示例#1
0
__isl_give isl_morph *isl_morph_alloc(
	__isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
	__isl_take isl_mat *map, __isl_take isl_mat *inv)
{
	isl_morph *morph;

	if (!dom || !ran || !map || !inv)
		goto error;

	morph = isl_alloc_type(dom->ctx, struct isl_morph);
	if (!morph)
		goto error;

	morph->ref = 1;
	morph->dom = dom;
	morph->ran = ran;
	morph->map = map;
	morph->inv = inv;

	return morph;
error:
	isl_basic_set_free(dom);
	isl_basic_set_free(ran);
	isl_mat_free(map);
	isl_mat_free(inv);
	return NULL;
}
示例#2
0
/* 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;
}
示例#3
0
/* 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;
}
示例#4
0
/* 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;
}
示例#5
0
void isl_morph_free(__isl_take isl_morph *morph)
{
	if (!morph)
		return;

	if (--morph->ref > 0)
		return;

	isl_basic_set_free(morph->dom);
	isl_basic_set_free(morph->ran);
	isl_mat_free(morph->map);
	isl_mat_free(morph->inv);
	free(morph);
}
示例#6
0
static __isl_give isl_mat *isl_basic_set_scan_samples(
	__isl_take isl_basic_set *bset)
{
	isl_ctx *ctx;
	isl_size dim;
	struct scan_samples ss;

	ctx = isl_basic_set_get_ctx(bset);
	dim = isl_basic_set_dim(bset, isl_dim_all);
	if (dim < 0)
		goto error;
	ss.callback.add = scan_samples_add_sample;
	ss.samples = isl_mat_alloc(ctx, 0, 1 + dim);
	if (!ss.samples)
		goto error;

	if (isl_basic_set_scan(bset, &ss.callback) < 0) {
		isl_mat_free(ss.samples);
		return NULL;
	}

	return ss.samples;
error:
	isl_basic_set_free(bset);
	return NULL;
}
示例#7
0
/* 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);
}
示例#8
0
/* Look for all equalities satisfied by the integer points in bmap
 * that are independent of the equalities already explicitly available
 * in bmap.
 *
 * We first remove all equalities already explicitly available,
 * then look for additional equalities in the reduced space
 * and then transform the result to the original space.
 * The original equalities are _not_ added to this set.  This is
 * the responsibility of the calling function.
 * The resulting basic set has all meaning about the dimensions removed.
 * In particular, dimensions that correspond to existential variables
 * in bmap and that are found to be fixed are not removed.
 */
static struct isl_basic_set *equalities_in_underlying_set(
						struct isl_basic_map *bmap)
{
	struct isl_mat *T1 = NULL;
	struct isl_mat *T2 = NULL;
	struct isl_basic_set *bset = NULL;
	struct isl_basic_set *hull = NULL;

	bset = isl_basic_map_underlying_set(bmap);
	if (!bset)
		return NULL;
	if (bset->n_eq)
		bset = isl_basic_set_remove_equalities(bset, &T1, &T2);
	if (!bset)
		goto error;

	hull = uset_affine_hull(bset);
	if (!T2)
		return hull;

	if (!hull) {
		isl_mat_free(T1);
		isl_mat_free(T2);
	} else {
		struct isl_vec *sample = isl_vec_copy(hull->sample);
		if (sample && sample->size > 0)
			sample = isl_mat_vec_product(T1, sample);
		else
			isl_mat_free(T1);
		hull = isl_basic_set_preimage(hull, T2);
		if (hull) {
			isl_vec_free(hull->sample);
			hull->sample = sample;
		} else
			isl_vec_free(sample);
	}

	return hull;
error:
	isl_mat_free(T2);
	isl_basic_set_free(bset);
	isl_basic_set_free(hull);
	return NULL;
}
示例#9
0
/* 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;
}
示例#10
0
int main(int argc, char **argv)
{
	struct isl_ctx *ctx = isl_ctx_alloc();
	struct isl_basic_set *bset;
	struct isl_mat *samples;

