/*

 * Copyright 2011      INRIA Saclay

 * Copyright 2012-2014 Ecole Normale Superieure

 *

 * Use of this software is governed by the MIT license

 *

 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,

 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,

 * 91893 Orsay, France

 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France

 */

#include <isl_ctx_private.h>

#include <isl_map_private.h>

#include <isl_local_space_private.h>

#include <isl_space_private.h>

#include <isl_mat_private.h>

#include <isl_aff_private.h>

#include <isl_vec_private.h>

#include <isl_seq.h>

isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)

{

	return ls ? ls->dim->ctx : NULL;

}

__isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,

	__isl_take isl_mat *div)

{

	isl_ctx *ctx;

	isl_local_space *ls = NULL;

	if (!dim || !div)

		goto error;

	ctx = isl_space_get_ctx(dim);

	ls = isl_calloc_type(ctx, struct isl_local_space);

	if (!ls)

		goto error;

	ls->ref = 1;

	ls->dim = dim;

	ls->div = div;

	return ls;

error:

	isl_mat_free(div);

	isl_space_free(dim);

	isl_local_space_free(ls);

	return NULL;

}

__isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,

	unsigned n_div)

{

	isl_ctx *ctx;

	isl_mat *div;

	unsigned total;

	if (!dim)

		return NULL;

	total = isl_space_dim(dim, isl_dim_all);

	ctx = isl_space_get_ctx(dim);

	div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);

	return isl_local_space_alloc_div(dim, div);

}

__isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)

{

	return isl_local_space_alloc(dim, 0);

}

__isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)

{

	if (!ls)

		return NULL;

	ls->ref++;

	return ls;

}

__isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)

{

	if (!ls)

		return NULL;

	return isl_local_space_alloc_div(isl_space_copy(ls->dim),

					 isl_mat_copy(ls->div));

}

__isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)

{

	if (!ls)

		return NULL;

	if (ls->ref == 1)

		return ls;

	ls->ref--;

	return isl_local_space_dup(ls);

}

__isl_null isl_local_space *isl_local_space_free(

	__isl_take isl_local_space *ls)

{

	if (!ls)

		return NULL;

	if (--ls->ref > 0)

		return NULL;

	isl_space_free(ls->dim);

	isl_mat_free(ls->div);

	free(ls);

	return NULL;

}

/* Is the local space that of a set?

 */

int isl_local_space_is_set(__isl_keep isl_local_space *ls)

{

	return ls ? isl_space_is_set(ls->dim) : -1;

}

/* Return true if the two local spaces are identical, with identical

 * expressions for the integer divisions.

 */

int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,

	__isl_keep isl_local_space *ls2)

{

	int equal;

	if (!ls1 || !ls2)

		return -1;

	equal = isl_space_is_equal(ls1->dim, ls2->dim);

	if (equal < 0 || !equal)

		return equal;

	if (!isl_local_space_divs_known(ls1))

		return 0;

	if (!isl_local_space_divs_known(ls2))

		return 0;

	return isl_mat_is_equal(ls1->div, ls2->div);

}

/* Compare two isl_local_spaces.

 *

 * Return -1 if "ls1" is "smaller" than "ls2", 1 if "ls1" is "greater"

 * than "ls2" and 0 if they are equal.

 *

 * The order is fairly arbitrary.  We do "prefer" divs that only involve

 * earlier dimensions in the sense that we consider local spaces where

 * the first differing div involves earlier dimensions to be smaller.

