jdk/src/share/classes/java/util/Timer.java
changeset 2 90ce3da70b43
child 1006 f0e0218ff458
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/jdk/src/share/classes/java/util/Timer.java	Sat Dec 01 00:00:00 2007 +0000
@@ -0,0 +1,715 @@
+/*
+ * Copyright 1999-2007 Sun Microsystems, Inc.  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.  Sun designates this
+ * particular file as subject to the "Classpath" exception as provided
+ * by Sun 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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
+ * CA 95054 USA or visit www.sun.com if you need additional information or
+ * have any questions.
+ */
+
+package java.util;
+import java.util.Date;
+
+/**
+ * A facility for threads to schedule tasks for future execution in a
+ * background thread.  Tasks may be scheduled for one-time execution, or for
+ * repeated execution at regular intervals.
+ *
+ * <p>Corresponding to each <tt>Timer</tt> object is a single background
+ * thread that is used to execute all of the timer's tasks, sequentially.
+ * Timer tasks should complete quickly.  If a timer task takes excessive time
+ * to complete, it "hogs" the timer's task execution thread.  This can, in
+ * turn, delay the execution of subsequent tasks, which may "bunch up" and
+ * execute in rapid succession when (and if) the offending task finally
+ * completes.
+ *
+ * <p>After the last live reference to a <tt>Timer</tt> object goes away
+ * <i>and</i> all outstanding tasks have completed execution, the timer's task
+ * execution thread terminates gracefully (and becomes subject to garbage
+ * collection).  However, this can take arbitrarily long to occur.  By
+ * default, the task execution thread does not run as a <i>daemon thread</i>,
+ * so it is capable of keeping an application from terminating.  If a caller
+ * wants to terminate a timer's task execution thread rapidly, the caller
+ * should invoke the timer's <tt>cancel</tt> method.
+ *
+ * <p>If the timer's task execution thread terminates unexpectedly, for
+ * example, because its <tt>stop</tt> method is invoked, any further
+ * attempt to schedule a task on the timer will result in an
+ * <tt>IllegalStateException</tt>, as if the timer's <tt>cancel</tt>
+ * method had been invoked.
+ *
+ * <p>This class is thread-safe: multiple threads can share a single
+ * <tt>Timer</tt> object without the need for external synchronization.
+ *
+ * <p>This class does <i>not</i> offer real-time guarantees: it schedules
+ * tasks using the <tt>Object.wait(long)</tt> method.
+ *
+ * <p>Java 5.0 introduced the {@code java.util.concurrent} package and
+ * one of the concurrency utilities therein is the {@link
+ * java.util.concurrent.ScheduledThreadPoolExecutor
+ * ScheduledThreadPoolExecutor} which is a thread pool for repeatedly
+ * executing tasks at a given rate or delay.  It is effectively a more
+ * versatile replacement for the {@code Timer}/{@code TimerTask}
+ * combination, as it allows multiple service threads, accepts various
+ * time units, and doesn't require subclassing {@code TimerTask} (just
+ * implement {@code Runnable}).  Configuring {@code
+ * ScheduledThreadPoolExecutor} with one thread makes it equivalent to
+ * {@code Timer}.
+ *
+ * <p>Implementation note: This class scales to large numbers of concurrently
+ * scheduled tasks (thousands should present no problem).  Internally,
+ * it uses a binary heap to represent its task queue, so the cost to schedule
+ * a task is O(log n), where n is the number of concurrently scheduled tasks.
+ *
+ * <p>Implementation note: All constructors start a timer thread.
+ *
+ * @author  Josh Bloch
+ * @see     TimerTask
+ * @see     Object#wait(long)
+ * @since   1.3
+ */
+
+public class Timer {
+    /**
+     * The timer task queue.  This data structure is shared with the timer
+     * thread.  The timer produces tasks, via its various schedule calls,
+     * and the timer thread consumes, executing timer tasks as appropriate,
+     * and removing them from the queue when they're obsolete.
