+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010 INRIA Saclay
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 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
+ */
+
#include "isl_map_private.h"
+#include "isl_seq.h"
#include "isl_tab.h"
#define STATUS_ERROR -1
#define STATUS_ADJ_EQ 5
#define STATUS_ADJ_INEQ 6
-static int status_in(struct isl_ctx *ctx, isl_int *ineq, struct isl_tab *tab)
+static int status_in(isl_int *ineq, struct isl_tab *tab)
{
- enum isl_ineq_type type = isl_tab_ineq_type(ctx, tab, ineq);
+ enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);
switch (type) {
case isl_ineq_error: return STATUS_ERROR;
case isl_ineq_redundant: return STATUS_VALID;
}
}
-/* Compute the position of the equalities of basic set "i"
- * with respect to basic set "j".
+/* Compute the position of the equalities of basic map "i"
+ * with respect to basic map "j".
* The resulting array has twice as many entries as the number
* of equalities corresponding to the two inequalties to which
* each equality corresponds.
*/
-static int *eq_status_in(struct isl_set *set, int i, int j,
+static int *eq_status_in(struct isl_map *map, int i, int j,
struct isl_tab **tabs)
{
int k, l;
- int *eq = isl_calloc_array(set->ctx, int, 2 * set->p[i]->n_eq);
+ int *eq = isl_calloc_array(map->ctx, int, 2 * map->p[i]->n_eq);
unsigned dim;
- dim = isl_basic_set_total_dim(set->p[i]);
- for (k = 0; k < set->p[i]->n_eq; ++k) {
+ dim = isl_basic_map_total_dim(map->p[i]);
+ for (k = 0; k < map->p[i]->n_eq; ++k) {
for (l = 0; l < 2; ++l) {
- isl_seq_neg(set->p[i]->eq[k], set->p[i]->eq[k], 1+dim);
- eq[2 * k + l] = status_in(set->ctx, set->p[i]->eq[k],
- tabs[j]);
+ isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
+ eq[2 * k + l] = status_in(map->p[i]->eq[k], tabs[j]);
if (eq[2 * k + l] == STATUS_ERROR)
goto error;
}
return NULL;
}
-/* Compute the position of the inequalities of basic set "i"
- * with respect to basic set "j".
+/* Compute the position of the inequalities of basic map "i"
+ * with respect to basic map "j".
*/
-static int *ineq_status_in(struct isl_set *set, int i, int j,
+static int *ineq_status_in(struct isl_map *map, int i, int j,
struct isl_tab **tabs)
{
int k;
- unsigned n_eq = set->p[i]->n_eq;
- int *ineq = isl_calloc_array(set->ctx, int, set->p[i]->n_ineq);
+ unsigned n_eq = map->p[i]->n_eq;
+ int *ineq = isl_calloc_array(map->ctx, int, map->p[i]->n_ineq);
- for (k = 0; k < set->p[i]->n_ineq; ++k) {
- if (isl_tab_is_redundant(set->ctx, tabs[i], n_eq + k)) {
+ for (k = 0; k < map->p[i]->n_ineq; ++k) {
+ if (isl_tab_is_redundant(tabs[i], n_eq + k)) {
ineq[k] = STATUS_REDUNDANT;
continue;
}
- ineq[k] = status_in(set->ctx, set->p[i]->ineq[k], tabs[j]);
+ ineq[k] = status_in(map->p[i]->ineq[k], tabs[j]);
if (ineq[k] == STATUS_ERROR)
goto error;
if (ineq[k] == STATUS_SEPARATE)
return 1;
}
-static void drop(struct isl_set *set, int i, struct isl_tab **tabs)
+static void drop(struct isl_map *map, int i, struct isl_tab **tabs)
{
- isl_basic_set_free(set->p[i]);
- isl_tab_free(set->ctx, tabs[i]);
+ isl_basic_map_free(map->p[i]);
+ isl_tab_free(tabs[i]);
- if (i != set->n - 1) {
- set->p[i] = set->p[set->n - 1];
- tabs[i] = tabs[set->n - 1];
+ if (i != map->n - 1) {
+ map->p[i] = map->p[map->n - 1];
+ tabs[i] = tabs[map->n - 1];
}
- tabs[set->n - 1] = NULL;
- set->n--;
+ tabs[map->n - 1] = NULL;
+ map->n--;
}
-/* Replace the pair of basic sets i and j but the basic set bounded
- * by the valid constraints in both basic sets.
+/* Replace the pair of basic maps i and j by the basic map bounded
+ * by the valid constraints in both basic maps and the constraint
+ * in extra (if not NULL).
