X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_local_space.c;h=a8e5ebacb39a5cdb935a1099ee6d81aa9e850873;hb=6d28e7c5ff2b41ec88fa32664cc446807af5843d;hp=8a6b91932d03f76806226587172bd1d76cf080d7;hpb=e14271136a0bbbd05dd38ac1ff435471a808eada;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_local_space.c b/isl_local_space.c
index 8a6b919..a8e5eba 100644
--- a/isl_local_space.c
+++ b/isl_local_space.c
@@ -1,18 +1,21 @@
 /*
  * Copyright 2011      INRIA Saclay
+ * Copyright 2012      Ecole Normale Superieure
  *
- * Use of this software is governed by the GNU LGPLv2.1 license
+ * 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_dim_private.h>
+#include <isl_space_private.h>
 #include <isl_mat_private.h>
+#include <isl_aff_private.h>
 #include <isl/seq.h>
 
 isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
@@ -20,16 +23,16 @@ 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_dim *dim,
+__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)
+	if (!dim || !div)
 		goto error;
 
-	ctx = isl_dim_get_ctx(dim);
+	ctx = isl_space_get_ctx(dim);
 	ls = isl_calloc_type(ctx, struct isl_local_space);
 	if (!ls)
 		goto error;
@@ -40,12 +43,13 @@ __isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_dim *dim,
 
 	return ls;
 error:
-	isl_dim_free(dim);
+	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_dim *dim,
+__isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
 	unsigned n_div)
 {
 	isl_ctx *ctx;
@@ -55,14 +59,14 @@ __isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_dim *dim,
 	if (!dim)
 		return NULL;
 
-	total = isl_dim_total(dim);
+	total = isl_space_dim(dim, isl_dim_all);
 
-	ctx = isl_dim_get_ctx(dim);
+	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_dim(__isl_take isl_dim *dim)
+__isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
 {
 	return isl_local_space_alloc(dim, 0);
 }
@@ -81,7 +85,7 @@ __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_dim_copy(ls->dim),
+	return isl_local_space_alloc_div(isl_space_copy(ls->dim),
 					 isl_mat_copy(ls->div));
 
 }
@@ -105,7 +109,7 @@ void *isl_local_space_free(__isl_take isl_local_space *ls)
 	if (--ls->ref > 0)
 		return NULL;
 
-	isl_dim_free(ls->dim);
+	isl_space_free(ls->dim);
 	isl_mat_free(ls->div);
 
 	free(ls);
@@ -113,6 +117,13 @@ void *isl_local_space_free(__isl_take isl_local_space *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.
  */
@@ -124,10 +135,15 @@ int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
 	if (!ls1 || !ls2)
 		return -1;
 
-	equal = isl_dim_equal(ls1->dim, ls2->dim);
+	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);
 }
 
@@ -139,14 +155,14 @@ int isl_local_space_dim(__isl_keep isl_local_space *ls,
 	if (type == isl_dim_div)
 		return ls->div->n_row;
 	if (type == isl_dim_all)
-		return isl_dim_size(ls->dim, isl_dim_all) + ls->div->n_row;
-	return isl_dim_size(ls->dim, type);
+		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_dim *dim;
+	isl_space *dim;
 
 	if (!ls)
 		return 0;
@@ -162,16 +178,36 @@ unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
 	}
 }
 
+/* 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_dim_get_name(ls->dim, type, pos) : NULL;
+	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_div *isl_local_space_get_div(__isl_keep isl_local_space *ls,
+__isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 	int pos)
 {
-	isl_basic_map *bmap;
+	isl_aff *aff;
 
 	if (!ls)
 		return NULL;
@@ -180,16 +216,26 @@ __isl_give isl_div *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 			"index out of bounds", return NULL);
 
-	bmap = isl_basic_map_from_local_space(isl_local_space_copy(ls));
-	return isl_basic_map_div(bmap, pos);
+	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_dim *isl_local_space_get_dim(__isl_keep isl_local_space *ls)
+__isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 {
 	if (!ls)
 		return NULL;
 
-	return isl_dim_copy(ls->dim);
+	return isl_space_copy(ls->dim);
 }
 
 __isl_give isl_local_space *isl_local_space_set_dim_name(
@@ -199,13 +245,105 @@ __isl_give isl_local_space *isl_local_space_set_dim_name(
 	ls = isl_local_space_cow(ls);
 	if (!ls)
 		return NULL;
-	ls->dim = isl_dim_set_name(ls->dim, type, pos, s);
+	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)
+		return isl_id_free(id);
+	ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
+	if (!ls->dim)
+		return isl_local_space_free(ls);
+
+	return ls;
+}
+
+__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)
 {
@@ -268,23 +406,87 @@ static void expand_row(__isl_keep isl_mat *dst, int d,
 