+     */
+    private TaskQueue queue = new TaskQueue();
+
+    /**
+     * The timer thread.
+     */
+    private TimerThread thread = new TimerThread(queue);
+
+    /**
+     * This object causes the timer's task execution thread to exit
+     * gracefully when there are no live references to the Timer object and no
+     * tasks in the timer queue.  It is used in preference to a finalizer on
+     * Timer as such a finalizer would be susceptible to a subclass's
+     * finalizer forgetting to call it.
+     */
+    private Object threadReaper = new Object() {
+        protected void finalize() throws Throwable {
+            synchronized(queue) {
+                thread.newTasksMayBeScheduled = false;
+                queue.notify(); // In case queue is empty.
+            }
+        }
+    };
+
+    /**
+     * This ID is used to generate thread names.  (It could be replaced
+     * by an AtomicInteger as soon as they become available.)
+     */
+    private static int nextSerialNumber = 0;
+    private static synchronized int serialNumber() {
+        return nextSerialNumber++;
+    }
+
+    /**
+     * Creates a new timer.  The associated thread does <i>not</i>
+     * {@linkplain Thread#setDaemon run as a daemon}.
+     */
+    public Timer() {
+        this("Timer-" + serialNumber());
+    }
+
+    /**
+     * Creates a new timer whose associated thread may be specified to
+     * {@linkplain Thread#setDaemon run as a daemon}.
+     * A daemon thread is called for if the timer will be used to
+     * schedule repeating "maintenance activities", which must be
+     * performed as long as the application is running, but should not
+     * prolong the lifetime of the application.
+     *
+     * @param isDaemon true if the associated thread should run as a daemon.
+     */
+    public Timer(boolean isDaemon) {
+        this("Timer-" + serialNumber(), isDaemon);
+    }
+
+    /**
+     * Creates a new timer whose associated thread has the specified name.
+     * The associated thread does <i>not</i>
+     * {@linkplain Thread#setDaemon run as a daemon}.
+     *
+     * @param name the name of the associated thread
+     * @throws NullPointerException if {@code name} is null
+     * @since 1.5
+     */
+    public Timer(String name) {
+        thread.setName(name);
+        thread.start();
+    }
+
+    /**
+     * Creates a new timer whose associated thread has the specified name,
+     * and may be specified to
+     * {@linkplain Thread#setDaemon run as a daemon}.
+     *
+     * @param name the name of the associated thread
+     * @param isDaemon true if the associated thread should run as a daemon
+     * @throws NullPointerException if {@code name} is null
+     * @since 1.5
+     */
+    public Timer(String name, boolean isDaemon) {
+        thread.setName(name);
+        thread.setDaemon(isDaemon);
+        thread.start();
+    }
+
+    /**
+     * Schedules the specified task for execution after the specified delay.
+     *
+     * @param task  task to be scheduled.
+     * @param delay delay in milliseconds before task is to be executed.
+     * @throws IllegalArgumentException if <tt>delay</tt> is negative, or
+     *         <tt>delay + System.currentTimeMillis()</tt> is negative.
+     * @throws IllegalStateException if task was already scheduled or
+     *         cancelled, timer was cancelled, or timer thread terminated.
+     * @throws NullPointerException if {@code task} is null
+     */
+    public void schedule(TimerTask task, long delay) {
+        if (delay < 0)
+            throw new IllegalArgumentException("Negative delay.");
+        sched(task, System.currentTimeMillis()+delay, 0);
+    }
+
+    /**
+     * Schedules the specified task for execution at the specified time.  If
+     * the time is in the past, the task is scheduled for immediate execution.
+     *
+     * @param task task to be scheduled.
+     * @param time time at which task is to be executed.
+     * @throws IllegalArgumentException if <tt>time.getTime()</tt> is negative.
+     * @throws IllegalStateException if task was already scheduled or
+     *         cancelled, timer was cancelled, or timer thread terminated.
