/* Given a set of modulo constraints
*
* c + A y = 0 mod d
*
* this function computes a particular solution y_0
*
* The input is given as a matrix B = [ c A ] and a vector d.
*
* The output is matrix containing the solution y_0 or
* a zero-column matrix if the constraints admit no integer solution.
*
* The given set of constrains is equivalent to
*
* c + A y = -D x
*
* with D = diag d and x a fresh set of variables.
* Reducing both c and A modulo d does not change the
* value of y in the solution and may lead to smaller coefficients.
* Let M = [ D A ] and [ H 0 ] = M U, the Hermite normal form of M.
* Then
* [ x ]
* M [ y ] = - c
* and so
* [ x ]
* [ H 0 ] U^{-1} [ y ] = - c
* Let
* [ A ] [ x ]
* [ B ] = U^{-1} [ y ]
* then
* H A + 0 B = -c
*
* so B may be chosen arbitrarily, e.g., B = 0, and then
*
* [ x ] = [ -c ]
* U^{-1} [ y ] = [ 0 ]
* or
* [ x ] [ -c ]
* [ y ] = U [ 0 ]
* specifically,
*
* y = U_{2,1} (-c)
*
* If any of the coordinates of this y are non-integer
* then the constraints admit no integer solution and
* a zero-column matrix is returned.
*/
static struct isl_mat *particular_solution(struct isl_mat *B, struct isl_vec *d)
{
int i, j;
struct isl_mat *M = NULL;
struct isl_mat *C = NULL;
struct isl_mat *U = NULL;
struct isl_mat *H = NULL;
struct isl_mat *cst = NULL;
struct isl_mat *T = NULL;
M = isl_mat_alloc(B->ctx, B->n_row, B->n_row + B->n_col - 1);
C = isl_mat_alloc(B->ctx, 1 + B->n_row, 1);
if (!M || !C)
goto error;
isl_int_set_si(C->row[0][0], 1);
for (i = 0; i < B->n_row; ++i) {
isl_seq_clr(M->row[i], B->n_row);
isl_int_set(M->row[i][i], d->block.data[i]);
isl_int_neg(C->row[1 + i][0], B->row[i][0]);
isl_int_fdiv_r(C->row[1+i][0], C->row[1+i][0], M->row[i][i]);
for (j = 0; j < B->n_col - 1; ++j)
isl_int_fdiv_r(M->row[i][B->n_row + j],
B->row[i][1 + j], M->row[i][i]);
}
M = isl_mat_left_hermite(M, 0, &U, NULL);
if (!M || !U)
goto error;
H = isl_mat_sub_alloc(M, 0, B->n_row, 0, B->n_row);
H = isl_mat_lin_to_aff(H);
C = isl_mat_inverse_product(H, C);
if (!C)
goto error;
for (i = 0; i < B->n_row; ++i) {
if (!isl_int_is_divisible_by(C->row[1+i][0], C->row[0][0]))
break;
isl_int_divexact(C->row[1+i][0], C->row[1+i][0], C->row[0][0]);
}
if (i < B->n_row)
cst = isl_mat_alloc(B->ctx, B->n_row, 0);
else
cst = isl_mat_sub_alloc(C, 1, B->n_row, 0, 1);
T = isl_mat_sub_alloc(U, B->n_row, B->n_col - 1, 0, B->n_row);
cst = isl_mat_product(T, cst);
isl_mat_free(M);
isl_mat_free(C);
isl_mat_free(U);
return cst;
error:
isl_mat_free(M);
isl_mat_free(C);
isl_mat_free(U);
return NULL;
}
struct isl_basic_set *isl_basic_set_recession_cone(struct isl_basic_set *bset)
{
int i;
bset = isl_basic_set_cow(bset);
if (!bset)
return NULL;
isl_assert(bset->ctx, bset->n_div == 0, goto error);
for (i = 0; i < bset->n_eq; ++i)
isl_int_set_si(bset->eq[i][0], 0);
for (i = 0; i < bset->n_ineq; ++i)
isl_int_set_si(bset->ineq[i][0], 0);
ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
return isl_basic_set_implicit_equalities(bset);
error:
isl_basic_set_free(bset);
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.
