+/*
+ * 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_lp.h"
#include "isl_map.h"
#include "isl_map_private.h"
(struct isl_basic_map **)bset, c, opt_n, opt_d);
}
-/* Compute the convex hull of a basic map, by removing the redundant
+/* Remove redundant
* constraints. If the minimal value along the normal of a constraint
* is the same if the constraint is removed, then the constraint is redundant.
*
* corresponding equality and the checked if the dimension was that
* of a facet.
*/
-struct isl_basic_map *isl_basic_map_convex_hull(struct isl_basic_map *bmap)
+__isl_give isl_basic_map *isl_basic_map_remove_redundancies(
+ __isl_take isl_basic_map *bmap)
{
struct isl_tab *tab;
return bmap;
tab = isl_tab_from_basic_map(bmap);
- tab = isl_tab_detect_equalities(tab);
- tab = isl_tab_detect_redundant(tab);
+ if (isl_tab_detect_implicit_equalities(tab) < 0)
+ goto error;
+ if (isl_tab_detect_redundant(tab) < 0)
+ goto error;
bmap = isl_basic_map_update_from_tab(bmap, 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;
+error:
+ isl_tab_free(tab);
+ isl_basic_map_free(bmap);
+ return NULL;
}
-struct isl_basic_set *isl_basic_set_convex_hull(struct isl_basic_set *bset)
+__isl_give isl_basic_set *isl_basic_set_remove_redundancies(
+ __isl_take isl_basic_set *bset)
{
return (struct isl_basic_set *)
- isl_basic_map_convex_hull((struct isl_basic_map *)bset);
+ isl_basic_map_remove_redundancies((struct isl_basic_map *)bset);
}
/* Check if the set set is bound in the direction of the affine
goto error;
continue;
}
- if (!isl_int_is_one(opt_denom))
- isl_seq_scale(c, c, opt_denom, len);
- if (first || isl_int_is_neg(opt))
+ if (first || isl_int_is_neg(opt)) {
+ if (!isl_int_is_one(opt_denom))
+ isl_seq_scale(c, c, opt_denom, len);
isl_int_sub(c[0], c[0], opt);
+ }
first = 0;
}
isl_int_clear(opt);
return -1;
}
-/* Check if "c" is a direction 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).
- * Assumes set "set" is bounded.
- */
-static int is_independent_bound(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;
- }
- }
-
- is_bound = uset_is_bound(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];
- for (k = n; k > i; --k)
- dirs->row[k] = dirs->row[k-1];
- dirs->row[i] = t;
- }
- return 1;
-}
-
-/* Compute and return a maximal set of linearly independent bounds
- * on the set "set", based on the constraints of the basic sets
- * in "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(set->ctx, dim, 1+dim);
- if (!dirs)
- goto error;
-
- n = 0;
- for (i = 0; n < dim && i < set->n; ++i) {
- int f;
- struct isl_basic_set *bset = set->p[i];
-
- for (j = 0; n < dim && j < bset->n_eq; ++j) {
- 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(set, bset->ineq[j], dirs, n);
- if (f < 0)
- goto error;
- if (f)
- ++n;
- }
- }
- dirs->n_row = n;
- return dirs;
-error:
- isl_mat_free(dirs);
- return NULL;
-}
-
struct isl_basic_set *isl_basic_set_set_rational(struct isl_basic_set *bset)
{
if (!bset)
struct isl_basic_set *bset, isl_int *c)
{
int i;
- unsigned total;
unsigned dim;
+ if (!bset)
+ return NULL;
+
if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))
return bset;
- isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
- isl_assert(ctx, bset->n_div == 0, goto error);
+ isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
+ isl_assert(bset->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);
return NULL;
}
-static struct isl_set *isl_set_add_equality(struct isl_set *set, isl_int *c)
+static struct isl_set *isl_set_add_basic_set_equality(struct isl_set *set, isl_int *c)
{
int i;
* In the original space, we need to take the same combination of the
* corresponding constraints "facet" and "ridge".
*
- * Note that a is always finite, since we only apply the wrapping
- * technique to a union of polytopes.