+     * @throws NullPointerException if {@code task} or {@code time} is null
+     */
+    public void schedule(TimerTask task, Date time) {
+        sched(task, time.getTime(), 0);
+    }
+
+    /**
+     * Schedules the specified task for repeated <i>fixed-delay execution</i>,
+     * beginning after the specified delay.  Subsequent executions take place
+     * at approximately regular intervals separated by the specified period.
+     *
+     * <p>In fixed-delay execution, each execution is scheduled relative to
+     * the actual execution time of the previous execution.  If an execution
+     * is delayed for any reason (such as garbage collection or other
+     * background activity), subsequent executions will be delayed as well.
+     * In the long run, the frequency of execution will generally be slightly
+     * lower than the reciprocal of the specified period (assuming the system
+     * clock underlying <tt>Object.wait(long)</tt> is accurate).
+     *
+     * <p>Fixed-delay execution is appropriate for recurring activities
+     * that require "smoothness."  In other words, it is appropriate for
+     * activities where it is more important to keep the frequency accurate
+     * in the short run than in the long run.  This includes most animation
+     * tasks, such as blinking a cursor at regular intervals.  It also includes
+     * tasks wherein regular activity is performed in response to human
+     * input, such as automatically repeating a character as long as a key
+     * is held down.
+     *
+     * @param task   task to be scheduled.
+     * @param delay  delay in milliseconds before task is to be executed.
+     * @param period time in milliseconds between successive task executions.
+     * @throws IllegalArgumentException if {@code delay < 0}, or
+     *         {@code delay + System.currentTimeMillis() < 0}, or
+     *         {@code period <= 0}
+     * @throws IllegalStateException if task was already scheduled or
+     *         cancelled, timer was cancelled, or timer thread terminated.
+     * @throws NullPointerException if {@code task} is null
+     */
+    public void schedule(TimerTask task, long delay, long period) {
+        if (delay < 0)
+            throw new IllegalArgumentException("Negative delay.");
+        if (period <= 0)
+            throw new IllegalArgumentException("Non-positive period.");
+        sched(task, System.currentTimeMillis()+delay, -period);
+    }
+
+    /**
+     * Schedules the specified task for repeated <i>fixed-delay execution</i>,
+     * beginning at the specified time. Subsequent executions take place at
+     * approximately regular intervals, separated by the specified period.
+     *
+     * <p>In fixed-delay execution, each execution is scheduled relative to
+     * the actual execution time of the previous execution.  If an execution
+     * is delayed for any reason (such as garbage collection or other
+     * background activity), subsequent executions will be delayed as well.
+     * In the long run, the frequency of execution will generally be slightly
+     * lower than the reciprocal of the specified period (assuming the system
+     * clock underlying <tt>Object.wait(long)</tt> is accurate).  As a
+     * consequence of the above, if the scheduled first time is in the past,
+     * it is scheduled for immediate execution.
+     *
+     * <p>Fixed-delay execution is appropriate for recurring activities
+     * that require "smoothness."  In other words, it is appropriate for
+     * activities where it is more important to keep the frequency accurate
+     * in the short run than in the long run.  This includes most animation
+     * tasks, such as blinking a cursor at regular intervals.  It also includes
+     * tasks wherein regular activity is performed in response to human
+     * input, such as automatically repeating a character as long as a key
+     * is held down.
+     *
+     * @param task   task to be scheduled.
+     * @param firstTime First time at which task is to be executed.
+     * @param period time in milliseconds between successive task executions.
+     * @throws IllegalArgumentException if {@code firstTime.getTime() < 0}, or
+     *         {@code period <= 0}
+     * @throws IllegalStateException if task was already scheduled or
+     *         cancelled, timer was cancelled, or timer thread terminated.
