X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_aff.c;h=6517d68380a701db5e5886f8aacc7d3e97be1533;hb=a9ac417a5062dc7e620fffae9b0143f3de98b697;hp=59216bb4682f75fef06772cd573fbfb233c2122f;hpb=d7f2a9e08113822dc3c10ebc2e3819c517d33d95;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_aff.c b/isl_aff.c
index 59216bb..6517d68 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
+ * 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>
+#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>
@@ -19,6 +23,7 @@
 #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)
@@ -83,6 +88,63 @@ __isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls)
 	return aff;
 }
 
+/* Return a piecewise affine expression defined on the specified domain
+ * that is equal to zero.
+ */
+__isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(__isl_take isl_local_space *ls)
+{
+	return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls));
+}
+
+/* Return an affine expression that is equal to the specified dimension
+ * in "ls".
+ */
+__isl_give isl_aff *isl_aff_var_on_domain(__isl_take isl_local_space *ls,
+	enum isl_dim_type type, unsigned pos)
+{
+	isl_space *space;
+	isl_aff *aff;
+
+	if (!ls)
+		return NULL;
+
+	space = isl_local_space_get_space(ls);
+	if (!space)
+		goto error;
+	if (isl_space_is_map(space))
+		isl_die(isl_space_get_ctx(space), isl_error_invalid,
+			"expecting (parameter) set space", goto error);
+	if (pos >= isl_local_space_dim(ls, type))
+		isl_die(isl_space_get_ctx(space), isl_error_invalid,
+			"position out of bounds", goto error);
+
+	isl_space_free(space);
+	aff = isl_aff_alloc(ls);
+	if (!aff)
+		return NULL;
+
+	pos += isl_local_space_offset(aff->ls, type);
+
+	isl_int_set_si(aff->v->el[0], 1);
+	isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
+	isl_int_set_si(aff->v->el[1 + pos], 1);
+
+	return aff;
+error:
+	isl_local_space_free(ls);
+	isl_space_free(space);
+	return NULL;
+}
+
+/* Return a piecewise affine expression that is equal to
+ * the specified dimension in "ls".
+ */
+__isl_give isl_pw_aff *isl_pw_aff_var_on_domain(__isl_take isl_local_space *ls,
+	enum isl_dim_type type, unsigned pos)
+{
+	return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls, type, pos));
+}
+
 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
 {
 	if (!aff)
@@ -279,6 +341,34 @@ 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)
@@ -400,6 +490,43 @@ __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
 	return aff;
 }
 
