if (i < total)
return 0;
- res = isl_solve_lp(*bmap, 0, c, (*bmap)->ctx->one, opt_n, opt_d);
+ res = isl_basic_map_solve_lp(*bmap, 0, c, (*bmap)->ctx->one,
+ opt_n, opt_d, NULL);
if (res == isl_lp_unbounded)
return 0;
if (res == isl_lp_error)
return bmap;
tab = isl_tab_from_basic_map(bmap);
- tab = isl_tab_detect_equalities(bmap->ctx, tab);
- tab = isl_tab_detect_redundant(bmap->ctx, tab);
+ tab = isl_tab_detect_equalities(tab);
+ tab = isl_tab_detect_redundant(tab);
bmap = isl_basic_map_update_from_tab(bmap, tab);
- isl_tab_free(bmap->ctx, tab);
+ isl_tab_free(tab);
ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
ISL_F_SET(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
return bmap;
* constraint c and if so, set the constant term such that the
* resulting constraint is a bounding constraint for the set.
*/
-static int uset_is_bound(struct isl_ctx *ctx, struct isl_set *set,
- isl_int *c, unsigned len)
+static int uset_is_bound(struct isl_set *set, isl_int *c, unsigned len)
{
int first;
int j;
if (ISL_F_ISSET(set->p[j], ISL_BASIC_SET_EMPTY))
continue;
- res = isl_solve_lp((struct isl_basic_map*)set->p[j],
- 0, c, ctx->one, &opt, &opt_denom);
+ res = isl_basic_set_solve_lp(set->p[j],
+ 0, c, set->ctx->one, &opt, &opt_denom, NULL);
if (res == isl_lp_unbounded)
break;
if (res == isl_lp_error)
* hyperplane (but not necessarily a facet).
* Assumes set "set" is bounded.
*/
-static int is_independent_bound(struct isl_ctx *ctx,
- struct isl_set *set, isl_int *c,
+static int is_independent_bound(struct isl_set *set, isl_int *c,
struct isl_mat *dirs, int n)
{
int is_bound;
}
}
- is_bound = uset_is_bound(ctx, set, dirs->row[n], dirs->n_col);
+ is_bound = uset_is_bound(set, dirs->row[n], dirs->n_col);
if (is_bound != 1)
return is_bound;
if (i < n) {
* on the set "set", based on the constraints of the basic sets
* in "set".
*/
-static struct isl_mat *independent_bounds(struct isl_ctx *ctx,
- struct isl_set *set)
+static struct isl_mat *independent_bounds(struct isl_set *set)
{
int i, j, n;
struct isl_mat *dirs = NULL;
unsigned dim = isl_set_n_dim(set);
- dirs = isl_mat_alloc(ctx, dim, 1+dim);
+ dirs = isl_mat_alloc(set->ctx, dim, 1+dim);
if (!dirs)
goto error;
struct isl_basic_set *bset = set->p[i];
for (j = 0; n < dim && j < bset->n_eq; ++j) {
- f = is_independent_bound(ctx, set, bset->eq[j],
- dirs, n);
+ f = is_independent_bound(set, bset->eq[j], dirs, n);
if (f < 0)
goto error;
if (f)
++n;
}
for (j = 0; n < dim && j < bset->n_ineq; ++j) {
- f = is_independent_bound(ctx, set, bset->ineq[j],
- dirs, n);
+ f = is_independent_bound(set, bset->ineq[j], dirs, n);
if (f < 0)
goto error;
if (f)
dirs->n_row = n;
return dirs;
error:
- isl_mat_free(ctx, dirs);
+ isl_mat_free(dirs);
return NULL;
}
-static struct isl_basic_set *isl_basic_set_set_rational(
- struct isl_basic_set *bset)
+struct isl_basic_set *isl_basic_set_set_rational(struct isl_basic_set *bset)
{
if (!bset)
return NULL;
return NULL;
}
-static struct isl_basic_set *isl_basic_set_add_equality(struct isl_ctx *ctx,
+static struct isl_basic_set *isl_basic_set_add_equality(
struct isl_basic_set *bset, isl_int *c)
{
int i;
isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
isl_assert(ctx, bset->n_div == 0, goto error);
dim = isl_basic_set_n_dim(bset);
+ bset = isl_basic_set_cow(bset);
bset = isl_basic_set_extend(bset, 0, dim, 0, 1, 0);
i = isl_basic_set_alloc_equality(bset);
if (i < 0)
return NULL;
}
-static struct isl_set *isl_set_add_equality(struct isl_ctx *ctx,
- struct isl_set *set, isl_int *c)
+static struct isl_set *isl_set_add_equality(struct isl_set *set, isl_int *c)
{
int i;
if (!set)
return NULL;
for (i = 0; i < set->n; ++i) {
- set->p[i] = isl_basic_set_add_equality(ctx, set->p[i], c);
+ set->p[i] = isl_basic_set_add_equality(set->p[i], c);
if (!set->p[i])
goto error;
}
* [ 1 ]
* A_i [ x ] >= 0
*
- * then the resulting set is of dimension n*(1+d) and has as contraints
+ * then the resulting set is of dimension n*(1+d) and has as constraints
*
* [ a_i ]
* A_i [ x_i ] >= 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.
+ * Note that a is always finite, since we only apply the wrapping
+ * technique to a union of polytopes.
