diff options
Diffstat (limited to 'cloog-0.17.0/isl/isl_convex_hull.c')
| -rw-r--r-- | cloog-0.17.0/isl/isl_convex_hull.c | 2432 |
1 files changed, 0 insertions, 2432 deletions
diff --git a/cloog-0.17.0/isl/isl_convex_hull.c b/cloog-0.17.0/isl/isl_convex_hull.c deleted file mode 100644 index a6e26b8..0000000 --- a/cloog-0.17.0/isl/isl_convex_hull.c +++ /dev/null @@ -1,2432 +0,0 @@ -/* - * 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/lp.h> -#include <isl/map.h> -#include <isl_mat_private.h> -#include <isl/set.h> -#include <isl/seq.h> -#include <isl_options_private.h> -#include "isl_equalities.h" -#include "isl_tab.h" - -static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set); - -/* 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); -} - -/* Remove redundant - * constraints. If the minimal value along the normal of a constraint - * is the same if the constraint is removed, then the constraint is redundant. - * - * Alternatively, we could have intersected the basic map with the - * corresponding equality and the checked if the dimension was that - * of a facet. - */ -__isl_give isl_basic_map *isl_basic_map_remove_redundancies( - __isl_take isl_basic_map *bmap) -{ - struct isl_tab *tab; - - if (!bmap) - return NULL; - - bmap = isl_basic_map_gauss(bmap, NULL); - if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) - return bmap; - if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NO_REDUNDANT)) - return bmap; - if (bmap->n_ineq <= 1) - return bmap; - - tab = isl_tab_from_basic_map(bmap); - if (isl_tab_detect_implicit_equalities(tab) < 0) - goto error; - if (isl_tab_detect_redundant(tab) < 0) - goto error; - bmap = isl_basic_map_update_from_tab(bmap, tab); - isl_tab_free(tab); - ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT); - ISL_F_SET(bmap, ISL_BASIC_MAP_NO_REDUNDANT); - return bmap; -error: - isl_tab_free(tab); - isl_basic_map_free(bmap); - return NULL; -} - -__isl_give isl_basic_set *isl_basic_set_remove_redundancies( - __isl_take isl_basic_set *bset) -{ - return (struct isl_basic_set *) - isl_basic_map_remove_redundancies((struct isl_basic_map *)bset); -} - -/* Remove redundant constraints in each of the basic maps. - */ -__isl_give isl_map *isl_map_remove_redundancies(__isl_take isl_map *map) -{ - return isl_map_inline_foreach_basic_map(map, - &isl_basic_map_remove_redundancies); -} - -__isl_give isl_set *isl_set_remove_redundancies(__isl_take isl_set *set) -{ - return isl_map_remove_redundancies(set); -} - -/* 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 uset_is_bound(struct isl_set *set, isl_int *c, unsigned len) -{ - int first; - int j; - isl_int opt; - isl_int opt_denom; - - isl_int_init(opt); - isl_int_init(opt_denom); - first = 1; - for (j = 0; j < set->n; ++j) { - enum isl_lp_result res; - - if (ISL_F_ISSET(set->p[j], ISL_BASIC_SET_EMPTY)) - continue; - - 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; - if (res == isl_lp_empty) { - set->p[j] = isl_basic_set_set_to_empty(set->p[j]); - if (!set->p[j]) - goto error; - continue; - } - 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); - return j >= set->n; -error: - isl_int_clear(opt); - isl_int_clear(opt_denom); - return -1; -} - -__isl_give isl_basic_map *isl_basic_map_set_rational( - __isl_take isl_basic_set *bmap) -{ - if (!bmap) - return NULL; - - if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) - return bmap; - - bmap = isl_basic_map_cow(bmap); - if (!bmap) - return NULL; - - ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL); - - return isl_basic_map_finalize(bmap); -} - -__isl_give isl_basic_set *isl_basic_set_set_rational( - __isl_take