/* 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));
}
int isl_basic_set_count_upto(__isl_keep isl_basic_set *bset,
isl_int max, isl_int *count)
{
struct isl_counter cnt = { { &increment_counter } };
if (!bset)
return -1;
isl_int_init(cnt.count);
isl_int_init(cnt.max);
isl_int_set_si(cnt.count, 0);
isl_int_set(cnt.max, max);
if (isl_basic_set_scan(isl_basic_set_copy(bset), &cnt.callback) < 0 &&
isl_int_lt(cnt.count, cnt.max))
goto error;
isl_int_set(*count, cnt.count);
isl_int_clear(cnt.max);
isl_int_clear(cnt.count);
return 0;
error:
isl_int_clear(cnt.count);
return -1;
}
/* 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;
}
int isl_set_foreach_point(__isl_keep isl_set *set,
int (*fn)(__isl_take isl_point *pnt, void *user), void *user)
{
struct isl_foreach_point fp = { { &foreach_point }, fn, user };
int i;
if (!set)
return -1;
fp.dim = isl_set_get_dim(set);
if (!fp.dim)
return -1;
set = isl_set_copy(set);
set = isl_set_cow(set);
set = isl_set_make_disjoint(set);
set = isl_set_compute_divs(set);
if (!set)
goto error;
for (i = 0; i < set->n; ++i)
if (isl_basic_set_scan(isl_basic_set_copy(set->p[i]),
&fp.callback) < 0)
goto error;
isl_set_free(set);
isl_dim_free(fp.dim);
return 0;
error:
isl_set_free(set);
isl_dim_free(fp.dim);
return -1;
}
/* Check whether the polynomial "poly" has sign "sign" over "bset",
* i.e., if sign == 1, check that the lower bound on the polynomial
* is non-negative and if sign == -1, check that the upper bound on
* the polynomial is non-positive.
*/
static int has_sign(__isl_keep isl_basic_set *bset,
__isl_keep isl_qpolynomial *poly, int sign, int *signs)
{
struct range_data data_m;
unsigned nparam;
isl_space *dim;
isl_val *opt;
int r;
enum isl_fold type;
nparam = isl_basic_set_dim(bset, isl_dim_param);
bset = isl_basic_set_copy(bset);
poly = isl_qpolynomial_copy(poly);
bset = isl_basic_set_move_dims(bset, isl_dim_set, 0,
isl_dim_param, 0, nparam);
poly = isl_qpolynomial_move_dims(poly, isl_dim_in, 0,
isl_dim_param, 0, nparam);
dim = isl_qpolynomial_get_space(poly);
dim = isl_space_params(dim);
dim = isl_space_from_domain(dim);
dim = isl_space_add_dims(dim, isl_dim_out, 1);
data_m.test_monotonicity = 0;
data_m.signs = signs;
data_m.sign = -sign;
type = data_m.sign < 0 ? isl_fold_min : isl_fold_max;
data_m.pwf = isl_pw_qpolynomial_fold_zero(dim, type);
data_m.tight = 0;
data_m.pwf_tight = NULL;
if (propagate_on_domain(bset, poly, &data_m) < 0)
goto error;
if (sign > 0)
opt = isl_pw_qpolynomial_fold_min(data_m.pwf);
else
opt = isl_pw_qpolynomial_fold_max(data_m.pwf);
if (!opt)
r = -1;
else if (isl_val_is_nan(opt) ||
isl_val_is_infty(opt) ||
isl_val_is_neginfty(opt))
r = 0;
else
r = sign * isl_val_sgn(opt) >= 0;
isl_val_free(opt);
return r;
error:
isl_pw_qpolynomial_fold_free(data_m.pwf);
return -1;
}
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;
}
/* 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));
}
__isl_give isl_morph *isl_basic_set_full_compression(
__isl_keep isl_basic_set *bset)
{
isl_morph *morph, *morph2;
bset = isl_basic_set_copy(bset);
morph = isl_basic_set_variable_compression(bset, isl_dim_param);
bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
morph2 = isl_basic_set_parameter_compression(bset);
bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
