/// @brief Create an isl map from a OpenScop matrix.
///
/// @param m The OpenScop matrix to translate.
/// @param Space The dimensions that are contained in the OpenScop matrix.
///
/// @return An isl map representing m.
isl_map *mapFromMatrix(scoplib_matrix_p m, __isl_take isl_space *Space,
unsigned scatteringDims) {
isl_basic_map *bmap = isl_basic_map_universe(isl_space_copy(Space));
for (unsigned i = 0; i < m->NbRows; ++i) {
isl_constraint *c;
c = constraintFromMatrixRow(m->p[i], isl_space_copy(Space));
mpz_t minusOne;
mpz_init(minusOne);
mpz_set_si(minusOne, -1);
isl_constraint_set_coefficient(c, isl_dim_out, i, minusOne);
bmap = isl_basic_map_add_constraint(bmap, c);
}
for (unsigned i = m->NbRows; i < scatteringDims; i++) {
isl_constraint *c;
c = isl_equality_alloc(isl_local_space_from_space(isl_space_copy(Space)));
mpz_t One;
mpz_init(One);
mpz_set_si(One, 1);
isl_constraint_set_coefficient(c, isl_dim_out, i, One);
bmap = isl_basic_map_add_constraint(bmap, c);
}
isl_space_free(Space);
return isl_map_from_basic_map(bmap);
}
static
isl_map* build_access_function (scoplib_scop_p scop,
scoplib_statement_p s,
scoplib_matrix_p m,
isl_space* space,
isl_ctx* ctxt,
int* row_pos,
int array_id)
{
isl_map* ret = NULL;
int i;
isl_val* tmp = isl_val_int_from_si (ctxt, 0);
for (i = *row_pos; i < m->NbRows; ++i)
{
if (SCOPVAL_get_si(m->p[i][0]) == array_id)
{
ret = isl_map_universe (isl_space_copy (space));
int pos = 0;
do
{
isl_local_space* ls =
isl_local_space_from_space (isl_space_copy (space));
isl_constraint* cst = isl_equality_alloc (isl_local_space_copy (ls));
// Set input dimensions.
int k;
for (k = 0; k < s->nb_iterators; ++k)
{
tmp = isl_val_set_si (tmp, SCOPVAL_get_si(m->p[i][k+1]));
cst = isl_constraint_set_coefficient_val (cst, isl_dim_in, k, isl_val_copy(tmp));
}
for (k = 0; k < scop->nb_parameters; ++k)
{
tmp =
isl_val_set_si (tmp, SCOPVAL_get_si(m->p[i][k+1+s->nb_iterators]));
cst =
isl_constraint_set_coefficient_val (cst, isl_dim_param, k,
isl_val_copy (tmp));
}
tmp = isl_val_set_si (tmp, SCOPVAL_get_si(m->p[i][m->NbColumns - 1]));
cst = isl_constraint_set_constant_val (cst, isl_val_copy(tmp));
// Set output dimension.
tmp = isl_val_set_si (tmp, -1);
isl_constraint_set_coefficient_val (cst, isl_dim_out, pos++, isl_val_copy (tmp));
// Insert constraint.
ret = isl_map_add_constraint (ret, cst);
++i;
}
while (i < m->NbRows && SCOPVAL_get_si(m->p[i][0]) == 0);
*row_pos = i;
break;
}
}
isl_val_free (tmp);
return ret;
}
/* 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;
}
/// @brief Create an isl map from a OpenScop matrix.
///
/// @param m The OpenScop matrix to translate.
/// @param Space The dimensions that are contained in the OpenScop matrix.
///
/// @return An isl map representing m.
isl_map *mapFromMatrix(scoplib_matrix_p m, __isl_take isl_space *Space) {
isl_basic_map *bmap = isl_basic_map_universe(isl_space_copy(Space));
for (unsigned i = 0; i < m->NbRows; ++i) {
isl_constraint *c;
c = constraintFromMatrixRowFull(m->p[i], isl_space_copy(Space));
bmap = isl_basic_map_add_constraint(bmap, c);
}
isl_space_free(Space);
return isl_map_from_basic_map(bmap);
}
/* Create a graft for "node" with no guards and no enforced conditions.
