+/*
+ * 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"
#include "isl_set.h"
#include "isl_seq.h"
#include "isl_equalities.h"
+#include "isl_tab.h"
-static struct isl_basic_set *uset_convex_hull(struct isl_set *set);
+static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set);
-static swap_ineq(struct isl_basic_map *bmap, unsigned i, unsigned j)
+static void swap_ineq(struct isl_basic_map *bmap, unsigned i, unsigned j)
{
isl_int *t;
}
}
+/* Return 1 if constraint c is redundant with respect to the constraints
+ * in bmap. If c is a lower [upper] bound in some variable and bmap
+ * does not have a lower [upper] bound in that variable, then c cannot
+ * be redundant and we do not need solve any lp.
+ */
+int isl_basic_map_constraint_is_redundant(struct isl_basic_map **bmap,
+ isl_int *c, isl_int *opt_n, isl_int *opt_d)
+{
+ enum isl_lp_result res;
+ unsigned total;
+ int i, j;
+
+ if (!bmap)
+ return -1;
+
+ total = isl_basic_map_total_dim(*bmap);
+ for (i = 0; i < total; ++i) {
+ int sign;
+ if (isl_int_is_zero(c[1+i]))
+ continue;
+ sign = isl_int_sgn(c[1+i]);
+ for (j = 0; j < (*bmap)->n_ineq; ++j)
+ if (sign == isl_int_sgn((*bmap)->ineq[j][1+i]))
+ break;
+ if (j == (*bmap)->n_ineq)
+ break;
+ }
+ if (i < total)
+ return 0;
+
+ 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 -1;
+ if (res == isl_lp_empty) {
+ *bmap = isl_basic_map_set_to_empty(*bmap);
+ return 0;
+ }
+ return !isl_int_is_neg(*opt_n);
+}
+
+int isl_basic_set_constraint_is_redundant(struct isl_basic_set **bset,
+ isl_int *c, isl_int *opt_n, isl_int *opt_d)
+{
+ return isl_basic_map_constraint_is_redundant(
+ (struct isl_basic_map **)bset, c, opt_n, opt_d);
+}
+
/* Compute the convex hull of a basic map, by removing the 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.
*/
struct isl_basic_map *isl_basic_map_convex_hull(struct isl_basic_map *bmap)
{
- int i;
- isl_int opt_n;
- isl_int opt_d;
- struct isl_ctx *ctx;
+ struct isl_tab *tab;
- bmap = isl_basic_map_implicit_equalities(bmap);
if (!bmap)
return NULL;
- 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_REDUNDANT))
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NO_REDUNDANT))
+ return bmap;
+ if (bmap->n_ineq <= 1)
return bmap;
- ctx = bmap->ctx;
- isl_int_init(opt_n);
- isl_int_init(opt_d);
- for (i = bmap->n_ineq-1; i >= 0; --i) {
- enum isl_lp_result res;
- swap_ineq(bmap, i, bmap->n_ineq-1);
- bmap->n_ineq--;
- res = isl_solve_lp(bmap, 0,
- bmap->ineq[bmap->n_ineq]+1, ctx->one, &opt_n, &opt_d);
- bmap->n_ineq++;
- swap_ineq(bmap, i, bmap->n_ineq-1);
- 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(bmap);
- break;
- }
- isl_int_addmul(opt_n, opt_d, bmap->ineq[i][0]);
- if (!isl_int_is_neg(opt_n))
- isl_basic_map_drop_inequality(bmap, i);
- }
- isl_int_clear(opt_n);
- isl_int_clear(opt_d);
-
- F_SET(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
+ tab = isl_tab_from_basic_map(bmap);
+ tab = isl_tab_detect_implicit_equalities(tab);
+ 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_int_clear(opt_n);
- isl_int_clear(opt_d);
+ isl_tab_free(tab);
isl_basic_map_free(bmap);
return NULL;
}
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).
+/* Check if the set set is bound in the direction of the affine
+ * constraint c and if so, set the constant term such that the
+ * resulting constraint is a bounding constraint for the set.
