuicksort.sort(a, b, b + n - 1, w, wb, n);
                s.tryComplete();
            }
        }

        static final class Merger extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final short[] a, w; // main and workspace arrays
            final int lbase, lsize, rbase, rsize, wbase, gran;
            Merger(CountedCompleter<?> par, short[] a, short[] w,
                   int lbase, int lsize, int rbase,
                   int rsize, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w;
                this.lbase = lbase; this.lsize = lsize;
                this.rbase = rbase; this.rsize = rsize;
                this.wbase = wbase; this.gran = gran;
            }

            public final void compute() {
                short[] a = this.a, w = this.w; // localize all params
                int lb = this.lbase, ln = this.lsize, rb = this.rbase,
                    rn = this.rsize, k = this.wbase, g = this.gran;
                if (a == null || w == null || lb < 0 || rb < 0 || k < 0)
                    throw new IllegalStateException(); // hoist checks
                for (int lh, rh;;) {  // split larger, find point in smaller
                    if (ln >= rn) {
                        if (ln <= g)
                            break;
                        rh = rn;
                        short split = a[(lh = ln >>> 1) + lb];
                        for (int lo = 0; lo < rh; ) {
                            int rm = (lo + rh) >>> 1;
                            if (split <= a[rm + rb])
                                rh = rm;
                            else
                                lo = rm + 1;
                        }
                    }
                    else {
                        if (rn <= g)
                            break;
                        lh = ln;
                        short split = a[(rh = rn >>> 1) + rb];
                        for (int lo = 0; lo < lh; ) {
                            int lm = (lo + lh) >>> 1;
                            if (split <= a[lm + lb])
                                lh = lm;
                            else
                                lo = lm + 1;
                        }
                    }
                    Merger m = new Merger(this, a, w, lb + lh, ln - lh,
                                          rb + rh, rn - rh,
                                          k + lh + rh, g);
                    rn = rh;
                    ln = lh;
                    addToPendingCount(1);
                    m.fork();
                }

                int lf = lb + ln, rf = rb + rn; // index bounds
                while (lb < lf && rb < rf) {
                    short t, al, ar;
                    if ((al = a[lb]) <= (ar = a[rb])) {
                        lb++; t = al;
                    }
                    else {
                        rb++; t = ar;
                    }
                    w[k++] = t;
                }
                if (rb < rf)
                    System.arraycopy(a, rb, w, k, rf - rb);
                else if (lb < lf)
                    System.arraycopy(a, lb, w, k, lf - lb);
                tryComplete();
            }
        }
    } // FJShort

    /** int support class */
    static final class FJInt {
        static final class Sorter extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final int[] a, w;
            final int base, size, wbase, gran;
            Sorter(CountedCompleter<?> par, int[] a, int[] w, int base,
                   int size, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w; this.base = base; this.size = size;
                this.wbase = wbase; this.gran = gran;
            }
            public final void compute() {
                CountedCompleter<?> s = this;
                int[] a = this.a, w = this.w; // localize all params
                int b = this.base, n = this.size, wb = this.wbase, g = this.gran;
                while (n > g) {
                    int h = n >>> 1, q = h >>> 1, u = h + q; // quartiles
                    Relay fc = new Relay(new Merger(s, w, a, wb, h,
                                                    wb+h, n-h, b, g));
                    Relay rc = new Relay(new Merger(fc, a, w, b+h, q,
                                                    b+u, n-u, wb+h, g));
                    new Sorter(rc, a, w, b+u, n-u, wb+u, g).fork();
                    new Sorter(rc, a, w, b+h, q, wb+h, g).fork();;
                    Relay bc = new Relay(new Merger(fc, a, w, b, q,
                                                    b+q, h-q, wb, g));
                    new Sorter(bc, a, w, b+q, h-q, wb+q, g).fork();
                    s = new EmptyCompleter(bc);
                    n = q;
                }
                DualPivotQuicksort.sort(a, b, b + n - 1, w, wb, n);
                s.tryComplete();
            }
        }

        static final class Merger extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final int[] a, w; // main and workspace arrays
            final int lbase, lsize, rbase, rsize, wbase, gran;
            Merger(CountedCompleter<?> par, int[] a, int[] w,
                   int lbase, int lsize, int rbase,
                   int rsize, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w;
                this.lbase = lbase; this.lsize = lsize;
                this.rbase = rbase; this.rsize = rsize;
                this.wbase = wbase; this.gran = gran;
            }

