X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_aff.c;h=ccd2b426c20a23e58a223e2dead30d405266eaa0;hb=f068f30e43903b246ea5aad7a57a1138435daf0e;hp=722da3b561e53627f97192d44af49ca8abe67e9c;hpb=556d287f982d8cc1a6f1fd6a318e926c95dbebf4;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_aff.c b/isl_aff.c
index 722da3b..ccd2b42 100644
--- a/isl_aff.c
+++ b/isl_aff.c
@@ -1,16 +1,20 @@
 /*
  * Copyright 2011      INRIA Saclay
  * Copyright 2011      Sven Verdoolaege
+ * Copyright 2012      Ecole Normale Superieure
  *
  * Use of this software is governed by the GNU LGPLv2.1 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>
+#define ISL_DIM_H
 #include <isl_map_private.h>
+#include <isl_union_map_private.h>
 #include <isl_aff_private.h>
 #include <isl_space_private.h>
 #include <isl_local_space_private.h>
@@ -280,6 +284,34 @@ error:
 	return NULL;
 }
 
+__isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
+	__isl_take isl_space *model)
+{
+	if (!aff || !model)
+		goto error;
+
+	if (!isl_space_match(aff->ls->dim, isl_dim_param,
+			     model, isl_dim_param)) {
+		isl_reordering *exp;
+
+		model = isl_space_drop_dims(model, isl_dim_in,
+					0, isl_space_dim(model, isl_dim_in));
+		model = isl_space_drop_dims(model, isl_dim_out,
+					0, isl_space_dim(model, isl_dim_out));
+		exp = isl_parameter_alignment_reordering(aff->ls->dim, model);
+		exp = isl_reordering_extend_space(exp,
+					isl_aff_get_domain_space(aff));
+		aff = isl_aff_realign_domain(aff, exp);
+	}
+
+	isl_space_free(model);
+	return aff;
+error:
+	isl_space_free(model);
+	isl_aff_free(aff);
+	return NULL;
+}
+
 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
 {
 	if (!aff)
@@ -544,6 +576,41 @@ __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
 	return aff;
 }
 
+/* Remove divs from the local space that do not appear in the affine
+ * expression.
+ * We currently only remove divs at the end.
+ * Some intermediate divs may also not appear directly in the affine
+ * expression, but we would also need to check that no other divs are
+ * defined in terms of them.
+ */
+__isl_give isl_aff *isl_aff_remove_unused_divs( __isl_take isl_aff *aff)
+{
+	int pos;
+	int off;
+	int n;
+
+	if (!aff)
+		return NULL;
+
+	n = isl_local_space_dim(aff->ls, isl_dim_div);
+	off = isl_local_space_offset(aff->ls, isl_dim_div);
+
+	pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1;
+	if (pos == n)
+		return aff;
+
+	aff = isl_aff_cow(aff);
+	if (!aff)
+		return NULL;
+
+	aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos);
+	aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos);
+	if (!aff->ls || !aff->v)
+		return isl_aff_free(aff);
+
+	return aff;
+}
+
 __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
 {
 	if (!aff)
@@ -551,6 +618,7 @@ __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
 	aff->v = isl_vec_normalize(aff->v);
 	if (!aff->v)
 		return isl_aff_free(aff);
+	aff = isl_aff_remove_unused_divs(aff);
 	return aff;
 }
 
@@ -936,6 +1004,7 @@ static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
 	}
 
 	isl_basic_set_free(eq);
+	aff = isl_aff_normalize(aff);
 	return aff;
 error:
 	isl_basic_set_free(eq);
@@ -1011,10 +1080,13 @@ __isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
 {
 	isl_constraint *ineq;
+	isl_basic_set *bset;
 
 	ineq = isl_inequality_from_aff(aff);
 
-	return isl_basic_set_from_constraint(ineq);
+	bset = isl_basic_set_from_constraint(ineq);
+	bset = isl_basic_set_simplify(bset);
+	return bset;
 }
 
 /* Return a basic set containing those elements in the space
@@ -1023,10 +1095,13 @@ __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
 {
 	isl_constraint *ineq;
+	isl_basic_set *bset;
 
 	ineq = isl_equality_from_aff(aff);
 