*/
-static int fuse(struct isl_set *set, int i, int j, struct isl_tab **tabs,
- int *ineq_i, int *ineq_j)
+static int fuse(struct isl_map *map, int i, int j,
+ struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j,
+ __isl_keep isl_mat *extra)
{
int k, l;
- struct isl_basic_set *fused = NULL;
+ struct isl_basic_map *fused = NULL;
struct isl_tab *fused_tab = NULL;
- unsigned total = isl_basic_set_total_dim(set->p[i]);
+ unsigned total = isl_basic_map_total_dim(map->p[i]);
+ unsigned extra_rows = extra ? extra->n_row : 0;
- fused = isl_basic_set_alloc_dim(isl_dim_copy(set->p[i]->dim),
- set->p[i]->n_div,
- set->p[i]->n_eq + set->p[j]->n_eq,
- set->p[i]->n_ineq + set->p[j]->n_ineq);
+ fused = isl_basic_map_alloc_dim(isl_dim_copy(map->p[i]->dim),
+ map->p[i]->n_div,
+ map->p[i]->n_eq + map->p[j]->n_eq,
+ map->p[i]->n_ineq + map->p[j]->n_ineq + extra_rows);
if (!fused)
goto error;
- for (k = 0; k < set->p[i]->n_eq; ++k) {
- int l = isl_basic_set_alloc_equality(fused);
- isl_seq_cpy(fused->eq[l], set->p[i]->eq[k], 1 + total);
+ for (k = 0; k < map->p[i]->n_eq; ++k) {
+ if (eq_i && (eq_i[2 * k] != STATUS_VALID ||
+ eq_i[2 * k + 1] != STATUS_VALID))
+ continue;
+ l = isl_basic_map_alloc_equality(fused);
+ if (l < 0)
+ goto error;
+ isl_seq_cpy(fused->eq[l], map->p[i]->eq[k], 1 + total);
}
- for (k = 0; k < set->p[j]->n_eq; ++k) {
- int l = isl_basic_set_alloc_equality(fused);
- isl_seq_cpy(fused->eq[l], set->p[j]->eq[k], 1 + total);
+ for (k = 0; k < map->p[j]->n_eq; ++k) {
+ if (eq_j && (eq_j[2 * k] != STATUS_VALID ||
+ eq_j[2 * k + 1] != STATUS_VALID))
+ continue;
+ l = isl_basic_map_alloc_equality(fused);
+ if (l < 0)
+ goto error;
+ isl_seq_cpy(fused->eq[l], map->p[j]->eq[k], 1 + total);
}
- for (k = 0; k < set->p[i]->n_ineq; ++k) {
+ for (k = 0; k < map->p[i]->n_ineq; ++k) {
if (ineq_i[k] != STATUS_VALID)
continue;
- l = isl_basic_set_alloc_inequality(fused);
- isl_seq_cpy(fused->ineq[l], set->p[i]->ineq[k], 1 + total);
+ l = isl_basic_map_alloc_inequality(fused);
+ if (l < 0)
+ goto error;
+ isl_seq_cpy(fused->ineq[l], map->p[i]->ineq[k], 1 + total);
}
- for (k = 0; k < set->p[j]->n_ineq; ++k) {
+ for (k = 0; k < map->p[j]->n_ineq; ++k) {
if (ineq_j[k] != STATUS_VALID)
continue;
- l = isl_basic_set_alloc_inequality(fused);
- isl_seq_cpy(fused->ineq[l], set->p[j]->ineq[k], 1 + total);
+ l = isl_basic_map_alloc_inequality(fused);
+ if (l < 0)
+ goto error;
+ isl_seq_cpy(fused->ineq[l], map->p[j]->ineq[k], 1 + total);
}
- for (k = 0; k < set->p[i]->n_div; ++k) {
- int l = isl_basic_set_alloc_div(fused);
- isl_seq_cpy(fused->div[l], set->p[i]->div[k], 1 + 1 + total);
+ for (k = 0; k < map->p[i]->n_div; ++k) {
+ int l = isl_basic_map_alloc_div(fused);
+ if (l < 0)
+ goto error;
+ isl_seq_cpy(fused->div[l], map->p[i]->div[k], 1 + 1 + total);
}
- fused = isl_basic_set_gauss(fused, NULL);
- ISL_F_SET(fused, ISL_BASIC_SET_FINAL);
+ for (k = 0; k < extra_rows; ++k) {
+ l = isl_basic_map_alloc_inequality(fused);
+ if (l < 0)
+ goto error;
+ isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total);
+ }
- fused_tab = isl_tab_from_basic_set(fused);
- fused_tab = isl_tab_detect_redundant(set->ctx, fused_tab);
- if (!fused_tab)
+ fused = isl_basic_map_gauss(fused, NULL);
+ ISL_F_SET(fused, ISL_BASIC_MAP_FINAL);
+ if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) &&
+ ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
+ ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
+
+ fused_tab = isl_tab_from_basic_map(fused);
+ if (isl_tab_detect_redundant(fused_tab) < 0)
goto error;
- isl_basic_set_free(set->p[i]);
- set->p[i] = fused;
- isl_tab_free(set->ctx, tabs[i]);
+ isl_basic_map_free(map->p[i]);
+ map->p[i] = fused;
+ isl_tab_free(tabs[i]);
tabs[i] = fused_tab;
- drop(set, j, tabs);
+ drop(map, j, tabs);
return 1;
error:
- isl_basic_set_free(fused);
+ isl_tab_free(fused_tab);
+ isl_basic_map_free(fused);
return -1;
}
-/* Given a pair of basic sets i and j such that all constraints are either
+/* Given a pair of basic maps i and j such that all constraints are either
* "valid" or "cut", check if the facets corresponding to the "cut"
- * constraints of i lie entirely within basic set j.
- * If so, replace the pair by the basic set consisting of the valid
- * constraints in both basic sets.
+ * constraints of i lie entirely within basic map j.
+ * If so, replace the pair by the basic map consisting of the valid
+ * constraints in both basic maps.
