| /* |
| * Copyright 2008-2009 Katholieke Universiteit Leuven |
| * |
| * Use of this software is governed by the GNU LGPLv2.1 license |
| * |
| * Written by Sven Verdoolaege, K.U.Leuven, Departement |
| * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium |
| */ |
| |
| #include <isl_ctx_private.h> |
| #include <isl_map_private.h> |
| #include <isl/seq.h> |
| #include <isl/set.h> |
| #include <isl/lp.h> |
| #include <isl/map.h> |
| #include "isl_equalities.h" |
| #include "isl_sample.h" |
| #include "isl_tab.h" |
| #include <isl_mat_private.h> |
| |
| struct isl_basic_map *isl_basic_map_implicit_equalities( |
| struct isl_basic_map *bmap) |
| { |
| 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; |
| |
| tab = isl_tab_from_basic_map(bmap); |
| if (isl_tab_detect_implicit_equalities(tab) < 0) |
| goto error; |
| bmap = isl_basic_map_update_from_tab(bmap, tab); |
| isl_tab_free(tab); |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT); |
| return bmap; |
| error: |
| isl_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 |
| * after column col are zero. |
| */ |
| static void set_common_multiple( |
| struct isl_basic_set *bset1, struct isl_basic_set *bset2, |
| unsigned row, unsigned col) |
| { |
| isl_int m, c; |
| |
| if (isl_int_eq(bset1->eq[row][col], bset2->eq[row][col])) |
| return; |
| |
| isl_int_init(c); |
| isl_int_init(m); |
| isl_int_lcm(m, bset1->eq[row][col], bset2->eq[row][col]); |
| isl_int_divexact(c, m, bset1->eq[row][col]); |
| isl_seq_scale(bset1->eq[row], bset1->eq[row], c, col+1); |
| isl_int_divexact(c, m, bset2->eq[row][col]); |
| isl_seq_scale(bset2->eq[row], bset2->eq[row], c, col+1); |
| isl_int_clear(c); |
| isl_int_clear(m); |
| } |
| |
| /* Delete a given equality, moving all the following equalities one up. |
| */ |
| static void delete_row(struct isl_basic_set *bset, unsigned row) |
| { |
| isl_int *t; |
| int r; |
| |
| t = bset->eq[row]; |
| bset->n_eq--; |
| for (r = row; r < bset->n_eq; ++r) |
| bset->eq[r] = bset->eq[r+1]; |
| bset->eq[bset->n_eq] = t; |
| } |
| |
| /* Make first row entries in column col of bset1 identical to |
| * those of bset2, using the fact that entry bset1->eq[row][col]=a |
| * is non-zero. Initially, these elements of bset1 are all zero. |
| * For each row i < row, we set |
| * A[i] = a * A[i] + B[i][col] * A[row] |
| * B[i] = a * B[i] |
| * so that |
| * A[i][col] = B[i][col] = a * old(B[i][col]) |
| */ |
| static void construct_column( |
| struct isl_basic_set *bset1, struct isl_basic_set *bset2, |
| unsigned row, unsigned col) |
| { |
| int r; |
| isl_int a; |
| isl_int b; |
| unsigned total; |
| |
| isl_int_init(a); |
| isl_int_init(b); |
| total = 1 + isl_basic_set_n_dim(bset1); |
| for (r = 0; r < row; ++r) { |
| if (isl_int_is_zero(bset2->eq[r][col])) |
| continue; |
| isl_int_gcd(b, bset2->eq[r][col], bset1->eq[row][col]); |
| isl_int_divexact(a, bset1->eq[row][col], b); |
| isl_int_divexact(b, bset2->eq[r][col], b); |
| isl_seq_combine(bset1->eq[r], a, bset1->eq[r], |
| b, bset1->eq[row], total); |
| isl_seq_scale(bset2->eq[r], bset2->eq[r], a, total); |
| } |
| isl_int_clear(a); |
| isl_int_clear(b); |
| delete_row(bset1, row); |
| } |
| |
| /* Make first row entries in column col of bset1 identical to |
| * those of bset2, using only these entries of the two matrices. |
| * Let t be the last row with different entries. |
| * For each row i < t, we set |
