/* 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;
}
/* Extend an initial (under-)approximation of the affine hull of basic
* set represented by the tableau "tab"
* by looking for points that do not satisfy one of the equalities
* in the current approximation and adding them to that approximation
* until no such points can be found any more.
*
* The caller of this function ensures that "tab" is bounded or
* that tab->basis and tab->n_unbounded have been set appropriately.
*/
static struct isl_basic_set *extend_affine_hull(struct isl_tab *tab,
struct isl_basic_set *hull)
{
int i, j;
unsigned dim;
if (!tab || !hull)
goto error;
dim = tab->n_var;
if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0)
goto error;
for (i = 0; i < dim; ++i) {
struct isl_vec *sample;
struct isl_basic_set *point;
for (j = 0; j < hull->n_eq; ++j) {
sample = outside_point(tab, hull->eq[j], 1);
if (!sample)
goto error;
if (sample->size > 0)
break;
isl_vec_free(sample);
sample = outside_point(tab, hull->eq[j], 0);
if (!sample)
goto error;
if (sample->size > 0)
break;
isl_vec_free(sample);
if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
goto error;
}
if (j == hull->n_eq)
break;
if (tab->samples)
tab = isl_tab_add_sample(tab, isl_vec_copy(sample));
if (!tab)
goto error;
point = isl_basic_set_from_vec(sample);
hull = affine_hull(hull, point);
if (!hull)
return NULL;
}
return hull;
error:
isl_basic_set_free(hull);
return NULL;
}
static int tab_add_divs(struct isl_tab *tab, __isl_keep isl_basic_map *bmap,
int **div_map)
{
int i, j;
struct isl_vec *vec;
unsigned total;
unsigned dim;
if (!bmap)
return -1;
if (!bmap->n_div)
return 0;
if (!*div_map)
*div_map = isl_alloc_array(bmap->ctx, int, bmap->n_div);
if (!*div_map)
return -1;
total = isl_basic_map_total_dim(tab->bmap);
dim = total - tab->bmap->n_div;
vec = isl_vec_alloc(bmap->ctx, 2 + total + bmap->n_div);
if (!vec)
return -1;
for (i = 0; i < bmap->n_div; ++i) {
isl_seq_cpy(vec->el, bmap->div[i], 2 + dim);
isl_seq_clr(vec->el + 2 + dim, tab->bmap->n_div);
for (j = 0; j < i; ++j)
isl_int_set(vec->el[2 + dim + (*div_map)[j]],
bmap->div[i][2 + dim + j]);
for (j = 0; j < tab->bmap->n_div; ++j)
if (isl_seq_eq(tab->bmap->div[j],
vec->el, 2 + dim + tab->bmap->n_div))
break;
(*div_map)[i] = j;
if (j == tab->bmap->n_div) {
vec->size = 2 + dim + tab->bmap->n_div;
if (isl_tab_add_div(tab, vec) < 0)
goto error;
}
}
isl_vec_free(vec);
return 0;
error:
isl_vec_free(vec);
return -1;
}
/* Add all constraints of bmap to tab. The equalities of bmap
* are added as a pair of inequalities.
*/
static int tab_add_constraints(struct isl_tab *tab,
__isl_keep isl_basic_map *bmap, int *div_map)
{
int i;
unsigned dim;
unsigned tab_total;
unsigned bmap_total;
isl_vec *v;
if (!tab || !bmap)
return -1;
tab_total = isl_basic_map_total_dim(tab->bmap);
bmap_total = isl_basic_map_total_dim(bmap);
dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
if (isl_tab_extend_cons(tab, 2 * bmap->n_eq + bmap->n_ineq) < 0)
return -1;
v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
if (!v)
return -1;
for (i = 0; i < bmap->n_eq; ++i) {
expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
if (isl_tab_add_ineq(tab, v->el) < 0)
goto error;
isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
if (isl_tab_add_ineq(tab, v->el) < 0)
goto error;
isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
if (tab->empty)
break;
}
for (i = 0; i < bmap->n_ineq; ++i) {
expand_constraint(v, dim, bmap->ineq[i], div_map, bmap->n_div);
if (isl_tab_add_ineq(tab, v->el) < 0)
goto error;
if (tab->empty)
break;
}
isl_vec_free(v);
return 0;
error:
isl_vec_free(v);
return -1;
}
/* Find an integer point in the set represented by "tab"
* that lies outside of the equality "eq" e(x) = 0.