+ * 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_set *set, isl_int *facet, isl_int *ridge)
+isl_int *isl_set_wrap_facet(__isl_keep isl_set *set,
+ isl_int *facet, isl_int *ridge)
{
int i;
+ isl_ctx *ctx;
struct isl_mat *T = NULL;
struct isl_basic_set *lp = NULL;
struct isl_vec *obj;
isl_int num, den;
unsigned dim;
+ if (!set)
+ return NULL;
+ ctx = set->ctx;
set = isl_set_copy(set);
+ set = isl_set_set_rational(set);
dim = 1 + isl_set_n_dim(set);
- T = isl_mat_alloc(set->ctx, 3, dim);
+ T = isl_mat_alloc(ctx, 3, dim);
if (!T)
goto error;
isl_int_set_si(T->row[0][0], 1);
if (!set)
goto error;
lp = wrap_constraints(set);
- obj = isl_vec_alloc(set->ctx, 1 + dim*set->n);
+ obj = isl_vec_alloc(ctx, 1 + dim*set->n);
if (!obj)
goto error;
isl_int_set_si(obj->block.data[0], 0);
isl_int_init(num);
isl_int_init(den);
res = isl_basic_set_solve_lp(lp, 0,
- obj->block.data, set->ctx->one, &num, &den, NULL);
+ obj->block.data, 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_vec_free(obj);
isl_basic_set_free(lp);
isl_set_free(set);
- isl_assert(set->ctx, res == isl_lp_ok, return NULL);
+ if (res == isl_lp_error)
+ return NULL;
+ isl_assert(ctx, res == isl_lp_ok || res == isl_lp_unbounded,
+ return NULL);
return facet;
error:
isl_basic_set_free(lp);
return NULL;
}
-/* Given a set of d linearly independent bounding constraints of the
- * convex hull of "set", compute the constraint of a facet of "set".
- *
- * We first compute the intersection with the first bounding hyperplane
- * and remove the component corresponding to this hyperplane from
- * other bounds (in homogeneous space).
- * We then wrap around one of the remaining bounding constraints
- * and continue the process until all bounding constraints have been
- * taken into account.
- * The resulting linear combination of the bounding constraints will
- * correspond to a facet of the convex hull.
+/* Compute the constraint of a facet of "set".
+ *
+ * We first compute the intersection with a bounding constraint
+ * that is orthogonal to one of the coordinate axes.
+ * If the affine hull of this intersection has only one equality,
+ * we have found a facet.
+ * Otherwise, we wrap the current bounding constraint around
+ * one of the equalities of the face (one that is not equal to
+ * the current bounding constraint).
+ * This process continues until we have found a facet.
+ * The dimension of the intersection increases by at least
+ * one on each iteration, so termination is guaranteed.
*/
-static struct isl_mat *initial_facet_constraint(struct isl_set *set,
- struct isl_mat *bounds)
+static __isl_give isl_mat *initial_facet_constraint(__isl_keep isl_set *set)
{
struct isl_set *slice = NULL;
struct isl_basic_set *face = NULL;
- struct isl_mat *m, *U, *Q;
int i;
unsigned dim = isl_set_n_dim(set);
+ int is_bound;
+ isl_mat *bounds;
+
+ isl_assert(set->ctx, set->n > 0, goto error);
+ bounds = isl_mat_alloc(set->ctx, 1, 1 + dim);
+ if (!bounds)
+ return NULL;
- isl_assert(ctx, set->n > 0, goto error);
- isl_assert(ctx, bounds->n_row == dim, goto error);
+ isl_seq_clr(bounds->row[0], dim);
+ isl_int_set_si(bounds->row[0][1 + dim - 1], 1);
+ is_bound = uset_is_bound(set, bounds->row[0], 1 + dim);
+ isl_assert(set->ctx, is_bound == 1, goto error);
+ isl_seq_normalize(set->ctx, bounds->row[0], 1 + dim);
+ bounds->n_row = 1;
- while (bounds->n_row > 1) {
+ for (;;) {
slice = isl_set_copy(set);
- slice = isl_set_add_equality(slice, bounds->row[0]);
+ slice = isl_set_add_basic_set_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(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(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--;
- isl_assert(ctx, bounds->n_row > 1, goto error);
- }
- if (!wrap_facet(set, bounds->row[0],
- bounds->row[bounds->n_row-1]))
+ if (!isl_seq_eq(bounds->row[0], face->eq[i], 1 + dim) &&
+ !isl_seq_is_neg(bounds->row[0],
+ face->eq[i], 1 + dim))
+ break;
+ isl_assert(set->ctx, i < face->n_eq, goto error);
+ if (!isl_set_wrap_facet(set, bounds->row[0], face->eq[i]))
goto error;
+ isl_seq_normalize(set->ctx, bounds->row[0], bounds->n_col);
isl_basic_set_free(face);
- bounds->n_row--;
}
+
return bounds;
error:
isl_basic_set_free(face);
set = isl_set_preimage(set, U);
facet = uset_convex_hull_wrap_bounded(set);
facet = isl_basic_set_preimage(facet, Q);
- isl_assert(ctx, facet->n_eq == 0, goto error);
+ if (facet)
+ isl_assert(ctx, facet->n_eq == 0, goto error);
return facet;
error:
isl_basic_set_free(facet);
int k;
struct isl_basic_set *facet = NULL;
