singular-data 4.0.3+ds-1 / usr / share / singular / LIB / tasks.lib

//////////////////////////////////////////////////////////////////////
version="version tasks.lib 4.0.0.0 Dec_2013 "; // $Id: 9c9ecb6bd816d6b914cdf4a7a223d8aa98905ed0 $
category="General purpose";
info="
LIBRARY:   tasks.lib  A parallel framework based on tasks

AUTHOR:    Andreas Steenpass, e-mail: steenpass@mathematik.uni-kl.de

OVERVIEW:
This library provides a parallel framework based on tasks. It introduces a new
Singular type @code{task}; an object of this type is a command (given by a
string) applied to a list of arguments. Tasks can be computed in parallel via
the procedures in this library and they can even be started recursively, i.e.
from within other tasks.

tasks.lib respects the limits for computational resources defined
in @ref{resources_lib}, i.e., all tasks within the same Singular session will
not use more computational resources than provided via resources.lib, even if
tasks are started recursively.

The Singular library @ref{parallel_lib} provides implementations of several
parallel 'skeletons' based on tasks.lib.

KEYWORDS:  parallelization; distributed computing; task

SEE ALSO:  resources_lib, parallel_lib

PROCEDURES:
  createTask();    create a task
  killTask();      kill a task
  copyTask();      copy a task
  compareTasks();  compare two tasks
  printTask();     print a task
  startTasks();    start tasks
  stopTask();      stop a task
  waitTasks();     wait for a certain number of tasks
  waitAllTasks();  wait for all tasks
  pollTask();      poll a task
  getCommand();    get the command of a task
  getArguments();  get the arguments of a task
  getResult();     get the result of a task
  getState();      get the state of a task
";

/*
RATIONALE FOR DEVELOPERS

The Singular type 'task'
------------------------
tasks.lib introduces a Singular type 'task' which makes use of a pointer-like
model in order to avoid unnecessary copying of data. 'task' is defined as a
newstruct whose only member is 'int index'. This index points to an entry in
the lib-internal list 'tasks'. The elements of this list are of the type
'internal_task' which is defined as a newstruct with the following members:
int id         - the internal ID
string command - the command
list arguments - the arguments
def result     - the result
string state   - the current state, see 'The life cycle of a task'
list links     - control handles, see 'Links'
int linkID     - the ID of the control handles


The life cycle of a task
------------------------
'uninitialized' --> 'created' --> 'started' --> 'completed'
                                     | ^
                                     v |
                                  'stopped'

The state of a task t is 'uninitialized' iff
(t.index == 0) or (typeof(tasks[t.index]) != "internal_task").

A task can be reset to 'uninitialized' by killTask() at any time.


Assigned members for 'internal_task'
------------------------------------
For each state, the following members of an internal_task must be assigned:

created:       command arguments        state
started:    id command arguments        state links linkID
stopped:       command arguments        state
completed:     command arguments result state

All other members should be wiped out.

Local supervisors
-----------------
A call of 'startTasks(t(1..n));' for tasks t(1), ..., t(n) creates a child
process which plays the role of a supervisor for these tasks. The computation
of the tasks is done in child processes of the supervisor.

The supervisor assigns an internal state to each task which is represented by
an integer. The meaning of these integers and their relation to the global
state of each task is as follows:

internal state | meaning           | corresponding global state
---------------|-------------------|---------------------------
             0 | waiting           | started
             1 | started           | started
             2 | (result) computed | started
             3 | (result) sent     | completed
            -1 | stopped           | stopped

Links
-----
The ssi link between the main process and the supervisor is named 'l(pid)'
where pid is the PID of the main process. The links between the supervisor and
its child processes are named 'll(pid)(1)', 'll(pid)(2)', ... where pid is the
PID of the supervisor. The link between the child processes of the supervisor
and the main process is named 'L(pid)' where pid is the PID of the main
process. This link is only for sending the results to the main process and must
not be used in the other direction!

For any task t whose state is 'started', tasks[t.index].links is
list(L(pid), l(pid)) where pid is the PID of the main process.

Communication model
-------------------
stopTask() <--> supervisor
    0, id -->

waitTasks() <--> supervisor
(demanded_task is an intvec containing the IDs of the tasks which are being
waited for; ndemanded is the number of tasks that is being waited for.)
    1, demanded_tasks, ndemanded -->
    [receiving results]
    1, 0:2, -1 -->
    results_sent <--
    [receiving remaining results]

pollTask() <--> supervisor
    2, id -->
    state <--
    [receive result if state == 2 (computed)]

startTasks_child() <--> startTasks_grandchild()
    [compute the result]
    1, id <--
    [wait until the result is requested]
    1 -->
    [send the result]
    2 <--

sending and receiving results:
main process <--> supervisor <--> startTasks_grandchild()
    [request the result, see above]
    index, result  (main process <-- startTasks_grandchild())
    3, id          (main process --> supervisor)
*/

