-#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"
-
-struct isl_basic_map *isl_basic_map_implicit_equalities(struct isl_ctx *ctx,
+/*
+ * 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_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)
{
- int i;
- isl_int opt;
+ struct isl_tab *tab;
if (!bmap)
return bmap;
- if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+ bmap = isl_basic_map_gauss(bmap, NULL);
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
return bmap;
- if (F_ISSET(bmap, ISL_BASIC_MAP_NO_IMPLICIT))
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NO_IMPLICIT))
+ return bmap;
+ if (bmap->n_ineq <= 1)
return bmap;
- isl_int_init(opt);
- for (i = 0; i < bmap->n_ineq; ++i) {
- enum isl_lp_result res;
- res = isl_solve_lp(bmap, 1, bmap->ineq[i]+1, ctx->one, &opt);
- if (res == isl_lp_unbounded)
- continue;
- if (res == isl_lp_error)
- goto error;
- if (res == isl_lp_empty) {
- bmap = isl_basic_map_set_to_empty(ctx, bmap);
- break;
- }
- isl_int_add(opt, opt, bmap->ineq[i][0]);
- if (isl_int_is_zero(opt)) {
- isl_basic_map_inequality_to_equality(ctx, bmap, i);
- --i;
- }
- }
- isl_int_clear(opt);
-
- F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
+ tab = isl_tab_from_basic_map(bmap);
+ 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_int_clear(opt);
- isl_basic_map_free(ctx, bmap);
+ isl_tab_free(tab);
+ isl_basic_map_free(bmap);
return NULL;
}
-struct isl_basic_map *isl_basic_map_affine_hull(struct isl_ctx *ctx,
- struct isl_basic_map *bmap)
+struct isl_basic_set *isl_basic_set_implicit_equalities(
+ struct isl_basic_set *bset)
{
- bmap = isl_basic_map_implicit_equalities(ctx, bmap);
- if (!bmap)
- return NULL;
- if (bmap->n_ineq == 0)
- return bmap;
- bmap = isl_basic_map_cow(ctx, bmap);
- if (!bmap)
- return NULL;
- isl_basic_map_free_inequality(ctx, bmap, bmap->n_ineq);
- return isl_basic_map_finalize(ctx, bmap);
+ return (struct isl_basic_set *)
+ isl_basic_map_implicit_equalities((struct isl_basic_map*)bset);
}
-struct isl_basic_set *isl_basic_set_affine_hull(struct isl_ctx *ctx,
- struct isl_basic_set *bset)
+struct isl_map *isl_map_implicit_equalities(struct isl_map *map)
{
- return (struct isl_basic_set *)
- isl_basic_map_affine_hull(ctx, (struct isl_basic_map *)bset);
+ int i;
+
+ if (!map)
+ return map;
+
+ for (i = 0; i < map->n; ++i) {
+ map->p[i] = isl_basic_map_implicit_equalities(map->p[i]);
+ if (!map->p[i])
+ goto error;
+ }
+
+ return map;
+error:
+ isl_map_free(map);
+ return NULL;
}
/* Make eq[row][col] of both bmaps equal so we can add the row
isl_int_init(a);
isl_int_init(b);
- total = 1 + bset1->dim;
+ total = 1 + isl_basic_set_n_dim(bset1);
for (r = 0; r < row; ++r) {
if (isl_int_is_zero(bset2->eq[r][col]))
continue;
if (t < 0)
return 0;
- total = 1 + bset1->dim;
+ total = 1 + isl_basic_set_n_dim(bset1);
isl_int_init(a);
isl_int_init(b);
isl_int_init(g);
* except that the echelon form we use starts from the last column
* and that we are dealing with integer coefficients.
*/
-static struct isl_basic_set *affine_hull(struct isl_ctx *ctx,
+static struct isl_basic_set *affine_hull(
struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
unsigned total;
int col;
int row;
- total = 1 + bset1->dim;
+ if (!bset1 || !bset2)
+ goto error;
+
+ total = 1 + isl_basic_set_n_dim(bset1);
row = 0;
for (col = total-1; col >= 0; --col) {
--row;
}
}
- isl_basic_set_free(ctx, 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 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.
