X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_aff.c;h=1147ceafcd0d0c5283e81bb8c217fe3d3ab0da54;hb=425f35468a61002282f6bc261c0ba403ab116a2a;hp=75b1c2039996480c78b94a805914399fc4340f8a;hpb=f600853f2f7dd332a98d1a4ca58d30567d36e04a;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_aff.c b/isl_aff.c
index 75b1c20..1147cea 100644
--- a/isl_aff.c
+++ b/isl_aff.c
@@ -1,5 +1,6 @@
 /*
  * Copyright 2011      INRIA Saclay
+ * Copyright 2011      Sven Verdoolaege
  *
  * Use of this software is governed by the GNU LGPLv2.1 license
  *
@@ -8,10 +9,17 @@
  * 91893 Orsay, France
  */
 
+#include <isl_ctx_private.h>
+#include <isl_map_private.h>
 #include <isl_aff_private.h>
+#include <isl_space_private.h>
 #include <isl_local_space_private.h>
 #include <isl_mat_private.h>
+#include <isl_list_private.h>
+#include <isl/constraint.h>
 #include <isl/seq.h>
+#include <isl/set.h>
+#include <isl_config.h>
 
 __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
 	__isl_take isl_vec *v)
@@ -49,6 +57,10 @@ __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
 	if (!isl_local_space_divs_known(ls))
 		isl_die(ctx, isl_error_invalid, "local space has unknown divs",
 			goto error);
+	if (!isl_local_space_is_set(ls))
+		isl_die(ctx, isl_error_invalid,
+			"domain of affine expression should be a set",
+			goto error);
 
 	total = isl_local_space_dim(ls, isl_dim_all);
 	v = isl_vec_alloc(ctx, 1 + 1 + total);
@@ -58,7 +70,7 @@ error:
 	return NULL;
 }
 
-__isl_give isl_aff *isl_aff_zero(__isl_take isl_local_space *ls)
+__isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls)
 {
 	isl_aff *aff;
 
@@ -122,25 +134,172 @@ isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
 	return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
 }
 
+/* Externally, an isl_aff has a map space, but internally, the
+ * ls field corresponds to the domain of that space.
+ */
 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
 {
-	return aff ? isl_local_space_dim(aff->ls, type) : 0;
+	if (!aff)
+		return 0;
+	if (type == isl_dim_out)
+		return 1;
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+	return isl_local_space_dim(aff->ls, type);
 }
 
-__isl_give isl_dim *isl_aff_get_dim(__isl_keep isl_aff *aff)
+__isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff)
 {
-	return aff ? isl_local_space_get_dim(aff->ls) : NULL;
+	return aff ? isl_local_space_get_space(aff->ls) : NULL;
 }
 
-__isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
+__isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff)
+{
+	isl_space *space;
+	if (!aff)
+		return NULL;
+	space = isl_local_space_get_space(aff->ls);
+	space = isl_space_from_domain(space);
+	space = isl_space_add_dims(space, isl_dim_out, 1);
+	return space;
+}
+
+__isl_give isl_local_space *isl_aff_get_domain_local_space(
+	__isl_keep isl_aff *aff)
 {
 	return aff ? isl_local_space_copy(aff->ls) : NULL;
 }
 
+__isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
+{
+	isl_local_space *ls;
+	if (!aff)
+		return NULL;
+	ls = isl_local_space_copy(aff->ls);
+	ls = isl_local_space_from_domain(ls);
+	ls = isl_local_space_add_dims(ls, isl_dim_out, 1);
+	return ls;
+}
+
+/* Externally, an isl_aff has a map space, but internally, the
+ * ls field corresponds to the domain of that space.
+ */
 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
 	enum isl_dim_type type, unsigned pos)
 {
-	return aff ? isl_local_space_get_dim_name(aff->ls, type, pos) : 0;
+	if (!aff)
+		return NULL;
+	if (type == isl_dim_out)
+		return NULL;
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+	return isl_local_space_get_dim_name(aff->ls, type, pos);
+}
+
+__isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff,
+	__isl_take isl_space *dim)
+{
+	aff = isl_aff_cow(aff);
+	if (!aff || !dim)
+		goto error;
+
+	aff->ls = isl_local_space_reset_space(aff->ls, dim);
+	if (!aff->ls)
+		return isl_aff_free(aff);
+
+	return aff;
+error:
+	isl_aff_free(aff);
+	isl_space_free(dim);
+	return NULL;
+}
+
+/* Reset the space of "aff".  This function is called from isl_pw_templ.c
+ * and doesn't know if the space of an element object is represented
+ * directly or through its domain.  It therefore passes along both.
+ */
+__isl_give isl_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff,
+	__isl_take isl_space *space, __isl_take isl_space *domain)
+{
+	isl_space_free(space);
+	return isl_aff_reset_domain_space(aff, domain);
+}
+
+/* Reorder the coefficients of the affine expression based
+ * on the given reodering.
+ * The reordering r is assumed to have been extended with the local
+ * variables.
+ */
+static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
+	__isl_take isl_reordering *r, int n_div)
+{
+	isl_vec *res;
+	int i;
+
+	if (!vec || !r)
+		goto error;
+
+	res = isl_vec_alloc(vec->ctx,
+			    2 + isl_space_dim(r->dim, isl_dim_all) + n_div);
+	isl_seq_cpy(res->el, vec->el, 2);
+	isl_seq_clr(res->el + 2, res->size - 2);
+	for (i = 0; i < r->len; ++i)
+		isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
+
+	isl_reordering_free(r);
+	isl_vec_free(vec);
+	return res;
+error:
+	isl_vec_free(vec);
+	isl_reordering_free(r);
+	return NULL;
+}
+
+/* Reorder the dimensions of the domain of "aff" according
+ * to the given reordering.
+ */
+__isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff,
+	__isl_take isl_reordering *r)
+{
+	aff = isl_aff_cow(aff);
+	if (!aff)
+		goto error;
+
+	r = isl_reordering_extend(r, aff->ls->div->n_row);
+	aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
+				aff->ls->div->n_row);
+	aff->ls = isl_local_space_realign(aff->ls, r);
+
+	if (!aff->v || !aff->ls)
+		return isl_aff_free(aff);
+
+	return aff;
+error:
+	isl_aff_free(aff);
+	isl_reordering_free(r);
+	return NULL;
+}
+
+int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
+{
+	if (!aff)
+		return -1;
+
+	return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
+}
+
+int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
+{
+	int equal;
+
+	if (!aff1 || !aff2)
+		return -1;
+
+	equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
+	if (equal < 0 || !equal)
+		return equal;
+
+	return isl_vec_is_equal(aff1->v, aff2->v);
 }
 
 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
@@ -165,6 +324,13 @@ int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
 	if (!aff)
 		return -1;
 
