| /* |
| * Copyright 2008-2009 Katholieke Universiteit Leuven |
| * |
| * 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 |
| */ |
| |
| #include <isl_ctx_private.h> |
| #include <isl_map_private.h> |
| #include "isl_sample.h" |
| #include <isl/vec.h> |
| #include <isl/mat.h> |
| #include <isl_seq.h> |
| #include "isl_equalities.h" |
| #include "isl_tab.h" |
| #include "isl_basis_reduction.h" |
| #include <isl_factorization.h> |
| #include <isl_point_private.h> |
| #include <isl_options_private.h> |
| #include <isl_vec_private.h> |
| |
| #include <bset_from_bmap.c> |
| #include <set_to_map.c> |
| |
| static __isl_give isl_vec *empty_sample(__isl_take isl_basic_set *bset) |
| { |
| struct isl_vec *vec; |
| |
| vec = isl_vec_alloc(bset->ctx, 0); |
| isl_basic_set_free(bset); |
| return vec; |
| } |
| |
| /* Construct a zero sample of the same dimension as bset. |
| * As a special case, if bset is zero-dimensional, this |
| * function creates a zero-dimensional sample point. |
| */ |
| static __isl_give isl_vec *zero_sample(__isl_take isl_basic_set *bset) |
| { |
| unsigned dim; |
| struct isl_vec *sample; |
| |
| dim = isl_basic_set_total_dim(bset); |
| sample = isl_vec_alloc(bset->ctx, 1 + dim); |
| if (sample) { |
| isl_int_set_si(sample->el[0], 1); |
| isl_seq_clr(sample->el + 1, dim); |
| } |
| isl_basic_set_free(bset); |
| return sample; |
| } |
| |
| static __isl_give isl_vec *interval_sample(__isl_take isl_basic_set *bset) |
| { |
| int i; |
| isl_int t; |
| struct isl_vec *sample; |
| |
| bset = isl_basic_set_simplify(bset); |
| if (!bset) |
| return NULL; |
| if (isl_basic_set_plain_is_empty(bset)) |
| return empty_sample(bset); |
| if (bset->n_eq == 0 && bset->n_ineq == 0) |
| return zero_sample(bset); |
| |
| sample = isl_vec_alloc(bset->ctx, 2); |
| if (!sample) |
| goto error; |
| if (!bset) |
| return NULL; |
| isl_int_set_si(sample->block.data[0], 1); |
| |
| if (bset->n_eq > 0) { |
| isl_assert(bset->ctx, bset->n_eq == 1, goto error); |
| isl_assert(bset->ctx, bset->n_ineq == 0, goto error); |
| if (isl_int_is_one(bset->eq[0][1])) |
| isl_int_neg(sample->el[1], bset->eq[0][0]); |
| else { |
| isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]), |
| goto error); |
| isl_int_set(sample->el[1], bset->eq[0][0]); |
| } |
| isl_basic_set_free(bset); |
| return sample; |
| } |
| |
| isl_int_init(t); |
| if (isl_int_is_one(bset->ineq[0][1])) |
| isl_int_neg(sample->block.data[1], bset->ineq[0][0]); |
| else |
| isl_int_set(sample->block.data[1], bset->ineq[0][0]); |
| for (i = 1; i < bset->n_ineq; ++i) { |
| isl_seq_inner_product(sample->block.data, |
| bset->ineq[i], 2, &t); |
| if (isl_int_is_neg(t)) |
| break; |
| } |
| isl_int_clear(t); |
| if (i < bset->n_ineq) { |
| isl_vec_free(sample); |
| return empty_sample(bset); |
| } |
| |
| isl_basic_set_free(bset); |
| return sample; |
| error: |
| isl_basic_set_free(bset); |
| isl_vec_free(sample); |
| return NULL; |
| } |
| |
| /* Find a sample integer point, if any, in bset, which is known |
| * to have equalities. If bset contains no integer points, then |
| * return a zero-length vector. |
| * We simply remove the known equalities, compute a sample |
| * in the resulting bset, using the specified recurse function, |
| * and then transform the sample back to the original space. |
| */ |
| static __isl_give isl_vec *sample_eq(__isl_take isl_basic_set *bset, |
| __isl_give isl_vec *(*recurse)(__isl_take isl_basic_set *)) |
| { |
| struct isl_mat *T; |
| struct isl_vec *sample; |
| |
| if (!bset) |
| return NULL; |
| |
| bset = isl_basic_set_remove_equalities(bset, &T, NULL); |
| sample = recurse(bset); |
| if (!sample || sample->size == 0) |
| isl_mat_free(T); |
| else |
| sample = isl_mat_vec_product(T, sample); |
| return sample; |
| } |
| |
| /* Return a matrix containing the equalities of the tableau |
| * in constraint form. The tableau is assumed to have |
| * an associated bset that has been kept up-to-date. |
| */ |
| static struct isl_mat *tab_equalities(struct isl_tab *tab) |
| { |
| int i, j; |
| int n_eq; |
| struct isl_mat *eq; |
| struct isl_basic_set *bset; |
| |
| if (!tab) |
| return NULL; |
| |
| bset = isl_tab_peek_bset(tab); |
| isl_assert(tab->mat->ctx, bset, return NULL); |
| |
| n_eq = tab->n_var - tab->n_col + tab->n_dead; |
| if (tab->empty || n_eq == 0) |
| return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var); |
| if (n_eq == tab->n_var) |
| return isl_mat_identity(tab->mat->ctx, tab->n_var); |
| |
| eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var); |
| if (!eq) |
| return NULL; |
| for (i = 0, j = 0; i < tab->n_con; ++i) { |
| if (tab->con[i].is_row) |
| continue; |
| if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead) |
| continue; |
| if (i < bset->n_eq) |
| isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var); |
| else |
| isl_seq_cpy(eq->row[j], |
| bset->ineq[i - bset->n_eq] + 1, tab->n_var); |
| ++j; |
| } |
| isl_assert(bset->ctx, j == n_eq, goto error); |
| return eq; |
