static void expand_constraint(isl_vec *v, unsigned dim,
isl_int *c, int *div_map, unsigned n_div)
{
int i;
isl_seq_cpy(v->el, c, 1 + dim);
isl_seq_clr(v->el + 1 + dim, v->size - (1 + dim));
for (i = 0; i < n_div; ++i)
isl_int_set(v->el[1 + dim + div_map[i]], c[1 + dim + i]);
}
/* 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;
}
/* 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;
}
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;
}
__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;
}
/* Given a matrix that maps a (possibly) parametric domain to
* a parametric domain, add in rows that map the "nparam" parameters onto
* themselves.
*/
static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
unsigned nparam)
{
int i;
if (nparam == 0)
return mat;
if (!mat)
return NULL;
mat = isl_mat_insert_rows(mat, 1, nparam);
if (!mat)
return NULL;
for (i = 0; i < nparam; ++i) {
isl_seq_clr(mat->row[1 + i], mat->n_col);
isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
}
return mat;
}
/* Add stride constraints to "bset" based on the inverse mapping
* that was plugged in. In particular, if morph maps x' to x,
* the the constraints of the original input
*
* A x' + b >= 0
*
* have been rewritten to
*
* A inv x + b >= 0
*
* However, this substitution may loose information on the integrality of x',
* so we need to impose that
*
* inv x
*
* is integral. If inv = B/d, this means that we need to impose that
*
* B x = 0 mod d
*
* or
*
* exists alpha in Z^m: B x = d alpha
*
*/
static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
__isl_keep isl_morph *morph)
{
int i, div, k;
isl_int gcd;
if (isl_int_is_one(morph->inv->row[0][0]))
return bset;
isl_int_init(gcd);
for (i = 0; 1 + i < morph->inv->n_row; ++i) {
isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
continue;
div = isl_basic_set_alloc_div(bset);
if (div < 0)
goto error;
k = isl_basic_set_alloc_equality(bset);
if (k < 0)
goto error;
isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
morph->inv->n_col);
isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
isl_int_set(bset->eq[k][morph->inv->n_col + div],
morph->inv->row[0][0]);
}
isl_int_clear(gcd);
return bset;
error:
isl_int_clear(gcd);
isl_basic_set_free(bset);
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;
}
__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;
}