+	if (type == isl_dim_out)
+		isl_die(aff->v->ctx, isl_error_invalid,
+			"output/set dimension does not have a coefficient",
+			return -1);
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+
 	if (pos >= isl_local_space_dim(aff->ls, type))
 		isl_die(aff->v->ctx, isl_error_invalid,
 			"position out of bounds", return -1);
@@ -223,6 +389,18 @@ __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
 	return aff;
 }
 
+__isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
+{
+	isl_int t;
+
+	isl_int_init(t);
+	isl_int_set_si(t, v);
+	aff = isl_aff_add_constant(aff, t);
+	isl_int_clear(t);
+
+	return aff;
+}
+
 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
 {
 	aff = isl_aff_cow(aff);
@@ -244,6 +422,13 @@ __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
 	if (!aff)
 		return NULL;
 
+	if (type == isl_dim_out)
+		isl_die(aff->v->ctx, isl_error_invalid,
+			"output/set dimension does not have a coefficient",
+			return isl_aff_free(aff));
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+
 	if (pos >= isl_local_space_dim(aff->ls, type))
 		isl_die(aff->v->ctx, isl_error_invalid,
 			"position out of bounds", return isl_aff_free(aff));
@@ -268,6 +453,13 @@ __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
 	if (!aff)
 		return NULL;
 
+	if (type == isl_dim_out)
+		isl_die(aff->v->ctx, isl_error_invalid,
+			"output/set dimension does not have a coefficient",
+			return isl_aff_free(aff));
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+
 	if (pos >= isl_local_space_dim(aff->ls, type))
 		isl_die(aff->v->ctx, isl_error_invalid,
 			"position out of bounds", return isl_aff_free(aff));
@@ -292,6 +484,13 @@ __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
 	if (!aff)
 		return NULL;
 
+	if (type == isl_dim_out)
+		isl_die(aff->v->ctx, isl_error_invalid,
+			"output/set dimension does not have a coefficient",
+			return isl_aff_free(aff));
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+
 	if (pos >= isl_local_space_dim(aff->ls, type))
 		isl_die(aff->v->ctx, isl_error_invalid,
 			"position out of bounds", return isl_aff_free(aff));
@@ -323,7 +522,7 @@ __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
 	return aff;
 }
 
-__isl_give isl_div *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
+__isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
 {
 	if (!aff)
 		return NULL;
@@ -345,14 +544,28 @@ __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
 	return aff;
 }
 
-/* Given f, return ceil(f).
+__isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
+{
+	if (!aff)
+		return NULL;
+	aff->v = isl_vec_normalize(aff->v);
+	if (!aff->v)
+		return isl_aff_free(aff);
+	return aff;
+}
+
+/* Given f, return floor(f).
  * If f is an integer expression, then just return f.
- * Otherwise, create a new div d = [-f] and return the expression -d.
+ * Otherwise, if f = g/m, write g = q m + r,
+ * create a new div d = [r/m] and return the expression q + d.
+ * The coefficients in r are taken to lie between -m/2 and m/2.
  */
-__isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
+__isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
 {
+	int i;
 	int size;
 	isl_ctx *ctx;
+	isl_vec *div;
 
 	if (!aff)
 		return NULL;
@@ -364,25 +577,88 @@ __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
 	if (!aff)
 		return NULL;
 
-	isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
-	aff->ls = isl_local_space_add_div(aff->ls, isl_vec_copy(aff->v));
-	if (!aff->ls)
-		goto error;
+	aff->v = isl_vec_cow(aff->v);
+	div = isl_vec_copy(aff->v);
+	div = isl_vec_cow(div);
+	if (!div)
+		return isl_aff_free(aff);
 
 	ctx = isl_aff_get_ctx(aff);
+	isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
+	for (i = 1; i < aff->v->size; ++i) {
+		isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
+		isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
+		if (isl_int_gt(div->el[i], aff->v->el[0])) {
+			isl_int_sub(div->el[i], div->el[i], div->el[0]);
+			isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
+		}
+	}
+
+	aff->ls = isl_local_space_add_div(aff->ls, div);
+	if (!aff->ls)
+		return isl_aff_free(aff);
+
 	size = aff->v->size;
-	isl_vec_free(aff->v);
-	aff->v = isl_vec_alloc(ctx, size + 1);
-	aff->v = isl_vec_clr(aff->v);
+	aff->v = isl_vec_extend(aff->v, size + 1);
 	if (!aff->v)
-		goto error;
+		return isl_aff_free(aff);
 	isl_int_set_si(aff->v->el[0], 1);
-	isl_int_set_si(aff->v->el[size], -1);
+	isl_int_set_si(aff->v->el[size], 1);
+
+	return aff;
+}
+
+/* Compute
+ *
+ *	aff mod m = aff - m * floor(aff/m)
+ */
+__isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m)
+{
+	isl_aff *res;
+
+	res = isl_aff_copy(aff);
+	aff = isl_aff_scale_down(aff, m);
+	aff = isl_aff_floor(aff);
+	aff = isl_aff_scale(aff, m);
+	res = isl_aff_sub(res, aff);
+
+	return res;
+}
+
+/* Compute
+ *
+ *	pwaff mod m = pwaff - m * floor(pwaff/m)
+ */
+__isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
+{
+	isl_pw_aff *res;
+
+	res = isl_pw_aff_copy(pwaff);
+	pwaff = isl_pw_aff_scale_down(pwaff, m);
+	pwaff = isl_pw_aff_floor(pwaff);
+	pwaff = isl_pw_aff_scale(pwaff, m);
+	res = isl_pw_aff_sub(res, pwaff);
+
+	return res;
+}
+
+/* Given f, return ceil(f).
+ * If f is an integer expression, then just return f.
+ * Otherwise, create a new div d = [-f] and return the expression -d.
+ */
+__isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
+{
+	if (!aff)
+		return NULL;
+
+	if (isl_int_is_one(aff->v->el[0]))
+		return aff;
+
+	aff = isl_aff_neg(aff);
+	aff = isl_aff_floor(aff);
+	aff = isl_aff_neg(aff);
 
 	return aff;
-error:
-	isl_aff_free(aff);
-	return NULL;
 }
 
 /* Apply the expansion computed by isl_merge_divs.
@@ -481,7 +757,7 @@ __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
 		goto error;
 
 	ctx = isl_aff_get_ctx(aff1);
-	if (!isl_dim_equal(aff1->ls->dim, aff2->ls->dim))
+	if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
 		isl_die(ctx, isl_error_invalid,
 			"spaces don't match", goto error);
 