*/
static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
{
isl_seq_clr(T->row[0]+1, dim - 1);
isl_seq_cpy(T->row[1], facet, dim);
isl_seq_cpy(T->row[2], ridge, dim);
- T = isl_mat_right_inverse(set->ctx, T);
+ T = isl_mat_right_inverse(T);
set = isl_set_preimage(set, T);
T = NULL;
if (!set)
}
isl_int_init(num);
isl_int_init(den);
- res = isl_solve_lp((struct isl_basic_map *)lp, 0,
- obj->block.data, set->ctx->one, &num, &den);
+ res = isl_basic_set_solve_lp(lp, 0,
+ obj->block.data, set->ctx->one, &num, &den, NULL);
if (res == isl_lp_ok) {
isl_int_neg(num, num);
isl_seq_combine(facet, num, facet, den, ridge, dim);
}
isl_int_clear(num);
isl_int_clear(den);
- isl_vec_free(set->ctx, obj);
+ isl_vec_free(obj);
isl_basic_set_free(lp);
isl_set_free(set);
- isl_assert(set->ctx, res == isl_lp_ok || res == isl_lp_unbounded,
- return NULL);
+ isl_assert(set->ctx, res == isl_lp_ok, return NULL);
return facet;
error:
isl_basic_set_free(lp);
- isl_mat_free(set->ctx, T);
+ isl_mat_free(T);
isl_set_free(set);
return NULL;
}
* The resulting linear combination of the bounding constraints will
* correspond to a facet of the convex hull.
*/
-static struct isl_mat *initial_facet_constraint(struct isl_ctx *ctx,
- struct isl_set *set, struct isl_mat *bounds)
+static struct isl_mat *initial_facet_constraint(struct isl_set *set,
+ struct isl_mat *bounds)
{
struct isl_set *slice = NULL;
struct isl_basic_set *face = NULL;
while (bounds->n_row > 1) {
slice = isl_set_copy(set);
- slice = isl_set_add_equality(ctx, slice, bounds->row[0]);
+ slice = isl_set_add_equality(slice, bounds->row[0]);
face = isl_set_affine_hull(slice);
if (!face)
goto error;
isl_basic_set_free(face);
break;
}
- m = isl_mat_alloc(ctx, 1 + face->n_eq, 1 + dim);
+ m = isl_mat_alloc(set->ctx, 1 + face->n_eq, 1 + dim);
if (!m)
goto error;
isl_int_set_si(m->row[0][0], 1);
isl_seq_clr(m->row[0]+1, dim);
for (i = 0; i < face->n_eq; ++i)
isl_seq_cpy(m->row[1 + i], face->eq[i], 1 + dim);
- U = isl_mat_right_inverse(ctx, m);
- Q = isl_mat_right_inverse(ctx, isl_mat_copy(ctx, U));
- U = isl_mat_drop_cols(ctx, U, 1 + face->n_eq,
- dim - face->n_eq);
- Q = isl_mat_drop_rows(ctx, Q, 1 + face->n_eq,
- dim - face->n_eq);
- U = isl_mat_drop_cols(ctx, U, 0, 1);
- Q = isl_mat_drop_rows(ctx, Q, 0, 1);
- bounds = isl_mat_product(ctx, bounds, U);
- bounds = isl_mat_product(ctx, bounds, Q);
+ U = isl_mat_right_inverse(m);
+ Q = isl_mat_right_inverse(isl_mat_copy(U));
+ U = isl_mat_drop_cols(U, 1 + face->n_eq, dim - face->n_eq);
+ Q = isl_mat_drop_rows(Q, 1 + face->n_eq, dim - face->n_eq);
+ U = isl_mat_drop_cols(U, 0, 1);
+ Q = isl_mat_drop_rows(Q, 0, 1);
+ bounds = isl_mat_product(bounds, U);
+ bounds = isl_mat_product(bounds, Q);
while (isl_seq_first_non_zero(bounds->row[bounds->n_row-1],
bounds->n_col) == -1) {
bounds->n_row--;
return bounds;
error:
isl_basic_set_free(face);
- isl_mat_free(ctx, bounds);
+ isl_mat_free(bounds);
return NULL;
}
isl_int_set_si(m->row[0][0], 1);
isl_seq_clr(m->row[0]+1, dim);
isl_seq_cpy(m->row[1], c, 1+dim);
- U = isl_mat_right_inverse(set->ctx, m);
- Q = isl_mat_right_inverse(set->ctx, isl_mat_copy(set->ctx, U));
- U = isl_mat_drop_cols(set->ctx, U, 1, 1);
- Q = isl_mat_drop_rows(set->ctx, Q, 1, 1);
+ U = isl_mat_right_inverse(m);
+ Q = isl_mat_right_inverse(isl_mat_copy(U));
+ U = isl_mat_drop_cols(U, 1, 1);
+ Q = isl_mat_drop_rows(Q, 1, 1);
set = isl_set_preimage(set, U);
facet = uset_convex_hull_wrap_bounded(set);
facet = isl_basic_set_preimage(facet, Q);
for (i = 0; i < hull->n_ineq; ++i) {
facet = compute_facet(set, hull->ineq[i]);
- facet = isl_basic_set_add_equality(facet->ctx, facet, hull->ineq[i]);
+ facet = isl_basic_set_add_equality(facet, hull->ineq[i]);
facet = isl_basic_set_gauss(facet, NULL);
facet = isl_basic_set_normalize_constraints(facet);
hull_facet = isl_basic_set_copy(hull);
- hull_facet = isl_basic_set_add_equality(hull_facet->ctx, hull_facet, hull->ineq[i]);
+ hull_facet = isl_basic_set_add_equality(hull_facet, hull->ineq[i]);
hull_facet = isl_basic_set_gauss(hull_facet, NULL);
hull_facet = isl_basic_set_normalize_constraints(hull_facet);
if (!facet)
goto error;
- if (facet->n_ineq + hull->n_ineq > hull->c_size)
- hull = isl_basic_set_extend_dim(hull,
- isl_dim_copy(hull->dim), 0, 0, facet->n_ineq);
+ hull = isl_basic_set_cow(hull);
+ hull = isl_basic_set_extend_dim(hull,
+ isl_dim_copy(hull->dim), 0, 0, facet->n_ineq);
for (j = 0; j < facet->n_ineq; ++j) {
for (f = 0; f < hull_facet->n_ineq; ++f)
if (isl_seq_eq(facet->ineq[j],
* We simply collect the lower and upper bounds of each basic set
* and the biggest of those.
