X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_affine_hull.c;h=0d66081eaec3ab462eab1b79e7a4157acb78aaf8;hb=ca90b151a05f17ccc1c3215ff24dc5d7b9198ff4;hp=cd991cc64751a41680957340884a9a4dbad06f85;hpb=5e07d663e19045190c70fc2195505354c5d85d4f;p=platform%2Fupstream%2Fisl.git diff --git a/isl_affine_hull.c b/isl_affine_hull.c index cd991cc..0d66081 100644 --- a/isl_affine_hull.c +++ b/isl_affine_hull.c @@ -1,64 +1,84 @@ -#include "isl_ctx.h" -#include "isl_seq.h" -#include "isl_set.h" -#include "isl_lp.h" -#include "isl_map.h" -#include "isl_map_private.h" +/* + * Copyright 2008-2009 Katholieke Universiteit Leuven + * Copyright 2010 INRIA Saclay + * Copyright 2012 Ecole Normale Superieure + * + * Use of this software is governed by the MIT license + * + * Written by Sven Verdoolaege, K.U.Leuven, Departement + * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium + * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite, + * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France + * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France + */ + +#include +#include +#include +#include +#include +#include #include "isl_equalities.h" #include "isl_sample.h" +#include "isl_tab.h" +#include struct isl_basic_map *isl_basic_map_implicit_equalities( struct isl_basic_map *bmap) { - int i; - int rational; - isl_int opt; - isl_int opt_denom; - struct isl_ctx *ctx; + struct isl_tab *tab; if (!bmap) return bmap; + 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_IMPLICIT)) return bmap; + if (bmap->n_ineq <= 1) + return bmap; - ctx = bmap->ctx; - rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); - isl_int_init(opt); - isl_int_init(opt_denom); - if (!rational) - isl_int_set_si(opt_denom, 1); - for (i = bmap->n_ineq - 1; i >= 0; --i) { - enum isl_lp_result res; - res = isl_solve_lp(bmap, 1, bmap->ineq[i]+1, ctx->one, - &opt, rational ? &opt_denom : NULL); - 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; - } - if (!isl_int_is_one(opt_denom)) - continue; - isl_int_add(opt, opt, bmap->ineq[i][0]); - if (isl_int_is_zero(opt)) - isl_basic_map_inequality_to_equality(bmap, i); - } - isl_int_clear(opt_denom); - isl_int_clear(opt); - + tab = isl_tab_from_basic_map(bmap, 0); + if (isl_tab_detect_implicit_equalities(tab) < 0) + goto error; + bmap = isl_basic_map_update_from_tab(bmap, tab); + isl_tab_free(tab); + bmap = isl_basic_map_gauss(bmap, NULL); ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT); return bmap; error: - isl_int_clear(opt); + isl_tab_free(tab); isl_basic_map_free(bmap); return NULL; } +struct isl_basic_set *isl_basic_set_implicit_equalities( + struct isl_basic_set *bset) +{ + return (struct isl_basic_set *) + isl_basic_map_implicit_equalities((struct isl_basic_map*)bset); +} + +struct isl_map *isl_map_implicit_equalities(struct isl_map *map) +{ + int i; + + if (!map) + return map; + + for (i = 0; i < map->n; ++i) { + map->p[i] = isl_basic_map_implicit_equalities(map->p[i]); + if (!map->p[i]) + goto error; + } + + return map; +error: + isl_map_free(map); + return NULL; +} + /* Make eq[row][col] of both bmaps equal so we can add the row * add the column to the common matrix. * Note that because of the echelon form, the columns of row row @@ -192,6 +212,9 @@ static struct isl_basic_set *affine_hull( int col; int row; + if (!bset1 || !bset2) + goto error; + total = 1 + isl_basic_set_n_dim(bset1); row = 0; @@ -212,89 +235,785 @@ static struct isl_basic_set *affine_hull( --row; } } + isl_assert(bset1->ctx, row == bset1->n_eq, goto error); isl_basic_set_free(bset2); - isl_assert(ctx, row == bset1->n_eq, goto error); + bset1 = isl_basic_set_normalize_constraints(bset1); return bset1; error: isl_basic_set_free(bset1); + isl_basic_set_free(bset2); + return NULL; +} + +/* Find an integer point in the set represented by "tab" + * that lies outside of the equality "eq" e(x) = 0. + * If "up" is true, look for a point satisfying e(x) - 1 >= 0. + * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1). + * The point, if found, is returned. + * If no point can be found, a zero-length vector is returned. + * + * Before solving an ILP problem, we first check if simply + * adding the normal of the constraint to one of the known + * integer points in the basic set represented by "tab" + * yields another point inside the basic set. + * + * The caller of this function ensures that the tableau is bounded or + * that tab->basis and tab->n_unbounded have been set appropriately. + */ +static struct isl_vec *outside_point(struct isl_tab *tab, isl_int *eq, int up) +{ + struct isl_ctx *ctx; + struct isl_vec *sample = NULL; + struct isl_tab_undo *snap; + unsigned dim; + + if (!tab) + return NULL; + ctx = tab->mat->ctx; + + dim = tab->n_var; + sample = isl_vec_alloc(ctx, 1 + dim); + if (!sample) + return NULL; + isl_int_set_si(sample->el[0], 1); + isl_seq_combine(sample->el + 1, + ctx->one, tab->bmap->sample->el + 1, + up ? ctx->one : ctx->negone, eq + 1, dim); + if (isl_basic_map_contains(tab->bmap, sample)) + return sample; + isl_vec_free(sample); + sample = NULL; + + snap = isl_tab_snap(tab); + + if (!up) + isl_seq_neg(eq, eq, 1 + dim); + isl_int_sub_ui(eq[0], eq[0], 1); + + if (isl_tab_extend_cons(tab, 1) < 0) + goto error; + if (isl_tab_add_ineq(tab, eq) < 0) + goto error; + + sample = isl_tab_sample(tab); + + isl_int_add_ui(eq[0], eq[0], 1); + if (!up) + isl_seq_neg(eq, eq, 1 + dim); + + if (sample && isl_tab_rollback(tab, snap) < 0) + goto error; + + return sample; +error: + isl_vec_free(sample); + return NULL; +} + +struct isl_basic_set *isl_basic_set_recession_cone(struct isl_basic_set *bset) +{ + int i; + + bset = isl_basic_set_cow(bset); + if (!bset) + return NULL; + isl_assert(bset->ctx, bset->n_div == 0, goto error); + + for (i = 0; i < bset->n_eq; ++i) + isl_int_set_si(bset->eq[i][0], 0); + + for (i = 0; i < bset->n_ineq; ++i) + isl_int_set_si(bset->ineq[i][0], 0); + + ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT); + return isl_basic_set_implicit_equalities(bset); +error: + isl_basic_set_free(bset); return NULL; } -static struct isl_basic_set *isl_basic_set_from_vec(struct isl_ctx *ctx, - struct isl_vec *vec) +__isl_give isl_set *isl_set_recession_cone(__isl_take isl_set *set) +{ + int i; + + if (!set) + return NULL; + if (set->n == 0) + return set; + + set = isl_set_remove_divs(set); + set = isl_set_cow(set); + if (!set) + return NULL; + + for (i = 0; i < set->n; ++i) { + set->p[i] = isl_basic_set_recession_cone(set->p[i]); + if (!set->p[i]) + goto error; + } + + return set; +error: + isl_set_free(set); + return NULL; +} + +/* Move "sample" to a point that is one up (or down) from the original + * point in dimension "pos". + */ +static void adjacent_point(__isl_keep isl_vec *sample, int pos, int up) +{ + if (up) + isl_int_add_ui(sample->el[1 + pos], sample->el[1 + pos], 1); + else + isl_int_sub_ui(sample->el[1 + pos], sample->el[1 + pos], 1); +} + +/* Check if any points that are adjacent to "sample" also belong to "bset". + * If so, add them to "hull" and return the updated hull. + * + * Before checking whether and adjacent point belongs to "bset", we first + * check whether it already belongs to "hull" as this test is typically + * much cheaper. + */ +static __isl_give isl_basic_set *add_adjacent_points( + __isl_take isl_basic_set *hull, __isl_take isl_vec *sample, + __isl_keep isl_basic_set *bset) +{ + int i, up; + int dim; + + if (!sample) + goto error; + + dim = isl_basic_set_dim(hull, isl_dim_set); + + for (i = 0; i < dim; ++i) { + for (up = 0; up <= 1; ++up) { + int contains; + isl_basic_set *point; + + adjacent_point(sample, i, up); + contains = isl_basic_set_contains(hull, sample); + if (contains < 0) + goto error; + if (contains) { + adjacent_point(sample, i, !up); + continue; + } + contains = isl_basic_set_contains(bset, sample); + if (contains < 0) + goto error; + if (contains) { + point = isl_basic_set_from_vec( + isl_vec_copy(sample)); + hull = affine_hull(hull, point); + } + adjacent_point(sample, i, !up); + if (contains) + break; + } + } + + isl_vec_free(sample); + + return hull; +error: + isl_vec_free(sample); + isl_basic_set_free(hull); + return NULL; +} + +/* Extend an initial (under-)approximation of the affine hull of basic + * set represented by the tableau "tab" + * by looking for points that do not satisfy one of the equalities + * in the current approximation and adding them to that approximation + * until no such points can be found any more. + * + * The caller of this function ensures that "tab" is bounded or + * that tab->basis and tab->n_unbounded have been set appropriately. + * + * "bset" may be either NULL or the basic set represented by "tab". + * If "bset" is not NULL, we check for any point we find if any + * of its adjacent points also belong to "bset". + */ +static __isl_give isl_basic_set *extend_affine_hull(struct isl_tab *tab, + __isl_take isl_basic_set *hull, __isl_keep isl_basic_set *bset) +{ + int i, j; + unsigned dim; + + if (!tab || !hull) + goto error; + + dim = tab->n_var; + + if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0) + goto error; + + for (i = 0; i < dim; ++i) { + struct isl_vec *sample; + struct isl_basic_set *point; + for (j = 0; j < hull->n_eq; ++j) { + sample = outside_point(tab, hull->eq[j], 1); + if (!sample) + goto error; + if (sample->size > 0) + break; + isl_vec_free(sample); + sample = outside_point(tab, hull->eq[j], 0); + if (!sample) + goto error; + if (sample->size > 0) + break; + isl_vec_free(sample); + + if (isl_tab_add_eq(tab, hull->eq[j]) < 0) + goto error; + } + if (j == hull->n_eq) + break; + if (tab->samples) + tab = isl_tab_add_sample(tab, isl_vec_copy(sample)); + if (!tab) + goto error; + if (bset) + hull = add_adjacent_points(hull, isl_vec_copy(sample), + bset); + point = isl_basic_set_from_vec(sample); + hull = affine_hull(hull, point); + if (!hull) + return NULL; + } + + return hull; +error: + isl_basic_set_free(hull); + return NULL; +} + +/* Drop all constraints in bmap that involve any of the dimensions + * first to first+n-1. + */ +static __isl_give isl_basic_map *isl_basic_map_drop_constraints_involving( + __isl_take isl_basic_map *bmap, unsigned first, unsigned n) +{ + int i; + + if (n == 0) + return bmap; + + bmap = isl_basic_map_cow(bmap); + + if (!bmap) + return NULL; + + for (i = bmap->n_eq - 1; i >= 0; --i) { + if (isl_seq_first_non_zero(bmap->eq[i] + 1 + first, n) == -1) + continue; + isl_basic_map_drop_equality(bmap, i); + } + + for (i = bmap->n_ineq - 1; i >= 0; --i) { + if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + first, n) == -1) + continue; + isl_basic_map_drop_inequality(bmap, i); + } + + return bmap; +} + +/* Drop all constraints in bset that involve any of the dimensions + * first to first+n-1. + */ +__isl_give isl_basic_set *isl_basic_set_drop_constraints_involving( + __isl_take isl_basic_set *bset, unsigned first, unsigned n) +{ + return isl_basic_map_drop_constraints_involving(bset, first, n); +} + +/* Drop all constraints in bmap that do not involve any of the dimensions + * first to first + n - 1 of the given type. + */ +__isl_give isl_basic_map *isl_basic_map_drop_constraints_not_involving_dims( + __isl_take isl_basic_map *bmap, + enum isl_dim_type type, unsigned first, unsigned n) +{ + int i; + unsigned dim; + + if (n == 0) + return isl_basic_map_set_to_empty(bmap); + bmap = isl_basic_map_cow(bmap); + if (!bmap) + return NULL; + + dim = isl_basic_map_dim(bmap, type); + if (first + n > dim || first + n < first) + isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid, + "index out of bounds", return isl_basic_map_free(bmap)); + + first += isl_basic_map_offset(bmap, type) - 1; + + for (i = bmap->n_eq - 1; i >= 0; --i) { + if (isl_seq_first_non_zero(bmap->eq[i] + 1 + first, n) != -1) + continue; + isl_basic_map_drop_equality(bmap, i); + } + + for (i = bmap->n_ineq - 1; i >= 0; --i) { + if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + first, n) != -1) + continue; + isl_basic_map_drop_inequality(bmap, i); + } + + return bmap; +} + +/* Drop all constraints in bset that do not involve any of the dimensions + * first to first + n - 1 of the given type. + */ +__isl_give isl_basic_set *isl_basic_set_drop_constraints_not_involving_dims( + __isl_take isl_basic_set *bset, + enum isl_dim_type type, unsigned first, unsigned n) +{ + return isl_basic_map_drop_constraints_not_involving_dims(bset, + type, first, n); +} + +/* Drop all constraints in bmap that involve any of the dimensions + * first to first + n - 1 of the given type. + */ +__isl_give isl_basic_map *isl_basic_map_drop_constraints_involving_dims( + __isl_take isl_basic_map *bmap, + enum isl_dim_type type, unsigned first, unsigned n) +{ + unsigned dim; + + if (!bmap) + return NULL; + if (n == 0) + return bmap; + + dim = isl_basic_map_dim(bmap, type); + if (first + n > dim || first + n < first) + isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid, + "index out of bounds", return isl_basic_map_free(bmap)); + + bmap = isl_basic_map_remove_divs_involving_dims(bmap, type, first, n); + first += isl_basic_map_offset(bmap, type) - 1; + return isl_basic_map_drop_constraints_involving(bmap, first, n); +} + +/* Drop all constraints in bset that involve any of the dimensions + * first to first + n - 1 of the given type. + */ +__isl_give isl_basic_set *isl_basic_set_drop_constraints_involving_dims( + __isl_take isl_basic_set *bset, + enum isl_dim_type type, unsigned first, unsigned n) +{ + return isl_basic_map_drop_constraints_involving_dims(bset, + type, first, n); +} + +/* Drop all constraints in map that involve any of the dimensions + * first to first + n - 1 of the given type. + */ +__isl_give isl_map *isl_map_drop_constraints_involving_dims( + __isl_take isl_map *map, + enum isl_dim_type type, unsigned first, unsigned n) +{ + int i; + unsigned dim; + + if (!map) + return NULL; + if (n == 0) + return map; + + dim = isl_map_dim(map, type); + if (first + n > dim || first + n < first) + isl_die(isl_map_get_ctx(map), isl_error_invalid, + "index out of bounds", return isl_map_free(map)); + + map = isl_map_cow(map); + if (!map) + return NULL; + + for (i = 0; i < map->n; ++i) { + map->p[i] = isl_basic_map_drop_constraints_involving_dims( + map->p[i], type, first, n); + if (!map->p[i]) + return isl_map_free(map); + } + + return map; +} + +/* Drop all constraints in set that involve any of the dimensions + * first to first + n - 1 of the given type. + */ +__isl_give isl_set *isl_set_drop_constraints_involving_dims( + __isl_take isl_set *set, + enum isl_dim_type type, unsigned first, unsigned n) +{ + return