* If "up" is true, look for a point satisfying e(x) - 1 >= 0.
* Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
* The point, if found, is returned.
* If no point can be found, a zero-length vector is returned.
*
* Before solving an ILP problem, we first check if simply
* adding the normal of the constraint to one of the known
* integer points in the basic set represented by "tab"
* yields another point inside the basic set.
*
* The caller of this function ensures that the tableau is bounded or
* that tab->basis and tab->n_unbounded have been set appropriately.
*/
static struct isl_vec *outside_point(struct isl_tab *tab, isl_int *eq, int up)
{
struct isl_ctx *ctx;
struct isl_vec *sample = NULL;
struct isl_tab_undo *snap;
unsigned dim;
if (!tab)
return NULL;
ctx = tab->mat->ctx;
dim = tab->n_var;
sample = isl_vec_alloc(ctx, 1 + dim);
if (!sample)
return NULL;
isl_int_set_si(sample->el[0], 1);
isl_seq_combine(sample->el + 1,
ctx->one, tab->bmap->sample->el + 1,
up ? ctx->one : ctx->negone, eq + 1, dim);
if (isl_basic_map_contains(tab->bmap, sample))
return sample;
isl_vec_free(sample);
sample = NULL;
snap = isl_tab_snap(tab);
if (!up)
isl_seq_neg(eq, eq, 1 + dim);
isl_int_sub_ui(eq[0], eq[0], 1);
if (isl_tab_extend_cons(tab, 1) < 0)
goto error;
if (isl_tab_add_ineq(tab, eq) < 0)
goto error;
sample = isl_tab_sample(tab);
isl_int_add_ui(eq[0], eq[0], 1);
if (!up)
isl_seq_neg(eq, eq, 1 + dim);
if (sample && isl_tab_rollback(tab, snap) < 0)
goto error;
return sample;
error:
isl_vec_free(sample);
return NULL;
}
int main(int argc, char **argv)
{
struct isl_ctx *ctx = isl_ctx_alloc();
struct isl_basic_set *bset;
struct isl_vec *obj;
struct isl_vec *sol;
isl_int opt;
unsigned dim;
enum isl_lp_result res;
isl_printer *p;
isl_int_init(opt);
bset = isl_basic_set_read_from_file(ctx, stdin);
assert(bset);
obj = isl_vec_read_from_file(ctx, stdin);
assert(obj);
dim = isl_basic_set_total_dim(bset);
assert(obj->size >= dim && obj->size <= dim + 1);
if (obj->size != dim + 1)
obj = isl_vec_lin_to_aff(obj);
else
obj = vec_ror(obj);
res = isl_basic_set_solve_ilp(bset, 0, obj->el, &opt, &sol);
switch (res) {
case isl_lp_error:
fprintf(stderr, "error\n");
return -1;
case isl_lp_empty:
fprintf(stdout, "empty\n");
break;
case isl_lp_unbounded:
fprintf(stdout, "unbounded\n");
break;
case isl_lp_ok:
p = isl_printer_to_file(ctx, stdout);
p = isl_printer_print_vec(p, sol);
p = isl_printer_end_line(p);
p = isl_printer_print_isl_int(p, opt);
p = isl_printer_end_line(p);
isl_printer_free(p);
}
isl_basic_set_free(bset);
isl_vec_free(obj);
isl_vec_free(sol);
isl_ctx_free(ctx);
isl_int_clear(opt);
return 0;
}
__isl_give isl_point *isl_point_alloc(__isl_take isl_dim *dim,
__isl_take isl_vec *vec)
{
struct isl_point *pnt;
if (!dim || !vec)
goto error;
if (vec->size > 1 + isl_dim_total(dim)) {
vec = isl_vec_cow(vec);
if (!vec)
goto error;
vec->size = 1 + isl_dim_total(dim);
}
pnt = isl_alloc_type(dim->ctx, struct isl_point);
if (!pnt)
goto error;
pnt->ref = 1;
pnt->dim = dim;
pnt->vec = vec;
return pnt;
error:
isl_dim_free(dim);
isl_vec_free(vec);
return NULL;
}
/* Return 1 if "bmap" contains the point "point".
