コード例 #1
0
ファイル: isl_point.c プロジェクト: xin3liang/toolchain_cloog
__isl_give isl_point *isl_point_alloc(__isl_take isl_dim *dim,
	__isl_take isl_vec *vec)
{
	struct isl_point *pnt;

	if (!dim || !vec)
		goto error;

	if (vec->size > 1 + isl_dim_total(dim)) {
		vec = isl_vec_cow(vec);
		if (!vec)
			goto error;
		vec->size = 1 + isl_dim_total(dim);
	}

	pnt = isl_alloc_type(dim->ctx, struct isl_point);
	if (!pnt)
		goto error;

	pnt->ref = 1;
	pnt->dim = dim;
	pnt->vec = vec;

	return pnt;
error:
	isl_dim_free(dim);
	isl_vec_free(vec);
	return NULL;
}
コード例 #2
0
ファイル: isl_point.c プロジェクト: xin3liang/toolchain_cloog
__isl_give isl_point *isl_point_sub_ui(__isl_take isl_point *pnt,
	enum isl_dim_type type, int pos, unsigned val)
{
	if (!pnt || isl_point_is_void(pnt))
		return pnt;

	pnt = isl_point_cow(pnt);
	if (!pnt)
		return NULL;
	pnt->vec = isl_vec_cow(pnt->vec);
	if (!pnt->vec)
		goto error;

	if (type == isl_dim_set)
		pos += isl_dim_size(pnt->dim, isl_dim_param);

	isl_int_sub_ui(pnt->vec->el[1 + pos], pnt->vec->el[1 + pos], val);

	return pnt;
error:
	isl_point_free(pnt);
	return NULL;
}
コード例 #3
0
ファイル: isl_equalities.c プロジェクト: eva-oss/isl
/* Given a set of modulo constraints
 *
 *		c + A y = 0 mod d
 *
 * this function returns an affine transformation T,
 *
 *		y = T y'
 *
 * that bijectively maps the integer vectors y' to integer
 * vectors y that satisfy the modulo constraints.
 *
 * This function is inspired by Section 2.5.3
 * of B. Meister, "Stating and Manipulating Periodicity in the Polytope
 * Model.  Applications to Program Analysis and Optimization".
 * However, the implementation only follows the algorithm of that
 * section for computing a particular solution and not for computing
 * a general homogeneous solution.  The latter is incomplete and
 * may remove some valid solutions.
 * Instead, we use an adaptation of the algorithm in Section 7 of
 * B. Meister, S. Verdoolaege, "Polynomial Approximations in the Polytope
 * Model: Bringing the Power of Quasi-Polynomials to the Masses".
 *
 * The input is given as a matrix B = [ c A ] and a vector d.
 * Each element of the vector d corresponds to a row in B.
 * The output is a lower triangular matrix.
 * If no integer vector y satisfies the given constraints then
 * a matrix with zero columns is returned.
 *
 * We first compute a particular solution y_0 to the given set of
 * modulo constraints in particular_solution.  If no such solution
 * exists, then we return a zero-columned transformation matrix.
 * Otherwise, we compute the generic solution to
 *
 *		A y = 0 mod d
 *
 * That is we want to compute G such that
 *
 *		y = G y''
 *
 * with y'' integer, describes the set of solutions.
 *
 * We first remove the common factors of each row.
 * In particular if gcd(A_i,d_i) != 1, then we divide the whole
 * row i (including d_i) by this common factor.  If afterwards gcd(A_i) != 1,
 * then we divide this row of A by the common factor, unless gcd(A_i) = 0.
 * In the later case, we simply drop the row (in both A and d).
 *
 * If there are no rows left in A, then G is the identity matrix. Otherwise,
 * for each row i, we now determine the lattice of integer vectors
 * that satisfies this row.  Let U_i be the unimodular extension of the
 * row A_i.  This unimodular extension exists because gcd(A_i) = 1.
 * The first component of
 *
 *		y' = U_i y
 *
 * needs to be a multiple of d_i.  Let y' = diag(d_i, 1, ..., 1) y''.
 * Then,
 *
 *		y = U_i^{-1} diag(d_i, 1, ..., 1) y''
 *
 * for arbitrary integer vectors y''.  That is, y belongs to the lattice
 * generated by the columns of L_i = U_i^{-1} diag(d_i, 1, ..., 1).
 * If there is only one row, then G = L_1.
 *
 * If there is more than one row left, we need to compute the intersection
 * of the lattices.  That is, we need to compute an L such that
 *
 *		L = L_i L_i'	for all i
 *
 * with L_i' some integer matrices.  Let A be constructed as follows
 *
 *		A = [ L_1^{-T} L_2^{-T} ... L_k^{-T} ]
 *
 * and computed the Hermite Normal Form of A = [ H 0 ] U
 * Then,
 *
 *		L_i^{-T} = H U_{1,i}
 *
 * or
 *
 *		H^{-T} = L_i U_{1,i}^T
 *
 * In other words G = L = H^{-T}.
 * To ensure that G is lower triangular, we compute and use its Hermite
 * normal form.
 *
 * The affine transformation matrix returned is then
 *
 *		[  1   0  ]
 *		[ y_0  G  ]
 *
 * as any y = y_0 + G y' with y' integer is a solution to the original
 * modulo constraints.
 */
struct isl_mat *isl_mat_parameter_compression(
			struct isl_mat *B, struct isl_vec *d)
{
	int i;
	struct isl_mat *cst = NULL;
	struct isl_mat *T = NULL;
	isl_int D;