*/
isl_stat isl_set_dim_residue_class_val(__isl_keep isl_set *set,
int pos, __isl_give isl_val **modulo, __isl_give isl_val **residue)
{
*modulo = NULL;
*residue = NULL;
if (!set)
return isl_stat_error;
*modulo = isl_val_alloc(isl_set_get_ctx(set));
*residue = isl_val_alloc(isl_set_get_ctx(set));
if (!*modulo || !*residue)
goto error;
if (isl_set_dim_residue_class(set, pos,
&(*modulo)->n, &(*residue)->n) < 0)
goto error;
isl_int_set_si((*modulo)->d, 1);
isl_int_set_si((*residue)->d, 1);
return isl_stat_ok;
error:
isl_val_free(*modulo);
isl_val_free(*residue);
return isl_stat_error;
}
/* Construct a zero sample of the same dimension as bset.
* As a special case, if bset is zero-dimensional, this
* function creates a zero-dimensional sample point.
*/
static struct isl_vec *zero_sample(struct isl_basic_set *bset)
{
unsigned dim;
struct isl_vec *sample;
dim = isl_basic_set_total_dim(bset);
sample = isl_vec_alloc(bset->ctx, 1 + dim);
if (sample) {
isl_int_set_si(sample->el[0], 1);
isl_seq_clr(sample->el + 1, dim);
}
isl_basic_set_free(bset);
return sample;
}
/* 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;
}
static int scan_0D(struct isl_basic_set *bset,
struct isl_scan_callback *callback)
{
struct isl_vec *sample;
sample = isl_vec_alloc(bset->ctx, 1);
isl_basic_set_free(bset);
if (!sample)
return -1;
isl_int_set_si(sample->el[0], 1);
return callback->add(callback, sample);
}
__isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim)
{
isl_vec *vec;
if (!dim)
return NULL;
vec = isl_vec_alloc(dim->ctx, 1 + isl_dim_total(dim));
if (!vec)
goto error;
isl_int_set_si(vec->el[0], 1);
isl_seq_clr(vec->el + 1, vec->size - 1);
return isl_point_alloc(dim, vec);
error:
isl_dim_free(dim);
return NULL;
}
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;
}
static void copy_solution(struct isl_vec *vec, int maximize, isl_int *opt,
isl_int *opt_denom, PipQuast *sol)
{
int i;
PipList *list;
isl_int tmp;
if (opt) {
if (opt_denom) {
isl_seq_cpy_from_pip(opt,
&sol->list->vector->the_vector[0], 1);
isl_seq_cpy_from_pip(opt_denom,
&sol->list->vector->the_deno[0], 1);
} else if (maximize)
mpz_fdiv_q(*opt, sol->list->vector->the_vector[0],
sol->list->vector->the_deno[0]);
else
mpz_cdiv_q(*opt, sol->list->vector->the_vector[0],
sol->list->vector->the_deno[0]);
}
if (!vec)
return;
isl_int_init(tmp);
isl_int_set_si(vec->el[0], 1);
for (i = 0, list = sol->list->next; list; ++i, list = list->next) {
isl_seq_cpy_from_pip(&vec->el[1 + i],
&list->vector->the_deno[0], 1);
isl_int_lcm(vec->el[0], vec->el[0], vec->el[1 + i]);
}
for (i = 0, list = sol->list->next; list; ++i, list = list->next) {
isl_seq_cpy_from_pip(&tmp, &list->vector->the_deno[0], 1);
isl_int_divexact(tmp, vec->el[0], tmp);
isl_seq_cpy_from_pip(&vec->el[1 + i],
&list->vector->the_vector[0], 1);
isl_int_mul(vec->el[1 + i], vec->el[1 + i], tmp);
}
isl_int_clear(tmp);
}
/// Create the memory access matrix for scoplib
///
/// @param S The polly statement the access matrix is created for.