LIB "resources.lib";

static proc mod_init()
{
    /* initialize the semaphores */
    if (!defined(Resources)) {
        LIB "resources.lib";
    }
    // the number of processor cores
    int sem_cores = Resources::sem_cores;
    exportto(Tasks, sem_cores);
    // the number of leaves in the parallel tree (not strict)
    int sem_leaves = semaphore(system("--cpus")+10);
    exportto(Tasks, sem_leaves);
    // the number of processes waiting for sem_cores with low priority
    int sem_queue = semaphore(2);
    exportto(Tasks, sem_queue);

    /* define the Singular type 'task' */
    newstruct("task", "int index");
    newstruct("internal_task", "int id, string command, list arguments,"
        +"def result, string state, list links, int linkID");
    system("install", "task", "=", createTask, 1);
    system("install", "task", "==", compareTasks, 2);
    system("install", "task", "print", printTask, 1);

    /* define (lib-)global variables */
    list tasks;     // the lib-internal list of tasks
    exportto(Tasks, tasks);
    int ntasks;     // the current maximal index in 'tasks'
    exportto(Tasks, ntasks);
    int nlinkIDs;   // the current maximal linkID
    exportto(Tasks, nlinkIDs);
}

proc createTask(alias string command, alias list arguments)
"USAGE:   createTask(command, arguments), command string, arguments list
RETURN:   a task with the given command and arguments whose state is 'created'.
NOTE:     't = command, arguments;' is a shortcut for
          't = createTask(command, arguments);'.
SEE ALSO: startTasks, getCommand, getArguments, getState, killTask, copyTask,
          compareTasks, printTask
EXAMPLE:  example createTask; shows an example"
{
    internal_task T;
    ntasks++;
    tasks[ntasks] = T;
    tasks[ntasks].command = command;
    tasks[ntasks].arguments = arguments;
    tasks[ntasks].state = "created";
    task t;
    t.index = ntasks;
    return(t);
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t = createTask("std", list(I));
    // This is the same as:
    // task t = "std", list(I);
    t;
    killTask(t);
}

proc killTask(task t)
"USAGE:   killTask(t), t task
RETURN:   nothing. If the state of t is 'started', then t is stopped first. The
          internal data structures of t are erased and its state is set to
          'uninitialized'.
NOTE:     'killTask(t);' is not the same as 'kill t;'. The latter command does
          not erase the internal data structures of t. Hence killTask() should
          be called for any no longer needed task in order to free memory.
SEE ALSO: stopTask, getState, createTask, printTask
EXAMPLE:  example killTask; shows an example"
{
    if (t.index == 0) {
        return();
    }
    if (typeof(tasks[t.index]) != "internal_task") {
        return();
    }
    if (tasks[t.index].state == "started") {
        stopTask(t);
    }
    tasks[t.index] = def(0);
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t = "std", list(I);
    startTasks(t);
    t;
    killTask(t);
    t;
    getState(t);
}

proc copyTask(task t)
"USAGE:   copyTask(t), t task
RETURN:   a copy of t.
NOTE:     'task t1 = copyTask(t2);' is not the same as 'task t1 = t2;'. After
          the latter command, t1 points to the same object as t2; any changes
          to t2 will also effect t1. In contrast to this, copyTask() creates a
          new independend task.
       @* A task whose state is 'started' cannot be copied.
SEE ALSO: getCommand, getArguments, getResult, getState, createTask, killTask,
          compareTasks, printTask
EXAMPLE:  example copyTask; shows an example"
{
    task t_copy;
    if (t.index == 0) {
        return(t_copy);
    }
    if (typeof(tasks[t.index]) != "internal_task") {
        return(t_copy);
    }
    if (tasks[t.index].state == "started") {
        ERROR("cannot copy a task whose state is 'started'");
    }
    ntasks++;
    tasks[ntasks] = tasks[t.index];
    t_copy.index = ntasks;
    return(t_copy);
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t1 = "std", list(I);
    startTasks(t1);
    waitAllTasks(t1);
    task t2 = copyTask(t1);
    killTask(t1);
    t2;   // t2 survived
    getResult(t2);
    killTask(t2);
}

proc compareTasks(task t1, task t2)
"USAGE:   compareTasks(t1, t2), t1, t2 tasks
RETURN:   1, if t1 and t2 coincide;
          0, otherwise.
NOTE:     The arguments and the results of t1 and t2 are not compared.
       @* 't1 == t2' is a shortcut for 'compareTasks(t1, t2)'.
SEE ALSO: getCommand, getArguments, getResult, getState, copyTask, printTask
EXAMPLE:  example compareTasks; shows an example"
{
    if (tasks[t1.index].id != tasks[t2.index].id) {
        return(0);
    }
    if (tasks[t1.index].command != tasks[t2.index].command) {
        return(0);
    }
    if (tasks[t1.index].state != tasks[t2.index].state) {
        return(0);
    }
    if (tasks[t1.index].linkID != tasks[t2.index].linkID) {
        return(0);
    }
    return(1);
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t1 = "std", list(I);
    task t2 = "std", list(I);
    compareTasks(t1, t2);
    startTasks(t1);
    waitAllTasks(t1);
    t1 == t2;   // the same as compareTasks(t1, t2);
    killTask(t1);
    killTask(t2);
    // The arguments and the result are not compared!
    ideal J = x;
    task t3 = "std", list(I);
    task t4 = "std", list(J);
    t3 == t4;
    killTask(t3);
    killTask(t4);
}

