/// Add an isl constraint to an ScopLib matrix. /// /// @param user The matrix /// @param c The constraint int ScopLib::accessToMatrix_constraint(isl_constraint *c, void *user) { scoplib_matrix_p m = (scoplib_matrix_p) user; int nb_params = isl_constraint_dim(c, isl_dim_param); int nb_in = isl_constraint_dim(c, isl_dim_in); int nb_div = isl_constraint_dim(c, isl_dim_div); assert(!nb_div && "Existentially quantified variables not yet supported"); scoplib_vector_p vec = scoplib_vector_malloc(nb_params + nb_in + 2); isl_int v; isl_int_init(v); // The access dimension has to be one. isl_constraint_get_coefficient(c, isl_dim_out, 0, &v); assert((isl_int_is_one(v) || isl_int_is_negone(v)) && "Access relations not supported in scoplib"); bool inverse = isl_int_is_one(v); // Assign variables for (int i = 0; i < nb_in; ++i) { isl_constraint_get_coefficient(c, isl_dim_in, i, &v); if (inverse) isl_int_neg(v,v); isl_int_set(vec->p[i + 1], v); } // Assign parameters for (int i = 0; i < nb_params; ++i) { isl_constraint_get_coefficient(c, isl_dim_param, i, &v); if (inverse) isl_int_neg(v,v); isl_int_set(vec->p[nb_in + i + 1], v); } // Assign constant isl_constraint_get_constant(c, &v); if (inverse) isl_int_neg(v,v); isl_int_set(vec->p[nb_in + nb_params + 1], v); scoplib_matrix_insert_vector(m, vec, m->NbRows); isl_constraint_free(c); isl_int_clear(v); return 0; }
static struct isl_vec *interval_sample(struct 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; }
/* Given a set of modulo constraints * * c + A y = 0 mod d * * this function computes a particular solution y_0 * * The input is given as a matrix B = [ c A ] and a vector d. * * The output is matrix containing the solution y_0 or * a zero-column matrix if the constraints admit no integer solution. * * The given set of constrains is equivalent to * * c + A y = -D x * * with D = diag d and x a fresh set of variables. * Reducing both c and A modulo d does not change the * value of y in the solution and may lead to smaller coefficients. * Let M = [ D A ] and [ H 0 ] = M U, the Hermite normal form of M. * Then * [ x ] * M [ y ] = - c * and so * [ x ] * [ H 0 ] U^{-1} [ y ] = - c * Let * [ A ] [ x ] * [ B ] = U^{-1} [ y ] * then * H A + 0 B = -c * * so B may be chosen arbitrarily, e.g., B = 0, and then * * [ x ] = [ -c ] * U^{-1} [ y ] = [ 0 ] * or * [ x ] [ -c ] * [ y ] = U [ 0 ] * specifically, * * y = U_{2,1} (-c) * * If any of the coordinates of this y are non-integer * then the constraints admit no integer solution and * a zero-column matrix is returned. */ static struct isl_mat *particular_solution(struct isl_mat *B, struct isl_vec *d) { int i, j; struct isl_mat *M = NULL; struct isl_mat *C = NULL; struct isl_mat *U = NULL; struct isl_mat *H = NULL; struct isl_mat *cst = NULL; struct isl_mat *T = NULL; M = isl_mat_alloc(B->ctx, B->n_row, B->n_row + B->n_col - 1); C = isl_mat_alloc(B->ctx, 1 + B->n_row, 1); if (!M || !C) goto error; isl_int_set_si(C->row[0][0], 1); for (i = 0; i < B->n_row; ++i) { isl_seq_clr(M->row[i], B->n_row); isl_int_set(M->row[i][i], d->block.data[i]); isl_int_neg(C->row[1 + i][0], B->row[i][0]); isl_int_fdiv_r(C->row[1+i][0], C->row[1+i][0], M->row[i][i]); for (j = 0; j < B->n_col - 1; ++j) isl_int_fdiv_r(M->row[i][B->n_row + j], B->row[i][1 + j], M->row[i][i]); } M = isl_mat_left_hermite(M, 0, &U, NULL); if (!M || !U) goto error; H = isl_mat_sub_alloc(M, 0, B->n_row, 0, B->n_row); H = isl_mat_lin_to_aff(H); C = isl_mat_inverse_product(H, C); if (!C) goto error; for (i = 0; i < B->n_row; ++i) { if (!isl_int_is_divisible_by(C->row[1+i][0], C->row[0][0])) break; isl_int_divexact(C->row[1+i][0], C->row[1+i][0], C->row[0][0]); } if (i < B->n_row) cst = isl_mat_alloc(B->ctx, B->n_row, 0); else cst = isl_mat_sub_alloc(C, 1, B->n_row, 0, 1); T = isl_mat_sub_alloc(U, B->n_row, B->n_col - 1, 0, B->n_row); cst = isl_mat_product(T, cst); isl_mat_free(M); isl_mat_free(C); isl_mat_free(U); return cst; error: isl_mat_free(M); isl_mat_free(C); isl_mat_free(U); 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; }