+ * 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 represented by "tab"
+ * yields another point inside the basic set.
+ *
+ * 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_vec *outside_point(struct isl_tab *tab, isl_int *eq, int up)
+{
+ struct isl_ctx *ctx;
+ struct isl_vec *sample = NULL;
+ struct isl_tab_undo *snap;
+ unsigned dim;
+
+ 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->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_map_contains(tab->bmap, sample))
+ return sample;
+ isl_vec_free(sample);
+ sample = NULL;
+
+ 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;
+ if (isl_tab_add_ineq(tab, eq) < 0)
+ goto error;
+
+ 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;
+
+ return sample;
+error:
+ isl_vec_free(sample);
+ return NULL;
+}
+
+struct isl_basic_set *isl_basic_set_recession_cone(struct isl_basic_set *bset)
+{
+ int i;
+
+ bset = isl_basic_set_cow(bset);
+ if (!bset)
+ return NULL;
+ isl_assert(bset->ctx, bset->n_div == 0, goto error);
+
+ for (i = 0; i < bset->n_eq; ++i)
+ isl_int_set_si(bset->eq[i][0], 0);
+
+ for (i = 0; i < bset->n_ineq; ++i)
+ isl_int_set_si(bset->ineq[i][0], 0);
+
+ ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
+ return isl_basic_set_implicit_equalities(bset);
+error:
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+__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 "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_tab *tab,
+ struct isl_basic_set *hull)
+{
+ int i, j;
+ unsigned dim;
+
+ 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) {
+ sample = outside_point(tab, hull->eq[j], 1);
+ if (!sample)
+ goto error;
+ if (sample->size > 0)
+ break;
+ isl_vec_free(sample);
+ sample = outside_point(tab, hull->eq[j], 0);
+ if (!sample)
+ goto error;
+ if (sample->size > 0)
+ break;
+ isl_vec_free(sample);
+
+ 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;
+ }
+
+ return hull;
+error:
+ isl_basic_set_free(hull);
+ return NULL;
+}
+
+/* Drop all constraints in bset that involve any of the dimensions
+ * first to first+n-1.
+ */
+__isl_give isl_basic_set *isl_basic_set_drop_constraints_involving(
+ __isl_take isl_basic_set *bset, unsigned first, unsigned n)
+{
+ int i;
+
+ if (n == 0)
+ return bset;
+
+ bset = isl_basic_set_cow(bset);
+
+ if (!bset)
+ return NULL;
+
+ for (i = bset->n_eq - 1; i >= 0; --i) {
+ if (isl_seq_first_non_zero(bset->eq[i] + 1 + first, n) == -1)
+ continue;
+ isl_basic_set_drop_equality(bset, i);
+ }
+
+ for (i = bset->n_ineq - 1; i >= 0; --i) {
+ if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1)
+ continue;
+ isl_basic_set_drop_inequality(bset, i);
+ }
+
+ return bset;
+}
+
+/* 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_fast_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);
+ if (!tab)
+ goto error;
+ if (tab->empty) {
+ isl_tab_free(tab);
+ isl_vec_free(sample);
+ 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)
+ goto error;
+ if (sample->size == 0) {
+ isl_tab_free(tab);
+ isl_vec_free(sample);
+ return isl_basic_set_set_to_empty(bset);
+ }
+
+ hull = isl_basic_set_from_vec(sample);
+
+ 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;
}
-struct isl_basic_map *isl_map_affine_hull(struct isl_ctx *ctx,
- struct isl_map *map)
+/* 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;
+ 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;
+}
+
+/* Compute the affine hull of "bset", where "cone" is the recession cone
+ * of "bset".
+ *
+ * We first compute a unimodular transformation that puts the unbounded
+ * directions in the last dimensions. In particular, we take a transformation
+ * that maps all equalities to equalities (in HNF) on the first dimensions.
