-#include "isl_ctx.h"
-#include "isl_seq.h"
-#include "isl_set.h"
-#include "isl_lp.h"
-#include "isl_map.h"
-#include "isl_map_private.h"
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010 INRIA Saclay
+ * Copyright 2012 Ecole Normale Superieure
+ *
+ * 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>
+#include <isl_map_private.h>
+#include <isl/seq.h>
+#include <isl/set.h>
+#include <isl/lp.h>
+#include <isl/map.h>
#include "isl_equalities.h"
#include "isl_sample.h"
#include "isl_tab.h"
+#include <isl_mat_private.h>
struct isl_basic_map *isl_basic_map_implicit_equalities(
struct isl_basic_map *bmap)
if (bmap->n_ineq <= 1)
return bmap;
- tab = isl_tab_from_basic_map(bmap);
- tab = isl_tab_detect_equalities(tab);
+ tab = isl_tab_from_basic_map(bmap, 0);
+ if (isl_tab_detect_implicit_equalities(tab) < 0)
+ goto error;
bmap = isl_basic_map_update_from_tab(bmap, tab);
isl_tab_free(tab);
bmap = isl_basic_map_gauss(bmap, NULL);
ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
return bmap;
+error:
+ isl_tab_free(tab);
+ isl_basic_map_free(bmap);
+ return NULL;
}
struct isl_basic_set *isl_basic_set_implicit_equalities(
int col;
int row;
+ if (!bset1 || !bset2)
+ goto error;
+
total = 1 + isl_basic_set_n_dim(bset1);
row = 0;
--row;
}
}
- isl_basic_set_free(bset2);
isl_assert(bset1->ctx, row == bset1->n_eq, goto error);
+ isl_basic_set_free(bset2);
bset1 = isl_basic_set_normalize_constraints(bset1);
return bset1;
error:
isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
return NULL;
}
-static struct isl_basic_set *isl_basic_set_from_vec(struct isl_vec *vec)
-{
- int i;
- int k;
- struct isl_basic_set *bset = NULL;
- struct isl_ctx *ctx;
- unsigned dim;
-
- if (!vec)
- return NULL;
- ctx = vec->ctx;
- isl_assert(ctx, vec->size != 0, goto error);
-
- bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
- if (!bset)
- goto error;
- dim = isl_basic_set_n_dim(bset);
- for (i = dim - 1; i >= 0; --i) {
- k = isl_basic_set_alloc_equality(bset);
- if (k < 0)
- goto error;
- isl_seq_clr(bset->eq[k], 1 + dim);
- isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
- isl_int_set(bset->eq[k][1 + i], vec->el[0]);
- }
- isl_vec_free(vec);
-
- return bset;
-error:
- isl_basic_set_free(bset);
- isl_vec_free(vec);
- return NULL;
-}
-
-/* Find an integer point in "bset" that lies outside of the equality
- * "eq" e(x) = 0.
+/* Find an integer point in the set represented by "tab"
+ * that lies outside of the equality "eq" e(x) = 0.
* If "up" is true, look for a point satisfying e(x) - 1 >= 0.
* Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
- * The point, if found, is returned as a singleton set.
- * If no point can be found, the empty set is returned.
+ * The point, if found, is returned.
+ * If no point can be found, a zero-length vector is returned.
*
* Before solving an ILP problem, we first check if simply
* adding the normal of the constraint to one of the known
- * integer points in the basic set yields another point
- * inside the basic set.
+ * integer points in the basic set represented by "tab"
+ * yields another point inside the basic set.
*
- * The caller of this function ensures that "bset" is bounded.
+ * The caller of this function ensures that the tableau is bounded or
+ * that tab->basis and tab->n_unbounded have been set appropriately.