*/
-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_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 (ISL_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);
+ 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)
goto 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);
+ 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);
isl_int_clear(opt_denom);
- if (j < set->n)
- return 0;
- isl_int_neg(dirs->row[n][0], dirs->row[n][0]);
+ return j >= set->n;
+error:
+ isl_int_clear(opt);
+ isl_int_clear(opt_denom);
+ 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;
+ isl_seq_normalize(set->ctx, dirs->row[n], dirs->n_col);
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
* 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, set->dim, 1+set->dim);
+ dirs = isl_mat_alloc(set->ctx, dim, 1+dim);
if (!dirs)
goto error;
n = 0;
- for (i = 0; n < set->dim && i < set->n; ++i) {
+ for (i = 0; n < dim && i < set->n; ++i) {
int f;
struct isl_basic_set *bset = set->p[i];
- for (j = 0; n < set->dim && j < bset->n_eq; ++j) {
- f = is_independent_bound(ctx, set, bset->eq[j],
- 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);
+ 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 < set->dim && j < bset->n_ineq; ++j) {
- f = is_independent_bound(ctx, set, bset->ineq[j],
- dirs, 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)
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;
- if (F_ISSET(bset, ISL_BASIC_MAP_RATIONAL))
+ if (ISL_F_ISSET(bset, ISL_BASIC_MAP_RATIONAL))
return bset;
bset = isl_basic_set_cow(bset);
if (!bset)
return NULL;
- F_SET(bset, ISL_BASIC_MAP_RATIONAL);
+ ISL_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)
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;
- unsigned total;
+ unsigned dim;
- if (F_ISSET(bset, ISL_BASIC_SET_EMPTY))
+ if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))
return bset;
- isl_assert(ctx, bset->nparam == 0, goto error);
- isl_assert(ctx, bset->n_div == 0, goto error);
- bset = isl_basic_set_extend(bset, 0, bset->dim, 0, 1, 0);
+ 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);
i = isl_basic_set_alloc_equality(bset);
if (i < 0)
goto error;
- isl_seq_cpy(bset->eq[i], c, 1 + bset->dim);
+ isl_seq_cpy(bset->eq[i], c, 1 + dim);
return bset;
error:
isl_basic_set_free(bset);
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_basic_set_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
*
* \sum_i x_{i,1} = 1
*/
-static struct isl_basic_set *wrap_constraints(struct isl_ctx *ctx,
- struct isl_set *set)
+static struct isl_basic_set *wrap_constraints(struct isl_set *set)
{
struct isl_basic_set *lp;
unsigned n_eq;
unsigned n_ineq;
int i, j, k;
- unsigned dim;
+ unsigned dim, lp_dim;
if (!set)
return NULL;
- dim = 1 + set->dim;
+ dim = 1 + isl_set_n_dim(set);
n_eq = 1;
n_ineq = set->n;
for (i = 0; i < set->n; ++i) {
n_eq += set->p[i]->n_eq;
n_ineq += set->p[i]->n_ineq;
}
- lp = isl_basic_set_alloc(ctx, 0, dim * set->n, 0, n_eq, n_ineq);
+ lp = isl_basic_set_alloc(set->ctx, 0, dim * set->n, 0, n_eq, n_ineq);
if (!lp)
return NULL;
+ lp_dim = isl_basic_set_n_dim(lp);
k = isl_basic_set_alloc_equality(lp);
isl_int_set_si(lp->eq[k][0], -1);
for (i = 0; i < set->n; ++i) {
}
for (i = 0; i < set->n; ++i) {
k = isl_basic_set_alloc_inequality(lp);
- isl_seq_clr(lp->ineq[k], 1+lp->dim);
+ isl_seq_clr(lp->ineq[k], 1+lp_dim);
isl_int_set_si(lp->ineq[k][1+dim*i], 1);
for (j = 0; j < set->p[i]->n_eq; ++j) {
*
* 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)
+static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
{
int i;
struct isl_mat *T = NULL;
set = isl_set_copy(set);
- dim = 1 + set->dim;
- T = isl_mat_alloc(ctx, 3, 1 + set->dim);
+ dim = 1 + isl_set_n_dim(set);
+ T = isl_mat_alloc(set->ctx, 3, dim);
if (!T)
goto error;
isl_int_set_si(T->row[0][0], 1);
- isl_seq_clr(T->row[0]+1, set->dim);
- isl_seq_cpy(T->row[1], facet, 1+set->dim);
- isl_seq_cpy(T->row[2], ridge, 1+set->dim);
- T = isl_mat_right_inverse(ctx, T);
- set = isl_set_preimage(ctx, set, T);
+ 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(T);
+ set = isl_set_preimage(set, T);
T = NULL;
if (!set)
goto error;
- lp = wrap_constraints(ctx, set);
- obj = isl_vec_alloc(ctx, dim*set->n);
+ lp = wrap_constraints(set);
+ obj = isl_vec_alloc(set->ctx, 1 + dim*set->n);
if (!obj)
goto error;
+ isl_int_set_si(obj->block.data[0], 0);
for (i = 0; i < set->n; ++i) {
- isl_seq_clr(obj->block.data+dim*i, 2);
- isl_int_set_si(obj->block.data[dim*i+2], 1);
- isl_seq_clr(obj->block.data+dim*i+3, dim-3);
+ isl_seq_clr(obj->block.data + 1 + dim*i, 2);
+ isl_int_set_si(obj->block.data[1 + dim*i+2], 1);
+ isl_seq_clr(obj->block.data + 1 + dim*i+3, dim-3);
}
isl_int_init(num);
isl_int_init(den);
- res = isl_solve_lp((struct isl_basic_map *)lp, 0,
- obj->block.data, 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(ctx, obj);
+ isl_vec_free(obj);
isl_basic_set_free(lp);
isl_set_free(set);
- isl_assert(ctx, res == isl_lp_ok, return NULL);
+ isl_assert(set->ctx, res == isl_lp_ok || res == isl_lp_unbounded,
+ return NULL);
return facet;
error:
isl_basic_set_free(lp);
- isl_mat_free(ctx, T);
+ isl_mat_free(T);
isl_set_free(set);
return NULL;
}
+/* Drop rows in "rows" that are redundant with respect to earlier rows,
+ * assuming that "rows" is of full column rank.
+ *
+ * We compute the column echelon form. The non-redundant rows are
+ * those that are the first to contain a non-zero entry in a column.
+ * All the other rows can be removed.