| * A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t] |
| * B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t] |
| * so that |
| * A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col]) |
| */ |
| static int transform_column( |
| struct isl_basic_set *bset1, struct isl_basic_set *bset2, |
| unsigned row, unsigned col) |
| { |
| int i, t; |
| isl_int a, b, g; |
| unsigned total; |
| |
| for (t = row-1; t >= 0; --t) |
| if (isl_int_ne(bset1->eq[t][col], bset2->eq[t][col])) |
| break; |
| if (t < 0) |
| return 0; |
| |
| total = 1 + isl_basic_set_n_dim(bset1); |
| isl_int_init(a); |
| isl_int_init(b); |
| isl_int_init(g); |
| isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col]); |
| for (i = 0; i < t; ++i) { |
| isl_int_sub(a, bset2->eq[i][col], bset1->eq[i][col]); |
| isl_int_gcd(g, a, b); |
| isl_int_divexact(a, a, g); |
| isl_int_divexact(g, b, g); |
| isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t], |
| total); |
| isl_seq_combine(bset2->eq[i], g, bset2->eq[i], a, bset2->eq[t], |
| total); |
| } |
| isl_int_clear(a); |
| isl_int_clear(b); |
| isl_int_clear(g); |
| delete_row(bset1, t); |
| delete_row(bset2, t); |
| return 1; |
| } |
| |
| /* The implementation is based on Section 5.2 of Michael Karr, |
| * "Affine Relationships Among Variables of a Program", |
| * except that the echelon form we use starts from the last column |
| * and that we are dealing with integer coefficients. |
| */ |
| static struct isl_basic_set *affine_hull( |
| struct isl_basic_set *bset1, struct isl_basic_set *bset2) |
| { |
| unsigned total; |
| int col; |
| int row; |
| |
| if (!bset1 || !bset2) |
| goto error; |
| |
| total = 1 + isl_basic_set_n_dim(bset1); |
| |
| row = 0; |
| for (col = total-1; col >= 0; --col) { |
| int is_zero1 = row >= bset1->n_eq || |
| isl_int_is_zero(bset1->eq[row][col]); |
| int is_zero2 = row >= bset2->n_eq || |
| isl_int_is_zero(bset2->eq[row][col]); |
| if (!is_zero1 && !is_zero2) { |
| set_common_multiple(bset1, bset2, row, col); |
| ++row; |
| } else if (!is_zero1 && is_zero2) { |
| construct_column(bset1, bset2, row, col); |
| } else if (is_zero1 && !is_zero2) { |
| construct_column(bset2, bset1, row, col); |
| } else { |
| if (transform_column(bset1, bset2, row, col)) |
| --row; |
| } |
| } |
| isl_assert(bset1->ctx, row == bset1->n_eq, goto error); |
| isl_basic_set_free(bset2); |
| bset1 = isl_basic_set_normalize_constraints(bset1); |
| return bset1; |
| error: |
| isl_basic_set_free(bset1); |
| isl_basic_set_free(bset2); |
| return NULL; |
| } |
| |
| /* Find an integer point in the set represented by "tab" |
| * that lies outside of the equality "eq" e(x) = 0. |
| * If "up" is true, look for a point satisfying e(x) - 1 >= 0. |
| * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1). |
| * The point, if found, is returned. |
| * If no point can be found, a zero-length vector is returned. |
| * |
| * Before solving an ILP problem, we first check if simply |
| * adding the normal of the constraint to one of the known |
| * integer points in the basic set represented by "tab" |
| * yields another point inside the basic set. |
| * |
| * The caller of this function ensures that the tableau is bounded or |
| * that tab->basis and tab->n_unbounded have been set appropriately. |
| */ |
| static struct isl_vec *outside_point(struct isl_tab *tab, isl_int *eq, int up) |
| { |
| struct isl_ctx *ctx; |