*/
__isl_give isl_ast_graft *isl_ast_graft_alloc(
__isl_take isl_ast_node *node, __isl_keep isl_ast_build *build)
{
isl_ctx *ctx;
isl_space *space;
isl_ast_graft *graft;
if (!node)
return NULL;
ctx = isl_ast_node_get_ctx(node);
graft = isl_calloc_type(ctx, isl_ast_graft);
if (!graft)
goto error;
space = isl_ast_build_get_space(build, 1);
graft->ref = 1;
graft->node = node;
graft->guard = isl_set_universe(isl_space_copy(space));
graft->enforced = isl_basic_set_universe(space);
if (!graft->guard || !graft->enforced)
return isl_ast_graft_free(graft);
return graft;
error:
isl_ast_node_free(node);
return NULL;
}
__isl_give isl_space *isl_morph_get_ran_space(__isl_keep isl_morph *morph)
{
if (!morph)
return NULL;
return isl_space_copy(morph->ran->dim);
}
/* Apply the morphism to the set.
*/
__isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
__isl_take isl_set *set)
{
int i;
if (!morph || !set)
goto error;
isl_assert(set->ctx, isl_space_is_equal(set->dim, morph->dom->dim), goto error);
set = isl_set_cow(set);
if (!set)
goto error;
isl_space_free(set->dim);
set->dim = isl_space_copy(morph->ran->dim);
if (!set->dim)
goto error;
for (i = 0; i < set->n; ++i) {
set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
if (!set->p[i])
goto error;
}
isl_morph_free(morph);
ISL_F_CLR(set, ISL_SET_NORMALIZED);
return set;
error:
isl_set_free(set);
isl_morph_free(morph);
return NULL;
}
/* Given a lower and upper bound on the final variable and constraints
* on the remaining variables where these bounds are active,
* eliminate the variable from data->poly based on these bounds.
* If the polynomial has been determined to be monotonic
* in the variable, then simply plug in the appropriate bound.
* If the current polynomial is tight and if this bound is integer,
* then the result is still tight. In all other cases, the results
* may not be tight.
* Otherwise, plug in the largest bound (in absolute value) in
* the positive terms (if an upper bound is wanted) or the negative terms
* (if a lower bounded is wanted) and the other bound in the other terms.
*
* If all variables have been eliminated, then record the result.
* Ohterwise, recurse on the next variable.
*/
static isl_stat propagate_on_bound_pair(__isl_take isl_constraint *lower,
__isl_take isl_constraint *upper, __isl_take isl_basic_set *bset,
void *user)
{
struct range_data *data = (struct range_data *)user;
int save_tight = data->tight;
isl_qpolynomial *poly;
isl_stat r;
unsigned nvar;
nvar = isl_basic_set_dim(bset, isl_dim_set);
if (data->monotonicity) {
isl_qpolynomial *sub;
isl_space *dim = isl_qpolynomial_get_domain_space(data->poly);
if (data->monotonicity * data->sign > 0) {
if (data->tight)
data->tight = bound_is_integer(upper, nvar);
sub = bound2poly(upper, dim, nvar, 1);
isl_constraint_free(lower);
} else {
if (data->tight)
data->tight = bound_is_integer(lower, nvar);
sub = bound2poly(lower, dim, nvar, -1);
isl_constraint_free(upper);
}
poly = isl_qpolynomial_copy(data->poly);
poly = plug_in_at_pos(poly, nvar, sub, data);
poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);
} else {
isl_qpolynomial *l, *u;
isl_qpolynomial *pos, *neg;
isl_space *dim = isl_qpolynomial_get_domain_space(data->poly);
unsigned nparam = isl_basic_set_dim(bset, isl_dim_param);
int sign = data->sign * data->signs[nparam + nvar];
data->tight = 0;
u = bound2poly(upper, isl_space_copy(dim), nvar, 1);
l = bound2poly(lower, dim, nvar, -1);
pos = isl_qpolynomial_terms_of_sign(data->poly, data->signs, sign);
neg = isl_qpolynomial_terms_of_sign(data->poly, data->signs, -sign);
pos = plug_in_at_pos(pos, nvar, u, data);
neg = plug_in_at_pos(neg, nvar, l, data);
poly = isl_qpolynomial_add(pos, neg);
poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);
}
if (isl_basic_set_dim(bset, isl_dim_set) == 0)
r = add_guarded_poly(bset, poly, data);
else
r = propagate_on_domain(bset, poly, data);
data->tight = save_tight;
return r;
}
/* Construct a basic set described by the "n" equalities of "bset" starting
* at "first".
