#include "isl_seq.h"
#include "isl_equalities.h"
-static struct isl_basic_set *uset_convex_hull(struct isl_set *set);
+static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set);
static swap_ineq(struct isl_basic_map *bmap, unsigned i, unsigned j)
{
isl_basic_map_convex_hull((struct isl_basic_map *)bset);
}
-/* Check if "c" is a direction with a lower bound in "set" that is independent
- * of the previously found "n" bounds in "dirs".
- * If so, add it to the list, with the negative of the lower bound
- * in the constant position, i.e., such that c correspond to a bounding
- * hyperplane (but not necessarily a facet).
- */
-static int is_independent_bound(struct isl_ctx *ctx,
- struct isl_set *set, isl_int *c,
- struct isl_mat *dirs, int n)
+static int uset_is_bound(struct isl_ctx *ctx, struct isl_set *set,
+ isl_int *c, unsigned len)
{
int first;
- int i = 0, j;
+ int j;
isl_int opt;
isl_int opt_denom;
- isl_seq_cpy(dirs->row[n]+1, c+1, dirs->n_col-1);
- if (n != 0) {
- int pos = isl_seq_first_non_zero(dirs->row[n]+1, dirs->n_col-1);
- if (pos < 0)
- return 0;
- for (i = 0; i < n; ++i) {
- int pos_i;
- pos_i = isl_seq_first_non_zero(dirs->row[i]+1, dirs->n_col-1);
- if (pos_i < pos)
- continue;
- if (pos_i > pos)
- break;
- isl_seq_elim(dirs->row[n]+1, dirs->row[i]+1, pos,
- dirs->n_col-1, NULL);
- pos = isl_seq_first_non_zero(dirs->row[n]+1, dirs->n_col-1);
- if (pos < 0)
- return 0;
- }
- }
-
isl_int_init(opt);
isl_int_init(opt_denom);
first = 1;
for (j = 0; j < set->n; ++j) {
enum isl_lp_result res;
- if (F_ISSET(set->p[j], ISL_BASIC_MAP_EMPTY))
+ if (F_ISSET(set->p[j], ISL_BASIC_SET_EMPTY))
continue;
res = isl_solve_lp((struct isl_basic_map*)set->p[j],
- 0, dirs->row[n]+1, ctx->one, &opt, &opt_denom);
+ 0, c+1, ctx->one, &opt, &opt_denom);
if (res == isl_lp_unbounded)
break;
if (res == isl_lp_error)
continue;
}
if (!isl_int_is_one(opt_denom))
- isl_seq_scale(dirs->row[n], dirs->row[n], opt_denom,
- dirs->n_col);
- if (first || isl_int_lt(opt, dirs->row[n][0]))
- isl_int_set(dirs->row[n][0], opt);
+ isl_seq_scale(c, c, opt_denom, len);
+ if (first || isl_int_lt(opt, c[0]))
+ isl_int_set(c[0], opt);
first = 0;
}
isl_int_clear(opt);
isl_int_clear(opt_denom);
- if (j < set->n)
- return 0;
- isl_int_neg(dirs->row[n][0], dirs->row[n][0]);
+ isl_int_neg(c[0], c[0]);
+ return j >= set->n;
+error:
+ isl_int_clear(opt);
+ isl_int_clear(opt_denom);
+ return -1;
+}
+
+/* Check if "c" is a direction with both a lower bound and an upper
+ * bound in "set" that is independent of the previously found "n"
+ * bounds in "dirs".
+ * If so, add it to the list, with the negative of the lower bound
+ * in the constant position, i.e., such that c corresponds to a bounding
+ * hyperplane (but not necessarily a facet).