*
* To see that we are not introducing any extra points, call the
- * two basic sets A and B and the resulting set U and let x
+ * two basic maps A and B and the resulting map U and let x
* be an element of U \setminus ( A \cup B ).
* Then there is a pair of cut constraints c_1 and c_2 in A and B such that x
* violates them. Let X be the intersection of U with the opposites
* c_2 must be opposites of each other, but then x could not violate
* both of them.
*/
-static int check_facets(struct isl_set *set, int i, int j,
+static int check_facets(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *ineq_i, int *ineq_j)
{
int k, l;
struct isl_tab_undo *snap;
- unsigned n_eq = set->p[i]->n_eq;
+ unsigned n_eq = map->p[i]->n_eq;
- snap = isl_tab_snap(set->ctx, tabs[i]);
+ snap = isl_tab_snap(tabs[i]);
- for (k = 0; k < set->p[i]->n_ineq; ++k) {
+ for (k = 0; k < map->p[i]->n_ineq; ++k) {
if (ineq_i[k] != STATUS_CUT)
continue;
- tabs[i] = isl_tab_select_facet(set->ctx, tabs[i], n_eq + k);
- for (l = 0; l < set->p[j]->n_ineq; ++l) {
+ tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
+ for (l = 0; l < map->p[j]->n_ineq; ++l) {
int stat;
if (ineq_j[l] != STATUS_CUT)
continue;
- stat = status_in(set->ctx, set->p[j]->ineq[l], tabs[i]);
+ stat = status_in(map->p[j]->ineq[l], tabs[i]);
if (stat != STATUS_VALID)
break;
}
- isl_tab_rollback(set->ctx, tabs[i], snap);
- if (l < set->p[j]->n_ineq)
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ return -1;
+ if (l < map->p[j]->n_ineq)
break;
}
- if (k < set->p[i]->n_ineq)
+ if (k < map->p[i]->n_ineq)
/* BAD CUT PAIR */
return 0;
- return fuse(set, i, j, tabs, ineq_i, ineq_j);
+ return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
}
-/* Both basic sets have at least one inequality with and adjacent
- * (but opposite) inequality in the other basic set.
+/* Both basic maps have at least one inequality with and adjacent
+ * (but opposite) inequality in the other basic map.
* Check that there are no cut constraints and that there is only
* a single pair of adjacent inequalities.
- * If so, we can replace the pair by a single basic set described
+ * If so, we can replace the pair by a single basic map described
* by all but the pair of adjacent inequalities.
* Any additional points introduced lie strictly between the two
* adjacent hyperplanes and can therefore be integral.
* \___||_/ \_____/
*
* The test for a single pair of adjancent inequalities is important
- * for avoiding the combination of two basic sets like the following
+ * for avoiding the combination of two basic maps like the following
*
* /|
* / |
* | |
* |___|
*/
-static int check_adj_ineq(struct isl_set *set, int i, int j,
+static int check_adj_ineq(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *ineq_i, int *ineq_j)
{
int changed = 0;
- if (any(ineq_i, set->p[i]->n_ineq, STATUS_CUT) ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_CUT))
+ if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT) ||
+ any(ineq_j, map->p[j]->n_ineq, STATUS_CUT))
/* ADJ INEQ CUT */
;
- else if (count(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_INEQ) == 1 &&
- count(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_INEQ) == 1)
- changed = fuse(set, i, j, tabs, ineq_i, ineq_j);
+ else if (count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) == 1 &&
+ count(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ) == 1)
+ changed = fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
/* else ADJ INEQ TOO MANY */
return changed;
}
-/* Check if basic set "i" contains the basic set represented
+/* Check if basic map "i" contains the basic map represented
* by the tableau "tab".
*/
-static int contains(struct isl_set *set, int i, int *ineq_i,
+static int contains(struct isl_map *map, int i, int *ineq_i,
struct isl_tab *tab)
{
int k, l;
unsigned dim;
- dim = isl_basic_set_total_dim(set->p[i]);
- for (k = 0; k < set->p[i]->n_eq; ++k) {
+ dim = isl_basic_map_total_dim(map->p[i]);
+ for (k = 0; k < map->p[i]->n_eq; ++k) {
for (l = 0; l < 2; ++l) {
int stat;
- isl_seq_neg(set->p[i]->eq[k], set->p[i]->eq[k], 1+dim);
- stat = status_in(set->ctx, set->p[i]->eq[k], tab);
+ isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
+ stat = status_in(map->p[i]->eq[k], tab);
if (stat != STATUS_VALID)
return 0;
}
}
- for (k = 0; k < set->p[i]->n_ineq; ++k) {
+ for (k = 0; k < map->p[i]->n_ineq; ++k) {
int stat;
- if (ineq_i[l] == STATUS_REDUNDANT)
+ if (ineq_i[k] == STATUS_REDUNDANT)
continue;
- stat = status_in(set->ctx, set->p[i]->ineq[k], tab);
+ stat = status_in(map->p[i]->ineq[k], tab);
if (stat != STATUS_VALID)
return 0;
}
return 1;
}
-/* At least one of the basic sets has an equality that is adjacent
- * to inequality. Make sure that only one of the basic sets has
- * such an equality and that the other basic set has exactly one
- * inequality adjacent to an equality.