*/
-static struct isl_basic_set *outside_point(struct isl_ctx *ctx,
- struct isl_basic_set *bset, isl_int *eq, int up)
+static struct isl_vec *outside_point(struct isl_tab *tab, isl_int *eq, int up)
{
- struct isl_basic_set *slice = NULL;
- struct isl_vec *sample;
- struct isl_basic_set *point;
+ struct isl_ctx *ctx;
+ struct isl_vec *sample = NULL;
+ struct isl_tab_undo *snap;
unsigned dim;
- int k;
- dim = isl_basic_set_n_dim(bset);
+ if (!tab)
+ return NULL;
+ ctx = tab->mat->ctx;
+
+ dim = tab->n_var;
sample = isl_vec_alloc(ctx, 1 + dim);
if (!sample)
return NULL;
- isl_int_set_si(sample->block.data[0], 1);
- isl_seq_combine(sample->block.data + 1,
- ctx->one, bset->sample->block.data + 1,
+ isl_int_set_si(sample->el[0], 1);
+ isl_seq_combine(sample->el + 1,
+ ctx->one, tab->bmap->sample->el + 1,
up ? ctx->one : ctx->negone, eq + 1, dim);
- if (isl_basic_set_contains(bset, sample))
- return isl_basic_set_from_vec(sample);
+ if (isl_basic_map_contains(tab->bmap, sample))
+ return sample;
isl_vec_free(sample);
sample = NULL;
- slice = isl_basic_set_copy(bset);
- if (!slice)
+ snap = isl_tab_snap(tab);
+
+ if (!up)
+ isl_seq_neg(eq, eq, 1 + dim);
+ isl_int_sub_ui(eq[0], eq[0], 1);
+
+ if (isl_tab_extend_cons(tab, 1) < 0)
goto error;
- slice = isl_basic_set_cow(slice);
- slice = isl_basic_set_extend(slice, 0, dim, 0, 0, 1);
- k = isl_basic_set_alloc_inequality(slice);
- if (k < 0)
+ if (isl_tab_add_ineq(tab, eq) < 0)
goto error;
- if (up)
- isl_seq_cpy(slice->ineq[k], eq, 1 + dim);
- else
- isl_seq_neg(slice->ineq[k], eq, 1 + dim);
- isl_int_sub_ui(slice->ineq[k][0], slice->ineq[k][0], 1);
- sample = isl_basic_set_sample_bounded(slice);
- if (!sample)
+ sample = isl_tab_sample(tab);
+
+ isl_int_add_ui(eq[0], eq[0], 1);
+ if (!up)
+ isl_seq_neg(eq, eq, 1 + dim);
+
+ if (sample && isl_tab_rollback(tab, snap) < 0)
goto error;
- if (sample->size == 0) {
- isl_vec_free(sample);
- point = isl_basic_set_empty_like(bset);
- } else
- point = isl_basic_set_from_vec(sample);
- return point;
+ return sample;
error:
- isl_basic_set_free(slice);
+ isl_vec_free(sample);
return NULL;
}
return NULL;
}
-/* Extend an initial (under-)approximation of the affine hull of "bset"
+__isl_give isl_set *isl_set_recession_cone(__isl_take isl_set *set)
+{
+ int i;
+
+ if (!set)
+ return NULL;
+ if (set->n == 0)
+ return set;
+
+ set = isl_set_remove_divs(set);
+ set = isl_set_cow(set);
+ if (!set)
+ return NULL;
+
+ for (i = 0; i < set->n; ++i) {
+ set->p[i] = isl_basic_set_recession_cone(set->p[i]);
+ if (!set->p[i])
+ goto error;
+ }
+
+ return set;
+error:
+ isl_set_free(set);
+ return NULL;
+}
+
+/* Move "sample" to a point that is one up (or down) from the original
+ * point in dimension "pos".
+ */
+static void adjacent_point(__isl_keep isl_vec *sample, int pos, int up)
+{
+ if (up)
+ isl_int_add_ui(sample->el[1 + pos], sample->el[1 + pos], 1);
+ else
+ isl_int_sub_ui(sample->el[1 + pos], sample->el[1 + pos], 1);
+}
+
+/* Check if any points that are adjacent to "sample" also belong to "bset".
+ * If so, add them to "hull" and return the updated hull.
+ *
+ * Before checking whether and adjacent point belongs to "bset", we first
+ * check whether it already belongs to "hull" as this test is typically
+ * much cheaper.