@@ -562,3 +838,1627 @@ __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
 
 	return aff;
 }
+
+__isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
+{
+	isl_int v;
+
+	if (f == 1)
+		return aff;
+
+	isl_int_init(v);
+	isl_int_set_ui(v, f);
+	aff = isl_aff_scale_down(aff, v);
+	isl_int_clear(v);
+
+	return aff;
+}
+
+__isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
+	enum isl_dim_type type, unsigned pos, const char *s)
+{
+	aff = isl_aff_cow(aff);
+	if (!aff)
+		return NULL;
+	if (type == isl_dim_out)
+		isl_die(aff->v->ctx, isl_error_invalid,
+			"cannot set name of output/set dimension",
+			return isl_aff_free(aff));
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+	aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
+	if (!aff->ls)
+		return isl_aff_free(aff);
+
+	return aff;
+}
+
+__isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
+	enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
+{
+	aff = isl_aff_cow(aff);
+	if (!aff)
+		return isl_id_free(id);
+	if (type == isl_dim_out)
+		isl_die(aff->v->ctx, isl_error_invalid,
+			"cannot set name of output/set dimension",
+			goto error);
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+	aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
+	if (!aff->ls)
+		return isl_aff_free(aff);
+
+	return aff;
+error:
+	isl_id_free(id);
+	isl_aff_free(aff);
+	return NULL;
+}
+
+/* Exploit the equalities in "eq" to simplify the affine expression
+ * and the expressions of the integer divisions in the local space.
+ * The integer divisions in this local space are assumed to appear
+ * as regular dimensions in "eq".
+ */
+static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
+	__isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
+{
+	int i, j;
+	unsigned total;
+	unsigned n_div;
+
+	if (!eq)
+		goto error;
+	if (eq->n_eq == 0) {
+		isl_basic_set_free(eq);
+		return aff;
+	}
+
+	aff = isl_aff_cow(aff);
+	if (!aff)
+		goto error;
+
+	aff->ls = isl_local_space_substitute_equalities(aff->ls,
+							isl_basic_set_copy(eq));
+	if (!aff->ls)
+		goto error;
+
+	total = 1 + isl_space_dim(eq->dim, isl_dim_all);
+	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;
+
+		isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
+				&aff->v->el[0]);
+	}
+
+	isl_basic_set_free(eq);
+	return aff;
+error:
+	isl_basic_set_free(eq);
+	isl_aff_free(aff);
+	return NULL;
+}
+
+/* Exploit the equalities in "eq" to simplify the affine expression
+ * and the expressions of the integer divisions in the local space.
+ */
+static __isl_give isl_aff *isl_aff_substitute_equalities(
+	__isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
+{
+	int n_div;
+
+	if (!aff || !eq)
+		goto error;
+	n_div = isl_local_space_dim(aff->ls, isl_dim_div);
+	if (n_div > 0)
+		eq = isl_basic_set_add(eq, isl_dim_set, n_div);
+	return isl_aff_substitute_equalities_lifted(aff, eq);
+error:
+	isl_basic_set_free(eq);
+	isl_aff_free(aff);
+	return NULL;
+}
+
+/* Look for equalities among the variables shared by context and aff
+ * and the integer divisions of aff, if any.
+ * The equalities are then used to eliminate coefficients and/or integer
+ * divisions from aff.
+ */
+__isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
+	__isl_take isl_set *context)
+{
+	isl_basic_set *hull;
+	int n_div;
+
+	if (!aff)
+		goto error;
+	n_div = isl_local_space_dim(aff->ls, isl_dim_div);
+	if (n_div > 0) {
+		isl_basic_set *bset;
+		isl_local_space *ls;
+		context = isl_set_add_dims(context, isl_dim_set, n_div);
+		ls = isl_aff_get_domain_local_space(aff);
+		bset = isl_basic_set_from_local_space(ls);
+		bset = isl_basic_set_lift(bset);
+		bset = isl_basic_set_flatten(bset);
+		context = isl_set_intersect(context,
+					    isl_set_from_basic_set(bset));
+	}
+
+	hull = isl_set_affine_hull(context);
+	return isl_aff_substitute_equalities_lifted(aff, hull);
+error:
+	isl_aff_free(aff);
+	isl_set_free(context);
+	return NULL;
+}
+
+/* Return a basic set containing those elements in the space
+ * of aff where it is non-negative.
+ */
+__isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
+{
+	isl_constraint *ineq;
+
+	ineq = isl_inequality_from_aff(aff);
+
+	return isl_basic_set_from_constraint(ineq);
+}
+
+/* Return a basic set containing those elements in the space
+ * of aff where it is zero.
+ */
+__isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
+{
+	isl_constraint *ineq;
+
+	ineq = isl_equality_from_aff(aff);
+
+	return isl_basic_set_from_constraint(ineq);
+}
+
+/* Return a basic set containing those elements in the shared space
+ * of aff1 and aff2 where aff1 is greater than or equal to aff2.
+ */
+__isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
+	__isl_take isl_aff *aff2)
+{
+	aff1 = isl_aff_sub(aff1, aff2);
+
+	return isl_aff_nonneg_basic_set(aff1);
+}
+
+/* Return a basic set containing those elements in the shared space
+ * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
+ */
+__isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
+	__isl_take isl_aff *aff2)
+{
+	return isl_aff_ge_basic_set(aff2, aff1);
+}
+
+__isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
+	__isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
+{
+	aff1 = isl_aff_add(aff1, aff2);
+	aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
+	return aff1;
+}
+
+int isl_aff_is_empty(__isl_keep isl_aff *aff)
+{
+	if (!aff)
+		return -1;
+
+	return 0;
+}
+
+/* Check whether the given affine expression has non-zero coefficient
+ * for any dimension in the given range or if any of these dimensions
+ * appear with non-zero coefficients in any of the integer divisions
+ * involved in the affine expression.
+ */
+int isl_aff_involves_dims(__isl_keep isl_aff *aff,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	int i;
+	isl_ctx *ctx;
+	int *active = NULL;
+	int involves = 0;
+
+	if (!aff)
+		return -1;
+	if (n == 0)
+		return 0;
+
+	ctx = isl_aff_get_ctx(aff);
+	if (first + n > isl_aff_dim(aff, type))
+		isl_die(ctx, isl_error_invalid,
+			"range out of bounds", return -1);
+
+	active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
+	if (!active)
+		goto error;
+
+	first += isl_local_space_offset(aff->ls, type) - 1;
+	for (i = 0; i < n; ++i)
+		if (active[first + i]) {
+			involves = 1;
+			break;
+		}
+
+	free(active);
+
+	return involves;
+error:
+	free(active);
+	return -1;
+}
+
+__isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	isl_ctx *ctx;
+
+	if (!aff)
+		return NULL;