struct isl_basic_set *hull_facet = NULL;
- unsigned total;
unsigned dim;
+ if (!hull)
+ return NULL;
+
isl_assert(set->ctx, set->n > 0, goto error);
dim = isl_set_n_dim(set);
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)
+ if (!facet || !hull_facet)
goto error;
hull = isl_basic_set_cow(hull);
hull = isl_basic_set_extend_dim(hull,
isl_dim_copy(hull->dim), 0, 0, facet->n_ineq);
+ if (!hull)
+ goto error;
for (j = 0; j < facet->n_ineq; ++j) {
for (f = 0; f < hull_facet->n_ineq; ++f)
if (isl_seq_eq(facet->ineq[j],
if (k < 0)
goto error;
isl_seq_cpy(hull->ineq[k], hull->ineq[i], 1+dim);
- if (!wrap_facet(set, hull->ineq[k], facet->ineq[j]))
+ if (!isl_set_wrap_facet(set, hull->ineq[k], facet->ineq[j]))
goto error;
}
isl_basic_set_free(hull_facet);
}
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);
+ hull = isl_basic_set_remove_redundancies(hull);
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return hull;
return NULL;
}
-static int isl_basic_set_is_bounded(struct isl_basic_set *bset)
+/* Is the set bounded for each value of the parameters?
+ */
+int isl_basic_set_is_bounded(__isl_keep isl_basic_set *bset)
{
struct isl_tab *tab;
int bounded;
- tab = isl_tab_from_recession_cone((struct isl_basic_map *)bset);
+ if (!bset)
+ return -1;
+ if (isl_basic_set_fast_is_empty(bset))
+ return 1;
+
+ tab = isl_tab_from_recession_cone(bset, 1);
bounded = isl_tab_cone_is_bounded(tab);
isl_tab_free(tab);
return bounded;
}
-static int isl_set_is_bounded(struct isl_set *set)
+/* Is the set bounded for each value of the parameters?
+ */
+int isl_set_is_bounded(__isl_keep isl_set *set)
{
int i;
+ if (!set)
+ return -1;
+
for (i = 0; i < set->n; ++i) {
int bounded = isl_basic_set_is_bounded(set->p[i]);
if (!bounded || bounded < 0)
* (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,
+ * In this formulation, 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 (*).
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_seq_normalize(bset1->ctx, dir->el, dir->size);
isl_basic_set_free(bset1);
isl_basic_set_free(bset2);
return dir;
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);
+ set = isl_set_add_basic_set(set, bset1);
+ set = isl_set_add_basic_set(set, bset2);
hull = uset_convex_hull(set);
hull = isl_basic_set_preimage(hull, T);
return NULL;
}
+static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set);
+static struct isl_basic_set *modulo_affine_hull(
+ struct isl_set *set, struct isl_basic_set *affine_hull);
+
/* Compute the convex hull of a pair of basic sets without any parameters or
* integer divisions.
*
+ * This function is called from uset_convex_hull_unbounded, which
+ * means that the complete convex hull is unbounded. Some pairs
+ * of basic sets may still be bounded, though.
+ * They may even lie inside a lower dimensional space, in which
+ * case they need to be handled inside their affine hull since
+ * the main algorithm assumes that the result is full-dimensional.
+ *
* 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;
+ isl_basic_set *lin, *aff;
+ int bounded1, bounded2;
+
+ aff = isl_set_affine_hull(isl_basic_set_union(isl_basic_set_copy(bset1),
+ isl_basic_set_copy(bset2)));
+ if (!aff)
+ goto error;
+ if (aff->n_eq != 0)
+ return modulo_affine_hull(isl_basic_set_union(bset1, bset2), aff);
+ isl_basic_set_free(aff);
+
+ bounded1 = isl_basic_set_is_bounded(bset1);
+ bounded2 = isl_basic_set_is_bounded(bset2);
- if (isl_basic_set_is_bounded(bset1) || isl_basic_set_is_bounded(bset2))
+ if (bounded1 < 0 || bounded2 < 0)
+ goto error;
+
+ if (bounded1 && bounded2)
+ uset_convex_hull_wrap(isl_basic_set_union(bset1, bset2));
+
+ if (bounded1 || bounded2)
return convex_hull_pair_pointed(bset1, bset2);
lin = induced_lineality_space(isl_basic_set_copy(bset1),
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);
+ set = isl_set_add_basic_set(set, bset1);
+ set = isl_set_add_basic_set(set, bset2);
return modulo_lineality(set, lin);
}
isl_basic_set_free(lin);
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,
+ lin = isl_set_add_basic_set(lin,
isl_basic_set_lineality_space(isl_basic_set_copy(set->p[i])));
isl_set_free(set);
return isl_set_affine_hull(lin);
break;
}
if (t->n_eq < isl_basic_set_total_dim(t)) {
- set = isl_set_add(set, convex_hull);
+ set = isl_set_add_basic_set(set, convex_hull);
return modulo_lineality(set, t);
}
isl_basic_set_free(t);
}
/* Compute an initial hull for wrapping containing a single initial
- * facet by first computing bounds on the set and then using these
- * bounds to construct an initial facet.