+ */
+static __isl_give isl_basic_set *add_adjacent_points(
+ __isl_take isl_basic_set *hull, __isl_take isl_vec *sample,
+ __isl_keep isl_basic_set *bset)
+{
+ int i, up;
+ int dim;
+
+ if (!sample)
+ goto error;
+
+ dim = isl_basic_set_dim(hull, isl_dim_set);
+
+ for (i = 0; i < dim; ++i) {
+ for (up = 0; up <= 1; ++up) {
+ int contains;
+ isl_basic_set *point;
+
+ adjacent_point(sample, i, up);
+ contains = isl_basic_set_contains(hull, sample);
+ if (contains < 0)
+ goto error;
+ if (contains) {
+ adjacent_point(sample, i, !up);
+ continue;
+ }
+ contains = isl_basic_set_contains(bset, sample);
+ if (contains < 0)
+ goto error;
+ if (contains) {
+ point = isl_basic_set_from_vec(
+ isl_vec_copy(sample));
+ hull = affine_hull(hull, point);
+ }
+ adjacent_point(sample, i, !up);
+ if (contains)
+ break;
+ }
+ }
+
+ isl_vec_free(sample);
+
+ return hull;
+error:
+ isl_vec_free(sample);
+ isl_basic_set_free(hull);
+ return NULL;
+}
+
+/* Extend an initial (under-)approximation of the affine hull of basic
+ * set represented by the tableau "tab"
* by looking for points that do not satisfy one of the equalities
* in the current approximation and adding them to that approximation
* until no such points can be found any more.
*
- * The caller of this function ensures that "bset" is bounded.
+ * The caller of this function ensures that "tab" is bounded or
+ * that tab->basis and tab->n_unbounded have been set appropriately.
+ *
+ * "bset" may be either NULL or the basic set represented by "tab".
+ * If "bset" is not NULL, we check for any point we find if any
+ * of its adjacent points also belong to "bset".
*/
-static struct isl_basic_set *extend_affine_hull(struct isl_basic_set *bset,
- struct isl_basic_set *hull)
+static __isl_give isl_basic_set *extend_affine_hull(struct isl_tab *tab,
+ __isl_take isl_basic_set *hull, __isl_keep isl_basic_set *bset)
{
- int i, j, k;
- struct isl_ctx *ctx;
+ int i, j;
unsigned dim;
- ctx = bset->ctx;
- dim = isl_basic_set_n_dim(bset);
+ if (!tab || !hull)
+ goto error;
+
+ dim = tab->n_var;
+
+ if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0)
+ goto error;
+
for (i = 0; i < dim; ++i) {
+ struct isl_vec *sample;
struct isl_basic_set *point;
for (j = 0; j < hull->n_eq; ++j) {
- point = outside_point(ctx, bset, hull->eq[j], 1);
- if (!point)
+ sample = outside_point(tab, hull->eq[j], 1);
+ if (!sample)
goto error;
- if (!ISL_F_ISSET(point, ISL_BASIC_SET_EMPTY))
+ if (sample->size > 0)
break;
- isl_basic_set_free(point);
- point = outside_point(ctx, bset, hull->eq[j], 0);
- if (!point)
+ isl_vec_free(sample);
+ sample = outside_point(tab, hull->eq[j], 0);
+ if (!sample)
goto error;
- if (!ISL_F_ISSET(point, ISL_BASIC_SET_EMPTY))
+ if (sample->size > 0)
break;
- isl_basic_set_free(point);
+ isl_vec_free(sample);
- bset = isl_basic_set_extend_constraints(bset, 1, 0);
- k = isl_basic_set_alloc_equality(bset);
- if (k < 0)
- goto error;
- isl_seq_cpy(bset->eq[k], hull->eq[j],
- 1 + isl_basic_set_total_dim(hull));
- bset = isl_basic_set_gauss(bset, NULL);
- if (!bset)
+ if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
goto error;
}
if (j == hull->n_eq)
break;
+ if (tab->samples)
+ tab = isl_tab_add_sample(tab, isl_vec_copy(sample));
+ if (!tab)
+ goto error;
+ if (bset)
+ hull = add_adjacent_points(hull, isl_vec_copy(sample),
+ bset);
+ point = isl_basic_set_from_vec(sample);
hull = affine_hull(hull, point);
+ if (!hull)
+ return NULL;
}
- isl_basic_set_free(bset);
return hull;
error:
- isl_basic_set_free(bset);
isl_basic_set_free(hull);
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.