+ */
+static __isl_give isl_mat *drop_redundant_rows(__isl_take isl_mat *rows)
+{
+ struct isl_mat *H = NULL;
+ int col;
+ int row;
+ int last_row;
+
+ if (!rows)
+ return NULL;
+
+ isl_assert(rows->ctx, rows->n_row >= rows->n_col, goto error);
+
+ if (rows->n_row == rows->n_col)
+ return rows;
+
+ H = isl_mat_left_hermite(isl_mat_copy(rows), 0, NULL, NULL);
+ if (!H)
+ goto error;
+
+ last_row = rows->n_row;
+ for (col = rows->n_col - 1; col >= 0; --col) {
+ for (row = col; row < last_row; ++row)
+ if (!isl_int_is_zero(H->row[row][col]))
+ break;
+ isl_assert(rows->ctx, row < last_row, goto error);
+ if (row + 1 < last_row) {
+ rows = isl_mat_drop_rows(rows, row + 1, last_row - (row + 1));
+ if (rows->n_row == rows->n_col)
+ break;
+ }
+ last_row = row;
+ }
+
+ isl_mat_free(H);
+
+ return rows;
+error:
+ isl_mat_free(H);
+ isl_mat_free(rows);
+ 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".
*
* 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;
struct isl_mat *m, *U, *Q;
int i;
+ unsigned dim = isl_set_n_dim(set);
- isl_assert(ctx, set->n > 0, goto error);
- isl_assert(ctx, bounds->n_row == set->dim, goto error);
+ isl_assert(set->ctx, set->n > 0, goto error);
+ isl_assert(set->ctx, bounds->n_row == dim, goto error);
while (bounds->n_row > 1) {
slice = isl_set_copy(set);
- slice = isl_set_add_equality(ctx, 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(ctx, 1 + face->n_eq, 1 + face->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, face->dim);
+ 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 + face->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,
- face->dim - face->n_eq);
- Q = isl_mat_drop_rows(ctx, Q, 1 + face->n_eq,
- face->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);
- 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(ctx, set, bounds->row[0],
+ 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 = drop_redundant_rows(bounds);
+ bounds = isl_mat_product(bounds, Q);
+ isl_assert(set->ctx, bounds->n_row > 1, goto error);
+ if (!wrap_facet(set, bounds->row[0],
bounds->row[bounds->n_row-1]))
goto error;
isl_basic_set_free(face);
return bounds;
error:
isl_basic_set_free(face);
- isl_mat_free(ctx, bounds);
+ isl_mat_free(bounds);
return NULL;
}
* After computing the facets of the facet in the z' space,
* we convert them back to the x space through Q.
*/
-static struct isl_basic_set *compute_facet(struct isl_ctx *ctx,
- struct isl_set *set, isl_int *c)
+static struct isl_basic_set *compute_facet(struct isl_set *set, isl_int *c)
{
struct isl_mat *m, *U, *Q;
- struct isl_basic_set *facet;
+ struct isl_basic_set *facet = NULL;
+ struct isl_ctx *ctx;
+ unsigned dim;
+ ctx = set->ctx;
set = isl_set_copy(set);
- m = isl_mat_alloc(ctx, 2, 1 + set->dim);
+ dim = isl_set_n_dim(set);
+ m = isl_mat_alloc(set->ctx, 2, 1 + dim);
if (!m)
goto error;
isl_int_set_si(m->row[0][0], 1);
- isl_seq_clr(m->row[0]+1, set->dim);
- isl_seq_cpy(m->row[1], c, 1+set->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, 1);
- Q = isl_mat_drop_rows(ctx, Q, 1, 1);
- set = isl_set_preimage(ctx, set, U);
- facet = uset_convex_hull(set);
- facet = isl_basic_set_preimage(ctx, facet, Q);
+ isl_seq_clr(m->row[0]+1, dim);
+ isl_seq_cpy(m->row[1], c, 1+dim);
+ 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);
+ isl_assert(ctx, facet->n_eq == 0, goto error);
return facet;
error:
+ isl_basic_set_free(facet);
isl_set_free(set);
return NULL;
}
* the adjacent facets through wrapping, adding those facets that we
* hadn't already found before.
*
+ * For each facet we have found so far, we first compute its facets
+ * in the resulting convex hull. That is, we compute the ridges
+ * of the resulting convex hull contained in the facet.
+ * We also compute the corresponding facet in the current approximation
+ * of the convex hull. There is no need to wrap around the ridges
+ * in this facet since that would result in a facet that is already
+ * present in the current approximation.
+ *
* This function can still be significantly optimized by checking which of
* the facets of the basic sets are also facets of the convex hull and
* using all the facets so far to help in constructing the facets of the
* using the technique in section "3.1 Ridge Generation" of
* "Extended Convex Hull" by Fukuda et al.