proc printTask(task t)
"USAGE:   printTask(t), t task
RETURN:   nothing. Prints information about t.
NOTE:     'print(t);' and 't;' are shortcuts for 'printTask(t)'.
SEE ALSO: getCommand, getArguments, getResult, getState, createTask, killTask
EXAMPLE:  example printTask; shows an example"
{
    if (t.index == 0) {
        "An uninitialized task";
        return();
    }
    if (typeof(tasks[t.index]) != "internal_task") {
        "An uninitialized task";
        return();
    }
    "A task with the following properties:"+newline
        +"command:          "+tasks[t.index].command+newline
        +"no. of arguments: "+string(size(tasks[t.index].arguments))+newline
        +"state:            "+tasks[t.index].state;
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t;
    printTask(t);
    t = "std", list(I);
    t;   // the same as printTask(t);
    startTasks(t);
    waitAllTasks(t);
    t;
    killTask(t);
}

proc startTasks(list #)
"USAGE:   startTasks(t1, t2, ...), t1, t2, ... tasks
RETURN:   nothing. Starts the tasks t1, t2, ... and sets their states to
          'started'.
NOTE:     A task whose state is neither 'created' nor 'stopped' cannot be
          started.
       @* If startTasks() is applied to a task whose state is 'stopped', then
          the computation of this task will be restarted from the beginning.
       @* Tasks can be started from within other tasks. A started task should
          not be accessed from within any task other than the one within which
          it was started.
       @* For each task, the start of its computation is subject to the
          internal scheduling.
SEE ALSO: stopTask, waitTasks, pollTask, getState, createTask, printTask
EXAMPLE:  example startTasks; shows an example"
{
    int nargs = size(#);
    if (nargs == 0) {
        ERROR("missing argument");
    }
    int i;
    for (i = nargs; i > 0; i--) {
        if (typeof(#[i]) != "task") {
            ERROR("argument not of type 'task' (argument no. "+string(i)+")");
        }
        if (#[i].index == 0) {
            ERROR("cannot start an uninitialized task (task no. "
                +string(i)+")");
        }
        if (typeof(tasks[#[i].index]) != "internal_task") {
            ERROR("cannot start an uninitialized task (task no. "
                +string(i)+")");
        }
        if (tasks[#[i].index].state != "created"
            && tasks[#[i].index].state != "stopped") {
            ERROR("cannot start a task whose state is not"+newline
                +"'created' or 'stopped'");
        }
    }
    for (i = nargs; i > 0; i--) {
        tasks[#[i].index].id = i;   // has to be set before forking
        tasks[#[i].index].state = "started";
    }
    int pid = system("pid");
    link l(pid) = "ssi:fork";
    open(l(pid));
    write(l(pid), quote(startTasks_child(#, eval(pid))));
    int port = read(l(pid));
    link L(pid) = "ssi:connect localhost:"+string(port);
    open(L(pid));
    nlinkIDs++;
    for (i = nargs; i > 0; i--) {
        tasks[#[i].index].links = list(L(pid), l(pid));
        tasks[#[i].index].linkID = nlinkIDs;
    }
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t1 = "std", list(I);
    task t2 = "slimgb", list(I);
    startTasks(t1, t2);
    waitAllTasks(t1, t2);
    getResult(t1);
    getResult(t2);
    killTask(t1);
    killTask(t2);
}

/* This procedure is started within the child after forking. */
static proc startTasks_child(list localtasks, int pid_parent)
{
    int port = system("reserve", 1);
    write(l(pid_parent), port);
    link L(pid_parent) = system("reservedLink");
    export(L(pid_parent));

    int sem_write = semaphore(1);
    int pid = system("pid");

    int nlocaltasks = size(localtasks);
    intvec state = 0:nlocaltasks;
        // the internal state of each localtask (see rationale)
    int nwaiting = nlocaltasks;
        // the number of local tasks with internal state 0 (waiting)
    int nfinished;
        // the number of local tasks with internal state 3 (result sent) or
        // -1 (stopped)
    intvec queue = 1..nlocaltasks;
    int next = 1;

    list links;
    links[nlocaltasks+1] = l(pid_parent);
    intvec assignment = 0:nlocaltasks;
        // the task with id = i is running in link no. assignment[i]
    int nlinks;

    // data sent by other processes
    int code;
    int id;
    if (!defined(demanded_tasks)) {
        intvec demanded_tasks;
        int demanded_tasks_index = 1;
        exportto(Tasks, demanded_tasks);
        exportto(Tasks, demanded_tasks_index);
    }
    else {
        demanded_tasks = 0;
        demanded_tasks_index = 1;
    }
    int ndemanded = -1;

    // internal counts
    int granted_leaves;
    int results_sent;