*/
-static struct isl_basic_set *drop_constraints_involving
- (struct isl_basic_set *bset, unsigned first, unsigned n)
+__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 (!bset)
+ if (n == 0)
+ 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));
+
+ 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 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"
+ * from "sample" and any of its adjacent points that also belong to "bset".
+ */
+static __isl_give isl_basic_set *initialize_hull(__isl_keep isl_basic_set *bset,
+ __isl_take isl_vec *sample)
+{
+ isl_basic_set *hull;
+
+ hull = isl_basic_set_from_vec(isl_vec_copy(sample));
+ hull = add_adjacent_points(hull, sample, bset);
+
+ return hull;
+}
+
+/* Look for all equalities satisfied by the integer points in bset,
+ * which is assumed to be bounded.
+ *
+ * The equalities are obtained by successively looking for
+ * a point that is affinely independent of the points found so far.
+ * In particular, for each equality satisfied by the points so far,
+ * we check if there is any point on a hyperplane parallel to the
+ * corresponding hyperplane shifted by at least one (in either direction).
+ */
+static struct isl_basic_set *uset_affine_hull_bounded(struct isl_basic_set *bset)
+{
+ struct isl_vec *sample = NULL;
+ struct isl_basic_set *hull;
+ struct isl_tab *tab = NULL;
+ unsigned dim;
+
+ if (isl_basic_set_plain_is_empty(bset))
+ return bset;
+
+ dim = isl_basic_set_n_dim(bset);
+
+ if (bset->sample && bset->sample->size == 1 + dim) {
+ int contains = isl_basic_set_contains(bset, bset->sample);
+ if (contains < 0)
+ goto error;
+ if (contains) {
+ if (dim == 0)
+ return bset;
+ sample = isl_vec_copy(bset->sample);
+ } else {
+ isl_vec_free(bset->sample);
+ bset->sample = NULL;
+ }
+ }
+
+ tab = isl_tab_from_basic_set(bset, 1);
+ if (!tab)
+ goto error;
+ if (tab->empty) {
+ isl_tab_free(tab);
+ isl_vec_free(sample);
+ return isl_basic_set_set_to_empty(bset);
+ }
+
+ if (!sample) {
+ struct isl_tab_undo *snap;
+ snap = isl_tab_snap(tab);
+ sample = isl_tab_sample(tab);
+ if (isl_tab_rollback(tab, snap) < 0)
+ goto error;
+ isl_vec_free(tab->bmap->sample);
+ tab->bmap->sample = isl_vec_copy(sample);
+ }
+
+ if (!sample)
+ goto error;
+ if (sample->size == 0) {
+ isl_tab_free(tab);
+ isl_vec_free(sample);
+ return isl_basic_set_set_to_empty(bset);
+ }
+
+ hull = initialize_hull(bset, sample);
+
+ hull = extend_affine_hull(tab, hull, bset);
+ isl_basic_set_free(bset);
+ isl_tab_free(tab);
+
+ return hull;
+error:
+ isl_vec_free(sample);
+ isl_tab_free(tab);
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Given an unbounded tableau and an integer point satisfying the tableau,
+ * construct an initial affine hull containing the recession cone
+ * shifted to the given point.
+ *
+ * The unbounded directions are taken from the last rows of the basis,
+ * which is assumed to have been initialized appropriately.
