starpu-max/src/profiling/bound.c

/*
 * StarPU
 * Copyright (C) Université Bordeaux 1, CNRS 2010 (see AUTHORS file)
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2.1 of the License, or (at
 * your option) any later version.
 *
 * This program 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 Lesser General Public License in COPYING.LGPL for more details.
 */

/*
 * Record which kinds of tasks have been executed, to later on compute an upper
 * bound of the performance that could have theoretically been achieved
 */

#include <starpu.h>
#include <starpu_config.h>
#include <profiling/bound.h>
#include <core/jobs.h>

#ifdef HAVE_GLPK_H
#include <glpk.h>
#endif /* HAVE_GLPK_H */

/* TODO: output duration between starpu_bound_start and starpu_bound_stop */

/*
 * Record without dependencies: just count each kind of task
 *
 * The linear programming problem will just have as variables:
 * - the number of tasks of kind `t' executed by worker `w'
 * - the total duration
 *
 * and the constraints will be:
 * - the time taken by each worker to complete its assigned tasks is lower than
 *   the total duration.
 * - the total numer of tasks of a given kind is equal to the number run by the
 *   application.
 */
struct bound_task_pool {
	/* Which codelet has been executed */
	struct starpu_codelet_t *cl;
	/* Task footprint key */
	uint32_t footprint;
	/* Number of tasks of this kind */
	unsigned long n;
	/* Other task kinds */
	struct bound_task_pool *next;
};

/*
 * Record with dependencies: each task is recorded separately
 *
 * The linear programming problem will have as variables:
 * - The start time of each task
 * - The completion time of each tag
 * - The total duration
 * - For each task and for each worker, whether the task is executing on that worker.
 * - For each pair of task, which task is scheduled first.
 *
 * and the constraints will be:
 * - All task start time plus duration are less than total duration
 * - Each task is executed on exactly one worker.
 * - Each task starts after all its task dependencies finish.
 * - Each task starts after all its tag dependencies finish.
 * - For each task pair and each worker, if both tasks are executed by that worker,
 *   one is started after the other's completion.
 */
/* Note: only task-task, implicit data dependencies or task-tag dependencies
 * are taken into account. Tags released in a callback or something like this
 * is not taken into account, only tags associated with a task are. */
struct bound_task {
	/* Unique ID */
	int id;
	/* Tag ID, if any */
	starpu_tag_t tag_id;
	int use_tag;
	/* Which codelet has been executed */
	struct starpu_codelet_t *cl;
	/* Task footprint key */
	uint32_t footprint;
	/* Task priority */
	int priority;
	/* Tasks this one depends on */
	struct bound_task **deps;
	int depsn;

	/* Estimated duration */
	double duration[STARPU_NARCH_VARIATIONS];

	/* Other tasks */
	struct bound_task *next;
};

struct bound_tag_dep {
	starpu_tag_t tag;
	starpu_tag_t dep_tag;
	struct bound_tag_dep *next;
};

static struct bound_task_pool *task_pools, *last;
static struct bound_task *tasks;
static struct bound_tag_dep *tag_deps;
static int recording;
static int recorddeps;
static int recordprio;

static pthread_mutex_t mutex = PTHREAD_MUTEX_INITIALIZER;

void starpu_bound_start(int deps, int prio)
{
	struct bound_task_pool *tp;
	struct bound_task *t;
	struct bound_tag_dep *td;

	PTHREAD_MUTEX_LOCK(&mutex);

	tp = task_pools;
	task_pools = NULL;
	last = NULL;

	t = tasks;
	tasks = NULL;

	td = tag_deps;
	tag_deps = NULL;

	recording = 1;
	recorddeps = deps;
	recordprio = prio;