            public final void compute() {
                int[] a = this.a, w = this.w; // localize all params
                int lb = this.lbase, ln = this.lsize, rb = this.rbase,
                    rn = this.rsize, k = this.wbase, g = this.gran;
                if (a == null || w == null || lb < 0 || rb < 0 || k < 0)
                    throw new IllegalStateException(); // hoist checks
                for (int lh, rh;;) {  // split larger, find point in smaller
                    if (ln >= rn) {
                        if (ln <= g)
                            break;
                        rh = rn;
                        int split = a[(lh = ln >>> 1) + lb];
                        for (int lo = 0; lo < rh; ) {
                            int rm = (lo + rh) >>> 1;
                            if (split <= a[rm + rb])
                                rh = rm;
                            else
                                lo = rm + 1;
                        }
                    }
                    else {
                        if (rn <= g)
                            break;
                        lh = ln;
                        int split = a[(rh = rn >>> 1) + rb];
                        for (int lo = 0; lo < lh; ) {
                            int lm = (lo + lh) >>> 1;
                            if (split <= a[lm + lb])
                                lh = lm;
                            else
                                lo = lm + 1;
                        }
                    }
                    Merger m = new Merger(this, a, w, lb + lh, ln - lh,
                                          rb + rh, rn - rh,
                                          k + lh + rh, g);
                    rn = rh;
                    ln = lh;
                    addToPendingCount(1);
                    m.fork();
                }

                int lf = lb + ln, rf = rb + rn; // index bounds
                while (lb < lf && rb < rf) {
                    int t, al, ar;
                    if ((al = a[lb]) <= (ar = a[rb])) {
                        lb++; t = al;
                    }
                    else {
                        rb++; t = ar;
                    }
                    w[k++] = t;
                }
                if (rb < rf)
                    System.arraycopy(a, rb, w, k, rf - rb);
                else if (lb < lf)
                    System.arraycopy(a, lb, w, k, lf - lb);
                tryComplete();
            }
        }
    } // FJInt

    /** long support class */
    static final class FJLong {
        static final class Sorter extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final long[] a, w;
            final int base, size, wbase, gran;
            Sorter(CountedCompleter<?> par, long[] a, long[] w, int base,
                   int size, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w; this.base = base; this.size = size;
                this.wbase = wbase; this.gran = gran;
            }
            public final void compute() {
                CountedCompleter<?> s = this;
                long[] a = this.a, w = this.w; // localize all params
                int b = this.base, n = this.size, wb = this.wbase, g = this.gran;
                while (n > g) {
                    int h = n >>> 1, q = h >>> 1, u = h + q; // quartiles
                    Relay fc = new Relay(new Merger(s, w, a, wb, h,
                                                    wb+h, n-h, b, g));
                    Relay rc = new Relay(new Merger(fc, a, w, b+h, q,
                                                    b+u, n-u, wb+h, g));
                    new Sorter(rc, a, w, b+u, n-u, wb+u, g).fork();
                    new Sorter(rc, a, w, b+h, q, wb+h, g).fork();;
                    Relay bc = new Relay(new Merger(fc, a, w, b, q,
                                                    b+q, h-q, wb, g));
                    new Sorter(bc, a, w, b+q, h-q, wb+q, g).fork();
                    s = new EmptyCompleter(bc);
                    n = q;
                }
                DualPivotQuicksort.sort(a, b, b + n - 1, w, wb, n);
                s.tryComplete();
            }
        }

        static final class Merger extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final long[] a, w; // main and workspace arrays
            final int lbase, lsize, rbase, rsize, wbase, gran;
            Merger(CountedCompleter<?> par, long[] a, long[] w,
                   int lbase, int lsize, int rbase,
                   int rsize, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w;
                this.lbase = lbase; this.lsize = lsize;
                this.rbase = rbase; this.rsize = rsize;
                this.wbase = wbase; this.gran = gran;
            }

            public final void compute() {
                long[] a = this.a, w = this.w; // localize all params
                int lb = this.lbase, ln = this.lsize, rb = this.rbase,
                    rn = this.rsize, k = this.wbase, g = this.gran;
                if (a == null || w == null || lb < 0 || rb < 0 || k < 0)
                    throw new IllegalStateException(); // hoist checks
                for (int lh, rh;;) {  // split larger, find point in smaller
                    if (ln >= rn) {
                        if (ln <= g)
                            break;
                        rh = rn;
                        long split = a[(lh = ln >>> 1) + lb];
                        for (int lo = 0; lo < rh; ) {
                            int rm = (lo + rh) >>> 1;
                            if (split <= a[rm + rb])
                                rh = rm;
                            else
                                lo = rm + 1;
                        }
                    }
                    else {
                        if (rn <= g)
                            break;
                        lh = ln;
                        long split = a[(rh = rn >>> 1) + rb];
                        for (int lo = 0; lo < lh; ) {
                            int lm = (lo + lh) >>> 1;
                            if (split <= a[lm + lb])
                                lh = lm;
                            else
                                lo = lm + 1;
                        }
                    }
                    Merger m = new Merger(this, a, w, lb + lh, ln - lh,
                                          rb + rh, rn - rh,
                                          k + lh + rh, g);
                    rn = rh;
                    ln = lh;
                    addToPendingCount(1);
                    m.fork();
                }