*/
-static struct isl_basic_set *convex_hull_1d(struct isl_ctx *ctx,
- struct isl_set *set)
+static struct isl_basic_set *convex_hull_1d(struct isl_set *set)
{
struct isl_mat *c = NULL;
isl_int *lower = NULL;
set = isl_set_remove_empty_parts(set);
if (!set)
goto error;
- isl_assert(ctx, set->n > 0, goto error);
- c = isl_mat_alloc(ctx, 2, 2);
+ isl_assert(set->ctx, set->n > 0, goto error);
+ c = isl_mat_alloc(set->ctx, 2, 2);
if (!c)
goto error;
if (set->p[0]->n_eq > 0) {
- isl_assert(ctx, set->p[0]->n_eq == 1, goto error);
+ isl_assert(set->ctx, set->p[0]->n_eq == 1, goto error);
lower = c->row[0];
upper = c->row[1];
if (isl_int_is_pos(set->p[0]->eq[0][1])) {
isl_int_clear(a);
isl_int_clear(b);
- hull = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
+ hull = isl_basic_set_alloc(set->ctx, 0, 1, 0, 0, 2);
hull = isl_basic_set_set_rational(hull);
if (!hull)
goto error;
}
hull = isl_basic_set_finalize(hull);
isl_set_free(set);
- isl_mat_free(ctx, c);
+ isl_mat_free(c);
return hull;
error:
isl_set_free(set);
- isl_mat_free(ctx, c);
+ isl_mat_free(c);
return NULL;
}
* to the two original basic sets, retaining only those corresponding
* to the convex hull.
*/
-static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1,
+static struct isl_basic_set *convex_hull_pair_elim(struct isl_basic_set *bset1,
struct isl_basic_set *bset2)
{
int i, j, k;
return NULL;
}
+static int isl_basic_set_is_bounded(struct isl_basic_set *bset)
+{
+ struct isl_tab *tab;
+ int bounded;
+
+ tab = isl_tab_from_recession_cone((struct isl_basic_map *)bset);
+ bounded = isl_tab_cone_is_bounded(tab);
+ isl_tab_free(tab);
+ return bounded;
+}
+
+static int isl_set_is_bounded(struct isl_set *set)
+{
+ int i;
+
+ for (i = 0; i < set->n; ++i) {
+ int bounded = isl_basic_set_is_bounded(set->p[i]);
+ if (!bounded || bounded < 0)
+ return bounded;
+ }
+ return 1;
+}
+
+/* Compute the lineality space of the convex hull of bset1 and bset2.
+ *
+ * We first compute the intersection of the recession cone of bset1
+ * with the negative of the recession cone of bset2 and then compute
+ * the linear hull of the resulting cone.
+ */
+static struct isl_basic_set *induced_lineality_space(
+ struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+{
+ int i, k;
+ struct isl_basic_set *lin = NULL;
+ unsigned dim;
+
+ if (!bset1 || !bset2)
+ goto error;
+
+ dim = isl_basic_set_total_dim(bset1);
+ lin = isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset1), 0,
+ bset1->n_eq + bset2->n_eq,
+ bset1->n_ineq + bset2->n_ineq);
+ lin = isl_basic_set_set_rational(lin);
+ if (!lin)
+ goto error;
+ for (i = 0; i < bset1->n_eq; ++i) {
+ k = isl_basic_set_alloc_equality(lin);
+ if (k < 0)
+ goto error;
+ isl_int_set_si(lin->eq[k][0], 0);
+ isl_seq_cpy(lin->eq[k] + 1, bset1->eq[i] + 1, dim);
+ }
+ for (i = 0; i < bset1->n_ineq; ++i) {
+ k = isl_basic_set_alloc_inequality(lin);
+ if (k < 0)
+ goto error;
+ isl_int_set_si(lin->ineq[k][0], 0);
+ isl_seq_cpy(lin->ineq[k] + 1, bset1->ineq[i] + 1, dim);
+ }
+ for (i = 0; i < bset2->n_eq; ++i) {
+ k = isl_basic_set_alloc_equality(lin);
+ if (k < 0)
+ goto error;
+ isl_int_set_si(lin->eq[k][0], 0);
+ isl_seq_neg(lin->eq[k] + 1, bset2->eq[i] + 1, dim);
+ }
+ for (i = 0; i < bset2->n_ineq; ++i) {
+ k = isl_basic_set_alloc_inequality(lin);
+ if (k < 0)
+ goto error;
+ isl_int_set_si(lin->ineq[k][0], 0);
+ isl_seq_neg(lin->ineq[k] + 1, bset2->ineq[i] + 1, dim);
+ }
+
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return isl_basic_set_affine_hull(lin);
+error:
+ isl_basic_set_free(lin);
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return NULL;
+}
+
+static struct isl_basic_set *uset_convex_hull(struct isl_set *set);
+
+/* Given a set and a linear space "lin" of dimension n > 0,
+ * project the linear space from the set, compute the convex hull
+ * and then map the set back to the original space.