    // auxiliary variables
    intvec waiting_tasks;
    int wait;
    int deadlock;
    int tmp;
    int i;
    int j;

    while (nwaiting > 0) {
        wait = 0;
        if (nlinks == 0) {
            wait = -1;
            granted_leaves++;
            while (-wait < nwaiting) {
                if (system("semaphore", "try_acquire", sem_leaves) == 1) {
                    wait--;
                }
                else {
                    break;
                }
            }
        }
        while (wait == 0) {
            wait = waitfirst(links, 500);
            if (wait == 0) {
                while (-wait < nwaiting) {
                    if (system("semaphore", "try_acquire", sem_leaves) == 1) {
                        wait--;
                    }
                    else {
                        break;
                    }
                }
            }
        }
        if (wait < 0) {   // open (-wait) new links
            while (wait < 0) {
                wait++;
                nlinks++;
                link ll(pid)(nlinks) = "ssi:fork";
                open(ll(pid)(nlinks));
                links[nlinks] = ll(pid)(nlinks);
                write(links[nlinks],
                    quote(startTasks_grandchild(
                    eval(localtasks[queue[next]].index), eval(pid_parent),
                    eval(pid), eval(nlinks), eval(sem_write))));
                assignment[queue[next]] = nlinks;
                state[queue[next]] = 1;
                nwaiting--;
                next++;
            }
            // wait == 0
        }
        if (wait > 0 && wait <= nlocaltasks) {
            code = read(links[wait]);
            if (code == 1) {   // result computed
                id = read(links[wait]);
                state[id] = 2;
                if (ndemanded > 0 && removeDemanded(id)) {
                    write(links[wait], 1);
                    ndemanded--;
                    results_sent++;
                }
            }
            // code == 2: startTasks_grandchild() ended, do nothing
        }
        if (wait == nlocaltasks+1) {
            code = read(l(pid_parent));
            if (code == 0) {   // stopTask
                id = read(l(pid_parent));
                if (state[id] == 0) {   // waiting
                    queue = give_priority(queue, intvec(id));
                    next++;
                }
                if (state[id] == 1 || state[id] == 2) {  // started or computed
                    close(links[assignment[id]]);
                    open(links[assignment[id]]);
                    write(links[assignment[id]],
                        quote(startTasks_grandchild(
                        eval(localtasks[queue[next]].index), eval(pid_parent),
                        eval(pid), eval(assignment[id]), eval(sem_write))));
                    assignment[queue[next]] = assignment[id];
                    assignment[id] = 0;
                    state[queue[next]] = 1;
                    next++;
                }
                // state[id] == -1 (stopped) or state[id] == 3 (sent)
                // should not happen
                nwaiting--;
                nfinished++;
                state[id] = -1;
            }
            if (code == 1) {   // waitTasks
                demanded_tasks = read(l(pid_parent));
                demanded_tasks_index = size(demanded_tasks);
                ndemanded = read(l(pid_parent));
                if (ndemanded > demanded_tasks_index) {
                    ndemanded = demanded_tasks_index;
                }
                if (demanded_tasks == 0 && ndemanded == -1) {
                    write(l(pid_parent), results_sent);
                    continue;
                }
                else {
                    results_sent = 0;
                }
                demanded_tasks = demanded_tasks[demanded_tasks_index..1];
                deadlock = 0;
                waiting_tasks = 0:demanded_tasks_index;
                j = 0;
                for (i = demanded_tasks_index; i > 0; i--) {
                    id = demanded_tasks[i];
                    if (state[id] == 0) {   // waiting
                        j++;
                        waiting_tasks[j] = id;
                        deadlock = 1;
                    }
                }
                if (j > 0) {
                    waiting_tasks = waiting_tasks[1..j];
                    queue = queue[next..size(queue)];
                    next = 1;
                    queue = give_priority(queue, waiting_tasks);
                    waiting_tasks = 0;
                }
                for (i = demanded_tasks_index; i > 0; i--) {
                    id = demanded_tasks[i];
                    if (state[id] == 1) {   // started
                        deadlock = 0;
                    }
                    if (state[id] == 2) {   // computed
                        write(links[assignment[id]], 1);
                        tmp = removeDemanded(id);
                        ndemanded--;
                        results_sent++;
                        deadlock = 0;
                    }
                }
                if (deadlock) {
                    granted_leaves++;
                    nlinks++;
                    link ll(pid)(nlinks) = "ssi:fork";
                    open(ll(pid)(nlinks));
                    links[nlinks] = ll(pid)(nlinks);
                    write(links[nlinks],
                        quote(startTasks_grandchild(
                        eval(localtasks[queue[next]].index), eval(pid_parent),
                        eval(pid), eval(nlinks), eval(sem_write))));
                    assignment[queue[next]] = nlinks;
                    state[queue[next]] = 1;
                    nwaiting--;
                    next++;
                }
            }
            if (code == 2) {   // pollTask
                id = read(l(pid_parent));
                if (state[id] == 0) {   // waiting
                    queue = queue[next..size(queue)];
                    next = 1;
                    queue = give_priority(queue, intvec(id));
                }
                if (state[id] == 2) {   // computed
                    write(links[assignment[id]], 1);
                }
                write(l(pid_parent), state[id]);
            }
            if (code == 3) {   // got result
                id = read(l(pid_parent));
                write(links[assignment[id]],
                    quote(startTasks_grandchild(
                    eval(localtasks[queue[next]].index), eval(pid_parent),
                    eval(pid), eval(assignment[id]), eval(sem_write))));
                assignment[queue[next]] = assignment[id];
                assignment[id] = 0;
                state[queue[next]] = 1;
                state[id] = 3;
                nwaiting--;
                nfinished++;
                next++;
            }
        }
    }
    while (nfinished < nlocaltasks || ndemanded != -1) {
        wait = waitfirst(links);
        if (wait <= nlocaltasks) {
            code = read(links[wait]);
            if (code == 1) {   // result computed
                id = read(links[wait]);
                state[id] = 2;
                if (ndemanded > 0 && removeDemanded(id)) {
                    write(links[wait], 1);
                    ndemanded--;
                    results_sent++;
                }
            }
            // code == 2: startTasks_grandchild() ended, do nothing
        }
        if (wait == nlocaltasks+1) {
            code = read(l(pid_parent));
            if (code == 0) {   // stopTask
                id = read(l(pid_parent));
                if (state[id] == 1 || state[id] == 2) {  // started or computed
                    close(links[assignment[id]]);
                    if (nlinks > granted_leaves) {
                        tmp = system("semaphore", "release", sem_leaves);
                    }
                    links[assignment[id]] = def(0);
                    nlinks--;
                    assignment[id] = 0;
                    nfinished++;
                }
                // else: nothing to do
                state[id] = -1;
            }
            if (code == 1) {   // waitTasks
                demanded_tasks = read(l(pid_parent));
                demanded_tasks_index = size(demanded_tasks);
                ndemanded = read(l(pid_parent));
                if (ndemanded > demanded_tasks_index) {
                    ndemanded = demanded_tasks_index;
                }
                if (demanded_tasks == 0 && ndemanded == -1) {
                    write(l(pid_parent), results_sent);
                    continue;
                }
                else {
                    results_sent = 0;
                }
                demanded_tasks = demanded_tasks[demanded_tasks_index..1];
                for (i = demanded_tasks_index; i > 0; i--) {
                    id = demanded_tasks[i];
                    if (state[id] == 2) {   // computed
                        write(links[assignment[id]], 1);
                        tmp = removeDemanded(id);
                        ndemanded--;
                        results_sent++;
                    }
                }
            }
            if (code == 2) {   // pollTask
                id = read(l(pid_parent));
                if (state[id] == 2) {   // computed
                    write(links[assignment[id]], 1);
                }
                write(l(pid_parent), state[id]);
            }
            if (code == 3) {   // got result
                id = read(l(pid_parent));
                close(links[assignment[id]]);
                if (nlinks > granted_leaves) {
                    tmp = system("semaphore", "release", sem_leaves);
                }
                links[assignment[id]] = def(0);
                nlinks--;
                assignment[id] = 0;
                state[id] = 3;
                nfinished++;
            }
        }
    }
}