- * We call the basic set that has the inequality "i" and the basic
- * set that has the equality "j".
- * If "i" has any "cut" inequality, then relaxing the inequality
- * by one would not result in a basic set that contains the other
- * basic set.
- * Otherwise, we relax the constraint, compute the corresponding
- * facet and check whether it is included in the other basic set.
- * If so, we know that relaxing the constraint extend the basic
- * set with exactly the other basic set (we already know that this
- * other basic set is included in the extension, because there
+/* Basic map "i" has an inequality "k" that is adjacent to some equality
+ * of basic map "j". All the other inequalities are valid for "j".
+ * Check if basic map "j" forms an extension of basic map "i".
+ *
+ * In particular, we relax constraint "k", compute the corresponding
+ * facet and check whether it is included in the other basic map.
+ * If so, we know that relaxing the constraint extends the basic
+ * map with exactly the other basic map (we already know that this
+ * other basic map is included in the extension, because there
* were no "cut" inequalities in "i") and we can replace the
- * two basic sets by thie extension.
+ * two basic maps by thie extension.
* ____ _____
* / || / |
* / || / |
* \ || \ |
* \___|| \____|
*/
-static int check_adj_eq(struct isl_set *set, int i, int j,
+static int is_extension(struct isl_map *map, int i, int j, int k,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
int super;
- int k;
struct isl_tab_undo *snap, *snap2;
- unsigned n_eq = set->p[i]->n_eq;
+ unsigned n_eq = map->p[i]->n_eq;
+
+ snap = isl_tab_snap(tabs[i]);
+ tabs[i] = isl_tab_relax(tabs[i], n_eq + k);
+ snap2 = isl_tab_snap(tabs[i]);
+ tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
+ super = contains(map, j, ineq_j, tabs[i]);
+ if (super) {
+ if (isl_tab_rollback(tabs[i], snap2) < 0)
+ return -1;
+ map->p[i] = isl_basic_map_cow(map->p[i]);
+ if (!map->p[i])
+ return -1;
+ isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ ISL_F_SET(map->p[i], ISL_BASIC_MAP_FINAL);
+ drop(map, j, tabs);
+ changed = 1;
+ } else
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ return -1;
+
+ return changed;
+}
+
+/* For each non-redundant constraint in "bmap" (as determined by "tab"),
+ * wrap the constraint around "bound" such that it includes the whole
+ * set "set" and append the resulting constraint to "wraps".
+ * "wraps" is assumed to have been pre-allocated to the appropriate size.
+ * wraps->n_row is the number of actual wrapped constraints that have
+ * been added.
+ * If any of the wrapping problems results in a constraint that is
+ * identical to "bound", then this means that "set" is unbounded in such
+ * way that no wrapping is possible. If this happens then wraps->n_row
+ * is reset to zero.
+ */
+static int add_wraps(__isl_keep isl_mat *wraps, __isl_keep isl_basic_map *bmap,
+ struct isl_tab *tab, isl_int *bound, __isl_keep isl_set *set)
+{
+ int l;
+ int w;
+ unsigned total = isl_basic_map_total_dim(bmap);
+
+ w = wraps->n_row;
+
+ for (l = 0; l < bmap->n_ineq; ++l) {
+ if (isl_seq_is_neg(bound, bmap->ineq[l], 1 + total))
+ continue;
+ if (isl_seq_eq(bound, bmap->ineq[l], 1 + total))
+ continue;
+ if (isl_tab_is_redundant(tab, bmap->n_eq + l))
+ continue;
+
+ isl_seq_cpy(wraps->row[w], bound, 1 + total);
+ if (!isl_set_wrap_facet(set, wraps->row[w], bmap->ineq[l]))
+ return -1;
+ if (isl_seq_eq(wraps->row[w], bound, 1 + total))
+ goto unbounded;
+ ++w;
+ }
+ for (l = 0; l < bmap->n_eq; ++l) {
+ if (isl_seq_is_neg(bound, bmap->eq[l], 1 + total))
+ continue;
+ if (isl_seq_eq(bound, bmap->eq[l], 1 + total))
+ continue;
+
+ isl_seq_cpy(wraps->row[w], bound, 1 + total);
+ isl_seq_neg(wraps->row[w + 1], bmap->eq[l], 1 + total);
+ if (!isl_set_wrap_facet(set, wraps->row[w], wraps->row[w + 1]))
+ return -1;
+ if (isl_seq_eq(wraps->row[w], bound, 1 + total))
+ goto unbounded;
+ ++w;
+
+ isl_seq_cpy(wraps->row[w], bound, 1 + total);
+ if (!isl_set_wrap_facet(set, wraps->row[w], bmap->eq[l]))
+ return -1;
+ if (isl_seq_eq(wraps->row[w], bound, 1 + total))
+ goto unbounded;
+ ++w;
+ }
+
+ wraps->n_row = w;
+ return 0;
+unbounded:
+ wraps->n_row = 0;
+ return 0;
+}
+
+/* Given a basic set i with a constraint k that is adjacent to either the
+ * whole of basic set j or a facet of basic set j, check if we can wrap
+ * both the facet corresponding to k and the facet of j (or the whole of j)
+ * around their ridges to include the other set.
+ * If so, replace the pair of basic sets by their union.