* "bmap" is assumed to have known divs.
* The point is first extended with the divs and then passed
* to basic_map_contains.
*/
int isl_basic_map_contains_point(__isl_keep isl_basic_map *bmap,
__isl_keep isl_point *point)
{
int i;
struct isl_vec *vec;
unsigned dim;
int contains;
if (!bmap || !point)
return -1;
isl_assert(bmap->ctx, isl_dim_equal(bmap->dim, point->dim), return -1);
if (bmap->n_div == 0)
return isl_basic_map_contains(bmap, point->vec);
dim = isl_basic_map_total_dim(bmap) - bmap->n_div;
vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
if (!vec)
return -1;
isl_seq_cpy(vec->el, point->vec->el, point->vec->size);
for (i = 0; i < bmap->n_div; ++i) {
isl_seq_inner_product(bmap->div[i] + 1, vec->el,
1 + dim + i, &vec->el[1+dim+i]);
isl_int_fdiv_q(vec->el[1+dim+i], vec->el[1+dim+i],
bmap->div[i][0]);
}
contains = isl_basic_map_contains(bmap, vec);
isl_vec_free(vec);
return contains;
}
static struct isl_vec *isl_vec_lin_to_aff(struct isl_vec *vec)
{
struct isl_vec *aff;
if (!vec)
return NULL;
aff = isl_vec_alloc(vec->ctx, 1 + vec->size);
if (!aff)
goto error;
isl_int_set_si(aff->el[0], 0);
isl_seq_cpy(aff->el + 1, vec->el, vec->size);
isl_vec_free(vec);
return aff;
error:
isl_vec_free(vec);
return NULL;
}
/* Look for all equalities satisfied by the integer points in bmap
* that are independent of the equalities already explicitly available
* in bmap.
*
* We first remove all equalities already explicitly available,
* then look for additional equalities in the reduced space
* and then transform the result to the original space.
* The original equalities are _not_ added to this set. This is
* the responsibility of the calling function.
* The resulting basic set has all meaning about the dimensions removed.
* In particular, dimensions that correspond to existential variables
* in bmap and that are found to be fixed are not removed.
*/
static struct isl_basic_set *equalities_in_underlying_set(
struct isl_basic_map *bmap)
{
struct isl_mat *T1 = NULL;
struct isl_mat *T2 = NULL;
struct isl_basic_set *bset = NULL;
struct isl_basic_set *hull = NULL;
bset = isl_basic_map_underlying_set(bmap);
if (!bset)
return NULL;
if (bset->n_eq)
bset = isl_basic_set_remove_equalities(bset, &T1, &T2);
if (!bset)
goto error;
hull = uset_affine_hull(bset);
if (!T2)
return hull;
if (!hull) {
isl_mat_free(T1);
isl_mat_free(T2);
} else {
struct isl_vec *sample = isl_vec_copy(hull->sample);
if (sample && sample->size > 0)
sample = isl_mat_vec_product(T1, sample);
else
isl_mat_free(T1);
hull = isl_basic_set_preimage(hull, T2);
if (hull) {
isl_vec_free(hull->sample);
hull->sample = sample;
} else
isl_vec_free(sample);
}
return hull;
error:
isl_mat_free(T2);
isl_basic_set_free(bset);
isl_basic_set_free(hull);
return NULL;
}
static int scan_samples_add_sample(struct isl_scan_callback *cb,
__isl_take isl_vec *sample)
{
struct scan_samples *ss = (struct scan_samples *)cb;
ss->samples = isl_mat_extend(ss->samples, ss->samples->n_row + 1,
ss->samples->n_col);
if (!ss->samples)
goto error;
isl_seq_cpy(ss->samples->row[ss->samples->n_row - 1],
sample->el, sample->size);
isl_vec_free(sample);
return 0;
error:
isl_vec_free(sample);
return -1;
}
/* 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;
}
void isl_point_free(__isl_take isl_point *pnt)
{
if (!pnt)
return;
if (--pnt->ref > 0)
return;
isl_dim_free(pnt->dim);
isl_vec_free(pnt->vec);
free(pnt);
}
/* Add a specific constraint of bmap (or its opposite) to tab.