	bset = isl_basic_set_read_from_file(ctx, stdin);
	samples = isl_basic_set_samples(bset);
	isl_mat_print_internal(samples, stdout, 0);
	isl_mat_free(samples);
	isl_ctx_free(ctx);

	return 0;
}
示例#11
0
/* 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;
}
示例#12
0
static struct isl_mat *isl_basic_set_scan_samples(struct isl_basic_set *bset)
{
	isl_ctx *ctx;
	unsigned dim;
	struct scan_samples ss;

	ctx = isl_basic_set_get_ctx(bset);
	dim = isl_basic_set_total_dim(bset);
	ss.callback.add = scan_samples_add_sample;
	ss.samples = isl_mat_alloc(ctx, 0, 1 + dim);
	if (!ss.samples)
		goto error;

	if (isl_basic_set_scan(bset, &ss.callback) < 0) {
		isl_mat_free(ss.samples);
		return NULL;
	}

	return ss.samples;
error:
	isl_basic_set_free(bset);
	return NULL;
}
示例#13
0
/* Look for all integer points in "bset", which is assumed to be bounded,
 * and call callback->add on each of them.
 *
 * We first compute a reduced basis for the set and then scan
 * the set in the directions of this basis.
 * We basically perform a depth first search, where in each level i
 * we compute the range in the i-th basis vector direction, given
 * fixed values in the directions of the previous basis vector.
 * We then add an equality to the tableau fixing the value in the
 * direction of the current basis vector to each value in the range
 * in turn and then continue to the next level.
 *
 * The search is implemented iteratively.  "level" identifies the current
 * basis vector.  "init" is true if we want the first value at the current
 * level and false if we want the next value.
 * Solutions are added in the leaves of the search tree, i.e., after
 * we have fixed a value in each direction of the basis.
 */
int isl_basic_set_scan(struct isl_basic_set *bset,
	struct isl_scan_callback *callback)
{
	unsigned dim;
	struct isl_mat *B = NULL;
	struct isl_tab *tab = NULL;
	struct isl_vec *min;
	struct isl_vec *max;
	struct isl_tab_undo **snap;
	int level;
	int init;
	enum isl_lp_result res;

	if (!bset)
		return -1;

	dim = isl_basic_set_total_dim(bset);
	if (dim == 0)
		return scan_0D(bset, callback);

	min = isl_vec_alloc(bset->ctx, dim);
	max = isl_vec_alloc(bset->ctx, dim);
	snap = isl_alloc_array(bset->ctx, struct isl_tab_undo *, dim);

	if (!min || !max || !snap)
		goto error;

	tab = isl_tab_from_basic_set(bset, 0);
	if (!tab)
		goto error;
	if (isl_tab_extend_cons(tab, dim + 1) < 0)
		goto error;

	tab->basis = isl_mat_identity(bset->ctx, 1 + dim);
	if (1)
		tab = isl_tab_compute_reduced_basis(tab);
	if (!tab)
		goto error;
	B = isl_mat_copy(tab->basis);
	if (!B)
		goto error;

	level = 0;
	init = 1;

	while (level >= 0) {
		int empty = 0;
		if (init) {
			res = isl_tab_min(tab, B->row[1 + level],
				    bset->ctx->one, &min->el[level], NULL, 0);
			if (res == isl_lp_empty)
				empty = 1;
			if (res == isl_lp_error || res == isl_lp_unbounded)
				goto error;
			isl_seq_neg(B->row[1 + level] + 1,
				    B->row[1 + level] + 1, dim);
			res = isl_tab_min(tab, B->row[1 + level],
				    bset->ctx->one, &max->el[level], NULL, 0);
			isl_seq_neg(B->row[1 + level] + 1,
				    B->row[1 + level] + 1, dim);
			isl_int_neg(max->el[level], max->el[level]);
			if (res == isl_lp_empty)
				empty = 1;
			if (res == isl_lp_error || res == isl_lp_unbounded)
				goto error;
			snap[level] = isl_tab_snap(tab);
		} else
			isl_int_add_ui(min->el[level], min->el[level], 1);