+     * @throws NullPointerException if {@code task} or {@code firstTime} is null
+     */
+    public void schedule(TimerTask task, Date firstTime, long period) {
+        if (period <= 0)
+            throw new IllegalArgumentException("Non-positive period.");
+        sched(task, firstTime.getTime(), -period);
+    }
+
+    /**
+     * Schedules the specified task for repeated <i>fixed-rate execution</i>,
+     * beginning after the specified delay.  Subsequent executions take place
+     * at approximately regular intervals, separated by the specified period.
+     *
+     * <p>In fixed-rate execution, each execution is scheduled relative to the
+     * scheduled execution time of the initial execution.  If an execution is
+     * delayed for any reason (such as garbage collection or other background
+     * activity), two or more executions will occur in rapid succession to
+     * "catch up."  In the long run, the frequency of execution will be
+     * exactly the reciprocal of the specified period (assuming the system
+     * clock underlying <tt>Object.wait(long)</tt> is accurate).
+     *
+     * <p>Fixed-rate execution is appropriate for recurring activities that
+     * are sensitive to <i>absolute</i> time, such as ringing a chime every
+     * hour on the hour, or running scheduled maintenance every day at a
+     * particular time.  It is also appropriate for recurring activities
+     * where the total time to perform a fixed number of executions is
+     * important, such as a countdown timer that ticks once every second for
+     * ten seconds.  Finally, fixed-rate execution is appropriate for
+     * scheduling multiple repeating timer tasks that must remain synchronized
+     * with respect to one another.
+     *
+     * @param task   task to be scheduled.
+     * @param delay  delay in milliseconds before task is to be executed.
+     * @param period time in milliseconds between successive task executions.
+     * @throws IllegalArgumentException if {@code delay < 0}, or
+     *         {@code delay + System.currentTimeMillis() < 0}, or
+     *         {@code period <= 0}
+     * @throws IllegalStateException if task was already scheduled or
+     *         cancelled, timer was cancelled, or timer thread terminated.
+     * @throws NullPointerException if {@code task} is null
+     */
+    public void scheduleAtFixedRate(TimerTask task, long delay, long period) {
+        if (delay < 0)
+            throw new IllegalArgumentException("Negative delay.");
+        if (period <= 0)
+            throw new IllegalArgumentException("Non-positive period.");
+        sched(task, System.currentTimeMillis()+delay, period);
+    }
+
+    /**
+     * Schedules the specified task for repeated <i>fixed-rate execution</i>,
+     * beginning at the specified time. Subsequent executions take place at
+     * approximately regular intervals, separated by the specified period.
+     *
+     * <p>In fixed-rate execution, each execution is scheduled relative to the
+     * scheduled execution time of the initial execution.  If an execution is
+     * delayed for any reason (such as garbage collection or other background
+     * activity), two or more executions will occur in rapid succession to
+     * "catch up."  In the long run, the frequency of execution will be
+     * exactly the reciprocal of the specified period (assuming the system
+     * clock underlying <tt>Object.wait(long)</tt> is accurate).  As a
+     * consequence of the above, if the scheduled first time is in the past,
+     * then any "missed" executions will be scheduled for immediate "catch up"
+     * execution.
+     *
+     * <p>Fixed-rate execution is appropriate for recurring activities that
+     * are sensitive to <i>absolute</i> time, such as ringing a chime every
+     * hour on the hour, or running scheduled maintenance every day at a
+     * particular time.  It is also appropriate for recurring activities
+     * where the total time to perform a fixed number of executions is
+     * important, such as a countdown timer that ticks once every second for
+     * ten seconds.  Finally, fixed-rate execution is appropriate for
+     * scheduling multiple repeating timer tasks that must remain synchronized
+     * with respect to one another.
+     *
+     * @param task   task to be scheduled.
+     * @param firstTime First time at which task is to be executed.
+     * @param period time in milliseconds between successive task executions.
+     * @throws IllegalArgumentException if {@code firstTime.getTime() < 0} or
+     *         {@code period <= 0}
+     * @throws IllegalStateException if task was already scheduled or
+     *         cancelled, timer was cancelled, or timer thread terminated.