isl_basic_set *bset) -{ - return isl_basic_map_set_rational(bset); -} - -__isl_give isl_map *isl_map_set_rational(__isl_take isl_map *map) -{ - int i; - - map = isl_map_cow(map); - if (!map) - return NULL; - for (i = 0; i < map->n; ++i) { - map->p[i] = isl_basic_map_set_rational(map->p[i]); - if (!map->p[i]) - goto error; - } - return map; -error: - isl_map_free(map); - return NULL; -} - -__isl_give isl_set *isl_set_set_rational(__isl_take isl_set *set) -{ - return isl_map_set_rational(set); -} - -static struct isl_basic_set *isl_basic_set_add_equality( - struct isl_basic_set *bset, isl_int *c) -{ - int i; - unsigned dim; - - if (!bset) - return NULL; - - if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY)) - return bset; - - 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 + dim); - return bset; -error: - isl_basic_set_free(bset); - return NULL; -} - -static struct isl_set *isl_set_add_basic_set_equality(struct isl_set *set, isl_int *c) -{ - int i; - - set = isl_set_cow(set); - if (!set) - return NULL; - for (i = 0; i < set->n; ++i) { - set->p[i] = isl_basic_set_add_equality(set->p[i], c); - if (!set->p[i]) - goto error; - } - return set; -error: - isl_set_free(set); - return NULL; -} - -/* Given a union of basic sets, construct the constraints for wrapping - * a facet around one of its ridges. - * In particular, if each of n the d-dimensional basic sets i in "set" - * contains the origin, satisfies the constraints x_1 >= 0 and x_2 >= 0 - * and is defined by the constraints - * [ 1 ] - * A_i [ x ] >= 0 - * - * then the resulting set is of dimension n*(1+d) and has as constraints - * - * [ a_i ] - * A_i [ x_i ] >= 0 - * - * a_i >= 0 - * - * \sum_i x_{i,1} = 1 - */ -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, lp_dim; - - if (!set) - return NULL; - - 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(set->ctx, 0, dim * set->n, 0, n_eq, n_ineq); - lp = isl_basic_set_set_rational(lp); - 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) { - isl_int_set_si(lp->eq[k][1+dim*i], 0); - isl_int_set_si(lp->eq[k][1+dim*i+1], 1); - isl_seq_clr(lp->eq[k]+1+dim*i+2, dim-2); - } - for (i = 0; i < set->n; ++i) { - k = isl_basic_set_alloc_inequality(lp); - 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) { - k = isl_basic_set_alloc_equality(lp); - isl_seq_clr(lp->eq[k], 1+dim*i); - isl_seq_cpy(lp->eq[k]+1+dim*i, set->p[i]->eq[j], dim); - isl_seq_clr(lp->eq[k]+1+dim*(i+1), dim*(set->n-i-1)); - } - - for (j = 0; j < set->p[i]->n_ineq; ++j) { - k = isl_basic_set_alloc_inequality(lp); - isl_seq_clr(lp->ineq[k], 1+dim*i); - isl_seq_cpy(lp->ineq[k]+1+dim*i, set->p[i]->ineq[j], dim); - isl_seq_clr(lp->ineq[k]+1+dim*(i+1), dim*(set->n-i-1)); - } - } - return lp; -} - -/* Given a facet "facet" of the convex hull of "set" and a facet "ridge" - * of that facet, compute the other facet of the convex hull that contains - * the ridge. - * - * We first transform the set such that the facet constraint becomes - * - * x_1 >= 0 - * - * I.e., the facet lies in - * - * x_1 = 0 - * - * and on that facet, the constraint that defines the ridge is - * - * x_2 >= 0 - * - * (This transformation is not strictly needed, all that is needed is - * that the ridge contains the origin.) - * - * Since the ridge contains the origin, the cone of the convex hull - * will be of the form - * - * x_1 >= 0 - * x_2 >= a x_1 - * - * with this second constraint defining the new facet. - * The constant a is obtained by settting x_1 in the cone of the - * convex hull to 1 and minimizing x_2. - * Now, each element in the cone of the convex hull is the sum - * of elements in the cones of the basic sets. - * If