+	if (type == isl_dim_out)
+		isl_die(aff->v->ctx, isl_error_invalid,
+			"cannot drop output/set dimension",
+			return isl_aff_free(aff));
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+	if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
+		return aff;
+
+	ctx = isl_aff_get_ctx(aff);
+	if (first + n > isl_local_space_dim(aff->ls, type))
+		isl_die(ctx, isl_error_invalid, "range out of bounds",
+			return isl_aff_free(aff));
+
+	aff = isl_aff_cow(aff);
+	if (!aff)
+		return NULL;
+
+	aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
+	if (!aff->ls)
+		return isl_aff_free(aff);
+
+	first += 1 + isl_local_space_offset(aff->ls, type);
+	aff->v = isl_vec_drop_els(aff->v, first, n);
+	if (!aff->v)
+		return isl_aff_free(aff);
+
+	return aff;
+}
+
+__isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	isl_ctx *ctx;
+
+	if (!aff)
+		return NULL;
+	if (type == isl_dim_out)
+		isl_die(aff->v->ctx, isl_error_invalid,
+			"cannot insert output/set dimensions",
+			return isl_aff_free(aff));
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+	if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
+		return aff;
+
+	ctx = isl_aff_get_ctx(aff);
+	if (first > isl_local_space_dim(aff->ls, type))
+		isl_die(ctx, isl_error_invalid, "position out of bounds",
+			return isl_aff_free(aff));
+
+	aff = isl_aff_cow(aff);
+	if (!aff)
+		return NULL;
+
+	aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
+	if (!aff->ls)
+		return isl_aff_free(aff);
+
+	first += 1 + isl_local_space_offset(aff->ls, type);
+	aff->v = isl_vec_insert_zero_els(aff->v, first, n);
+	if (!aff->v)
+		return isl_aff_free(aff);
+
+	return aff;
+}
+
+__isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
+	enum isl_dim_type type, unsigned n)
+{
+	unsigned pos;
+
+	pos = isl_aff_dim(aff, type);
+
+	return isl_aff_insert_dims(aff, type, pos, n);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
+	enum isl_dim_type type, unsigned n)
+{
+	unsigned pos;
+
+	pos = isl_pw_aff_dim(pwaff, type);
+
+	return isl_pw_aff_insert_dims(pwaff, type, pos, n);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
+{
+	isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
+	return isl_pw_aff_alloc(dom, aff);
+}
+
+#undef PW
+#define PW isl_pw_aff
+#undef EL
+#define EL isl_aff
+#undef EL_IS_ZERO
+#define EL_IS_ZERO is_empty
+#undef ZERO
+#define ZERO empty
+#undef IS_ZERO
+#define IS_ZERO is_empty
+#undef FIELD
+#define FIELD aff
+
+#define NO_EVAL
+#define NO_OPT
+#define NO_MOVE_DIMS
+#define NO_LIFT
+#define NO_MORPH
+
+#include <isl_pw_templ.c>
+
+static __isl_give isl_set *align_params_pw_pw_set_and(
+	__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
+	__isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
+				    __isl_take isl_pw_aff *pwaff2))
+{
+	if (!pwaff1 || !pwaff2)
+		goto error;
+	if (isl_space_match(pwaff1->dim, isl_dim_param,
+			  pwaff2->dim, isl_dim_param))
+		return fn(pwaff1, pwaff2);
+	if (!isl_space_has_named_params(pwaff1->dim) ||
+	    !isl_space_has_named_params(pwaff2->dim))
+		isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
+			"unaligned unnamed parameters", goto error);
+	pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
+	pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
+	return fn(pwaff1, pwaff2);
+error:
+	isl_pw_aff_free(pwaff1);
+	isl_pw_aff_free(pwaff2);
+	return NULL;
+}
+
+/* Compute a piecewise quasi-affine expression with a domain that
+ * is the union of those of pwaff1 and pwaff2 and such that on each
+ * cell, the quasi-affine expression is the better (according to cmp)
+ * of those of pwaff1 and pwaff2.  If only one of pwaff1 or pwaff2
+ * is defined on a given cell, then the associated expression
+ * is the defined one.
+ */
+static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2,
+	__isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1,
+					__isl_take isl_aff *aff2))
+{
+	int i, j, n;
+	isl_pw_aff *res;
+	isl_ctx *ctx;
+	isl_set *set;
+
+	if (!pwaff1 || !pwaff2)
+		goto error;
+
+	ctx = isl_space_get_ctx(pwaff1->dim);
+	if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim))
+		isl_die(ctx, isl_error_invalid,
+			"arguments should live in same space", goto error);
+
+	if (isl_pw_aff_is_empty(pwaff1)) {
+		isl_pw_aff_free(pwaff1);
+		return pwaff2;
+	}
+
+	if (isl_pw_aff_is_empty(pwaff2)) {
+		isl_pw_aff_free(pwaff2);
+		return pwaff1;
+	}
+
+	n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
+	res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
+
+	for (i = 0; i < pwaff1->n; ++i) {
+		set = isl_set_copy(pwaff1->p[i].set);
+		for (j = 0; j < pwaff2->n; ++j) {
+			struct isl_set *common;
+			isl_set *better;
+
+			common = isl_set_intersect(
+					isl_set_copy(pwaff1->p[i].set),
+					isl_set_copy(pwaff2->p[j].set));
+			better = isl_set_from_basic_set(cmp(
+					isl_aff_copy(pwaff2->p[j].aff),
+					isl_aff_copy(pwaff1->p[i].aff)));
+			better = isl_set_intersect(common, better);
+			if (isl_set_plain_is_empty(better)) {
+				isl_set_free(better);
+				continue;
+			}
+			set = isl_set_subtract(set, isl_set_copy(better));
+
+			res = isl_pw_aff_add_piece(res, better,
+						isl_aff_copy(pwaff2->p[j].aff));
+		}
+		res = isl_pw_aff_add_piece(res, set,
+						isl_aff_copy(pwaff1->p[i].aff));
+	}
+
+	for (j = 0; j < pwaff2->n; ++j) {
+		set = isl_set_copy(pwaff2->p[j].set);
+		for (i = 0; i < pwaff1->n; ++i)
+			set = isl_set_subtract(set,
+					isl_set_copy(pwaff1->p[i].set));
+		res = isl_pw_aff_add_piece(res, set,
+						isl_aff_copy(pwaff2->p[j].aff));
+	}
+
+	isl_pw_aff_free(pwaff1);
+	isl_pw_aff_free(pwaff2);
+
+	return res;
+error:
+	isl_pw_aff_free(pwaff1);
+	isl_pw_aff_free(pwaff2);
+	return NULL;
+}
+
+/* Compute a piecewise quasi-affine expression with a domain that
+ * is the union of those of pwaff1 and pwaff2 and such that on each
+ * cell, the quasi-affine expression is the maximum of those of pwaff1
+ * and pwaff2.  If only one of pwaff1 or pwaff2 is defined on a given
+ * cell, then the associated expression is the defined one.
+ */
+static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
+							&pw_aff_union_max);
+}
+
+/* Compute a piecewise quasi-affine expression with a domain that
+ * is the union of those of pwaff1 and pwaff2 and such that on each
+ * cell, the quasi-affine expression is the minimum of those of pwaff1
+ * and pwaff2.  If only one of pwaff1 or pwaff2 is defined on a given
+ * cell, then the associated expression is the defined one.