/* Look for all integer points in "bset", which is assumed to be bounded, * and call callback->add on each of them. * * We first compute a reduced basis for the set and then scan * the set in the directions of this basis. * We basically perform a depth first search, where in each level i * we compute the range in the i-th basis vector direction, given * fixed values in the directions of the previous basis vector. * We then add an equality to the tableau fixing the value in the * direction of the current basis vector to each value in the range * in turn and then continue to the next level. * * 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. * Solutions are added in the leaves of the search tree, i.e., after * we have fixed a value in each direction of the basis. */ int isl_basic_set_scan(struct isl_basic_set *bset, struct isl_scan_callback *callback) { unsigned dim; struct isl_mat *B = NULL; struct isl_tab *tab = NULL; struct isl_vec *min; struct isl_vec *max; struct isl_tab_undo **snap; int level; int init; enum isl_lp_result res; if (!bset) return -1; dim = isl_basic_set_total_dim(bset); if (dim == 0) return scan_0D(bset, callback); min = isl_vec_alloc(bset->ctx, dim); max = isl_vec_alloc(bset->ctx, dim); snap = isl_alloc_array(bset->ctx, struct isl_tab_undo *, dim); if (!min || !max || !snap) goto error; tab = isl_tab_from_basic_set(bset, 0); if (!tab) goto error; if (isl_tab_extend_cons(tab, dim + 1) < 0) goto error; tab->basis = isl_mat_identity(bset->ctx, 1 + dim); if (1) tab = isl_tab_compute_reduced_basis(tab); if (!tab) goto error; B = isl_mat_copy(tab->basis); if (!B) goto error; level = 0; init = 1; while (level >= 0) { int empty = 0; if (init) { res = isl_tab_min(tab, B->row[1 + level], bset->ctx->one, &min->el[level], NULL, 0); if (res == isl_lp_empty) empty = 1; if (res == isl_lp_error || res == isl_lp_unbounded) goto error; isl_seq_neg(B->row[1 + level] + 1, B->row[1 + level] + 1, dim); res = isl_tab_min(tab, B->row[1 + level], bset->ctx->one, &max->el[level], NULL, 0); isl_seq_neg(B->row[1 + level] + 1, B->row[1 + level] + 1, dim); isl_int_neg(max->el[level], max->el[level]); if (res == isl_lp_empty) empty = 1; if (res == isl_lp_error || res == isl_lp_unbounded) goto error; snap[level] = isl_tab_snap(tab); } else isl_int_add_ui(min->el[level], min->el[level], 1); if (empty || 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; } if (level == dim - 1 && callback->add == increment_counter) { if (increment_range(callback, min->el[level], max->el[level])) goto error; level--; init = 0; if (level >= 0) if (isl_tab_rollback(tab, snap[level]) < 0) goto error; continue; } isl_int_neg(B->row[1 + level][0], min->el[level]); if (isl_tab_add_valid_eq(tab, B->row[1 + level]) < 0) goto error; isl_int_set_si(B->row[1 + level][0], 0); if (level < dim - 1) { ++level; init = 1; continue; } if (add_solution(tab, callback) < 0) goto error; init = 0; if (isl_tab_rollback(tab, snap[level]) < 0) goto error; } isl_tab_free(tab); free(snap); isl_vec_free(min); isl_vec_free(max); isl_basic_set_free(bset); isl_mat_free(B); return 0; error: isl_tab_free(tab); free(snap); isl_vec_free(min); isl_vec_free(max); isl_basic_set_free(bset); isl_mat_free(B); return -1; }
__isl_give isl_basic_set *isl_basic_set_box_from_points( __isl_take isl_point *pnt1, __isl_take isl_point *pnt2) { isl_basic_set *bset; unsigned total; int i; int k; isl_int t; isl_int_init(t); if (!pnt1 || !pnt2) goto error; isl_assert(pnt1->dim->ctx, isl_dim_equal(pnt1->dim, pnt2->dim), goto error); if (isl_point_is_void(pnt1) && isl_point_is_void(pnt2)) { isl_dim *dim = isl_dim_copy(pnt1->dim); isl_point_free(pnt1); isl_point_free(pnt2); isl_int_clear(t); return isl_basic_set_empty(dim); } if (isl_point_is_void(pnt1)) { isl_point_free(pnt1); isl_int_clear(t); return isl_basic_set_from_point(pnt2); } if (isl_point_is_void(pnt2)) { isl_point_free(pnt2); isl_int_clear(t); return isl_basic_set_from_point(pnt1); } total = isl_dim_total(pnt1->dim); bset = isl_basic_set_alloc_dim(isl_dim_copy(pnt1->dim), 0, 0, 2 * total); for (i = 0; i < total; ++i) { isl_int_mul(t, pnt1->vec->el[1 + i], pnt2->vec->el[0]); isl_int_submul(t, pnt2->vec->el[1 + i], pnt1->vec->el[0]); k = isl_basic_set_alloc_inequality(bset); if (k < 0) goto error; isl_seq_clr(bset->ineq[k] + 1, total); if (isl_int_is_pos(t)) { isl_int_set_si(bset->ineq[k][1 + i], -1); isl_int_set(bset->ineq[k][0], pnt1->vec->el[1 + i]); } else { isl_int_set_si(bset->ineq[k][1 + i], 1); isl_int_neg(bset->ineq[k][0], pnt1->vec->el[1 + i]); } isl_int_fdiv_q(bset->ineq[k][0], bset->ineq[k][0], pnt1->vec->el[0]); k = isl_basic_set_alloc_inequality(bset); if (k < 0) goto error; isl_seq_clr(bset->ineq[k] + 1, total); if (isl_int_is_pos(t)) { isl_int_set_si(bset->ineq[k][1 + i], 1); isl_int_neg(bset->ineq[k][0], pnt2->vec->el[1 + i]); } else { isl_int_set_si(bset->ineq[k][1 + i], -1); isl_int_set(bset->ineq[k][0], pnt2->vec->el[1 + i]); } isl_int_fdiv_q(bset->ineq[k][0], bset->ineq[k][0], pnt2->vec->el[0]); } bset = isl_basic_set_finalize(bset); isl_point_free(pnt1); isl_point_free(pnt2); isl_int_clear(t); return bset; error: isl_point_free(pnt1); isl_point_free(pnt2); isl_int_clear(t); return NULL; }