*/
-static struct isl_basic_set *extend(struct isl_ctx *ctx, struct isl_set *set,
- struct isl_mat *initial)
+static struct isl_basic_set *extend(struct isl_basic_set *hull,
+ struct isl_set *set)
{
int i, j, f;
int k;
- struct isl_basic_set *hull = NULL;
struct isl_basic_set *facet = NULL;
- unsigned n_ineq;
- unsigned total;
-
- isl_assert(ctx, set->n > 0, goto error);
+ struct isl_basic_set *hull_facet = NULL;
+ unsigned dim;
- n_ineq = 1;
- for (i = 0; i < set->n; ++i) {
- n_ineq += set->p[i]->n_eq;
- n_ineq += set->p[i]->n_ineq;
- }
- isl_assert(ctx, 1 + set->dim == initial->n_col, goto error);
- hull = isl_basic_set_alloc(ctx, 0, set->dim, 0, 0, n_ineq);
- hull = isl_basic_set_set_rational(hull);
if (!hull)
- goto error;
- k = isl_basic_set_alloc_inequality(hull);
- if (k < 0)
- goto error;
- isl_seq_cpy(hull->ineq[k], initial->row[0], initial->n_col);
+ return NULL;
+
+ isl_assert(set->ctx, set->n > 0, goto error);
+
+ dim = isl_set_n_dim(set);
+
for (i = 0; i < hull->n_ineq; ++i) {
- facet = compute_facet(ctx, set, hull->ineq[i]);
+ facet = compute_facet(set, 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, 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 > n_ineq) {
- hull = isl_basic_set_extend(hull,
- hull->nparam, hull->dim, 0, 0, facet->n_ineq);
- n_ineq = hull->n_ineq + 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],
+ hull_facet->ineq[f], 1 + dim))
+ break;
+ if (f < hull_facet->n_ineq)
+ continue;
k = isl_basic_set_alloc_inequality(hull);
if (k < 0)
goto error;
- isl_seq_cpy(hull->ineq[k], hull->ineq[i], 1+hull->dim);
- if (!wrap_facet(ctx, set, hull->ineq[k], facet->ineq[j]))
+ isl_seq_cpy(hull->ineq[k], hull->ineq[i], 1+dim);
+ if (!wrap_facet(set, hull->ineq[k], facet->ineq[j]))
goto error;
- for (f = 0; f < k; ++f)
- if (isl_seq_eq(hull->ineq[f], hull->ineq[k],
- 1+hull->dim))
- break;
- if (f < k)
- isl_basic_set_free_inequality(hull, 1);
}
+ isl_basic_set_free(hull_facet);
isl_basic_set_free(facet);
}
hull = isl_basic_set_simplify(hull);
hull = isl_basic_set_finalize(hull);
return hull;
error:
+ isl_basic_set_free(hull_facet);
isl_basic_set_free(facet);
isl_basic_set_free(hull);
return NULL;
* 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;
}
static struct isl_set *set_project_out(struct isl_ctx *ctx,
struct isl_set *set, unsigned n)
{
- return isl_set_remove_dims(set, set->dim - n, n);
+ return isl_set_remove_dims(set, isl_set_n_dim(set) - n, n);
+}
+
+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(isl_dim_copy(set->dim));
+ else
+ convex_hull = isl_basic_set_universe(isl_dim_copy(set->dim));
+ isl_set_free(set);
+ return convex_hull;
}
-/* 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.
+/* 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_elim(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 = isl_basic_set_n_dim(bset1);
+ hull = isl_basic_set_alloc(bset1->ctx, 0, 2 + 3 * dim, 0,
+ 1 + 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+2+3*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+2+3*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_set_free(set);
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ isl_basic_set_free(hull);
return NULL;
}
-/* This is the core procedure, where "set" is a "pure" set, i.e.,
- * 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 int isl_basic_set_is_bounded(struct isl_basic_set *bset)
+{
+ struct isl_tab *tab;
+ int bounded;
+
+ tab = isl_tab_from_recession_cone(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;
- struct isl_basic_set *convex_hull = NULL;
- struct isl_mat *bounds;
- if (set->dim == 0) {
- convex_hull = isl_basic_set_universe(set->ctx, 0, 0);
- isl_set_free(set);
- convex_hull = isl_basic_set_set_rational(convex_hull);
- return convex_hull;
+ 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;
+}
- set = isl_set_set_rational(set);
+/* 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 (!set)
+ if (!bset1 || !bset2)
goto error;
- for (i = 0; i < set->n; ++i) {
- set->p[i] = isl_basic_set_convex_hull(set->p[i]);
- if (!set->p[i])
+
+ 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);
}
- set = isl_set_remove_empty_parts(set);
- if (!set)
- goto error;
- if (set->n == 1) {
- convex_hull = isl_basic_set_copy(set->p[0]);
- isl_set_free(set);
- return convex_hull;
+ 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);
}
- 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 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;
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
+ return isl_basic_set_affine_hull(lin);
error:
- isl_set_free(set);
+ isl_basic_set_free(lin);
+ isl_basic_set_free(bset1);
+ isl_basic_set_free(bset2);
return NULL;
}
-/* Compute the convex hull of set "set" with affine hull "affine_hull",
- * We first remove the equalities (transforming the set), compute the
- * convex hull of the transformed set and then add the equalities back
- * (after performing the inverse transformation.
+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_basic_set(set, bset1);
+ set = isl_set_add_basic_set(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_basic_set(set, bset1);
+ set = isl_set_add_basic_set(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_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);
+}
+
+/* Compute the convex hull of a set without any parameters or
+ * 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_unbounded(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);
+ 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_basic_set(set, convex_hull);
+ return modulo_lineality(set, t);
+ }
+ isl_basic_set_free(t);
+ }
+ isl_set_free(set);
+ return convex_hull;
+error:
+ isl_set_free(set);
+ isl_basic_set_free(convex_hull);
+ return NULL;
+}
+
+/* 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.