+ */
+static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
+							&pw_aff_union_min);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2, int max)
+{
+	if (max)
+		return isl_pw_aff_union_max(pwaff1, pwaff2);
+	else
+		return isl_pw_aff_union_min(pwaff1, pwaff2);
+}
+
+/* Construct a map with as domain the domain of pwaff and
+ * one-dimensional range corresponding to the affine expressions.
+ */
+static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
+{
+	int i;
+	isl_space *dim;
+	isl_map *map;
+
+	if (!pwaff)
+		return NULL;
+
+	dim = isl_pw_aff_get_space(pwaff);
+	map = isl_map_empty(dim);
+
+	for (i = 0; i < pwaff->n; ++i) {
+		isl_basic_map *bmap;
+		isl_map *map_i;
+
+		bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
+		map_i = isl_map_from_basic_map(bmap);
+		map_i = isl_map_intersect_domain(map_i,
+						isl_set_copy(pwaff->p[i].set));
+		map = isl_map_union_disjoint(map, map_i);
+	}
+
+	isl_pw_aff_free(pwaff);
+
+	return map;
+}
+
+/* Construct a map with as domain the domain of pwaff and
+ * one-dimensional range corresponding to the affine expressions.
+ */
+__isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
+{
+	if (isl_space_is_set(pwaff->dim))
+		isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
+			"space of input is not a map",
+			return isl_pw_aff_free(pwaff));
+	return map_from_pw_aff(pwaff);
+}
+
+/* Construct a one-dimensional set with as parameter domain
+ * the domain of pwaff and the single set dimension
+ * corresponding to the affine expressions.
+ */
+__isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
+{
+	if (!isl_space_is_set(pwaff->dim))
+		isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
+			"space of input is not a set",
+			return isl_pw_aff_free(pwaff));
+	return map_from_pw_aff(pwaff);
+}
+
+/* Return a set containing those elements in the domain
+ * of pwaff where it is non-negative.
+ */
+__isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
+{
+	int i;
+	isl_set *set;
+
+	if (!pwaff)
+		return NULL;
+
+	set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
+
+	for (i = 0; i < pwaff->n; ++i) {
+		isl_basic_set *bset;
+		isl_set *set_i;
+
+		bset = isl_aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff));
+		set_i = isl_set_from_basic_set(bset);
+		set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
+		set = isl_set_union_disjoint(set, set_i);
+	}
+
+	isl_pw_aff_free(pwaff);
+
+	return set;
+}
+
+/* Return a set containing those elements in the domain
+ * of pwaff where it is zero.
+ */
+__isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
+{
+	int i;
+	isl_set *set;
+
+	if (!pwaff)
+		return NULL;
+
+	set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
+
+	for (i = 0; i < pwaff->n; ++i) {
+		isl_basic_set *bset;
+		isl_set *set_i;
+
+		bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff));
+		set_i = isl_set_from_basic_set(bset);
+		set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
+		set = isl_set_union_disjoint(set, set_i);
+	}
+
+	isl_pw_aff_free(pwaff);
+
+	return set;
+}
+
+/* Return a set containing those elements in the domain
+ * of pwaff where it is not zero.
+ */
+__isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
+{
+	return isl_set_complement(isl_pw_aff_zero_set(pwaff));
+}
+
+/* Return a set containing those elements in the shared domain
+ * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
+ *
+ * We compute the difference on the shared domain and then construct
+ * the set of values where this difference is non-negative.
+ * If strict is set, we first subtract 1 from the difference.
+ * If equal is set, we only return the elements where pwaff1 and pwaff2
+ * are equal.
+ */
+static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2, int strict, int equal)
+{
+	isl_set *set1, *set2;
+
+	set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
+	set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
+	set1 = isl_set_intersect(set1, set2);
+	pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
+	pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
+	pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
+
+	if (strict) {
+		isl_space *dim = isl_set_get_space(set1);
+		isl_aff *aff;
+		aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
+		aff = isl_aff_add_constant_si(aff, -1);
+		pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
+	} else
+		isl_set_free(set1);
+
+	if (equal)
+		return isl_pw_aff_zero_set(pwaff1);
+	return isl_pw_aff_nonneg_set(pwaff1);
+}
+
+/* Return a set containing those elements in the shared domain
+ * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
+ */
+static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
+}
+
+__isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
+}
+
+/* Return a set containing those elements in the shared domain
+ * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
+ */
+static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
+}
+
+__isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
+}
+
+/* Return a set containing those elements in the shared domain
+ * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
+ */
+static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
+}
+
+__isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
+}
+
+__isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_ge_set(pwaff2, pwaff1);
+}
+
+__isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_gt_set(pwaff2, pwaff1);
+}
+
+/* Return a set containing those elements in the shared domain
+ * of the elements of list1 and list2 where each element in list1
+ * has the relation specified by "fn" with each element in list2.
+ */
+static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
+	__isl_take isl_pw_aff_list *list2,
+	__isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
+				    __isl_take isl_pw_aff *pwaff2))
+{
+	int i, j;
+	isl_ctx *ctx;
+	isl_set *set;
+
+	if (!list1 || !list2)
+		goto error;
+
+	ctx = isl_pw_aff_list_get_ctx(list1);
+	if (list1->n < 1 || list2->n < 1)
+		isl_die(ctx, isl_error_invalid,
+			"list should contain at least one element", goto error);
+
+	set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
+	for (i = 0; i < list1->n; ++i)
+		for (j = 0; j < list2->n; ++j) {
+			isl_set *set_ij;
+
+			set_ij = fn(isl_pw_aff_copy(list1->p[i]),
+				    isl_pw_aff_copy(list2->p[j]));
+			set = isl_set_intersect(set, set_ij);
+		}
+
+	isl_pw_aff_list_free(list1);
+	isl_pw_aff_list_free(list2);