 /* 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_keep isl_mat *div, int i, int j)
+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;
 
-	if (isl_int_is_zero(div->row[j][0]))
-		return -1;
-	if (isl_int_is_zero(div->row[i][0]))
-		return 1;
+	unknown_i = isl_int_is_zero(row_i[0]);
+	unknown_j = isl_int_is_zero(row_j[0]);
 
-	li = isl_seq_last_non_zero(div->row[i], div->n_col);
-	lj = isl_seq_last_non_zero(div->row[j], div->n_col);
+	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(div->row[i], div->row[j], div->n_col);
+	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.
@@ -300,8 +502,12 @@ __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 {
 	int i, j, k;
 	isl_mat *div = NULL;
-	unsigned d = div1->n_col - div1->n_row;
+	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)
@@ -313,7 +519,7 @@ __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 		expand_row(div, k, div1, i, exp1);
 		expand_row(div, k + 1, div2, j, exp2);
 
-		cmp = cmp_row(div, k, k + 1);
+		cmp = isl_mat_cmp_div(div, k, k + 1);
 		if (cmp == 0) {
 			exp1[i++] = k;
 			exp2[j++] = k;
@@ -339,6 +545,80 @@ __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 	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;
+
+	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;
+
+	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;
+}
+
 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 {
 	int i;
@@ -353,6 +633,35 @@ int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 	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.
  */
@@ -362,7 +671,7 @@ __isl_give isl_local_space *isl_local_space_from_domain(
 	ls = isl_local_space_cow(ls);
 	if (!ls)
 		return NULL;
-	ls->dim = isl_dim_from_domain(ls->dim);
+	ls->dim = isl_space_from_domain(ls->dim);
 	if (!ls->dim)
 		return isl_local_space_free(ls);
 	return ls;
@@ -373,30 +682,10 @@ __isl_give isl_local_space *isl_local_space_add_dims(
 {
 	int pos;
 
-	if (n == 0)
-		return ls;
-
-	ls = isl_local_space_cow(ls);
 	if (!ls)
 		return NULL;
-
-	pos = isl_local_space_offset(ls, type);
-	pos += isl_local_space_dim(ls, type);
-
-	ls->div = isl_mat_insert_zero_cols(ls->div, 1 + pos, n);
-
-	if (type == isl_dim_div) {
-		ls->div = isl_mat_add_zero_rows(ls->div, n);
-	} else {
-		ls->dim = isl_dim_add(ls->dim, type, n);
-		if (!ls->dim)
-			return isl_local_space_free(ls);
-	}
-
-	if (!ls->div)
-		return isl_local_space_free(ls);
-
-	return ls;
+	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.
@@ -436,10 +725,10 @@ __isl_give isl_local_space *isl_local_space_substitute_equalities(
 	if (!ls || !eq)
 		goto error;
 
-	total = isl_dim_total(eq->dim);
+	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,
-			"dimensions don't match", goto error);
+			"spaces don't match", goto error);
 	total++;
 	n_div = eq->n_div;
 	for (i = 0; i < eq->n_eq; ++i) {
@@ -464,12 +753,99 @@ error:
 	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;
+	isl_int v;
+
+	if (n == 0)
+		return ls;
+	ls = isl_local_space_cow(ls);
+	if (!ls)
+		return NULL;
+	ls->div = isl_mat_cow(ls->div);
+	if (!ls->div)
+		return isl_local_space_free(ls);
+
+	if (first + n > 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));
+
+	pos += isl_local_space_offset(ls, type);
+
+	isl_int_init(v);
+	for (i = first; i < ls->div->n_row; ++i) {
+		if (isl_int_is_zero(ls->div->row[i][1 + pos]))
+			continue;
+		isl_seq_substitute(ls->div->row[i], pos, subs,
+			ls->div->n_col, subs_len, v);
+		normalize_div(ls, i);
+	}
+	isl_int_clear(v);
+
+	return ls;
+}
+
+/* Plug in "subs" for dimension "type", "pos" in the integer divisions
+ * of "ls".
+ *
+ * Let i be the dimension to replace and let "subs" be of the form
+ *
+ *	f/d
+ *
+ * Any integer division 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(
+	__isl_take isl_local_space *ls,
+	enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
+{
+	ls = isl_local_space_cow(ls);
+	if (!ls || !subs)
+		return isl_local_space_free(ls);
+
+	if (!isl_space_is_equal(ls->dim, subs->ls->dim))
+		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
+			"spaces don't match", return isl_local_space_free(ls));
+	if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
+		isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
+			"cannot handle divs yet",
+			return isl_local_space_free(ls));
+
+	return isl_local_space_substitute_seq(ls, type, pos, subs->v->el,
+					    subs->v->size, 0, ls->div->n_row);
+}
+
 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 	enum isl_dim_type type)
 {
 	if (!ls)
 		return -1;
-	return isl_dim_is_named_or_nested(ls->dim, type);
+	return isl_space_is_named_or_nested(ls->dim, type);
 }
 