+ */
+static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
+ struct isl_set *set)
+{
+ struct isl_mat *bounds = NULL;
+ unsigned dim;
+ int k;
+
+ 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);
+ if (!bounds)
+ goto error;
+ k = isl_basic_set_alloc_inequality(hull);
+ if (k < 0)
+ goto error;
+ 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(bounds);
+
+ return hull;
+error:
+ isl_basic_set_free(hull);
+ isl_mat_free(bounds);
+ return NULL;
+}
+
+struct max_constraint {
+ struct isl_mat *c;
+ int count;
+ int ineq;
+};
+
+static int max_constraint_equal(const void *entry, const void *val)
+{
+ struct max_constraint *a = (struct max_constraint *)entry;
+ isl_int *b = (isl_int *)val;
+
+ return isl_seq_eq(a->c->row[0] + 1, b, a->c->n_col - 1);
+}
+
+static void update_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
+ isl_int *con, unsigned len, int n, int ineq)
+{
+ struct isl_hash_table_entry *entry;
+ struct max_constraint *c;
+ uint32_t c_hash;
+
+ c_hash = isl_seq_get_hash(con + 1, len);
+ entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
+ con + 1, 0);
+ if (!entry)
+ return;
+ c = entry->data;
+ if (c->count < n) {
+ isl_hash_table_remove(ctx, table, entry);
+ return;
+ }
+ c->count++;
+ if (isl_int_gt(c->c->row[0][0], con[0]))
+ return;
+ if (isl_int_eq(c->c->row[0][0], con[0])) {
+ if (ineq)
+ c->ineq = ineq;
+ return;
+ }
+ c->c = isl_mat_cow(c->c);
+ isl_int_set(c->c->row[0][0], con[0]);
+ c->ineq = ineq;
+}
+
+/* Check whether the constraint hash table "table" constains the constraint
+ * "con".
+ */
+static int has_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
+ isl_int *con, unsigned len, int n)
+{
+ struct isl_hash_table_entry *entry;
+ struct max_constraint *c;
+ uint32_t c_hash;
+
+ c_hash = isl_seq_get_hash(con + 1, len);
+ entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
+ con + 1, 0);
+ if (!entry)
+ return 0;
+ c = entry->data;
+ if (c->count < n)
+ return 0;
+ return isl_int_eq(c->c->row[0][0], con[0]);
+}
+
+/* Check for inequality constraints of a basic set without equalities
+ * such that the same or more stringent copies of the constraint appear
+ * in all of the basic sets. Such constraints are necessarily facet
+ * constraints of the convex hull.
+ *
+ * If the resulting basic set is by chance identical to one of
+ * the basic sets in "set", then we know that this basic set contains
+ * all other basic sets and is therefore the convex hull of set.
+ * In this case we set *is_hull to 1.
+ */
+static struct isl_basic_set *common_constraints(struct isl_basic_set *hull,
+ struct isl_set *set, int *is_hull)
+{
+ int i, j, s, n;
+ int min_constraints;
+ int best;
+ struct max_constraint *constraints = NULL;
+ struct isl_hash_table *table = NULL;
+ unsigned total;
+
+ *is_hull = 0;
+
+ for (i = 0; i < set->n; ++i)
+ if (set->p[i]->n_eq == 0)
+ break;
+ if (i >= set->n)
+ return hull;
+ min_constraints = set->p[i]->n_ineq;
+ best = i;
+ for (i = best + 1; i < set->n; ++i) {
+ if (set->p[i]->n_eq != 0)
+ continue;
+ if (set->p[i]->n_ineq >= min_constraints)
+ continue;
+ min_constraints = set->p[i]->n_ineq;
+ best = i;
+ }
+ constraints = isl_calloc_array(hull->ctx, struct max_constraint,
+ min_constraints);
+ if (!constraints)
+ return hull;
+ table = isl_alloc_type(hull->ctx, struct isl_hash_table);
+ if (isl_hash_table_init(hull->ctx, table, min_constraints))
+ goto error;
+
+ total = isl_dim_total(set->dim);
+ for (i = 0; i < set->p[best]->n_ineq; ++i) {
+ constraints[i].c = isl_mat_sub_alloc(hull->ctx,
+ set->p[best]->ineq + i, 0, 1, 0, 1 + total);
+ if (!constraints[i].c)
+ goto error;
+ constraints[i].ineq = 1;
+ }
+ for (i = 0; i < min_constraints; ++i) {
+ struct isl_hash_table_entry *entry;
+ uint32_t c_hash;
+ c_hash = isl_seq_get_hash(constraints[i].c->row[0] + 1, total);
+ entry = isl_hash_table_find(hull->ctx, table, c_hash,
+ max_constraint_equal, constraints[i].c->row[0] + 1, 1);
+ if (!entry)
+ goto error;
+ isl_assert(hull->ctx, !entry->data, goto error);
+ entry->data = &constraints[i];
+ }
+
+ n = 0;
+ for (s = 0; s < set->n; ++s) {
+ if (s == best)
+ continue;
+
+ for (i = 0; i < set->p[s]->n_eq; ++i) {
+ isl_int *eq = set->p[s]->eq[i];
+ for (j = 0; j < 2; ++j) {
+ isl_seq_neg(eq, eq, 1 + total);
+ update_constraint(hull->ctx, table,
+ eq, total, n, 0);
+ }
+ }
+ for (i = 0; i < set->p[s]->n_ineq; ++i) {
+ isl_int *ineq = set->p[s]->ineq[i];
+ update_constraint(hull->ctx, table, ineq, total, n,
+ set->p[s]->n_eq == 0);
+ }
+ ++n;
+ }
+
+ for (i = 0; i < min_constraints; ++i) {
+ if (constraints[i].count < n)
+ continue;
+ if (!constraints[i].ineq)
+ continue;
+ j = isl_basic_set_alloc_inequality(hull);
+ if (j < 0)
+ goto error;
+ isl_seq_cpy(hull->ineq[j], constraints[i].c->row[0], 1 + total);
+ }
+
+ for (s = 0; s < set->n; ++s) {
+ if (set->p[s]->n_eq)
+ continue;
+ if (set->p[s]->n_ineq != hull->n_ineq)
+ continue;
+ for (i = 0; i < set->p[s]->n_ineq; ++i) {
+ isl_int *ineq = set->p[s]->ineq[i];
+ if (!has_constraint(hull->ctx, table, ineq, total, n))
+ break;
+ }
+ if (i == set->p[s]->n_ineq)
+ *is_hull = 1;
+ }
+
+ isl_hash_table_clear(table);
+ for (i = 0; i < min_constraints; ++i)
+ isl_mat_free(constraints[i].c);
+ free(constraints);
+ free(table);
+ return hull;
+error:
+ isl_hash_table_clear(table);
+ free(table);
+ if (constraints)
+ for (i = 0; i < min_constraints; ++i)
+ isl_mat_free(constraints[i].c);
+ free(constraints);
+ return hull;
+}
+
+/* Create a template for the convex hull of "set" and fill it up
+ * obvious facet constraints, if any. If the result happens to
+ * be the convex hull of "set" then *is_hull is set to 1.