	PTHREAD_MUTEX_UNLOCK(&mutex);

	for ( ; tp; tp = tp->next)
		free(tp);

	for ( ; t; t = t->next)
		free(t);

	for ( ; td; td = td->next)
		free(td);
}

static int good_job(starpu_job_t j)
{
	/* No codelet, nothing to measure */
	if (j->exclude_from_dag)
		return 0;
	if (!j->task->cl)
		return 0;
	/* No performance model, no time duration estimation */
	if (!j->task->cl->model)
		return 0;
	/* Only support history based */
	if (j->task->cl->model->type != STARPU_HISTORY_BASED)
		return 0;
	return 1;
}

static void new_task(starpu_job_t j)
{
	struct bound_task *t;
	static int task_ids;

	if (j->bound_task)
		return;

	if (STARPU_UNLIKELY(!j->footprint_is_computed))
		_starpu_compute_buffers_footprint(j);

	t = malloc(sizeof(*t));
	memset(t, 0, sizeof(*t));
	t->id = task_ids++;
	t->tag_id = j->task->tag_id;
	t->use_tag = j->task->use_tag;
	t->cl = j->task->cl;
	t->footprint = j->footprint;
	t->priority = j->task->priority;
	t->deps = NULL;
	t->depsn = 0;
	t->next = tasks;
	j->bound_task = t;
	tasks = t;
}

void _starpu_bound_record(starpu_job_t j)
{
	if (!recording)
		return;

	if (!good_job(j))
		return;

	PTHREAD_MUTEX_LOCK(&mutex);
	/* Re-check, this time with mutex held */
	if (!recording) {
		PTHREAD_MUTEX_UNLOCK(&mutex);
		return;
	}

	if (recorddeps) {
		new_task(j);
	} else {
		struct bound_task_pool *tp;

		if (STARPU_UNLIKELY(!j->footprint_is_computed))
			_starpu_compute_buffers_footprint(j);

		if (last && last->cl == j->task->cl && last->footprint == j->footprint)
			tp = last;
		else
			for (tp = task_pools; tp; tp = tp->next)
				if (tp->cl == j->task->cl && tp->footprint == j->footprint)
					break;

		if (!tp) {
			tp = malloc(sizeof(*tp));
			tp->cl = j->task->cl;
			tp->footprint = j->footprint;
			tp->n = 0;
			tp->next = task_pools;
			task_pools = tp;
		}

		/* One more task of this kind */
		tp->n++;
	}

	PTHREAD_MUTEX_UNLOCK(&mutex);
}

void _starpu_bound_tag_dep(starpu_tag_t id, starpu_tag_t dep_id)
{
	struct bound_tag_dep *td;

	if (!recording || !recorddeps)
		return;

	PTHREAD_MUTEX_LOCK(&mutex);
	/* Re-check, this time with mutex held */
	if (!recording || !recorddeps) {
		PTHREAD_MUTEX_UNLOCK(&mutex);
		return;
	}

	td = malloc(sizeof(*td));
	td->tag = id;
	td->dep_tag = dep_id;
	td->next = tag_deps;
	tag_deps = td;
	PTHREAD_MUTEX_UNLOCK(&mutex);
}

void _starpu_bound_task_dep(starpu_job_t j, starpu_job_t dep_j)
{
	struct bound_task *t;

	if (!recording || !recorddeps)
		return;

	if (!good_job(j) || !good_job(dep_j))
		return;

	PTHREAD_MUTEX_LOCK(&mutex);
	/* Re-check, this time with mutex held */
	if (!recording || !recorddeps) {
		PTHREAD_MUTEX_UNLOCK(&mutex);
		return;
	}

	new_task(j);
	new_task(dep_j);
	t = j->bound_task;
	t->deps = realloc(t->deps, ++t->depsn * sizeof(t->deps[0]));
	t->deps[t->depsn-1] = dep_j->bound_task;
	PTHREAD_MUTEX_UNLOCK(&mutex);
}

void starpu_bound_stop(void)
{
	PTHREAD_MUTEX_LOCK(&mutex);
	recording = 0;
	PTHREAD_MUTEX_UNLOCK(&mutex);
}