/// @param isRead Are we looking for read or write accesses?
/// @param ArrayMap A map translating from the memory references to the scoplib
/// indeces
///
/// @return The memory access matrix, as it is required by scoplib.
scoplib_matrix_p ScopLib::createAccessMatrix(ScopStmt *S, bool isRead) {
unsigned NbColumns = S->getNumIterators() + S->getNumParams() + 2;
scoplib_matrix_p m = scoplib_matrix_malloc(0, NbColumns);
for (ScopStmt::memacc_iterator MI = S->memacc_begin(), ME = S->memacc_end();
MI != ME; ++MI)
if ((*MI)->isRead() == isRead) {
// Extract the access function.
isl_map *AccessRelation = (*MI)->getAccessRelation();
isl_map_foreach_basic_map(AccessRelation,
&accessToMatrix_basic_map, m);
isl_map_free(AccessRelation);
// Set the index of the memory access base element.
std::map<const Value*, int>::iterator BA =
ArrayMap.find((*MI)->getBaseAddr());
isl_int_set_si(m->p[m->NbRows - 1][0], (*BA).second + 1);
}
return m;
}
/* 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;
}
/* 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;
}
/* Given a set of equalities
*
* M x - c = 0
*
* this function computes a unimodular transformation from a lower-dimensional
* space to the original space that bijectively maps the integer points x'
* in the lower-dimensional space to the integer points x in the original
* space that satisfy the equalities.
*
* The input is given as a matrix B = [ -c M ] and the output is a
* matrix that maps [1 x'] to [1 x].
* If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x'].
*
* 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
*
* H1 x1' - c = 0 or x1' = H1^{-1} c = c'
*
* If any of the c' is non-integer, then the original set has no
* integer solutions (since the x' are a unimodular transformation
* of the x) and a zero-column matrix is returned.
* Otherwise, the transformation is given by
*
* x = U1 H1^{-1} c + U2 x2'
*
* The inverse transformation is simply
*
* x2' = Q2 x
*/
__isl_give isl_mat *isl_mat_variable_compression(__isl_take isl_mat *B,
__isl_give isl_mat **T2)
{
int i;
struct isl_mat *H = NULL, *C = NULL, *H1, *U = NULL, *U1, *U2, *TC;
unsigned dim;
if (T2)
*T2 = NULL;
if (!B)
goto error;
dim = B->n_col - 1;
H = isl_mat_sub_alloc(B, 0, B->n_row, 1, dim);
H = isl_mat_left_hermite(H, 0, &U, T2);
if (!H || !U || (T2 && !*T2))
goto error;
if (T2) {
*T2 = isl_mat_drop_rows(*T2, 0, B->n_row);
*T2 = isl_mat_lin_to_aff(*T2);
if (!*T2)
goto error;
}
C = isl_mat_alloc(B->ctx, 1+B->n_row, 1);
if (!C)
goto error;
isl_int_set_si(C->row[0][0], 1);
isl_mat_sub_neg(C->ctx, C->row+1, B->row, B->n_row, 0, 0, 1);
H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
H1 = isl_mat_lin_to_aff(H1);
TC = isl_mat_inverse_product(H1, C);
if (!TC)
goto error;
isl_mat_free(H);
if (!isl_int_is_one(TC->row[0][0])) {
for (i = 0; i < B->n_row; ++i) {