morph = isl_morph_compose(morph2, morph);
morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
isl_basic_set_free(bset);
morph = isl_morph_compose(morph2, morph);
return morph;
}
int main(int argc, char **argv)
{
struct isl_ctx *ctx = isl_ctx_alloc();
struct isl_basic_set *bset;
struct isl_vec *sample;
isl_printer *p;
bset = isl_basic_set_read_from_file(ctx, stdin);
sample = isl_basic_set_sample_vec(isl_basic_set_copy(bset));
p = isl_printer_to_file(ctx, stdout);
p = isl_printer_print_vec(p, sample);
p = isl_printer_end_line(p);
isl_printer_free(p);
assert(sample);
if (sample->size > 0)
assert(isl_basic_set_contains(bset, sample));
isl_basic_set_free(bset);
isl_vec_free(sample);
isl_ctx_free(ctx);
return 0;
}
int isl_set_scan(__isl_take isl_set *set, struct isl_scan_callback *callback)
{
int i;
if (!set || !callback)
goto error;
set = isl_set_cow(set);
set = isl_set_make_disjoint(set);
set = isl_set_compute_divs(set);
if (!set)
goto error;
for (i = 0; i < set->n; ++i)
if (isl_basic_set_scan(isl_basic_set_copy(set->p[i]),
callback) < 0)
goto error;
isl_set_free(set);
return 0;
error:
isl_set_free(set);
return -1;
}
/* 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;
}
/* Check if dimension dim belongs to a residue class
* i_dim \equiv r mod m
* with m != 1 and if so return m in *modulo and r in *residue.
* As a special case, when i_dim has a fixed value v, then
* *modulo is set to 0 and *residue to v.
*
* If i_dim does not belong to such a residue class, then *modulo
* is set to 1 and *residue is set to 0.
*/
int isl_basic_set_dim_residue_class(struct isl_basic_set *bset,
int pos, isl_int *modulo, isl_int *residue)
{
struct isl_ctx *ctx;
struct isl_mat *H = NULL, *U = NULL, *C, *H1, *U1;
unsigned total;
unsigned nparam;
if (!bset || !modulo || !residue)
return -1;
if (isl_basic_set_plain_dim_is_fixed(bset, pos, residue)) {
isl_int_set_si(*modulo, 0);
return 0;
}
ctx = isl_basic_set_get_ctx(bset);
total = isl_basic_set_total_dim(bset);
nparam = isl_basic_set_n_param(bset);
H = isl_mat_sub_alloc6(ctx, bset->eq, 0, bset->n_eq, 1, total);
H = isl_mat_left_hermite(H, 0, &U, NULL);
if (!H)
return -1;
isl_seq_gcd(U->row[nparam + pos]+bset->n_eq,
total-bset->n_eq, modulo);
if (isl_int_is_zero(*modulo))
isl_int_set_si(*modulo, 1);
if (isl_int_is_one(*modulo)) {
isl_int_set_si(*residue, 0);
isl_mat_free(H);
isl_mat_free(U);
return 0;
}
C = isl_mat_alloc(ctx, 1 + bset->n_eq, 1);
if (!C)
goto error;
isl_int_set_si(C->row[0][0], 1);
isl_mat_sub_neg(ctx, C->row + 1, bset->eq, bset->n_eq, 0, 0, 1);
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);
isl_mat_free(H);
U1 = isl_mat_sub_alloc(U, nparam+pos, 1, 0, bset->n_eq);
U1 = isl_mat_lin_to_aff(U1);
isl_mat_free(U);
C = isl_mat_product(U1, C);
if (!C)
return -1;
if (!isl_int_is_divisible_by(C->row[1][0], C->row[0][0])) {
bset = isl_basic_set_copy(bset);
bset = isl_basic_set_set_to_empty(bset);
isl_basic_set_free(bset);
isl_int_set_si(*modulo, 1);
isl_int_set_si(*residue, 0);
return 0;
}
isl_int_divexact(*residue, C->row[1][0], C->row[0][0]);
isl_int_fdiv_r(*residue, *residue, *modulo);
isl_mat_free(C);
return 0;
error:
isl_mat_free(H);
isl_mat_free(U);
return -1;
}
/**
* Reduce the modulo guard expressed by "constraints" using equalities
* found in outer nesting levels (stored in "equal").