 */

int isl_local_space_cmp(__isl_keep isl_local_space *ls1,

	__isl_keep isl_local_space *ls2)

{

	int i;

	int cmp;

	int known1, known2;

	int last1, last2;

	int n_col;

	if (ls1 == ls2)

		return 0;

	if (!ls1)

		return -1;

	if (!ls2)

		return 1;

	cmp = isl_space_cmp(ls1->dim, ls2->dim);

	if (cmp != 0)

		return cmp;

	if (ls1->div->n_row != ls2->div->n_row)

		return ls1->div->n_row - ls2->div->n_row;

	n_col = isl_mat_cols(ls1->div);

	for (i = 0; i < ls1->div->n_row; ++i) {

		known1 = isl_local_space_div_is_known(ls1, i);

		known2 = isl_local_space_div_is_known(ls2, i);

		if (!known1 && !known2)

			continue;

		if (!known1)

			return 1;

		if (!known2)

			return -1;

		last1 = isl_seq_last_non_zero(ls1->div->row[i] + 1, n_col - 1);

		last2 = isl_seq_last_non_zero(ls2->div->row[i] + 1, n_col - 1);

		if (last1 != last2)

			return last1 - last2;

		cmp = isl_seq_cmp(ls1->div->row[i], ls2->div->row[i], n_col);

		if (cmp != 0)

			return cmp;

	}

	return 0;

}

int isl_local_space_dim(__isl_keep isl_local_space *ls,

	enum isl_dim_type type)

{

	if (!ls)

		return 0;

	if (type == isl_dim_div)

		return ls->div->n_row;

	if (type == isl_dim_all)

		return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;

	return isl_space_dim(ls->dim, type);

}

unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,

	enum isl_dim_type type)

{

	isl_space *dim;

	if (!ls)

		return 0;

	dim = ls->dim;

	switch (type) {

	case isl_dim_cst:	return 0;

	case isl_dim_param:	return 1;

	case isl_dim_in:	return 1 + dim->nparam;

	case isl_dim_out:	return 1 + dim->nparam + dim->n_in;

	case isl_dim_div:	return 1 + dim->nparam + dim->n_in + dim->n_out;

	default:		return 0;

	}

}

/* Does the given dimension have a name?

 */

int isl_local_space_has_dim_name(__isl_keep isl_local_space *ls,

	enum isl_dim_type type, unsigned pos)

{

	return ls ? isl_space_has_dim_name(ls->dim, type, pos) : -1;

}

const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,

	enum isl_dim_type type, unsigned pos)

{

	return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;

}

int isl_local_space_has_dim_id(__isl_keep isl_local_space *ls,

	enum isl_dim_type type, unsigned pos)

{

	return ls ? isl_space_has_dim_id(ls->dim, type, pos) : -1;

}

__isl_give isl_id *isl_local_space_get_dim_id(__isl_keep isl_local_space *ls,

	enum isl_dim_type type, unsigned pos)

{

	return ls ? isl_space_get_dim_id(ls->dim, type, pos) : NULL;

}

__isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,

	int pos)

{

	isl_aff *aff;

	if (!ls)

		return NULL;

	if (pos < 0 || pos >= ls->div->n_row)

		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,

			"index out of bounds", return NULL);

	if (isl_int_is_zero(ls->div->row[pos][0]))

		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,

			"expression of div unknown", return NULL);

	if (!isl_local_space_is_set(ls))

		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,

			"cannot represent divs of map spaces", return NULL);

	aff = isl_aff_alloc(isl_local_space_copy(ls));

	if (!aff)

		return NULL;

	isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);

	return aff;

}

__isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)

{

	if (!ls)

		return NULL;

	return isl_space_copy(ls->dim);

}

/* Replace the identifier of the tuple of type "type" by "id".