/* This procedure has to be started within the grandchildren after forking. */
static proc startTasks_grandchild(int index, int pid_grandparent,
    int pid_parent, int link_no, int sem_write)
{
    def result;
    int tmp = system("semaphore", "acquire", sem_queue);
    tmp = system("semaphore", "acquire", sem_cores);
    tmp = system("semaphore", "release", sem_queue);
    execute("result = "+tasks[index].command+"("
        +argsToString("tasks[index].arguments", size(tasks[index].arguments))
        +");");
    tmp = system("semaphore", "release", sem_cores);
    write(ll(pid_parent)(link_no), 1);
    write(ll(pid_parent)(link_no), tasks[index].id);
    tmp = read(ll(pid_parent)(link_no));
    tmp = system("semaphore", "acquire", sem_write);
    write(L(pid_grandparent), index);
    write(L(pid_grandparent), result);
    tmp = system("semaphore", "release", sem_write);
    return(2);
}

/* Remove id from demanded_tasks and return 1, if id is an element of
 * demanded_tasks; return 0, otherwise. Note:
 * - demanded_tasks and demanded_tasks_index are (lib-)global objects
 *   exported in startTasks_child().
 * - demanded_tasks_index is used to avoid copying. It is defined to be
 *   the greatest integer with demanded_tasks[demanded_tasks_index] != 0
 *   and demanded_tasks[demanded_tasks_index+1] == 0 (if defined).
 */
static proc removeDemanded(alias int id)
{
    if (demanded_tasks[demanded_tasks_index] == id) {
        demanded_tasks[demanded_tasks_index] = 0;
        demanded_tasks_index--;
        return(1);
    }
    int i;
    for (i = demanded_tasks_index-1; i > 0; i--) {
        if (demanded_tasks[i] == id) {
            demanded_tasks[i..demanded_tasks_index]
                = demanded_tasks[(i+1)..demanded_tasks_index], 0;
            demanded_tasks_index--;
            return(1);
        }
    }
    return(0);
}