+ */
+static struct isl_basic_set *proto_hull(struct isl_set *set, int *is_hull)
+{
+ struct isl_basic_set *hull;
+ unsigned n_ineq;
+ int i;
+
+ n_ineq = 1;
+ for (i = 0; i < set->n; ++i) {
+ n_ineq += set->p[i]->n_eq;
+ n_ineq += set->p[i]->n_ineq;
+ }
+ hull = isl_basic_set_alloc_dim(isl_dim_copy(set->dim), 0, 0, n_ineq);
+ hull = isl_basic_set_set_rational(hull);
+ if (!hull)
+ return NULL;
+ return common_constraints(hull, set, is_hull);
+}
+
+static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set)
+{
+ struct isl_basic_set *hull;
+ int is_hull;
+
+ hull = proto_hull(set, &is_hull);
+ if (hull && !is_hull) {
+ if (hull->n_ineq == 0)
+ hull = initial_hull(hull, set);
+ hull = extend(hull, set);
+ }
+ isl_set_free(set);
+
+ return hull;
+}
+
+/* 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)
+{
+ 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;
+ if (!set)
+ return NULL;
+ if (set->n == 1) {
+ convex_hull = isl_basic_set_copy(set->p[0]);
+ isl_set_free(set);
+ return convex_hull;
+ }
+ if (isl_set_n_dim(set) == 1)
+ return convex_hull_1d(set);
+
+ if (isl_set_is_bounded(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);
+ return NULL;
+}
+
+/* This is the core procedure, where "set" is a "pure" set, i.e.,
+ * 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_wrap_bounded(struct isl_set *set)
+{
+ struct isl_basic_set *convex_hull = NULL;
+
+ if (isl_set_n_dim(set) == 0) {
+ convex_hull = isl_basic_set_universe(isl_dim_copy(set->dim));
+ isl_set_free(set);
+ convex_hull = isl_basic_set_set_rational(convex_hull);
+ return convex_hull;
+ }
+
+ set = isl_set_set_rational(set);
+
+ if (!set)
+ goto error;
+ set = isl_set_coalesce(set);
+ if (!set)
+ goto error;
+ if (set->n == 1) {
+ convex_hull = isl_basic_set_copy(set->p[0]);
+ isl_set_free(set);
+ return convex_hull;
+ }
+ if (isl_set_n_dim(set) == 1)
+ return convex_hull_1d(set);
+
+ return uset_convex_hull_wrap(set);
+error:
+ isl_set_free(set);
+ return NULL;
+}
+
+/* Compute the convex hull of set "set" with affine hull "affine_hull",
+ * We first remove the equalities (transforming the set), compute the
+ * 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,
struct isl_set *set, struct isl_basic_set *affine_hull)
if (!dummy)
goto error;
isl_basic_set_free(dummy);
- set = isl_set_preimage(ctx, set, T);
+ set = isl_set_preimage(set, T);
convex_hull = uset_convex_hull(set);
- convex_hull = isl_basic_set_preimage(ctx, convex_hull, T2);
+ convex_hull = isl_basic_set_preimage(convex_hull, T2);
convex_hull = isl_basic_set_intersect(convex_hull, affine_hull);
return convex_hull;
error:
struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
{
struct isl_basic_set *bset;
+ struct isl_basic_map *model = NULL;
struct isl_basic_set *affine_hull = NULL;
struct isl_basic_map *convex_hull = NULL;
struct isl_set *set = NULL;
ctx = map->ctx;
if (map->n == 0) {
- convex_hull = isl_basic_map_empty(ctx,
- map->nparam, map->n_in, map->n_out);
+ convex_hull = isl_basic_map_empty_like_map(map);
isl_map_free(map);
return convex_hull;
}
- set = isl_map_underlying_set(isl_map_copy(map));
+ 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);
if (!set)
goto error;
bset = uset_convex_hull(set);
}
- convex_hull = isl_basic_map_overlying_set(bset,
- isl_basic_map_copy(map->p[0]));
+ convex_hull = isl_basic_map_overlying_set(bset, model);
- isl_map_free(map);
+ 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_set_free(set);
- isl_map_free(map);
+ isl_basic_map_free(model);
return NULL;
}
return (struct isl_basic_set *)
isl_map_convex_hull((struct isl_map *)set);
}
+
+struct sh_data_entry {
+ struct isl_hash_table *table;
+ struct isl_tab *tab;
+};
+
+/* Holds the data needed during the simple hull computation.