| struct isl_vec *sample = NULL; |
| struct isl_tab_undo *snap; |
| unsigned dim; |
| |
| if (!tab) |
| return NULL; |
| ctx = tab->mat->ctx; |
| |
| dim = tab->n_var; |
| sample = isl_vec_alloc(ctx, 1 + dim); |
| if (!sample) |
| return NULL; |
| isl_int_set_si(sample->el[0], 1); |
| isl_seq_combine(sample->el + 1, |
| ctx->one, tab->bmap->sample->el + 1, |
| up ? ctx->one : ctx->negone, eq + 1, dim); |
| if (isl_basic_map_contains(tab->bmap, sample)) |
| return sample; |
| isl_vec_free(sample); |
| sample = NULL; |
| |
| snap = isl_tab_snap(tab); |
| |
| if (!up) |
| isl_seq_neg(eq, eq, 1 + dim); |
| isl_int_sub_ui(eq[0], eq[0], 1); |
| |
| if (isl_tab_extend_cons(tab, 1) < 0) |
| goto error; |
| if (isl_tab_add_ineq(tab, eq) < 0) |
| goto error; |
| |
| sample = isl_tab_sample(tab); |
| |
| isl_int_add_ui(eq[0], eq[0], 1); |
| if (!up) |
| isl_seq_neg(eq, eq, 1 + dim); |
| |
| if (sample && isl_tab_rollback(tab, snap) < 0) |
| goto error; |
| |
| return sample; |
| error: |
| isl_vec_free(sample); |
| return NULL; |
| } |
| |
| struct isl_basic_set *isl_basic_set_recession_cone(struct isl_basic_set *bset) |
| { |
| int i; |
| |
| bset = isl_basic_set_cow(bset); |
| if (!bset) |
| return NULL; |
| isl_assert(bset->ctx, bset->n_div == 0, goto error); |
| |
| for (i = 0; i < bset->n_eq; ++i) |
| isl_int_set_si(bset->eq[i][0], 0); |
| |
| for (i = 0; i < bset->n_ineq; ++i) |
| isl_int_set_si(bset->ineq[i][0], 0); |
| |
| ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT); |
| return isl_basic_set_implicit_equalities(bset); |
| error: |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| __isl_give isl_set *isl_set_recession_cone(__isl_take isl_set *set) |
| { |
| int i; |
| |
| if (!set) |
| return NULL; |
| if (set->n == 0) |
| return set; |
| |
| set = isl_set_remove_divs(set); |
| set = isl_set_cow(set); |
| if (!set) |
| return NULL; |
| |
| for (i = 0; i < set->n; ++i) { |
| set->p[i] = isl_basic_set_recession_cone(set->p[i]); |
| if (!set->p[i]) |
| goto error; |
| } |
| |
| return set; |
| error: |
| isl_set_free(set); |
| return NULL; |
| } |
| |
| /* Extend an initial (under-)approximation of the affine hull of basic |
| * set represented by the tableau "tab" |
| * by looking for points that do not satisfy one of the equalities |
| * in the current approximation and adding them to that approximation |
| * until no such points can be found any more. |
| * |
| * The caller of this function ensures that "tab" is bounded or |
| * that tab->basis and tab->n_unbounded have been set appropriately. |
| */ |
| static struct isl_basic_set *extend_affine_hull(struct isl_tab *tab, |
| struct isl_basic_set *hull) |
| { |
| int i, j; |
| unsigned dim; |
| |
| if (!tab || !hull) |
| goto error; |
| |
| dim = tab->n_var; |
| |
| if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0) |
| goto error; |
| |
| for (i = 0; i < dim; ++i) { |
| struct isl_vec *sample; |
| struct isl_basic_set *point; |
| for (j = 0; j < hull->n_eq; ++j) { |
| sample = outside_point(tab, hull->eq[j], 1); |
| if (!sample) |
| goto error; |
| if (sample->size > 0) |
| break; |
| isl_vec_free(sample); |
| sample = outside_point(tab, hull->eq[j], 0); |
| if (!sample) |
| goto error; |
| if (sample->size > 0) |
| break; |
| isl_vec_free(sample); |
| |
| if (isl_tab_add_eq(tab, hull->eq[j]) < 0) |
| goto error; |
| } |
| if (j == hull->n_eq) |
| break; |
