+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * 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
+ */
+
#include "isl_ctx.h"
#include "isl_seq.h"
#include "isl_set.h"
return bmap;
tab = isl_tab_from_basic_map(bmap);
- tab = isl_tab_detect_implicit_equalities(tab);
+ 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;
}
-/* 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;
+}
+
+/* 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.
*/
-static struct isl_basic_set *extend_affine_hull(struct isl_basic_set *bset,
+static struct isl_basic_set *extend_affine_hull(struct isl_tab *tab,
struct isl_basic_set *hull)
{
- 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;
+ 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;
}
{
struct isl_vec *sample = NULL;
struct isl_basic_set *hull;
+ struct isl_tab *tab = NULL;
+ unsigned dim;
- if (isl_basic_set_is_empty(bset))
+ if (isl_basic_set_fast_is_empty(bset))
return bset;
- sample = isl_basic_set_sample_vec(isl_basic_set_copy(bset));
- if (!sample)
+ 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);
+ if (!tab)
goto error;
- if (sample->size == 0) {
- struct isl_basic_set *hull;
+ if (tab->empty) {
+ isl_tab_free(tab);
isl_vec_free(sample);
- hull = isl_basic_set_empty_like(bset);
- isl_basic_set_free(bset);
- return hull;
+ return isl_basic_set_set_to_empty(bset);
+ }
+ if (isl_tab_track_bset(tab, isl_basic_set_copy(bset)) < 0)
+ goto error;
+
+ 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->size == 1) {
+
+ if (!sample)
+ goto error;
+ if (sample->size == 0) {
+ isl_tab_free(tab);
isl_vec_free(sample);
- return bset;
+ return isl_basic_set_set_to_empty(bset);
}
hull = isl_basic_set_from_vec(sample);
- return extend_affine_hull(bset, hull);
+ isl_basic_set_free(bset);
+ hull = extend_affine_hull(tab, hull);
+ 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 intial 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 eqaulities 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;
+ 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);
+ 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_tab_free(tab);
return NULL;
}
else
isl_mat_free(U);
hull = isl_basic_set_preimage(hull, Q);
- isl_vec_free(hull->sample);
- hull->sample = sample;
+ if (hull) {
+ isl_vec_free(hull->sample);
+ hull->sample = sample;
+ } else
+ isl_vec_free(sample);
}
isl_basic_set_free(cone);
if (!T2)
return hull;
- if (!hull)
+ if (!hull) {
isl_mat_free(T1);
- else {
+ 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);
- isl_vec_free(hull->sample);
- hull->sample = sample;
+ if (hull) {
+ isl_vec_free(hull->sample);
+ hull->sample = sample;
+ } else
+ isl_vec_free(sample);
}
return hull;
{
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);
return bmap;
}
struct isl_basic_map *hull = NULL;
struct isl_set *set;
+ map = isl_map_detect_equalities(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);