/* 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; }