*/
static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
unsigned first, unsigned n)
{
int i, k;
isl_basic_set *eq;
unsigned total;
isl_assert(bset->ctx, bset->n_div == 0, return NULL);
total = isl_basic_set_total_dim(bset);
eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);
if (!eq)
return NULL;
for (i = 0; i < n; ++i) {
k = isl_basic_set_alloc_equality(eq);
if (k < 0)
goto error;
isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
}
return eq;
error:
isl_basic_set_free(eq);
return NULL;
}
// Init
void init_solver (void) {
context = isl_ctx_alloc ();
isl_space * vars = isl_space_set_alloc (context, 0, v_nb ());
ls = isl_local_space_from_space (isl_space_copy (vars));
solutions = isl_set_universe (vars);
solution = 0;
next_max_var = 0;
}
enum lp_result isl_constraints_opt(Matrix *C, Value *obj, Value denom,
enum lp_dir dir, Value *opt)
{
int i;
isl_ctx *ctx = isl_ctx_alloc();
isl_space *dim;
isl_local_space *ls;
isl_mat *eq, *ineq;
isl_basic_set *bset;
isl_aff *aff;
isl_val *v;
enum isl_lp_result res;
int max = dir == lp_max;
eq = extract_equalities(ctx, C);
ineq = extract_inequalities(ctx, C);
dim = isl_space_set_alloc(ctx, 0, C->NbColumns - 2);
ls = isl_local_space_from_space(isl_space_copy(dim));
bset = isl_basic_set_from_constraint_matrices(dim, eq, ineq,
isl_dim_set, isl_dim_div, isl_dim_param, isl_dim_cst);
aff = isl_aff_zero_on_domain(ls);
for (i = 0; i < C->NbColumns - 2; ++i) {
v = isl_val_int_from_gmp(ctx, obj[i]);
aff = isl_aff_set_coefficient_val(aff, isl_dim_in, i, v);
}
v = isl_val_int_from_gmp(ctx, obj[C->NbColumns - 2]);
aff = isl_aff_set_constant_val(aff, v);
v = isl_val_int_from_gmp(ctx, denom);
aff = isl_aff_scale_down_val(aff, v);
if (max)
v = isl_val_floor(isl_basic_set_max_lp_val(bset, aff));
else
v = isl_val_ceil(isl_basic_set_min_lp_val(bset, aff));
if (!v)
res = isl_lp_error;
else if (isl_val_is_nan(v))
res = isl_lp_empty;
else if (!isl_val_is_rat(v))
res = isl_lp_unbounded;
else {
res = isl_lp_ok;
isl_val_get_num_gmp(v, *opt);
}
isl_val_free(v);
isl_aff_free(aff);
isl_basic_set_free(bset);
isl_ctx_free(ctx);
return isl_lp_result2lp_result(res);
}
/* 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));
}
/* Return 1 if poly is monotonically increasing in the last set variable,
* -1 if poly is monotonically decreasing in the last set variable,
* 0 if no conclusion,
* -2 on error.
*
* We simply check the sign of p(x+1)-p(x)
*/
static int monotonicity(__isl_keep isl_basic_set *bset,
__isl_keep isl_qpolynomial *poly, struct range_data *data)
{
isl_ctx *ctx;
isl_space *dim;
isl_qpolynomial *sub = NULL;
isl_qpolynomial *diff = NULL;
int result = 0;
int s;
unsigned nvar;
ctx = isl_qpolynomial_get_ctx(poly);
dim = isl_qpolynomial_get_domain_space(poly);
nvar = isl_basic_set_dim(bset, isl_dim_set);
sub = isl_qpolynomial_var_on_domain(isl_space_copy(dim), isl_dim_set, nvar - 1);
sub = isl_qpolynomial_add(sub,
isl_qpolynomial_rat_cst_on_domain(dim, ctx->one, ctx->one));
diff = isl_qpolynomial_substitute(isl_qpolynomial_copy(poly),
isl_dim_in, nvar - 1, 1, &sub);
diff = isl_qpolynomial_sub(diff, isl_qpolynomial_copy(poly));
s = has_sign(bset, diff, 1, data->signs);
if (s < 0)
goto error;
if (s)
result = 1;
else {
s = has_sign(bset, diff, -1, data->signs);
if (s < 0)
goto error;
if (s)
result = -1;
}
isl_qpolynomial_free(diff);
isl_qpolynomial_free(sub);
return result;
error:
isl_qpolynomial_free(diff);
isl_qpolynomial_free(sub);
return -2;
}
static
isl_set* build_iteration_domain (scoplib_scop_p scop,
scoplib_statement_p s,
isl_space* space,
isl_ctx* ctxt)
{
isl_set* ret = isl_set_universe (isl_space_domain (isl_space_copy (space)));
int i;
isl_val* tmp = isl_val_int_from_si (ctxt, 0);
scoplib_matrix_p m = s->domain->elt;
for (i = 0; i < m->NbRows; ++i)
{
isl_local_space* ls =
isl_local_space_from_space (isl_set_get_space (ret));
isl_constraint* cst;
if (SCOPVAL_get_si(m->p[i][0]) == 0)
cst = isl_equality_alloc (isl_local_space_copy (ls));
else
cst = isl_inequality_alloc (isl_local_space_copy (ls));
// Set input dimensions.