 */

__isl_give isl_local_space *isl_local_space_set_tuple_id(

	__isl_take isl_local_space *ls,

	enum isl_dim_type type, __isl_take isl_id *id)

{

	ls = isl_local_space_cow(ls);

	if (!ls)

		goto error;

	ls->dim = isl_space_set_tuple_id(ls->dim, type, id);

	if (!ls->dim)

		return isl_local_space_free(ls);

	return ls;

error:

	isl_id_free(id);

	return NULL;

}

__isl_give isl_local_space *isl_local_space_set_dim_name(

	__isl_take isl_local_space *ls,

	enum isl_dim_type type, unsigned pos, const char *s)

{

	ls = isl_local_space_cow(ls);

	if (!ls)

		return NULL;

	ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);

	if (!ls->dim)

		return isl_local_space_free(ls);

	return ls;

}

__isl_give isl_local_space *isl_local_space_set_dim_id(

	__isl_take isl_local_space *ls,

	enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)

{

	ls = isl_local_space_cow(ls);

	if (!ls)

		goto error;

	ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);

	if (!ls->dim)

		return isl_local_space_free(ls);

	return ls;

error:

	isl_id_free(id);

	return NULL;

}

__isl_give isl_local_space *isl_local_space_reset_space(

	__isl_take isl_local_space *ls, __isl_take isl_space *dim)

{

	ls = isl_local_space_cow(ls);

	if (!ls || !dim)

		goto error;

	isl_space_free(ls->dim);

	ls->dim = dim;

	return ls;

error:

	isl_local_space_free(ls);

	isl_space_free(dim);

	return NULL;

}

/* Reorder the columns of the given div definitions according to the

 * given reordering.

 * The order of the divs themselves is assumed not to change.

 */

static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,

	__isl_take isl_reordering *r)

{

	int i, j;

	isl_mat *mat;

	int extra;

	if (!div || !r)

		goto error;

	extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;

	mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);

	if (!mat)

		goto error;

	for (i = 0; i < div->n_row; ++i) {

		isl_seq_cpy(mat->row[i], div->row[i], 2);

		isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);

		for (j = 0; j < r->len; ++j)

			isl_int_set(mat->row[i][2 + r->pos[j]],

				    div->row[i][2 + j]);

	}

	isl_reordering_free(r);

	isl_mat_free(div);

	return mat;

error:

	isl_reordering_free(r);

	isl_mat_free(div);

	return NULL;

}

/* Reorder the dimensions of "ls" according to the given reordering.

 * The reordering r is assumed to have been extended with the local

 * variables, leaving them in the same order.

 */

__isl_give isl_local_space *isl_local_space_realign(

	__isl_take isl_local_space *ls, __isl_take isl_reordering *r)

{

	ls = isl_local_space_cow(ls);

	if (!ls || !r)

		goto error;

	ls->div = reorder_divs(ls->div, isl_reordering_copy(r));

	if (!ls->div)

		goto error;

	ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));

	isl_reordering_free(r);

	return ls;

error:

	isl_local_space_free(ls);

	isl_reordering_free(r);

	return NULL;

}

__isl_give isl_local_space *isl_local_space_add_div(

	__isl_take isl_local_space *ls, __isl_take isl_vec *div)

{

	ls = isl_local_space_cow(ls);

	if (!ls || !div)

		goto error;

	if (ls->div->n_col != div->size)

		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,

			"incompatible dimensions", goto error);

	ls->div = isl_mat_add_zero_cols(ls->div, 1);

	ls->div = isl_mat_add_rows(ls->div, 1);

	if (!ls->div)

		goto error;

	isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);

	isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);

	isl_vec_free(div);

	return ls;

error:

	isl_local_space_free(ls);

	isl_vec_free(div);

	return NULL;

}

__isl_give isl_local_space *isl_local_space_replace_divs(

	__isl_take isl_local_space *ls, __isl_take isl_mat *div)

{

	ls = isl_local_space_cow(ls);

	if (!ls || !div)

		goto error;

	isl_mat_free(ls->div);

	ls->div = div;

	return ls;

error:

	isl_mat_free(div);

	isl_local_space_free(ls);

	return NULL;

}

/* Copy row "s" of "src" to row "d" of "dst", applying the expansion

 * defined by "exp".