+	return set;
+error:
+	isl_pw_aff_list_free(list1);
+	isl_pw_aff_list_free(list2);
+	return NULL;
+}
+
+/* Return a set containing those elements in the shared domain
+ * of the elements of list1 and list2 where each element in list1
+ * is equal to each element in list2.
+ */
+__isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
+	__isl_take isl_pw_aff_list *list2)
+{
+	return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
+}
+
+__isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
+	__isl_take isl_pw_aff_list *list2)
+{
+	return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
+}
+
+/* Return a set containing those elements in the shared domain
+ * of the elements of list1 and list2 where each element in list1
+ * is less than or equal to each element in list2.
+ */
+__isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
+	__isl_take isl_pw_aff_list *list2)
+{
+	return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
+}
+
+__isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
+	__isl_take isl_pw_aff_list *list2)
+{
+	return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
+}
+
+__isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
+	__isl_take isl_pw_aff_list *list2)
+{
+	return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
+}
+
+__isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
+	__isl_take isl_pw_aff_list *list2)
+{
+	return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
+}
+
+
+/* Return a set containing those elements in the shared domain
+ * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
+ */
+static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	isl_set *set_lt, *set_gt;
+
+	set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
+				   isl_pw_aff_copy(pwaff2));
+	set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
+	return isl_set_union_disjoint(set_lt, set_gt);
+}
+
+__isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
+	isl_int v)
+{
+	int i;
+
+	if (isl_int_is_one(v))
+		return pwaff;
+	if (!isl_int_is_pos(v))
+		isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
+			"factor needs to be positive",
+			return isl_pw_aff_free(pwaff));
+	pwaff = isl_pw_aff_cow(pwaff);
+	if (!pwaff)
+		return NULL;
+	if (pwaff->n == 0)
+		return pwaff;
+
+	for (i = 0; i < pwaff->n; ++i) {
+		pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
+		if (!pwaff->p[i].aff)
+			return isl_pw_aff_free(pwaff);
+	}
+
+	return pwaff;
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
+{
+	int i;
+
+	pwaff = isl_pw_aff_cow(pwaff);
+	if (!pwaff)
+		return NULL;
+	if (pwaff->n == 0)
+		return pwaff;
+
+	for (i = 0; i < pwaff->n; ++i) {
+		pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
+		if (!pwaff->p[i].aff)
+			return isl_pw_aff_free(pwaff);
+	}
+
+	return pwaff;
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
+{
+	int i;
+
+	pwaff = isl_pw_aff_cow(pwaff);
+	if (!pwaff)
+		return NULL;
+	if (pwaff->n == 0)
+		return pwaff;
+
+	for (i = 0; i < pwaff->n; ++i) {
+		pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
+		if (!pwaff->p[i].aff)
+			return isl_pw_aff_free(pwaff);
+	}
+
+	return pwaff;
+}
+
+/* Return an affine expression that is equal to pwaff_true for elements
+ * in "cond" and to pwaff_false for elements not in "cond".
+ * That is, return cond ? pwaff_true : pwaff_false;
+ */
+__isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_set *cond,
+	__isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
+{
+	isl_set *comp;
+
+	comp = isl_set_complement(isl_set_copy(cond));
+	pwaff_true = isl_pw_aff_intersect_domain(pwaff_true, cond);
+	pwaff_false = isl_pw_aff_intersect_domain(pwaff_false, comp);
+
+	return isl_pw_aff_add_disjoint(pwaff_true, pwaff_false);
+}
+
+int isl_aff_is_cst(__isl_keep isl_aff *aff)
+{
+	if (!aff)
+		return -1;
+
+	return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
+}
+
+/* Check whether pwaff is a piecewise constant.
+ */
+int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
+{
+	int i;
+
+	if (!pwaff)
+		return -1;
+
+	for (i = 0; i < pwaff->n; ++i) {
+		int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
+		if (is_cst < 0 || !is_cst)
+			return is_cst;
+	}
+
+	return 1;
+}
+
+__isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
+	__isl_take isl_aff *aff2)
+{
+	if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
+		return isl_aff_mul(aff2, aff1);
+
+	if (!isl_aff_is_cst(aff2))
+		isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
+			"at least one affine expression should be constant",
+			goto error);
+
+	aff1 = isl_aff_cow(aff1);
+	if (!aff1 || !aff2)
+		goto error;
+
+	aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
+	aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
+
+	isl_aff_free(aff2);
+	return aff1;
+error:
+	isl_aff_free(aff1);
+	isl_aff_free(aff2);
+	return NULL;
+}
+
+static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
+}
+
+static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	isl_set *le;
+
+	le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
+				isl_pw_aff_copy(pwaff2));
+	return isl_pw_aff_cond(le, pwaff1, pwaff2);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
+}
+
+static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	isl_set *le;
+
+	le = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
+				isl_pw_aff_copy(pwaff2));
+	return isl_pw_aff_cond(le, pwaff1, pwaff2);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
+}
+
+static __isl_give isl_pw_aff *pw_aff_list_reduce(
+	__isl_take isl_pw_aff_list *list,
+	__isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
+					__isl_take isl_pw_aff *pwaff2))
+{
+	int i;
+	isl_ctx *ctx;
+	isl_pw_aff *res;
+
+	if (!list)
+		return NULL;
+
+	ctx = isl_pw_aff_list_get_ctx(list);
+	if (list->n < 1)
+		isl_die(ctx, isl_error_invalid,
+			"list should contain at least one element",
+			return isl_pw_aff_list_free(list));
+
+	res = isl_pw_aff_copy(list->p[0]);
+	for (i = 1; i < list->n; ++i)
+		res = fn(res, isl_pw_aff_copy(list->p[i]));
+
+	isl_pw_aff_list_free(list);
+	return res;
+}
+
+/* Return an isl_pw_aff that maps each element in the intersection of the
+ * domains of the elements of list to the minimal corresponding affine
+ * expression.
+ */
+__isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
+{
+	return pw_aff_list_reduce(list, &isl_pw_aff_min);
+}
+
+/* Return an isl_pw_aff that maps each element in the intersection of the
