/* 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;
}
/* Construct a morphism that first does morph2 and then morph1.
*/
__isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
__isl_take isl_morph *morph2)
{
isl_mat *map, *inv;
isl_basic_set *dom, *ran;
if (!morph1 || !morph2)
goto error;
map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
isl_basic_set_copy(morph1->dom));
dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
ran = isl_morph_basic_set(isl_morph_copy(morph1),
isl_basic_set_copy(morph2->ran));
ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
isl_morph_free(morph1);
isl_morph_free(morph2);
return isl_morph_alloc(dom, ran, map, inv);
error:
isl_morph_free(morph1);
isl_morph_free(morph2);
return NULL;
}
__isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
{
if (!morph)
return NULL;
return isl_morph_alloc(isl_basic_set_copy(morph->dom),
isl_basic_set_copy(morph->ran),
isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
}
/* 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;
}
__isl_give isl_vec *isl_morph_vec(__isl_take isl_morph *morph,
__isl_take isl_vec *vec)
{
if (!morph)
goto error;
vec = isl_mat_vec_product(isl_mat_copy(morph->map), vec);
isl_morph_free(morph);
return vec;
error:
isl_morph_free(morph);
isl_vec_free(vec);
return NULL;
}
/* Create a(n identity) morphism between empty sets of the same dimension
* a "bset".
*/
__isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
{
isl_mat *id;
isl_basic_set *empty;
unsigned total;
if (!bset)
return NULL;
total = isl_basic_set_total_dim(bset);
id = isl_mat_identity(bset->ctx, 1 + total);
empty = isl_basic_set_empty(isl_space_copy(bset->dim));
return isl_morph_alloc(empty, isl_basic_set_copy(empty),
id, isl_mat_copy(id));
}
__isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
{
isl_mat *id;
isl_basic_set *universe;
unsigned total;
if (!bset)
return NULL;
total = isl_basic_set_total_dim(bset);
id = isl_mat_identity(bset->ctx, 1 + total);
universe = isl_basic_set_universe(isl_space_copy(bset->dim));
return isl_morph_alloc(universe, isl_basic_set_copy(universe),
id, isl_mat_copy(id));
}
/* Use the n equalities of bset to unimodularly transform the
* variables x such that n transformed variables x1' have a constant value
* and rewrite the constraints of bset in terms of the remaining
* transformed variables x2'. The matrix pointed to by T maps
* the new variables x2' back to the original variables x, while T2
* maps the original variables to the new variables.
*/
static struct isl_basic_set *compress_variables(
struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)
{
struct isl_mat *B, *TC;
unsigned dim;
if (T)
*T = NULL;
if (T2)
*T2 = NULL;
if (!bset)
goto error;
isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
isl_assert(bset->ctx, bset->n_div == 0, goto error);
dim = isl_basic_set_n_dim(bset);
isl_assert(bset->ctx, bset->n_eq <= dim, goto error);
if (bset->n_eq == 0)
return bset;
B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + dim);
TC = isl_mat_variable_compression(B, T2);
if (!TC)
goto error;
if (TC->n_col == 0) {
isl_mat_free(TC);
if (T2) {
isl_mat_free(*T2);
*T2 = NULL;
}
return isl_basic_set_set_to_empty(bset);
}
bset = isl_basic_set_preimage(bset, T ? isl_mat_copy(TC) : TC);
if (T)
*T = TC;
return bset;
error:
isl_basic_set_free(bset);
return NULL;
}
/* Apply the morphism to the basic set.
* We basically just compute the preimage of "bset" under the inverse mapping
* in morph, add in stride constraints and intersect with the range
* of the morphism.
*/
__isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
__isl_take isl_basic_set *bset)
{
isl_basic_set *res = NULL;
isl_mat *mat = NULL;
int i, k;
int max_stride;
if (!morph || !bset)
goto error;
isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),
goto error);
max_stride = morph->inv->n_row - 1;
if (isl_int_is_one(morph->inv->row[0][0]))
max_stride = 0;
res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),
bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
for (i = 0; i < bset->n_div; ++i)
if (isl_basic_set_alloc_div(res) < 0)
goto error;
mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
0, morph->inv->n_row);
mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
if (!mat)
goto error;
for (i = 0; i < bset->n_eq; ++i) {
k = isl_basic_set_alloc_equality(res);
if (k < 0)
goto error;
isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
morph->inv->row[0][0], bset->n_div);
}
isl_mat_free(mat);
mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,
0, morph->inv->n_row);
mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
if (!mat)
goto error;
for (i = 0; i < bset->n_ineq; ++i) {
k = isl_basic_set_alloc_inequality(res);
if (k < 0)
goto error;
isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
isl_seq_scale(res->ineq[k] + mat->n_col,
bset->ineq[i] + mat->n_col,
morph->inv->row[0][0], bset->n_div);
}
isl_mat_free(mat);
mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,
1, morph->inv->n_row);
mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
if (!mat)
goto error;
for (i = 0; i < bset->n_div; ++i) {
isl_int_mul(res->div[i][0],
morph->inv->row[0][0], bset->div[i][0]);
isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
isl_seq_scale(res->div[i] + 1 + mat->n_col,
bset->div[i] + 1 + mat->n_col,
morph->inv->row[0][0], bset->n_div);
}
isl_mat_free(mat);
res = add_strides(res, morph);
if (isl_basic_set_is_rational(bset))
res = isl_basic_set_set_rational(res);
res = isl_basic_set_simplify(res);
res = isl_basic_set_finalize(res);
res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
isl_morph_free(morph);
isl_basic_set_free(bset);
return res;
error:
isl_mat_free(mat);
isl_morph_free(morph);
isl_basic_set_free(bset);
isl_basic_set_free(res);
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;
}