 */

static void expand_row(__isl_keep isl_mat *dst, int d,

	__isl_keep isl_mat *src, int s, int *exp)

{

	int i;

	unsigned c = src->n_col - src->n_row;

	isl_seq_cpy(dst->row[d], src->row[s], c);

	isl_seq_clr(dst->row[d] + c, dst->n_col - c);

	for (i = 0; i < s; ++i)

		isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);

}

/* Compare (known) divs.

 * Return non-zero if at least one of the two divs is unknown.

 * In particular, if both divs are unknown, we respect their

 * current order.  Otherwise, we sort the known div after the unknown

 * div only if the known div depends on the unknown div.

 */

static int cmp_row(isl_int *row_i, isl_int *row_j, int i, int j,

	unsigned n_row, unsigned n_col)

{

	int li, lj;

	int unknown_i, unknown_j;

	unknown_i = isl_int_is_zero(row_i[0]);

	unknown_j = isl_int_is_zero(row_j[0]);

	if (unknown_i && unknown_j)

		return i - j;

	if (unknown_i)

		li = n_col - n_row + i;

	else

		li = isl_seq_last_non_zero(row_i, n_col);

	if (unknown_j)

		lj = n_col - n_row + j;

	else

		lj = isl_seq_last_non_zero(row_j, n_col);

	if (li != lj)

		return li - lj;

	return isl_seq_cmp(row_i, row_j, n_col);

}

/* Call cmp_row for divs in a matrix.

 */

int isl_mat_cmp_div(__isl_keep isl_mat *div, int i, int j)

{

	return cmp_row(div->row[i], div->row[j], i, j, div->n_row, div->n_col);

}

/* Call cmp_row for divs in a basic map.

 */

static int bmap_cmp_row(__isl_keep isl_basic_map *bmap, int i, int j,

	unsigned total)

{

	return cmp_row(bmap->div[i], bmap->div[j], i, j, bmap->n_div, total);

}

/* Sort the divs in "bmap".

 *

 * We first make sure divs are placed after divs on which they depend.

 * Then we perform a simple insertion sort based on the same ordering

 * that is used in isl_merge_divs.

 */

__isl_give isl_basic_map *isl_basic_map_sort_divs(

	__isl_take isl_basic_map *bmap)

{

	int i, j;

	unsigned total;

	bmap = isl_basic_map_order_divs(bmap);

	if (!bmap)

		return NULL;

	if (bmap->n_div <= 1)

		return bmap;

	total = 2 + isl_basic_map_total_dim(bmap);

	for (i = 1; i < bmap->n_div; ++i) {

		for (j = i - 1; j >= 0; --j) {

			if (bmap_cmp_row(bmap, j, j + 1, total) <= 0)

				break;

			isl_basic_map_swap_div(bmap, j, j + 1);

		}

	}

	return bmap;

}

/* Sort the divs in the basic maps of "map".

 */

__isl_give isl_map *isl_map_sort_divs(__isl_take isl_map *map)

{

	return isl_map_inline_foreach_basic_map(map, &isl_basic_map_sort_divs);

}

/* Combine the two lists of divs into a single list.

 * For each row i in div1, exp1[i] is set to the position of the corresponding

 * row in the result.  Similarly for div2 and exp2.

 * This function guarantees

 *	exp1[i] >= i

 *	exp1[i+1] > exp1[i]

 * For optimal merging, the two input list should have been sorted.

 */

__isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,

	__isl_keep isl_mat *div2, int *exp1, int *exp2)

{

	int i, j, k;

	isl_mat *div = NULL;

	unsigned d;

	if (!div1 || !div2)

		return NULL;

	d = div1->n_col - div1->n_row;

	div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,

				d + div1->n_row + div2->n_row);

	if (!div)

		return NULL;

	for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {

		int cmp;

		expand_row(div, k, div1, i, exp1);

		expand_row(div, k + 1, div2, j, exp2);

		cmp = isl_mat_cmp_div(div, k, k + 1);

		if (cmp == 0) {

			exp1[i++] = k;

			exp2[j++] = k;