+ * domains of the elements of list to the maximal corresponding affine
+ * expression.
+ */
+__isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
+{
+	return pw_aff_list_reduce(list, &isl_pw_aff_max);
+}
+
+#undef BASE
+#define BASE aff
+
+#include <isl_multi_templ.c>
+
+__isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
+	__isl_take isl_multi_aff *maff2)
+{
+	int i;
+	isl_ctx *ctx;
+
+	maff1 = isl_multi_aff_cow(maff1);
+	if (!maff1 || !maff2)
+		goto error;
+
+	ctx = isl_multi_aff_get_ctx(maff1);
+	if (!isl_space_is_equal(maff1->space, maff2->space))
+		isl_die(ctx, isl_error_invalid,
+			"spaces don't match", goto error);
+
+	for (i = 0; i < maff1->n; ++i) {
+		maff1->p[i] = isl_aff_add(maff1->p[i],
+					    isl_aff_copy(maff2->p[i]));
+		if (!maff1->p[i])
+			goto error;
+	}
+
+	isl_multi_aff_free(maff2);
+	return maff1;
+error:
+	isl_multi_aff_free(maff1);
+	isl_multi_aff_free(maff2);
+	return NULL;
+}
+
+/* Exploit the equalities in "eq" to simplify the affine expressions.
+ */
+static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
+	__isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
+{
+	int i;
+
+	maff = isl_multi_aff_cow(maff);
+	if (!maff || !eq)
+		goto error;
+
+	for (i = 0; i < maff->n; ++i) {
+		maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
+						    isl_basic_set_copy(eq));
+		if (!maff->p[i])
+			goto error;
+	}
+
+	isl_basic_set_free(eq);
+	return maff;
+error:
+	isl_basic_set_free(eq);
+	isl_multi_aff_free(maff);
+	return NULL;
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
+	isl_int f)
+{
+	int i;
+
+	maff = isl_multi_aff_cow(maff);
+	if (!maff)
+		return NULL;
+
+	for (i = 0; i < maff->n; ++i) {
+		maff->p[i] = isl_aff_scale(maff->p[i], f);
+		if (!maff->p[i])
+			return isl_multi_aff_free(maff);
+	}
+
+	return maff;
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
+	__isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
+{
+	maff1 = isl_multi_aff_add(maff1, maff2);
+	maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
+	return maff1;
+}
+
+int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
+{
+	if (!maff)
+		return -1;
+
+	return 0;
+}
+
+int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
+	__isl_keep isl_multi_aff *maff2)
+{
+	int i;
+	int equal;
+
+	if (!maff1 || !maff2)
+		return -1;
+	if (maff1->n != maff2->n)
+		return 0;
+	equal = isl_space_is_equal(maff1->space, maff2->space);
+	if (equal < 0 || !equal)
+		return equal;
+
+	for (i = 0; i < maff1->n; ++i) {
+		equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]);
+		if (equal < 0 || !equal)
+			return equal;
+	}
+
+	return 1;
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
+	__isl_take isl_multi_aff *maff,
+	enum isl_dim_type type, unsigned pos, const char *s)
+{
+	int i;
+
+	maff = isl_multi_aff_cow(maff);
+	if (!maff)
+		return NULL;
+
+	maff->space = isl_space_set_dim_name(maff->space, type, pos, s);
+	if (!maff->space)
+		return isl_multi_aff_free(maff);
+	for (i = 0; i < maff->n; ++i) {
+		maff->p[i] = isl_aff_set_dim_name(maff->p[i], type, pos, s);
+		if (!maff->p[i])
+			return isl_multi_aff_free(maff);
+	}
+
+	return maff;
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	int i;
+
+	maff = isl_multi_aff_cow(maff);
+	if (!maff)
+		return NULL;
+
+	maff->space = isl_space_drop_dims(maff->space, type, first, n);
+	if (!maff->space)
+		return isl_multi_aff_free(maff);
+	for (i = 0; i < maff->n; ++i) {
+		maff->p[i] = isl_aff_drop_dims(maff->p[i], type, first, n);
+		if (!maff->p[i])
+			return isl_multi_aff_free(maff);
+	}
+
+	return maff;
+}
+
+#undef PW
+#define PW isl_pw_multi_aff
+#undef EL
+#define EL isl_multi_aff
+#undef EL_IS_ZERO
+#define EL_IS_ZERO is_empty
+#undef ZERO
+#define ZERO empty
+#undef IS_ZERO
+#define IS_ZERO is_empty
+#undef FIELD
+#define FIELD maff
+
+#define NO_NEG
+#define NO_EVAL
+#define NO_OPT
+#define NO_INVOLVES_DIMS
+#define NO_MOVE_DIMS
+#define NO_INSERT_DIMS
+#define NO_LIFT
+#define NO_MORPH
+
+#include <isl_pw_templ.c>
+
+/* Construct a map mapping the domain the piecewise multi-affine expression
+ * to its range, with each dimension in the range equated to the
+ * corresponding affine expression on its cell.
+ */
+__isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
+{
+	int i;
+	isl_map *map;
+
+	if (!pma)
+		return NULL;
+
+	map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
+
+	for (i = 0; i < pma->n; ++i) {
+		isl_multi_aff *maff;
+		isl_basic_map *bmap;
+		isl_map *map_i;
+
+		maff = isl_multi_aff_copy(pma->p[i].maff);
+		bmap = isl_basic_map_from_multi_aff(maff);
+		map_i = isl_map_from_basic_map(bmap);
+		map_i = isl_map_intersect_domain(map_i,
+						isl_set_copy(pma->p[i].set));
+		map = isl_map_union_disjoint(map, map_i);
+	}
+
+	isl_pw_multi_aff_free(pma);
+	return map;
+}
+
+__isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
+{
+	if (!isl_space_is_set(pma->dim))
+		isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
+			"isl_pw_multi_aff cannot be converted into an isl_set",
+			return isl_pw_multi_aff_free(pma));
+
+	return isl_map_from_pw_multi_aff(pma);
+}
+
+/* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
+ * This obivously only works if the input "map" is single-valued.
+ * If so, we compute the lexicographic minimum of the image in the form
+ * of an isl_pw_multi_aff.  Since the image is unique, it is equal
+ * to its lexicographic minimum.
+ * If the input is not single-valued, we produce an error.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
+{
+	int i;
+	int sv;
+	isl_pw_multi_aff *pma;
+
+	if (!map)
+		return NULL;
+
+	sv = isl_map_is_single_valued(map);
+	if (sv < 0)
+		goto error;
+	if (!sv)
+		isl_die(isl_map_get_ctx(map), isl_error_invalid,
+			"map is not single-valued", goto error);
+	map = isl_map_make_disjoint(map);
+	if (!map)
+		return NULL;
+
+	pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
+
+	for (i = 0; i < map->n; ++i) {
+		isl_pw_multi_aff *pma_i;
+		isl_basic_map *bmap;
+		bmap = isl_basic_map_copy(map->p[i]);
+		pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
+		pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
+	}
+
+	isl_map_free(map);
+	return pma;
+error:
+	isl_map_free(map);
+	return NULL;
+}
+
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
+{
+	return isl_pw_multi_aff_from_map(set);
+}
+
+/* Plug in "subs" for dimension "type", "pos" of "aff".
+ *
+ * Let i be the dimension to replace and let "subs" be of the form
+ *
+ *	f/d
+ *
+ * and "aff" of the form