a_i is the dilation factor of basic set i, then the problem - * we need to solve is - * - * min \sum_i x_{i,2} - * st - * \sum_i x_{i,1} = 1 - * a_i >= 0 - * [ a_i ] - * A [ x_i ] >= 0 - * - * with - * [ 1 ] - * A_i [ x_i ] >= 0 - * - * the constraints of each (transformed) basic set. - * 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. - */ -isl_int *isl_set_wrap_facet(__isl_keep isl_set *set, - isl_int *facet, isl_int *ridge) -{ - int i; - isl_ctx *ctx; - struct isl_mat *T = NULL; - struct isl_basic_set *lp = NULL; - struct isl_vec *obj; - enum isl_lp_result res; - isl_int num, den; - unsigned dim; - - if (!set) - return NULL; - ctx = set->ctx; - set = isl_set_copy(set); - set = isl_set_set_rational(set); - - dim = 1 + isl_set_n_dim(set); - T = isl_mat_alloc(ctx, 3, dim); - if (!T) - goto error; - isl_int_set_si(T->row[0][0], 1); - 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(set); - obj = isl_vec_alloc(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 + 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_basic_set_solve_lp(lp, 0, - obj->block.data, ctx->one, &num, &den, NULL); - if (res == isl_lp_ok) { - isl_int_neg(num, num); - isl_seq_combine(facet, num, facet, den, ridge, dim); - isl_seq_normalize(ctx, facet, dim); - } - isl_int_clear(num); - isl_int_clear(den); - isl_vec_free(obj); - isl_basic_set_free(lp); - isl_set_free(set); - if (res == isl_lp_error) - return NULL; - isl_assert(ctx, res == isl_lp_ok || res == isl_lp_unbounded, - return NULL); - return facet; -error: - isl_basic_set_free(lp); - isl_mat_free(T); - isl_set_free(set); - return NULL; -} - -/* Compute the constraint of a facet of "set". - * - * We first compute the intersection with a bounding constraint - * that is orthogonal to one of the coordinate axes. - * If the affine hull of this intersection has only one equality, - * we have found a facet. - * Otherwise, we wrap the current bounding constraint around - * one of the equalities of the face (one that is not equal to - * the current bounding constraint). - * This process continues until we have found a facet. - * The dimension of the intersection increases by at least - * one on each iteration, so termination is guaranteed. - */ -static __isl_give isl_mat *initial_facet_constraint(__isl_keep isl_set *set) -{ - struct isl_set *slice = NULL; - struct isl_basic_set *face = NULL; - int i; - unsigned dim = isl_set_n_dim(set); - int is_bound; - isl_mat *bounds; - - isl_assert(set->ctx, set->n > 0, goto error); - bounds = isl_mat_alloc(set->ctx, 1, 1 + dim); - if (!bounds) - return NULL; - - isl_seq_clr(bounds->row[0], dim); - isl_int_set_si(bounds->row[0][1 + dim - 1], 1); - is_bound = uset_is_bound(set, bounds->row[0], 1 + dim); - if (is_bound < 0) - goto error; - isl_assert(set->ctx, is_bound, goto error); - isl_seq_normalize(set->ctx, bounds->row[0], 1 + dim); - bounds->n_row = 1; - - for (;;) { - slice = isl_set_copy(set); - slice = isl_set_add_basic_set_equality(slice, bounds->row[0]); - face = isl_set_affine_hull(slice); - if (!face) - goto error; - if (face->n_eq == 1) { - isl_basic_set_free(face); - break; - } - for (i = 0; i < face->n_eq; ++i) - if (!isl_seq_eq(bounds->row[0], face->eq[i], 1 + dim) && - !isl_seq_is_neg(bounds->row[0], - face->eq[i], 1 + dim)) - break; - isl_assert(set->ctx, i < face->n_eq, goto error); - if (!isl_set_wrap_facet(set, bounds->row[0], face->eq[i])) - goto error; - isl_seq_normalize(set->ctx, bounds->row[0], bounds->n_col); - isl_basic_set_free(face); - } - - return bounds; -error: - isl_basic_set_free(face); - isl_mat_free(bounds); - return NULL; -} - -/* Given the bounding constraint "c" of a facet of the convex hull of "set", - * compute a hyperplane description of the facet, i.e., compute the facets - * of the facet. - * - * We compute an affine transformation that transforms the constraint - * - * [ 1 ] - * c [ x ] = 0 - * - * to the constraint - * - * z_1 = 0 - * - * by computing the right inverse U of a matrix that starts with the rows - * - * [ 1 0 ] - * [ c ] - * - * Then - * [ 1 ] [ 1 ] - * [ x ] = U [ z ] - * and - * [ 1 ] [ 1 ] - * [ z ] = Q [ x ] - * - * with Q = U^{-1} - * Since z_1 is zero, we can drop this variable as well as the corresponding - * column of U to obtain - * - * [ 1 ] [ 1 ] - * [ x ] = U' [ z' ] - * and - * [ 1 ] [ 1 ] - * [ z' ] = Q' [ x ] - * - * with Q' equal to Q, but without the corresponding row. - * 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_set *set, isl_int *c) -{ - struct isl_mat *m, *U, *Q; - struct isl_basic_set *facet = NULL; - struct isl_ctx *ctx; - unsigned dim; - - ctx = set->ctx; - set = isl_set_copy(set); - 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, 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); - if (facet) - isl_assert(ctx, facet->n_eq == 0, goto error); - return facet; -error: - isl_basic_set_free(facet); - isl_set_free(set); - return NULL; -} - -/* Given an initial facet constraint, compute the remaining facets. - * We do this by running through all facets found so far and computing - * 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 - * facets - * and/or - * 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_basic_set *hull, - struct isl_set *set) -{ - int i, j, f; - int k; - struct isl_basic_set *facet = NULL; - struct isl_basic_set *hull_facet = NULL; - unsigned dim; - - if (!hull) - 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(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 || !hull_facet) - goto error; - hull = isl_basic_set_cow(hull); - hull = isl_basic_set_extend_space(hull, - isl_space_copy(hull->dim), 0, 0, facet->n_ineq); - if (!hull) - goto error; - for (j = 0; j < facet->n_ineq; ++j) { - for (f = 0; f < hull_facet->n_ineq; ++f) - if (isl_seq_eq(facet->ineq[j], - 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+dim); - if (!isl_set_wrap_facet(set, hull->ineq[k], facet->ineq[j])) - goto error; - } - 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; -} - -/* Special case for computing the convex hull of a one dimensional set. - * 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_set *set) -{ - struct isl_mat *c = NULL; - isl_int *lower = NULL; - isl_int *upper = NULL; - int i, j, k; - isl_int a, b; - struct isl_basic_set *hull; - - for (i = 0; i < set->n; ++i) { - set->p[i] = isl_basic_set_simplify(set->p[i]); - if (!set->p[i]) - goto error; - } - set = isl_set_remove_empty_parts(set); - if (!set) - goto error; - 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(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_seq_cpy(lower, set->p[0]->eq[0], 2); - isl_seq_neg(upper, set->p[0]->eq[0], 2); - } else { - isl_seq_neg(lower, set->p[0]->eq[0], 2); - isl_seq_cpy(upper, set->p[0]->eq[0], 2); - } - } else { - for (j = 0; j < set->p[0]->n_ineq; ++j) { - if (isl_int_is_pos(set->p[0]->ineq[j][1])) { - lower = c->row[0]; - isl_seq_cpy(lower, set->p[0]->ineq[j], 2); - } else { - upper = c->row[1]; - isl_seq_cpy(upper, set->p[0]->ineq[j], 2); - } - } - } - - isl_int_init(a); - isl_int_init(b); - for (i = 0; i < set->n; ++i) { - struct isl_basic_set *bset = set->p[i]; - int has_lower = 0; - int has_upper = 0; - - for (j = 0; j < bset->n_eq; ++j) { - has_lower = 1; - has_upper = 1; - if (lower) { - isl_int_mul(a, lower[0], bset->eq[j][1]); - isl_int_mul(b, lower[1], bset->eq[j][0]); - if (isl_int_lt(a, b) && isl_int_is_pos(bset->eq[j][1])) - isl_seq_cpy(lower, bset->eq[j], 2); - if (isl_int_gt(a, b) && isl_int_is_neg(bset->eq[j][1])) - isl_seq_neg(lower, bset->eq[j], 2); - } - if (upper) { - isl_int_mul(a, upper[0], bset->eq[j][1]); - isl_int_mul(b, upper[1], bset->eq[j][0]); - if (isl_int_lt(a, b) && isl_int_is_pos(bset->eq[j][1])) - isl_seq_neg(upper, bset->eq[j], 2); - if (isl_int_gt(a, b) && isl_int_is_neg(bset->eq[j][1])) - isl_seq_cpy(upper, bset->eq[j], 2); - } - } - for (j = 0; j < bset->n_ineq; ++j) { - if (isl_int_is_pos(bset->ineq[j][1])) - has_lower = 1; - if (isl_int_is_neg(bset->ineq[j][1])) - has_upper = 1; - if (lower && isl_int_is_pos(bset->ineq[j][1])) { - isl_int_mul(a, lower[0], bset->ineq[j][1]); - isl_int_mul(b, lower[1], bset->ineq[j][0]); - if (isl_int_lt(a, b)) - isl_seq_cpy(lower, bset->ineq[j], 2); - } - if (upper && isl_int_is_neg(bset->ineq[j][1])) { - isl_int_mul(a, upper[0], bset->ineq[j][1]); - isl_int_mul(b, upper[1], bset->ineq[j][0]); - if (isl_int_gt(a, b)) - isl_seq_cpy(upper, bset->ineq[j], 2); - } - } - if (!has_lower) - lower = NULL; - if (!has_upper) - upper = NULL; - } - isl_int_clear(a); - isl_int_clear(b); - - hull = isl_basic_set_alloc(set->ctx, 0, 1, 0, 0, 2); - hull = isl_basic_set_set_rational(hull); - if (!hull) - goto error; - if (lower) { - k = isl_basic_set_alloc_inequality(hull); - isl_seq_cpy(hull->ineq[k], lower, 2); - } - if (upper) { - k = isl_basic_set_alloc_inequality(hull); - isl_seq_cpy(hull->ineq[k], upper, 2); - } - hull = isl_basic_set_finalize(hull); - isl_set_free(set); - isl_mat_free(c); - return hull; -error: - isl_set_free(set); - isl_mat_free(c); - return NULL; -} - -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_space_copy(set->dim)); - else - convex_hull = isl_basic_set_universe(isl_space_copy(set->dim)); - isl_set_free(set); - return convex_hull; -} - -/* Compute the convex hull of a pair of basic sets without any parameters or - * integer divisions using Fourier-Motzkin elimination. - * The convex hull is the set of all points that can be written as - * the sum of points from both basic sets (in homogeneous coordinates). - * We set up the constraints in a space with dimensions for each of - * the three sets and then project out the dimensions corresponding - * to the two original basic sets, retaining only those corresponding - * to the convex hull. - */ -static struct isl_basic_set *convex_hull_pair_elim(struct isl_basic_set *bset1, - struct isl_basic_set *bset2) -{ - int i, j, k; - struct isl_basic_set *bset[2]; - struct isl_basic_set *hull = NULL; - unsigned dim; - - if (!bset1 || !bset2) - goto error; - - 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, isl_dim_set, dim, 2*(1+dim)); - hull = isl_basic_set_remove_redundancies(hull); - isl_basic_set_free(bset1); - isl_basic_set_free(bset2); - return hull; -error: - isl_basic_set_free(bset1); - isl_basic_set_free(bset2); - isl_basic_set_free(hull); - return NULL; -} - -/* Is the set bounded for each value of the parameters? - */ -int isl_basic_set_is_bounded(__isl_keep isl_basic_set *bset) -{ - struct isl_tab *tab; - int bounded; - - if (!bset) - return -1; - if (isl_basic_set_plain_is_empty(bset)) - return 1; - - tab = isl_tab_from_recession_cone(bset, 1); - bounded = isl_tab_cone_is_bounded(tab); - isl_tab_free(tab); - return bounded; -} - -/* Is the image bounded for each value of the parameters and - * the domain variables? - */ -int isl_basic_map_image_is_bounded(__isl_keep isl_basic_map *bmap) -{ - unsigned nparam = isl_basic_map_dim(bmap, isl_dim_param); - unsigned