		} else if (cmp < 0) {

			exp1[i++] = k;

		} else {

			exp2[j++] = k;

			isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);

		}

	}

	for (; i < div1->n_row; ++i, ++k) {

		expand_row(div, k, div1, i, exp1);

		exp1[i] = k;

	}

	for (; j < div2->n_row; ++j, ++k) {

		expand_row(div, k, div2, j, exp2);

		exp2[j] = k;

	}

	div->n_row = k;

	div->n_col = d + k;

	return div;

}

/* Swap divs "a" and "b" in "ls".

 */

__isl_give isl_local_space *isl_local_space_swap_div(

	__isl_take isl_local_space *ls, int a, int b)

{

	int offset;

	ls = isl_local_space_cow(ls);

	if (!ls)

		return NULL;

	if (a < 0 || a >= ls->div->n_row || b < 0 || b >= ls->div->n_row)

		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,

			"index out of bounds", return isl_local_space_free(ls));

	offset = ls->div->n_col - ls->div->n_row;

	ls->div = isl_mat_swap_cols(ls->div, offset + a, offset + b);

	ls->div = isl_mat_swap_rows(ls->div, a, b);

	if (!ls->div)

		return isl_local_space_free(ls);

	return ls;

}

/* Construct a local space that contains all the divs in either

 * "ls1" or "ls2".

 */

__isl_give isl_local_space *isl_local_space_intersect(

	__isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)

{

	isl_ctx *ctx;

	int *exp1 = NULL;

	int *exp2 = NULL;

	isl_mat *div;

	int equal;

	if (!ls1 || !ls2)

		goto error;

	ctx = isl_local_space_get_ctx(ls1);

	if (!isl_space_is_equal(ls1->dim, ls2->dim))

		isl_die(ctx, isl_error_invalid,

			"spaces should be identical", goto error);

	if (ls2->div->n_row == 0) {

		isl_local_space_free(ls2);

		return ls1;

	}

	if (ls1->div->n_row == 0) {

		isl_local_space_free(ls1);

		return ls2;

	}

	exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);

	exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);

	if (!exp1 || !exp2)

		goto error;

	div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);

	if (!div)

		goto error;

	equal = isl_mat_is_equal(ls1->div, div);

	if (equal < 0)

		goto error;

	if (!equal)

		ls1 = isl_local_space_cow(ls1);

	if (!ls1)

		goto error;

	free(exp1);

	free(exp2);

	isl_local_space_free(ls2);

	isl_mat_free(ls1->div);

	ls1->div = div;

	return ls1;

error:

	free(exp1);

	free(exp2);

	isl_local_space_free(ls1);

	isl_local_space_free(ls2);

	return NULL;

}

/* Does "ls" have an explicit representation for div "div"?

 */

int isl_local_space_div_is_known(__isl_keep isl_local_space *ls, int div)

{

	if (!ls)

		return -1;

	if (div < 0 || div >= ls->div->n_row)

		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,

			"position out of bounds", return -1);

	return !isl_int_is_zero(ls->div->row[div][0]);

}

int isl_local_space_divs_known(__isl_keep isl_local_space *ls)

{

	int i;

	if (!ls)

		return -1;

	for (i = 0; i < ls->div->n_row; ++i)

		if (isl_int_is_zero(ls->div->row[i][0]))

			return 0;

	return 1;

}

__isl_give isl_local_space *isl_local_space_domain(

	__isl_take isl_local_space *ls)

{

	ls = isl_local_space_drop_dims(ls, isl_dim_out,

					0, isl_local_space_dim(ls, isl_dim_out));

	ls = isl_local_space_cow(ls);

	if (!ls)

		return NULL;

	ls->dim = isl_space_domain(ls->dim);

	if (!ls->dim)

		return isl_local_space_free(ls);

	return ls;

}

__isl_give isl_local_space *isl_local_space_range(

	__isl_take isl_local_space *ls)

{

	ls = isl_local_space_drop_dims(ls, isl_dim_in,

					0, isl_local_space_dim(ls, isl_dim_in));

	ls = isl_local_space_cow(ls);

	if (!ls)

		return NULL;

	ls->dim = isl_space_range(ls->dim);

	if (!ls->dim)

		return isl_local_space_free(ls);

	return ls;

}

/* Construct a local space for a map that has the given local

 * space as domain and that has a zero-dimensional range.