 __isl_give isl_local_space *isl_local_space_drop_dims(
@@ -495,7 +871,7 @@ __isl_give isl_local_space *isl_local_space_drop_dims(
 	if (type == isl_dim_div) {
 		ls->div = isl_mat_drop_rows(ls->div, first, n);
 	} else {
-		ls->dim = isl_dim_drop(ls->dim, type, first, n);
+		ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 		if (!ls->dim)
 			return isl_local_space_free(ls);
 	}
@@ -507,3 +883,245 @@ __isl_give isl_local_space *isl_local_space_drop_dims(
 
 	return ls;
 }
+
+__isl_give isl_local_space *isl_local_space_insert_dims(
+	__isl_take isl_local_space *ls,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	isl_ctx *ctx;
+
+	if (!ls)
+		return NULL;
+	if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
+		return ls;
+
+	ctx = isl_local_space_get_ctx(ls);
+	if (first > isl_local_space_dim(ls, type))
+		isl_die(ctx, isl_error_invalid, "position out of bounds",
+			return isl_local_space_free(ls));
+
+	ls = isl_local_space_cow(ls);
+	if (!ls)
+		return NULL;
+
+	if (type == isl_dim_div) {
+		ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
+	} else {
+		ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
+		if (!ls->dim)
+			return isl_local_space_free(ls);
+	}
+
+	first += 1 + isl_local_space_offset(ls, type);
+	ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
+	if (!ls->div)
+		return isl_local_space_free(ls);
+
+	return ls;
+}
+
+/* Check if the constraints pointed to by "constraint" is a div
+ * constraint corresponding to div "div" in "ls".
+ *
+ * That is, if div = floor(f/m), then check if the constraint is
+ *
+ *		f - m d >= 0
+ * or
+ *		-(f-(m-1)) + m d >= 0
+ */
+int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
+	isl_int *constraint, unsigned div)
+{
+	unsigned pos;
+
+	if (!ls)
+		return -1;
+
+	if (isl_int_is_zero(ls->div->row[div][0]))
+		return 0;
+
+	pos = isl_local_space_offset(ls, isl_dim_div) + div;
+
+	if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
+		int neg;
+		isl_int_sub(ls->div->row[div][1],
+				ls->div->row[div][1], ls->div->row[div][0]);
+		isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
+		neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
+		isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
+		isl_int_add(ls->div->row[div][1],
+				ls->div->row[div][1], ls->div->row[div][0]);
+		if (!neg)
+			return 0;
+		if (isl_seq_first_non_zero(constraint+pos+1,
+					    ls->div->n_row-div-1) != -1)
+			return 0;
+	} else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
+		if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
+			return 0;
+		if (isl_seq_first_non_zero(constraint+pos+1,
+					    ls->div->n_row-div-1) != -1)
+			return 0;
+	} else
+		return 0;
+
+	return 1;
+}
+
+/*
+ * Set active[i] to 1 if the dimension at position i is involved
+ * in the linear expression l.
+ */
+int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
+{
+	int i, j;
+	isl_ctx *ctx;
+	int *active = NULL;
+	unsigned total;
+	unsigned offset;
+
+	ctx = isl_local_space_get_ctx(ls);
+	total = isl_local_space_dim(ls, isl_dim_all);
+	active = isl_calloc_array(ctx, int, total);
+	if (!active)
+		return NULL;
+
+	for (i = 0; i < total; ++i)
+		active[i] = !isl_int_is_zero(l[i]);
+
+	offset = isl_local_space_offset(ls, isl_dim_div) - 1;
+	for (i = ls->div->n_row - 1; i >= 0; --i) {
+		if (!active[offset + i])
+			continue;
+		for (j = 0; j < total; ++j)
+			active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
+	}
+