+ *
+ * Let
+ *
+ * M x = 0
+ *
+ * describe the linear space. We first compute the Hermite normal
+ * form H = M U of M = H Q, to obtain
+ *
+ * H Q x = 0
+ *
+ * The last n rows of H will be zero, so the last n variables of x' = Q x
+ * are the one we want to project out. We do this by transforming each
+ * basic set A x >= b to A U x' >= b and then removing the last n dimensions.
+ * After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
+ * we transform the hull back to the original space as A' Q_1 x >= b',
+ * with Q_1 all but the last n rows of Q.
+ */
+static struct isl_basic_set *modulo_lineality(struct isl_set *set,
+ struct isl_basic_set *lin)
+{
+ unsigned total = isl_basic_set_total_dim(lin);
+ unsigned lin_dim;
+ struct isl_basic_set *hull;
+ struct isl_mat *M, *U, *Q;
+
+ if (!set || !lin)
+ goto error;
+ lin_dim = total - lin->n_eq;
+ M = isl_mat_sub_alloc(set->ctx, lin->eq, 0, lin->n_eq, 1, total);
+ M = isl_mat_left_hermite(M, 0, &U, &Q);
+ if (!M)
+ goto error;
+ isl_mat_free(M);
+ isl_basic_set_free(lin);
+
+ Q = isl_mat_drop_rows(Q, Q->n_row - lin_dim, lin_dim);
+
+ U = isl_mat_lin_to_aff(U);
+ Q = isl_mat_lin_to_aff(Q);
+
+ set = isl_set_preimage(set, U);
+ set = isl_set_remove_dims(set, total - lin_dim, lin_dim);
+ hull = uset_convex_hull(set);
+ hull = isl_basic_set_preimage(hull, Q);
+
+ return hull;
+error:
+ isl_basic_set_free(lin);
+ isl_set_free(set);
+ return NULL;
+}
+
+/* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
+ * set up an LP for solving
+ *
+ * \sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
+ *
+ * \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
+ * The next \alpha{ij} correspond to the equalities and come in pairs.
+ * The final \alpha{ij} correspond to the inequalities.
+ */
+static struct isl_basic_set *valid_direction_lp(
+ struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+{
+ struct isl_dim *dim;
+ struct isl_basic_set *lp;
+ unsigned d;
+ int n;
+ int i, j, k;
+
+ if (!bset1 || !bset2)
+ goto error;
+ d = 1 + isl_basic_set_total_dim(bset1);
+ n = 2 +
+ 2 * bset1->n_eq + bset1->n_ineq + 2 * bset2->n_eq + bset2->n_ineq;
+ dim = isl_dim_set_alloc(bset1->ctx, 0, n);
+ lp = isl_basic_set_alloc_dim(dim, 0, d, n);
+ if (!lp)
+ goto error;
+ for (i = 0; i < n; ++i) {
+ k = isl_basic_set_alloc_inequality(lp);
+ if (k < 0)
+ goto error;
+ isl_seq_clr(lp->ineq[k] + 1, n);
+ isl_int_set_si(lp->ineq[k][0], -1);
+ isl_int_set_si(lp->ineq[k][1 + i], 1);
+ }
+ for (i = 0; i < d; ++i) {
+ k = isl_basic_set_alloc_equality(lp);
+ if (k < 0)
+ goto error;
+ n = 0;
+ isl_int_set_si(lp->eq[k][n++], 0);
+ /* positivity constraint 1 >= 0 */
+ isl_int_set_si(lp->eq[k][n++], i == 0);
+ for (j = 0; j < bset1->n_eq; ++j) {
+ isl_int_set(lp->eq[k][n++], bset1->eq[j][i]);
+ isl_int_neg(lp->eq[k][n++], bset1->eq[j][i]);
+ }
+ for (j = 0; j < bset1->n_ineq; ++j)
+ isl_int_set(lp->eq[k][n++], bset1->ineq[j][i]);
+ /* positivity constraint 1 >= 0 */
+ isl_int_set_si(lp->eq[k][n++], -(i == 0));
+ for (j = 0; j < bset2->n_eq; ++j) {
+ isl_int_neg(lp->eq[k][n++], bset2->eq[j][i]);
+ isl_int_set(lp->eq[k][n++], bset2->eq[j][i]);
+ }
+ for (j = 0; j < bset2->n_ineq; ++j)
+ isl_int_neg(lp->eq[k][n++], bset2->ineq[j][i]);
+ }
+ lp = isl_basic_set_gauss(lp, NULL);
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return lp;
+error:
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return NULL;
+}
+
+/* Compute a vector s in the homogeneous space such that <s, r> > 0
+ * for all rays in the homogeneous space of the two cones that correspond
+ * to the input polyhedra bset1 and bset2.
+ *
+ * We compute s as a vector that satisfies
+ *
+ * s = \sum_j \alpha_{ij} h_{ij} for i = 1,2 (*)
+ *
+ * with h_{ij} the normals of the facets of polyhedron i
+ * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
+ * strictly positive numbers. For simplicity we impose \alpha_{ij} >= 1.
+ * We first set up an LP with as variables the \alpha{ij}.
+ * In this formulateion, for each polyhedron i,
+ * the first constraint is the positivity constraint, followed by pairs
+ * of variables for the equalities, followed by variables for the inequalities.