isl_map_drop_constraints_involving_dims(set, type, first, n); +} + +/* Construct an initial underapproximatino of the hull of "bset" + * from "sample" and any of its adjacent points that also belong to "bset". + */ +static __isl_give isl_basic_set *initialize_hull(__isl_keep isl_basic_set *bset, + __isl_take isl_vec *sample) +{ + isl_basic_set *hull; + + hull = isl_basic_set_from_vec(isl_vec_copy(sample)); + hull = add_adjacent_points(hull, sample, bset); + + return hull; +} + +/* Look for all equalities satisfied by the integer points in bset, + * which is assumed to be bounded. + * + * The equalities are obtained by successively looking for + * a point that is affinely independent of the points found so far. + * In particular, for each equality satisfied by the points so far, + * we check if there is any point on a hyperplane parallel to the + * corresponding hyperplane shifted by at least one (in either direction). + */ +static struct isl_basic_set *uset_affine_hull_bounded(struct isl_basic_set *bset) +{ + struct isl_vec *sample = NULL; + struct isl_basic_set *hull; + struct isl_tab *tab = NULL; + unsigned dim; + + if (isl_basic_set_plain_is_empty(bset)) + return bset; + + dim = isl_basic_set_n_dim(bset); + + if (bset->sample && bset->sample->size == 1 + dim) { + int contains = isl_basic_set_contains(bset, bset->sample); + if (contains < 0) + goto error; + if (contains) { + if (dim == 0) + return bset; + sample = isl_vec_copy(bset->sample); + } else { + isl_vec_free(bset->sample); + bset->sample = NULL; + } + } + + tab = isl_tab_from_basic_set(bset, 1); + if (!tab) + goto error; + if (tab->empty) { + isl_tab_free(tab); + isl_vec_free(sample); + return isl_basic_set_set_to_empty(bset); + } + + if (!sample) { + struct isl_tab_undo *snap; + snap = isl_tab_snap(tab); + sample = isl_tab_sample(tab); + if (isl_tab_rollback(tab, snap) < 0) + goto error; + isl_vec_free(tab->bmap->sample); + tab->bmap->sample = isl_vec_copy(sample); + } + + if (!sample) + goto error; + if (sample->size == 0) { + isl_tab_free(tab); + isl_vec_free(sample); + return isl_basic_set_set_to_empty(bset); + } + + hull = initialize_hull(bset, sample); + + hull = extend_affine_hull(tab, hull, bset); + isl_basic_set_free(bset); + isl_tab_free(tab); + + return hull; +error: + isl_vec_free(sample); + isl_tab_free(tab); + isl_basic_set_free(bset); + return NULL; +} + +/* Given an unbounded tableau and an integer point satisfying the tableau, + * construct an initial affine hull containing the recession cone + * shifted to the given point. + * + * The unbounded directions are taken from the last rows of the basis, + * which is assumed to have been initialized appropriately. + */ +static __isl_give isl_basic_set *initial_hull(struct isl_tab *tab, + __isl_take isl_vec *vec) { int i; int k; struct isl_basic_set *bset = NULL; + struct isl_ctx *ctx; unsigned dim; - if (!vec) + if (!vec || !tab) return NULL; + ctx = vec->ctx; isl_assert(ctx, vec->size != 0, goto error); bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0); if (!bset) goto error; - dim = isl_basic_set_n_dim(bset); - for (i = dim - 1; i >= 0; --i) { + dim = isl_basic_set_n_dim(bset) - tab->n_unbounded; + for (i = 0; i < dim; ++i) { k = isl_basic_set_alloc_equality(bset); if (k < 0) goto error; - isl_seq_clr(bset->eq[k], 1 + dim); - isl_int_neg(bset->eq[k][0], vec->block.data[1 + i]); - isl_int_set(bset->eq[k][1 + i], vec->block.data[0]); + isl_seq_cpy(bset->eq[k] + 1, tab->basis->row[1 + i] + 1, + vec->size - 1); + isl_seq_inner_product(bset->eq[k] + 1, vec->el +1, + vec->size - 1, &bset->eq[k][0]); + isl_int_neg(bset->eq[k][0], bset->eq[k][0]); } - isl_vec_free(ctx, vec); + bset->sample = vec; + bset = isl_basic_set_gauss(bset, NULL); return bset; error: isl_basic_set_free(bset); - isl_vec_free(ctx, vec); + isl_vec_free(vec); return NULL; } -/* Find an integer point in "bset" that lies outside of the equality - * "eq" e(x) = 0. - * If "up" is true, look for a point satisfying e(x) - 1 >= 0. - * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1). - * The point, if found, is returned as a singleton set. - * If no point can be found, the empty set is returned. +/* Given a tableau of a set and a tableau of the corresponding + * recession cone, detect and add all equalities to the tableau. + * If the tableau is bounded, then we can simply keep the + * tableau in its state after the return from extend_affine_hull. + * However, if the tableau is unbounded, then + * isl_tab_set_initial_basis_with_cone will add some additional + * constraints to the tableau that have to be removed again. + * In this case, we therefore rollback to the state before + * any constraints were added and then add the equalities back in. */ -static struct isl_basic_set *outside_point(struct isl_ctx *ctx, - struct isl_basic_set *bset, isl_int *eq, int