n_in = isl_basic_map_dim(bmap, isl_dim_in); - int bounded; - - bmap = isl_basic_map_copy(bmap); - bmap = isl_basic_map_cow(bmap); - bmap = isl_basic_map_move_dims(bmap, isl_dim_param, nparam, - isl_dim_in, 0, n_in); - bounded = isl_basic_set_is_bounded((isl_basic_set *)bmap); - isl_basic_map_free(bmap); - - return bounded; -} - -/* Is the set bounded for each value of the parameters? - */ -int isl_set_is_bounded(__isl_keep isl_set *set) -{ - int i; - - if (!set) - return -1; - - for (i = 0; i < set->n; ++i) { - int bounded = isl_basic_set_is_bounded(set->p[i]); - if (!bounded || bounded < 0) - return bounded; - } - return 1; -} - -/* Compute the lineality space of the convex hull of bset1 and bset2. - * - * We first compute the intersection of the recession cone of bset1 - * with the negative of the recession cone of bset2 and then compute - * the linear hull of the resulting cone. - */ -static struct isl_basic_set *induced_lineality_space( - struct isl_basic_set *bset1, struct isl_basic_set *bset2) -{ - int i, k; - struct isl_basic_set *lin = NULL; - unsigned dim; - - if (!bset1 || !bset2) - goto error; - - dim = isl_basic_set_total_dim(bset1); - lin = isl_basic_set_alloc_space(isl_basic_set_get_space(bset1), 0, - bset1->n_eq + bset2->n_eq, - bset1->n_ineq + bset2->n_ineq); - lin = isl_basic_set_set_rational(lin); - if (!lin) - goto error; - for (i = 0; i < bset1->n_eq; ++i) { - k = isl_basic_set_alloc_equality(lin); - if (k < 0) - goto error; - isl_int_set_si(lin->eq[k][0], 0); - isl_seq_cpy(lin->eq[k] + 1, bset1->eq[i] + 1, dim); - } - for (i = 0; i < bset1->n_ineq; ++i) { - k = isl_basic_set_alloc_inequality(lin); - if (k < 0) - goto error; - isl_int_set_si(lin->ineq[k][0], 0); - isl_seq_cpy(lin->ineq[k] + 1, bset1->ineq[i] + 1, dim); - } - for (i = 0; i < bset2->n_eq; ++i) { - k = isl_basic_set_alloc_equality(lin); - if (k < 0) - goto error; - isl_int_set_si(lin->eq[k][0], 0); - isl_seq_neg(lin->eq[k] + 1, bset2->eq[i] + 1, dim); - } - for (i = 0; i < bset2->n_ineq; ++i) { - k = isl_basic_set_alloc_inequality(lin); - if (k < 0) - goto error; - isl_int_set_si(lin->ineq[k][0], 0); - isl_seq_neg(lin->ineq[k] + 1, bset2->ineq[i] + 1, dim); - } - - isl_basic_set_free(bset1); - isl_basic_set_free(bset2); - return isl_basic_set_affine_hull(lin); -error: - isl_basic_set_free(lin); - isl_basic_set_free(bset1); - isl_basic_set_free(bset2); - return NULL; -} - -static struct isl_basic_set *uset_convex_hull(struct isl_set *set); - -/* Given a set and a linear space "lin" of dimension n > 0, - * project the linear space from the set, compute the convex hull - * and then map the set back to the original space. - * - * Let - * - * M x = 0 - * - * describe the linear space. We first compute the Hermite normal - * form H = M U of M = H Q, to obtain - * - * H Q x = 0 - * - * The last n rows of H will be zero, so the last n variables of x' = Q x - * are the one we want to project out. We do this by transforming each - * basic set A x >= b to A U x' >= b and then removing the last n dimensions. - * After computing the convex hull in x'_1, i.e., A' x'_1 >= b', - * we transform the hull back to the original space as A' Q_1 x >= b', - * with Q_1 all but the last n rows of Q. - */ -static struct isl_basic_set *modulo_lineality(struct isl_set *set, - struct isl_basic_set *lin) -{ - unsigned total = isl_basic_set_total_dim(lin); - unsigned lin_dim; - struct isl_basic_set *hull; - struct isl_mat *M, *U, *Q; - - if (!set || !lin) - goto error; - lin_dim = total - lin->n_eq; - M = isl_mat_sub_alloc6(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, isl_dim_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) -{ - isl_space *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_space_set_alloc(bset1->ctx, 0, n); - lp = isl_basic_set_alloc_space(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); n++; - /* positivity constraint 1 >= 0 */ - isl_int_set_si(lp->eq[k][n], i == 0); n++; - for (j = 0; j < bset1->n_eq; ++j) { - isl_int_set(lp->eq[k][n], bset1->eq[j][i]); n++; - isl_int_neg(lp->eq[k][n], bset1->eq[j][i]); n++; - } - for (j = 0; j < bset1->n_ineq; ++j) { - isl_int_set(lp->eq[k][n], bset1->ineq[j][i]); n++; - } - /* positivity constraint 1 >= 0 */ - isl_int_set_si(lp->eq[k][n], -(i == 0)); n++; - for (j = 0; j < bset2->n_eq; ++j) { - isl_int_neg(lp->eq[k][n], bset2->eq[j][i]); n++; - isl_int_set(lp->eq[k][n], bset2->eq[j][i]); n++; - } - for (j = 0; j < bset2->n_ineq; ++j) { - isl_int_neg(lp->eq[k][n], bset2->ineq[j][i]); n++; - } - } - 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 formulation, for each polyhedron i, - * the first constraint is the positivity constraint, followed by pairs - * of variables for the equalities, followed by variables for the inequalities. - * We then simply pick a feasible solution and compute s using (*). - * - * 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]); 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->el, dir->size); - 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_space(isl_basic_set_get_space(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; -} - -static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set); -static struct isl_basic_set *modulo_affine_hull( - struct isl_set *set, struct isl_basic_set *affine_hull); - -/* Compute the convex hull of a pair of basic sets without any parameters or - * integer divisions. - * - * This function is called from uset_convex_hull_unbounded, which - * means that the complete convex hull is unbounded. Some pairs - * of basic sets may still be bounded, though. - * They may even lie inside a lower dimensional space, in which - * case they need to be handled inside their affine hull since - * the main algorithm assumes that the result is full-dimensional. - * - * If the convex hull of the two basic sets would have a non-trivial - * lineality space, we first project out this lineality space. - */ -static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1, - struct isl_basic_set *bset2) -{ - isl_basic_set *lin, *aff; - int bounded1, bounded2; - - if (bset1->ctx->opt->convex == ISL_CONVEX_HULL_FM) - return convex_hull_pair_elim(bset1, bset2); - - aff = isl_set_affine_hull(isl_basic_set_union(isl_basic_set_copy(bset1), - isl_basic_set_copy(bset2))); - if (!aff) - goto error; - if (aff->n_eq != 0) - return modulo_affine_hull(isl_basic_set_union(bset1, bset2), aff); - isl_basic_set_free(aff); - - bounded1 = isl_basic_set_is_bounded(bset1); - bounded2 = isl_basic_set_is_bounded(bset2); - - if (bounded1 < 0 || bounded2 < 0) - goto error; - - if (bounded1 && bounded2) - uset_convex_hull_wrap(isl_basic_set_union(bset1, bset2)); - - if (bounded1 || bounded2) - return convex_hull_pair_pointed(bset1, bset2); - - lin = induced_lineality_space(isl_basic_set_copy(bset1), - 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_space(isl_basic_set_get_space(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_space(isl_basic_set_get_space(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) { - isl_space *dim = isl_set_get_space(set); - isl_set_free(set); - return isl_basic_set_empty(dim); - } - - lin = isl_set_alloc_space(isl_set_get_space(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. - * This function assumes that the given set is