| if (tab->samples) |
| tab = isl_tab_add_sample(tab, isl_vec_copy(sample)); |
| if (!tab) |
| goto error; |
| point = isl_basic_set_from_vec(sample); |
| hull = affine_hull(hull, point); |
| if (!hull) |
| return NULL; |
| } |
| |
| return hull; |
| error: |
| isl_basic_set_free(hull); |
| return NULL; |
| } |
| |
| /* Drop all constraints in bset that involve any of the dimensions |
| * first to first+n-1. |
| */ |
| __isl_give isl_basic_set *isl_basic_set_drop_constraints_involving( |
| __isl_take isl_basic_set *bset, unsigned first, unsigned n) |
| { |
| int i; |
| |
| if (n == 0) |
| return bset; |
| |
| bset = isl_basic_set_cow(bset); |
| |
| if (!bset) |
| return NULL; |
| |
| for (i = bset->n_eq - 1; i >= 0; --i) { |
| if (isl_seq_first_non_zero(bset->eq[i] + 1 + first, n) == -1) |
| continue; |
| isl_basic_set_drop_equality(bset, i); |
| } |
| |
| for (i = bset->n_ineq - 1; i >= 0; --i) { |
| if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1) |
| continue; |
| isl_basic_set_drop_inequality(bset, i); |
| } |
| |
| return bset; |
| } |
| |
| /* Look for all equalities satisfied by the integer points in bset, |
| * which is assumed to be bounded. |
| * |
| * The equalities are obtained by successively looking for |
| * a point that is affinely independent of the points found so far. |
| * In particular, for each equality satisfied by the points so far, |
| * we check if there is any point on a hyperplane parallel to the |
| * corresponding hyperplane shifted by at least one (in either direction). |
| */ |
| static struct isl_basic_set *uset_affine_hull_bounded(struct isl_basic_set *bset) |
| { |
| struct isl_vec *sample = NULL; |
| struct isl_basic_set *hull; |
| struct isl_tab *tab = NULL; |
| unsigned dim; |
| |
| if (isl_basic_set_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); |
| if (!tab) |
| goto error; |
| if (tab->empty) { |
| isl_tab_free(tab); |
| isl_vec_free(sample); |
| return isl_basic_set_set_to_empty(bset); |
| } |
| if (isl_tab_track_bset(tab, isl_basic_set_copy(bset)) < 0) |
| goto error; |
| |
| if (!sample) { |
| struct isl_tab_undo *snap; |
| snap = isl_tab_snap(tab); |
| sample = isl_tab_sample(tab); |
| if (isl_tab_rollback(tab, snap) < 0) |
| goto error; |
| isl_vec_free(tab->bmap->sample); |
| tab->bmap->sample = isl_vec_copy(sample); |
| } |
| |
| if (!sample) |
| goto error; |
| if (sample->size == 0) { |
| isl_tab_free(tab); |
| isl_vec_free(sample); |
| return isl_basic_set_set_to_empty(bset); |
| } |
| |
| hull = isl_basic_set_from_vec(sample); |
| |
| isl_basic_set_free(bset); |
| hull = extend_affine_hull(tab, hull); |
| isl_tab_free(tab); |
| |
| return hull; |
| error: |
| isl_vec_free(sample); |
| isl_tab_free(tab); |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| /* Given an unbounded tableau and an integer point satisfying the tableau, |
| * construct an initial affine hull containing the recession cone |
| * shifted to the given point. |
| * |
| * The unbounded directions are taken from the last rows of the basis, |
| * which is assumed to have been initialized appropriately. |
| */ |
| static __isl_give isl_basic_set *initial_hull(struct isl_tab *tab, |
| __isl_take isl_vec *vec) |
| { |
| int i; |
| int k; |
| struct isl_basic_set *bset = NULL; |
| struct isl_ctx *ctx; |
| unsigned dim; |
| |
| if (!vec || !tab) |
| return NULL; |
| ctx = vec->ctx; |