+ *
+ * All constraints of i (except k) are assumed to be valid for j.
+ *
+ * In the case where j has a facet adjacent to i, tab[j] is assumed
+ * to have been restricted to this facet, so that the non-redundant
+ * constraints in tab[j] are the ridges of the facet.
+ * Note that for the purpose of wrapping, it does not matter whether
+ * we wrap the ridges of i around the whole of j or just around
+ * the facet since all the other constraints are assumed to be valid for j.
+ * In practice, we wrap to include the whole of j.
+ * ____ _____
+ * / | / \
+ * / || / |
+ * \ || => \ |
+ * \ || \ |
+ * \___|| \____|
+ *
+ */
+static int can_wrap_in_facet(struct isl_map *map, int i, int j, int k,
+ struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
+{
+ int changed = 0;
+ struct isl_mat *wraps = NULL;
+ struct isl_set *set_i = NULL;
+ struct isl_set *set_j = NULL;
+ struct isl_vec *bound = NULL;
+ unsigned total = isl_basic_map_total_dim(map->p[i]);
+ struct isl_tab_undo *snap;
+
+ snap = isl_tab_snap(tabs[i]);
+
+ set_i = isl_set_from_basic_set(
+ isl_basic_map_underlying_set(isl_basic_map_copy(map->p[i])));
+ set_j = isl_set_from_basic_set(
+ isl_basic_map_underlying_set(isl_basic_map_copy(map->p[j])));
+ wraps = isl_mat_alloc(map->ctx, 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
+ map->p[i]->n_ineq + map->p[j]->n_ineq,
+ 1 + total);
+ bound = isl_vec_alloc(map->ctx, 1 + total);
+ if (!set_i || !set_j || !wraps || !bound)
+ goto error;
+
+ isl_seq_cpy(bound->el, map->p[i]->ineq[k], 1 + total);
+ isl_int_add_ui(bound->el[0], bound->el[0], 1);
+
+ isl_seq_cpy(wraps->row[0], bound->el, 1 + total);
+ wraps->n_row = 1;
+
+ if (add_wraps(wraps, map->p[j], tabs[j], bound->el, set_i) < 0)
+ goto error;
+ if (!wraps->n_row)
+ goto unbounded;
+
+ tabs[i] = isl_tab_select_facet(tabs[i], map->p[i]->n_eq + k);
+ if (isl_tab_detect_redundant(tabs[i]) < 0)
+ goto error;
+
+ isl_seq_neg(bound->el, map->p[i]->ineq[k], 1 + total);
+
+ if (add_wraps(wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
+ goto error;
+ if (!wraps->n_row)
+ goto unbounded;
- if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ADJ_INEQ) &&
- any(eq_j, 2 * set->p[j]->n_eq, STATUS_ADJ_INEQ))
+ changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps);
+
+ if (!changed) {
+unbounded:
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ goto error;
+ }
+
+ isl_mat_free(wraps);
+
+ isl_set_free(set_i);
+ isl_set_free(set_j);
+
+ isl_vec_free(bound);
+
+ return changed;
+error:
+ isl_vec_free(bound);
+ isl_mat_free(wraps);
+ isl_set_free(set_i);
+ isl_set_free(set_j);
+ return -1;
+}
+
+/* Given two basic sets i and j such that i has exactly one cut constraint,
+ * check if we can wrap the corresponding facet around its ridges to include
+ * the other basic set (and nothing else).
+ * If so, replace the pair by their union.
+ *
+ * We first check if j has a facet adjacent to the cut constraint of i.
+ * If so, we try to wrap in the facet.
+ * ____ _____
+ * / ___|_ / \
+ * / | | / |
+ * \ | | => \ |
+ * \|____| \ |
+ * \___| \____/
+ */
+static int can_wrap_in_set(struct isl_map *map, int i, int j,
+ struct isl_tab **tabs, int *ineq_i, int *ineq_j)
+{
+ int changed = 0;
+ int k, l;
+ unsigned total = isl_basic_map_total_dim(map->p[i]);
+ struct isl_tab_undo *snap;
+
+ for (k = 0; k < map->p[i]->n_ineq; ++k)
+ if (ineq_i[k] == STATUS_CUT)
+ break;
+
+ isl_assert(map->ctx, k < map->p[i]->n_ineq, return -1);
+
+ isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ for (l = 0; l < map->p[j]->n_ineq; ++l) {
+ if (isl_tab_is_redundant(tabs[j], map->p[j]->n_eq + l))
+ continue;
+ if (isl_seq_eq(map->p[i]->ineq[k],
+ map->p[j]->ineq[l], 1 + total))
+ break;
+ }
+ isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+
+ if (l >= map->p[j]->n_ineq)
+ return 0;
+
+ snap = isl_tab_snap(tabs[j]);
+ tabs[j] = isl_tab_select_facet(tabs[j], map->p[j]->n_eq + l);
+ if (isl_tab_detect_redundant(tabs[j]) < 0)
+ return -1;
+
+ changed = can_wrap_in_facet(map, i, j, k, tabs, NULL, ineq_i, NULL, ineq_j);
+
+ if (!changed && isl_tab_rollback(tabs[j], snap) < 0)
+ return -1;
+
+ return changed;
+}
+
+/* Check if either i or j has a single cut constraint that can
+ * be used to wrap in (a facet of) the other basic set.