/* Move the elements in 'preferred' to the beginning of 'queue'. We may assume
 * that
 * - 'preferred' is a subset of 'queue';
 * - the elements of 'preferred' are distinct and non-zero;
 * - the elements of 'queue' are distinct and non-zero.
 * For performance reasons, we may also assume that 'queue' and 'preferred' are
 * more or less ordered in most cases. Note that queue has the format
 * '0, indices, 0'.
 */
static proc give_priority(intvec queue, intvec preferred)
{
    int size_queue = size(queue);
    int size_preferred = size(preferred);
    if (size_queue == size_preferred) {
        return(queue);
    }
    int index = size_queue;
    int i;
    int j;
    for (i = size_preferred; i > 0; i--) {
        for (j = size_queue; j > 0; j--) {
            if (queue[index] == preferred[i]) {
                queue[index] = 0;
                break;
            }
            index--;
            if (index == 0) {
                index = size_queue;
            }
        }
    }
    intvec not_preferred = 0:(size_queue-size_preferred);
    index = 1;
    for (i = 1; i <= size_queue; i++) {
        if (queue[i]) {
            not_preferred[index] = queue[i];
            index++;
        }
    }
    queue = preferred, not_preferred;
    return(queue);
}

proc stopTask(task t)
"USAGE:   stopTask(t), t task
RETURN:   nothing. Stops the t and sets its state to 'stopped'.
NOTE:     A task whose state is not 'started' cannot be stopped.
       @* Intermediate results are discarded when a task is stopped.
       @* killTask() should be called for any no longer needed task.
SEE ALSO: startTasks, waitTasks, pollTask, getState, killTask, printTask
EXAMPLE:  example stopTask; shows an example"
{
    if (t.index == 0) {
        ERROR("cannot stop an uninitialized task");
    }
    if (typeof(tasks[t.index]) != "internal_task") {
        ERROR("cannot stop an uninitialized task");
    }
    if (tasks[t.index].state != "started") {
        ERROR("cannot stop a task whose state is not 'started'");
    }
    write(tasks[t.index].links[2], 0);
    write(tasks[t.index].links[2], tasks[t.index].id);
    tasks[t.index].id = 0;
    tasks[t.index].links = list();
    tasks[t.index].linkID = 0;
    tasks[t.index].state = "stopped";
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t = "std", list(I);
    startTasks(t);
    stopTask(t);
    t;
    killTask(t);
}

proc waitTasks(list T, int N, list #)
"USAGE:   waitTasks(T, N[, timeout]), T list of tasks, N int, timeout int
RETURN:   an ordered list of the indices of those tasks which have been
          successfully completed. The state of these tasks is set to
          'completed'.
       @* The procedure waits for N tasks to complete.
       @* An optional timeout in ms can be provided. Default is 0 which
          disables the timeout.
NOTE:     A task whose state is neither 'started' nor 'completed' cannot be
          waited for.
       @* The result of any completed task can be accessed via @ref{getResult}.
       @* The returned list may contain more than N entries if the computation
          of some tasks has already finished and/or if several tasks finish
          \"at the same time\". It may contain less than N entries in
          the case of timeout or errors occurring.
       @* Polling is guaranteed, i.e. the index of any task t for which
          'pollTask(t);' would return 1 will appear in the returned list.
SEE ALSO: startTasks, pollTask, getResult, getState, printTask
EXAMPLE:  example waitTasks; shows an example"
{
    /* initialize the timer */
    int oldtimerresolution = system("--ticks-per-sec");
    system("--ticks-per-sec", 1000);
    int starting_time = rtimer;

    /* read optional parameters */
    int timeout;
    if (size(#) > 0) {
        if (size(#) > 1 || typeof(#[1]) != "int") {
            ERROR("wrong optional parameter");
        }
        timeout = #[1];
    }

    /* check for errors */
    if (timeout < 0) {
        ERROR("negative timeout");
    }
    int nargs = size(T);
    if (nargs == 0) {
        ERROR("missing task");
    }
    if (N < 1 || N > nargs) {
        ERROR("wrong number of tasks to wait for");
    }
    int i;
    for (i = nargs; i > 0; i--) {
        if (typeof(T[i]) != "task") {
            ERROR("element not of type 'task' (element no. "+string(i)+")");
        }
        if (T[i].index == 0) {
            ERROR("cannot wait for an uninitialized task (task no. "+string(i)
                +")");
        }
        if (typeof(tasks[T[i].index]) != "internal_task") {
            ERROR("cannot wait for an uninitialized task (task no. "+string(i)
                +")");
        }
        if (tasks[T[i].index].state != "started"
            && tasks[T[i].index].state != "completed") {
            ERROR("cannot wait for a task whose state is not"+newline
                +"'started' or 'completed' (task no. "+string(i)+")");
        }
    }