| isl_assert(ctx, vec->size != 0, goto error); |
| |
| bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0); |
| if (!bset) |
| goto error; |
| dim = isl_basic_set_n_dim(bset) - tab->n_unbounded; |
| for (i = 0; i < dim; ++i) { |
| k = isl_basic_set_alloc_equality(bset); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(bset->eq[k] + 1, tab->basis->row[1 + i] + 1, |
| vec->size - 1); |
| isl_seq_inner_product(bset->eq[k] + 1, vec->el +1, |
| vec->size - 1, &bset->eq[k][0]); |
| isl_int_neg(bset->eq[k][0], bset->eq[k][0]); |
| } |
| bset->sample = vec; |
| bset = isl_basic_set_gauss(bset, NULL); |
| |
| return bset; |
| error: |
| isl_basic_set_free(bset); |
| isl_vec_free(vec); |
| return NULL; |
| } |
| |
| /* Given a tableau of a set and a tableau of the corresponding |
| * recession cone, detect and add all equalities to the tableau. |
| * If the tableau is bounded, then we can simply keep the |
| * tableau in its state after the return from extend_affine_hull. |
| * However, if the tableau is unbounded, then |
| * isl_tab_set_initial_basis_with_cone will add some additional |
| * constraints to the tableau that have to be removed again. |
| * In this case, we therefore rollback to the state before |
| * any constraints were added and then add the equalities back in. |
| */ |
| struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab, |
| struct isl_tab *tab_cone) |
| { |
| int j; |
| struct isl_vec *sample; |
| struct isl_basic_set *hull; |
| struct isl_tab_undo *snap; |
| |
| if (!tab || !tab_cone) |
| goto error; |
| |
| snap = isl_tab_snap(tab); |
| |
| isl_mat_free(tab->basis); |
| tab->basis = NULL; |
| |
| isl_assert(tab->mat->ctx, tab->bmap, goto error); |
| isl_assert(tab->mat->ctx, tab->samples, goto error); |
| isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error); |
| isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error); |
| |
| if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0) |
| goto error; |
| |
| sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var); |
| if (!sample) |
| goto error; |
| |
| isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size); |
| |
| isl_vec_free(tab->bmap->sample); |
| tab->bmap->sample = isl_vec_copy(sample); |
| |
| if (tab->n_unbounded == 0) |
| hull = isl_basic_set_from_vec(isl_vec_copy(sample)); |
| else |
| hull = initial_hull(tab, isl_vec_copy(sample)); |
| |
| for (j = tab->n_outside + 1; j < tab->n_sample; ++j) { |
| isl_seq_cpy(sample->el, tab->samples->row[j], sample->size); |
| hull = affine_hull(hull, |
| isl_basic_set_from_vec(isl_vec_copy(sample))); |
| } |
| |
| isl_vec_free(sample); |
| |
| hull = extend_affine_hull(tab, hull); |
| if (!hull) |
| goto error; |
| |
| if (tab->n_unbounded == 0) { |
| isl_basic_set_free(hull); |
| return tab; |
| } |
| |
| if (isl_tab_rollback(tab, snap) < 0) |
| goto error; |
| |
| if (hull->n_eq > tab->n_zero) { |
| for (j = 0; j < hull->n_eq; ++j) { |
| isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var); |
| if (isl_tab_add_eq(tab, hull->eq[j]) < 0) |
| goto error; |
| } |
| } |
| |
| isl_basic_set_free(hull); |
| |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| /* Compute the affine hull of "bset", where "cone" is the recession cone |
| * of "bset". |
| * |
| * We first compute a unimodular transformation that puts the unbounded |
| * directions in the last dimensions. In particular, we take a transformation |
