X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_aff.c;h=7c46d345338c274b61f33293ae64413631307695;hb=4812e46bc3d8f879ef9ff10098bb265a2430ceda;hp=ed66c74cdd1c9f49633228d06a22766a21e12c0e;hpb=e01cedf8eb2a55f31d3f48dc8a2775f4ad65189a;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_aff.c b/isl_aff.c
index ed66c74..7c46d34 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
  *
@@ -8,11 +9,13 @@
  * 91893 Orsay, France
  */
 
+#include <isl_ctx_private.h>
 #include <isl_map_private.h>
 #include <isl_aff_private.h>
 #include <isl_dim_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>
@@ -147,6 +150,77 @@ const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
 	return aff ? isl_local_space_get_dim_name(aff->ls, type, pos) : 0;
 }
 
+__isl_give isl_aff *isl_aff_reset_dim(__isl_take isl_aff *aff,
+	__isl_take isl_dim *dim)
+{
+	aff = isl_aff_cow(aff);
+	if (!aff || !dim)
+		goto error;
+
+	aff->ls = isl_local_space_reset_dim(aff->ls, dim);
+	if (!aff->ls)
+		return isl_aff_free(aff);
+
+	return aff;
+error:
+	isl_aff_free(aff);
+	isl_dim_free(dim);
+	return NULL;
+}
+
+/* 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_dim_total(r->dim) + 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 "aff" according to the given reordering.
+ */
+__isl_give isl_aff *isl_aff_realign(__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)
@@ -385,12 +459,16 @@ __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *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_floor(__isl_take isl_aff *aff)
 {
+	int i;
 	int size;
 	isl_ctx *ctx;
+	isl_vec *div;
 
 	if (!aff)
 		return NULL;
@@ -402,15 +480,29 @@ __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
 	if (!aff)
 		return NULL;
 
-	aff->ls = isl_local_space_add_div(aff->ls, isl_vec_copy(aff->v));
-	if (!aff->ls)
+	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)
 		return isl_aff_free(aff);
 	isl_int_set_si(aff->v->el[0], 1);
@@ -419,6 +511,40 @@ __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
 	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.
@@ -649,7 +775,7 @@ __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
  * 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(
+static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
 	__isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
 {
 	int i, j;
@@ -691,6 +817,26 @@ error:
 	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
@@ -717,7 +863,7 @@ __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
 	}
 
 	hull = isl_set_affine_hull(context);
-	return isl_aff_substitute_equalities(aff, hull);
+	return isl_aff_substitute_equalities_lifted(aff, hull);
 error:
 	isl_aff_free(aff);
 	isl_set_free(context);
@@ -736,6 +882,18 @@ __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_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.
  */
@@ -747,6 +905,15 @@ __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
 	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)
 {
@@ -916,6 +1083,23 @@ __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
 	return isl_pw_aff_insert_dims(pwaff, type, pos, n);
 }
 
+__isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(__isl_take isl_pw_aff *pwaff,
+	__isl_take isl_id *id)
+{
+	isl_dim *dim;
+
+	dim = isl_pw_aff_get_dim(pwaff);
+	dim = isl_dim_set_tuple_id(dim, isl_dim_set, id);
+
+	return isl_pw_aff_reset_dim(pwaff, dim);
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
+{
+	isl_set *dom = isl_set_universe(isl_aff_get_dim(aff));
+	return isl_pw_aff_alloc(dom, aff);
+}
+
 #undef PW
 #define PW isl_pw_aff
 #undef EL
@@ -932,21 +1116,45 @@ __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
 #define NO_EVAL
 #define NO_OPT
 #define NO_MOVE_DIMS
-#define NO_REALIGN
 #define NO_LIFT
 #define NO_MORPH
-#define NO_RESET_DIM
 
 #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_dim_match(pwaff1->dim, isl_dim_param,
+			  pwaff2->dim, isl_dim_param))
+		return fn(pwaff1, pwaff2);
+	if (!isl_dim_has_named_params(pwaff1->dim) ||
+	    !isl_dim_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_dim(pwaff2));
+	pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_dim(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 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.
+ * 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.
  */
-__isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
-	__isl_take isl_pw_aff *pwaff2)
+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;
@@ -978,22 +1186,22 @@ __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
 		set = isl_set_copy(pwaff1->p[i].set);
 		for (j = 0; j < pwaff2->n; ++j) {
 			struct isl_set *common;
-			isl_set *ge;
+			isl_set *better;
 
 			common = isl_set_intersect(
 					isl_set_copy(pwaff1->p[i].set),
 					isl_set_copy(pwaff2->p[j].set));
-			ge = isl_set_from_basic_set(isl_aff_ge_basic_set(
+			better = isl_set_from_basic_set(cmp(
 					isl_aff_copy(pwaff2->p[j].aff),
 					isl_aff_copy(pwaff1->p[i].aff)));
-			ge = isl_set_intersect(common, ge);
-			if (isl_set_plain_is_empty(ge)) {
-				isl_set_free(ge);
+			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(ge));
+			set = isl_set_subtract(set, isl_set_copy(better));
 
-			res = isl_pw_aff_add_piece(res, ge,
+			res = isl_pw_aff_add_piece(res, better,
 						isl_aff_copy(pwaff2->p[j].aff));
 		}
 		res = isl_pw_aff_add_piece(res, set,
@@ -1019,6 +1227,51 @@ error:
 	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 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 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.
  */
@@ -1080,11 +1333,53 @@ __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *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_dim(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.
+ * 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.
  */
-__isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
-	__isl_take isl_pw_aff *pwaff2)
+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;
 
@@ -1092,8 +1387,435 @@ __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *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, 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_dim *dim = isl_set_get_dim(set1);
+		isl_aff *aff;
+		aff = isl_aff_zero(isl_local_space_from_dim(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_dim(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)
+{
+	int i, j, n;
+	isl_pw_aff *res;
+
+	if (!pwaff1 || !pwaff2)
+		goto error;
+
+	n = pwaff1->n * pwaff2->n;
+	res = isl_pw_aff_alloc_(isl_dim_copy(pwaff1->dim), n);
+
+	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;
+			}
+
+			prod = isl_aff_mul(isl_aff_copy(pwaff1->p[i].aff),
+					    isl_aff_copy(pwaff2->p[j].aff));
+
+			res = isl_pw_aff_add_piece(res, common, prod);
+		}
+	}
+
+	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;
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
+	__isl_take isl_pw_aff *pwaff2)
+{
+	return 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 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 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);
+}