-	return isl_basic_set_from_constraint(ineq);
+	bset = isl_basic_set_from_constraint(ineq);
+	bset = isl_basic_set_simplify(bset);
+	return bset;
 }
 
 /* Return a basic set containing those elements in the shared space
@@ -1144,6 +1219,30 @@ __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
 	return aff;
 }
 
+/* Project the domain of the affine expression onto its parameter space.
+ * The affine expression may not involve any of the domain dimensions.
+ */
+__isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
+{
+	isl_space *space;
+	unsigned n;
+	int involves;
+
+	n = isl_aff_dim(aff, isl_dim_in);
+	involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
+	if (involves < 0)
+		return isl_aff_free(aff);
+	if (involves)
+		isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
+		    "affine expression involves some of the domain dimensions",
+		    return isl_aff_free(aff));
+	aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
+	space = isl_aff_get_domain_space(aff);
+	space = isl_space_params(space);
+	aff = isl_aff_reset_domain_space(aff, space);
+	return aff;
+}
+
 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
 	enum isl_dim_type type, unsigned first, unsigned n)
 {
@@ -1472,9 +1571,11 @@ __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
 }
 
 /* Return a set containing those elements in the domain
- * of pwaff where it is zero.
+ * of pwaff where it is zero (if complement is 0) or not zero
+ * (if complement is 1).
  */
-__isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
+static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
+	int complement)
 {
 	int i;
 	isl_set *set;
@@ -1486,11 +1587,15 @@ __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
 
 	for (i = 0; i < pwaff->n; ++i) {
 		isl_basic_set *bset;
-		isl_set *set_i;
+		isl_set *set_i, *zero;
 
 		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));
+		zero = isl_set_from_basic_set(bset);
+		set_i = isl_set_copy(pwaff->p[i].set);
+		if (complement)
+			set_i = isl_set_subtract(set_i, zero);
+		else
+			set_i = isl_set_intersect(set_i, zero);
 		set = isl_set_union_disjoint(set, set_i);
 	}
 
@@ -1500,11 +1605,19 @@ __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
 }
 
 /* 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)
+{
+	return pw_aff_zero_set(pwaff, 0);
+}
+
+/* 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 pw_aff_zero_set(pwaff, 1);
 }
 
 /* Return a set containing those elements in the shared domain
@@ -1768,20 +1881,34 @@ __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
 	return pwaff;
 }
 
+/* Assuming that "cond1" and "cond2" are disjoint,
+ * return an affine expression that is equal to pwaff1 on cond1
+ * and to pwaff2 on cond2.
+ */
+static __isl_give isl_pw_aff *isl_pw_aff_select(
+	__isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
+{
+	pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
+	pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);
+
+	return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
+}
+
 /* Return an affine expression that is equal to pwaff_true for elements
- * in "cond" and to pwaff_false for elements not in "cond".
+ * where "cond" is non-zero and to pwaff_false for elements where "cond"
+ * is zero.
  * That is, return cond ? pwaff_true : pwaff_false;
  */
-__isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_set *cond,
+__isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *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);
+	isl_set *cond_true, *cond_false;
 
-	return isl_pw_aff_add_disjoint(pwaff_true, pwaff_false);
+	cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
+	cond_false = isl_pw_aff_zero_set(cond);
+	return isl_pw_aff_select(cond_true, pwaff_true,
+				 cond_false, pwaff_false);
 }
 
 int isl_aff_is_cst(__isl_keep isl_aff *aff)
@@ -1870,10 +1997,14 @@ static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
 	__isl_take isl_pw_aff *pwaff2)
 {
 	isl_set *le;
+	isl_set *dom;
 
+	dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
+				isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
 	le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
 				isl_pw_aff_copy(pwaff2));
-	return isl_pw_aff_cond(le, pwaff1, pwaff2);
+	dom = isl_set_subtract(dom, isl_set_copy(le));
+	return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
 }
 
 __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
@@ -1885,11 +2016,15 @@ __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
 static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
 	__isl_take isl_pw_aff *pwaff2)
 {
-	isl_set *le;
+	isl_set *ge;
+	isl_set *dom;
 