+ *
+ *	(a i + g)/m
+ *
+ * The result is
+ *
+ *	floor((a f + d g')/(m d))
+ *
+ * where g' is the result of plugging in "subs" in each of the integer
+ * divisions in g.
+ */
+__isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
+	enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
+{
+	isl_ctx *ctx;
+	isl_int v;
+
+	aff = isl_aff_cow(aff);
+	if (!aff || !subs)
+		return isl_aff_free(aff);
+
+	ctx = isl_aff_get_ctx(aff);
+	if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
+		isl_die(ctx, isl_error_invalid,
+			"spaces don't match", return isl_aff_free(aff));
+	if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
+		isl_die(ctx, isl_error_unsupported,
+			"cannot handle divs yet", return isl_aff_free(aff));
+
+	aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
+	if (!aff->ls)
+		return isl_aff_free(aff);
+
+	aff->v = isl_vec_cow(aff->v);
+	if (!aff->v)
+		return isl_aff_free(aff);
+
+	pos += isl_local_space_offset(aff->ls, type);
+
+	isl_int_init(v);
+	isl_int_set(v, aff->v->el[1 + pos]);
+	isl_int_set_si(aff->v->el[1 + pos], 0);
+	isl_seq_combine(aff->v->el + 1, subs->v->el[0], aff->v->el + 1,
+			v, subs->v->el + 1, subs->v->size - 1);
+	isl_int_mul(aff->v->el[0], aff->v->el[0], subs->v->el[0]);
+	isl_int_clear(v);
+
+	return aff;
+}
+
+/* Plug in "subs" for dimension "type", "pos" in each of the affine
+ * expressions in "maff".
+ */
+__isl_give isl_multi_aff *isl_multi_aff_substitute(
+	__isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
+	__isl_keep isl_aff *subs)
+{
+	int i;
+
+	maff = isl_multi_aff_cow(maff);
+	if (!maff || !subs)
+		return isl_multi_aff_free(maff);
+
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+
+	for (i = 0; i < maff->n; ++i) {
+		maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
+		if (!maff->p[i])
+			return isl_multi_aff_free(maff);
+	}
+
+	return maff;
+}
+
+/* Plug in "subs" for dimension "type", "pos" of "pma".
+ *
+ * pma is of the form
+ *
+ *	A_i(v) -> M_i(v)
+ *
+ * while subs is of the form
+ *
+ *	v' = B_j(v) -> S_j
+ *
+ * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
+ * has a contribution in the result, in particular
+ *
+ *	C_ij(S_j) -> M_i(S_j)
+ *
+ * Note that plugging in S_j in C_ij may also result in an empty set
+ * and this contribution should simply be discarded.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
+	__isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
+	__isl_keep isl_pw_aff *subs)
+{
+	int i, j, n;
+	isl_pw_multi_aff *res;
+
+	if (!pma || !subs)
+		return isl_pw_multi_aff_free(pma);
+
+	n = pma->n * subs->n;
+	res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
+
+	for (i = 0; i < pma->n; ++i) {
+		for (j = 0; j < subs->n; ++j) {
+			isl_set *common;
+			isl_multi_aff *res_ij;
+			common = isl_set_intersect(
+					isl_set_copy(pma->p[i].set),
+					isl_set_copy(subs->p[j].set));
+			common = isl_set_substitute(common,
+					type, pos, subs->p[j].aff);
+			if (isl_set_plain_is_empty(common)) {
+				isl_set_free(common);
+				continue;
+			}
+
+			res_ij = isl_multi_aff_substitute(
+					isl_multi_aff_copy(pma->p[i].maff),
+					type, pos, subs->p[j].aff);
+
+			res = isl_pw_multi_aff_add_piece(res, common, res_ij);
+		}
+	}
+
+	isl_pw_multi_aff_free(pma);
+	return res;
+}
+
+/* Extend the local space of "dst" to include the divs
+ * in the local space of "src".
+ */
+__isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
+	__isl_keep isl_aff *src)
+{
+	isl_ctx *ctx;
+	int *exp1 = NULL;
+	int *exp2 = NULL;
+	isl_mat *div;
+
+	if (!src || !dst)
+		return isl_aff_free(dst);
+
+	ctx = isl_aff_get_ctx(src);
+	if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
+		isl_die(ctx, isl_error_invalid,
+			"spaces don't match", goto error);
+
+	if (src->ls->div->n_row == 0)
+		return dst;
+
+	exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
+	exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
+	if (!exp1 || !exp2)
+		goto error;
+
+	div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
+	dst = isl_aff_expand_divs(dst, div, exp2);
+	free(exp1);
+	free(exp2);
+
+	return dst;
+error:
+	free(exp1);
+	free(exp2);
+	return isl_aff_free(dst);
+}
+
+/* Adjust the local spaces of the affine expressions in "maff"
+ * such that they all have the save divs.
+ */
+__isl_give isl_multi_aff *isl_multi_aff_align_divs(
+	__isl_take isl_multi_aff *maff)
+{
+	int i;
+
+	if (!maff)
+		return NULL;
+	if (maff->n == 0)
+		return maff;
+	maff = isl_multi_aff_cow(maff);
+	if (!maff)
+		return NULL;
+
+	for (i = 1; i < maff->n; ++i)
+		maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
+	for (i = 1; i < maff->n; ++i) {
+		maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
+		if (!maff->p[i])
+			return isl_multi_aff_free(maff);
+	}
+
+	return maff;
+}
+
+__isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
+{
+	aff = isl_aff_cow(aff);
+	if (!aff)
+		return NULL;
+
+	aff->ls = isl_local_space_lift(aff->ls);
+	if (!aff->ls)
+		return isl_aff_free(aff);
+
+	return aff;
+}
+
+/* Lift "maff" to a space with extra dimensions such that the result
+ * has no more existentially quantified variables.
+ * If "ls" is not NULL, then *ls is assigned the local space that lies
+ * at the basis of the lifting applied to "maff".
+ */
+__isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
+	__isl_give isl_local_space **ls)
+{
+	int i;
+	isl_space *space;
+	unsigned n_div;
+
+	if (ls)
+		*ls = NULL;
+
+	if (!maff)
+		return NULL;
+
+	if (maff->n == 0) {
+		if (ls) {
+			isl_space *space = isl_multi_aff_get_domain_space(maff);
+			*ls = isl_local_space_from_space(space);
+			if (!*ls)
+				return isl_multi_aff_free(maff);
+		}
+		return maff;
+	}
+
+	maff = isl_multi_aff_cow(maff);
+	maff = isl_multi_aff_align_divs(maff);
+	if (!maff)
+		return NULL;
+
+	n_div = isl_aff_dim(maff->p[0], isl_dim_div);
+	space = isl_multi_aff_get_space(maff);
+	space = isl_space_lift(isl_space_domain(space), n_div);
+	space = isl_space_extend_domain_with_range(space,
+						isl_multi_aff_get_space(maff));
+	if (!space)
+		return isl_multi_aff_free(maff);
+	isl_space_free(maff->space);
+	maff->space = space;
+
+	if (ls) {
+		*ls = isl_aff_get_domain_local_space(maff->p[0]);
+		if (!*ls)
+			return isl_multi_aff_free(maff);
+	}
+
+	for (i = 0; i < maff->n; ++i) {
+		maff->p[i] = isl_aff_lift(maff->p[i]);
+		if (!maff->p[i])
+			goto error;
+	}
+
+	return maff;
+error:
+	if (ls)
+		isl_local_space_free(*ls);
+	return isl_multi_aff_free(maff);
+}