X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_affine_hull.c;h=0d66081eaec3ab462eab1b79e7a4157acb78aaf8;hb=2a76a4d88b65873ed5437c8f16f0b1ebd39e4c35;hp=250195bed62f5fc0eb2dc16d9cd7e1de9f37191d;hpb=e44993c4bf00a4b1e970300fc8a9ce8905eb62c7;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_affine_hull.c b/isl_affine_hull.c
index 250195b..0d66081 100644
--- a/isl_affine_hull.c
+++ b/isl_affine_hull.c
@@ -1,10 +1,15 @@
 /*
  * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010      INRIA Saclay
+ * Copyright 2012      Ecole Normale Superieure
  *
- * Use of this software is governed by the GNU LGPLv2.1 license
+ * Use of this software is governed by the MIT license
  *
  * Written by Sven Verdoolaege, K.U.Leuven, Departement
  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
+ * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
+ * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
  */
 
 #include <isl_ctx_private.h>
@@ -487,35 +492,172 @@ error:
 	return NULL;
 }
 
+/* Drop all constraints in bmap that involve any of the dimensions
+ * first to first+n-1.
+ */
+static __isl_give isl_basic_map *isl_basic_map_drop_constraints_involving(
+	__isl_take isl_basic_map *bmap, unsigned first, unsigned n)
+{
+	int i;
+
+	if (n == 0)
+		return bmap;
+
+	bmap = isl_basic_map_cow(bmap);
+
+	if (!bmap)
+		return NULL;
+
+	for (i = bmap->n_eq - 1; i >= 0; --i) {
+		if (isl_seq_first_non_zero(bmap->eq[i] + 1 + first, n) == -1)
+			continue;
+		isl_basic_map_drop_equality(bmap, i);
+	}
+
+	for (i = bmap->n_ineq - 1; i >= 0; --i) {
+		if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + first, n) == -1)
+			continue;
+		isl_basic_map_drop_inequality(bmap, i);
+	}
+
+	return bmap;
+}
+
 /* Drop all constraints in bset that involve any of the dimensions
  * first to first+n-1.
  */
 __isl_give isl_basic_set *isl_basic_set_drop_constraints_involving(
 	__isl_take isl_basic_set *bset, unsigned first, unsigned n)
 {
+	return isl_basic_map_drop_constraints_involving(bset, first, n);
+}
+
+/* Drop all constraints in bmap that do not involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_basic_map *isl_basic_map_drop_constraints_not_involving_dims(
+	__isl_take isl_basic_map *bmap,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
 	int i;
+	unsigned dim;
 
 	if (n == 0)
-		return bset;
+		return isl_basic_map_set_to_empty(bmap);
+	bmap = isl_basic_map_cow(bmap);
+	if (!bmap)
+		return NULL;
 
-	bset = isl_basic_set_cow(bset);
+	dim = isl_basic_map_dim(bmap, type);
+	if (first + n > dim || first + n < first)
+		isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
+			"index out of bounds", return isl_basic_map_free(bmap));
 
-	if (!bset)
-		return NULL;
+	first += isl_basic_map_offset(bmap, type) - 1;
 
-	for (i = bset->n_eq - 1; i >= 0; --i) {
-		if (isl_seq_first_non_zero(bset->eq[i] + 1 + first, n) == -1)
+	for (i = bmap->n_eq - 1; i >= 0; --i) {
+		if (isl_seq_first_non_zero(bmap->eq[i] + 1 + first, n) != -1)
 			continue;
-		isl_basic_set_drop_equality(bset, i);
+		isl_basic_map_drop_equality(bmap, i);
 	}
 
-	for (i = bset->n_ineq - 1; i >= 0; --i) {
-		if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1)
+	for (i = bmap->n_ineq - 1; i >= 0; --i) {
+		if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + first, n) != -1)
 			continue;
-		isl_basic_set_drop_inequality(bset, i);
+		isl_basic_map_drop_inequality(bmap, i);
 	}
 