| error: |
| isl_mat_free(eq); |
| return NULL; |
| } |
| |
| /* Compute and return an initial basis for the bounded tableau "tab". |
| * |
| * If the tableau is either full-dimensional or zero-dimensional, |
| * the we simply return an identity matrix. |
| * Otherwise, we construct a basis whose first directions correspond |
| * to equalities. |
| */ |
| static struct isl_mat *initial_basis(struct isl_tab *tab) |
| { |
| int n_eq; |
| struct isl_mat *eq; |
| struct isl_mat *Q; |
| |
| tab->n_unbounded = 0; |
| tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead; |
| if (tab->empty || n_eq == 0 || n_eq == tab->n_var) |
| return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var); |
| |
| eq = tab_equalities(tab); |
| eq = isl_mat_left_hermite(eq, 0, NULL, &Q); |
| if (!eq) |
| return NULL; |
| isl_mat_free(eq); |
| |
| Q = isl_mat_lin_to_aff(Q); |
| return Q; |
| } |
| |
| /* Compute the minimum of the current ("level") basis row over "tab" |
| * and store the result in position "level" of "min". |
| * |
| * This function assumes that at least one more row and at least |
| * one more element in the constraint array are available in the tableau. |
| */ |
| static enum isl_lp_result compute_min(isl_ctx *ctx, struct isl_tab *tab, |
| __isl_keep isl_vec *min, int level) |
| { |
| return isl_tab_min(tab, tab->basis->row[1 + level], |
| ctx->one, &min->el[level], NULL, 0); |
| } |
| |
| /* Compute the maximum of the current ("level") basis row over "tab" |
| * and store the result in position "level" of "max". |
| * |
| * This function assumes that at least one more row and at least |
| * one more element in the constraint array are available in the tableau. |
| */ |
| static enum isl_lp_result compute_max(isl_ctx *ctx, struct isl_tab *tab, |
| __isl_keep isl_vec *max, int level) |
| { |
| enum isl_lp_result res; |
| unsigned dim = tab->n_var; |
| |
| isl_seq_neg(tab->basis->row[1 + level] + 1, |
| tab->basis->row[1 + level] + 1, dim); |
| res = isl_tab_min(tab, tab->basis->row[1 + level], |
| ctx->one, &max->el[level], NULL, 0); |
| isl_seq_neg(tab->basis->row[1 + level] + 1, |
| tab->basis->row[1 + level] + 1, dim); |
| isl_int_neg(max->el[level], max->el[level]); |
| |
| return res; |
| } |
| |
| /* Perform a greedy search for an integer point in the set represented |
| * by "tab", given that the minimal rational value (rounded up to the |
| * nearest integer) at "level" is smaller than the maximal rational |
| * value (rounded down to the nearest integer). |
| * |
| * Return 1 if we have found an integer point (if tab->n_unbounded > 0 |
| * then we may have only found integer values for the bounded dimensions |
| * and it is the responsibility of the caller to extend this solution |
| * to the unbounded dimensions). |
| * Return 0 if greedy search did not result in a solution. |
| * Return -1 if some error occurred. |
| * |
| * We assign a value half-way between the minimum and the maximum |
| * to the current dimension and check if the minimal value of the |
| * next dimension is still smaller than (or equal) to the maximal value. |
| * We continue this process until either |
| * - the minimal value (rounded up) is greater than the maximal value |
| * (rounded down). In this case, greedy search has failed. |
| * - we have exhausted all bounded dimensions, meaning that we have |
| * found a solution. |
| * - the sample value of the tableau is integral. |
| * - some error has occurred. |
| */ |
| static int greedy_search(isl_ctx *ctx, struct isl_tab *tab, |
| __isl_keep isl_vec *min, __isl_keep isl_vec *max, int level) |
| { |
| struct isl_tab_undo *snap; |
| enum isl_lp_result res; |
| |
| snap = isl_tab_snap(tab); |
| |
| do { |
| isl_int_add(tab->basis->row[1 + level][0], |
| min->el[level], max->el[level]); |
| isl_int_fdiv_q_ui(tab->basis->row[1 + level][0], |
| tab->basis->row[1 + level][0], 2); |
| isl_int_neg(tab->basis->row[1 + level][0], |
| tab->basis->row[1 + level][0]); |
| if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0) |
| return -1; |
| isl_int_set_si(tab->basis->row[1 + level][0], 0); |
| |
| if (++level >= tab->n_var - tab->n_unbounded) |
| return 1; |
| if (isl_tab_sample_is_integer(tab)) |
| return 1; |
| |
| res = compute_min(ctx, tab, min, level); |
| if (res == isl_lp_error) |
| return -1; |
| if (res != isl_lp_ok) |
| isl_die(ctx, isl_error_internal, |
| "expecting bounded rational solution", |
| return -1); |
| res = compute_max(ctx, tab, max, level); |
| if (res == isl_lp_error) |
| return -1; |
| if (res != isl_lp_ok) |
| isl_die(ctx, isl_error_internal, |
| "expecting bounded rational solution", |
| return -1); |
| } while (isl_int_le(min->el[level], max->el[level])); |
| |
| if (isl_tab_rollback(tab, snap) < 0) |
| return -1; |
| |
| return 0; |
| } |
| |
| /* Given a tableau representing a set, find and return |
| * an integer point in the set, if there is any. |
| * |
| * We perform a depth first search |
| * for an integer point, by scanning all possible values in the range |