| * that maps all equalities to equalities (in HNF) on the first dimensions. |
| * Let x be the original dimensions and y the transformed, with y_1 bounded |
| * and y_2 unbounded. |
| * |
| * [ y_1 ] [ y_1 ] [ Q_1 ] |
| * x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x |
| * |
| * Let's call the input basic set S. We compute S' = preimage(S, U) |
| * and drop the final dimensions including any constraints involving them. |
| * This results in set S''. |
| * Then we compute the affine hull A'' of S''. |
| * Let F y_1 >= g be the constraint system of A''. In the transformed |
| * space the y_2 are unbounded, so we can add them back without any constraints, |
| * resulting in |
| * |
| * [ y_1 ] |
| * [ F 0 ] [ y_2 ] >= g |
| * or |
| * [ Q_1 ] |
| * [ F 0 ] [ Q_2 ] x >= g |
| * or |
| * F Q_1 x >= g |
| * |
| * The affine hull in the original space is then obtained as |
| * A = preimage(A'', Q_1). |
| */ |
| static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset, |
| struct isl_basic_set *cone) |
| { |
| unsigned total; |
| unsigned cone_dim; |
| struct isl_basic_set *hull; |
| struct isl_mat *M, *U, *Q; |
| |
| if (!bset || !cone) |
| goto error; |
| |
| total = isl_basic_set_total_dim(cone); |
| cone_dim = total - cone->n_eq; |
| |
| M = isl_mat_sub_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(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; |
| } |
| |
| /* Look for all equalities satisfied by the integer points in bmap |
| * that are independent of the equalities already explicitly available |
| * in bmap. |
| * |
| * We first remove all equalities already explicitly available, |
| * then look for additional equalities in the reduced space |
| * and then transform the result to the original space. |
| * The original equalities are _not_ added to this set. This is |
| * the responsibility of the calling function. |
| * The resulting basic set has all meaning about the dimensions removed. |
| * In particular, dimensions that correspond to existential variables |
| * in bmap and that are found to be fixed are not removed. |
| */ |
| static struct isl_basic_set *equalities_in_underlying_set( |
| struct isl_basic_map *bmap) |
| { |
| struct isl_mat *T1 = NULL; |
| struct isl_mat *T2 = NULL; |
| struct isl_basic_set *bset = NULL; |
| struct isl_basic_set *hull = NULL; |
| |
| bset = isl_basic_map_underlying_set(bmap); |
| if (!bset) |
| return NULL; |
| if (bset->n_eq) |
| bset = isl_basic_set_remove_equalities(bset, &T1, &T2); |
| if (!bset) |
| goto error; |
| |
| hull = uset_affine_hull(bset); |
| if (!T2) |
| return hull; |
| |
| if (!hull) { |
| isl_mat_free(T1); |
| isl_mat_free(T2); |
| } else { |
| struct isl_vec *sample = isl_vec_copy(hull->sample); |
| if (sample && sample->size > 0) |
| sample = isl_mat_vec_product(T1, sample); |
| else |
| isl_mat_free(T1); |
| hull = isl_basic_set_preimage(hull, T2); |
| if (hull) { |
| isl_vec_free(hull->sample); |
| hull->sample = sample; |
| } else |
| isl_vec_free(sample); |
| } |
| |
| return hull; |
| error: |
| isl_mat_free(T2); |
| isl_basic_set_free(bset); |
| isl_basic_set_free(hull); |
| return NULL; |
| } |
| |
| /* Detect and make explicit all equalities satisfied by the (integer) |
| * points in bmap. |
| */ |
| struct isl_basic_map *isl_basic_map_detect_equalities( |
| struct isl_basic_map *bmap) |
| { |
| int i, j; |
| struct isl_basic_set *hull = NULL; |