+	return active;
+}
+
+/* Given a local space "ls" of a set, create a local space
+ * for the lift of the set.  In particular, the result
+ * is of the form [dim -> local[..]], with ls->div->n_row variables in the
+ * range of the wrapped map.
+ */
+__isl_give isl_local_space *isl_local_space_lift(
+	__isl_take isl_local_space *ls)
+{
+	ls = isl_local_space_cow(ls);
+	if (!ls)
+		return NULL;
+
+	ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
+	ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
+	if (!ls->dim || !ls->div)
+		return isl_local_space_free(ls);
+
+	return ls;
+}
+
+/* Construct a basic map that maps a set living in local space "ls"
+ * to the corresponding lifted local space.
+ */
+__isl_give isl_basic_map *isl_local_space_lifting(
+	__isl_take isl_local_space *ls)
+{
+	isl_basic_map *lifting;
+	isl_basic_set *bset;
+
+	if (!ls)
+		return NULL;
+	if (!isl_local_space_is_set(ls))
+		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
+			"lifting only defined on set spaces",
+			return isl_local_space_free(ls));
+
+	bset = isl_basic_set_from_local_space(ls);
+	lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
+	lifting = isl_basic_map_domain_map(lifting);
+	lifting = isl_basic_map_reverse(lifting);
+
+	return lifting;
+}
+
+/* Compute the preimage of "ls" under the function represented by "ma".
+ * In other words, plug in "ma" in "ls".  The result is a local space
+ * that is part of the domain space of "ma".
+ *
+ * If the divs in "ls" are represented as
+ *
+ *	floor((a_i(p) + b_i x + c_i(divs))/n_i)
+ *
+ * and ma is represented by
+ *
+ *	x = D(p) + F(y) + G(divs')
+ *
+ * then the resulting divs are
+ *
+ *	floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
+ *
+ * We first copy over the divs from "ma" and then
+ * we add the modified divs from "ls".
+ */
+__isl_give isl_local_space *isl_local_space_preimage_multi_aff(
+	__isl_take isl_local_space *ls, __isl_take isl_multi_aff *ma)
+{
+	int i;
+	isl_space *space;
+	isl_local_space *res = NULL;
+	int n_div_ls, n_div_ma;
+	isl_int f, c1, c2, g;
+
+	ma = isl_multi_aff_align_divs(ma);
+	if (!ls || !ma)
+		goto error;
+	if (!isl_space_is_range_internal(ls->dim, ma->space))
+		isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
+			"spaces don't match", goto error);
+
+	n_div_ls = isl_local_space_dim(ls, isl_dim_div);
+	n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
+
+	space = isl_space_domain(isl_multi_aff_get_space(ma));
+	res = isl_local_space_alloc(space, n_div_ma + n_div_ls);
+	if (!res)
+		goto error;
+
+	if (n_div_ma) {
+		isl_mat_free(res->div);
+		res->div = isl_mat_copy(ma->p[0]->ls->div);
+		res->div = isl_mat_add_zero_cols(res->div, n_div_ls);
+		res->div = isl_mat_add_rows(res->div, n_div_ls);
+		if (!res->div)
+			goto error;
+	}
+
+	isl_int_init(f);
+	isl_int_init(c1);
+	isl_int_init(c2);
+	isl_int_init(g);
+
+	for (i = 0; i < ls->div->n_row; ++i) {
+		if (isl_int_is_zero(ls->div->row[i][0])) {
+			isl_int_set_si(res->div->row[n_div_ma + i][0], 0);
+			continue;
+		}
+		isl_seq_preimage(res->div->row[n_div_ma + i], ls->div->row[i],
+				ma, 0, 0, n_div_ma, n_div_ls, f, c1, c2, g, 1);
+		normalize_div(res, n_div_ma + i);
+	}
+
+	isl_int_clear(f);
+	isl_int_clear(c1);
+	isl_int_clear(c2);
+	isl_int_clear(g);
+
+	isl_local_space_free(ls);
+	isl_multi_aff_free(ma);
+	return res;
+error:
+	isl_local_space_free(ls);
+	isl_multi_aff_free(ma);
+	isl_local_space_free(res);
+	return NULL;
+}