if (!isl_int_is_divisible_by(TC->row[1+i][0], TC->row[0][0])) {
struct isl_ctx *ctx = B->ctx;
isl_mat_free(B);
isl_mat_free(TC);
isl_mat_free(U);
if (T2) {
isl_mat_free(*T2);
*T2 = NULL;
}
return isl_mat_alloc(ctx, 1 + dim, 0);
}
isl_seq_scale_down(TC->row[1+i], TC->row[1+i], TC->row[0][0], 1);
}
isl_int_set_si(TC->row[0][0], 1);
}
U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, B->n_row);
U1 = isl_mat_lin_to_aff(U1);
U2 = isl_mat_sub_alloc(U, 0, U->n_row, B->n_row, U->n_row - B->n_row);
U2 = isl_mat_lin_to_aff(U2);
isl_mat_free(U);
TC = isl_mat_product(U1, TC);
TC = isl_mat_aff_direct_sum(TC, U2);
isl_mat_free(B);
return TC;
error:
isl_mat_free(B);
isl_mat_free(H);
isl_mat_free(U);
if (T2) {
isl_mat_free(*T2);
*T2 = NULL;
}
return NULL;
}
/**
* 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 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;
}
__isl_give isl_basic_set *isl_basic_set_box_from_points(
__isl_take isl_point *pnt1, __isl_take isl_point *pnt2)
{
isl_basic_set *bset;
unsigned total;
int i;
int k;
isl_int t;
isl_int_init(t);
if (!pnt1 || !pnt2)
goto error;
isl_assert(pnt1->dim->ctx,
isl_dim_equal(pnt1->dim, pnt2->dim), goto error);
if (isl_point_is_void(pnt1) && isl_point_is_void(pnt2)) {
isl_dim *dim = isl_dim_copy(pnt1->dim);
isl_point_free(pnt1);
isl_point_free(pnt2);
isl_int_clear(t);
return isl_basic_set_empty(dim);
}
if (isl_point_is_void(pnt1)) {
isl_point_free(pnt1);
isl_int_clear(t);
return isl_basic_set_from_point(pnt2);
}
if (isl_point_is_void(pnt2)) {
isl_point_free(pnt2);
isl_int_clear(t);
return isl_basic_set_from_point(pnt1);
}
total = isl_dim_total(pnt1->dim);
bset = isl_basic_set_alloc_dim(isl_dim_copy(pnt1->dim), 0, 0, 2 * total);
for (i = 0; i < total; ++i) {
isl_int_mul(t, pnt1->vec->el[1 + i], pnt2->vec->el[0]);
isl_int_submul(t, pnt2->vec->el[1 + i], pnt1->vec->el[0]);
k = isl_basic_set_alloc_inequality(bset);
if (k < 0)
goto error;
isl_seq_clr(bset->ineq[k] + 1, total);
if (isl_int_is_pos(t)) {
isl_int_set_si(bset->ineq[k][1 + i], -1);
isl_int_set(bset->ineq[k][0], pnt1->vec->el[1 + i]);
} else {
isl_int_set_si(bset->ineq[k][1 + i], 1);
isl_int_neg(bset->ineq[k][0], pnt1->vec->el[1 + i]);
}
isl_int_fdiv_q(bset->ineq[k][0], bset->ineq[k][0], pnt1->vec->el[0]);
k = isl_basic_set_alloc_inequality(bset);
if (k < 0)
goto error;
isl_seq_clr(bset->ineq[k] + 1, total);
if (isl_int_is_pos(t)) {
isl_int_set_si(bset->ineq[k][1 + i], 1);
isl_int_neg(bset->ineq[k][0], pnt2->vec->el[1 + i]);
} else {
isl_int_set_si(bset->ineq[k][1 + i], -1);
isl_int_set(bset->ineq[k][0], pnt2->vec->el[1 + i]);
}
isl_int_fdiv_q(bset->ineq[k][0], bset->ineq[k][0], pnt2->vec->el[0]);
}
bset = isl_basic_set_finalize(bset);
isl_point_free(pnt1);
isl_point_free(pnt2);
isl_int_clear(t);
return bset;
error:
isl_point_free(pnt1);
isl_point_free(pnt2);
isl_int_clear(t);
return NULL;
}