| |
| if (!bmap) |
| return NULL; |
| if (bmap->n_ineq == 0) |
| return bmap; |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) |
| return bmap; |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES)) |
| return bmap; |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) |
| return isl_basic_map_implicit_equalities(bmap); |
| |
| hull = equalities_in_underlying_set(isl_basic_map_copy(bmap)); |
| if (!hull) |
| goto error; |
| if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) { |
| isl_basic_set_free(hull); |
| return isl_basic_map_set_to_empty(bmap); |
| } |
| bmap = isl_basic_map_extend_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); |
| if (j < 0) |
| goto error; |
| isl_seq_cpy(bmap->eq[j], hull->eq[i], |
| 1 + isl_basic_set_total_dim(hull)); |
| } |
| isl_vec_free(bmap->sample); |
| bmap->sample = isl_vec_copy(hull->sample); |
| isl_basic_set_free(hull); |
| ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES); |
| bmap = isl_basic_map_simplify(bmap); |
| return isl_basic_map_finalize(bmap); |
| error: |
| isl_basic_set_free(hull); |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| __isl_give isl_basic_set *isl_basic_set_detect_equalities( |
| __isl_take isl_basic_set *bset) |
| { |
| return (isl_basic_set *) |
| isl_basic_map_detect_equalities((isl_basic_map *)bset); |
| } |
| |
| __isl_give isl_map *isl_map_inline_foreach_basic_map(__isl_take isl_map *map, |
| __isl_give isl_basic_map *(*fn)(__isl_take isl_basic_map *bmap)) |
| { |
| struct isl_basic_map *bmap; |
| int i; |
| |
| if (!map) |
| return NULL; |
| |
| for (i = 0; i < map->n; ++i) { |
| bmap = isl_basic_map_copy(map->p[i]); |
| bmap = fn(bmap); |
| if (!bmap) |
| goto error; |
| isl_basic_map_free(map->p[i]); |
| map->p[i] = bmap; |
| } |
| |
| return map; |
| error: |
| isl_map_free(map); |
| return NULL; |
| } |
| |
| __isl_give isl_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) |
| { |
| bmap = isl_basic_map_detect_equalities(bmap); |
| bmap = isl_basic_map_cow(bmap); |
| if (bmap) |
| isl_basic_map_free_inequality(bmap, bmap->n_ineq); |
| bmap = isl_basic_map_finalize(bmap); |
| return bmap; |
| } |
| |
| struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset) |
| { |
| return (struct isl_basic_set *) |
| isl_basic_map_affine_hull((struct isl_basic_map *)bset); |
| } |
| |
| struct isl_basic_map *isl_map_affine_hull(struct isl_map *map) |
| { |
| int i; |
| struct isl_basic_map *model = NULL; |
| struct isl_basic_map *hull = NULL; |
| struct isl_set *set; |
| |
| map = isl_map_detect_equalities(map); |
| map = isl_map_align_divs(map); |
| |
| if (!map) |
| return NULL; |
| |
| if (map->n == 0) { |
| hull = isl_basic_map_empty_like_map(map); |
| isl_map_free(map); |
| return hull; |
| } |
| |
| model = isl_basic_map_copy(map->p[0]); |
| set = isl_map_underlying_set(map); |
| set = isl_set_cow(set); |
| if (!set) |
| goto error; |
| |
| for (i = 0; i < set->n; ++i) { |
| set->p[i] = isl_basic_set_cow(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); |
| } |
| isl_set_free(set); |
| hull = isl_basic_map_simplify(hull); |
| return isl_basic_map_finalize(hull); |
| error: |
| isl_basic_map_free(model); |
| isl_set_free(set); |
| return NULL; |
| } |
| |
| struct isl_basic_set *isl_set_affine_hull(struct isl_set *set) |
| { |
| return (struct isl_basic_set *) |
| isl_map_affine_hull((struct isl_map *)set); |
| } |