+/* Add "v" to the numerator of the constant term of "aff".
+ */
+__isl_give isl_aff *isl_aff_add_constant_num(__isl_take isl_aff *aff, isl_int v)
+{
+	if (isl_int_is_zero(v))
+		return aff;
+
+	aff = isl_aff_cow(aff);
+	if (!aff)
+		return NULL;
+
+	aff->v = isl_vec_cow(aff->v);
+	if (!aff->v)
+		return isl_aff_free(aff);
+
+	isl_int_add(aff->v->el[1], aff->v->el[1], v);
+
+	return aff;
+}
+
+/* Add "v" to the numerator of the constant term of "aff".
+ */
+__isl_give isl_aff *isl_aff_add_constant_num_si(__isl_take isl_aff *aff, int v)
+{
+	isl_int t;
+
+	if (v == 0)
+		return aff;
+
+	isl_int_init(t);
+	isl_int_set_si(t, v);
+	aff = isl_aff_add_constant_num(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);
@@ -543,8 +670,233 @@ __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;
+}
+
+/* Given two affine expressions "p" of length p_len (including the
+ * denominator and the constant term) and "subs" of length subs_len,
+ * plug in "subs" for the variable at position "pos".
+ * The variables of "subs" and "p" are assumed to match up to subs_len,
+ * but "p" may have additional variables.
+ * "v" is an initialized isl_int that can be used internally.
+ *
+ * In particular, if "p" represents the expression
+ *
+ *	(a i + g)/m
+ *
+ * with i the variable at position "pos" and "subs" represents the expression
+ *
+ *	f/d
+ *
+ * then the result represents the expression
+ *
+ *	(a f + d g)/(m d)
+ *
+ */
+void isl_seq_substitute(isl_int *p, int pos, isl_int *subs,
+	int p_len, int subs_len, isl_int v)
+{
+	isl_int_set(v, p[1 + pos]);
+	isl_int_set_si(p[1 + pos], 0);
+	isl_seq_combine(p + 1, subs[0], p + 1, v, subs + 1, subs_len - 1);
+	isl_seq_scale(p + subs_len, p + subs_len, subs[0], p_len - subs_len);
+	isl_int_mul(p[0], p[0], subs[0]);
+}
+
+/* Look for any divs in the aff->ls with a denominator equal to one
+ * and plug them into the affine expression and any subsequent divs
+ * that may reference the div.
+ */
+static __isl_give isl_aff *plug_in_integral_divs(__isl_take isl_aff *aff)
+{
+	int i, n;
+	int len;
+	isl_int v;
+	isl_vec *vec;
+	isl_local_space *ls;
+	unsigned pos;
+
+	if (!aff)
+		return NULL;
+
+	n = isl_local_space_dim(aff->ls, isl_dim_div);
+	len = aff->v->size;
+	for (i = 0; i < n; ++i) {
+		if (!isl_int_is_one(aff->ls->div->row[i][0]))
+			continue;
+		ls = isl_local_space_copy(aff->ls);
+		ls = isl_local_space_substitute_seq(ls, isl_dim_div, i,
+					    aff->ls->div->row[i], len, i + 1);
+		vec = isl_vec_copy(aff->v);
+		vec = isl_vec_cow(vec);
+		if (!ls || !vec)
+			goto error;
+
+		isl_int_init(v);
+
+		pos = isl_local_space_offset(aff->ls, isl_dim_div) + i;
+		isl_seq_substitute(vec->el, pos, aff->ls->div->row[i],
+					len, len, v);
+
+		isl_int_clear(v);
+
+		isl_vec_free(aff->v);
+		aff->v = vec;
+		isl_local_space_free(aff->ls);
+		aff->ls = ls;
+	}
+
+	return aff;
+error:
+	isl_vec_free(vec);
+	isl_local_space_free(ls);
+	return isl_aff_free(aff);
+}
+
+/* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
+ *
+ * Even though this function is only called on isl_affs with a single
+ * reference, we are careful to only change aff->v and aff->ls together.
+ */
+static __isl_give isl_aff *swap_div(__isl_take isl_aff *aff, int a, int b)
+{
+	unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
+	isl_local_space *ls;
+	isl_vec *v;
+
+	ls = isl_local_space_copy(aff->ls);
+	ls = isl_local_space_swap_div(ls, a, b);
+	v = isl_vec_copy(aff->v);
+	v = isl_vec_cow(v);
+	if (!ls || !v)
+		goto error;
+
+	isl_int_swap(v->el[1 + off + a], v->el[1 + off + b]);
+	isl_vec_free(aff->v);
+	aff->v = v;
+	isl_local_space_free(aff->ls);
+	aff->ls = ls;
+
+	return aff;
+error:
+	isl_vec_free(v);
+	isl_local_space_free(ls);
+	return isl_aff_free(aff);
+}
+
+/* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
+ *
+ * We currently do not actually remove div "b", but simply add its
+ * coefficient to that of "a" and then zero it out.
+ */
+static __isl_give isl_aff *merge_divs(__isl_take isl_aff *aff, int a, int b)
+{
+	unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
+
+	if (isl_int_is_zero(aff->v->el[1 + off + b]))
+		return aff;
+
+	aff->v = isl_vec_cow(aff->v);
+	if (!aff->v)
+		return isl_aff_free(aff);
+
+	isl_int_add(aff->v->el[1 + off + a],
+		    aff->v->el[1 + off + a], aff->v->el[1 + off + b]);
+	isl_int_set_si(aff->v->el[1 + off + b], 0);
+
+	return aff;
+}
+
+/* Sort the divs in the local space of "aff" according to
+ * the comparison function "cmp_row" in isl_local_space.c,
+ * combining the coefficients of identical divs.
+ *
+ * Reordering divs does not change the semantics of "aff",
+ * so there is no need to call isl_aff_cow.
+ * Moreover, this function is currently only called on isl_affs
+ * with a single reference.
+ */
+static __isl_give isl_aff *sort_divs(__isl_take isl_aff *aff)
+{
+	int i, j, n;
+	unsigned off;
+
+	if (!aff)
+		return NULL;
+
+	off = isl_local_space_offset(aff->ls, isl_dim_div);
+	n = isl_aff_dim(aff, isl_dim_div);
+	for (i = 1; i < n; ++i) {
+		for (j = i - 1; j >= 0; --j) {
+			int cmp = isl_mat_cmp_div(aff->ls->div, j, j + 1);
+			if (cmp < 0)
+				break;
+			if (cmp == 0)
+				aff = merge_divs(aff, j, j + 1);
+			else
+				aff = swap_div(aff, j, j + 1);
+			if (!aff)
+				return NULL;
+		}
+	}
+
+	return aff;
+}
+
+/* Normalize the representation of "aff".
+ *
+ * This function should only be called of "new" isl_affs, i.e.,
+ * with only a single reference.  We therefore do not need to
+ * worry about affecting other instances.
+ */
+__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);
+	aff = plug_in_integral_divs(aff);
+	aff = sort_divs(aff);
+	aff = isl_aff_remove_unused_divs(aff);
+	return aff;
+}
+
 /* Given f, return floor(f).
  * If f is an integer expression, then just return f.
+ * If f is a constant, then return the constant floor(f).
  * 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.
@@ -567,6 +919,15 @@ __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
 		return NULL;
 
 	aff->v = isl_vec_cow(aff->v);
+	if (!aff->v)
+		return isl_aff_free(aff);
+
+	if (isl_aff_is_cst(aff)) {
+		isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
+		isl_int_set_si(aff->v->el[0], 1);
+		return aff;
+	}
+
 	div = isl_vec_copy(aff->v);
 	div = isl_vec_cow(div);
 	if (!div)
@@ -813,6 +1174,11 @@ __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
 	aff = isl_aff_cow(aff);
 	if (!aff)
 		return NULL;
+
+	if (isl_int_is_zero(f))
+		isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
+			"cannot scale down by zero", return isl_aff_free(aff));
+
 	aff->v = isl_vec_cow(aff->v);
 	if (!aff->v)
 		return isl_aff_free(aff);
@@ -925,6 +1291,7 @@ 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);
@@ -986,28 +1353,64 @@ error:
 	return NULL;
 }
 