| * attained by a basis vector, where an initial basis may have been set |
| * by the calling function. Otherwise an initial basis that exploits |
| * the equalities in the tableau is created. |
| * tab->n_zero is currently ignored and is clobbered by this function. |
| * |
| * The tableau is allowed to have unbounded direction, but then |
| * the calling function needs to set an initial basis, with the |
| * unbounded directions last and with tab->n_unbounded set |
| * to the number of unbounded directions. |
| * Furthermore, the calling functions needs to add shifted copies |
| * of all constraints involving unbounded directions to ensure |
| * that any feasible rational value in these directions can be rounded |
| * up to yield a feasible integer value. |
| * In particular, let B define the given basis x' = B x |
| * and let T be the inverse of B, i.e., X = T x'. |
| * Let a x + c >= 0 be a constraint of the set represented by the tableau, |
| * or a T x' + c >= 0 in terms of the given basis. Assume that |
| * the bounded directions have an integer value, then we can safely |
| * round up the values for the unbounded directions if we make sure |
| * that x' not only satisfies the original constraint, but also |
| * the constraint "a T x' + c + s >= 0" with s the sum of all |
| * negative values in the last n_unbounded entries of "a T". |
| * The calling function therefore needs to add the constraint |
| * a x + c + s >= 0. The current function then scans the first |
| * directions for an integer value and once those have been found, |
| * it can compute "T ceil(B x)" to yield an integer point in the set. |
| * Note that during the search, the first rows of B may be changed |
| * by a basis reduction, but the last n_unbounded rows of B remain |
| * unaltered and are also not mixed into the first rows. |
| * |
| * The search is implemented iteratively. "level" identifies the current |
| * basis vector. "init" is true if we want the first value at the current |
| * level and false if we want the next value. |
| * |
| * At the start of each level, we first check if we can find a solution |
| * using greedy search. If not, we continue with the exhaustive search. |
| * |
| * The initial basis is the identity matrix. If the range in some direction |
| * contains more than one integer value, we perform basis reduction based |
| * on the value of ctx->opt->gbr |
| * - ISL_GBR_NEVER: never perform basis reduction |
| * - ISL_GBR_ONCE: only perform basis reduction the first |
| * time such a range is encountered |
| * - ISL_GBR_ALWAYS: always perform basis reduction when |
| * such a range is encountered |
| * |
| * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis |
| * reduction computation to return early. That is, as soon as it |
| * finds a reasonable first direction. |
| */ |
| struct isl_vec *isl_tab_sample(struct isl_tab *tab) |
| { |
| unsigned dim; |
| unsigned gbr; |
| struct isl_ctx *ctx; |
| struct isl_vec *sample; |
| struct isl_vec *min; |
| struct isl_vec *max; |
| enum isl_lp_result res; |
| int level; |
| int init; |
| int reduced; |
| struct isl_tab_undo **snap; |
| |
| if (!tab) |
| return NULL; |
| if (tab->empty) |
| return isl_vec_alloc(tab->mat->ctx, 0); |
| |
| if (!tab->basis) |
| tab->basis = initial_basis(tab); |
| if (!tab->basis) |
| return NULL; |
| isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1, |
| return NULL); |
| isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1, |
| return NULL); |
| |
| ctx = tab->mat->ctx; |
| dim = tab->n_var; |
| gbr = ctx->opt->gbr; |
| |
| if (tab->n_unbounded == tab->n_var) { |
| sample = isl_tab_get_sample_value(tab); |
| sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample); |
| sample = isl_vec_ceil(sample); |
| sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis), |
| sample); |
| return sample; |
| } |
| |
| if (isl_tab_extend_cons(tab, dim + 1) < 0) |
| return NULL; |
| |
| min = isl_vec_alloc(ctx, dim); |
| max = isl_vec_alloc(ctx, dim); |
| snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim); |
| |
| if (!min || !max || !snap) |
| goto error; |
| |
| level = 0; |
| init = 1; |
| reduced = 0; |
| |
| while (level >= 0) { |
| if (init) { |
| int choice; |
| |
| res = compute_min(ctx, tab, min, level); |
| if (res == isl_lp_error) |
| goto error; |
| if (res != isl_lp_ok) |
| isl_die(ctx, isl_error_internal, |
| "expecting bounded rational solution", |
| goto error); |
| if (isl_tab_sample_is_integer(tab)) |
| break; |
| res = compute_max(ctx, tab, max, level); |
| if (res == isl_lp_error) |
| goto error; |
| if (res != isl_lp_ok) |
| isl_die(ctx, isl_error_internal, |
| "expecting bounded rational solution", |
| goto error); |
| if (isl_tab_sample_is_integer(tab)) |
| break; |
| choice = isl_int_lt(min->el[level], max->el[level]); |
| if (choice) { |
| int g; |
| g = greedy_search(ctx, tab, min, max, level); |
| if (g < 0) |
| goto error; |
| if (g) |
| break; |
| } |