+ * In particular,
+ * n the number of basic sets in the original set
+ * hull_table a hash table of already computed constraints
+ * in the simple hull
+ * p for each basic set,
+ * table a hash table of the constraints
+ * tab the tableau corresponding to the basic set
+ */
+struct sh_data {
+ struct isl_ctx *ctx;
+ unsigned n;
+ struct isl_hash_table *hull_table;
+ struct sh_data_entry p[1];
+};
+
+static void sh_data_free(struct sh_data *data)
+{
+ int i;
+
+ if (!data)
+ return;
+ 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->p[i].tab);
+ }
+ free(data);
+}
+
+struct ineq_cmp_data {
+ unsigned len;
+ isl_int *p;
+};
+
+static int has_ineq(const void *entry, const void *val)
+{
+ isl_int *row = (isl_int *)entry;
+ struct ineq_cmp_data *v = (struct ineq_cmp_data *)val;
+
+ return isl_seq_eq(row + 1, v->p + 1, v->len) ||
+ isl_seq_is_neg(row + 1, v->p + 1, v->len);
+}
+
+static int hash_ineq(struct isl_ctx *ctx, struct isl_hash_table *table,
+ isl_int *ineq, unsigned len)
+{
+ uint32_t c_hash;
+ struct ineq_cmp_data v;
+ struct isl_hash_table_entry *entry;
+
+ v.len = len;
+ v.p = ineq;
+ c_hash = isl_seq_get_hash(ineq + 1, len);
+ entry = isl_hash_table_find(ctx, table, c_hash, has_ineq, &v, 1);
+ if (!entry)
+ return - 1;
+ entry->data = ineq;
+ return 0;
+}
+
+/* Fill hash table "table" with the constraints of "bset".
+ * Equalities are added as two inequalities.
+ * The value in the hash table is a pointer to the (in)equality of "bset".
+ */
+static int hash_basic_set(struct isl_hash_table *table,
+ struct isl_basic_set *bset)
+{
+ int i, j;
+ unsigned dim = isl_basic_set_total_dim(bset);
+
+ for (i = 0; i < bset->n_eq; ++i) {
+ for (j = 0; j < 2; ++j) {
+ isl_seq_neg(bset->eq[i], bset->eq[i], 1 + dim);
+ if (hash_ineq(bset->ctx, table, bset->eq[i], dim) < 0)
+ return -1;
+ }
+ }
+ for (i = 0; i < bset->n_ineq; ++i) {
+ if (hash_ineq(bset->ctx, table, bset->ineq[i], dim) < 0)
+ return -1;
+ }
+ return 0;
+}
+
+static struct sh_data *sh_data_alloc(struct isl_set *set, unsigned n_ineq)
+{
+ struct sh_data *data;
+ int i;
+
+ data = isl_calloc(set->ctx, struct sh_data,
+ sizeof(struct sh_data) +
+ (set->n - 1) * sizeof(struct sh_data_entry));
+ if (!data)
+ return NULL;
+ data->ctx = set->ctx;
+ data->n = set->n;
+ data->hull_table = isl_hash_table_alloc(set->ctx, n_ineq);
+ if (!data->hull_table)
+ goto error;
+ for (i = 0; i < set->n; ++i) {
+ data->p[i].table = isl_hash_table_alloc(set->ctx,
+ 2 * set->p[i]->n_eq + set->p[i]->n_ineq);
+ if (!data->p[i].table)
+ goto error;
+ if (hash_basic_set(data->p[i].table, set->p[i]) < 0)
+ goto error;
+ }
+ return data;
+error:
+ sh_data_free(data);
+ return NULL;
+}
+
+/* Check if inequality "ineq" is a bound for basic set "j" or if
+ * it can be relaxed (by increasing the constant term) to become
+ * a bound for that basic set. In the latter case, the constant
+ * term is updated.
+ * Return 1 if "ineq" is a bound
+ * 0 if "ineq" may attain arbitrarily small values on basic set "j"
+ * -1 if some error occurred
+ */
+static int is_bound(struct sh_data *data, struct isl_set *set, int j,
+ isl_int *ineq)
+{
+ enum isl_lp_result res;
+ isl_int opt;
+
+ if (!data->p[j].tab) {
+ data->p[j].tab = isl_tab_from_basic_set(set->p[j]);
+ if (!data->p[j].tab)
+ return -1;
+ }
+
+ isl_int_init(opt);
+
+ 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);
+
+ isl_int_clear(opt);
+
+ return res == isl_lp_ok ? 1 :
+ res == isl_lp_unbounded ? 0 : -1;
+}
+
+/* Check if inequality "ineq" from basic set "i" can be relaxed to
+ * become a bound on the whole set. If so, add the (relaxed) inequality
+ * to "hull".
+ *
+ * We first check if "hull" already contains a translate of the inequality.
+ * If so, we are done.
+ * Then, we check if any of the previous basic sets contains a translate
+ * of the inequality. If so, then we have already considered this
+ * inequality and we are done.