+ */
+static __isl_give isl_basic_set *initial_hull(struct isl_tab *tab,
+ __isl_take isl_vec *vec)
+{
+ int i;
+ int k;
+ struct isl_basic_set *bset = NULL;
+ struct isl_ctx *ctx;
+ unsigned dim;
+
+ if (!vec || !tab)
+ return NULL;
+ ctx = vec->ctx;
+ isl_assert(ctx, vec->size != 0, goto error);
+
+ bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
+ if (!bset)
+ goto error;
+ dim = isl_basic_set_n_dim(bset) - tab->n_unbounded;
+ for (i = 0; i < dim; ++i) {
+ k = isl_basic_set_alloc_equality(bset);
+ if (k < 0)
+ goto error;
+ isl_seq_cpy(bset->eq[k] + 1, tab->basis->row[1 + i] + 1,
+ vec->size - 1);
+ isl_seq_inner_product(bset->eq[k] + 1, vec->el +1,
+ vec->size - 1, &bset->eq[k][0]);
+ isl_int_neg(bset->eq[k][0], bset->eq[k][0]);
+ }
+ bset->sample = vec;
+ bset = isl_basic_set_gauss(bset, NULL);
+
return bset;
+error:
+ isl_basic_set_free(bset);
+ isl_vec_free(vec);
+ return NULL;
+}
+
+/* Given a tableau of a set and a tableau of the corresponding
+ * recession cone, detect and add all equalities to the tableau.
+ * If the tableau is bounded, then we can simply keep the
+ * tableau in its state after the return from extend_affine_hull.
+ * However, if the tableau is unbounded, then
+ * isl_tab_set_initial_basis_with_cone will add some additional
+ * constraints to the tableau that have to be removed again.
+ * In this case, we therefore rollback to the state before
+ * any constraints were added and then add the equalities back in.
+ */
+struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
+ struct isl_tab *tab_cone)
+{
+ int j;
+ struct isl_vec *sample;
+ struct isl_basic_set *hull = NULL;
+ struct isl_tab_undo *snap;
+
+ if (!tab || !tab_cone)
+ goto error;
+
+ snap = isl_tab_snap(tab);
+
+ isl_mat_free(tab->basis);
+ tab->basis = NULL;
+
+ isl_assert(tab->mat->ctx, tab->bmap, goto error);
+ isl_assert(tab->mat->ctx, tab->samples, goto error);
+ isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
+ isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error);
+
+ if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0)
+ goto error;
+
+ sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
+ if (!sample)
+ goto error;
+
+ isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size);
+
+ isl_vec_free(tab->bmap->sample);
+ tab->bmap->sample = isl_vec_copy(sample);
+
+ if (tab->n_unbounded == 0)
+ hull = isl_basic_set_from_vec(isl_vec_copy(sample));
+ else
+ hull = initial_hull(tab, isl_vec_copy(sample));
+
+ for (j = tab->n_outside + 1; j < tab->n_sample; ++j) {
+ isl_seq_cpy(sample->el, tab->samples->row[j], sample->size);
+ hull = affine_hull(hull,
+ isl_basic_set_from_vec(isl_vec_copy(sample)));
+ }
+
+ isl_vec_free(sample);
+
+ hull = extend_affine_hull(tab, hull, NULL);
+ if (!hull)
+ goto error;
+
+ if (tab->n_unbounded == 0) {
+ isl_basic_set_free(hull);
+ return tab;
+ }
+
+ if (isl_tab_rollback(tab, snap) < 0)
+ goto error;
+
+ if (hull->n_eq > tab->n_zero) {
+ for (j = 0; j < hull->n_eq; ++j) {
+ isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var);
+ if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
+ goto error;
+ }
+ }
+
+ isl_basic_set_free(hull);
+
+ return tab;
+error:
+ isl_basic_set_free(hull);
+ isl_tab_free(tab);
+ return NULL;
}
-/* Compute the affine hull of "bset", where "hull" is an initial approximation
- * with only a single point of "bset" and "cone" is the recession cone
+/* Compute the affine hull of "bset", where "cone" is the recession cone
* of "bset".
*
* We first compute a unimodular transformation that puts the unbounded
* [ y_1 ] [ y_1 ] [ Q_1 ]
* x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x
*
- * Let's call the input basic set S and the initial hull H.