static void _starpu_get_tasks_times(int nw, int nt, double times[nw][nt]) {
	struct bound_task_pool *tp;
	int w, t;
	for (w = 0; w < nw; w++) {
		for (t = 0, tp = task_pools; tp; t++, tp = tp->next) {
			struct starpu_job_s j = {
				.footprint = tp->footprint,
				.footprint_is_computed = 1,
			};
			enum starpu_perf_archtype arch = starpu_worker_get_perf_archtype(w);
			double length = _starpu_history_based_job_expected_length(tp->cl->model, arch, &j);
			if (length == -1.0)
				times[w][t] = -1.0;
			else
				times[w][t] = length / 1000.;
		}
	}
}

static int ancestor(struct bound_task *child, struct bound_task *parent) {
	int i;
	for (i = 0; i < child->depsn; i++) {
		if (parent == child->deps[i])
			return 1;
		if (ancestor(child->deps[i], parent))
			return -1;
	}
	return 0;
}

/*
 * lp_solve format
 */
void starpu_bound_print_lp(FILE *output)
{
	int nt; /* Number of different kinds of tasks */
	int nw; /* Number of different workers */
	int t, w;

	PTHREAD_MUTEX_LOCK(&mutex);
	nw = starpu_worker_get_count();

	if (recorddeps) {
		struct bound_task *t, *t2;
		struct bound_tag_dep *td;
		int i;

		nt = 0;
		for (t = tasks; t; t = t->next) {
			struct starpu_job_s j = {
				.footprint = t->footprint,
				.footprint_is_computed = 1,
			};
			for (w = 0; w < nw; w++) {
				enum starpu_perf_archtype arch = starpu_worker_get_perf_archtype(w);
				if (t->duration[arch] == 0.) {
					double length = _starpu_history_based_job_expected_length(t->cl->model, arch, &j);
					if (length == -1.0)
						/* Avoid problems with binary coding of doubles */
						t->duration[arch] = -1.0;
					else
						t->duration[arch] = length / 1000.;
				}
			}
			nt++;
		}
		fprintf(output, "/* StarPU upper bound linear programming problem, to be run in lp_solve. */\n\n");
		fprintf(output, "/* !! This is a big system, it will be long to solve !! */\n\n");
		fprintf(output, "/* We want to minimize total execution time (ms) */\n");
		fprintf(output, "min: tmax;\n\n");

		fprintf(output, "/* Which is the maximum of all task completion times (ms) */\n");
		for (t = tasks; t; t = t->next)
			fprintf(output, "c%u <= tmax;\n", t->id);

		fprintf(output, "\n/* We have tasks executing on workers, exactly one worker executes each task */\n");
		for (t = tasks; t; t = t->next) {
			for (w = 0; w < nw; w++) {
				enum starpu_perf_archtype arch = starpu_worker_get_perf_archtype(w);
				if (t->duration[arch] != -1.0)
					fprintf(output, " +t%uw%u", t->id, w);
			}
			fprintf(output, " = 1;\n");
		}

		fprintf(output, "\n/* Completion time is start time plus computation time */\n");
		fprintf(output, "/* According to where the task is indeed executed */\n");
		for (t = tasks; t; t = t->next) {
			fprintf(output, "/* %s %x */\tc%u = s%u", t->cl->model->symbol, (unsigned) t->footprint, t->id, t->id);
			for (w = 0; w < nw; w++) {
				enum starpu_perf_archtype arch = starpu_worker_get_perf_archtype(w);
				if (t->duration[arch] != -1.0)
					fprintf(output, " + %f t%uw%u", t->duration[arch], t->id, w);
			}
			fprintf(output, ";\n");
		}

		fprintf(output, "\n/* Each task starts after all its task dependencies finish. */\n");
		fprintf(output, "/* Note that the dependency finish time depends on the worker where it's working */\n");
		for (t = tasks; t; t = t->next)
			for (i = 0; i < t->depsn; i++)
				fprintf(output, "s%u >= c%u;\n", t->id, t->deps[i]->id);

		fprintf(output, "\n/* Each tag finishes when its corresponding task finishes */");
		for (t = tasks; t; t = t->next)
			if (t->use_tag) {
				for (w = 0; w < nw; w++)
					fprintf(output, "c%u = tag%lu;\n", t->id, (unsigned long) t->tag_id);
			}

		fprintf(output, "\n/* tags start after all their tag dependencies finish. */\n");
		for (td = tag_deps; td; td = td->next)
			fprintf(output, "tag%lu >= tag%lu;\n", (unsigned long) td->tag, (unsigned long) td->dep_tag);