		if (empty || isl_int_gt(min->el[level], max->el[level])) {
			level--;
			init = 0;
			if (level >= 0)
				if (isl_tab_rollback(tab, snap[level]) < 0)
					goto error;
			continue;
		}
		if (level == dim - 1 && callback->add == increment_counter) {
			if (increment_range(callback,
					    min->el[level], max->el[level]))
				goto error;
			level--;
			init = 0;
			if (level >= 0)
				if (isl_tab_rollback(tab, snap[level]) < 0)
					goto error;
			continue;
		}
		isl_int_neg(B->row[1 + level][0], min->el[level]);
		if (isl_tab_add_valid_eq(tab, B->row[1 + level]) < 0)
			goto error;
		isl_int_set_si(B->row[1 + level][0], 0);
		if (level < dim - 1) {
			++level;
			init = 1;
			continue;
		}
		if (add_solution(tab, callback) < 0)
			goto error;
		init = 0;
		if (isl_tab_rollback(tab, snap[level]) < 0)
			goto error;
	}

	isl_tab_free(tab);
	free(snap);
	isl_vec_free(min);
	isl_vec_free(max);
	isl_basic_set_free(bset);
	isl_mat_free(B);
	return 0;
error:
	isl_tab_free(tab);
	free(snap);
	isl_vec_free(min);
	isl_vec_free(max);
	isl_basic_set_free(bset);
	isl_mat_free(B);
	return -1;
}
示例#14
0
/* 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;
}
示例#15
0
/* 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;
}
示例#16
0
/* 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;
}
示例#17
0
/* Given a set of equalities
 *
 *		M x - c = 0
 *
 * this function computes a unimodular transformation from a lower-dimensional
 * space to the original space that bijectively maps the integer points x'
 * in the lower-dimensional space to the integer points x in the original
 * space that satisfy the equalities.
 *
 * The input is given as a matrix B = [ -c M ] and the output is a
 * matrix that maps [1 x'] to [1 x].
 * If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x'].
 *
 * 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
 *
 *		H1 x1' - c = 0   or   x1' = H1^{-1} c = c'
 *
 * If any of the c' is non-integer, then the original set has no
 * integer solutions (since the x' are a unimodular transformation
 * of the x) and a zero-column matrix is returned.
 * Otherwise, the transformation is given by
 *
 *		x = U1 H1^{-1} c + U2 x2'
 *
 * The inverse transformation is simply
 *
 *		x2' = Q2 x
 */
__isl_give isl_mat *isl_mat_variable_compression(__isl_take isl_mat *B,
	__isl_give isl_mat **T2)
{
	int i;
	struct isl_mat *H = NULL, *C = NULL, *H1, *U = NULL, *U1, *U2, *TC;
	unsigned dim;

	if (T2)
		*T2 = NULL;
	if (!B)
		goto error;