+__isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
+	__isl_take isl_set *context)
+{
+	isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
+	dom_context = isl_set_intersect_params(dom_context, context);
+	return isl_aff_gist(aff, dom_context);
+}
+
 /* 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;
+	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 domain space
+ * of aff where it is negative.
+ */
+__isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff)
+{
+	aff = isl_aff_neg(aff);
+	aff = isl_aff_add_constant_num_si(aff, -1);
+	return isl_aff_nonneg_basic_set(aff);
 }
 
 /* Return a basic set containing those elements in the space
  * of aff where it is zero.
+ * If "rational" is set, then return a rational basic set.
  */
-__isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
+static __isl_give isl_basic_set *aff_zero_basic_set(__isl_take isl_aff *aff,
+	int rational)
 {
 	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);
+	if (rational)
+		bset = isl_basic_set_set_rational(bset);
+	bset = isl_basic_set_simplify(bset);
+	return bset;
+}
+
+/* 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)
+{
+	return aff_zero_basic_set(aff, 0);
 }
 
 /* Return a basic set containing those elements in the shared space
@@ -1125,6 +1528,30 @@ __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)
 {
@@ -1200,6 +1627,8 @@ __isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
 #define IS_ZERO is_empty
 #undef FIELD
 #define FIELD aff
+#undef DEFAULT_IS_ZERO
+#define DEFAULT_IS_ZERO 0
 
 #define NO_EVAL
 #define NO_OPT
@@ -1398,6 +1827,8 @@ static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
  */
 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
 {
+	if (!pwaff)
+		return NULL;
 	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",
@@ -1411,6 +1842,8 @@ __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
  */
 __isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
 {
+	if (!pwaff)
+		return NULL;
 	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",
@@ -1447,9 +1880,11 @@ __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;
@@ -1461,11 +1896,18 @@ __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;
-
-		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));
+		isl_set *set_i, *zero;
+		int rational;
+
+		rational = isl_set_has_rational(pwaff->p[i].set);
+		bset = aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff),
+						rational);
+		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);
 	}
 
@@ -1475,11 +1917,19 @@ __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
@@ -1743,20 +2193,34 @@ __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)
@@ -1811,60 +2275,183 @@ error:
 	return NULL;
 }
 
-static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
-	__isl_take isl_pw_aff *pwaff2)
+/* Divide "aff1" by "aff2", assuming "aff2" is a piecewise constant.
+ */
+__isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
+	__isl_take isl_aff *aff2)
 {
-	int i, j, n;
-	isl_pw_aff *res;
+	int is_cst;
+	int neg;
 
-	if (!pwaff1 || !pwaff2)
+	is_cst = isl_aff_is_cst(aff2);
+	if (is_cst < 0)
 		goto error;
+	if (!is_cst)
+		isl_die(isl_aff_get_ctx(aff2), isl_error_invalid,
+			"second argument should be a constant", goto error);
 
-	n = pwaff1->n * pwaff2->n;
-	res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
+	if (!aff2)
+		goto error;
 
-	for (i = 0; i < pwaff1->n; ++i) {
-		for (j = 0; j < pwaff2->n; ++j) {
-			isl_set *common;
-			isl_aff *prod;
-			common = isl_set_intersect(
-					isl_set_copy(pwaff1->p[i].set),
-					isl_set_copy(pwaff2->p[j].set));
-			if (isl_set_plain_is_empty(common)) {
-				isl_set_free(common);
-				continue;
-			}
+	neg = isl_int_is_neg(aff2->v->el[1]);
+	if (neg) {
+		isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
+		isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
+	}
 
-			prod = isl_aff_mul(isl_aff_copy(pwaff1->p[i].aff),
-					    isl_aff_copy(pwaff2->p[j].aff));
+	aff1 = isl_aff_scale(aff1, aff2->v->el[0]);
+	aff1 = isl_aff_scale_down(aff1, aff2->v->el[1]);
 
-			res = isl_pw_aff_add_piece(res, common, prod);
-		}
+	if (neg) {
+		isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
+		isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
 	}
 
-	isl_pw_aff_free(pwaff1);
-	isl_pw_aff_free(pwaff2);
-	return res;
+	isl_aff_free(aff2);
+	return aff1;
 error:
-	isl_pw_aff_free(pwaff1);
-	isl_pw_aff_free(pwaff2);
+	isl_aff_free(aff1);
+	isl_aff_free(aff2);
 	return NULL;
 }
 