/* TODO: factorize ancestor calls */
		fprintf(output, "\n/* For each task pair and each worker, if both tasks are executed by the same worker,\n");
		fprintf(output, "   one is started after the other's completion */\n");
		for (t = tasks; t; t = t->next) {
			for (t2 = t->next; t2; t2 = t2->next)
			{
				if (!ancestor(t, t2) && !ancestor(t2, t)) {
					for (w = 0; w < nw; w++) {
						enum starpu_perf_archtype arch = starpu_worker_get_perf_archtype(w);
						if (t->duration[arch] != -1.0) {
							fprintf(output, "s%u - c%u >= -3e5 + 1e5 t%uw%u + 1e5 t%uw%u + 1e5 t%uafter%u;\n",
									t->id, t2->id, t->id, w, t2->id, w, t->id, t2->id);
							fprintf(output, "s%u - c%u >= -2e5 + 1e5 t%uw%u + 1e5 t%uw%u - 1e5 t%uafter%u;\n",
									t2->id, t->id, t->id, w, t2->id, w, t->id, t2->id);
						}
					}
				}
			}
		}

#if 0
/* Doesn't help at all to actually express what "after" means */
		for (t = tasks; t; t = t->next)
			for (t2 = t->next; t2; t2 = t2->next)
				if (!ancestor(t, t2) && !ancestor(t2, t))
				{
					fprintf(output, "s%u - s%u >= -1e5 + 1e5 t%uafter%u;\n", t->id, t2->id, t->id, t2->id);
					fprintf(output, "s%u - s%u >= -1e5 t%uafter%u;\n", t2->id, t->id, t->id, t2->id);
				}
#endif

		if (recordprio) {
			fprintf(output, "\n/* For StarPU, a priority means given schedulable tasks it will consider the\n");
			fprintf(output, " * more prioritized first */\n");
			for (t = tasks; t; t = t->next) {
				for (t2 = t->next; t2; t2 = t2->next)
				{
					if (!ancestor(t, t2) && !ancestor(t2, t)
					     && t->priority != t2->priority) {
						if (t->priority > t2->priority) {
							/* Either t2 is scheduled before t, but then it
							   needs to be scheduled before some t dep finishes */

							/* One of the t deps to give the maximum start time for t2 */
							if (t->depsn > 1) {
								for (i = 0; i < t->depsn; i++)
									fprintf(output, " + t%ut%ud%u", t2->id, t->id, i);
								fprintf(output, " = 1;\n");
							}

							for (i = 0; i < t->depsn; i++) {
								fprintf(output, "c%u - s%u >= ", t->deps[i]->id, t2->id);
								if (t->depsn > 1)
									/* Only checks this when it's this dependency that is chosen */
									fprintf(output, "-2e5 + 1e5 t%ut%ud%u", t2->id, t->id, i);
								else
									fprintf(output, "-1e5");
								/* Only check this if t is after t2 */
								fprintf(output, " + 1e5 t%uafter%u", t->id, t2->id);
								fprintf(output, ";\n");
							}

							/* Or t2 is scheduled after t is.  */
							fprintf(output, "s%u - s%u >= -1e5 t%uafter%u;\n", t2->id, t->id, t->id, t2->id);
						} else {
							/* Either t is scheduled before t2, but then it
							   needs to be scheduled before some t2 dep finishes */

							/* One of the t2 deps to give the maximum start time for t */
							if (t2->depsn > 1) {
								for (i = 0; i < t2->depsn; i++)
									fprintf(output, " + t%ut%ud%u", t->id, t2->id, i);
								fprintf(output, " = 1;\n");
							}

							for (i = 0; i < t2->depsn; i++) {
								fprintf(output, "c%u - s%u >= ", t2->deps[i]->id, t->id);
								if (t2->depsn > 1)
									/* Only checks this when it's this dependency that is chosen */
									fprintf(output, "-1e5 + 1e5 t%ut%ud%u", t->id, t2->id, i);
								/* Only check this if t2 is after t */
								fprintf(output, " - 1e5 t%uafter%u;\n", t->id, t2->id);
							}