| if (!reduced && choice && |
| ctx->opt->gbr != ISL_GBR_NEVER) { |
| unsigned gbr_only_first; |
| if (ctx->opt->gbr == ISL_GBR_ONCE) |
| ctx->opt->gbr = ISL_GBR_NEVER; |
| tab->n_zero = level; |
| gbr_only_first = ctx->opt->gbr_only_first; |
| ctx->opt->gbr_only_first = |
| ctx->opt->gbr == ISL_GBR_ALWAYS; |
| tab = isl_tab_compute_reduced_basis(tab); |
| ctx->opt->gbr_only_first = gbr_only_first; |
| if (!tab || !tab->basis) |
| goto error; |
| reduced = 1; |
| continue; |
| } |
| reduced = 0; |
| snap[level] = isl_tab_snap(tab); |
| } else |
| isl_int_add_ui(min->el[level], min->el[level], 1); |
| |
| if (isl_int_gt(min->el[level], max->el[level])) { |
| level--; |
| init = 0; |
| if (level >= 0) |
| if (isl_tab_rollback(tab, snap[level]) < 0) |
| goto error; |
| continue; |
| } |
| isl_int_neg(tab->basis->row[1 + level][0], min->el[level]); |
| if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0) |
| goto error; |
| isl_int_set_si(tab->basis->row[1 + level][0], 0); |
| if (level + tab->n_unbounded < dim - 1) { |
| ++level; |
| init = 1; |
| continue; |
| } |
| break; |
| } |
| |
| if (level >= 0) { |
| sample = isl_tab_get_sample_value(tab); |
| if (!sample) |
| goto error; |
| if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) { |
| sample = isl_mat_vec_product(isl_mat_copy(tab->basis), |
| sample); |
| sample = isl_vec_ceil(sample); |
| sample = isl_mat_vec_inverse_product( |
| isl_mat_copy(tab->basis), sample); |
| } |
| } else |
| sample = isl_vec_alloc(ctx, 0); |
| |
| ctx->opt->gbr = gbr; |
| isl_vec_free(min); |
| isl_vec_free(max); |
| free(snap); |
| return sample; |
| error: |
| ctx->opt->gbr = gbr; |
| isl_vec_free(min); |
| isl_vec_free(max); |
| free(snap); |
| return NULL; |
| } |
| |
| static __isl_give isl_vec *sample_bounded(__isl_take isl_basic_set *bset); |
| |
| /* Compute a sample point of the given basic set, based on the given, |
| * non-trivial factorization. |
| */ |
| static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset, |
| __isl_take isl_factorizer *f) |
| { |
| int i, n; |
| isl_vec *sample = NULL; |
| isl_ctx *ctx; |
| unsigned nparam; |
| unsigned nvar; |
| |
| ctx = isl_basic_set_get_ctx(bset); |
| if (!ctx) |
| goto error; |
| |
| nparam = isl_basic_set_dim(bset, isl_dim_param); |
| nvar = isl_basic_set_dim(bset, isl_dim_set); |
| |
| sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset)); |
| if (!sample) |
| goto error; |
| isl_int_set_si(sample->el[0], 1); |
| |
| bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset); |
| |
| for (i = 0, n = 0; i < f->n_group; ++i) { |
| isl_basic_set *bset_i; |
| isl_vec *sample_i; |
| |
| bset_i = isl_basic_set_copy(bset); |
| bset_i = isl_basic_set_drop_constraints_involving(bset_i, |
| nparam + n + f->len[i], nvar - n - f->len[i]); |
| bset_i = isl_basic_set_drop_constraints_involving(bset_i, |
| nparam, n); |
| bset_i = isl_basic_set_drop(bset_i, isl_dim_set, |
| n + f->len[i], nvar - n - f->len[i]); |
| bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n); |
| |
| sample_i = sample_bounded(bset_i); |
| if (!sample_i) |
| goto error; |
| if (sample_i->size == 0) { |
| isl_basic_set_free(bset); |
| isl_factorizer_free(f); |
| isl_vec_free(sample); |
| return sample_i; |
| } |
| isl_seq_cpy(sample->el + 1 + nparam + n, |
| sample_i->el + 1, f->len[i]); |
| isl_vec_free(sample_i); |
| |
| n += f->len[i]; |
| } |
| |
| f->morph = isl_morph_inverse(f->morph); |
| sample = isl_morph_vec(isl_morph_copy(f->morph), sample); |
| |
| isl_basic_set_free(bset); |
| isl_factorizer_free(f); |
| return sample; |
| error: |
| isl_basic_set_free(bset); |
| isl_factorizer_free(f); |
| isl_vec_free(sample); |
| return NULL; |
| } |
| |
| /* Given a basic set that is known to be bounded, find and return |
| * an integer point in the basic set, if there is any. |
| * |
| * After handling some trivial cases, we construct a tableau |
| * and then use isl_tab_sample to find a sample, passing it |
| * the identity matrix as initial basis. |
| */ |
| static __isl_give isl_vec *sample_bounded(__isl_take isl_basic_set *bset) |
| { |
| unsigned dim; |
| struct isl_vec *sample; |
| struct isl_tab *tab = NULL; |
| isl_factorizer *f; |
| |
| if (!bset) |
| return NULL; |
| |
| if (isl_basic_set_plain_is_empty(bset)) |
| return empty_sample(bset); |
| |
| dim = isl_basic_set_total_dim(bset); |
| if (dim == 0) |
| return zero_sample(bset); |
| if (dim == 1) |
| return interval_sample(bset); |
| if (bset->n_eq > 0) |
| return sample_eq(bset, sample_bounded); |
| |
| f = isl_basic_set_factorizer(bset); |
| if (!f) |
| goto error; |
| if (f->n_group != 0) |
| return factored_sample(bset, f); |
| isl_factorizer_free(f); |
| |
| tab = isl_tab_from_basic_set(bset, 1); |
| if (tab && tab->empty) { |
| isl_tab_free(tab); |
| ISL_F_SET(bset, ISL_BASIC_SET_EMPTY); |
| sample = isl_vec_alloc(isl_basic_set_get_ctx(bset), 0); |
| isl_basic_set_free(bset); |
| return sample; |
| } |
| |
| if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT)) |