up) +struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab, + struct isl_tab *tab_cone) { - struct isl_basic_set *slice = NULL; + int j; struct isl_vec *sample; - struct isl_basic_set *point; - unsigned dim; - int k; + struct isl_basic_set *hull = NULL; + struct isl_tab_undo *snap; - slice = isl_basic_set_copy(bset); - if (!slice) + if (!tab || !tab_cone) goto error; - dim = isl_basic_set_n_dim(slice); - slice = isl_basic_set_extend(slice, 0, dim, 0, 0, 1); - k = isl_basic_set_alloc_inequality(slice); - if (k < 0) + + snap = isl_tab_snap(tab); + + isl_mat_free(tab->basis); + tab->basis = NULL; + + isl_assert(tab->mat->ctx, tab->bmap, goto error); + isl_assert(tab->mat->ctx, tab->samples, goto error); + isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error); + isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error); + + if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0) goto error; - if (up) - isl_seq_cpy(slice->ineq[k], eq, 1 + dim); - else - isl_seq_neg(slice->ineq[k], eq, 1 + dim); - isl_int_sub_ui(slice->ineq[k][0], slice->ineq[k][0], 1); - sample = isl_basic_set_sample(slice); + sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var); if (!sample) goto error; - if (sample->size == 0) { - isl_vec_free(ctx, sample); - point = isl_basic_set_empty_like(bset); - } else - point = isl_basic_set_from_vec(ctx, sample); - return point; + isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size); + + isl_vec_free(tab->bmap->sample); + tab->bmap->sample = isl_vec_copy(sample); + + if (tab->n_unbounded == 0) + hull = isl_basic_set_from_vec(isl_vec_copy(sample)); + else + hull = initial_hull(tab, isl_vec_copy(sample)); + + for (j = tab->n_outside + 1; j < tab->n_sample; ++j) { + isl_seq_cpy(sample->el, tab->samples->row[j], sample->size); + hull = affine_hull(hull, + isl_basic_set_from_vec(isl_vec_copy(sample))); + } + + isl_vec_free(sample); + + hull = extend_affine_hull(tab, hull, NULL); + if (!hull) + goto error; + + if (tab->n_unbounded == 0) { + isl_basic_set_free(hull); + return tab; + } + + if (isl_tab_rollback(tab, snap) < 0) + goto error; + + if (hull->n_eq > tab->n_zero) { + for (j = 0; j < hull->n_eq; ++j) { + isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var); + if (isl_tab_add_eq(tab, hull->eq[j]) < 0) + goto error; + } + } + + isl_basic_set_free(hull); + + return tab; error: - isl_basic_set_free(slice); + isl_basic_set_free(hull); + isl_tab_free(tab); + return NULL; +} + +/* Compute the affine hull of "bset", where "cone" is the recession cone + * of "bset". + * + * We first compute a unimodular transformation that puts the unbounded + * directions in the last dimensions. In particular, we take a transformation + * that maps all equalities to equalities (in HNF) on the first dimensions. + * Let x be the original dimensions and y the transformed, with y_1 bounded + * and y_2 unbounded. + * + * [ y_1 ] [ y_1 ] [ Q_1 ] + * x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x + * + * Let's call the input basic set S. We compute S' = preimage(S, U) + * and drop the final dimensions including any constraints involving them. + * This results in set S''. + * Then we compute the affine hull A'' of S''. + * Let F y_1 >= g be the constraint system of A''. In the transformed + * space the y_2 are unbounded, so we can add them back without any constraints, + * resulting in + * + * [ y_1 ] + * [ F 0 ] [ y_2 ] >= g + * or + * [ Q_1 ] + * [ F 0 ] [ Q_2 ] x >= g + * or + * F Q_1 x >= g + * + * The affine hull in the original space is then obtained as + * A = preimage(A'', Q_1). + */ +static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset, + struct isl_basic_set *cone) +{ + unsigned total; + unsigned cone_dim; + struct isl_basic_set *hull; + struct isl_mat *M, *U, *Q; + + if (!bset || !cone) + goto error; + + total = isl_basic_set_total_dim(cone); + cone_dim = total - cone->n_eq; + + M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total); + M = isl_mat_left_hermite(M, 0, &U, &Q); + if (!M) + goto error; + isl_mat_free(M); + + U = isl_mat_lin_to_aff(U); + bset = isl_basic_set_preimage(bset, isl_mat_copy(U)); + + bset = isl_basic_set_drop_constraints_involving(bset, total - cone_dim, + cone_dim); + bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim); + + Q = isl_mat_lin_to_aff(Q); + Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim); + + if (bset && bset->sample && bset->sample->size == 1 + total) + bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample); + + hull = uset_affine_hull_bounded(bset); + + if (!hull) { + isl_mat_free(Q); + isl_mat_free(U); + } else { + struct isl_vec *sample = isl_vec_copy(hull->sample); + U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim); + if (sample && sample->size > 0) + sample = isl_mat_vec_product(U, sample); + else + isl_mat_free(U); + hull = isl_basic_set_preimage(hull, Q); + if (hull) { + isl_vec_free(hull->sample); + hull->sample = sample; + } else + isl_vec_free(sample); + } + + isl_basic_set_free(cone); + + return hull; +error: + isl_basic_set_free(bset); + isl_basic_set_free(cone); + return NULL; +} + +/* Look for all equalities satisfied by the integer points in bset, + * which is assumed not to have any explicit equalities. + * + * The equalities are obtained by successively looking for + * a point that is affinely independent of the points found so far. + * In particular, for each equality satisfied by the points so far, + * we check if there is any point on a hyperplane parallel to the + * corresponding hyperplane shifted by at least one (in either direction). + * + * Before looking for any outside points, we first compute the recession + * cone. The directions of this recession cone will always be part + * of the affine hull, so there is no need for looking for any points + * in these directions. + * In particular, if the recession cone is full-dimensional, then + * the affine hull is simply the whole universe. + */ +static struct isl_basic_set *uset_affine_hull(struct isl_basic_set *bset) +{ + struct isl_basic_set *cone; + + if (isl_basic_set_plain_is_empty(bset)) + return bset; + + cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset)); + if (!cone) + goto error; + if (cone->n_eq == 0) { + struct isl_basic_set *hull; + isl_basic_set_free(cone); + hull = isl_basic_set_universe_like(bset); + isl_basic_set_free(bset); + return hull; + } + + if (cone->n_eq < isl_basic_set_total_dim(cone)) + return affine_hull_with_cone(bset, cone); + + isl_basic_set_free(cone); + return uset_affine_hull_bounded(bset); +error: + isl_basic_set_free(bset); return NULL; } @@ -310,69 +1029,48 @@ error: * The resulting basic set has all meaning about the dimensions removed. * In particular, dimensions that correspond to existential variables * in bmap and that are found to be fixed are not removed. - * - * The additional equalities are obtained by successively looking for - * a point that is affinely independent of the points found so far. - * In particular, for each equality satisfied by the points so far, - * we check if there is any point on a hyperplane parallel to the - * corresponding hyperplane shifted by at least one (in either direction). */ static struct isl_basic_set *equalities_in_underlying_set( struct isl_basic_map *bmap) { - int i, j; + struct isl_mat *T1 = NULL; struct isl_mat *T2 = NULL; struct isl_basic_set *bset = NULL; struct isl_basic_set *hull = NULL; - struct isl_vec *sample; - struct isl_ctx *ctx; - unsigned dim; bset = isl_basic_map_underlying_set(bmap); - bset = isl_basic_set_remove_equalities(bset, NULL, &T2); + if (!bset) + return NULL; + if (bset->n_eq) + bset = isl_basic_set_remove_equalities(bset, &T1, &T2); if (!bset) goto error; - ctx = bset->ctx; - sample = isl_basic_set_sample(isl_basic_set_copy(bset)); - if (!sample) - goto error; - if (sample->size == 0) { - isl_vec_free(ctx, sample); - hull = isl_basic_set_empty_like(bset); - } else - hull = isl_basic_set_from_vec(ctx, sample); + hull = uset_affine_hull(bset); + if (!T2) + return hull; - dim = isl_basic_set_n_dim(bset); - for (i = 0; i < dim; ++i) { - struct isl_basic_set *point; - if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) - break; - for (j = 0; j < hull->n_eq; ++j) { - point = outside_point(ctx, bset, hull->eq[j], 1); - if (!point) - goto error; - if (!ISL_F_ISSET(point, ISL_BASIC_SET_EMPTY)) - break; - isl_basic_set_free(point); - point = outside_point(ctx, bset, hull->eq[j], 0); - if (!point) - goto error; - if (!ISL_F_ISSET(point, ISL_BASIC_SET_EMPTY)) - break; - isl_basic_set_free(point); - } - if (j == hull->n_eq) - break; - hull = affine_hull(hull, point); - } - isl_basic_set_free(bset); - if (T2) + if (!hull) { + isl_mat_free(T1); + isl_mat_free(T2); + } else { + struct isl_vec *sample = isl_vec_copy(hull->sample); + if (sample && sample->size > 0) + sample = isl_mat_vec_product(T1, sample); + else + isl_mat_free(T1); hull = isl_basic_set_preimage(hull, T2); + if (hull) { + isl_vec_free(hull->sample); + hull->sample = sample; + } else + isl_vec_free(sample); + } return hull; error: - isl_mat_free(ctx, T2); + isl_mat_free(T1); + isl_mat_free(T2); isl_basic_set_free(bset); isl_basic_set_free(hull); return NULL; @@ -401,7 +1099,11 @@ struct isl_basic_map *isl_basic_map_detect_equalities( hull = equalities_in_underlying_set(isl_basic_map_copy(bmap)); if (!hull) goto error; - bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim), 0, + if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) { + isl_basic_set_free(hull); + return isl_basic_map_set_to_empty(bmap); + } + bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), 0, hull->n_eq, 0); for (i = 0; i < hull->n_eq; ++i) { j = isl_basic_map_alloc_equality(bmap); @@ -410,6 +1112,8 @@ struct isl_basic_map *isl_basic_map_detect_equalities( isl_seq_cpy(bmap->eq[j], hull->eq[i], 1 + isl_basic_set_total_dim(hull)); } + isl_vec_free(bmap->sample); + bmap->sample = isl_vec_copy(hull->sample); isl_basic_set_free(hull); ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES); bmap = isl_basic_map_simplify(bmap); @@ -420,57 +1124,244 @@ error: return NULL; } +__isl_give isl_basic_set *isl_basic_set_detect_equalities( + __isl_take isl_basic_set *bset) +{ + return (isl_basic_set *) + isl_basic_map_detect_equalities((isl_basic_map *)bset); +} + +__isl_give isl_map *isl_map_detect_equalities(__isl_take isl_map *map) +{ + return isl_map_inline_foreach_basic_map(map, + &isl_basic_map_detect_equalities); +} + +__isl_give isl_set *isl_set_detect_equalities(__isl_take isl_set *set) +{ + return (isl_set *)isl_map_detect_equalities((isl_map *)set); +} + /* After computing the rational affine hull (by detecting the implicit * equalities), we compute the additional equalities satisfied by * the integer points (if any) and add the original equalities back in. */ struct isl_basic_map *isl_basic_map_affine_hull(struct isl_basic_map *bmap) { - struct isl_basic_set *hull = NULL; + bmap = isl_basic_map_detect_equalities(bmap); + bmap = isl_basic_map_cow(bmap); + if (bmap) + isl_basic_map_free_inequality(bmap, bmap->n_ineq); + bmap = isl_basic_map_finalize(bmap); + return bmap; +} - bmap = isl_basic_map_implicit_equalities(bmap); - if (!bmap) - return NULL; - if (bmap->n_ineq == 0) - return bmap; +struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset) +{ + return (struct isl_basic_set *) + isl_basic_map_affine_hull((struct isl_basic_map *)bset); +} - if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) { - bmap = isl_basic_map_cow(bmap); - isl_basic_map_free_inequality(bmap, bmap->n_ineq); +/* Given a rational affine matrix "M", add stride constraints to "bmap" + * that ensure that + * + * M(x) + * + * is an integer vector. The variables x include all the variables + * of "bmap" except the unknown divs. + * + * If d is the common denominator of M, then we need to impose that + * + * d M(x) = 0 mod d + * + * or + * + * exists alpha : d M(x) = d alpha + * + * This function is similar to add_strides in isl_morph.c + */ +static __isl_give isl_basic_map *add_strides(__isl_take isl_basic_map *bmap, + __isl_keep isl_mat *M, int n_known) +{ + int i, div, k; + isl_int gcd; + + if (isl_int_is_one(M->row[0][0])) return bmap; - } - hull = equalities_in_underlying_set(isl_basic_map_copy(bmap)); - if (!hull) - goto error; + bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), + M->n_row - 1, M->n_row - 1, 0); - bmap = isl_basic_map_cow(bmap); - if (!bmap) - goto error; - isl_basic_map_free_inequality(bmap, bmap->n_ineq); - bmap = isl_basic_map_intersect(bmap, - isl_basic_map_overlying_set(hull, - isl_basic_map_copy(bmap))); + isl_int_init(gcd); + for (i = 1; i < M->n_row; ++i) { + isl_seq_gcd(M->row[i], M->n_col, &gcd); + if (isl_int_is_divisible_by(gcd, M->row[0][0])) + continue; + div = isl_basic_map_alloc_div(bmap); + if (div < 0) + goto error; + isl_int_set_si(bmap->div[div][0], 0); + k = isl_basic_map_alloc_equality(bmap); + if (k < 0) + goto error; + isl_seq_cpy(bmap->eq[k], M->row[i], M->n_col); + isl_seq_clr(bmap->eq[k] + M->n_col, bmap->n_div - n_known); + isl_int_set(bmap->eq[k][M->n_col - n_known + div], + M->row[0][0]); + } + isl_int_clear(gcd); - return isl_basic_map_finalize(bmap); + return bmap; error: - isl_basic_set_free(hull); + isl_int_clear(gcd); isl_basic_map_free(bmap); return NULL; } -struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset) +/* If there are any equalities that involve (multiple) unknown divs, + * then extract the stride information encoded by those equalities + * and make it explicitly available in "bmap". + * + * We first sort the divs so that the unknown divs appear last and + * then we count how many equalities involve these divs. + * + * Let these equalities be of the form + * + * A(x) + B y = 0 + * + * where y represents the unknown divs and x the remaining variables. + * Let [H 0] be the Hermite Normal Form of B, i.e., + * + * B = [H 0] Q + * + * Then x is a solution of the equalities iff + * + * H^-1 A(x) (= - [I 0] Q y) + * + * is an integer vector. Let d be the common denominator of H^-1. + * We impose + * + * d H^-1 A(x) = d alpha + * + * in add_strides, with alpha fresh existentially quantified variables. + */ +static __isl_give isl_basic_map *isl_basic_map_make_strides_explicit( + __isl_take isl_basic_map *bmap) { - return (struct isl_basic_set *) - isl_basic_map_affine_hull((struct isl_basic_map *)bset); + int known; + int n_known; + int n, n_col; + int total; + isl_ctx *ctx; + isl_mat *A, *B, *M; + + known = isl_basic_map_divs_known(bmap); + if (known < 0) + return isl_basic_map_free(bmap); + if (known) + return bmap; + bmap = isl_basic_map_sort_divs(bmap); + bmap = isl_basic_map_gauss(bmap, NULL); + if (!bmap) + return NULL; + + for (n_known = 0; n_known < bmap->n_div; ++n_known) + if (isl_int_is_zero(bmap->div[n_known][0])) + break; + ctx = isl_basic_map_get_ctx(bmap); + total = isl_space_dim(bmap->dim, isl_dim_all); + for (n = 0; n < bmap->n_eq; ++n) + if (isl_seq_first_non_zero(bmap->eq[n] + 1 + total + n_known, + bmap->n_div - n_known) == -1) + break; + if (n == 0) + return bmap; + B = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 0, 1 + total + n_known); + n_col = bmap->n_div - n_known; + A = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 1 + total + n_known, n_col); + A = isl_mat_left_hermite(A, 0, NULL, NULL); + A = isl_mat_drop_cols(A, n, n_col - n); + A = isl_mat_lin_to_aff(A); + A = isl_mat_right_inverse(A); + B = isl_mat_insert_zero_rows(B, 0, 1); + B = isl_mat_set_element_si(B, 0, 0, 1); + M = isl_mat_product(A, B); + if (!M) + return isl_basic_map_free(bmap); + bmap = add_strides(bmap, M, n_known); + bmap = isl_basic_map_gauss(bmap, NULL); + isl_mat_free(M); + + return bmap; } -struct isl_basic_map *isl_map_affine_hull(struct isl_map *map) +/* Compute the affine hull of each basic map in "map" separately + * and make all stride information explicit so that we can remove + * all unknown divs without losing this information. + * The result is also guaranteed to be gaussed. + * + * In simple cases where a div is determined by an equality, + * calling isl_basic_map_gauss is enough to make the stride information + * explicit, as it will derive an explicit representation for the div + * from the equality. If, however, the stride information + * is encoded through multiple unknown divs then we need to make + * some extra effort in isl_basic_map_make_strides_explicit. + */ +static __isl_give isl_map *isl_map_local_affine_hull(__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_affine_hull(map->p[i]); + map->p[i] = isl_basic_map_gauss(map->p[i], NULL); + map->p[i] = isl_basic_map_make_strides_explicit(map->p[i]); + if (!map->p[i]) + return isl_map_free(map); + } + + return map; +} + +static __isl_give isl_set *isl_set_local_affine_hull(__isl_take isl_set *set) +{ + return isl_map_local_affine_hull(set); +} + +/* Compute the affine hull of "map". + * + * We first compute the affine hull of each basic map separately. + * Then we align the divs and recompute the affine hulls of the basic + * maps since some of them may now have extra divs. + * In order to avoid performing parametric integer programming to + * compute explicit expressions for the divs, possible leading to + * an explosion in the number of basic maps, we first drop all unknown + * divs before aligning the divs. Note that isl_map_local_affine_hull tries + * to make sure that all stride information is explicitly available + * in terms of known divs. This involves calling isl_basic_set_gauss, + * which is also needed because affine_hull assumes its input has been gaussed, + * while isl_map_affine_hull may be called on input that has not been gaussed, + * in particular from initial_facet_constraint. + * Similarly, align_divs may reorder some divs so that we need to + * gauss the result again. + * Finally, we combine the individual affine hulls into a single + * affine hull. + */ +__isl_give isl_basic_map *isl_map_affine_hull(__isl_take isl_map *map) +{ struct isl_basic_map *model = NULL; struct isl_basic_map *hull = NULL; struct isl_set *set; + isl_basic_set *bset; + + map = isl_map_detect_equalities(map); + map = isl_map_local_affine_hull(map); + map = isl_map_remove_empty_parts(map); + map = isl_map_remove_unknown_divs(map); + map = isl_map_align_divs(map); if (!map) return NULL; @@ -481,34 +1372,18 @@ struct isl_basic_map *isl_map_affine_hull(struct isl_map *map) return hull; } - map = isl_map_align_divs(map); model = isl_basic_map_copy(map->p[0]); set = isl_map_underlying_set(map); set = isl_set_cow(set); + set = isl_set_local_affine_hull(set); if (!set) goto error; - for (i = 0; i < set->n; ++i) { - set->p[i] = isl_basic_set_cow(set->p[i]); - set->p[i] = isl_basic_set_affine_hull(set->p[i]); - set->p[i] = isl_basic_set_gauss(set->p[i], NULL); - if (!set->p[i]) - goto error; - } - set = isl_set_remove_empty_parts(set); - if (set->n == 0) { - hull = isl_basic_map_empty_like(model); - isl_basic_map_free(model); - } else { - struct isl_basic_set *bset; - while (set->n > 1) { - set->p[0] = affine_hull(set->p[0], set->p[--set->n]); - if (!set->p[0]) - goto error; - } - bset = isl_basic_set_copy(set->p[0]); - hull = isl_basic_map_overlying_set(bset, model); - } + while (set->n > 1) + set->p[0] = affine_hull(set->p[0], set->p[--set->n]); + + bset = isl_basic_set_copy(set->p[0]); + hull = isl_basic_map_overlying_set(bset, model); isl_set_free(set); hull = isl_basic_map_simplify(hull); return isl_basic_map_finalize(hull);