+static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_add(__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_add);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return isl_pw_aff_union_add_(pwaff1, pwaff2);
+}
+
+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_div(__isl_take isl_pw_aff *pa1,
+	__isl_take isl_pw_aff *pa2)
+{
+	return isl_pw_aff_on_shared_domain(pa1, pa2, &isl_aff_div);
+}
+
+/* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant.
+ */
+__isl_give isl_pw_aff *isl_pw_aff_div(__isl_take isl_pw_aff *pa1,
+	__isl_take isl_pw_aff *pa2)
+{
+	int is_cst;
+
+	is_cst = isl_pw_aff_is_cst(pa2);
+	if (is_cst < 0)
+		goto error;
+	if (!is_cst)
+		isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
+			"second argument should be a piecewise constant",
+			goto error);
+	return isl_pw_aff_align_params_pw_pw_and(pa1, pa2, &pw_aff_div);
+error:
+	isl_pw_aff_free(pa1);
+	isl_pw_aff_free(pa2);
+	return NULL;
+}
+
+/* Compute the quotient of the integer division of "pa1" by "pa2"
+ * with rounding towards zero.
+ * "pa2" is assumed to be a piecewise constant.
+ *
+ * In particular, return
+ *
+ *	pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)
+ *
+ */
+__isl_give isl_pw_aff *isl_pw_aff_tdiv_q(__isl_take isl_pw_aff *pa1,
+	__isl_take isl_pw_aff *pa2)
+{
+	int is_cst;
+	isl_set *cond;
+	isl_pw_aff *f, *c;
+
+	is_cst = isl_pw_aff_is_cst(pa2);
+	if (is_cst < 0)
+		goto error;
+	if (!is_cst)
+		isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
+			"second argument should be a piecewise constant",
+			goto error);
+
+	pa1 = isl_pw_aff_div(pa1, pa2);
+
+	cond = isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1));
+	f = isl_pw_aff_floor(isl_pw_aff_copy(pa1));
+	c = isl_pw_aff_ceil(pa1);
+	return isl_pw_aff_cond(isl_set_indicator_function(cond), f, c);
+error:
+	isl_pw_aff_free(pa1);
+	isl_pw_aff_free(pa2);
+	return NULL;
+}
+
+/* Compute the remainder of the integer division of "pa1" by "pa2"
+ * with rounding towards zero.
+ * "pa2" is assumed to be a piecewise constant.
+ *
+ * In particular, return
+ *
+ *	pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2))
+ *
+ */
+__isl_give isl_pw_aff *isl_pw_aff_tdiv_r(__isl_take isl_pw_aff *pa1,
+	__isl_take isl_pw_aff *pa2)
+{
+	int is_cst;
+	isl_pw_aff *res;
+
+	is_cst = isl_pw_aff_is_cst(pa2);
+	if (is_cst < 0)
+		goto error;
+	if (!is_cst)
+		isl_die(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
+			"second argument should be a piecewise constant",
+			goto error);
+	res = isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1), isl_pw_aff_copy(pa2));
+	res = isl_pw_aff_mul(pa2, res);
+	res = isl_pw_aff_sub(pa1, res);
+	return res;
+error:
+	isl_pw_aff_free(pa1);
+	isl_pw_aff_free(pa2);
+	return NULL;
+}
+
 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,
@@ -1876,11 +2463,15 @@ __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,
@@ -1933,11 +2524,74 @@ __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);
 }
 
+/* Mark the domains of "pwaff" as rational.
+ */
+__isl_give isl_pw_aff *isl_pw_aff_set_rational(__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].set = isl_set_set_rational(pwaff->p[i].set);
+		if (!pwaff->p[i].set)
+			return isl_pw_aff_free(pwaff);
+	}
+
+	return pwaff;
+}
+
+/* Mark the domains of the elements of "list" as rational.
+ */
+__isl_give isl_pw_aff_list *isl_pw_aff_list_set_rational(
+	__isl_take isl_pw_aff_list *list)
+{
+	int i;
+
+	if (!list)
+		return NULL;
+	if (list->n == 0)
+		return list;
+
+	for (i = 0; i < list->n; ++i) {
+		isl_pw_aff *pa;
+
+		pa = isl_pw_aff_list_get_pw_aff(list, i);
+		pa = isl_pw_aff_set_rational(pa);
+		list = isl_pw_aff_list_set_pw_aff(list, i, pa);
+	}
+
+	return list;
+}
+
 #undef BASE
 #define BASE aff
 
 #include <isl_multi_templ.c>
 
+/* 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);
+}
+
+/* Create a piecewise multi-affine expression in the given space that maps each
+ * input dimension to the corresponding output dimension.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
+	__isl_take isl_space *space)
+{
+	return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space));
+}
+
 __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
 	__isl_take isl_multi_aff *maff2)
 {
@@ -1968,6 +2622,47 @@ error:
 	return NULL;
 }
 
+/* Given two multi-affine expressions A -> B and C -> D,
+ * construct a multi-affine expression [A -> C] -> [B -> D].
+ */
+__isl_give isl_multi_aff *isl_multi_aff_product(
+	__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
+{
+	int i;
+	isl_aff *aff;
+	isl_space *space;
+	isl_multi_aff *res;
+	int in1, in2, out1, out2;
+
+	in1 = isl_multi_aff_dim(ma1, isl_dim_in);
+	in2 = isl_multi_aff_dim(ma2, isl_dim_in);
+	out1 = isl_multi_aff_dim(ma1, isl_dim_out);
+	out2 = isl_multi_aff_dim(ma2, isl_dim_out);
+	space = isl_space_product(isl_multi_aff_get_space(ma1),
+				  isl_multi_aff_get_space(ma2));
+	res = isl_multi_aff_alloc(isl_space_copy(space));
+	space = isl_space_domain(space);
+
+	for (i = 0; i < out1; ++i) {
+		aff = isl_multi_aff_get_aff(ma1, i);
+		aff = isl_aff_insert_dims(aff, isl_dim_in, in1, in2);
+		aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
+		res = isl_multi_aff_set_aff(res, i, aff);
+	}
+
+	for (i = 0; i < out2; ++i) {
+		aff = isl_multi_aff_get_aff(ma2, i);
+		aff = isl_aff_insert_dims(aff, isl_dim_in, 0, in1);
+		aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
+		res = isl_multi_aff_set_aff(res, out1 + i, aff);
+	}
+
+	isl_space_free(space);
+	isl_multi_aff_free(ma1);
+	isl_multi_aff_free(ma2);
+	return res;
+}
+
 /* Exploit the equalities in "eq" to simplify the affine expressions.
  */
 static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
@@ -2051,47 +2746,34 @@ int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
 	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)
+/* Return the set of domain elements where "ma1" is lexicographically
+ * smaller than or equal to "ma2".
+ */
+__isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1,
+	__isl_take isl_multi_aff *ma2)
 {
-	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;
+	return isl_multi_aff_lex_ge_set(ma2, ma1);
 }
 