| if (isl_tab_detect_implicit_equalities(tab) < 0) |
| goto error; |
| |
| sample = isl_tab_sample(tab); |
| if (!sample) |
| goto error; |
| |
| if (sample->size > 0) { |
| isl_vec_free(bset->sample); |
| bset->sample = isl_vec_copy(sample); |
| } |
| |
| isl_basic_set_free(bset); |
| isl_tab_free(tab); |
| return sample; |
| error: |
| isl_basic_set_free(bset); |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| /* Given a basic set "bset" and a value "sample" for the first coordinates |
| * of bset, plug in these values and drop the corresponding coordinates. |
| * |
| * We do this by computing the preimage of the transformation |
| * |
| * [ 1 0 ] |
| * x = [ s 0 ] x' |
| * [ 0 I ] |
| * |
| * where [1 s] is the sample value and I is the identity matrix of the |
| * appropriate dimension. |
| */ |
| static __isl_give isl_basic_set *plug_in(__isl_take isl_basic_set *bset, |
| __isl_take isl_vec *sample) |
| { |
| int i; |
| unsigned total; |
| struct isl_mat *T; |
| |
| if (!bset || !sample) |
| goto error; |
| |
| total = isl_basic_set_total_dim(bset); |
| T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1)); |
| if (!T) |
| goto error; |
| |
| for (i = 0; i < sample->size; ++i) { |
| isl_int_set(T->row[i][0], sample->el[i]); |
| isl_seq_clr(T->row[i] + 1, T->n_col - 1); |
| } |
| for (i = 0; i < T->n_col - 1; ++i) { |
| isl_seq_clr(T->row[sample->size + i], T->n_col); |
| isl_int_set_si(T->row[sample->size + i][1 + i], 1); |
| } |
| isl_vec_free(sample); |
| |
| bset = isl_basic_set_preimage(bset, T); |
| return bset; |
| error: |
| isl_basic_set_free(bset); |
| isl_vec_free(sample); |
| return NULL; |
| } |
| |
| /* Given a basic set "bset", return any (possibly non-integer) point |
| * in the basic set. |
| */ |
| static __isl_give isl_vec *rational_sample(__isl_take isl_basic_set *bset) |
| { |
| struct isl_tab *tab; |
| struct isl_vec *sample; |
| |
| if (!bset) |
| return NULL; |
| |
| tab = isl_tab_from_basic_set(bset, 0); |
| sample = isl_tab_get_sample_value(tab); |
| isl_tab_free(tab); |
| |
| isl_basic_set_free(bset); |
| |
| return sample; |
| } |
| |
| /* Given a linear cone "cone" and a rational point "vec", |
| * construct a polyhedron with shifted copies of the constraints in "cone", |
| * i.e., a polyhedron with "cone" as its recession cone, such that each |
| * point x in this polyhedron is such that the unit box positioned at x |
| * lies entirely inside the affine cone 'vec + cone'. |
| * Any rational point in this polyhedron may therefore be rounded up |
| * to yield an integer point that lies inside said affine cone. |
| * |
| * Denote the constraints of cone by "<a_i, x> >= 0" and the rational |
| * point "vec" by v/d. |
| * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given |
| * by <a_i, x> - b/d >= 0. |
| * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone. |
| * We prefer this polyhedron over the actual affine cone because it doesn't |
| * require a scaling of the constraints. |
| * If each of the vertices of the unit cube positioned at x lies inside |
| * this polyhedron, then the whole unit cube at x lies inside the affine cone. |
| * We therefore impose that x' = x + \sum e_i, for any selection of unit |
| * vectors lies inside the polyhedron, i.e., |
| * |
| * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0 |
| * |
| * The most stringent of these constraints is the one that selects |
| * all negative a_i, so the polyhedron we are looking for has constraints |
| * |
| * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0 |
| * |
| * Note that if cone were known to have only non-negative rays |
| * (which can be accomplished by a unimodular transformation), |
| * then we would only have to check the points x' = x + e_i |
| * and we only have to add the smallest negative a_i (if any) |
| * instead of the sum of all negative a_i. |
| */ |
| static __isl_give isl_basic_set *shift_cone(__isl_take isl_basic_set *cone, |
| __isl_take isl_vec *vec) |
| { |
| int i, j, k; |
| unsigned total; |
| |
| struct isl_basic_set *shift = NULL; |
| |
| if (!cone || !vec) |
| goto error; |
| |
| isl_assert(cone->ctx, cone->n_eq == 0, goto error); |
| |
| total = isl_basic_set_total_dim(cone); |
| |
| shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone), |
| 0, 0, cone->n_ineq); |
| |
| for (i = 0; i < cone->n_ineq; ++i) { |
| k = isl_basic_set_alloc_inequality(shift); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total); |
| isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total, |
| &shift->ineq[k][0]); |
| isl_int_cdiv_q(shift->ineq[k][0], |
| shift->ineq[k][0], vec->el[0]); |
| isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]); |
| for (j = 0; j < total; ++j) { |
| if (isl_int_is_nonneg(shift->ineq[k][1 + j])) |
| continue; |
| isl_int_add(shift->ineq[k][0], |
| shift->ineq[k][0], shift->ineq[k][1 + j]); |
| } |
| } |
| |
| isl_basic_set_free(cone); |
| isl_vec_free(vec); |
| |
| return isl_basic_set_finalize(shift); |
| error: |