- * We compute S' = preimage(S, U) and H' = preimage(H, U)
+ * Let's call the input basic set S. We compute S' = preimage(S, U)
* and drop the final dimensions including any constraints involving them.
- * This results in sets S'' and H''.
- * Then we extend H'' to the affine hull A'' of S''.
+ * This results in set S''.
+ * Then we compute the affine hull A'' of S''.
* Let F y_1 >= g be the constraint system of A''. In the transformed
* space the y_2 are unbounded, so we can add them back without any constraints,
* resulting in
* A = preimage(A'', Q_1).
*/
static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
- struct isl_basic_set *hull, struct isl_basic_set *cone)
+ struct isl_basic_set *cone)
{
unsigned total;
unsigned cone_dim;
+ struct isl_basic_set *hull;
struct isl_mat *M, *U, *Q;
- if (!bset || !hull || !cone)
+ if (!bset || !cone)
goto error;
total = isl_basic_set_total_dim(cone);
cone_dim = total - cone->n_eq;
- M = isl_mat_sub_alloc(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
+ M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
M = isl_mat_left_hermite(M, 0, &U, &Q);
if (!M)
goto error;
U = isl_mat_lin_to_aff(U);
bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
- hull = isl_basic_set_preimage(hull, U);
- bset = drop_constraints_involving(bset, total - cone_dim, cone_dim);
+ bset = isl_basic_set_drop_constraints_involving(bset, total - cone_dim,
+ cone_dim);
bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim);
- hull = drop_constraints_involving(hull, total - cone_dim, cone_dim);
- hull = isl_basic_set_drop_dims(hull, total - cone_dim, cone_dim);
Q = isl_mat_lin_to_aff(Q);
Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
- if (bset && bset->sample)
+ if (bset && bset->sample && bset->sample->size == 1 + total)
bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
- hull = extend_affine_hull(bset, hull);
+ hull = uset_affine_hull_bounded(bset);
- hull = isl_basic_set_preimage(hull, Q);
+ if (!hull) {
+ isl_mat_free(Q);
+ isl_mat_free(U);
+ } 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)
+ sample = isl_mat_vec_product(U, sample);
+ else
+ isl_mat_free(U);
+ hull = isl_basic_set_preimage(hull, Q);
+ if (hull) {
+ isl_vec_free(hull->sample);
+ hull->sample = sample;
+ } else
+ isl_vec_free(sample);
+ }
isl_basic_set_free(cone);
return hull;
error:
isl_basic_set_free(bset);
- isl_basic_set_free(hull);
isl_basic_set_free(cone);
return NULL;
}
*/
static struct isl_basic_set *uset_affine_hull(struct isl_basic_set *bset)
{
- struct isl_basic_set *hull = NULL;
- struct isl_vec *sample = NULL;
struct isl_basic_set *cone;
- if (isl_basic_set_is_empty(bset))
- return bset;
-
- sample = isl_basic_set_sample(isl_basic_set_copy(bset));
- if (!sample)
- goto error;
- if (sample->size == 0) {
- isl_vec_free(sample);
- hull = isl_basic_set_empty_like(bset);
- isl_basic_set_free(bset);
- return hull;
- }
- if (sample->size == 1) {
- isl_vec_free(sample);
+ if (isl_basic_set_plain_is_empty(bset))
return bset;
- }
cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
if (!cone)
goto error;
if (cone->n_eq == 0) {
+ struct isl_basic_set *hull;
isl_basic_set_free(cone);
- isl_vec_free(sample);
hull = isl_basic_set_universe_like(bset);
isl_basic_set_free(bset);
return hull;
}
- hull = isl_basic_set_from_vec(sample);
if (cone->n_eq < isl_basic_set_total_dim(cone))
- return affine_hull_with_cone(bset, hull, cone);