-__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)
+/* Return the set of domain elements where "ma1" is lexicographically
+ * greater than or equal to "ma2".
+ */
+__isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1,
+	__isl_take isl_multi_aff *ma2)
 {
-	int i;
-
-	maff = isl_multi_aff_cow(maff);
-	if (!maff)
-		return NULL;
+	isl_space *space;
+	isl_map *map1, *map2;
+	isl_map *map, *ge;
 
-	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);
-	}
+	map1 = isl_map_from_multi_aff(ma1);
+	map2 = isl_map_from_multi_aff(ma2);
+	map = isl_map_range_product(map1, map2);
+	space = isl_space_range(isl_map_get_space(map));
+	space = isl_space_domain(isl_space_unwrap(space));
+	ge = isl_map_lex_ge(space);
+	map = isl_map_intersect_range(map, isl_map_wrap(ge));
 
-	return maff;
+	return isl_map_domain(map);
 }
 
 #undef PW
@@ -2106,6 +2788,8 @@ __isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff
 #define IS_ZERO is_empty
 #undef FIELD
 #define FIELD maff
+#undef DEFAULT_IS_ZERO
+#define DEFAULT_IS_ZERO 0
 
 #define NO_NEG
 #define NO_EVAL
@@ -2118,7 +2802,239 @@ __isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff
 