+ */
+static int is_independent_bound(struct isl_ctx *ctx,
+ struct isl_set *set, isl_int *c,
+ struct isl_mat *dirs, int n)
+{
+ int is_bound;
+ int i = 0;
+
+ isl_seq_cpy(dirs->row[n]+1, c+1, dirs->n_col-1);
+ if (n != 0) {
+ int pos = isl_seq_first_non_zero(dirs->row[n]+1, dirs->n_col-1);
+ if (pos < 0)
+ return 0;
+ for (i = 0; i < n; ++i) {
+ int pos_i;
+ pos_i = isl_seq_first_non_zero(dirs->row[i]+1, dirs->n_col-1);
+ if (pos_i < pos)
+ continue;
+ if (pos_i > pos)
+ break;
+ isl_seq_elim(dirs->row[n]+1, dirs->row[i]+1, pos,
+ dirs->n_col-1, NULL);
+ pos = isl_seq_first_non_zero(dirs->row[n]+1, dirs->n_col-1);
+ if (pos < 0)
+ return 0;
+ }
+ }
+
+ isl_seq_neg(dirs->row[n] + 1, dirs->row[n] + 1, dirs->n_col - 1);
+ is_bound = uset_is_bound(ctx, set, dirs->row[n], dirs->n_col);
+ isl_seq_neg(dirs->row[n] + 1, dirs->row[n] + 1, dirs->n_col - 1);
+ if (is_bound != 1)
+ return is_bound;
+ is_bound = uset_is_bound(ctx, set, dirs->row[n], dirs->n_col);
+ if (is_bound != 1)
+ return is_bound;
if (i < n) {
int k;
isl_int *t = dirs->row[n];
dirs->row[i] = t;
}
return 1;
-error:
- isl_int_clear(opt);
- isl_int_clear(opt_denom);
- return -1;
}
/* Compute and return a maximal set of linearly independent bounds
dirs, n);
if (f < 0)
goto error;
- if (f) {
- ++n;
- continue;
- }
- isl_seq_neg(bset->eq[j], bset->eq[j], 1+set->dim);
- f = is_independent_bound(ctx, set, bset->eq[j],
- dirs, n);
- isl_seq_neg(bset->eq[j], bset->eq[j], 1+set->dim);
- if (f < 0)
- goto error;
if (f)
++n;
}
F_SET(bset, ISL_BASIC_MAP_RATIONAL);
- return bset;
+ return isl_basic_set_finalize(bset);
}
static struct isl_set *isl_set_set_rational(struct isl_set *set)
*
* x_1 >= 0
*
- * I.e., the facet is
+ * I.e., the facet lies in
*
* x_1 = 0
*
* A_i [ x_i ] >= 0
*
* the constraints of each (transformed) basic set.
- * If a = n/d, then the consstraint defining the new facet (in the transformed
+ * If a = n/d, then the constraint defining the new facet (in the transformed
* space) is
*
* -n x_1 + d x_2 >= 0
*
* In the original space, we need to take the same combination of the
* corresponding constraints "facet" and "ridge".
+ *
+ * If a = -infty = "-1/0", then we just return the original facet constraint.
+ * This means that the facet is unbounded, but has a bounded intersection
+ * with the union of sets.
*/
static isl_int *wrap_facet(struct isl_ctx *ctx, struct isl_set *set,
isl_int *facet, isl_int *ridge)
isl_vec_free(ctx, obj);
isl_basic_set_free(lp);
isl_set_free(set);
- isl_assert(ctx, res == isl_lp_ok, return NULL);
+ isl_assert(ctx, res == isl_lp_ok || res == isl_lp_unbounded,
+ return NULL);
return facet;
error:
isl_basic_set_free(lp);
U = isl_mat_drop_cols(ctx, U, 1, 1);
Q = isl_mat_drop_rows(ctx, Q, 1, 1);
set = isl_set_preimage(ctx, set, U);
- facet = uset_convex_hull(set);
+ facet = uset_convex_hull_wrap(set);
facet = isl_basic_set_preimage(ctx, facet, Q);
return facet;
error:
return isl_set_remove_dims(set, set->dim - n, n);
}
-/* If the number of linearly independent bounds we found is smaller
- * than the dimension, then the convex hull will have a lineality space,
- * so we may as well project out this lineality space.
- * We first transform the set such that the first variables correspond
- * to the directions of the linearly independent bounds and then
- * project out the remaining variables.
+static struct isl_basic_set *convex_hull_0d(struct isl_set *set)
+{
+ struct isl_basic_set *convex_hull;
+
+ if (!set)
+ return NULL;
+
+ if (isl_set_is_empty(set))
+ convex_hull = isl_basic_set_empty(set->ctx, 0, 0);
+ else
+ convex_hull = isl_basic_set_universe(set->ctx, 0, 0);
+ isl_set_free(set);
+ return convex_hull;
+}
+
+/* Compute the convex hull of a pair of basic sets without any parameters or
+ * integer divisions using Fourier-Motzkin elimination.