- * This function is a remnant of an older implementation where the
- * bounds were also used to check whether the set was bounded.
- * Since this function will now only be called when we know the
- * set to be bounded, the initial facet should probably be constructed
- * by simply using the coordinate directions instead.
+ * facet.
+ * This function assumes that the given set is bounded.
*/
static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
struct isl_set *set)
if (!hull)
goto error;
- 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, bounds);
+ bounds = initial_facet_constraint(set);
if (!bounds)
goto error;
k = isl_basic_set_alloc_inequality(hull);
*/
static struct isl_basic_set *uset_convex_hull(struct isl_set *set)
{
- int i;
struct isl_basic_set *convex_hull = NULL;
struct isl_basic_set *lin;
*/
static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set)
{
- int i;
struct isl_basic_set *convex_hull = NULL;
+ if (!set)
+ goto error;
+
if (isl_set_n_dim(set) == 0) {
convex_hull = isl_basic_set_universe(isl_dim_copy(set->dim));
isl_set_free(set);
}
set = isl_set_set_rational(set);
-
- if (!set)
- goto error;
set = isl_set_coalesce(set);
if (!set)
goto error;
* convex hull of the transformed set and then add the equalities back
* (after performing the inverse transformation.
*/
-static struct isl_basic_set *modulo_affine_hull(struct isl_ctx *ctx,
+static struct isl_basic_set *modulo_affine_hull(
struct isl_set *set, struct isl_basic_set *affine_hull)
{
struct isl_mat *T;
map = isl_map_detect_equalities(map);
map = isl_map_align_divs(map);
+ if (!map)
+ goto error;
model = isl_basic_map_copy(map->p[0]);
set = isl_map_underlying_set(map);
if (!set)
if (!affine_hull)
goto error;
if (affine_hull->n_eq != 0)
- bset = modulo_affine_hull(ctx, set, affine_hull);
+ bset = modulo_affine_hull(set, affine_hull);
else {
isl_basic_set_free(affine_hull);
bset = uset_convex_hull(set);
}
convex_hull = isl_basic_map_overlying_set(bset, model);
+ if (!convex_hull)
+ return NULL;
ISL_F_SET(convex_hull, ISL_BASIC_MAP_NO_IMPLICIT);
ISL_F_SET(convex_hull, ISL_BASIC_MAP_ALL_EQUALITIES);
isl_int_clear(opt);
- return res == isl_lp_ok ? 1 :
+ return (res == isl_lp_ok || res == isl_lp_empty) ? 1 :
res == isl_lp_unbounded ? 0 : -1;
}
for (j = 0; j < set->p[i]->n_eq; ++j) {
for (k = 0; k < 2; ++k) {
isl_seq_neg(set->p[i]->eq[j], set->p[i]->eq[j], 1+dim);
- add_bound(bset, data, set, i, set->p[i]->eq[j]);
+ bset = add_bound(bset, data, set, i, set->p[i]->eq[j]);
}
}
for (j = 0; j < set->p[i]->n_ineq; ++j)
- add_bound(bset, data, set, i, set->p[i]->ineq[j]);
+ bset = add_bound(bset, data, set, i, set->p[i]->ineq[j]);
return bset;
}
struct sh_data *data = NULL;
struct isl_basic_set *hull = NULL;
unsigned n_ineq;
- int i, j;
+ int i;
if (!set)
return NULL;
hull = isl_basic_map_overlying_set(bset, model);
hull = isl_basic_map_intersect(hull, affine_hull);
- hull = isl_basic_map_convex_hull(hull);
+ hull = isl_basic_map_remove_redundancies(hull);
ISL_F_SET(hull, ISL_BASIC_MAP_NO_IMPLICIT);
ISL_F_SET(hull, ISL_BASIC_MAP_ALL_EQUALITIES);
projects / platform / upstream / isl.git / blobdiff