int k;
for (k = 0; k < s->nb_iterators; ++k)
{
tmp = isl_val_set_si (tmp, SCOPVAL_get_si(m->p[i][k+1]));
cst = isl_constraint_set_coefficient_val (cst, isl_dim_set, k, isl_val_copy (tmp));
}
for (k = 0; k < scop->nb_parameters; ++k)
{
tmp =
isl_val_set_si (tmp, SCOPVAL_get_si(m->p[i][k+1+s->nb_iterators]));
cst =
isl_constraint_set_coefficient_val (cst, isl_dim_param, k,
isl_val_copy (tmp));
}
tmp = isl_val_set_si (tmp, SCOPVAL_get_si(m->p[i][m->NbColumns - 1]));
cst = isl_constraint_set_constant_val (cst, isl_val_copy (tmp));
// Insert constraint.
ret = isl_set_add_constraint (ret, cst);
}
isl_val_free (tmp);
return ret;
}
__isl_give isl_val *FN(UNION,eval)(__isl_take UNION *u,
__isl_take isl_point *pnt)
{
uint32_t hash;
struct isl_hash_table_entry *entry;
isl_bool is_void;
isl_space *space;
isl_val *v;
if (!u || !pnt)
goto error;
is_void = isl_point_is_void(pnt);
if (is_void < 0)
goto error;
if (is_void)
return FN(UNION,eval_void)(u, pnt);
space = isl_space_copy(pnt->dim);
if (!space)
goto error;
hash = isl_space_get_hash(space);
entry = isl_hash_table_find(u->space->ctx, &u->table,
hash, &FN(UNION,has_domain_space),
space, 0);
isl_space_free(space);
if (!entry) {
v = isl_val_zero(isl_point_get_ctx(pnt));
isl_point_free(pnt);
} else {
v = FN(PART,eval)(FN(PART,copy)(entry->data), pnt);
}
FN(UNION,free)(u);
return v;
error:
FN(UNION,free)(u);
isl_point_free(pnt);
return NULL;
}
/* Construct a unique identifier for a group in "grouping".
*
* The name is of the form G_n, with n the first value starting at
* grouping->group_id that does not result in an identifier
* that is already in use in the domain of the original schedule
* constraints.
*/
static isl_id *construct_group_id(struct ppcg_grouping *grouping,
__isl_take isl_space *space)
{
isl_ctx *ctx;
isl_id *id;
isl_bool empty;
isl_union_set *domain;
if (!space)
return NULL;
ctx = isl_space_get_ctx(space);
domain = isl_schedule_constraints_get_domain(grouping->sc);
do {
char buffer[20];
isl_id *id;
isl_set *set;
snprintf(buffer, sizeof(buffer), "G_%d", grouping->group_id);
grouping->group_id++;
id = isl_id_alloc(ctx, buffer, NULL);
space = isl_space_set_tuple_id(space, isl_dim_set, id);
set = isl_union_set_extract_set(domain, isl_space_copy(space));
empty = isl_set_plain_is_empty(set);
isl_set_free(set);
} while (empty >= 0 && !empty);
if (empty < 0)
space = isl_space_free(space);
id = isl_space_get_tuple_id(space, isl_dim_set);
isl_space_free(space);
isl_union_set_free(domain);
return id;
}
/* 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;
}
/* 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;
}
static
isl_map* build_schedule (scoplib_scop_p scop,
scoplib_statement_p s,
isl_space* sp,
isl_ctx* ctxt)
{
// Set up the space.