+ * Otherwise, for each basic set other than "i", we check if the inequality
+ * is a bound on the basic set.
+ * For previous basic sets, we know that they do not contain a translate
+ * of the inequality, so we directly call is_bound.
+ * For following basic sets, we first check if a translate of the
+ * inequality appears in its description and if so directly update
+ * the inequality accordingly.
+ */
+static struct isl_basic_set *add_bound(struct isl_basic_set *hull,
+ struct sh_data *data, struct isl_set *set, int i, isl_int *ineq)
+{
+ uint32_t c_hash;
+ struct ineq_cmp_data v;
+ struct isl_hash_table_entry *entry;
+ int j, k;
+
+ if (!hull)
+ return NULL;
+
+ v.len = isl_basic_set_total_dim(hull);
+ v.p = ineq;
+ c_hash = isl_seq_get_hash(ineq + 1, v.len);
+
+ entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
+ has_ineq, &v, 0);
+ if (entry)
+ return hull;
+
+ for (j = 0; j < i; ++j) {
+ entry = isl_hash_table_find(hull->ctx, data->p[j].table,
+ c_hash, has_ineq, &v, 0);
+ if (entry)
+ break;
+ }
+ if (j < i)
+ return hull;
+
+ k = isl_basic_set_alloc_inequality(hull);
+ isl_seq_cpy(hull->ineq[k], ineq, 1 + v.len);
+ if (k < 0)
+ goto error;
+
+ for (j = 0; j < i; ++j) {
+ int bound;
+ bound = is_bound(data, set, j, hull->ineq[k]);
+ if (bound < 0)
+ goto error;
+ if (!bound)
+ break;
+ }
+ if (j < i) {
+ isl_basic_set_free_inequality(hull, 1);
+ return hull;
+ }
+
+ for (j = i + 1; j < set->n; ++j) {
+ int bound, neg;
+ isl_int *ineq_j;
+ entry = isl_hash_table_find(hull->ctx, data->p[j].table,
+ c_hash, has_ineq, &v, 0);
+ if (entry) {
+ ineq_j = entry->data;
+ neg = isl_seq_is_neg(ineq_j + 1,
+ hull->ineq[k] + 1, v.len);
+ if (neg)
+ isl_int_neg(ineq_j[0], ineq_j[0]);
+ if (isl_int_gt(ineq_j[0], hull->ineq[k][0]))
+ isl_int_set(hull->ineq[k][0], ineq_j[0]);
+ if (neg)
+ isl_int_neg(ineq_j[0], ineq_j[0]);
+ continue;
+ }
+ bound = is_bound(data, set, j, hull->ineq[k]);
+ if (bound < 0)
+ goto error;
+ if (!bound)
+ break;
+ }
+ if (j < set->n) {
+ isl_basic_set_free_inequality(hull, 1);
+ return hull;
+ }
+
+ entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
+ has_ineq, &v, 1);
+ if (!entry)
+ goto error;
+ entry->data = hull->ineq[k];
+
+ return hull;
+error:
+ isl_basic_set_free(hull);
+ return NULL;
+}
+
+/* Check if any inequality from basic set "i" can be relaxed to
+ * become a bound on the whole set. If so, add the (relaxed) inequality
+ * to "hull".
+ */
+static struct isl_basic_set *add_bounds(struct isl_basic_set *bset,
+ struct sh_data *data, struct isl_set *set, int i)
+{
+ int j, k;
+ unsigned dim = isl_basic_set_total_dim(bset);
+
+ 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]);
+ }
+ }
+ for (j = 0; j < set->p[i]->n_ineq; ++j)
+ add_bound(bset, data, set, i, set->p[i]->ineq[j]);
+ return bset;
+}
+
+/* Compute a superset of the convex hull of set that is described
+ * by only translates of the constraints in the constituents of set.
+ */
+static struct isl_basic_set *uset_simple_hull(struct isl_set *set)
+{
+ struct sh_data *data = NULL;
+ struct isl_basic_set *hull = NULL;
+ unsigned n_ineq;
+ int i;
+
+ if (!set)
+ return NULL;
+
+ n_ineq = 0;
+ for (i = 0; i < set->n; ++i) {
+ if (!set->p[i])
+ goto error;
+ n_ineq += 2 * set->p[i]->n_eq + set->p[i]->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;
+
+ for (i = 0; i < set->n; ++i)
+ hull = add_bounds(hull, data, set, i);
+
+ sh_data_free(data);
+ isl_set_free(set);
+
+ return hull;
+error:
+ sh_data_free(data);
+ isl_basic_set_free(hull);
+ isl_set_free(set);
+ return NULL;
+}
+
+/* Compute a superset of the convex hull of map that is described
+ * by only translates of the constraints in the constituents of map.
+ */
+struct isl_basic_map *isl_map_simple_hull(struct isl_map *map)
+{
+ 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 NULL;
+ if (map->n == 0) {
+ hull = isl_basic_map_empty_like_map(map);
+ isl_map_free(map);
+ return hull;
+ }
+ if (map->n == 1) {
+ hull = isl_basic_map_copy(map->p[0]);
+ isl_map_free(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]);
+
+ set = isl_map_underlying_set(map);
+
+ bset = uset_simple_hull(set);
+
+ 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;
+}
+
+struct isl_basic_set *isl_set_simple_hull(struct isl_set *set)
+{
+ 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