* The position of the constraint is specified by "c", where
* the equalities of bmap are counted twice, once for the inequality
* that is equal to the equality, and once for its negation.
*
* Each of these constraints has been added to "tab" before by
* tab_add_constraints (and later removed again), so there should
* already be a row available for the constraint.
*/
static int tab_add_constraint(struct isl_tab *tab,
__isl_keep isl_basic_map *bmap, int *div_map, int c, int oppose)
{
unsigned dim;
unsigned tab_total;
unsigned bmap_total;
isl_vec *v;
int r;
if (!tab || !bmap)
return -1;
tab_total = isl_basic_map_total_dim(tab->bmap);
bmap_total = isl_basic_map_total_dim(bmap);
dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
if (!v)
return -1;
if (c < 2 * bmap->n_eq) {
if ((c % 2) != oppose)
isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
1 + bmap_total);
if (oppose)
isl_int_sub_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
expand_constraint(v, dim, bmap->eq[c/2], div_map, bmap->n_div);
r = isl_tab_add_ineq(tab, v->el);
if (oppose)
isl_int_add_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
if ((c % 2) != oppose)
isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
1 + bmap_total);
} else {
c -= 2 * bmap->n_eq;
if (oppose) {
isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
1 + bmap_total);
isl_int_sub_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
}
expand_constraint(v, dim, bmap->ineq[c], div_map, bmap->n_div);
r = isl_tab_add_ineq(tab, v->el);
if (oppose) {
isl_int_add_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
1 + bmap_total);
}
}
isl_vec_free(v);
return r;
}
static int increment_counter(struct isl_scan_callback *cb,
__isl_take isl_vec *sample)
{
struct isl_counter *cnt = (struct isl_counter *)cb;
isl_int_add_ui(cnt->count, cnt->count, 1);
isl_vec_free(sample);
if (isl_int_is_zero(cnt->max) || isl_int_lt(cnt->count, cnt->max))
return 0;
return -1;
}
__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;
}
/* Detect and make explicit all equalities satisfied by the (integer)
* points in bmap.
*/
struct isl_basic_map *isl_basic_map_detect_equalities(
struct isl_basic_map *bmap)
{
int i, j;
struct isl_basic_set *hull = NULL;
if (!bmap)
return NULL;
if (bmap->n_ineq == 0)
return bmap;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
return bmap;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES))
return bmap;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
return isl_basic_map_implicit_equalities(bmap);
hull = equalities_in_underlying_set(isl_basic_map_copy(bmap));
if (!hull)
goto error;
if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) {
isl_basic_set_free(hull);
return isl_basic_map_set_to_empty(bmap);
}
bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim), 0,
hull->n_eq, 0);
for (i = 0; i < hull->n_eq; ++i) {
j = isl_basic_map_alloc_equality(bmap);
if (j < 0)
goto error;
isl_seq_cpy(bmap->eq[j], hull->eq[i],
1 + isl_basic_set_total_dim(hull));
}
isl_vec_free(bmap->sample);
bmap->sample = isl_vec_copy(hull->sample);
isl_basic_set_free(hull);
ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES);
bmap = isl_basic_map_simplify(bmap);
return isl_basic_map_finalize(bmap);
error:
isl_basic_set_free(hull);
isl_basic_map_free(bmap);
return NULL;
}
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;
}
/* 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;
}
/* Given a set of modulo constraints
*
* c + A y = 0 mod d
*
* this function returns an affine transformation T,
*
* y = T y'
*
* that bijectively maps the integer vectors y' to integer
* vectors y that satisfy the modulo constraints.