| isl_basic_set_free(shift); |
| isl_basic_set_free(cone); |
| isl_vec_free(vec); |
| return NULL; |
| } |
| |
| /* Given a rational point vec in a (transformed) basic set, |
| * such that cone is the recession cone of the original basic set, |
| * "round up" the rational point to an integer point. |
| * |
| * We first check if the rational point just happens to be integer. |
| * If not, we transform the cone in the same way as the basic set, |
| * pick a point x in this cone shifted to the rational point such that |
| * the whole unit cube at x is also inside this affine cone. |
| * Then we simply round up the coordinates of x and return the |
| * resulting integer point. |
| */ |
| static __isl_give isl_vec *round_up_in_cone(__isl_take isl_vec *vec, |
| __isl_take isl_basic_set *cone, __isl_take isl_mat *U) |
| { |
| unsigned total; |
| |
| if (!vec || !cone || !U) |
| goto error; |
| |
| isl_assert(vec->ctx, vec->size != 0, goto error); |
| if (isl_int_is_one(vec->el[0])) { |
| isl_mat_free(U); |
| isl_basic_set_free(cone); |
| return vec; |
| } |
| |
| total = isl_basic_set_total_dim(cone); |
| cone = isl_basic_set_preimage(cone, U); |
| cone = isl_basic_set_remove_dims(cone, isl_dim_set, |
| 0, total - (vec->size - 1)); |
| |
| cone = shift_cone(cone, vec); |
| |
| vec = rational_sample(cone); |
| vec = isl_vec_ceil(vec); |
| return vec; |
| error: |
| isl_mat_free(U); |
| isl_vec_free(vec); |
| isl_basic_set_free(cone); |
| return NULL; |
| } |
| |
| /* Concatenate two integer vectors, i.e., two vectors with denominator |
| * (stored in element 0) equal to 1. |
| */ |
| static __isl_give isl_vec *vec_concat(__isl_take isl_vec *vec1, |
| __isl_take isl_vec *vec2) |
| { |
| struct isl_vec *vec; |
| |
| if (!vec1 || !vec2) |
| goto error; |
| isl_assert(vec1->ctx, vec1->size > 0, goto error); |
| isl_assert(vec2->ctx, vec2->size > 0, goto error); |
| isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error); |
| isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error); |
| |
| vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1); |
| if (!vec) |
| goto error; |
| |
| isl_seq_cpy(vec->el, vec1->el, vec1->size); |
| isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1); |
| |
| isl_vec_free(vec1); |
| isl_vec_free(vec2); |
| |
| return vec; |
| error: |
| isl_vec_free(vec1); |
| isl_vec_free(vec2); |
| return NULL; |
| } |
| |
| /* Give a basic set "bset" with recession cone "cone", compute and |
| * return an integer point in bset, if any. |
| * |
| * If the recession cone is full-dimensional, then we know that |
| * bset contains an infinite number of integer points and it is |
| * fairly easy to pick one of them. |
| * If the recession cone is not full-dimensional, then we first |
| * transform bset such that the bounded directions appear as |
| * the first dimensions of the transformed basic set. |
| * We do this by using a unimodular transformation that transforms |
| * the equalities in the recession cone to equalities on the first |
| * dimensions. |
| * |
| * The transformed set is then projected onto its bounded dimensions. |
| * Note that to compute this projection, we can simply drop all constraints |
| * involving any of the unbounded dimensions since these constraints |
| * cannot be combined to produce a constraint on the bounded dimensions. |
| * To see this, assume that there is such a combination of constraints |
| * that produces a constraint on the bounded dimensions. This means |
| * that some combination of the unbounded dimensions has both an upper |
| * bound and a lower bound in terms of the bounded dimensions, but then |
| * this combination would be a bounded direction too and would have been |
| * transformed into a bounded dimensions. |
| * |
| * We then compute a sample value in the bounded dimensions. |
| * If no such value can be found, then the original set did not contain |
| * any integer points and we are done. |
| * Otherwise, we plug in the value we found in the bounded dimensions, |
| * project out these bounded dimensions and end up with a set with |
| * a full-dimensional recession cone. |
| * A sample point in this set is computed by "rounding up" any |
| * rational point in the set. |
| * |
| * The sample points in the bounded and unbounded dimensions are |
| * then combined into a single sample point and transformed back |
| * to the original space. |
| */ |
| __isl_give isl_vec *isl_basic_set_sample_with_cone( |
| __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone) |
| { |
| unsigned total; |
| unsigned cone_dim; |
| struct isl_mat *M, *U; |
| struct isl_vec *sample; |
| struct isl_vec *cone_sample; |
| struct isl_ctx *ctx; |
| struct isl_basic_set *bounded; |
| |
| if (!bset || !cone) |
| goto error; |
| |
| ctx = isl_basic_set_get_ctx(bset); |
| total = isl_basic_set_total_dim(cone); |
| cone_dim = total - cone->n_eq; |
| |
| M = isl_mat_sub_alloc6(ctx, cone->eq, 0, cone->n_eq, 1, total); |
| M = isl_mat_left_hermite(M, 0, &U, NULL); |