-	le = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
+	dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
+				isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
+	ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
 				isl_pw_aff_copy(pwaff2));
-	return isl_pw_aff_cond(le, pwaff1, pwaff2);
+	dom = isl_set_subtract(dom, isl_set_copy(ge));
+	return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
 }
 
 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
@@ -1947,6 +2082,50 @@ __isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
 
 #include <isl_multi_templ.c>
 
+/* Construct an isl_multi_aff in the given space with value zero in
+ * each of the output dimensions.
+ */
+__isl_give isl_multi_aff *isl_multi_aff_zero(__isl_take isl_space *space)
+{
+	int n;
+	isl_multi_aff *ma;
+
+	if (!space)
+		return NULL;
+
+	n = isl_space_dim(space , isl_dim_out);
+	ma = isl_multi_aff_alloc(isl_space_copy(space));
+
+	if (!n)
+		isl_space_free(space);
+	else {
+		int i;
+		isl_local_space *ls;
+		isl_aff *aff;
+
+		space = isl_space_domain(space);
+		ls = isl_local_space_from_space(space);
+		aff = isl_aff_zero_on_domain(ls);
+
+		for (i = 0; i < n; ++i)
+			ma = isl_multi_aff_set_aff(ma, i, isl_aff_copy(aff));
+
+		isl_aff_free(aff);
+	}
+
+	return ma;
+}
+
+/* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
+ * domain.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
+	__isl_take isl_multi_aff *ma)
+{
+	isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
+	return isl_pw_multi_aff_alloc(dom, ma);
+}
+
 __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
 	__isl_take isl_multi_aff *maff2)
 {
@@ -2094,6 +2273,16 @@ __isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff
 	maff->space = isl_space_drop_dims(maff->space, type, first, n);
 	if (!maff->space)
 		return isl_multi_aff_free(maff);
+
+	if (type == isl_dim_out) {
+		for (i = 0; i < n; ++i)
+			isl_aff_free(maff->p[first + i]);
+		for (i = first; i + n < maff->n; ++i)
+			maff->p[i] = maff->p[i + n];
+		maff->n -= n;
+		return 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])
@@ -2129,6 +2318,18 @@ __isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff
 
 #include <isl_pw_templ.c>
 
+#undef UNION
+#define UNION isl_union_pw_multi_aff
+#undef PART
+#define PART isl_pw_multi_aff
+#undef PARTS
+#define PARTS pw_multi_aff
+#define ALIGN_DOMAIN
+
+#define NO_EVAL
+
+#include <isl_union_templ.c>
+
 static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
 	__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
 {
@@ -2190,22 +2391,145 @@ __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
 	return isl_map_from_pw_multi_aff(pma);
 }
 