							/* Or t is scheduled after t2 is.  */
							fprintf(output, "s%u - s%u >= -1e5 + 1e5 t%uafter%u;\n", t->id, t2->id, t->id, t2->id);
						}
					}
				}
			}
		}


		for (t = tasks; t; t = t->next)
			for (t2 = t->next; t2; t2 = t2->next)
				if (!ancestor(t, t2) && !ancestor(t2, t)) {
					fprintf(output, "bin t%uafter%u;\n", t->id, t2->id);
					if (recordprio && t->priority != t2->priority) {
						if (t->priority > t2->priority) {
							if (t->depsn > 1)
								for (i = 0; i < t->depsn; i++)
									fprintf(output, "bin t%ut%ud%u;\n", t2->id, t->id, i);
						} else {
							if (t2->depsn > 1)
								for (i = 0; i < t2->depsn; i++)
									fprintf(output, "bin t%ut%ud%u;\n", t->id, t2->id, i);
						}
					}
				}

		for (t = tasks; t; t = t->next)
			for (w = 0; w < nw; w++)
				fprintf(output, "bin t%uw%u;\n", t->id, w);
	} else {
		struct bound_task_pool *tp;
		nt = 0;
		for (tp = task_pools; tp; tp = tp->next)
			nt++;

		{
			double times[nw][nt];

			_starpu_get_tasks_times(nw, nt, times);

			fprintf(output, "/* StarPU upper bound linear programming problem, to be run in lp_solve. */\n\n");
			fprintf(output, "/* We want to minimize total execution time (ms) */\n");
			fprintf(output, "min: tmax;\n\n");

			fprintf(output, "/* Which is the maximum of all worker execution times (ms) */\n");
			for (w = 0; w < nw; w++) {
				char name[32];
				starpu_worker_get_name(w, name, sizeof(name));
				fprintf(output, "/* worker %s */\n", name);
				for (t = 0, tp = task_pools; tp; t++, tp = tp->next) {
					if (times[w][t] != -1.0)
						fprintf(output, "\t%+f * w%ut%un", (float) times[w][t], w, t);
				}
				fprintf(output, " <= tmax;\n");
			}
			fprintf(output, "\n");

			fprintf(output, "/* And we have to have computed exactly all tasks */\n");
			for (t = 0, tp = task_pools; tp; t++, tp = tp->next) {
				fprintf(output, "/* task %s key %x */\n", tp->cl->model->symbol, (unsigned) tp->footprint);
				for (w = 0; w < nw; w++)
					if (times[w][t] != -1.0)
						fprintf(output, "\t+w%ut%un", w, t);
				fprintf(output, " = %ld;\n", tp->n);
				/* Show actual values */
				fprintf(output, "/*");
				for (w = 0; w < nw; w++)
					fprintf(output, "\t+%ld", tp->cl->per_worker_stats[w]);
				fprintf(output, "\t*/\n\n");
			}

			fprintf(output, "/* Optionally tell that tasks can not be divided */\n");
			fprintf(output, "/* int ");
			int first = 1;
			for (w = 0; w < nw; w++)
				for (t = 0, tp = task_pools; tp; t++, tp = tp->next) {
					if (!first)
						fprintf(output, ",");
					else
						first = 0;
					fprintf(output, "w%ut%un", w, t);
				}
			fprintf(output, "; */\n");
		}
	}

	PTHREAD_MUTEX_UNLOCK(&mutex);
}

/*
 * MPS output format
 */
void starpu_bound_print_mps(FILE *output)
{
	struct bound_task_pool * tp;
	int nt; /* Number of different kinds of tasks */
	int nw; /* Number of different workers */
	int t, w;

	if (recorddeps) {
		fprintf(output, "Not supported\n");
		return;
	}

	PTHREAD_MUTEX_LOCK(&mutex);

	nw = starpu_worker_get_count();
	nt = 0;
	for (tp = task_pools; tp; tp = tp->next)
		nt++;