+ * We then simply pick a feasible solution and compute s using (*).
+ *
+ * Note that we simply pick any valid direction and make no attempt
+ * to pick a "good" or even the "best" valid direction.
+ */
+static struct isl_vec *valid_direction(
+ struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+{
+ struct isl_basic_set *lp;
+ struct isl_tab *tab;
+ struct isl_vec *sample = NULL;
+ struct isl_vec *dir;
+ unsigned d;
+ int i;
+ int n;
+
+ if (!bset1 || !bset2)
+ goto error;
+ lp = valid_direction_lp(isl_basic_set_copy(bset1),
+ isl_basic_set_copy(bset2));
+ tab = isl_tab_from_basic_set(lp);
+ sample = isl_tab_get_sample_value(tab);
+ isl_tab_free(tab);
+ isl_basic_set_free(lp);
+ if (!sample)
+ goto error;
+ d = isl_basic_set_total_dim(bset1);
+ dir = isl_vec_alloc(bset1->ctx, 1 + d);
+ if (!dir)
+ goto error;
+ isl_seq_clr(dir->block.data + 1, dir->size - 1);
+ n = 1;
+ /* positivity constraint 1 >= 0 */
+ isl_int_set(dir->block.data[0], sample->block.data[n++]);
+ for (i = 0; i < bset1->n_eq; ++i) {
+ isl_int_sub(sample->block.data[n],
+ sample->block.data[n], sample->block.data[n+1]);
+ isl_seq_combine(dir->block.data,
+ bset1->ctx->one, dir->block.data,
+ sample->block.data[n], bset1->eq[i], 1 + d);
+
+ n += 2;
+ }
+ for (i = 0; i < bset1->n_ineq; ++i)
+ isl_seq_combine(dir->block.data,
+ bset1->ctx->one, dir->block.data,
+ sample->block.data[n++], bset1->ineq[i], 1 + d);
+ isl_vec_free(sample);
+ isl_seq_normalize(bset1->ctx, dir->block.data + 1, dir->size - 1);
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return dir;
+error:
+ isl_vec_free(sample);
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return NULL;
+}
+
+/* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
+ * compute b_i' + A_i' x' >= 0, with
+ *
+ * [ b_i A_i ] [ y' ] [ y' ]
+ * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
+ *
+ * In particular, add the "positivity constraint" and then perform
+ * the mapping.
+ */
+static struct isl_basic_set *homogeneous_map(struct isl_basic_set *bset,
+ struct isl_mat *T)
+{
+ int k;
+
+ if (!bset)
+ goto error;
+ bset = isl_basic_set_extend_constraints(bset, 0, 1);
+ k = isl_basic_set_alloc_inequality(bset);
+ if (k < 0)
+ goto error;
+ isl_seq_clr(bset->ineq[k] + 1, isl_basic_set_total_dim(bset));
+ isl_int_set_si(bset->ineq[k][0], 1);
+ bset = isl_basic_set_preimage(bset, T);
+ return bset;
+error:
+ isl_mat_free(T);
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Compute the convex hull of a pair of basic sets without any parameters or
+ * integer divisions, where the convex hull is known to be pointed,
+ * but the basic sets may be unbounded.
+ *
+ * We turn this problem into the computation of a convex hull of a pair
+ * _bounded_ polyhedra by "changing the direction of the homogeneous
+ * dimension". This idea is due to Matthias Koeppe.
+ *
+ * Consider the cones in homogeneous space that correspond to the
+ * input polyhedra. The rays of these cones are also rays of the
+ * polyhedra if the coordinate that corresponds to the homogeneous
+ * dimension is zero. That is, if the inner product of the rays
+ * with the homogeneous direction is zero.
+ * The cones in the homogeneous space can also be considered to
+ * correspond to other pairs of polyhedra by chosing a different
+ * homogeneous direction. To ensure that both of these polyhedra
+ * are bounded, we need to make sure that all rays of the cones
+ * correspond to vertices and not to rays.
+ * Let s be a direction such that <s, r> > 0 for all rays r of both cones.
+ * Then using s as a homogeneous direction, we obtain a pair of polytopes.
+ * The vector s is computed in valid_direction.
+ *
+ * Note that we need to consider _all_ rays of the cones and not just
+ * the rays that correspond to rays in the polyhedra. If we were to
+ * only consider those rays and turn them into vertices, then we
+ * may inadvertently turn some vertices into rays.
+ *
+ * The standard homogeneous direction is the unit vector in the 0th coordinate.
+ * We therefore transform the two polyhedra such that the selected
+ * direction is mapped onto this standard direction and then proceed
+ * with the normal computation.
+ * Let S be a non-singular square matrix with s as its first row,
+ * then we want to map the polyhedra to the space
+ *
+ * [ y' ] [ y ] [ y ] [ y' ]
+ * [ x' ] = S [ x ] i.e., [ x ] = S^{-1} [ x' ]
+ *
+ * We take S to be the unimodular completion of s to limit the growth
+ * of the coefficients in the following computations.
+ *
+ * Let b_i + A_i x >= 0 be the constraints of polyhedron i.