 #include <isl_pw_templ.c>
 
-/* Construct a map mapping the domain the piecewise multi-affine expression
+#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>
+
+/* Given a function "cmp" that returns the set of elements where
+ * "ma1" is "better" than "ma2", return the intersection of this
+ * set with "dom1" and "dom2".
+ */
+static __isl_give isl_set *shared_and_better(__isl_keep isl_set *dom1,
+	__isl_keep isl_set *dom2, __isl_keep isl_multi_aff *ma1,
+	__isl_keep isl_multi_aff *ma2,
+	__isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
+				    __isl_take isl_multi_aff *ma2))
+{
+	isl_set *common;
+	isl_set *better;
+	int is_empty;
+
+	common = isl_set_intersect(isl_set_copy(dom1), isl_set_copy(dom2));
+	is_empty = isl_set_plain_is_empty(common);
+	if (is_empty >= 0 && is_empty)
+		return common;
+	if (is_empty < 0)
+		return isl_set_free(common);
+	better = cmp(isl_multi_aff_copy(ma1), isl_multi_aff_copy(ma2));
+	better = isl_set_intersect(common, better);
+
+	return better;
+}
+
+/* Given a function "cmp" that returns the set of elements where
+ * "ma1" is "better" than "ma2", return a piecewise multi affine
+ * expression defined on the union of the definition domains
+ * of "pma1" and "pma2" that maps to the "best" of "pma1" and
+ * "pma2" on each cell.  If only one of the two input functions
+ * is defined on a given cell, then it is considered the best.
+ */
+static __isl_give isl_pw_multi_aff *pw_multi_aff_union_opt(
+	__isl_take isl_pw_multi_aff *pma1,
+	__isl_take isl_pw_multi_aff *pma2,
+	__isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
+				    __isl_take isl_multi_aff *ma2))
+{
+	int i, j, n;
+	isl_pw_multi_aff *res = NULL;
+	isl_ctx *ctx;
+	isl_set *set = NULL;
+
+	if (!pma1 || !pma2)
+		goto error;
+
+	ctx = isl_space_get_ctx(pma1->dim);
+	if (!isl_space_is_equal(pma1->dim, pma2->dim))
+		isl_die(ctx, isl_error_invalid,
+			"arguments should live in the same space", goto error);
+
+	if (isl_pw_multi_aff_is_empty(pma1)) {
+		isl_pw_multi_aff_free(pma1);
+		return pma2;
+	}
+
+	if (isl_pw_multi_aff_is_empty(pma2)) {
+		isl_pw_multi_aff_free(pma2);
+		return pma1;
+	}
+
+	n = 2 * (pma1->n + 1) * (pma2->n + 1);
+	res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma1->dim), n);
+
+	for (i = 0; i < pma1->n; ++i) {
+		set = isl_set_copy(pma1->p[i].set);
+		for (j = 0; j < pma2->n; ++j) {
+			isl_set *better;
+			int is_empty;
+
+			better = shared_and_better(pma2->p[j].set,
+					pma1->p[i].set, pma2->p[j].maff,
+					pma1->p[i].maff, cmp);
+			is_empty = isl_set_plain_is_empty(better);
+			if (is_empty < 0 || is_empty) {
+				isl_set_free(better);
+				if (is_empty < 0)
+					goto error;
+				continue;
+			}
+			set = isl_set_subtract(set, isl_set_copy(better));
+
+			res = isl_pw_multi_aff_add_piece(res, better,
+					isl_multi_aff_copy(pma2->p[j].maff));
+		}
+		res = isl_pw_multi_aff_add_piece(res, set,
+					isl_multi_aff_copy(pma1->p[i].maff));
+	}
+
+	for (j = 0; j < pma2->n; ++j) {
+		set = isl_set_copy(pma2->p[j].set);
+		for (i = 0; i < pma1->n; ++i)
+			set = isl_set_subtract(set,
+					isl_set_copy(pma1->p[i].set));
+		res = isl_pw_multi_aff_add_piece(res, set,
+					isl_multi_aff_copy(pma2->p[j].maff));
+	}
+
+	isl_pw_multi_aff_free(pma1);
+	isl_pw_multi_aff_free(pma2);
+
+	return res;
+error:
+	isl_pw_multi_aff_free(pma1);
+	isl_pw_multi_aff_free(pma2);
+	isl_set_free(set);
+	return isl_pw_multi_aff_free(res);
+}
+
+static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax(
+	__isl_take isl_pw_multi_aff *pma1,
+	__isl_take isl_pw_multi_aff *pma2)
+{
+	return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_ge_set);
+}
+
+/* Given two piecewise multi affine expressions, return a piecewise
+ * multi-affine expression defined on the union of the definition domains
+ * of the inputs that is equal to the lexicographic maximum of the two
+ * inputs on each cell.  If only one of the two inputs is defined on
+ * a given cell, then it is considered to be the maximum.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
+	__isl_take isl_pw_multi_aff *pma1,
+	__isl_take isl_pw_multi_aff *pma2)
+{
+	return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+						    &pw_multi_aff_union_lexmax);
+}
+
+static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin(
+	__isl_take isl_pw_multi_aff *pma1,
+	__isl_take isl_pw_multi_aff *pma2)
+{
+	return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_le_set);
+}
+
+/* Given two piecewise multi affine expressions, return a piecewise
+ * multi-affine expression defined on the union of the definition domains
+ * of the inputs that is equal to the lexicographic minimum of the two
+ * inputs on each cell.  If only one of the two inputs is defined on
+ * a given cell, then it is considered to be the minimum.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
+	__isl_take isl_pw_multi_aff *pma1,
+	__isl_take isl_pw_multi_aff *pma2)
+{
+	return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+						    &pw_multi_aff_union_lexmin);
+}
+
+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)
+{
+	return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
+						&isl_multi_aff_add);
+}
+
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
+	__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+	return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+						&pw_multi_aff_add);
+}
+
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
+	__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+	return isl_pw_multi_aff_union_add_(pma1, pma2);
+}
+
+/* Given two piecewise multi-affine expressions A -> B and C -> D,
+ * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
+ */
+static __isl_give isl_pw_multi_aff *pw_multi_aff_product(
+	__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+	int i, j, n;
+	isl_space *space;
+	isl_pw_multi_aff *res;
+
+	if (!pma1 || !pma2)
+		goto error;
+
+	n = pma1->n * pma2->n;
+	space = isl_space_product(isl_space_copy(pma1->dim),
+				  isl_space_copy(pma2->dim));
+	res = isl_pw_multi_aff_alloc_size(space, n);
+
+	for (i = 0; i < pma1->n; ++i) {
+		for (j = 0; j < pma2->n; ++j) {
+			isl_set *domain;
+			isl_multi_aff *ma;
+
+			domain = isl_set_product(isl_set_copy(pma1->p[i].set),
+						 isl_set_copy(pma2->p[j].set));
+			ma = isl_multi_aff_product(
+					isl_multi_aff_copy(pma1->p[i].maff),
+					isl_multi_aff_copy(pma2->p[i].maff));
+			res = isl_pw_multi_aff_add_piece(res, domain, ma);
+		}
+	}
+
+	isl_pw_multi_aff_free(pma1);
+	isl_pw_multi_aff_free(pma2);
+	return res;
+error:
+	isl_pw_multi_aff_free(pma1);
+	isl_pw_multi_aff_free(pma2);
+	return NULL;
+}
+
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
+	__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+	return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+						&pw_multi_aff_product);
+}
+
+/* Construct a map mapping the domain of the piecewise multi-affine expression
  * to its range, with each dimension in the range equated to the
  * corresponding affine expression on its cell.
  */
@@ -2151,6 +3067,9 @@ __isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
 
 __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
 {
+	if (!pma)
+		return NULL;
+
 	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",
@@ -2159,25 +3078,214 @@ __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);
 }
 
