add isl_map_power and isl_map_transitive_closure

1 files changed, 304 insertions, 0 deletions

diff --git a/isl_transitive_closure.c b/isl_transitive_closure.c
new file mode 100644
index 00000000..6095d6a5
--- /dev/null
+++ b/isl_transitive_closure.c
@@ -0,0 +1,304 @@
+/*
+ * Copyright 2010      INRIA Saclay
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
+ * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
+ * 91893 Orsay, France 
+ */
+
+#include "isl_map.h"
+#include "isl_map_private.h"
+ 
+/*
+ * The transitive closure implementation is based on the paper
+ * "Computing the Transitive Closure of a Union of Affine Integer
+ * Tuple Relations" by Anna Beletska, Denis Barthou, Wlodzimierz Bielecki and
+ * Albert Cohen.
+ */
+
+/* Given a union of translations (uniform dependences), return a matrix
+ * with as many rows as there are disjuncts in the union and as many
+ * columns as there are input dimensions (which should be equal to
+ * the number of output dimensions).
+ * Each row contains the translation performed by the corresponding disjunct.
+ * If "map" turns out not to be a union of translations, then the contents
+ * of the returned matrix are undefined and *ok is set to 0.
+ */
+static __isl_give isl_mat *extract_steps(__isl_keep isl_map *map, int *ok)
+{
+	int i, j;
+	struct isl_mat *steps;
+	unsigned dim = isl_map_dim(map, isl_dim_in);
+
+	*ok = 1;
+
+	steps = isl_mat_alloc(map->ctx, map->n, dim);
+	if (!steps)
+		return NULL;
+
+	for (i = 0; i < map->n; ++i) {
+		struct isl_basic_set *delta;
+
+		delta = isl_basic_map_deltas(isl_basic_map_copy(map->p[i]));
+
+		for (j = 0; j < dim; ++j) {
+			int fixed;
+
+			fixed = isl_basic_set_fast_dim_is_fixed(delta, j,
+							    &steps->row[i][j]);
+			if (fixed < 0) {
+				isl_basic_set_free(delta);
+				goto error;
+			}
+			if (!fixed)
+				break;
+		}
+
+		isl_basic_set_free(delta);
+
+		if (j < dim)
+			break;
+	}
+
+	if (i < map->n)
+		*ok = 0;
+
+	return steps;
+error:
+	isl_mat_free(steps);
+	return NULL;
+}
+
+/* Given a set of n offsets v_i (the rows of "steps"), construct a relation
+ * of the given dimension specification that maps a element x to any
+ * element that can be reached by taking a positive number of steps
+ * along any of the offsets, where the number of steps k is equal to
+ * parameter "param".  That is, construct
+ *
+ * { [x] -> [y] : exists k_i >= 0, y = x + \sum_i k_i v_i, k = \sum_i k_i > 0 }
+ *
+ * If strict is non-negative, then at least one step should be taken
+ * along the given offset v_strict, i.e., k_strict > 0.
+ */
+static __isl_give isl_map *path_along_steps(__isl_take isl_dim *dim,
+	__isl_keep isl_mat *steps, unsigned param, int strict)
+{
+	int i, j, k;
+	struct isl_basic_map *path = NULL;
+	unsigned d;
+	unsigned n;
+	unsigned nparam;
+
+	if (!dim || !steps)
+		goto error;
+
+	d = isl_dim_size(dim, isl_dim_in);
+	n = steps->n_row;
+	nparam = isl_dim_size(dim, isl_dim_param);
+
+	path = isl_basic_map_alloc_dim(isl_dim_copy(dim), n, d + 1, n + 1);
+
+	for (i = 0; i < n; ++i) {
+		k = isl_basic_map_alloc_div(path);
+		if (k < 0)
+			goto error;
+		isl_assert(steps->ctx, i == k, goto error);
+		isl_int_set_si(path->div[k][0], 0);
+	}
+
+	for (i = 0; i < d; ++i) {
+		k = isl_basic_map_alloc_equality(path);
+		if (k < 0)
+			goto error;
+		isl_seq_clr(path->eq[k], 1 + isl_basic_map_total_dim(path));
+		isl_int_set_si(path->eq[k][1 + nparam + i], 1);
+		isl_int_set_si(path->eq[k][1 + nparam + d + i], -1);
+		for (j = 0; j < n; ++j)
+			isl_int_set(path->eq[k][1 + nparam + 2 * d + j],
+				    steps->row[j][i]);
+	}
+
+	k = isl_basic_map_alloc_equality(path);
+	if (k < 0)
+		goto error;
+	isl_seq_clr(path->eq[k], 1 + isl_basic_map_total_dim(path));
+	isl_int_set_si(path->eq[k][1 + param], -1);
+	for (j = 0; j < n; ++j)
+		isl_int_set_si(path->eq[k][1 + nparam + 2 * d + j], 1);
+
+	for (i = 0; i < n; ++i) {
+		k = isl_basic_map_alloc_inequality(path);
+		if (k < 0)
+			goto error;
+		isl_seq_clr(path->ineq[k], 1 + isl_basic_map_total_dim(path));
+		isl_int_set_si(path->ineq[k][1 + nparam + 2 * d + i], 1);
+		if (i == strict)
+			isl_int_set_si(path->ineq[k][0], -1);
+	}
+
+	k = isl_basic_map_alloc_inequality(path);
+	if (k < 0)
+		goto error;
+	isl_seq_clr(path->ineq[k], 1 + isl_basic_map_total_dim(path));
+	isl_int_set_si(path->ineq[k][1 + param], 1);
+	isl_int_set_si(path->ineq[k][0], -1);
+
+	isl_dim_free(dim);
+
+	path = isl_basic_map_simplify(path);
+	path = isl_basic_map_finalize(path);
+	return isl_map_from_basic_map(path);
+error:
+	isl_dim_free(dim);
+	isl_basic_map_free(path);
+	return NULL;
+}
+
+/* Check whether the overapproximation of the power of "map" is exactly
+ * the power of "map".  In particular, for each path of a given length
+ * that starts of in domain or range and ends up in the range,
+ * check whether there is at least one path of the same length
+ * with a valid first segment, i.e., one in "map".