+ * We first move to the homogeneous dimension
+ *
+ * b_i y + A_i x >= 0 [ b_i A_i ] [ y ] [ 0 ]
+ * y >= 0 or [ 1 0 ] [ x ] >= [ 0 ]
+ *
+ * Then we change directoin
+ *
+ * [ b_i A_i ] [ y' ] [ y' ]
+ * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
+ *
+ * Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
+ * resulting in b' + A' x' >= 0, which we then convert back
+ *
+ * [ y ] [ y ]
+ * [ b' A' ] S [ x ] >= 0 or [ b A ] [ x ] >= 0
+ *
+ * The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
+ */
+static struct isl_basic_set *convex_hull_pair_pointed(
+ struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+{
+ struct isl_ctx *ctx = NULL;
+ struct isl_vec *dir = NULL;
+ struct isl_mat *T = NULL;
+ struct isl_mat *T2 = NULL;
+ struct isl_basic_set *hull;
+ struct isl_set *set;
+
+ if (!bset1 || !bset2)
+ goto error;
+ ctx = bset1->ctx;
+ dir = valid_direction(isl_basic_set_copy(bset1),
+ isl_basic_set_copy(bset2));
+ if (!dir)
+ goto error;
+ T = isl_mat_alloc(bset1->ctx, dir->size, dir->size);
+ if (!T)
+ goto error;
+ isl_seq_cpy(T->row[0], dir->block.data, dir->size);
+ T = isl_mat_unimodular_complete(T, 1);
+ T2 = isl_mat_right_inverse(isl_mat_copy(T));
+
+ bset1 = homogeneous_map(bset1, isl_mat_copy(T2));
+ bset2 = homogeneous_map(bset2, T2);
+ set = isl_set_alloc_dim(isl_basic_set_get_dim(bset1), 2, 0);
+ set = isl_set_add(set, bset1);
+ set = isl_set_add(set, bset2);
+ hull = uset_convex_hull(set);
+ hull = isl_basic_set_preimage(hull, T);
+
+ isl_vec_free(dir);
+
+ return hull;
+error:
+ isl_vec_free(dir);
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return NULL;
+}
+
+/* Compute the convex hull of a pair of basic sets without any parameters or
+ * integer divisions.
+ *
+ * If the convex hull of the two basic sets would have a non-trivial
+ * lineality space, we first project out this lineality space.
+ */
+static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1,
+ struct isl_basic_set *bset2)
+{
+ struct isl_basic_set *lin;
+
+ if (isl_basic_set_is_bounded(bset1) || isl_basic_set_is_bounded(bset2))
+ return convex_hull_pair_pointed(bset1, bset2);
+
+ lin = induced_lineality_space(isl_basic_set_copy(bset1),
+ isl_basic_set_copy(bset2));
+ if (!lin)
+ goto error;
+ if (isl_basic_set_is_universe(lin)) {
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return lin;
+ }
+ if (lin->n_eq < isl_basic_set_total_dim(lin)) {
+ struct isl_set *set;
+ set = isl_set_alloc_dim(isl_basic_set_get_dim(bset1), 2, 0);
+ set = isl_set_add(set, bset1);
+ set = isl_set_add(set, bset2);
+ return modulo_lineality(set, lin);
+ }
+ isl_basic_set_free(lin);
+
+ return convex_hull_pair_pointed(bset1, bset2);
+error:
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return NULL;
+}
+
+/* Compute the lineality space of a basic set.
+ * We currently do not allow the basic set to have any divs.
+ * We basically just drop the constants and turn every inequality
+ * into an equality.
+ */
+struct isl_basic_set *isl_basic_set_lineality_space(struct isl_basic_set *bset)
+{
+ int i, k;
+ struct isl_basic_set *lin = NULL;
+ unsigned dim;
+
+ if (!bset)
+ goto error;
+ isl_assert(bset->ctx, bset->n_div == 0, goto error);
+ dim = isl_basic_set_total_dim(bset);
+
+ lin = isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset), 0, dim, 0);
+ if (!lin)
+ goto error;
+ for (i = 0; i < bset->n_eq; ++i) {
+ k = isl_basic_set_alloc_equality(lin);
+ if (k < 0)
+ goto error;
+ isl_int_set_si(lin->eq[k][0], 0);
+ isl_seq_cpy(lin->eq[k] + 1, bset->eq[i] + 1, dim);
+ }
+ lin = isl_basic_set_gauss(lin, NULL);
+ if (!lin)
+ goto error;
+ for (i = 0; i < bset->n_ineq && lin->n_eq < dim; ++i) {
+ k = isl_basic_set_alloc_equality(lin);
+ if (k < 0)
+ goto error;
+ isl_int_set_si(lin->eq[k][0], 0);
+ isl_seq_cpy(lin->eq[k] + 1, bset->ineq[i] + 1, dim);
+ lin = isl_basic_set_gauss(lin, NULL);
+ if (!lin)
+ goto error;
+ }
+ isl_basic_set_free(bset);
+ return lin;
+error:
+ isl_basic_set_free(lin);
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Compute the (linear) hull of the lineality spaces of the basic sets in the
+ * "underlying" set "set".
+ */
+static struct isl_basic_set *uset_combined_lineality_space(struct isl_set *set)
+{
+ int i;
+ struct isl_set *lin = NULL;
+
+ if (!set)
+ return NULL;
+ if (set->n == 0) {
+ struct isl_dim *dim = isl_set_get_dim(set);
+ isl_set_free(set);
+ return isl_basic_set_empty(dim);
+ }
+
+ lin = isl_set_alloc_dim(isl_set_get_dim(set), set->n, 0);
+ for (i = 0; i < set->n; ++i)
+ lin = isl_set_add(lin,
+ isl_basic_set_lineality_space(isl_basic_set_copy(set->p[i])));
+ isl_set_free(set);
+ return isl_set_affine_hull(lin);
+}
+
/* Compute the convex hull of a set without any parameters or
- * integer divisions using Fourier-Motzkin elimination.
+ * integer divisions.