+/* Given a basic map with a single output dimension that is defined
+ * in terms of the parameters and input dimensions using an equality,
+ * extract an isl_aff that expresses the output dimension in terms
+ * of the parameters and input dimensions.
+ *
+ * Since some applications expect the result of isl_pw_multi_aff_from_map
+ * to only contain integer affine expressions, we compute the floor
+ * of the expression before returning.
+ *
+ * This function shares some similarities with
+ * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
+ */
+static __isl_give isl_aff *extract_isl_aff_from_basic_map(
+	__isl_take isl_basic_map *bmap)
+{
+	int i;
+	unsigned offset;
+	unsigned total;
+	isl_local_space *ls;
+	isl_aff *aff;
+
+	if (!bmap)
+		return NULL;
+	if (isl_basic_map_dim(bmap, isl_dim_out) != 1)
+		isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
+			"basic map should have a single output dimension",
+			goto error);
+	offset = isl_basic_map_offset(bmap, isl_dim_out);
+	total = isl_basic_map_total_dim(bmap);
+	for (i = 0; i < bmap->n_eq; ++i) {
+		if (isl_int_is_zero(bmap->eq[i][offset]))
+			continue;
+		if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1,
+					   1 + total - (offset + 1)) != -1)
+			continue;
+		break;
+	}
+	if (i >= bmap->n_eq)
+		isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
+			"unable to find suitable equality", goto error);
+	ls = isl_basic_map_get_local_space(bmap);
+	aff = isl_aff_alloc(isl_local_space_domain(ls));
+	if (!aff)
+		goto error;
+	if (isl_int_is_neg(bmap->eq[i][offset]))
+		isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset);
+	else
+		isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset);
+	isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset));
+	isl_int_abs(aff->v->el[0], bmap->eq[i][offset]);
+	isl_basic_map_free(bmap);
+
+	aff = isl_aff_remove_unused_divs(aff);
+	aff = isl_aff_floor(aff);
+	return aff;
+error:
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* Given a basic map where each output dimension is defined
+ * in terms of the parameters and input dimensions using an equality,
+ * extract an isl_multi_aff that expresses the output dimensions in terms
+ * of the parameters and input dimensions.
+ */
+static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
+	__isl_take isl_basic_map *bmap)
+{
+	int i;
+	unsigned n_out;
+	isl_multi_aff *ma;
+
+	if (!bmap)
+		return NULL;
+
+	ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
+	n_out = isl_basic_map_dim(bmap, isl_dim_out);
+
+	for (i = 0; i < n_out; ++i) {
+		isl_basic_map *bmap_i;
+		isl_aff *aff;
+
+		bmap_i = isl_basic_map_copy(bmap);
+		bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out,
+							i + 1, n_out - (1 + i));
+		bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i);
+		aff = extract_isl_aff_from_basic_map(bmap_i);
+		ma = isl_multi_aff_set_aff(ma, i, aff);
+	}
+
+	isl_basic_map_free(bmap);
+
+	return ma;
+}
+
+/* Create an isl_pw_multi_aff that is equivalent to
+ * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
+ * The given basic map is such that each output dimension is defined
+ * in terms of the parameters and input dimensions using an equality.
+ */
+static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
+	__isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
+{
+	isl_multi_aff *ma;
+
+	ma = extract_isl_multi_aff_from_basic_map(bmap);
+	return isl_pw_multi_aff_alloc(domain, ma);
+}
+
 /* 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.
+ *
+ * As a special case, we first check if all output dimensions are uniquely
+ * defined in terms of the parameters and input dimensions over the entire
+ * domain.  If so, we extract the desired isl_pw_multi_aff directly
+ * from the affine hull of "map" and its domain.
  */
 __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;
+	isl_basic_map *hull;
 
 	if (!map)
 		return NULL;
 
+	hull = isl_map_affine_hull(isl_map_copy(map));
+	sv = isl_basic_map_plain_is_single_valued(hull);
+	if (sv >= 0 && sv)
+		return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
+	isl_basic_map_free(hull);
+	if (sv < 0)
+		goto error;
+
 	sv = isl_map_is_single_valued(map);
 	if (sv < 0)
 		goto error;
@@ -2238,6 +2562,24 @@ __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);
 }
 
+/* Return the piecewise affine expression "set ? 1 : 0".
+ */
+__isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
+{
+	isl_pw_aff *pa;
+	isl_space *space = isl_set_get_space(set);
+	isl_local_space *ls = isl_local_space_from_space(space);
+	isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
+	isl_aff *one = isl_aff_zero_on_domain(ls);
+
+	one = isl_aff_add_constant_si(one, 1);
+	pa = isl_pw_aff_alloc(isl_set_copy(set), one);
+	set = isl_set_complement(set);
+	pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));
+
+	return pa;
+}
+
 /* Plug in "subs" for dimension "type", "pos" of "aff".
  *
  * Let i be the dimension to replace and let "subs" be of the form
@@ -2516,3 +2858,37 @@ error:
 		isl_local_space_free(*ls);
 	return isl_multi_aff_free(maff);
 }
+
+
+/* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
+ */
+__isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
+	__isl_keep isl_pw_multi_aff *pma, int pos)
+{
+	int i;
+	int n_out;
+	isl_space *space;
+	isl_pw_aff *pa;
+
+	if (!pma)
+		return NULL;
+
+	n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
+	if (pos < 0 || pos >= n_out)
+		isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
+			"index out of bounds", return NULL);
+
+	space = isl_pw_multi_aff_get_space(pma);
+	space = isl_space_drop_dims(space, isl_dim_out,
+				    pos + 1, n_out - pos - 1);
+	space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
+
+	pa = isl_pw_aff_alloc_size(space, pma->n);
+	for (i = 0; i < pma->n; ++i) {
+		isl_aff *aff;
+		aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
+		pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
+	}
+
+	return pa;
+}