+ * if so, replace the pair by their union.
+ */
+static int check_wrap(struct isl_map *map, int i, int j,
+ struct isl_tab **tabs, int *ineq_i, int *ineq_j)
+{
+ int changed = 0;
+
+ if (count(ineq_i, map->p[i]->n_ineq, STATUS_CUT) == 1)
+ changed = can_wrap_in_set(map, i, j, tabs, ineq_i, ineq_j);
+ if (changed)
+ return changed;
+
+ if (count(ineq_j, map->p[j]->n_ineq, STATUS_CUT) == 1)
+ changed = can_wrap_in_set(map, j, i, tabs, ineq_j, ineq_i);
+ return changed;
+}
+
+/* At least one of the basic maps has an equality that is adjacent
+ * to inequality. Make sure that only one of the basic maps has
+ * such an equality and that the other basic map has exactly one
+ * inequality adjacent to an equality.
+ * We call the basic map that has the inequality "i" and the basic
+ * map that has the equality "j".
+ * If "i" has any "cut" inequality, then relaxing the inequality
+ * by one would not result in a basic map that contains the other
+ * basic map.
+ */
+static int check_adj_eq(struct isl_map *map, int i, int j,
+ struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
+{
+ int changed = 0;
+ int k;
+
+ if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) &&
+ any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ))
/* ADJ EQ TOO MANY */
return 0;
- if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ADJ_INEQ))
- return check_adj_eq(set, j, i, tabs,
+ if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ))
+ return check_adj_eq(map, j, i, tabs,
eq_j, ineq_j, eq_i, ineq_i);
/* j has an equality adjacent to an inequality in i */
- if (any(ineq_i, set->p[i]->n_ineq, STATUS_CUT))
+ if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT))
/* ADJ EQ CUT */
return 0;
- if (count(eq_j, 2 * set->p[j]->n_eq, STATUS_ADJ_INEQ) != 1 ||
- count(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_EQ) != 1 ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_EQ) ||
- any(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_INEQ))
+ if (count(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ) != 1 ||
+ count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) != 1 ||
+ any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ) ||
+ any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
+ any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ))
/* ADJ EQ TOO MANY */
return 0;
- for (k = 0; k < set->p[i]->n_ineq ; ++k)
+ for (k = 0; k < map->p[i]->n_ineq ; ++k)
if (ineq_i[k] == STATUS_ADJ_EQ)
break;
- snap = isl_tab_snap(set->ctx, tabs[i]);
- tabs[i] = isl_tab_relax(set->ctx, tabs[i], n_eq + k);
- snap2 = isl_tab_snap(set->ctx, tabs[i]);
- tabs[i] = isl_tab_select_facet(set->ctx, tabs[i], n_eq + k);
- super = contains(set, j, ineq_j, tabs[i]);
- if (super) {
- isl_tab_rollback(set->ctx, tabs[i], snap2);
- set->p[i] = isl_basic_set_cow(set->p[i]);
- if (!set->p[i])
- return -1;
- isl_int_add_ui(set->p[i]->ineq[k][0], set->p[i]->ineq[k][0], 1);
- ISL_F_SET(set->p[i], ISL_BASIC_SET_FINAL);
- drop(set, j, tabs);
- changed = 1;
- } else
- isl_tab_rollback(set->ctx, tabs[i], snap);
+ changed = is_extension(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
+ if (changed)
+ return changed;
+
+ changed = can_wrap_in_facet(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
return changed;
}
-/* Check if the union of the given pair of basic sets
- * can be represented by a single basic set.
- * If so, replace the pair by the single basic set and return 1.
+/* Check if the union of the given pair of basic maps
+ * can be represented by a single basic map.
+ * If so, replace the pair by the single basic map and return 1.
* Otherwise, return 0;
*
- * We first check the effect of each constraint of one basic set
- * on the other basic set.
+ * We first check the effect of each constraint of one basic map
+ * on the other basic map.
* The constraint may be
* redundant the constraint is redundant in its own
- * basic set and should be ignore and removed
+ * basic map and should be ignore and removed
* in the end
- * valid all (integer) points of the other basic set
+ * valid all (integer) points of the other basic map
* satisfy the constraint
- * separate no (integer) point of the other basic set
+ * separate no (integer) point of the other basic map
* satisfies the constraint
- * cut some but not all points of the other basic set
+ * cut some but not all points of the other basic map
* satisfy the constraint
* adj_eq the given constraint is adjacent (on the outside)
- * to an equality of the other basic set
+ * to an equality of the other basic map
* adj_ineq the given constraint is adjacent (on the outside)
- * to an inequality of the other basic set
+ * to an inequality of the other basic map
*
- * We consider four cases in which we can replace the pair by a single
- * basic set. We ignore all "redundant" constraints.
+ * We consider six cases in which we can replace the pair by a single
+ * basic map. We ignore all "redundant" constraints.