+     * @throws NullPointerException if {@code task} or {@code firstTime} is null
+     */
+    public void scheduleAtFixedRate(TimerTask task, Date firstTime,
+                                    long period) {
+        if (period <= 0)
+            throw new IllegalArgumentException("Non-positive period.");
+        sched(task, firstTime.getTime(), period);
+    }
+
+    /**
+     * Schedule the specified timer task for execution at the specified
+     * time with the specified period, in milliseconds.  If period is
+     * positive, the task is scheduled for repeated execution; if period is
+     * zero, the task is scheduled for one-time execution. Time is specified
+     * in Date.getTime() format.  This method checks timer state, task state,
+     * and initial execution time, but not period.
+     *
+     * @throws IllegalArgumentException if <tt>time</tt> is negative.
+     * @throws IllegalStateException if task was already scheduled or
+     *         cancelled, timer was cancelled, or timer thread terminated.
+     * @throws NullPointerException if {@code task} is null
+     */
+    private void sched(TimerTask task, long time, long period) {
+        if (time < 0)
+            throw new IllegalArgumentException("Illegal execution time.");
+
+        synchronized(queue) {
+            if (!thread.newTasksMayBeScheduled)
+                throw new IllegalStateException("Timer already cancelled.");
+
+            synchronized(task.lock) {
+                if (task.state != TimerTask.VIRGIN)
+                    throw new IllegalStateException(
+                        "Task already scheduled or cancelled");
+                task.nextExecutionTime = time;
+                task.period = period;
+                task.state = TimerTask.SCHEDULED;
+            }
+
+            queue.add(task);
+            if (queue.getMin() == task)
+                queue.notify();
+        }
+    }
+
+    /**
+     * Terminates this timer, discarding any currently scheduled tasks.
+     * Does not interfere with a currently executing task (if it exists).
+     * Once a timer has been terminated, its execution thread terminates
+     * gracefully, and no more tasks may be scheduled on it.
+     *
+     * <p>Note that calling this method from within the run method of a
+     * timer task that was invoked by this timer absolutely guarantees that
+     * the ongoing task execution is the last task execution that will ever
+     * be performed by this timer.
+     *
+     * <p>This method may be called repeatedly; the second and subsequent
+     * calls have no effect.
+     */
+    public void cancel() {
+        synchronized(queue) {
+            thread.newTasksMayBeScheduled = false;
+            queue.clear();
+            queue.notify();  // In case queue was already empty.
+        }
+    }
+
+    /**
+     * Removes all cancelled tasks from this timer's task queue.  <i>Calling
+     * this method has no effect on the behavior of the timer</i>, but
+     * eliminates the references to the cancelled tasks from the queue.
+     * If there are no external references to these tasks, they become
+     * eligible for garbage collection.
+     *
+     * <p>Most programs will have no need to call this method.
+     * It is designed for use by the rare application that cancels a large
+     * number of tasks.  Calling this method trades time for space: the
+     * runtime of the method may be proportional to n + c log n, where n
+     * is the number of tasks in the queue and c is the number of cancelled
+     * tasks.
+     *
+     * <p>Note that it is permissible to call this method from within a
+     * a task scheduled on this timer.
+     *
+     * @return the number of tasks removed from the queue.
+     * @since 1.5
+     */
+     public int purge() {
+         int result = 0;
+
+         synchronized(queue) {
+             for (int i = queue.size(); i > 0; i--) {
+                 if (queue.get(i).state == TimerTask.CANCELLED) {
+                     queue.quickRemove(i);
+                     result++;
+                 }
+             }
+
+             if (result != 0)
+                 queue.heapify();
+         }
+
+         return result;
+     }
+}
+
+/**
+ * This "helper class" implements the timer's task execution thread, which
+ * waits for tasks on the timer queue, executions them when they fire,
+ * reschedules repeating tasks, and removes cancelled tasks and spent
+ * non-repeating tasks from the queue.