	dim = B->n_col - 1;
	H = isl_mat_sub_alloc(B, 0, B->n_row, 1, dim);
	H = isl_mat_left_hermite(H, 0, &U, T2);
	if (!H || !U || (T2 && !*T2))
		goto error;
	if (T2) {
		*T2 = isl_mat_drop_rows(*T2, 0, B->n_row);
		*T2 = isl_mat_lin_to_aff(*T2);
		if (!*T2)
			goto error;
	}
	C = isl_mat_alloc(B->ctx, 1+B->n_row, 1);
	if (!C)
		goto error;
	isl_int_set_si(C->row[0][0], 1);
	isl_mat_sub_neg(C->ctx, C->row+1, B->row, B->n_row, 0, 0, 1);
	H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
	H1 = isl_mat_lin_to_aff(H1);
	TC = isl_mat_inverse_product(H1, C);
	if (!TC)
		goto error;
	isl_mat_free(H);
	if (!isl_int_is_one(TC->row[0][0])) {
		for (i = 0; i < B->n_row; ++i) {
			if (!isl_int_is_divisible_by(TC->row[1+i][0], TC->row[0][0])) {
				struct isl_ctx *ctx = B->ctx;
				isl_mat_free(B);
				isl_mat_free(TC);
				isl_mat_free(U);
				if (T2) {
					isl_mat_free(*T2);
					*T2 = NULL;
				}
				return isl_mat_alloc(ctx, 1 + dim, 0);
			}
			isl_seq_scale_down(TC->row[1+i], TC->row[1+i], TC->row[0][0], 1);
		}
		isl_int_set_si(TC->row[0][0], 1);
	}
	U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, B->n_row);
	U1 = isl_mat_lin_to_aff(U1);
	U2 = isl_mat_sub_alloc(U, 0, U->n_row, B->n_row, U->n_row - B->n_row);
	U2 = isl_mat_lin_to_aff(U2);
	isl_mat_free(U);
	TC = isl_mat_product(U1, TC);
	TC = isl_mat_aff_direct_sum(TC, U2);

	isl_mat_free(B);

	return TC;
error:
	isl_mat_free(B);
	isl_mat_free(H);
	isl_mat_free(U);
	if (T2) {
		isl_mat_free(*T2);
		*T2 = NULL;
	}
	return NULL;
}
示例#18
0
/* Given a tableau of a set and a tableau of the corresponding
 * recession cone, detect and add all equalities to the tableau.
 * If the tableau is bounded, then we can simply keep the
 * tableau in its state after the return from extend_affine_hull.
 * However, if the tableau is unbounded, then
 * isl_tab_set_initial_basis_with_cone will add some additional
 * constraints to the tableau that have to be removed again.
 * In this case, we therefore rollback to the state before
 * any constraints were added and then add the equalities back in.
 */
struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
	struct isl_tab *tab_cone)
{
	int j;
	struct isl_vec *sample;
	struct isl_basic_set *hull;
	struct isl_tab_undo *snap;

	if (!tab || !tab_cone)
		goto error;

	snap = isl_tab_snap(tab);

	isl_mat_free(tab->basis);
	tab->basis = NULL;

	isl_assert(tab->mat->ctx, tab->bmap, goto error);
	isl_assert(tab->mat->ctx, tab->samples, goto error);
	isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
	isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error);

	if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0)
		goto error;

	sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
	if (!sample)
		goto error;

	isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size);

	isl_vec_free(tab->bmap->sample);
	tab->bmap->sample = isl_vec_copy(sample);

	if (tab->n_unbounded == 0)
		hull = isl_basic_set_from_vec(isl_vec_copy(sample));
	else
		hull = initial_hull(tab, isl_vec_copy(sample));

	for (j = tab->n_outside + 1; j < tab->n_sample; ++j) {
		isl_seq_cpy(sample->el, tab->samples->row[j], sample->size);
		hull = affine_hull(hull,
				isl_basic_set_from_vec(isl_vec_copy(sample)));
	}

	isl_vec_free(sample);

	hull = extend_affine_hull(tab, hull);
	if (!hull)
		goto error;

	if (tab->n_unbounded == 0) {
		isl_basic_set_free(hull);
		return tab;
	}

	if (isl_tab_rollback(tab, snap) < 0)
		goto error;

	if (hull->n_eq > tab->n_zero) {
		for (j = 0; j < hull->n_eq; ++j) {
			isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var);
			if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
				goto error;
		}
	}

	isl_basic_set_free(hull);

	return tab;
error:
	isl_tab_free(tab);
	return NULL;
}
示例#19
0
/* 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;
}