*
- * 1. all constraints of one basic set are valid
- * => the other basic set is a subset and can be removed
+ * 1. all constraints of one basic map are valid
+ * => the other basic map is a subset and can be removed
*
- * 2. all constraints of both basic sets are either "valid" or "cut"
+ * 2. all constraints of both basic maps are either "valid" or "cut"
* and the facets corresponding to the "cut" constraints
- * of one of the basic sets lies entirely inside the other basic set
- * => the pair can be replaced by a basic set consisting
- * of the valid constraints in both basic sets
+ * of one of the basic maps lies entirely inside the other basic map
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps
*
* 3. there is a single pair of adjacent inequalities
* (all other constraints are "valid")
- * => the pair can be replaced by a basic set consisting
- * of the valid constraints in both basic sets
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps
*
* 4. there is a single adjacent pair of an inequality and an equality,
- * the other constraints of the basic set containing the equality are
- * "valid". Moreover, if the inequality the basic set is relaxed
+ * the other constraints of the basic map containing the inequality are
+ * "valid". Moreover, if the inequality the basic map is relaxed
* and then turned into an equality, then resulting facet lies
- * entirely inside the other basic set
- * => the pair can be replaced by the basic set containing
+ * entirely inside the other basic map
+ * => the pair can be replaced by the basic map containing
* the inequality, with the inequality relaxed.
*
+ * 5. there is a single adjacent pair of an inequality and an equality,
+ * the other constraints of the basic map containing the inequality are
+ * "valid". Moreover, the facets corresponding to both
+ * the inequality and the equality can be wrapped around their
+ * ridges to include the other basic map
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps together
+ * with all wrapping constraints
+ *
+ * 6. one of the basic maps has a single cut constraint and
+ * the other basic map has a constraint adjacent to this constraint.
+ * Moreover, the facets corresponding to both constraints
+ * can be wrapped around their ridges to include the other basic map
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps together
+ * with all wrapping constraints
+ *
* Throughout the computation, we maintain a collection of tableaus
- * corresponding to the basic sets. When the basic sets are dropped
+ * corresponding to the basic maps. When the basic maps are dropped
* or combined, the tableaus are modified accordingly.
*/
-static int coalesce_pair(struct isl_set *set, int i, int j,
+static int coalesce_pair(struct isl_map *map, int i, int j,
struct isl_tab **tabs)
{
int changed = 0;
int *ineq_i = NULL;
int *ineq_j = NULL;
- eq_i = eq_status_in(set, i, j, tabs);
- if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ERROR))
+ eq_i = eq_status_in(map, i, j, tabs);
+ if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ERROR))
goto error;
- if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_SEPARATE))
+ if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_SEPARATE))
goto done;
- eq_j = eq_status_in(set, j, i, tabs);
- if (any(eq_j, 2 * set->p[j]->n_eq, STATUS_ERROR))
+ eq_j = eq_status_in(map, j, i, tabs);
+ if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ERROR))
goto error;
- if (any(eq_j, 2 * set->p[j]->n_eq, STATUS_SEPARATE))
+ if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_SEPARATE))
goto done;
- ineq_i = ineq_status_in(set, i, j, tabs);
- if (any(ineq_i, set->p[i]->n_ineq, STATUS_ERROR))
+ ineq_i = ineq_status_in(map, i, j, tabs);
+ if (any(ineq_i, map->p[i]->n_ineq, STATUS_ERROR))
goto error;
- if (any(ineq_i, set->p[i]->n_ineq, STATUS_SEPARATE))
+ if (any(ineq_i, map->p[i]->n_ineq, STATUS_SEPARATE))
goto done;
- ineq_j = ineq_status_in(set, j, i, tabs);
- if (any(ineq_j, set->p[j]->n_ineq, STATUS_ERROR))
+ ineq_j = ineq_status_in(map, j, i, tabs);
+ if (any(ineq_j, map->p[j]->n_ineq, STATUS_ERROR))
goto error;
- if (any(ineq_j, set->p[j]->n_ineq, STATUS_SEPARATE))
+ if (any(ineq_j, map->p[j]->n_ineq, STATUS_SEPARATE))
goto done;
- if (all(eq_i, 2 * set->p[i]->n_eq, STATUS_VALID) &&
- all(ineq_i, set->p[i]->n_ineq, STATUS_VALID)) {
- drop(set, j, tabs);
+ if (all(eq_i, 2 * map->p[i]->n_eq, STATUS_VALID) &&
+ all(ineq_i, map->p[i]->n_ineq, STATUS_VALID)) {
+ drop(map, j, tabs);
changed = 1;
- } else if (all(eq_j, 2 * set->p[j]->n_eq, STATUS_VALID) &&
- all(ineq_j, set->p[j]->n_ineq, STATUS_VALID)) {
- drop(set, i, tabs);
+ } else if (all(eq_j, 2 * map->p[j]->n_eq, STATUS_VALID) &&
+ all(ineq_j, map->p[j]->n_ineq, STATUS_VALID)) {
+ drop(map, i, tabs);
changed = 1;
- } else if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_CUT) ||
- any(eq_j, 2 * set->p[j]->n_eq, STATUS_CUT)) {
+ } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) ||
+ any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT)) {