    /* sort the tasks */
    int ncompleted;
    list requests;
    list links;
    int sorted_in;
    int j;
    for (i = 1; i <= nargs; i++) {
        if (tasks[T[i].index].state == "completed") {
            ncompleted++;
        }
        else {   // tasks[T[i].index].state == "started"
            sorted_in = 0;
            for (j = size(requests); j > 0; j--) {
                if (requests[j][1] == tasks[T[i].index].linkID) {
                    requests[j][2][size(requests[j][2])+1] =
                        tasks[T[i].index].id;
                    sorted_in = 1;
                    break;
                }
            }
            if (!sorted_in) {
                requests[size(requests)+1] = list(tasks[T[i].index].linkID,
                    intvec(tasks[T[i].index].id),
                    tasks[T[i].index].links[2]);
                links[size(links)+1] = tasks[T[i].index].links[1];
            }
        }
    }

    /* send the reqests */
    for (j = size(requests); j > 0; j--) {
        write(requests[j][3], 1);
        write(requests[j][3], requests[j][2]);
        write(requests[j][3], N-ncompleted);
    }

    /* wait for the results */
    int wait;
    int index;
    int results_got;
    int remaining_time;
    int tmp;
    while (ncompleted < N) {
        wait = waitfirst(links, 0);
        if (wait == 0) {
            if (timeout == 0) {
                tmp = system("semaphore", "release", sem_cores);
                wait = waitfirst(links);
                tmp = system("semaphore", "acquire", sem_cores);
            }
            else {
                remaining_time = timeout-(rtimer-starting_time);
                if (remaining_time < 0) {
                    break;
                }
                else {
                    tmp = system("semaphore", "release", sem_cores);
                    wait = waitfirst(links, remaining_time);
                    tmp = system("semaphore", "acquire", sem_cores);
                }
            }
        }
        if (wait < 1) {
            break;
        }
        index = read(links[wait]);
        tasks[index].result = read(links[wait]);
        write(tasks[index].links[2], 3);
        write(tasks[index].links[2], tasks[index].id);
        tasks[index].id = 0;
        tasks[index].links = list();
        tasks[index].linkID = 0;
        tasks[index].state = "completed";
        ncompleted++;
        results_got++;
    }
    if (wait == -1) {
        ERROR("error in waitfirst()");
    }

    /* end communication process */
    for (j = size(requests); j > 0; j--) {
        write(requests[j][3], 1);
        write(requests[j][3], 0);
        write(requests[j][3], -1);
    }
    int results_sent;
    for (j = size(requests); j > 0; j--) {
        results_sent = results_sent + read(requests[j][3]);
    }
    while (results_sent > results_got) {
        wait = waitfirst(links);
        if (wait == -1) {
            ERROR("error in waitfirst()");
        }
        index = read(links[wait]);
        tasks[index].result = read(links[wait]);
        write(tasks[index].links[2], 3);
        write(tasks[index].links[2], tasks[index].id);
        tasks[index].id = 0;
        tasks[index].links = list();
        tasks[index].linkID = 0;
        tasks[index].state = "completed";
        results_got++;
    }

    /* list completed tasks */
    list completed;
    completed[nargs+1] = 0;
    j = 0;
    for (i = 1; i <= nargs; i++) {
        if (tasks[T[i].index].state == "completed") {
            j++;
            completed[j] = i;
        }
    }
    completed[nargs+1] = def(0);

    /* return the result */
    system("--ticks-per-sec", oldtimerresolution);
    return(completed);
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t1 = "std", list(I);
    task t2 = "slimgb", list(I);
    startTasks(t1, t2);
    waitTasks(list(t1, t2), 2);   // wait for both tasks
    getResult(t1);
    getResult(t2);
    killTask(t1);
    killTask(t2);
}

proc waitAllTasks(list #)
"USAGE:   waitAllTasks(t1, t2, ...), t1, t2, ... tasks
RETURN:   nothing. Waits for all the tasks t1, t2, ... to complete. The state
          of the tasks is set to 'completed'.
NOTE:     A task whose state is neither 'started' nor 'completed' cannot be
          waited for.
       @* The result of any completed task can be accessed via @ref{getResult}.
       @* 'waitAllTasks(t1, t2, ...);' is a shortcut for
          'waitTasks(list(t1, t2, ...), size(list(t1, t2, ...)));'. Since
          returning a list of the indices of the completed tasks does not make
          sense in this case, nothing is returned.
SEE ALSO: waitTasks, startTasks, pollTask, getResult, getState, printTask
EXAMPLE:  example waitAllTasks; shows an example"
{
    list tmp = waitTasks(#, size(#));
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t1 = "std", list(I);
    task t2 = "slimgb", list(I);
    startTasks(t1, t2);
    waitAllTasks(t1, t2);   // the same as 'waitTasks(list(t1, t2), 2);',
                            // but without return value
    getResult(t1);
    getResult(t2);
    killTask(t1);
    killTask(t2);
}