* The modulo guard may be an equality or a pair of inequalities.
* In case of a pair of inequalities, *bound contains the bound on the
* corresponding modulo expression. If any reduction is performed
* then this bound is recomputed.
*
* "level" may not correspond to an existentially quantified variable.
*
* We first check if there are any equalities we can use. If not,
* there is again nothing to reduce.
* For the actual reduction, we use isl_basic_set_gist, but this
* function will only perform the reduction we want here if the
* the variable that imposes the modulo constraint has been projected
* out (i.e., turned into an existentially quantified variable).
* After the call to isl_basic_set_gist, we need to move the
* existential variable back into the position where the calling
* function expects it (assuming there are any constraints left).
* We do this by adding an equality between the given dimension and
* the existentially quantified variable.
*
* If there are no existentially quantified variables left, then
* we don't need to add this equality.
* If, on the other hand, the resulting basic set involves more
* than one existentially quantified variable, then the caller
* will not be able to handle the result, so we just return the
* original input instead.
*/
CloogConstraintSet *cloog_constraint_set_reduce(CloogConstraintSet *constraints,
int level, CloogEqualities *equal, int nb_par, cloog_int_t *bound)
{
int j;
isl_space *idim;
struct isl_basic_set *eq;
struct isl_basic_map *id;
struct cloog_isl_dim dim;
struct isl_constraint *c;
unsigned constraints_dim;
unsigned n_div;
isl_basic_set *bset, *orig;
bset = cloog_constraints_set_to_isl(constraints);
orig = isl_basic_set_copy(bset);
dim = set_cloog_dim_to_isl_dim(constraints, level - 1);
assert(dim.type == isl_dim_set);
eq = NULL;
for (j = 0; j < level - 1; ++j) {
isl_basic_set *bset_j;
if (equal->types[j] != EQTYPE_EXAFFINE)
continue;
bset_j = equality_to_basic_set(equal, j);
if (!eq)
eq = bset_j;
else
eq = isl_basic_set_intersect(eq, bset_j);
}
if (!eq) {
isl_basic_set_free(orig);
return cloog_constraint_set_from_isl_basic_set(bset);
}
idim = isl_space_map_from_set(isl_basic_set_get_space(bset));
id = isl_basic_map_identity(idim);
id = isl_basic_map_remove_dims(id, isl_dim_out, dim.pos, 1);
bset = isl_basic_set_apply(bset, isl_basic_map_copy(id));
bset = isl_basic_set_apply(bset, isl_basic_map_reverse(id));
constraints_dim = isl_basic_set_dim(bset, isl_dim_set);
eq = isl_basic_set_remove_dims(eq, isl_dim_set, constraints_dim,
isl_basic_set_dim(eq, isl_dim_set) - constraints_dim);
bset = isl_basic_set_gist(bset, eq);
n_div = isl_basic_set_dim(bset, isl_dim_div);
if (n_div > 1) {
isl_basic_set_free(bset);
return cloog_constraint_set_from_isl_basic_set(orig);
}
if (n_div < 1) {
isl_basic_set_free(orig);
return cloog_constraint_set_from_isl_basic_set(bset);
}
c = isl_equality_alloc(isl_basic_set_get_local_space(bset));
c = isl_constraint_set_coefficient_si(c, isl_dim_div, 0, 1);
c = isl_constraint_set_coefficient_si(c, isl_dim_set, dim.pos, -1);
bset = isl_basic_set_add_constraint(bset, c);
isl_int_set_si(*bound, 0);
constraints = cloog_constraint_set_from_isl_basic_set(bset);
cloog_constraint_set_foreach_constraint(constraints,
add_constant_term, bound);
isl_basic_set_free(orig);
return cloog_constraint_set_from_isl_basic_set(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;
}