                int lf = lb + ln, rf = rb + rn; // index bounds
                while (lb < lf && rb < rf) {
                    long t, al, ar;
                    if ((al = a[lb]) <= (ar = a[rb])) {
                        lb++; t = al;
                    }
                    else {
                        rb++; t = ar;
                    }
                    w[k++] = t;
                }
                if (rb < rf)
                    System.arraycopy(a, rb, w, k, rf - rb);
                else if (lb < lf)
                    System.arraycopy(a, lb, w, k, lf - lb);
                tryComplete();
            }
        }
    } // FJLong

    /** float support class */
    static final class FJFloat {
        static final class Sorter extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final float[] a, w;
            final int base, size, wbase, gran;
            Sorter(CountedCompleter<?> par, float[] a, float[] w, int base,
                   int size, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w; this.base = base; this.size = size;
                this.wbase = wbase; this.gran = gran;
            }
            public final void compute() {
                CountedCompleter<?> s = this;
                float[] a = this.a, w = this.w; // localize all params
                int b = this.base, n = this.size, wb = this.wbase, g = this.gran;
                while (n > g) {
                    int h = n >>> 1, q = h >>> 1, u = h + q; // quartiles
                    Relay fc = new Relay(new Merger(s, w, a, wb, h,
                                                    wb+h, n-h, b, g));
                    Relay rc = new Relay(new Merger(fc, a, w, b+h, q,
                                                    b+u, n-u, wb+h, g));
                    new Sorter(rc, a, w, b+u, n-u, wb+u, g).fork();
                    new Sorter(rc, a, w, b+h, q, wb+h, g).fork();;
                    Relay bc = new Relay(new Merger(fc, a, w, b, q,
                                                    b+q, h-q, wb, g));
                    new Sorter(bc, a, w, b+q, h-q, wb+q, g).fork();
                    s = new EmptyCompleter(bc);
                    n = q;
                }
                DualPivotQuicksort.sort(a, b, b + n - 1, w, wb, n);
                s.tryComplete();
            }
        }

        static final class Merger extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final float[] a, w; // main and workspace arrays
            final int lbase, lsize, rbase, rsize, wbase, gran;
            Merger(CountedCompleter<?> par, float[] a, float[] w,
                   int lbase, int lsize, int rbase,
                   int rsize, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w;
                this.lbase = lbase; this.lsize = lsize;
                this.rbase = rbase; this.rsize = rsize;
                this.wbase = wbase; this.gran = gran;
            }

            public final void compute() {
                float[] a = this.a, w = this.w; // localize all params
                int lb = this.lbase, ln = this.lsize, rb = this.rbase,
                    rn = this.rsize, k = this.wbase, g = this.gran;
                if (a == null || w == null || lb < 0 || rb < 0 || k < 0)
                    throw new IllegalStateException(); // hoist checks
                for (int lh, rh;;) {  // split larger, find point in smaller
                    if (ln >= rn) {
                        if (ln <= g)
                            break;
                        rh = rn;
                        float split = a[(lh = ln >>> 1) + lb];
                        for (int lo = 0; lo < rh; ) {
                            int rm = (lo + rh) >>> 1;
                            if (split <= a[rm + rb])
                                rh = rm;
                            else
                                lo = rm + 1;
                        }
                    }
                    else {
                        if (rn <= g)
                            break;
                        lh = ln;
                        float split = a[(rh = rn >>> 1) + rb];
                        for (int lo = 0; lo < lh; ) {
                            int lm = (lo + lh) >>> 1;
                            if (split <= a[lm + lb])
                                lh = lm;
                            else
                                lo = lm + 1;
                        }
                    }
                    Merger m = new Merger(this, a, w, lb + lh, ln - lh,
                                          rb + rh, rn - rh,
                                          k + lh + rh, g);
                    rn = rh;
                    ln = lh;
                    addToPendingCount(1);
                    m.fork();
                }

                int lf = lb + ln, rf = rb + rn; // index bounds
                while (lb < lf && rb < rf) {
                    float t, al, ar;
                    if ((al = a[lb]) <= (ar = a[rb])) {
                        lb++; t = al;
                    }
                    else {
                        rb++; t = ar;
                    }
                    w[k++] = t;
                }
                if (rb < rf)
                    System.arraycopy(a, rb, w, k, rf - rb);
                else if (lb < lf)
                    System.arraycopy(a, lb, w, k, lf - lb);
                tryComplete();
            }
        }
    } // FJFloat