| 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)); |
| |
| bounded = isl_basic_set_copy(bset); |
| bounded = isl_basic_set_drop_constraints_involving(bounded, |
| total - cone_dim, cone_dim); |
| bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim); |
| sample = sample_bounded(bounded); |
| if (!sample || sample->size == 0) { |
| isl_basic_set_free(bset); |
| isl_basic_set_free(cone); |
| isl_mat_free(U); |
| return sample; |
| } |
| bset = plug_in(bset, isl_vec_copy(sample)); |
| cone_sample = rational_sample(bset); |
| cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U)); |
| sample = vec_concat(sample, cone_sample); |
| sample = isl_mat_vec_product(U, sample); |
| return sample; |
| error: |
| isl_basic_set_free(cone); |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| static void vec_sum_of_neg(struct isl_vec *v, isl_int *s) |
| { |
| int i; |
| |
| isl_int_set_si(*s, 0); |
| |
| for (i = 0; i < v->size; ++i) |
| if (isl_int_is_neg(v->el[i])) |
| isl_int_add(*s, *s, v->el[i]); |
| } |
| |
| /* Given a tableau "tab", a tableau "tab_cone" that corresponds |
| * to the recession cone and the inverse of a new basis U = inv(B), |
| * with the unbounded directions in B last, |
| * add constraints to "tab" that ensure any rational value |
| * in the unbounded directions can be rounded up to an integer value. |
| * |
| * The new basis is given by x' = B x, i.e., x = U x'. |
| * For any rational value of the last tab->n_unbounded coordinates |
| * in the update tableau, the value that is obtained by rounding |
| * up this value should be contained in the original tableau. |
| * For any constraint "a x + c >= 0", we therefore need to add |
| * a constraint "a x + c + s >= 0", with s the sum of all negative |
| * entries in the last elements of "a U". |
| * |
| * Since we are not interested in the first entries of any of the "a U", |
| * we first drop the columns of U that correpond to bounded directions. |
| */ |
| static int tab_shift_cone(struct isl_tab *tab, |
| struct isl_tab *tab_cone, struct isl_mat *U) |
| { |
| int i; |
| isl_int v; |
| struct isl_basic_set *bset = NULL; |
| |
| if (tab && tab->n_unbounded == 0) { |
| isl_mat_free(U); |
| return 0; |
| } |
| isl_int_init(v); |
| if (!tab || !tab_cone || !U) |
| goto error; |
| bset = isl_tab_peek_bset(tab_cone); |
| U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded); |
| for (i = 0; i < bset->n_ineq; ++i) { |
| int ok; |
| struct isl_vec *row = NULL; |
| if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i)) |
| continue; |
| row = isl_vec_alloc(bset->ctx, tab_cone->n_var); |
| if (!row) |
| goto error; |
| isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var); |
| row = isl_vec_mat_product(row, isl_mat_copy(U)); |
| if (!row) |
| goto error; |
| vec_sum_of_neg(row, &v); |
| isl_vec_free(row); |
| if (isl_int_is_zero(v)) |
| continue; |
| if (isl_tab_extend_cons(tab, 1) < 0) |
| goto error; |
| isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v); |
| ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0; |
| isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v); |
| if (!ok) |
| goto error; |
| } |
| |
| isl_mat_free(U); |
| isl_int_clear(v); |
| return 0; |
| error: |
| isl_mat_free(U); |
| isl_int_clear(v); |
| return -1; |
| } |
| |
| /* Compute and return an initial basis for the possibly |
| * unbounded tableau "tab". "tab_cone" is a tableau |
| * for the corresponding recession cone. |
| * Additionally, add constraints to "tab" that ensure |
| * that any rational value for the unbounded directions |
| * can be rounded up to an integer value. |
| * |
| * If the tableau is bounded, i.e., if the recession cone |
| * is zero-dimensional, then we just use inital_basis. |
| * Otherwise, we construct a basis whose first directions |
| * correspond to equalities, followed by bounded directions, |
| * i.e., equalities in the recession cone. |
| * The remaining directions are then unbounded. |
| */ |
| int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab, |
| struct isl_tab *tab_cone) |
| { |
| struct isl_mat *eq; |
| struct isl_mat *cone_eq; |
| struct isl_mat *U, *Q; |
| |
| if (!tab || !tab_cone) |
| return -1; |
| |
| if (tab_cone->n_col == tab_cone->n_dead) { |
| tab->basis = initial_basis(tab); |
| return tab->basis ? 0 : -1; |
| } |
| |
| eq = tab_equalities(tab); |
| if (!eq) |
| return -1; |
| tab->n_zero = eq->n_row; |
| cone_eq = tab_equalities(tab_cone); |
| eq = isl_mat_concat(eq, cone_eq); |
| if (!eq) |
| return -1; |
| tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero); |
| eq = isl_mat_left_hermite(eq, 0, &U, &Q); |
| if (!eq) |
| return -1; |
| isl_mat_free(eq); |
| tab->basis = isl_mat_lin_to_aff(Q); |
| if (tab_shift_cone(tab, tab_cone, U) < 0) |
| return -1; |
| if (!tab->basis) |
| return -1; |
| return 0; |
| } |
| |
| /* Compute and return a sample point in bset using generalized basis |
| * reduction. We first check if the input set has a non-trivial |