*
* This function is inspired by Section 2.5.3
* of B. Meister, "Stating and Manipulating Periodicity in the Polytope
* Model. Applications to Program Analysis and Optimization".
* However, the implementation only follows the algorithm of that
* section for computing a particular solution and not for computing
* a general homogeneous solution. The latter is incomplete and
* may remove some valid solutions.
* Instead, we use an adaptation of the algorithm in Section 7 of
* B. Meister, S. Verdoolaege, "Polynomial Approximations in the Polytope
* Model: Bringing the Power of Quasi-Polynomials to the Masses".
*
* The input is given as a matrix B = [ c A ] and a vector d.
* Each element of the vector d corresponds to a row in B.
* The output is a lower triangular matrix.
* If no integer vector y satisfies the given constraints then
* a matrix with zero columns is returned.
*
* We first compute a particular solution y_0 to the given set of
* modulo constraints in particular_solution. If no such solution
* exists, then we return a zero-columned transformation matrix.
* Otherwise, we compute the generic solution to
*
* A y = 0 mod d
*
* That is we want to compute G such that
*
* y = G y''
*
* with y'' integer, describes the set of solutions.
*
* We first remove the common factors of each row.
* In particular if gcd(A_i,d_i) != 1, then we divide the whole
* row i (including d_i) by this common factor. If afterwards gcd(A_i) != 1,
* then we divide this row of A by the common factor, unless gcd(A_i) = 0.
* In the later case, we simply drop the row (in both A and d).
*
* If there are no rows left in A, then G is the identity matrix. Otherwise,
* for each row i, we now determine the lattice of integer vectors
* that satisfies this row. Let U_i be the unimodular extension of the
* row A_i. This unimodular extension exists because gcd(A_i) = 1.
* The first component of
*
* y' = U_i y
*
* needs to be a multiple of d_i. Let y' = diag(d_i, 1, ..., 1) y''.
* Then,
*
* y = U_i^{-1} diag(d_i, 1, ..., 1) y''
*
* for arbitrary integer vectors y''. That is, y belongs to the lattice
* generated by the columns of L_i = U_i^{-1} diag(d_i, 1, ..., 1).
* If there is only one row, then G = L_1.
*
* If there is more than one row left, we need to compute the intersection
* of the lattices. That is, we need to compute an L such that
*
* L = L_i L_i' for all i
*
* with L_i' some integer matrices. Let A be constructed as follows
*
* A = [ L_1^{-T} L_2^{-T} ... L_k^{-T} ]
*
* and computed the Hermite Normal Form of A = [ H 0 ] U
* Then,
*
* L_i^{-T} = H U_{1,i}
*
* or
*
* H^{-T} = L_i U_{1,i}^T
*
* In other words G = L = H^{-T}.
* To ensure that G is lower triangular, we compute and use its Hermite
* normal form.
*
* The affine transformation matrix returned is then
*
* [ 1 0 ]
* [ y_0 G ]
*
* as any y = y_0 + G y' with y' integer is a solution to the original
* modulo constraints.