    /** double support class */
    static final class FJDouble {
        static final class Sorter extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final double[] a, w;
            final int base, size, wbase, gran;
            Sorter(CountedCompleter<?> par, double[] a, double[] w, int base,
                   int size, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w; this.base = base; this.size = size;
                this.wbase = wbase; this.gran = gran;
            }
            public final void compute() {
                CountedCompleter<?> s = this;
                double[] a = this.a, w = this.w; // localize all params
                int b = this.base, n = this.size, wb = this.wbase, g = this.gran;
                while (n > g) {
                    int h = n >>> 1, q = h >>> 1, u = h + q; // quartiles
                    Relay fc = new Relay(new Merger(s, w, a, wb, h,
                                                    wb+h, n-h, b, g));
                    Relay rc = new Relay(new Merger(fc, a, w, b+h, q,
                                                    b+u, n-u, wb+h, g));
                    new Sorter(rc, a, w, b+u, n-u, wb+u, g).fork();
                    new Sorter(rc, a, w, b+h, q, wb+h, g).fork();;
                    Relay bc = new Relay(new Merger(fc, a, w, b, q,
                                                    b+q, h-q, wb, g));
                    new Sorter(bc, a, w, b+q, h-q, wb+q, g).fork();
                    s = new EmptyCompleter(bc);
                    n = q;
                }
                DualPivotQuicksort.sort(a, b, b + n - 1, w, wb, n);
                s.tryComplete();
            }
        }

        static final class Merger extends CountedCompleter<Void> {
            static final long serialVersionUID = 2446542900576103244L;
            final double[] a, w; // main and workspace arrays
            final int lbase, lsize, rbase, rsize, wbase, gran;
            Merger(CountedCompleter<?> par, double[] a, double[] w,
                   int lbase, int lsize, int rbase,
                   int rsize, int wbase, int gran) {
                super(par);
                this.a = a; this.w = w;
                this.lbase = lbase; this.lsize = lsize;
                this.rbase = rbase; this.rsize = rsize;
                this.wbase = wbase; this.gran = gran;
            }

            public final void compute() {
                double[] a = this.a, w = this.w; // localize all params
                int lb = this.lbase, ln = this.lsize, rb = this.rbase,
                    rn = this.rsize, k = this.wbase, g = this.gran;
                if (a == null || w == null || lb < 0 || rb < 0 || k < 0)
                    throw new IllegalStateException(); // hoist checks
                for (int lh, rh;;) {  // split larger, find point in smaller
                    if (ln >= rn) {
                        if (ln <= g)
                            break;
                        rh = rn;
                        double split = a[(lh = ln >>> 1) + lb];
                        for (int lo = 0; lo < rh; ) {
                            int rm = (lo + rh) >>> 1;
                            if (split <= a[rm + rb])
                                rh = rm;
                            else
                                lo = rm + 1;
                        }
                    }
                    else {
                        if (rn <= g)
                            break;
                        lh = ln;
                        double split = a[(rh = rn >>> 1) + rb];
                        for (int lo = 0; lo < lh; ) {
                            int lm = (lo + lh) >>> 1;
                            if (split <= a[lm + lb])
                                lh = lm;
                            else
                                lo = lm + 1;
                        }
                    }
                    Merger m = new Merger(this, a, w, lb + lh, ln - lh,
                                          rb + rh, rn - rh,
                                          k + lh + rh, g);
                    rn = rh;
                    ln = lh;
                    addToPendingCount(1);
                    m.fork();
                }

                int lf = lb + ln, rf = rb + rn; // index bounds
                while (lb < lf && rb < rf) {
                    double t, al, ar;
                    if ((al = a[lb]) <= (ar = a[rb])) {
                        lb++; t = al;
                    }
                    else {
                        rb++; t = ar;
                    }
                    w[k++] = t;
                }
                if (rb < rf)
                    System.arraycopy(a, rb, w, k, rf - rb);
                else if (lb < lf)
                    System.arraycopy(a, lb, w, k, lf - lb);
                tryComplete();
            }
        }
    } // FJDouble

}