| * recession cone. If so, we perform some extra preprocessing in |
| * sample_with_cone. Otherwise, we directly perform generalized basis |
| * reduction. |
| */ |
| static __isl_give isl_vec *gbr_sample(__isl_take isl_basic_set *bset) |
| { |
| unsigned dim; |
| struct isl_basic_set *cone; |
| |
| dim = isl_basic_set_total_dim(bset); |
| |
| cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset)); |
| if (!cone) |
| goto error; |
| |
| if (cone->n_eq < dim) |
| return isl_basic_set_sample_with_cone(bset, cone); |
| |
| isl_basic_set_free(cone); |
| return sample_bounded(bset); |
| error: |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| static __isl_give isl_vec *basic_set_sample(__isl_take isl_basic_set *bset, |
| int bounded) |
| { |
| struct isl_ctx *ctx; |
| unsigned dim; |
| if (!bset) |
| return NULL; |
| |
| ctx = bset->ctx; |
| if (isl_basic_set_plain_is_empty(bset)) |
| return empty_sample(bset); |
| |
| dim = isl_basic_set_n_dim(bset); |
| isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error); |
| isl_assert(ctx, bset->n_div == 0, goto error); |
| |
| if (bset->sample && bset->sample->size == 1 + dim) { |
| int contains = isl_basic_set_contains(bset, bset->sample); |
| if (contains < 0) |
| goto error; |
| if (contains) { |
| struct isl_vec *sample = isl_vec_copy(bset->sample); |
| isl_basic_set_free(bset); |
| return sample; |
| } |
| } |
| isl_vec_free(bset->sample); |
| bset->sample = NULL; |
| |
| if (bset->n_eq > 0) |
| return sample_eq(bset, bounded ? isl_basic_set_sample_bounded |
| : isl_basic_set_sample_vec); |
| if (dim == 0) |
| return zero_sample(bset); |
| if (dim == 1) |
| return interval_sample(bset); |
| |
| return bounded ? sample_bounded(bset) : gbr_sample(bset); |
| error: |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| __isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset) |
| { |
| return basic_set_sample(bset, 0); |
| } |
| |
| /* Compute an integer sample in "bset", where the caller guarantees |
| * that "bset" is bounded. |
| */ |
| __isl_give isl_vec *isl_basic_set_sample_bounded(__isl_take isl_basic_set *bset) |
| { |
| return basic_set_sample(bset, 1); |
| } |
| |
| __isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec) |
| { |
| int i; |
| int k; |
| struct isl_basic_set *bset = NULL; |
| struct isl_ctx *ctx; |
| unsigned dim; |
| |
| if (!vec) |
| 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) { |
| 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->el[1 + i]); |
| isl_int_set(bset->eq[k][1 + i], vec->el[0]); |
| } |
| bset->sample = vec; |
| |
| return bset; |
| error: |
| isl_basic_set_free(bset); |
| isl_vec_free(vec); |
| return NULL; |
| } |
| |
| __isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap) |
| { |
| struct isl_basic_set *bset; |
| struct isl_vec *sample_vec; |
| |
| bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap)); |
| sample_vec = isl_basic_set_sample_vec(bset); |
| if (!sample_vec) |
| goto error; |
| if (sample_vec->size == 0) { |
| isl_vec_free(sample_vec); |
| return isl_basic_map_set_to_empty(bmap); |
| } |
| isl_vec_free(bmap->sample); |
| bmap->sample = isl_vec_copy(sample_vec); |
| bset = isl_basic_set_from_vec(sample_vec); |
| return isl_basic_map_overlying_set(bset, bmap); |
| error: |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| __isl_give isl_basic_set *isl_basic_set_sample(__isl_take isl_basic_set *bset) |
| { |
| return isl_basic_map_sample(bset); |
| } |
| |
| __isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map) |
| { |
| int i; |
| isl_basic_map *sample = NULL; |
| |
| if (!map) |
| goto error; |
| |
| for (i = 0; i < map->n; ++i) { |
| sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i])); |
| if (!sample) |
| goto error; |
| if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY)) |
| break; |
| isl_basic_map_free(sample); |
| } |
| if (i == map->n) |
| sample = isl_basic_map_empty(isl_map_get_space(map)); |
| isl_map_free(map); |
| return sample; |
| error: |
| isl_map_free(map); |
| return NULL; |
| } |
| |
| __isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set) |
| { |
| return bset_from_bmap(isl_map_sample(set_to_map(set))); |
| } |
| |
| __isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset) |
| { |
| isl_vec *vec; |
| isl_space *dim; |
| |
| dim = isl_basic_set_get_space(bset); |
| bset = isl_basic_set_underlying_set(bset); |
| vec = isl_basic_set_sample_vec(bset); |
| |
| return isl_point_alloc(dim, vec); |
| } |
| |
| __isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set) |
| { |
| int i; |
| isl_point *pnt; |
| |
| if (!set) |
| return NULL; |
| |
| for (i = 0; i < set->n; ++i) { |
| pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i])); |
| if (!pnt) |
| goto error; |
| if (!isl_point_is_void(pnt)) |
| break; |
| isl_point_free(pnt); |
| } |
| if (i == set->n) |
| pnt = isl_point_void(isl_set_get_space(set)); |
| |
| isl_set_free(set); |
| return pnt; |
| error: |
| isl_set_free(set); |
| return NULL; |
| } |