コード例 #1
0
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]);
}
コード例 #2
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 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;
}
コード例 #3
0
ファイル: isl_sample.c プロジェクト: king-mahdi/IEGenLib
/* 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;
}
コード例 #4
0
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;
}
コード例 #5
0
ファイル: isl_point.c プロジェクト: xin3liang/toolchain_cloog
__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;
}
コード例 #6
0
ファイル: isl_morph.c プロジェクト: xin3liang/toolchain_cloog
/* 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;
}
コード例 #7
0
ファイル: isl_morph.c プロジェクト: xin3liang/toolchain_cloog
/* 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;
}
コード例 #8
0
ファイル: isl_morph.c プロジェクト: xin3liang/toolchain_cloog
/* 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;
}
コード例 #9
0
ファイル: isl_point.c プロジェクト: xin3liang/toolchain_cloog
__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;
}