bounded. - */ -static struct isl_basic_set *initial_hull(struct isl_basic_set *hull, - struct isl_set *set) -{ - struct isl_mat *bounds = NULL; - unsigned dim; - int k; - - if (!hull) - goto error; - bounds = initial_facet_constraint(set); - 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_space_dim(set->dim, isl_dim_all); - for (i = 0; i < set->p[best]->n_ineq; ++i) { - constraints[i].c = isl_mat_sub_alloc6(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_space(isl_space_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) && - set->ctx->opt->convex == ISL_CONVEX_HULL_WRAP) - 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 (!set) - goto error; - - if (isl_set_n_dim(set) == 0) { - convex_hull = isl_basic_set_universe(isl_space_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); - 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_set *set, struct isl_basic_set *affine_hull) -{ - struct isl_mat *T; - struct isl_mat *T2; - struct isl_basic_set *dummy; - struct isl_basic_set *convex_hull; - - dummy = isl_basic_set_remove_equalities( - isl_basic_set_copy(affine_hull), &T, &T2); - if (!dummy) - goto error; - isl_basic_set_free(dummy); - set = isl_set_preimage(set, T); - convex_hull = uset_convex_hull(set); - convex_hull = isl_basic_set_preimage(convex_hull, T2); - convex_hull = isl_basic_set_intersect(convex_hull, affine_hull); - return convex_hull; -error: - isl_basic_set_free(affine_hull); - isl_set_free(set); - return NULL; -} - -/* Compute the convex hull of a map. - * - * The implementation was inspired by "Extended Convex Hull" by Fukuda et al., - * specifically, the wrapping of facets to obtain new facets. - */ -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; - struct isl_ctx *ctx; - - if (!map) - goto error; - - ctx = map->ctx; - if (map->n == 0) { - convex_hull = isl_basic_map_empty_like_map(map); - isl_map_free(map); - return convex_hull; - } - - map = isl_map_detect_equalities(map); - map = isl_map_align_divs(map); - if (!map) - goto error; - model = isl_basic_map_copy(map->p[0]); - set = isl_map_underlying_set(map); - if (!set) - goto error; - - affine_hull = isl_set_affine_hull(isl_set_copy(set)); - if (!affine_hull) - goto error; - if (affine_hull->n_eq != 0) - bset = modulo_affine_hull(set, affine_hull); - else { - isl_basic_set_free(affine_hull); - bset = uset_convex_hull(set); - } - - convex_hull = isl_basic_map_overlying_set(bset, model); - if (!convex_hull) - return NULL; - - ISL_F_SET(convex_hull, ISL_BASIC_MAP_NO_IMPLICIT); - ISL_F_SET(convex_hull, ISL_BASIC_MAP_ALL_EQUALITIES); - ISL_F_CLR(convex_hull, ISL_BASIC_MAP_RATIONAL); - return convex_hull; -error: - isl_set_free(set); - isl_basic_map_free(model); - return NULL; -} - -struct isl_basic_set *isl_set_convex_hull(struct isl_set *set) -{ - return (struct isl_basic_set *) - isl_map_convex_hull((struct isl_map *)set); -} - -__isl_give isl_basic_map *isl_map_polyhedral_hull(__isl_take isl_map *map) -{ - isl_basic_map *hull; - - hull = isl_map_convex_hull(map); - return isl_basic_map_remove_divs(hull); -} - -__isl_give isl_basic_set *isl_set_polyhedral_hull(__isl_take isl_set *set) -{ - return (isl_basic_set *)isl_map_polyhedral_hull((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 || res == isl_lp_empty) ? 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); - bset = add_bound(bset, data, set, i, set->p[i]->eq[j]); - } - } - for (j = 0; j < set->p[i]->n_ineq; ++j) - bset = 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_space(isl_space_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_remove_redundancies(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; -} |