proc pollTask(task t)
"USAGE:   pollTask(t), t task
RETURN:   1, if the computation of the task t has successfully finished;
          0, otherwise.
       @* The state of any task whose computation has successfully finished is
          set to 'completed'.
NOTE:     A task whose state is neither 'started' nor 'completed' cannot be
          polled.
       @* The result of any completed task can be accessed via @ref{getResult}.
       @* pollTask() should return immediately. However, receiving the result
          of the task may take some time.
SEE ALSO: startTasks, waitTasks, getResult, getState, printTask
EXAMPLE:  example pollTask; shows an example"
{
    if (t.index == 0) {
        ERROR("cannot poll an uninitialized task");
    }
    if (typeof(tasks[t.index]) != "internal_task") {
        ERROR("cannot poll an uninitialized task");
    }
    if (tasks[t.index].state != "started"
        && tasks[t.index].state != "completed") {
        ERROR("cannot poll a task whose state is not"+newline
            +"'started' or 'completed'");
    }
    if (tasks[t.index].state == "completed") {
        return(1);
    }
    // tasks[t.index].state == "started"
    write(tasks[t.index].links[2], 2);
    write(tasks[t.index].links[2], tasks[t.index].id);
    int state = read(tasks[t.index].links[2]);
    if (state == 0 || state == 1) {   // waiting or started
        return(0);
    }
    if (state == 2) {   // computed
        int index = read(tasks[t.index].links[1]);   // index == t.index
        tasks[t.index].result = read(tasks[t.index].links[1]);
        write(tasks[t.index].links[2], 3);
        write(tasks[t.index].links[2], tasks[t.index].id);
        tasks[t.index].id = 0;
        tasks[t.index].links = list();
        tasks[t.index].linkID = 0;
        tasks[t.index].state = "completed";
        return(1);
    }
    // state == -1 (stopped) or state == 3 (sent) should not happen
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t = "std", list(I);
    startTasks(t);
    waitAllTasks(t);
    pollTask(t);   // task already completed
    t;
    getResult(t);
    killTask(t);
}

proc getCommand(task t)
"USAGE:   getCommand(t), t task
RETURN:   a string, the command of t.
NOTE:     This command cannot be applied to tasks whose state is
          'uninitialized'.
SEE ALSO: getArguments, getResult, getState, createTask, printTask
EXAMPLE:  example getCommand; shows an example"
{
    if (t.index == 0) {
        ERROR("cannot get command of an uninitialized task");
    }
    if (typeof(tasks[t.index]) != "internal_task") {
        ERROR("cannot get command of an uninitialized task");
    }
    return(tasks[t.index].command);
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t = "std", list(I);
    getCommand(t);
    killTask(t);
}

proc getArguments(task t)
"USAGE:   getArguments(t), t task
RETURN:   a list, the arguments of t.
NOTE:     This command cannot be applied to tasks whose state is
          'uninitialized'.
SEE ALSO: getCommand, getResult, getState, createTask, printTask
EXAMPLE:  example getArguments; shows an example"
{
    if (t.index == 0) {
        ERROR("cannot get arguments of an uninitialized task");
    }
    if (typeof(tasks[t.index]) != "internal_task") {
        ERROR("cannot get arguments of an uninitialized task");
    }
    return(tasks[t.index].arguments);
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t = "std", list(I);
    getArguments(t);
    killTask(t);
}

proc getResult(task t)
"USAGE:   getResult(t), t task
RETURN:   the result of t.
NOTE:     This command cannot be applied to tasks whose state is not
          'completed'.
SEE ALSO: getCommand, getArguments, getState, waitTasks, pollTask, printTask
EXAMPLE:  example getResult; shows an example"
{
    if (t.index == 0) {
        ERROR("cannot get result of an uninitialized task");
    }
    if (typeof(tasks[t.index]) != "internal_task") {
        ERROR("cannot get result of an uninitialized task");
    }
    if (tasks[t.index].state != "completed") {
        ERROR("cannot get result of a task which is not completed");
    }
    return(tasks[t.index].result);
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t = "std", list(I);
    startTasks(t);
    waitAllTasks(t);
    getResult(t);
    killTask(t);
}

proc getState(task t)
"USAGE:   getState(t), t task
RETURN:   a string, the state of t.
SEE ALSO: getCommand, getArguments, getResult, printTask, createTask,
          startTasks, stopTask, waitTasks, pollTask, killTask
EXAMPLE:  example getState; shows an example"
{
    if (t.index == 0) {
        return("uninitialized");
    }
    if (typeof(tasks[t.index]) != "internal_task") {
        return("uninitialized");
    }
    return(tasks[t.index].state);
}
example
{
    "EXAMPLE:";
    echo = 2;
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    task t = "std", list(I);
    getState(t);
    startTasks(t);
    getState(t);
    waitAllTasks(t);
    getState(t);
    killTask(t);
    getState(t);
}

/ * construct the string "name[1], name[2], name[3], ..., name[length]" */
static proc argsToString(string name, int length)
{
    string output;
    if (length > 0) {
        output = name+"[1]";
    }
    int i;
    for (i = 2; i <= length; i++) {
        output = output+", "+name+"["+string(i)+"]";
    }
    return(output);
}