/* 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;
}
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;
}
/* Construct a parameter compression for "bset".
* We basically just call isl_mat_parameter_compression with the right input
* and then extend the resulting matrix to include the variables.
*
* Let the equalities be given as
*
* B(p) + A x = 0
*
* and let [H 0] be the Hermite Normal Form of A, then
*
* H^-1 B(p)
*
* needs to be integer, so we impose that each row is divisible by
* the denominator.
*/
__isl_give isl_morph *isl_basic_set_parameter_compression(
__isl_keep isl_basic_set *bset)
{
unsigned nparam;
unsigned nvar;
int n_eq;
isl_mat *H, *B;
isl_vec *d;
isl_mat *map, *inv;
isl_basic_set *dom, *ran;
if (!bset)
return NULL;
if (isl_basic_set_plain_is_empty(bset))
return isl_morph_empty(bset);
if (bset->n_eq == 0)
return isl_morph_identity(bset);
isl_assert(bset->ctx, bset->n_div == 0, return NULL);
n_eq = bset->n_eq;
nparam = isl_basic_set_dim(bset, isl_dim_param);
nvar = isl_basic_set_dim(bset, isl_dim_set);
isl_assert(bset->ctx, n_eq <= nvar, return NULL);
d = isl_vec_alloc(bset->ctx, n_eq);
B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
H = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
H = isl_mat_left_hermite(H, 0, NULL, NULL);
H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
H = isl_mat_lin_to_aff(H);
H = isl_mat_right_inverse(H);
if (!H || !d)
goto error;
isl_seq_set(d->el, H->row[0][0], d->size);
H = isl_mat_drop_rows(H, 0, 1);
H = isl_mat_drop_cols(H, 0, 1);
B = isl_mat_product(H, B);
inv = isl_mat_parameter_compression(B, d);
inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
map = isl_mat_right_inverse(isl_mat_copy(inv));
dom = isl_basic_set_universe(isl_space_copy(bset->dim));
ran = isl_basic_set_universe(isl_space_copy(bset->dim));
return isl_morph_alloc(dom, ran, map, inv);
error:
isl_mat_free(H);
isl_mat_free(B);
isl_vec_free(d);
return NULL;
}
/* Given a basic set, exploit the equalties in the a basic set to construct
* a morphishm that maps the basic set to a lower-dimensional space.
* Specifically, the morphism reduces the number of dimensions of type "type".
*
* This function is a slight generalization of isl_mat_variable_compression
* in that it allows the input to be parametric and that it allows for the
* compression of either parameters or set variables.
*
* We first select the equalities of interest, that is those that involve
* variables of type "type" and no later variables.
* Denote those equalities as
*
* -C(p) + M x = 0
*
* where C(p) depends on the parameters if type == isl_dim_set and
* is a constant if type == isl_dim_param.
*
* First compute the (left) Hermite normal form of M,
*
* M [U1 U2] = M U = H = [H1 0]
* or
* M = H Q = [H1 0] [Q1]
* [Q2]
*
* with U, Q unimodular, Q = U^{-1} (and H lower triangular).
* Define the transformed variables as
*
* x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
* [ x2' ] [Q2]
*
* The equalities then become
*
* -C(p) + H1 x1' = 0 or x1' = H1^{-1} C(p) = C'(p)
*
* If the denominator of the constant term does not divide the
* the common denominator of the parametric terms, then every
* integer point is mapped to a non-integer point and then the original set has no
* integer solutions (since the x' are a unimodular transformation
* of the x). In this case, an empty morphism is returned.
* Otherwise, the transformation is given by
*
* x = U1 H1^{-1} C(p) + U2 x2'
*
* The inverse transformation is simply
*
* x2' = Q2 x
*
* Both matrices are extended to map the full original space to the full
* compressed space.
*/
__isl_give isl_morph *isl_basic_set_variable_compression(
__isl_keep isl_basic_set *bset, enum isl_dim_type type)
{
unsigned otype;
unsigned ntype;
unsigned orest;
unsigned nrest;
int f_eq, n_eq;
isl_space *dim;
isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
isl_basic_set *dom, *ran;
if (!bset)
return NULL;
if (isl_basic_set_plain_is_empty(bset))
return isl_morph_empty(bset);
isl_assert(bset->ctx, bset->n_div == 0, return NULL);
otype = 1 + isl_space_offset(bset->dim, type);
ntype = isl_basic_set_dim(bset, type);
orest = otype + ntype;
nrest = isl_basic_set_total_dim(bset) - (orest - 1);
for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
break;
for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
break;
if (n_eq == 0)
return isl_morph_identity(bset);
H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
H = isl_mat_left_hermite(H, 0, &U, &Q);
if (!H || !U || !Q)
goto error;
Q = isl_mat_drop_rows(Q, 0, n_eq);
Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
if (!C)
goto error;
isl_int_set_si(C->row[0][0], 1);
isl_seq_clr(C->row[0] + 1, otype - 1);
isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
H1 = isl_mat_lin_to_aff(H1);
C = isl_mat_inverse_product(H1, C);
if (!C)
goto error;
isl_mat_free(H);
if (!isl_int_is_one(C->row[0][0])) {
int i;
isl_int g;
isl_int_init(g);
for (i = 0; i < n_eq; ++i) {
isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
isl_int_gcd(g, g, C->row[0][0]);
if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
break;
}
isl_int_clear(g);
if (i < n_eq) {
isl_mat_free(C);
isl_mat_free(U);
isl_mat_free(Q);
return isl_morph_empty(bset);
}
C = isl_mat_normalize(C);
}
U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);
U1 = isl_mat_lin_to_aff(U1);
U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);
U2 = isl_mat_lin_to_aff(U2);
isl_mat_free(U);
C = isl_mat_product(U1, C);
C = isl_mat_aff_direct_sum(C, U2);
C = insert_parameter_rows(C, otype - 1);
C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
dim = isl_space_copy(bset->dim);
dim = isl_space_drop_dims(dim, type, 0, ntype);
dim = isl_space_add_dims(dim, type, ntype - n_eq);
ran = isl_basic_set_universe(dim);
dom = copy_equalities(bset, f_eq, n_eq);
return isl_morph_alloc(dom, ran, Q, C);
error:
isl_mat_free(C);
isl_mat_free(H);
isl_mat_free(U);
isl_mat_free(Q);
return NULL;
}
/* 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;
}