	if (!B || !d)
		goto error;
	isl_assert(B->ctx, B->n_row == d->size, goto error);
	cst = particular_solution(B, d);
	if (!cst)
		goto error;
	if (cst->n_col == 0) {
		T = isl_mat_alloc(B->ctx, B->n_col, 0);
		isl_mat_free(cst);
		isl_mat_free(B);
		isl_vec_free(d);
		return T;
	}
	isl_int_init(D);
	/* Replace a*g*row = 0 mod g*m by row = 0 mod m */
	for (i = 0; i < B->n_row; ++i) {
		isl_seq_gcd(B->row[i] + 1, B->n_col - 1, &D);
		if (isl_int_is_one(D))
			continue;
		if (isl_int_is_zero(D)) {
			B = isl_mat_drop_rows(B, i, 1);
			d = isl_vec_cow(d);
			if (!B || !d)
				goto error2;
			isl_seq_cpy(d->block.data+i, d->block.data+i+1,
							d->size - (i+1));
			d->size--;
			i--;
			continue;
		}
		B = isl_mat_cow(B);
		if (!B)
			goto error2;
		isl_seq_scale_down(B->row[i] + 1, B->row[i] + 1, D, B->n_col-1);
		isl_int_gcd(D, D, d->block.data[i]);
		d = isl_vec_cow(d);
		if (!d)
			goto error2;
		isl_int_divexact(d->block.data[i], d->block.data[i], D);
	}
	isl_int_clear(D);
	if (B->n_row == 0)
		T = isl_mat_identity(B->ctx, B->n_col);
	else if (B->n_row == 1)
		T = parameter_compression_1(B, d);
	else
		T = parameter_compression_multi(B, d);
	T = isl_mat_left_hermite(T, 0, NULL, NULL);
	if (!T)
		goto error;
	isl_mat_sub_copy(T->ctx, T->row + 1, cst->row, cst->n_row, 0, 0, 1);
	isl_mat_free(cst);
	isl_mat_free(B);
	isl_vec_free(d);
	return T;
error2:
	isl_int_clear(D);
error:
	isl_mat_free(cst);
	isl_mat_free(B);
	isl_vec_free(d);
	return NULL;
}