 */

__isl_give isl_local_space *isl_local_space_from_domain(

	__isl_take isl_local_space *ls)

{

	ls = isl_local_space_cow(ls);

	if (!ls)

		return NULL;

	ls->dim = isl_space_from_domain(ls->dim);

	if (!ls->dim)

		return isl_local_space_free(ls);

	return ls;

}

__isl_give isl_local_space *isl_local_space_add_dims(

	__isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)

{

	int pos;

	if (!ls)

		return NULL;

	pos = isl_local_space_dim(ls, type);

	return isl_local_space_insert_dims(ls, type, pos, n);

}

/* Remove common factor of non-constant terms and denominator.

 */

static void normalize_div(__isl_keep isl_local_space *ls, int div)

{

	isl_ctx *ctx = ls->div->ctx;

	unsigned total = ls->div->n_col - 2;

	isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);

	isl_int_gcd(ctx->normalize_gcd,

		    ctx->normalize_gcd, ls->div->row[div][0]);

	if (isl_int_is_one(ctx->normalize_gcd))

		return;

	isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,

			    ctx->normalize_gcd, total);

	isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],

			    ctx->normalize_gcd);

	isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],

			    ctx->normalize_gcd);

}

/* Exploit the equalities in "eq" to simplify the expressions of

 * the integer divisions in "ls".

 * The integer divisions in "ls" are assumed to appear as regular

 * dimensions in "eq".

 */

__isl_give isl_local_space *isl_local_space_substitute_equalities(

	__isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)

{

	int i, j, k;

	unsigned total;

	unsigned n_div;

	if (!ls || !eq)

		goto error;

	total = isl_space_dim(eq->dim, isl_dim_all);

	if (isl_local_space_dim(ls, isl_dim_all) != total)

		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,

			"spaces don't match", goto error);

	total++;

	n_div = eq->n_div;

	for (i = 0; i < eq->n_eq; ++i) {

		j = isl_seq_last_non_zero(eq->eq[i], total + n_div);

		if (j < 0 || j == 0 || j >= total)

			continue;

		for (k = 0; k < ls->div->n_row; ++k) {

			if (isl_int_is_zero(ls->div->row[k][1 + j]))

				continue;

			ls = isl_local_space_cow(ls);

			if (!ls)

				goto error;

			ls->div = isl_mat_cow(ls->div);

			if (!ls->div)

				goto error;

			isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,

					&ls->div->row[k][0]);

			normalize_div(ls, k);

		}

	}

	isl_basic_set_free(eq);

	return ls;

error:

	isl_basic_set_free(eq);

	isl_local_space_free(ls);

	return NULL;

}

/* Plug in the affine expressions "subs" of length "subs_len" (including

 * the denominator and the constant term) into the variable at position "pos"

 * of the "n" div expressions starting at "first".

 *

 * Let i be the dimension to replace and let "subs" be of the form

 *

 *	f/d

 *

 * Any integer division starting at "first" with a non-zero coefficient for i,

 *

 *	floor((a i + g)/m)

 *

 * is replaced by

 *

 *	floor((a f + d g)/(m d))

 */

__isl_give isl_local_space *isl_local_space_substitute_seq(

	__isl_take isl_local_space *ls,

	enum isl_dim_type type, unsigned pos, isl_int *subs, int subs_len,

	int first, int n)

{

	int i;