-	return bset;
+	return bmap;
+}
+
+/* Drop all constraints in bset that do not involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_basic_set *isl_basic_set_drop_constraints_not_involving_dims(
+	__isl_take isl_basic_set *bset,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	return isl_basic_map_drop_constraints_not_involving_dims(bset,
+							    type, first, n);
+}
+
+/* Drop all constraints in bmap that involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_basic_map *isl_basic_map_drop_constraints_involving_dims(
+	__isl_take isl_basic_map *bmap,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	unsigned dim;
+
+	if (!bmap)
+		return NULL;
+	if (n == 0)
+		return bmap;
+
+	dim = isl_basic_map_dim(bmap, type);
+	if (first + n > dim || first + n < first)
+		isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
+			"index out of bounds", return isl_basic_map_free(bmap));
+
+	bmap = isl_basic_map_remove_divs_involving_dims(bmap, type, first, n);
+	first += isl_basic_map_offset(bmap, type) - 1;
+	return isl_basic_map_drop_constraints_involving(bmap, first, n);
+}
+
+/* Drop all constraints in bset that involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_basic_set *isl_basic_set_drop_constraints_involving_dims(
+	__isl_take isl_basic_set *bset,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	return isl_basic_map_drop_constraints_involving_dims(bset,
+							    type, first, n);
+}
+
+/* Drop all constraints in map that involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_map *isl_map_drop_constraints_involving_dims(
+	__isl_take isl_map *map,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	int i;
+	unsigned dim;
+
+	if (!map)
+		return NULL;
+	if (n == 0)
+		return map;
+
+	dim = isl_map_dim(map, type);
+	if (first + n > dim || first + n < first)
+		isl_die(isl_map_get_ctx(map), isl_error_invalid,
+			"index out of bounds", return isl_map_free(map));
+
+	map = isl_map_cow(map);
+	if (!map)
+		return NULL;
+
+	for (i = 0; i < map->n; ++i) {
+		map->p[i] = isl_basic_map_drop_constraints_involving_dims(
+						    map->p[i], type, first, n);
+		if (!map->p[i])
+			return isl_map_free(map);
+	}
+
+	return map;
+}
+
+/* Drop all constraints in set that involve any of the dimensions
+ * first to first + n - 1 of the given type.
+ */
+__isl_give isl_set *isl_set_drop_constraints_involving_dims(
+	__isl_take isl_set *set,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	return isl_map_drop_constraints_involving_dims(set, type, first, n);
 }
 
 /* Construct an initial underapproximatino of the hull of "bset"
@@ -668,7 +810,7 @@ struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
 {
 	int j;
 	struct isl_vec *sample;
-	struct isl_basic_set *hull;
+	struct isl_basic_set *hull = NULL;
 	struct isl_tab_undo *snap;
 
 	if (!tab || !tab_cone)
@@ -733,6 +875,7 @@ struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
 
 	return tab;
 error:
+	isl_basic_set_free(hull);
 	isl_tab_free(tab);
 	return NULL;
 }
@@ -803,9 +946,10 @@ static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
 
 	hull = uset_affine_hull_bounded(bset);
 
-	if (!hull)
+	if (!hull) {
+		isl_mat_free(Q);
 		isl_mat_free(U);
-	else {
+	} else {
 		struct isl_vec *sample = isl_vec_copy(hull->sample);
 		U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim);
 		if (sample && sample->size > 0)
@@ -925,6 +1069,7 @@ static struct isl_basic_set *equalities_in_underlying_set(
 
 	return hull;
 error:
+	isl_mat_free(T1);
 	isl_mat_free(T2);
 	isl_basic_set_free(bset);
 	isl_basic_set_free(hull);
@@ -986,30 +1131,6 @@ __isl_give isl_basic_set *isl_basic_set_detect_equalities(
 		isl_basic_map_detect_equalities((isl_basic_map *)bset);
 }
 
-__isl_give isl_map *isl_map_inline_foreach_basic_map(__isl_take isl_map *map,
-	__isl_give isl_basic_map *(*fn)(__isl_take isl_basic_map *bmap))
-{
-	struct isl_basic_map *bmap;
-	int i;
-
-	if (!map)
-		return NULL;
-
-	for (i = 0; i < map->n; ++i) {
-		bmap = isl_basic_map_copy(map->p[i]);
-		bmap = fn(bmap);
-		if (!bmap)
-			goto error;
-		isl_basic_map_free(map->p[i]);
-		map->p[i] = bmap;
-	}
-
-	return map;
-error:
-	isl_map_free(map);
-	return NULL;
-}
-
 __isl_give isl_map *isl_map_detect_equalities(__isl_take isl_map *map)
 {
 	return isl_map_inline_foreach_basic_map(map,
@@ -1041,14 +1162,205 @@ struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset)
 		isl_basic_map_affine_hull((struct isl_basic_map *)bset);
 }
 