isl_space* space_in = isl_space_domain (isl_space_copy (sp));
int dout = s->schedule->NbRows;
isl_space* space_out = isl_space_set_alloc(ctxt, scop->nb_parameters, dout);
int i;
char buffer[32];
char* name;
for (i = 0; i < dout; ++i)
{
sprintf (buffer, "t%d", i);
name = strdup (buffer);
space_out = isl_space_set_dim_name (space_out, isl_dim_set, i, name);
}
for (i = 0; i < scop->nb_parameters; ++i)
{
name = strdup (((SgVariableSymbol*)(scop->parameters[i]))->get_name().str());
space_out = isl_space_set_dim_name (space_out, isl_dim_param, i, name);
}
isl_space* space = isl_space_map_from_domain_and_range
(isl_space_copy (space_in), isl_space_copy (space_out));
isl_map* ret = isl_map_universe (isl_space_copy (space));
isl_val* tmp = isl_val_int_from_si (ctxt, 0);
scoplib_matrix_p m = s->schedule;
for (i = 0; i < m->NbRows; ++i)
{
isl_local_space* ls =
isl_local_space_from_space (isl_space_copy (space));
isl_constraint* cst;
if (SCOPVAL_get_si(m->p[i][0]) == 0)
cst = isl_equality_alloc (isl_local_space_copy (ls));
else
cst = isl_inequality_alloc (isl_local_space_copy (ls));
// Set input dimensions.
int k;
for (k = 0; k < s->nb_iterators; ++k)
{
tmp = isl_val_set_si (tmp, SCOPVAL_get_si(m->p[i][k+1]));
cst = isl_constraint_set_coefficient_val (cst, isl_dim_in, k, isl_val_copy (tmp));
}
for (k = 0; k < scop->nb_parameters; ++k)
{
tmp =
isl_val_set_si (tmp, SCOPVAL_get_si(m->p[i][k+1+s->nb_iterators]));
cst =
isl_constraint_set_coefficient_val (cst, isl_dim_param, k,
isl_val_copy (tmp));
}
tmp = isl_val_set_si (tmp, SCOPVAL_get_si(m->p[i][m->NbColumns - 1]));
cst = isl_constraint_set_constant_val (cst, isl_val_copy (tmp));
// Set output dimension.
tmp = isl_val_set_si (tmp, -1);
isl_constraint_set_coefficient_val (cst, isl_dim_out, i, isl_val_copy (tmp));
// Insert constraint.
ret = isl_map_add_constraint (ret, cst);
}
isl_val_free (tmp);
return ret;
}
enum order_sign isl_polyhedron_affine_sign(Polyhedron *D, Matrix *T,
struct barvinok_options *options)
{
int i;
isl_ctx *ctx = isl_ctx_alloc();
isl_space *dim;
isl_local_space *ls;
isl_aff *aff;
isl_basic_set *bset;
isl_val *min, *max = NULL;
isl_val *v;
enum order_sign sign = order_undefined;
assert(D->Dimension == T->NbColumns - 1);
dim = isl_space_set_alloc(ctx, 0, D->Dimension);
ls = isl_local_space_from_space(isl_space_copy(dim));
bset = isl_basic_set_new_from_polylib(D, dim);
aff = isl_aff_zero_on_domain(ls);
for (i = 0; i < D->Dimension; ++i) {
v = isl_val_int_from_gmp(ctx, T->p[0][i]);
aff = isl_aff_set_coefficient_val(aff, isl_dim_in, i, v);
}
v = isl_val_int_from_gmp(ctx, T->p[0][D->Dimension]);
aff = isl_aff_set_constant_val(aff, v);
v = isl_val_int_from_gmp(ctx, T->p[1][D->Dimension]);
aff = isl_aff_scale_down_val(aff, v);
min = isl_basic_set_min_lp_val(bset, aff);
min = isl_val_ceil(min);
assert(min);
if (isl_val_is_nan(min))
sign = order_undefined;
else if (isl_val_is_pos(min))
sign = order_gt;
else {
max = isl_basic_set_max_lp_val(bset, aff);
max = isl_val_floor(max);
assert(max);
if (isl_val_is_neg(max))
sign = order_lt;
else if (isl_val_is_zero(min) && isl_val_is_zero(max))
sign = order_eq;
else if (isl_val_is_zero(min))
sign = order_ge;
else if (isl_val_is_zero(max))
sign = order_le;
else
sign = order_unknown;
}
isl_basic_set_free(bset);
isl_aff_free(aff);
isl_val_free(min);
isl_val_free(max);
isl_ctx_free(ctx);
return sign;
}
