/* 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;
}
/* 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;
}
/* Use the n equalities of bset to unimodularly transform the
* variables x such that n transformed variables x1' have a constant value
* and rewrite the constraints of bset in terms of the remaining
* transformed variables x2'. The matrix pointed to by T maps
* the new variables x2' back to the original variables x, while T2
* maps the original variables to the new variables.
*/
static struct isl_basic_set *compress_variables(
struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)
{
struct isl_mat *B, *TC;
unsigned dim;
if (T)
*T = NULL;
if (T2)
*T2 = NULL;
if (!bset)
goto error;
isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
isl_assert(bset->ctx, bset->n_div == 0, goto error);
dim = isl_basic_set_n_dim(bset);
isl_assert(bset->ctx, bset->n_eq <= dim, goto error);
if (bset->n_eq == 0)
return bset;
B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + dim);
TC = isl_mat_variable_compression(B, T2);
if (!TC)
goto error;
if (TC->n_col == 0) {
isl_mat_free(TC);
if (T2) {
isl_mat_free(*T2);
*T2 = NULL;
}
return isl_basic_set_set_to_empty(bset);
}
bset = isl_basic_set_preimage(bset, T ? isl_mat_copy(TC) : TC);
if (T)
*T = TC;
return bset;
error:
isl_basic_set_free(bset);
return NULL;
}
/* 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;
}
/* 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;
}