+ */
+class TimerThread extends Thread {
+    /**
+     * This flag is set to false by the reaper to inform us that there
+     * are no more live references to our Timer object.  Once this flag
+     * is true and there are no more tasks in our queue, there is no
+     * work left for us to do, so we terminate gracefully.  Note that
+     * this field is protected by queue's monitor!
+     */
+    boolean newTasksMayBeScheduled = true;
+
+    /**
+     * Our Timer's queue.  We store this reference in preference to
+     * a reference to the Timer so the reference graph remains acyclic.
+     * Otherwise, the Timer would never be garbage-collected and this
+     * thread would never go away.
+     */
+    private TaskQueue queue;
+
+    TimerThread(TaskQueue queue) {
+        this.queue = queue;
+    }
+
+    public void run() {
+        try {
+            mainLoop();
+        } finally {
+            // Someone killed this Thread, behave as if Timer cancelled
+            synchronized(queue) {
+                newTasksMayBeScheduled = false;
+                queue.clear();  // Eliminate obsolete references
+            }
+        }
+    }
+
+    /**
+     * The main timer loop.  (See class comment.)
+     */
+    private void mainLoop() {
+        while (true) {
+            try {
+                TimerTask task;
+                boolean taskFired;
+                synchronized(queue) {
+                    // Wait for queue to become non-empty
+                    while (queue.isEmpty() && newTasksMayBeScheduled)
+                        queue.wait();
+                    if (queue.isEmpty())
+                        break; // Queue is empty and will forever remain; die
+
+                    // Queue nonempty; look at first evt and do the right thing
+                    long currentTime, executionTime;
+                    task = queue.getMin();
+                    synchronized(task.lock) {
+                        if (task.state == TimerTask.CANCELLED) {
+                            queue.removeMin();
+                            continue;  // No action required, poll queue again
+                        }
+                        currentTime = System.currentTimeMillis();
+                        executionTime = task.nextExecutionTime;
+                        if (taskFired = (executionTime<=currentTime)) {
+                            if (task.period == 0) { // Non-repeating, remove
+                                queue.removeMin();
+                                task.state = TimerTask.EXECUTED;
+                            } else { // Repeating task, reschedule
+                                queue.rescheduleMin(
+                                  task.period<0 ? currentTime   - task.period
+                                                : executionTime + task.period);
+                            }
+                        }
+                    }
+                    if (!taskFired) // Task hasn't yet fired; wait
+                        queue.wait(executionTime - currentTime);
+                }
+                if (taskFired)  // Task fired; run it, holding no locks
+                    task.run();
+            } catch(InterruptedException e) {
+            }
+        }
+    }
+}
+
+/**
+ * This class represents a timer task queue: a priority queue of TimerTasks,
+ * ordered on nextExecutionTime.  Each Timer object has one of these, which it
+ * shares with its TimerThread.  Internally this class uses a heap, which
+ * offers log(n) performance for the add, removeMin and rescheduleMin
+ * operations, and constant time performance for the getMin operation.
+ */
+class TaskQueue {
+    /**
+     * Priority queue represented as a balanced binary heap: the two children
+     * of queue[n] are queue[2*n] and queue[2*n+1].  The priority queue is
+     * ordered on the nextExecutionTime field: The TimerTask with the lowest
+     * nextExecutionTime is in queue[1] (assuming the queue is nonempty).  For
+     * each node n in the heap, and each descendant of n, d,
+     * n.nextExecutionTime <= d.nextExecutionTime.
+     */
+    private TimerTask[] queue = new TimerTask[128];
+
+    /**
+     * The number of tasks in the priority queue.  (The tasks are stored in
+     * queue[1] up to queue[size]).
+     */
+    private int size = 0;
+
+    /**
+     * Returns the number of tasks currently on the queue.