/* BAD CUT */
- } else if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ADJ_EQ) ||
- any(eq_j, 2 * set->p[j]->n_eq, STATUS_ADJ_EQ)) {
+ } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ) ||
+ any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
/* ADJ EQ PAIR */
- } else if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ADJ_INEQ) ||
- any(eq_j, 2 * set->p[j]->n_eq, STATUS_ADJ_INEQ)) {
- changed = check_adj_eq(set, i, j, tabs,
+ } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) ||
+ any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ)) {
+ changed = check_adj_eq(map, i, j, tabs,
eq_i, ineq_i, eq_j, ineq_j);
- } else if (any(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_EQ) ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_EQ)) {
+ } else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) ||
+ any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ)) {
/* Can't happen */
/* BAD ADJ INEQ */
- } else if (any(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_INEQ)) {
- changed = check_adj_ineq(set, i, j, tabs, ineq_i, ineq_j);
- } else
- changed = check_facets(set, i, j, tabs, ineq_i, ineq_j);
+ } else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
+ any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ)) {
+ changed = check_adj_ineq(map, i, j, tabs, ineq_i, ineq_j);
+ } else {
+ changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
+ if (!changed)
+ changed = check_wrap(map, i, j, tabs, ineq_i, ineq_j);
+ }
done:
free(eq_i);
return -1;
}
-static struct isl_set *coalesce(struct isl_set *set, struct isl_tab **tabs)
+static struct isl_map *coalesce(struct isl_map *map, struct isl_tab **tabs)
{
int i, j;
- for (i = 0; i < set->n - 1; ++i)
- for (j = i + 1; j < set->n; ++j) {
+ for (i = 0; i < map->n - 1; ++i)
+ for (j = i + 1; j < map->n; ++j) {
int changed;
- changed = coalesce_pair(set, i, j, tabs);
+ changed = coalesce_pair(map, i, j, tabs);
if (changed < 0)
goto error;
if (changed)
- return coalesce(set, tabs);
+ return coalesce(map, tabs);
}
- return set;
+ return map;
error:
- isl_set_free(set);
+ isl_map_free(map);
return NULL;
}
-/* For each pair of basic sets in the set, check if the union of the two
- * can be represented by a single basic set.
- * If so, replace the pair by the single basic set and start over.
+/* For each pair of basic maps in the map, check if the union of the two
+ * can be represented by a single basic map.
+ * If so, replace the pair by the single basic map and start over.
*/
-struct isl_set *isl_set_coalesce(struct isl_set *set)
+struct isl_map *isl_map_coalesce(struct isl_map *map)
{
int i;
unsigned n;
- struct isl_ctx *ctx;
struct isl_tab **tabs = NULL;
- if (!set)
+ if (!map)
return NULL;
- if (set->n <= 1)
- return set;
+ if (map->n <= 1)
+ return map;
- set = isl_set_align_divs(set);
+ map = isl_map_align_divs(map);
- tabs = isl_calloc_array(set->ctx, struct isl_tab *, set->n);
+ tabs = isl_calloc_array(map->ctx, struct isl_tab *, map->n);
if (!tabs)
goto error;
- n = set->n;
- ctx = set->ctx;
- for (i = 0; i < set->n; ++i) {
- tabs[i] = isl_tab_from_basic_set(set->p[i]);
+ n = map->n;
+ for (i = 0; i < map->n; ++i) {
+ tabs[i] = isl_tab_from_basic_map(map->p[i]);
if (!tabs[i])
goto error;
- if (!ISL_F_ISSET(set->p[i], ISL_BASIC_SET_NO_IMPLICIT))
- tabs[i] = isl_tab_detect_equalities(set->ctx, tabs[i]);
- if (!ISL_F_ISSET(set->p[i], ISL_BASIC_SET_NO_REDUNDANT))
- tabs[i] = isl_tab_detect_redundant(set->ctx, tabs[i]);
+ if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT))
+ tabs[i] = isl_tab_detect_implicit_equalities(tabs[i]);
+ if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT))
+ if (isl_tab_detect_redundant(tabs[i]) < 0)
+ goto error;
}
- for (i = set->n - 1; i >= 0; --i)
+ for (i = map->n - 1; i >= 0; --i)
if (tabs[i]->empty)
- drop(set, i, tabs);
+ drop(map, i, tabs);
- set = coalesce(set, tabs);
+ map = coalesce(map, tabs);
- if (set)
- for (i = 0; i < set->n; ++i) {
- set->p[i] = isl_basic_set_update_from_tab(set->p[i],
+ if (map)
+ for (i = 0; i < map->n; ++i) {
+ map->p[i] = isl_basic_map_update_from_tab(map->p[i],
tabs[i]);
- if (!set->p[i])
+ map->p[i] = isl_basic_map_finalize(map->p[i]);
+ if (!map->p[i])
goto error;
- ISL_F_SET(set->p[i], ISL_BASIC_SET_NO_IMPLICIT);
- ISL_F_SET(set->p[i], ISL_BASIC_SET_NO_REDUNDANT);
+ ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT);
+ ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT);
}
for (i = 0; i < n; ++i)
- isl_tab_free(ctx, tabs[i]);
+ isl_tab_free(tabs[i]);
free(tabs);
- return set;
+ return map;
error:
if (tabs)
for (i = 0; i < n; ++i)
- isl_tab_free(ctx, tabs[i]);
+ isl_tab_free(tabs[i]);
free(tabs);
return NULL;
}
+
+/* For each pair of basic sets in the set, check if the union of the two
+ * can be represented by a single basic set.
+ * If so, replace the pair by the single basic set and start over.
+ */
+struct isl_set *isl_set_coalesce(struct isl_set *set)
+{
+ return (struct isl_set *)isl_map_coalesce((struct isl_map *)set);
+}