+ * Let x be the original dimensions and y the transformed, with y_1 bounded
+ * and y_2 unbounded.
+ *
+ * [ y_1 ] [ y_1 ] [ Q_1 ]
+ * x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x
+ *
+ * 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 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
+ *
+ * [ y_1 ]
+ * [ F 0 ] [ y_2 ] >= g
+ * or
+ * [ Q_1 ]
+ * [ F 0 ] [ Q_2 ] x >= g
+ * or
+ * F Q_1 x >= g
+ *
+ * The affine hull in the original space is then obtained as
+ * A = preimage(A'', Q_1).
+ */
+static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
+ struct isl_basic_set *cone)
+{
+ unsigned total;
+ unsigned cone_dim;
+ struct isl_basic_set *hull;
+ struct isl_mat *M, *U, *Q;
+
+ 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_left_hermite(M, 0, &U, &Q);
+ if (!M)
+ goto error;
+ isl_mat_free(M);
+
+ U = isl_mat_lin_to_aff(U);
+ bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
+
+ 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);
+
+ Q = isl_mat_lin_to_aff(Q);
+ Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
+
+ if (bset && bset->sample && bset->sample->size == 1 + total)
+ bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
+
+ hull = uset_affine_hull_bounded(bset);
+
+ if (!hull)
+ 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(cone);
+ return NULL;
+}
+
+/* Look for all equalities satisfied by the integer points in bset,
+ * which is assumed not to have any explicit equalities.
+ *
+ * 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).
+ *
+ * Before looking for any outside points, we first compute the recession
+ * cone. The directions of this recession cone will always be part
+ * of the affine hull, so there is no need for looking for any points
+ * in these directions.
+ * In particular, if the recession cone is full-dimensional, then
+ * the affine hull is simply the whole universe.
+ */
+static struct isl_basic_set *uset_affine_hull(struct isl_basic_set *bset)
+{
+ struct isl_basic_set *cone;
+
+ if (isl_basic_set_fast_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);
+ hull = isl_basic_set_universe_like(bset);
+ isl_basic_set_free(bset);
+ return hull;
+ }
+
+ if (cone->n_eq < isl_basic_set_total_dim(cone))
+ return affine_hull_with_cone(bset, cone);
+
+ isl_basic_set_free(cone);
+ return uset_affine_hull_bounded(bset);
+error:
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Look for all equalities satisfied by the integer points in bmap
+ * that are independent of the equalities already explicitly available
+ * in bmap.
+ *
+ * We first remove all equalities already explicitly available,
+ * then look for additional equalities in the reduced space
+ * and then transform the result to the original space.
+ * The original equalities are _not_ added to this set. This is
+ * the responsibility of the calling function.
+ * The resulting basic set has all meaning about the dimensions removed.
+ * In particular, dimensions that correspond to existential variables
+ * in bmap and that are found to be fixed are not removed.
+ */
+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);
+ 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)
+ 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(T2);
+ isl_basic_set_free(bset);
+ isl_basic_set_free(hull);
+ return NULL;
+}
+
+/* Detect and make explicit all equalities satisfied by the (integer)
+ * points in bmap.
+ */
+struct isl_basic_map *isl_basic_map_detect_equalities(
+ struct isl_basic_map *bmap)
+{
+ int i, j;
+ struct isl_basic_set *hull = NULL;
+
+ if (!bmap)
+ return NULL;
+ if (bmap->n_ineq == 0)
+ return bmap;
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+ return bmap;
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES))
+ return bmap;
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
+ return isl_basic_map_implicit_equalities(bmap);
+
+ hull = equalities_in_underlying_set(isl_basic_map_copy(bmap));
+ if (!hull)
+ goto error;
+ if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) {
+ 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,
+ hull->n_eq, 0);
+ for (i = 0; i < hull->n_eq; ++i) {
+ j = isl_basic_map_alloc_equality(bmap);
+ if (j < 0)
+ goto error;
+ 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 isl_basic_map_finalize(bmap);
+error:
+ isl_basic_set_free(hull);
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+__isl_give isl_basic_set *isl_basic_set_detect_equalities(
+ __isl_take isl_basic_set *bset)
+{
+ return (isl_basic_set *)
+ isl_basic_map_detect_equalities((isl_basic_map *)bset);
+}
+
+struct isl_map *isl_map_detect_equalities(struct isl_map *map)
+{
+ struct isl_basic_map *bmap;
+ int i;
+
+ if (!map)
+ return NULL;
+
+ 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;
+ }
+
+ 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
+ * equalities), we compute the additional equalities satisfied by
+ * the integer points (if any) and add the original equalities back in.