+ * The convex hull is the set of all points that can be written as
+ * the sum of points from both basic sets (in homogeneous coordinates).
+ * We set up the constraints in a space with dimensions for each of
+ * the three sets and then project out the dimensions corresponding
+ * to the two original basic sets, retaining only those corresponding
+ * to the convex hull.
*/
-static struct isl_basic_set *modulo_lineality(struct isl_ctx *ctx,
- struct isl_set *set, struct isl_mat *bounds)
+static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1,
+ struct isl_basic_set *bset2)
{
- int i, j;
- unsigned old_dim, new_dim;
- struct isl_mat *H = NULL, *U = NULL, *Q = NULL;
- struct isl_basic_set *hull;
+ int i, j, k;
+ struct isl_basic_set *bset[2];
+ struct isl_basic_set *hull = NULL;
+ unsigned dim;
- old_dim = set->dim;
- new_dim = bounds->n_row;
- H = isl_mat_sub_alloc(ctx, bounds->row, 0, bounds->n_row, 1, set->dim);
- H = isl_mat_left_hermite(ctx, H, 0, &U, &Q);
- if (!H)
+ if (!bset1 || !bset2)
goto error;
- U = isl_mat_lin_to_aff(ctx, U);
- Q = isl_mat_lin_to_aff(ctx, Q);
- Q->n_row = 1 + new_dim;
- isl_mat_free(ctx, H);
- set = isl_set_preimage(ctx, set, U);
- set = set_project_out(ctx, set, old_dim - new_dim);
- hull = uset_convex_hull(set);
- hull = isl_basic_set_preimage(ctx, hull, Q);
- isl_mat_free(ctx, bounds);
+
+ dim = bset1->dim;
+ hull = isl_basic_set_alloc(bset1->ctx, 0, 2 + 3 * bset1->dim, 0,
+ 1 + bset1->dim + bset1->n_eq + bset2->n_eq,
+ 2 + bset1->n_ineq + bset2->n_ineq);
+ bset[0] = bset1;
+ bset[1] = bset2;
+ for (i = 0; i < 2; ++i) {
+ for (j = 0; j < bset[i]->n_eq; ++j) {
+ k = isl_basic_set_alloc_equality(hull);
+ if (k < 0)
+ goto error;
+ isl_seq_clr(hull->eq[k], (i+1) * (1+dim));
+ isl_seq_clr(hull->eq[k]+(i+2)*(1+dim), (1-i)*(1+dim));
+ isl_seq_cpy(hull->eq[k]+(i+1)*(1+dim), bset[i]->eq[j],
+ 1+dim);
+ }
+ for (j = 0; j < bset[i]->n_ineq; ++j) {
+ k = isl_basic_set_alloc_inequality(hull);
+ if (k < 0)
+ goto error;
+ isl_seq_clr(hull->ineq[k], (i+1) * (1+dim));
+ isl_seq_clr(hull->ineq[k]+(i+2)*(1+dim), (1-i)*(1+dim));
+ isl_seq_cpy(hull->ineq[k]+(i+1)*(1+dim),
+ bset[i]->ineq[j], 1+dim);
+ }
+ k = isl_basic_set_alloc_inequality(hull);
+ if (k < 0)
+ goto error;
+ isl_seq_clr(hull->ineq[k], 1+hull->dim);
+ isl_int_set_si(hull->ineq[k][(i+1)*(1+dim)], 1);
+ }
+ for (j = 0; j < 1+dim; ++j) {
+ k = isl_basic_set_alloc_equality(hull);
+ if (k < 0)
+ goto error;
+ isl_seq_clr(hull->eq[k], 1+hull->dim);
+ isl_int_set_si(hull->eq[k][j], -1);
+ isl_int_set_si(hull->eq[k][1+dim+j], 1);
+ isl_int_set_si(hull->eq[k][2*(1+dim)+j], 1);
+ }
+ hull = isl_basic_set_set_rational(hull);
+ hull = isl_basic_set_remove_dims(hull, dim, 2*(1+dim));
+ hull = isl_basic_set_convex_hull(hull);
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
return hull;
error:
- isl_mat_free(ctx, bounds);
- isl_mat_free(ctx, Q);
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ isl_basic_set_free(hull);
+ return NULL;
+}
+
+/* Compute the convex hull of a set without any parameters or
+ * integer divisions using Fourier-Motzkin elimination.