-/* 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
+/* 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.
  *
- *	(a i + g)/m
- *
- * The result is
- *
- *	floor((a f + d g')/(m d))
+ * 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.
  *
- * where g' is the result of plugging in "subs" in each of the integer
- * divisions in g.
+ * This function shares some similarities with
+ * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
  */
-__isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
-	enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
+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 obviously 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;
+	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);
+}
+
+/* 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
+ *
+ *	f/d
+ *
+ * and "aff" of the form
+ *
+ *	(a i + g)/m
+ *
+ * The result is
+ *
+ *	(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;
@@ -2205,11 +3313,8 @@ __isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *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_seq_substitute(aff->v->el, pos, subs->v->el,
+			    aff->v->size, subs->v->size, v);
 	isl_int_clear(v);
 
 	return aff;
@@ -2296,3 +3401,507 @@ __isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
 	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);
+}
+
+
+/* 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;
+}
+
+/* Return an isl_pw_multi_aff with the given "set" as domain and
+ * an unnamed zero-dimensional range.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
+	__isl_take isl_set *set)
+{
+	isl_multi_aff *ma;
+	isl_space *space;
+
+	space = isl_set_get_space(set);
+	space = isl_space_from_domain(space);
+	ma = isl_multi_aff_zero(space);
+	return isl_pw_multi_aff_alloc(set, ma);
+}
+
+/* Add an isl_pw_multi_aff with the given "set" as domain and
+ * an unnamed zero-dimensional range to *user.
+ */
+static int add_pw_multi_aff_from_domain(__isl_take isl_set *set, void *user)
+{
+	isl_union_pw_multi_aff **upma = user;
+	isl_pw_multi_aff *pma;
+
+	pma = isl_pw_multi_aff_from_domain(set);
+	*upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
+
+	return 0;
+}
+
+/* Return an isl_union_pw_multi_aff with the given "uset" as domain and
+ * an unnamed zero-dimensional range.
+ */
+__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_domain(
+	__isl_take isl_union_set *uset)
+{
+	isl_space *space;
+	isl_union_pw_multi_aff *upma;
+
+	if (!uset)
+		return NULL;
+
+	space = isl_union_set_get_space(uset);
+	upma = isl_union_pw_multi_aff_empty(space);
+
+	if (isl_union_set_foreach_set(uset,
+				    &add_pw_multi_aff_from_domain, &upma) < 0)
+		goto error;
+
+	isl_union_set_free(uset);
+	return upma;
+error:
+	isl_union_set_free(uset);
+	isl_union_pw_multi_aff_free(upma);
+	return NULL;
+}
+
+/* Convert "pma" to an isl_map and add it to *umap.
+ */
+static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user)
+{
+	isl_union_map **umap = user;
+	isl_map *map;
+
+	map = isl_map_from_pw_multi_aff(pma);
+	*umap = isl_union_map_add_map(*umap, map);
+
+	return 0;
+}
+
+/* Construct a union map mapping the domain of the union
+ * 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_union_map *isl_union_map_from_union_pw_multi_aff(
+	__isl_take isl_union_pw_multi_aff *upma)
+{
+	isl_space *space;
+	isl_union_map *umap;
+
+	if (!upma)
+		return NULL;
+
+	space = isl_union_pw_multi_aff_get_space(upma);
+	umap = isl_union_map_empty(space);
+
+	if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
+					&map_from_pw_multi_aff, &umap) < 0)
+		goto error;
+
+	isl_union_pw_multi_aff_free(upma);
+	return umap;
+error:
+	isl_union_pw_multi_aff_free(upma);
+	isl_union_map_free(umap);
+	return NULL;
+}
+
+/* Local data for bin_entry and the callback "fn".
+ */
+struct isl_union_pw_multi_aff_bin_data {
+	isl_union_pw_multi_aff *upma2;
+	isl_union_pw_multi_aff *res;
+	isl_pw_multi_aff *pma;
+	int (*fn)(void **entry, void *user);
+};
+
+/* Given an isl_pw_multi_aff from upma1, store it in data->pma
+ * and call data->fn for each isl_pw_multi_aff in data->upma2.
+ */
+static int bin_entry(void **entry, void *user)
+{
+	struct isl_union_pw_multi_aff_bin_data *data = user;
+	isl_pw_multi_aff *pma = *entry;
+
+	data->pma = pma;
+	if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table,
+				   data->fn, data) < 0)
+		return -1;
+
+	return 0;
+}
+
+/* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
+ * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
+ * passed as user field) and the isl_pw_multi_aff from upma2 is available
+ * as *entry.  The callback should adjust data->res if desired.
+ */
+static __isl_give isl_union_pw_multi_aff *bin_op(
+	__isl_take isl_union_pw_multi_aff *upma1,
+	__isl_take isl_union_pw_multi_aff *upma2,
+	int (*fn)(void **entry, void *user))
+{
+	isl_space *space;
+	struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn };
+
+	space = isl_union_pw_multi_aff_get_space(upma2);
+	upma1 = isl_union_pw_multi_aff_align_params(upma1, space);
+	space = isl_union_pw_multi_aff_get_space(upma1);
+	upma2 = isl_union_pw_multi_aff_align_params(upma2, space);
+
+	if (!upma1 || !upma2)
+		goto error;
+
+	data.upma2 = upma2;
+	data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma1->dim),
+				       upma1->table.n);
+	if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table,
+				   &bin_entry, &data) < 0)
+		goto error;
+