* In each step, we combined two basic sets until only one
* basic set is left.
+ * The input basic sets are assumed not to have a non-trivial
+ * lineality space. If any of the intermediate results has
+ * a non-trivial lineality space, it is projected out.
*/
-static struct isl_basic_set *uset_convex_hull_elim(struct isl_set *set)
+static struct isl_basic_set *uset_convex_hull_unbounded(struct isl_set *set)
{
struct isl_basic_set *convex_hull = NULL;
if (!set)
goto error;
convex_hull = convex_hull_pair(convex_hull, t);
+ if (set->n == 0)
+ break;
+ t = isl_basic_set_lineality_space(isl_basic_set_copy(convex_hull));
+ if (!t)
+ goto error;
+ if (isl_basic_set_is_universe(t)) {
+ isl_basic_set_free(convex_hull);
+ convex_hull = t;
+ break;
+ }
+ if (t->n_eq < isl_basic_set_total_dim(t)) {
+ set = isl_set_add(set, convex_hull);
+ return modulo_lineality(set, t);
+ }
+ isl_basic_set_free(t);
}
isl_set_free(set);
return convex_hull;
if (!hull)
goto error;
- bounds = independent_bounds(set->ctx, set);
+ bounds = independent_bounds(set);
if (!bounds)
goto error;
isl_assert(set->ctx, bounds->n_row == isl_set_n_dim(set), goto error);
- bounds = initial_facet_constraint(set->ctx, set, bounds);
+ bounds = initial_facet_constraint(set, bounds);
if (!bounds)
goto error;
k = isl_basic_set_alloc_inequality(hull);
dim = isl_set_n_dim(set);
isl_assert(set->ctx, 1 + dim == bounds->n_col, goto error);
isl_seq_cpy(hull->ineq[k], bounds->row[0], bounds->n_col);
- isl_mat_free(set->ctx, bounds);
+ isl_mat_free(bounds);
return hull;
error:
isl_basic_set_free(hull);
- isl_mat_free(set->ctx, bounds);
+ isl_mat_free(bounds);
return NULL;
}
c->ineq = ineq;
return;
}
- c->c = isl_mat_cow(ctx, c->c);
+ c->c = isl_mat_cow(c->c);
isl_int_set(c->c->row[0][0], con[0]);
c->ineq = ineq;
}
isl_hash_table_clear(table);
for (i = 0; i < min_constraints; ++i)
- isl_mat_free(hull->ctx, constraints[i].c);
+ isl_mat_free(constraints[i].c);
free(constraints);
free(table);
return hull;
free(table);
if (constraints)
for (i = 0; i < min_constraints; ++i)
- isl_mat_free(hull->ctx, constraints[i].c);
+ isl_mat_free(constraints[i].c);
free(constraints);
return hull;
}
return hull;
}
-static int isl_basic_set_is_bounded(struct isl_basic_set *bset)
-{
- struct isl_tab *tab;
- int bounded;
-
- tab = isl_tab_from_recession_cone((struct isl_basic_map *)bset);
- bounded = isl_tab_cone_is_bounded(bset->ctx, tab);
- isl_tab_free(bset->ctx, tab);
- return bounded;
-}
-
-static int isl_set_is_bounded(struct isl_set *set)
-{
- int i;
-
- for (i = 0; i < set->n; ++i) {
- int bounded = isl_basic_set_is_bounded(set->p[i]);
- if (!bounded || bounded < 0)
- return bounded;
- }
- return 1;
-}
-
/* 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
{
int i;
struct isl_basic_set *convex_hull = NULL;
+ struct isl_basic_set *lin;
if (isl_set_n_dim(set) == 0)
return convex_hull_0d(set);
+ set = isl_set_coalesce(set);
set = isl_set_set_rational(set);
if (!set)
goto error;
- set = isl_set_normalize(set);
if (!set)
return NULL;
if (set->n == 1) {
return convex_hull;
}
if (isl_set_n_dim(set) == 1)
- return convex_hull_1d(set->ctx, set);
+ return convex_hull_1d(set);
- if (!isl_set_is_bounded(set))
- return uset_convex_hull_elim(set);
+ if (isl_set_is_bounded(set))
+ return uset_convex_hull_wrap(set);
- return uset_convex_hull_wrap(set);
+ lin = uset_combined_lineality_space(isl_set_copy(set));
+ if (!lin)
+ goto error;
+ if (isl_basic_set_is_universe(lin)) {
+ isl_set_free(set);
+ return lin;
+ }
+ if (lin->n_eq < isl_basic_set_total_dim(lin))
+ return modulo_lineality(set, lin);
+ isl_basic_set_free(lin);
+
+ return uset_convex_hull_unbounded(set);
error:
isl_set_free(set);
isl_basic_set_free(convex_hull);
if (!set)
goto error;
- set = isl_set_normalize(set);
+ set = isl_set_coalesce(set);
if (!set)
goto error;
if (set->n == 1) {
return convex_hull;
}
if (isl_set_n_dim(set) == 1)
- return convex_hull_1d(set->ctx, set);
+ return convex_hull_1d(set);
return uset_convex_hull_wrap(set);
error:
return convex_hull;
}
+ map = isl_map_detect_equalities(map);
map = isl_map_align_divs(map);