	{
		double times[nw][nt];

		_starpu_get_tasks_times(nw, nt, times);

		fprintf(output, "NAME           StarPU theoretical bound\n");

		fprintf(output, "\nROWS\n");

		fprintf(output, "* We want to minimize total execution time (ms)\n");
		fprintf(output, " N  TMAX\n");

		fprintf(output, "\n* Which is the maximum of all worker execution times (ms)\n");
		for (w = 0; w < nw; w++) {
			char name[32];
			starpu_worker_get_name(w, name, sizeof(name));
			fprintf(output, "* worker %s\n", name);
			fprintf(output, " L  W%u\n", w);
		}

		fprintf(output, "\n* And we have to have computed exactly all tasks\n");
		for (t = 0, tp = task_pools; tp; t++, tp = tp->next) {
			fprintf(output, "* task %s key %x\n", tp->cl->model->symbol, (unsigned) tp->footprint);
			fprintf(output, " E  T%u\n", t);
		}

		fprintf(output, "\nCOLUMNS\n");

		fprintf(output, "\n* Execution times and completion of all tasks\n");
		for (w = 0; w < nw; w++)
			for (t = 0, tp = task_pools; tp; t++, tp = tp->next)
				if (times[w][t] != -1.0) {
					char name[9];
					snprintf(name, sizeof(name), "W%uT%u", w, t);
					fprintf(stderr,"    %-8s  W%-7u  %12f\n", name, w, times[w][t]);
					fprintf(stderr,"    %-8s  T%-7u  %12u\n", name, t, 1);
				}

		fprintf(output, "\n* Total execution time\n");
		for (w = 0; w < nw; w++)
			fprintf(stderr,"    TMAX      W%-2u       %12u\n", w, -1);
		fprintf(stderr,"    TMAX      TMAX      %12u\n", 1);

		fprintf(output, "\nRHS\n");

		fprintf(output, "\n* Total number of tasks\n");
		for (t = 0, tp = task_pools; tp; t++, tp = tp->next)
			fprintf(stderr,"    NT%-2u      T%-7u  %12lu\n", t, t, tp->n);

		fprintf(output, "ENDATA\n");
	}

	PTHREAD_MUTEX_UNLOCK(&mutex);
}

/*
 * GNU Linear Programming Kit backend
 */
#ifdef HAVE_GLPK_H
static glp_prob *_starpu_bound_glp_resolve(void)
{
	struct bound_task_pool * tp;
	int nt; /* Number of different kinds of tasks */
	int nw; /* Number of different workers */
	int t, w;
	glp_prob *lp;
	int ret;

	nw = starpu_worker_get_count();
	nt = 0;
	for (tp = task_pools; tp; tp = tp->next)
		nt++;

	lp = glp_create_prob();
	glp_set_prob_name(lp, "StarPU theoretical bound");
	glp_set_obj_dir(lp, GLP_MIN);
	glp_set_obj_name(lp, "total execution time");

	{
		double times[nw][nt];
		int ne =
			nw * (nt+1)	/* worker execution time */
			+ nt * nw
			+ 1; /* glp dumbness */
		int n = 1;
		int ia[ne], ja[ne];
		double ar[ne];

		_starpu_get_tasks_times(nw, nt, times);

		/* Variables: number of tasks i assigned to worker j, and tmax */
		glp_add_cols(lp, nw*nt+1);
#define colnum(w, t) ((t)*nw+(w)+1)
		glp_set_obj_coef(lp, nw*nt+1, 1.);

		for (w = 0; w < nw; w++)
			for (t = 0, tp = task_pools; tp; t++, tp = tp->next) {
				char name[32];
				snprintf(name, sizeof(name), "w%ut%un", w, t);
				glp_set_col_name(lp, colnum(w, t), name);
				glp_set_col_kind(lp, colnum(w, t), GLP_IV);
				glp_set_col_bnds(lp, colnum(w, t), GLP_LO, 0., 0.);
			}
		glp_set_col_bnds(lp, nw*nt+1, GLP_LO, 0., 0.);