+	isl_union_pw_multi_aff_free(upma1);
+	isl_union_pw_multi_aff_free(upma2);
+	return data.res;
+error:
+	isl_union_pw_multi_aff_free(upma1);
+	isl_union_pw_multi_aff_free(upma2);
+	isl_union_pw_multi_aff_free(data.res);
+	return NULL;
+}
+
+/* Given two aligned isl_pw_multi_affs A -> B and C -> D,
+ * construct an isl_pw_multi_aff (A * C) -> [B -> D].
+ */
+static __isl_give isl_pw_multi_aff *pw_multi_aff_range_product(
+	__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+	isl_space *space;
+
+	space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
+					isl_pw_multi_aff_get_space(pma2));
+	return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
+					    &isl_multi_aff_range_product);
+}
+
+/* Given two isl_pw_multi_affs A -> B and C -> D,
+ * construct an isl_pw_multi_aff (A * C) -> [B -> D].
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_product(
+	__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+	return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+					    &pw_multi_aff_range_product);
+}
+
+/* Given two aligned isl_pw_multi_affs A -> B and C -> D,
+ * construct an isl_pw_multi_aff (A * C) -> (B, D).
+ */
+static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product(
+	__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+	isl_space *space;
+
+	space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
+					isl_pw_multi_aff_get_space(pma2));
+	space = isl_space_flatten_range(space);
+	return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
+					    &isl_multi_aff_flat_range_product);
+}
+
+/* Given two isl_pw_multi_affs A -> B and C -> D,
+ * construct an isl_pw_multi_aff (A * C) -> (B, D).
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product(
+	__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+	return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+					    &pw_multi_aff_flat_range_product);
+}
+
+/* If data->pma and *entry have the same domain space, then compute
+ * their flat range product and the result to data->res.
+ */
+static int flat_range_product_entry(void **entry, void *user)
+{
+	struct isl_union_pw_multi_aff_bin_data *data = user;
+	isl_pw_multi_aff *pma2 = *entry;
+
+	if (!isl_space_tuple_match(data->pma->dim, isl_dim_in,
+				 pma2->dim, isl_dim_in))
+		return 0;
+
+	pma2 = isl_pw_multi_aff_flat_range_product(
+					isl_pw_multi_aff_copy(data->pma),
+					isl_pw_multi_aff_copy(pma2));
+
+	data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2);
+
+	return 0;
+}
+
+/* Given two isl_union_pw_multi_affs A -> B and C -> D,
+ * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
+ */
+__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product(
+	__isl_take isl_union_pw_multi_aff *upma1,
+	__isl_take isl_union_pw_multi_aff *upma2)
+{
+	return bin_op(upma1, upma2, &flat_range_product_entry);
+}
+
+/* Replace the affine expressions at position "pos" in "pma" by "pa".
+ * The parameters are assumed to have been aligned.
+ *
+ * The implementation essentially performs an isl_pw_*_on_shared_domain,
+ * except that it works on two different isl_pw_* types.
+ */
+static __isl_give isl_pw_multi_aff *pw_multi_aff_set_pw_aff(
+	__isl_take isl_pw_multi_aff *pma, unsigned pos,
+	__isl_take isl_pw_aff *pa)
+{
+	int i, j, n;
+	isl_pw_multi_aff *res = NULL;
+
+	if (!pma || !pa)
+		goto error;
+
+	if (!isl_space_tuple_match(pma->dim, isl_dim_in, pa->dim, isl_dim_in))
+		isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
+			"domains don't match", goto error);
+	if (pos >= isl_pw_multi_aff_dim(pma, isl_dim_out))
+		isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
+			"index out of bounds", goto error);
+
+	n = pma->n * pa->n;
+	res = isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma), n);
+
+	for (i = 0; i < pma->n; ++i) {
+		for (j = 0; j < pa->n; ++j) {
+			isl_set *common;
+			isl_multi_aff *res_ij;
+			int empty;
+
+			common = isl_set_intersect(isl_set_copy(pma->p[i].set),
+						   isl_set_copy(pa->p[j].set));
+			empty = isl_set_plain_is_empty(common);
+			if (empty < 0 || empty) {
+				isl_set_free(common);
+				if (empty < 0)
+					goto error;
+				continue;
+			}
+
+			res_ij = isl_multi_aff_set_aff(
+					isl_multi_aff_copy(pma->p[i].maff), pos,
+					isl_aff_copy(pa->p[j].aff));
+			res_ij = isl_multi_aff_gist(res_ij,
+					isl_set_copy(common));
+
+			res = isl_pw_multi_aff_add_piece(res, common, res_ij);
+		}
+	}
+
+	isl_pw_multi_aff_free(pma);
+	isl_pw_aff_free(pa);
+	return res;
+error:
+	isl_pw_multi_aff_free(pma);
+	isl_pw_aff_free(pa);
+	return isl_pw_multi_aff_free(res);
+}
+
+/* Replace the affine expressions at position "pos" in "pma" by "pa".
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
+	__isl_take isl_pw_multi_aff *pma, unsigned pos,
+	__isl_take isl_pw_aff *pa)
+{
+	if (!pma || !pa)
+		goto error;
+	if (isl_space_match(pma->dim, isl_dim_param, pa->dim, isl_dim_param))
+		return pw_multi_aff_set_pw_aff(pma, pos, pa);
+	if (!isl_space_has_named_params(pma->dim) ||
+	    !isl_space_has_named_params(pa->dim))
+		isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
+			"unaligned unnamed parameters", goto error);
+	pma = isl_pw_multi_aff_align_params(pma, isl_pw_aff_get_space(pa));
+	pa = isl_pw_aff_align_params(pa, isl_pw_multi_aff_get_space(pma));
+	return pw_multi_aff_set_pw_aff(pma, pos, pa);
+error:
+	isl_pw_multi_aff_free(pma);
+	isl_pw_aff_free(pa);
+	return NULL;
+}
+
+#undef BASE
+#define BASE pw_aff
+
+#include <isl_multi_templ.c>