+ */
+struct isl_basic_map *isl_basic_map_affine_hull(struct isl_basic_map *bmap)
+{
+ bmap = isl_basic_map_detect_equalities(bmap);
+ bmap = isl_basic_map_cow(bmap);
+ if (bmap)
+ isl_basic_map_free_inequality(bmap, bmap->n_ineq);
+ bmap = isl_basic_map_finalize(bmap);
+ return bmap;
+}
+
+struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset)
+{
+ return (struct isl_basic_set *)
+ isl_basic_map_affine_hull((struct isl_basic_map *)bset);
+}
+
+struct isl_basic_map *isl_map_affine_hull(struct isl_map *map)
{
int i;
struct isl_basic_map *model = NULL;
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;
if (map->n == 0) {
- hull = isl_basic_map_empty(ctx,
- map->nparam, map->n_in, map->n_out);
- isl_map_free(ctx, map);
+ hull = isl_basic_map_empty_like_map(map);
+ isl_map_free(map);
return hull;
}
- map = isl_map_align_divs(ctx, map);
- model = isl_basic_map_copy(ctx, map->p[0]);
- set = isl_map_underlying_set(ctx, map);
- set = isl_set_cow(ctx, set);
+ model = isl_basic_map_copy(map->p[0]);
+ set = isl_map_underlying_set(map);
+ set = isl_set_cow(set);
if (!set)
goto error;
for (i = 0; i < set->n; ++i) {
- set->p[i] = isl_basic_set_cow(ctx, set->p[i]);
- set->p[i] = isl_basic_set_affine_hull(ctx, set->p[i]);
- set->p[i] = isl_basic_set_gauss(ctx, set->p[i], NULL);
+ 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(ctx, set);
+ set = isl_set_remove_empty_parts(set);
if (set->n == 0) {
- hull = isl_basic_map_empty(ctx,
- model->nparam, model->n_in, model->n_out);
- isl_basic_map_free(ctx, model);
+ 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(ctx, set->p[0],
- set->p[--set->n]);
+ set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
if (!set->p[0])
goto error;
}
- bset = isl_basic_set_copy(ctx, set->p[0]);
- hull = isl_basic_map_overlying_set(ctx, bset, model);
+ bset = isl_basic_set_copy(set->p[0]);
+ hull = isl_basic_map_overlying_set(bset, model);
}
- isl_set_free(ctx, set);
- hull = isl_basic_map_simplify(ctx, hull);
- return isl_basic_map_finalize(ctx, hull);
+ isl_set_free(set);
+ hull = isl_basic_map_simplify(hull);
+ return isl_basic_map_finalize(hull);
error:
- isl_basic_map_free(ctx, model);
- isl_set_free(ctx, set);
+ isl_basic_map_free(model);
+ isl_set_free(set);
return NULL;
}
-struct isl_basic_set *isl_set_affine_hull(struct isl_ctx *ctx,
- struct isl_set *set)
+struct isl_basic_set *isl_set_affine_hull(struct isl_set *set)
{
return (struct isl_basic_set *)
- isl_map_affine_hull(ctx, (struct isl_map *)set);
+ isl_map_affine_hull((struct isl_map *)set);
}
projects / platform / upstream / isl.git / blobdiff