+ return affine_hull_with_cone(bset, cone);
isl_basic_set_free(cone);
- return extend_affine_hull(bset, hull);
+ return uset_affine_hull_bounded(bset);
error:
- isl_vec_free(sample);
isl_basic_set_free(bset);
- isl_basic_set_free(hull);
return NULL;
}
static struct isl_basic_set *equalities_in_underlying_set(
struct isl_basic_map *bmap)
{
+ struct isl_mat *T1 = NULL;
struct isl_mat *T2 = NULL;
struct isl_basic_set *bset = NULL;
struct isl_basic_set *hull = NULL;
bset = isl_basic_map_underlying_set(bmap);
- bset = isl_basic_set_remove_equalities(bset, NULL, &T2);
+ if (!bset)
+ return NULL;
+ if (bset->n_eq)
+ bset = isl_basic_set_remove_equalities(bset, &T1, &T2);
if (!bset)
goto error;
hull = uset_affine_hull(bset);
- if (T2)
+ if (!T2)
+ return hull;
+
+ if (!hull) {
+ isl_mat_free(T1);
+ isl_mat_free(T2);
+ } else {
+ struct isl_vec *sample = isl_vec_copy(hull->sample);
+ if (sample && sample->size > 0)
+ sample = isl_mat_vec_product(T1, sample);
+ else
+ isl_mat_free(T1);
hull = isl_basic_set_preimage(hull, T2);
+ if (hull) {
+ isl_vec_free(hull->sample);
+ hull->sample = sample;
+ } else
+ isl_vec_free(sample);
+ }
return hull;
error:
+ isl_mat_free(T1);
isl_mat_free(T2);
isl_basic_set_free(bset);
isl_basic_set_free(hull);
isl_basic_set_free(hull);
return isl_basic_map_set_to_empty(bmap);
}
- bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim), 0,
+ bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), 0,
hull->n_eq, 0);
for (i = 0; i < hull->n_eq; ++i) {
j = isl_basic_map_alloc_equality(bmap);
isl_seq_cpy(bmap->eq[j], hull->eq[i],
1 + isl_basic_set_total_dim(hull));
}
+ isl_vec_free(bmap->sample);
+ bmap->sample = isl_vec_copy(hull->sample);
isl_basic_set_free(hull);
ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES);
bmap = isl_basic_map_simplify(bmap);
return NULL;
}
-struct isl_map *isl_map_detect_equalities(struct isl_map *map)
+__isl_give isl_basic_set *isl_basic_set_detect_equalities(
+ __isl_take isl_basic_set *bset)
{
- struct isl_basic_map *bmap;
- int i;
-
- if (!map)
- return NULL;
+ return (isl_basic_set *)
+ isl_basic_map_detect_equalities((isl_basic_map *)bset);
+}
- for (i = 0; i < map->n; ++i) {
- bmap = isl_basic_map_copy(map->p[i]);
- bmap = isl_basic_map_detect_equalities(bmap);
- if (!bmap)
- goto error;
- isl_basic_map_free(map->p[i]);
- map->p[i] = bmap;
- }
+__isl_give isl_map *isl_map_detect_equalities(__isl_take isl_map *map)
+{
+ return isl_map_inline_foreach_basic_map(map,
+ &isl_basic_map_detect_equalities);
+}
- return map;
-error:
- isl_map_free(map);
- return NULL;
+__isl_give isl_set *isl_set_detect_equalities(__isl_take isl_set *set)
+{
+ return (isl_set *)isl_map_detect_equalities((isl_map *)set);
}
/* After computing the rational affine hull (by detecting the implicit
*/
struct isl_basic_map *isl_basic_map_affine_hull(struct isl_basic_map *bmap)
{
- struct isl_basic_set *hull = NULL;
-
bmap = isl_basic_map_detect_equalities(bmap);
bmap = isl_basic_map_cow(bmap);
- isl_basic_map_free_inequality(bmap, bmap->n_ineq);
+ if (bmap)
+ isl_basic_map_free_inequality(bmap, bmap->n_ineq);
+ bmap = isl_basic_map_finalize(bmap);
return bmap;
}
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)
return NULL;
return hull;
}
- map = isl_map_detect_equalities(map);
- map = isl_map_align_divs(map);
- if (!map)
- return NULL;
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);
projects / platform / upstream / isl.git / blobdiff