/* 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;
}
/* Given a set of equalities
*
* B(y) + A x = 0 (*)
*
* compute and return an affine transformation T,
*
* y = T y'
*
* that bijectively maps the integer vectors y' to integer
* vectors y that satisfy the modulo constraints for some value of x.
*
* Let [H 0] be the Hermite Normal Form of A, i.e.,
*
* A = [H 0] Q
*
* Then y is a solution of (*) iff
*
* H^-1 B(y) (= - [I 0] Q x)
*
* is an integer vector. Let d be the common denominator of H^-1.
* We impose
*
* d H^-1 B(y) = 0 mod d
*
* and compute the solution using isl_mat_parameter_compression.
*/
__isl_give isl_mat *isl_mat_parameter_compression_ext(__isl_take isl_mat *B,
__isl_take isl_mat *A)
{
isl_ctx *ctx;
isl_vec *d;
int n_row, n_col;
if (!A)
return isl_mat_free(B);
ctx = isl_mat_get_ctx(A);
n_row = A->n_row;
n_col = A->n_col;
A = isl_mat_left_hermite(A, 0, NULL, NULL);
A = isl_mat_drop_cols(A, n_row, n_col - n_row);
A = isl_mat_lin_to_aff(A);
A = isl_mat_right_inverse(A);
d = isl_vec_alloc(ctx, n_row);
if (A)
d = isl_vec_set(d, A->row[0][0]);
A = isl_mat_drop_rows(A, 0, 1);
A = isl_mat_drop_cols(A, 0, 1);
B = isl_mat_product(A, B);
return isl_mat_parameter_compression(B, d);
}
/* Compute a common lattice of solutions to the linear modulo
* constraints specified by B and d.
* See also the documentation of isl_mat_parameter_compression.
* We put the matrix
*
* A = [ L_1^{-T} L_2^{-T} ... L_k^{-T} ]
*
* on a common denominator. This denominator D is the lcm of modulos d.
* Since L_i = U_i^{-1} diag(d_i, 1, ... 1), we have
* L_i^{-T} = U_i^T diag(d_i, 1, ... 1)^{-T} = U_i^T diag(1/d_i, 1, ..., 1).
* Putting this on the common denominator, we have
* D * L_i^{-T} = U_i^T diag(D/d_i, D, ..., D).
*/
static struct isl_mat *parameter_compression_multi(
struct isl_mat *B, struct isl_vec *d)
{
int i, j, k;
isl_int D;
struct isl_mat *A = NULL, *U = NULL;
struct isl_mat *T;
unsigned size;
isl_int_init(D);
isl_vec_lcm(d, &D);
size = B->n_col - 1;
A = isl_mat_alloc(B->ctx, size, B->n_row * size);
U = isl_mat_alloc(B->ctx, size, size);
if (!U || !A)
goto error;
for (i = 0; i < B->n_row; ++i) {
isl_seq_cpy(U->row[0], B->row[i] + 1, size);
U = isl_mat_unimodular_complete(U, 1);
if (!U)
goto error;
isl_int_divexact(D, D, d->block.data[i]);
for (k = 0; k < U->n_col; ++k)
isl_int_mul(A->row[k][i*size+0], D, U->row[0][k]);
isl_int_mul(D, D, d->block.data[i]);
for (j = 1; j < U->n_row; ++j)
for (k = 0; k < U->n_col; ++k)
isl_int_mul(A->row[k][i*size+j],
D, U->row[j][k]);
}
A = isl_mat_left_hermite(A, 0, NULL, NULL);
T = isl_mat_sub_alloc(A, 0, A->n_row, 0, A->n_row);
T = isl_mat_lin_to_aff(T);
if (!T)
goto error;
isl_int_set(T->row[0][0], D);
T = isl_mat_right_inverse(T);
if (!T)
goto error;
isl_assert(T->ctx, isl_int_is_one(T->row[0][0]), goto error);
T = isl_mat_transpose(T);
isl_mat_free(A);
isl_mat_free(U);
isl_int_clear(D);
return T;
error:
isl_mat_free(A);
isl_mat_free(U);
isl_int_clear(D);
return NULL;
}
/* Compute and return the matrix
*
* U_1^{-1} diag(d_1, 1, ..., 1)
*
* with U_1 the unimodular completion of the first (and only) row of B.
* The columns of this matrix generate the lattice that satisfies
* the single (linear) modulo constraint.
*/
static struct isl_mat *parameter_compression_1(
struct isl_mat *B, struct isl_vec *d)
{
struct isl_mat *U;
U = isl_mat_alloc(B->ctx, B->n_col - 1, B->n_col - 1);
if (!U)
return NULL;
isl_seq_cpy(U->row[0], B->row[0] + 1, B->n_col - 1);
U = isl_mat_unimodular_complete(U, 1);
U = isl_mat_right_inverse(U);
if (!U)
return NULL;
isl_mat_col_mul(U, 0, d->block.data[0], 0);
U = isl_mat_lin_to_aff(U);
return U;
}