-struct isl_basic_map *isl_map_affine_hull(struct isl_map *map)
+/* Given a rational affine matrix "M", add stride constraints to "bmap"
+ * that ensure that
+ *
+ *		M(x)
+ *
+ * is an integer vector.  The variables x include all the variables
+ * of "bmap" except the unknown divs.
+ *
+ * If d is the common denominator of M, then we need to impose that
+ *
+ *		d M(x) = 0 	mod d
+ *
+ * or
+ *
+ *		exists alpha : d M(x) = d alpha
+ *
+ * This function is similar to add_strides in isl_morph.c
+ */
+static __isl_give isl_basic_map *add_strides(__isl_take isl_basic_map *bmap,
+	__isl_keep isl_mat *M, int n_known)
+{
+	int i, div, k;
+	isl_int gcd;
+
+	if (isl_int_is_one(M->row[0][0]))
+		return bmap;
+
+	bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
+					M->n_row - 1, M->n_row - 1, 0);
+
+	isl_int_init(gcd);
+	for (i = 1; i < M->n_row; ++i) {
+		isl_seq_gcd(M->row[i], M->n_col, &gcd);
+		if (isl_int_is_divisible_by(gcd, M->row[0][0]))
+			continue;
+		div = isl_basic_map_alloc_div(bmap);
+		if (div < 0)
+			goto error;
+		isl_int_set_si(bmap->div[div][0], 0);
+		k = isl_basic_map_alloc_equality(bmap);
+		if (k < 0)
+			goto error;
+		isl_seq_cpy(bmap->eq[k], M->row[i], M->n_col);
+		isl_seq_clr(bmap->eq[k] + M->n_col, bmap->n_div - n_known);
+		isl_int_set(bmap->eq[k][M->n_col - n_known + div],
+			    M->row[0][0]);
+	}
+	isl_int_clear(gcd);
+
+	return bmap;
+error:
+	isl_int_clear(gcd);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* If there are any equalities that involve (multiple) unknown divs,
+ * then extract the stride information encoded by those equalities
+ * and make it explicitly available in "bmap".
+ *
+ * We first sort the divs so that the unknown divs appear last and
+ * then we count how many equalities involve these divs.
+ *
+ * Let these equalities be of the form
+ *
+ *		A(x) + B y = 0
+ *
+ * where y represents the unknown divs and x the remaining variables.
+ * Let [H 0] be the Hermite Normal Form of B, i.e.,
+ *
+ *		B = [H 0] Q
+ *
+ * Then x is a solution of the equalities iff
+ *
+ *		H^-1 A(x) (= - [I 0] Q y)
+ *
+ * is an integer vector.  Let d be the common denominator of H^-1.
+ * We impose
+ *
+ *		d H^-1 A(x) = d alpha
+ *
+ * in add_strides, with alpha fresh existentially quantified variables.
+ */
+static __isl_give isl_basic_map *isl_basic_map_make_strides_explicit(
+	__isl_take isl_basic_map *bmap)
+{
+	int known;
+	int n_known;
+	int n, n_col;
+	int total;
+	isl_ctx *ctx;
+	isl_mat *A, *B, *M;
+
+	known = isl_basic_map_divs_known(bmap);
+	if (known < 0)
+		return isl_basic_map_free(bmap);
+	if (known)
+		return bmap;
+	bmap = isl_basic_map_sort_divs(bmap);
+	bmap = isl_basic_map_gauss(bmap, NULL);
+	if (!bmap)
+		return NULL;
+
+	for (n_known = 0; n_known < bmap->n_div; ++n_known)
+		if (isl_int_is_zero(bmap->div[n_known][0]))
+			break;
+	ctx = isl_basic_map_get_ctx(bmap);
+	total = isl_space_dim(bmap->dim, isl_dim_all);
+	for (n = 0; n < bmap->n_eq; ++n)
+		if (isl_seq_first_non_zero(bmap->eq[n] + 1 + total + n_known,
+					    bmap->n_div - n_known) == -1)
+			break;
+	if (n == 0)
+		return bmap;
+	B = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 0, 1 + total + n_known);
+	n_col = bmap->n_div - n_known;
+	A = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 1 + total + n_known, n_col);
+	A = isl_mat_left_hermite(A, 0, NULL, NULL);
+	A = isl_mat_drop_cols(A, n, n_col - n);
+	A = isl_mat_lin_to_aff(A);
+	A = isl_mat_right_inverse(A);
+	B = isl_mat_insert_zero_rows(B, 0, 1);
+	B = isl_mat_set_element_si(B, 0, 0, 1);
+	M = isl_mat_product(A, B);
+	if (!M)
+		return isl_basic_map_free(bmap);
+	bmap = add_strides(bmap, M, n_known);
+	bmap = isl_basic_map_gauss(bmap, NULL);
+	isl_mat_free(M);
+
+	return bmap;
+}
+
+/* Compute the affine hull of each basic map in "map" separately
+ * and make all stride information explicit so that we can remove
+ * all unknown divs without losing this information.
+ * The result is also guaranteed to be gaussed.
+ *
+ * In simple cases where a div is determined by an equality,
+ * calling isl_basic_map_gauss is enough to make the stride information
+ * explicit, as it will derive an explicit representation for the div
+ * from the equality.  If, however, the stride information
+ * is encoded through multiple unknown divs then we need to make
+ * some extra effort in isl_basic_map_make_strides_explicit.
+ */
+static __isl_give isl_map *isl_map_local_affine_hull(__isl_take isl_map *map)
 {
 	int i;
+
+	map = isl_map_cow(map);
+	if (!map)
+		return NULL;
+
+	for (i = 0; i < map->n; ++i) {
+		map->p[i] = isl_basic_map_affine_hull(map->p[i]);
+		map->p[i] = isl_basic_map_gauss(map->p[i], NULL);
+		map->p[i] = isl_basic_map_make_strides_explicit(map->p[i]);
+		if (!map->p[i])
+			return isl_map_free(map);
+	}
+
+	return map;
+}
+
+static __isl_give isl_set *isl_set_local_affine_hull(__isl_take isl_set *set)
+{
+	return isl_map_local_affine_hull(set);
+}
+
+/* Compute the affine hull of "map".
+ *
+ * We first compute the affine hull of each basic map separately.
+ * Then we align the divs and recompute the affine hulls of the basic
+ * maps since some of them may now have extra divs.
+ * In order to avoid performing parametric integer programming to
+ * compute explicit expressions for the divs, possible leading to
+ * an explosion in the number of basic maps, we first drop all unknown
+ * divs before aligning the divs.  Note that isl_map_local_affine_hull tries
+ * to make sure that all stride information is explicitly available
+ * in terms of known divs.  This involves calling isl_basic_set_gauss,
+ * which is also needed because affine_hull assumes its input has been gaussed,
+ * while isl_map_affine_hull may be called on input that has not been gaussed,
+ * in particular from initial_facet_constraint.
+ * Similarly, align_divs may reorder some divs so that we need to
+ * gauss the result again.
+ * Finally, we combine the individual affine hulls into a single
+ * affine hull.
+ */
+__isl_give isl_basic_map *isl_map_affine_hull(__isl_take isl_map *map)
+{
 	struct isl_basic_map *model = NULL;
 	struct isl_basic_map *hull = NULL;
 	struct isl_set *set;
+	isl_basic_set *bset;
 