+ *
+ * "domain" and "range" are the domain and range of "map"
+ * "steps" represents the translations of "map"
+ * "path" is a path along "steps"
+ *
+ * "domain", "range", "steps" and "path" have been precomputed by the calling
+ * function.
+ */
+static int check_exactness(__isl_take isl_map *map, __isl_take isl_set *domain,
+	__isl_take isl_set *range, __isl_take isl_map *path,
+	__isl_keep isl_mat *steps, unsigned param)
+{
+	isl_map *test;
+	int ok;
+	int i;
+
+	if (!map)
+		goto error;
+
+	test = isl_map_empty(isl_map_get_dim(map));
+	for (i = 0; i < map->n; ++i) {
+		struct isl_map *path_i;
+		struct isl_set *dom_i;
+		path_i = path_along_steps(isl_map_get_dim(map), steps, param, i);
+		dom_i = isl_set_from_basic_set(
+			isl_basic_map_domain(isl_basic_map_copy(map->p[i])));
+		path_i = isl_map_intersect_domain(path_i, dom_i);
+		test = isl_map_union(test, path_i);
+	}
+	isl_map_free(map);
+	test = isl_map_intersect_range(test, isl_set_copy(range));
+
+	domain = isl_set_union(domain, isl_set_copy(range));
+	path = isl_map_intersect_domain(path, domain);
+	path = isl_map_intersect_range(path, range);
+
+	ok = isl_map_is_subset(path, test);
+
+	isl_map_free(path);
+	isl_map_free(test);
+
+	return ok;
+error:
+	isl_map_free(map);
+	isl_set_free(domain);
+	isl_set_free(range);
+	isl_map_free(path);
+	return -1;
+}
+
+/* Compute the positive powers of "map", or an overapproximation.
+ * The power is given by parameter "param".  If the result is exact,
+ * then *exact is set to 1.
+ */
+__isl_give isl_map *isl_map_power(__isl_take isl_map *map, unsigned param,
+	int *exact)
+{
+	struct isl_mat *steps = NULL;
+	struct isl_set *domain = NULL;
+	struct isl_set *range = NULL;
+	struct isl_map *app = NULL;
+	struct isl_map *path = NULL;
+	int ok;
+
+	if (exact)
+		*exact = 1;
+
+	map = isl_map_remove_empty_parts(map);
+	if (!map)
+		return NULL;
+
+	if (isl_map_fast_is_empty(map))
+		return map;
+
+	isl_assert(map->ctx, param < isl_map_dim(map, isl_dim_param), goto error);
+	isl_assert(map->ctx,
+		isl_map_dim(map, isl_dim_in) == isl_map_dim(map, isl_dim_out),
+		goto error);
+
+	domain = isl_map_domain(isl_map_copy(map));
+	range = isl_map_range(isl_map_copy(map));
+	app = isl_map_from_domain_and_range(isl_set_copy(domain),
+					    isl_set_copy(range));
+
+	steps = extract_steps(map, &ok);
+	if (!ok)
+		goto not_exact;
+
+	path = path_along_steps(isl_map_get_dim(map), steps, param, -1);
+	app = isl_map_intersect(app, isl_map_copy(path));
+
+	if (exact &&
+	    (*exact = check_exactness(isl_map_copy(map), isl_set_copy(domain),
+				  isl_set_copy(range), isl_map_copy(path),
+				  steps, param)) < 0)
+		goto error;
+
+	if (0) {
+not_exact:
+		if (exact)
+			*exact = 0;
+	}
+	isl_set_free(domain);
+	isl_set_free(range);
+	isl_mat_free(steps);
+	isl_map_free(path);
+	isl_map_free(map);
+	return app;
+error:
+	isl_set_free(domain);
+	isl_set_free(range);
+	isl_mat_free(steps);
+	isl_map_free(path);
+	isl_map_free(map);
+	isl_map_free(app);
+	return NULL;
+}
+
+/* Compute the transitive closure  of "map", or an overapproximation.
+ * If the result is exact, then *exact is set to 1.
+ * Simply compute the powers of map and then project out the parameter
+ * describing the power.
+ */
+__isl_give isl_map *isl_map_transitive_closure(__isl_take isl_map *map,
+	int *exact)
+{
+	unsigned param;
+
+	if (!map)
+		goto error;
+
+	param = isl_map_dim(map, isl_dim_param);
+	map = isl_map_add(map, isl_dim_param, 1);
+	map = isl_map_power(map, param, exact);
+	map = isl_map_project_out(map, isl_dim_param, param, 1);
+
+	return map;
+error:
+	isl_map_free(map);
+	return NULL;
+}