*/
struct isl_mat *isl_mat_parameter_compression(
struct isl_mat *B, struct isl_vec *d)
{
int i;
struct isl_mat *cst = NULL;
struct isl_mat *T = NULL;
isl_int D;
if (!B || !d)
goto error;
isl_assert(B->ctx, B->n_row == d->size, goto error);
cst = particular_solution(B, d);
if (!cst)
goto error;
if (cst->n_col == 0) {
T = isl_mat_alloc(B->ctx, B->n_col, 0);
isl_mat_free(cst);
isl_mat_free(B);
isl_vec_free(d);
return T;
}
isl_int_init(D);
/* Replace a*g*row = 0 mod g*m by row = 0 mod m */
for (i = 0; i < B->n_row; ++i) {
isl_seq_gcd(B->row[i] + 1, B->n_col - 1, &D);
if (isl_int_is_one(D))
continue;
if (isl_int_is_zero(D)) {
B = isl_mat_drop_rows(B, i, 1);
d = isl_vec_cow(d);
if (!B || !d)
goto error2;
isl_seq_cpy(d->block.data+i, d->block.data+i+1,
d->size - (i+1));
d->size--;
i--;
continue;
}
B = isl_mat_cow(B);
if (!B)
goto error2;
isl_seq_scale_down(B->row[i] + 1, B->row[i] + 1, D, B->n_col-1);
isl_int_gcd(D, D, d->block.data[i]);
d = isl_vec_cow(d);
if (!d)
goto error2;
isl_int_divexact(d->block.data[i], d->block.data[i], D);
}
isl_int_clear(D);
if (B->n_row == 0)
T = isl_mat_identity(B->ctx, B->n_col);
else if (B->n_row == 1)
T = parameter_compression_1(B, d);
else
T = parameter_compression_multi(B, d);
T = isl_mat_left_hermite(T, 0, NULL, NULL);
if (!T)
goto error;
isl_mat_sub_copy(T->ctx, T->row + 1, cst->row, cst->n_row, 0, 0, 1);
isl_mat_free(cst);
isl_mat_free(B);
isl_vec_free(d);
return T;
error2:
isl_int_clear(D);
error:
isl_mat_free(cst);
isl_mat_free(B);
isl_vec_free(d);
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;
}
/* Given a tableau of a set and a tableau of the corresponding
* recession cone, detect and add all equalities to the tableau.
* If the tableau is bounded, then we can simply keep the
* tableau in its state after the return from extend_affine_hull.
* However, if the tableau is unbounded, then
* isl_tab_set_initial_basis_with_cone will add some additional
* constraints to the tableau that have to be removed again.
* In this case, we therefore rollback to the state before
* any constraints were added and then add the equalities back in.
*/
struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
struct isl_tab *tab_cone)
{
int j;
struct isl_vec *sample;
struct isl_basic_set *hull;
struct isl_tab_undo *snap;
if (!tab || !tab_cone)
goto error;
snap = isl_tab_snap(tab);
isl_mat_free(tab->basis);
tab->basis = NULL;
isl_assert(tab->mat->ctx, tab->bmap, goto error);
isl_assert(tab->mat->ctx, tab->samples, goto error);
isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error);
if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0)
goto error;
sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
if (!sample)
goto error;
isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size);
isl_vec_free(tab->bmap->sample);
tab->bmap->sample = isl_vec_copy(sample);
if (tab->n_unbounded == 0)
hull = isl_basic_set_from_vec(isl_vec_copy(sample));
else
hull = initial_hull(tab, isl_vec_copy(sample));
for (j = tab->n_outside + 1; j < tab->n_sample; ++j) {
isl_seq_cpy(sample->el, tab->samples->row[j], sample->size);
hull = affine_hull(hull,
isl_basic_set_from_vec(isl_vec_copy(sample)));
}
isl_vec_free(sample);
hull = extend_affine_hull(tab, hull);
if (!hull)
goto error;
if (tab->n_unbounded == 0) {
isl_basic_set_free(hull);
return tab;
}
if (isl_tab_rollback(tab, snap) < 0)
goto error;
if (hull->n_eq > tab->n_zero) {
for (j = 0; j < hull->n_eq; ++j) {
isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var);
if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
goto error;
}
}
isl_basic_set_free(hull);
return tab;
error:
isl_tab_free(tab);
return NULL;
}