		/* Total worker execution time */
		glp_add_rows(lp, nw);
		for (w = 0; w < nw; w++) {
			char name[32], title[64];
			starpu_worker_get_name(w, name, sizeof(name));
			snprintf(title, sizeof(title), "worker %s", name);
			glp_set_row_name(lp, w+1, title);
			for (t = 0, tp = task_pools; tp; t++, tp = tp->next) {
				ia[n] = w+1;
				ja[n] = colnum(w, t);
				if (times[w][t] == -1.)
					ar[n] = INFINITY;
				else
					ar[n] = times[w][t];
				n++;
			}
			/* tmax */
			ia[n] = w+1;
			ja[n] = nw*nt+1;
			ar[n] = -1;
			n++;
			glp_set_row_bnds(lp, w+1, GLP_UP, 0, 0);
		}

		/* Total task completion */
		glp_add_rows(lp, nt);
		for (t = 0, tp = task_pools; tp; t++, tp = tp->next) {
			char name[32], title[64];
			starpu_worker_get_name(w, name, sizeof(name));
			snprintf(title, sizeof(title), "task %s key %x", tp->cl->model->symbol, (unsigned) tp->footprint);
			glp_set_row_name(lp, nw+t+1, title);
			for (w = 0; w < nw; w++) {
				ia[n] = nw+t+1;
				ja[n] = colnum(w, t);
				ar[n] = 1;
				n++;
			}
			glp_set_row_bnds(lp, nw+t+1, GLP_FX, tp->n, tp->n);
		}

		STARPU_ASSERT(n == ne);

		glp_load_matrix(lp, ne-1, ia, ja, ar);
	}

	glp_smcp parm;
	glp_init_smcp(&parm);
	parm.msg_lev = GLP_MSG_OFF;
	ret = glp_simplex(lp, &parm);
	glp_iocp iocp;
	glp_init_iocp(&iocp);
	iocp.msg_lev = GLP_MSG_OFF;
	glp_intopt(lp, &iocp);
	if (ret) {
		glp_delete_prob(lp);
		lp = NULL;
	}

	return lp;
}
#endif /* HAVE_GLPK_H */

void starpu_bound_print(FILE *output) {
#ifdef HAVE_GLPK_H
	if (recorddeps) {
		fprintf(output, "Not supported\n");
		return;
	}

	PTHREAD_MUTEX_LOCK(&mutex);
	glp_prob *lp = _starpu_bound_glp_resolve();
	if (lp) {
		struct bound_task_pool * tp;
		int t, w;
		int nw; /* Number of different workers */
		double tmax;

		nw = starpu_worker_get_count();

		tmax = glp_get_obj_val(lp);

		fprintf(output, "Theoretical minimum execution time: %f ms\n", tmax);

		for (t = 0, tp = task_pools; tp; t++, tp = tp->next) {
			fprintf(output, "%s key %x\n", tp->cl->model->symbol, (unsigned) tp->footprint);
			for (w = 0; w < nw; w++)
				fprintf(output, "\tw%ut%un %f", w, t, glp_mip_col_val(lp, colnum(w, t)));
			fprintf(output, "\n");
		}

		glp_delete_prob(lp);
	} else {
		fprintf(stderr, "Simplex failed\n");
	}
	PTHREAD_MUTEX_UNLOCK(&mutex);
#else /* HAVE_GLPK_H */
	fprintf(output, "Please rebuild StarPU with glpk installed.\n");
#endif /* HAVE_GLPK_H */
}

void starpu_bound_compute(double *res) {
#ifdef HAVE_GLPK_H
	double ret;

	if (recorddeps) {
		*res = 0.;
		return;
	}

	PTHREAD_MUTEX_LOCK(&mutex);
	glp_prob *lp = _starpu_bound_glp_resolve();
	if (lp) {
		ret = glp_get_obj_val(lp);
		glp_delete_prob(lp);
	} else
		ret = 0.;
	PTHREAD_MUTEX_UNLOCK(&mutex);
	*res = ret;
#else /* HAVE_GLPK_H */
	*res = 0.;
#endif /* HAVE_GLPK_H */
}