+ * In each step, we combined two basic sets until only one
+ * basic set is left.
+ */
+static struct isl_basic_set *uset_convex_hull_elim(struct isl_set *set)
+{
+ struct isl_basic_set *convex_hull = NULL;
+
+ convex_hull = isl_set_copy_basic_set(set);
+ set = isl_set_drop_basic_set(set, convex_hull);
+ if (!set)
+ goto error;
+ while (set->n > 0) {
+ struct isl_basic_set *t;
+ t = isl_set_copy_basic_set(set);
+ if (!t)
+ goto error;
+ set = isl_set_drop_basic_set(set, t);
+ if (!set)
+ goto error;
+ convex_hull = convex_hull_pair(convex_hull, t);
+ }
+ isl_set_free(set);
+ return convex_hull;
+error:
+ isl_set_free(set);
+ isl_basic_set_free(convex_hull);
+ return NULL;
+}
+
+static struct isl_basic_set *uset_convex_hull_wrap_with_bounds(
+ struct isl_set *set, struct isl_mat *bounds)
+{
+ struct isl_basic_set *convex_hull = NULL;
+
+ isl_assert(set->ctx, bounds->n_row == set->dim, goto error);
+ bounds = initial_facet_constraint(set->ctx, set, bounds);
+ if (!bounds)
+ goto error;
+ convex_hull = extend(set->ctx, set, bounds);
+ isl_mat_free(set->ctx, bounds);
+ isl_set_free(set);
+
+ return convex_hull;
+error:
+ isl_set_free(set);
+ return NULL;
+}
+
+/* Compute the convex hull of a set without any parameters or
+ * integer divisions. Depending on whether the set is bounded,
+ * we pass control to the wrapping based convex hull or
+ * the Fourier-Motzkin elimination based convex hull.
+ * We also handle a few special cases before checking the boundedness.
+ */
+static struct isl_basic_set *uset_convex_hull(struct isl_set *set)
+{
+ int i;
+ struct isl_basic_set *convex_hull = NULL;
+ struct isl_mat *bounds;
+
+ if (set->dim == 0)
+ return convex_hull_0d(set);
+
+ set = isl_set_set_rational(set);
+
+ if (!set)
+ goto error;
+ for (i = 0; i < set->n; ++i) {
+ set->p[i] = isl_basic_set_convex_hull(set->p[i]);
+ if (!set->p[i])
+ goto error;
+ }
+ set = isl_set_remove_empty_parts(set);
+ if (!set)
+ return NULL;
+ if (set->n == 0) {
+ convex_hull = isl_basic_set_empty(set->ctx, 0, 0);
+ isl_set_free(set);
+ return convex_hull;
+ }
+ if (set->n == 1) {
+ convex_hull = isl_basic_set_copy(set->p[0]);
+ isl_set_free(set);
+ return convex_hull;
+ }
+ if (set->dim == 1)
+ return convex_hull_1d(set->ctx, set);
+
+ bounds = independent_bounds(set->ctx, set);
+ if (!bounds)
+ goto error;
+ if (bounds->n_row == set->dim)
+ return uset_convex_hull_wrap_with_bounds(set, bounds);
+ isl_mat_free(set->ctx, bounds);
+
+ return uset_convex_hull_elim(set);
+error:
isl_set_free(set);
+ isl_basic_set_free(convex_hull);
return NULL;
}
* without parameters or divs and where the convex hull of set is
* known to be full-dimensional.
*/
-static struct isl_basic_set *uset_convex_hull(struct isl_set *set)
+static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set)
{
int i;
struct isl_basic_set *convex_hull = NULL;
bounds = independent_bounds(set->ctx, set);
if (!bounds)
goto error;
- if (bounds->n_row < set->dim)
- return modulo_lineality(set->ctx, set, bounds);
- bounds = initial_facet_constraint(set->ctx, set, bounds);
- if (!bounds)
- goto error;
- convex_hull = extend(set->ctx, set, bounds);
- isl_mat_free(set->ctx, bounds);
- isl_set_free(set);
-
- return convex_hull;
+ return uset_convex_hull_wrap_with_bounds(set, bounds);
error:
isl_set_free(set);
return NULL;
projects / platform / upstream / isl.git / commitdiff