+     */
+    int size() {
+        return size;
+    }
+
+    /**
+     * Adds a new task to the priority queue.
+     */
+    void add(TimerTask task) {
+        // Grow backing store if necessary
+        if (size + 1 == queue.length)
+            queue = Arrays.copyOf(queue, 2*queue.length);
+
+        queue[++size] = task;
+        fixUp(size);
+    }
+
+    /**
+     * Return the "head task" of the priority queue.  (The head task is an
+     * task with the lowest nextExecutionTime.)
+     */
+    TimerTask getMin() {
+        return queue[1];
+    }
+
+    /**
+     * Return the ith task in the priority queue, where i ranges from 1 (the
+     * head task, which is returned by getMin) to the number of tasks on the
+     * queue, inclusive.
+     */
+    TimerTask get(int i) {
+        return queue[i];
+    }
+
+    /**
+     * Remove the head task from the priority queue.
+     */
+    void removeMin() {
+        queue[1] = queue[size];
+        queue[size--] = null;  // Drop extra reference to prevent memory leak
+        fixDown(1);
+    }
+
+    /**
+     * Removes the ith element from queue without regard for maintaining
+     * the heap invariant.  Recall that queue is one-based, so
+     * 1 <= i <= size.
+     */
+    void quickRemove(int i) {
+        assert i <= size;
+
+        queue[i] = queue[size];
+        queue[size--] = null;  // Drop extra ref to prevent memory leak
+    }
+
+    /**
+     * Sets the nextExecutionTime associated with the head task to the
+     * specified value, and adjusts priority queue accordingly.
+     */
+    void rescheduleMin(long newTime) {
+        queue[1].nextExecutionTime = newTime;
+        fixDown(1);
+    }
+
+    /**
+     * Returns true if the priority queue contains no elements.
+     */
+    boolean isEmpty() {
+        return size==0;
+    }
+
+    /**
+     * Removes all elements from the priority queue.
+     */
+    void clear() {
+        // Null out task references to prevent memory leak
+        for (int i=1; i<=size; i++)
+            queue[i] = null;
+
+        size = 0;
+    }
+
+    /**
+     * Establishes the heap invariant (described above) assuming the heap
+     * satisfies the invariant except possibly for the leaf-node indexed by k
+     * (which may have a nextExecutionTime less than its parent's).
+     *
+     * This method functions by "promoting" queue[k] up the hierarchy
+     * (by swapping it with its parent) repeatedly until queue[k]'s
+     * nextExecutionTime is greater than or equal to that of its parent.
+     */
+    private void fixUp(int k) {
+        while (k > 1) {
+            int j = k >> 1;
+            if (queue[j].nextExecutionTime <= queue[k].nextExecutionTime)
+                break;
+            TimerTask tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;
+            k = j;
+        }
+    }
+
+    /**
+     * Establishes the heap invariant (described above) in the subtree
+     * rooted at k, which is assumed to satisfy the heap invariant except
+     * possibly for node k itself (which may have a nextExecutionTime greater
+     * than its children's).
+     *
+     * This method functions by "demoting" queue[k] down the hierarchy
+     * (by swapping it with its smaller child) repeatedly until queue[k]'s
+     * nextExecutionTime is less than or equal to those of its children.
+     */
+    private void fixDown(int k) {
+        int j;
+        while ((j = k << 1) <= size && j > 0) {
+            if (j < size &&
+                queue[j].nextExecutionTime > queue[j+1].nextExecutionTime)
+                j++; // j indexes smallest kid
+            if (queue[k].nextExecutionTime <= queue[j].nextExecutionTime)
+                break;
+            TimerTask tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;
+            k = j;
+        }
+    }
+
+    /**
+     * Establishes the heap invariant (described above) in the entire tree,
+     * assuming nothing about the order of the elements prior to the call.
+     */
+    void heapify() {
+        for (int i = size/2; i >= 1; i--)
+            fixDown(i);
+    }
+}