 	map = isl_map_detect_equalities(map);
+	map = isl_map_local_affine_hull(map);
+	map = isl_map_remove_empty_parts(map);
+	map = isl_map_remove_unknown_divs(map);
 	map = isl_map_align_divs(map);
 
 	if (!map)
@@ -1063,30 +1375,15 @@ struct isl_basic_map *isl_map_affine_hull(struct isl_map *map)
 	model = isl_basic_map_copy(map->p[0]);
 	set = isl_map_underlying_set(map);
 	set = isl_set_cow(set);
+	set = isl_set_local_affine_hull(set);
 	if (!set)
 		goto error;
 
-	for (i = 0; i < set->n; ++i) {
-		set->p[i] = isl_basic_set_cow(set->p[i]);
-		set->p[i] = isl_basic_set_affine_hull(set->p[i]);
-		set->p[i] = isl_basic_set_gauss(set->p[i], NULL);
-		if (!set->p[i])
-			goto error;
-	}
-	set = isl_set_remove_empty_parts(set);
-	if (set->n == 0) {
-		hull = isl_basic_map_empty_like(model);
-		isl_basic_map_free(model);
-	} else {
-		struct isl_basic_set *bset;
-		while (set->n > 1) {
-			set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
-			if (!set->p[0])
-				goto error;
-		}
-		bset = isl_basic_set_copy(set->p[0]);
-		hull = isl_basic_map_overlying_set(bset, model);
-	}
+	while (set->n > 1)
+		set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
+
+	bset = isl_basic_set_copy(set->p[0]);
+	hull = isl_basic_map_overlying_set(bset, model);
 	isl_set_free(set);
 	hull = isl_basic_map_simplify(hull);
 	return isl_basic_map_finalize(hull);