model = isl_basic_map_copy(map->p[0]);
set = isl_map_underlying_set(map);
convex_hull = isl_basic_map_overlying_set(bset, model);
+ ISL_F_SET(convex_hull, ISL_BASIC_MAP_NO_IMPLICIT);
+ ISL_F_SET(convex_hull, ISL_BASIC_MAP_ALL_EQUALITIES);
ISL_F_CLR(convex_hull, ISL_BASIC_MAP_RATIONAL);
return convex_hull;
error:
isl_hash_table_free(data->ctx, data->hull_table);
for (i = 0; i < data->n; ++i) {
isl_hash_table_free(data->ctx, data->p[i].table);
- isl_tab_free(data->ctx, data->p[i].tab);
+ isl_tab_free(data->p[i].tab);
}
free(data);
}
isl_int_init(opt);
- res = isl_tab_min(data->ctx, data->p[j].tab, ineq, data->ctx->one,
- &opt, NULL);
+ res = isl_tab_min(data->p[j].tab, ineq, data->ctx->one,
+ &opt, NULL, 0);
if (res == isl_lp_ok && isl_int_is_neg(opt))
isl_int_sub(ineq[0], ineq[0], opt);
n_ineq += 2 * set->p[i]->n_eq + set->p[i]->n_ineq;
}
- hull = isl_set_affine_hull(isl_set_copy(set));
- if (!hull)
- goto error;
- hull = isl_basic_set_extend_dim(hull, isl_dim_copy(hull->dim),
- 0, 0, n_ineq);
+ hull = isl_basic_set_alloc_dim(isl_dim_copy(set->dim), 0, 0, n_ineq);
if (!hull)
goto error;
data = sh_data_alloc(set, n_ineq);
if (!data)
goto error;
- if (hash_basic_set(data->hull_table, hull) < 0)
- goto error;
for (i = 0; i < set->n; ++i)
hull = add_bounds(hull, data, set, i);
- hull = isl_basic_set_convex_hull(hull);
-
sh_data_free(data);
isl_set_free(set);
struct isl_set *set = NULL;
struct isl_basic_map *model = NULL;
struct isl_basic_map *hull;
+ struct isl_basic_map *affine_hull;
struct isl_basic_set *bset = NULL;
if (!map)
return hull;
}
+ map = isl_map_detect_equalities(map);
+ affine_hull = isl_map_affine_hull(isl_map_copy(map));
map = isl_map_align_divs(map);
model = isl_basic_map_copy(map->p[0]);
hull = isl_basic_map_overlying_set(bset, model);
+ hull = isl_basic_map_intersect(hull, affine_hull);
+ hull = isl_basic_map_convex_hull(hull);
+ ISL_F_SET(hull, ISL_BASIC_MAP_NO_IMPLICIT);
+ ISL_F_SET(hull, ISL_BASIC_MAP_ALL_EQUALITIES);
+
return hull;
}
return (struct isl_basic_set *)
isl_map_simple_hull((struct isl_map *)set);
}
+
+/* Given a set "set", return parametric bounds on the dimension "dim".
+ */
+static struct isl_basic_set *set_bounds(struct isl_set *set, int dim)
+{
+ unsigned set_dim = isl_set_dim(set, isl_dim_set);
+ set = isl_set_copy(set);
+ set = isl_set_eliminate_dims(set, dim + 1, set_dim - (dim + 1));
+ set = isl_set_eliminate_dims(set, 0, dim);
+ return isl_set_convex_hull(set);
+}
+
+/* Computes a "simple hull" and then check if each dimension in the
+ * resulting hull is bounded by a symbolic constant. If not, the
+ * hull is intersected with the corresponding bounds on the whole set.
+ */
+struct isl_basic_set *isl_set_bounded_simple_hull(struct isl_set *set)
+{
+ int i, j;
+ struct isl_basic_set *hull;
+ unsigned nparam, left;
+ int removed_divs = 0;
+
+ hull = isl_set_simple_hull(isl_set_copy(set));
+ if (!hull)
+ goto error;
+
+ nparam = isl_basic_set_dim(hull, isl_dim_param);
+ for (i = 0; i < isl_basic_set_dim(hull, isl_dim_set); ++i) {
+ int lower = 0, upper = 0;
+ struct isl_basic_set *bounds;
+
+ left = isl_basic_set_total_dim(hull) - nparam - i - 1;
+ for (j = 0; j < hull->n_eq; ++j) {
+ if (isl_int_is_zero(hull->eq[j][1 + nparam + i]))
+ continue;
+ if (isl_seq_first_non_zero(hull->eq[j]+1+nparam+i+1,
+ left) == -1)
+ break;
+ }
+ if (j < hull->n_eq)
+ continue;
+
+ for (j = 0; j < hull->n_ineq; ++j) {
+ if (isl_int_is_zero(hull->ineq[j][1 + nparam + i]))
+ continue;
+ if (isl_seq_first_non_zero(hull->ineq[j]+1+nparam+i+1,
+ left) != -1 ||
+ isl_seq_first_non_zero(hull->ineq[j]+1+nparam,
+ i) != -1)
+ continue;
+ if (isl_int_is_pos(hull->ineq[j][1 + nparam + i]))
+ lower = 1;
+ else
+ upper = 1;
+ if (lower && upper)
+ break;
+ }
+
+ if (lower && upper)
+ continue;
+
+ if (!removed_divs) {
+ set = isl_set_remove_divs(set);
+ if (!set)
+ goto error;
+ removed_divs = 1;
+ }
+ bounds = set_bounds(set, i);
+ hull = isl_basic_set_intersect(hull, bounds);
+ if (!hull)
+ goto error;
+ }
+
+ isl_set_free(set);
+ return hull;
+error:
+ isl_set_free(set);
+ return NULL;
+}
projects / platform / upstream / isl.git / blobdiff