X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_pw_templ.c;h=39939740247bbf4587ec83d5282c53c383a35511;hb=63fb8a7f484648c3caa25351c8c94ac2395ec563;hp=e89d4a3d1941f74fe2058892e061851251d77209;hpb=c6e1542f82dc3d289eb32625ca1b3252e600693e;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_pw_templ.c b/isl_pw_templ.c
index e89d4a3..3993974 100644
--- a/isl_pw_templ.c
+++ b/isl_pw_templ.c
@@ -1,13 +1,15 @@
+#include <isl/aff.h>
+
 #define xFN(TYPE,NAME) TYPE ## _ ## NAME
 #define FN(TYPE,NAME) xFN(TYPE,NAME)
 #define xS(TYPE,NAME) struct TYPE ## _ ## NAME
 #define S(TYPE,NAME) xS(TYPE,NAME)
 
 #ifdef HAS_TYPE
-static __isl_give PW *FN(PW,alloc_)(__isl_take isl_dim *dim,
+__isl_give PW *FN(PW,alloc_size)(__isl_take isl_space *dim,
 	enum isl_fold type, int n)
 #else
-static __isl_give PW *FN(PW,alloc_)(__isl_take isl_dim *dim, int n)
+__isl_give PW *FN(PW,alloc_size)(__isl_take isl_space *dim, int n)
 #endif
 {
 	isl_ctx *ctx;
@@ -15,7 +17,7 @@ static __isl_give PW *FN(PW,alloc_)(__isl_take isl_dim *dim, int n)
 
 	if (!dim)
 		return NULL;
-	ctx = isl_dim_get_ctx(dim);
+	ctx = isl_space_get_ctx(dim);
 	isl_assert(ctx, n >= 0, goto error);
 	pw = isl_alloc(ctx, struct PW,
 			sizeof(struct PW) + (n - 1) * sizeof(S(PW,piece)));
@@ -31,19 +33,19 @@ static __isl_give PW *FN(PW,alloc_)(__isl_take isl_dim *dim, int n)
 	pw->dim = dim;
 	return pw;
 error:
-	isl_dim_free(dim);
+	isl_space_free(dim);
 	return NULL;
 }
 
 #ifdef HAS_TYPE
-__isl_give PW *FN(PW,ZERO)(__isl_take isl_dim *dim, enum isl_fold type)
+__isl_give PW *FN(PW,ZERO)(__isl_take isl_space *dim, enum isl_fold type)
 {
-	return FN(PW,alloc_)(dim, type, 0);
+	return FN(PW,alloc_size)(dim, type, 0);
 }
 #else
-__isl_give PW *FN(PW,ZERO)(__isl_take isl_dim *dim)
+__isl_give PW *FN(PW,ZERO)(__isl_take isl_space *dim)
 {
-	return FN(PW,alloc_)(dim, 0);
+	return FN(PW,alloc_size)(dim, 0);
 }
 #endif
 
@@ -51,7 +53,7 @@ __isl_give PW *FN(PW,add_piece)(__isl_take PW *pw,
 	__isl_take isl_set *set, __isl_take EL *el)
 {
 	isl_ctx *ctx;
-	isl_dim *el_dim = NULL;
+	isl_space *el_dim = NULL;
 
 	if (!pw || !set || !el)
 		goto error;
@@ -68,18 +70,18 @@ __isl_give PW *FN(PW,add_piece)(__isl_take PW *pw,
 		isl_die(ctx, isl_error_invalid, "fold types don't match",
 			goto error);
 #endif
-	el_dim = FN(EL,get_dim(el));
-	isl_assert(ctx, isl_dim_equal(pw->dim, el_dim), goto error);
+	el_dim = FN(EL,get_space(el));
+	isl_assert(ctx, isl_space_is_equal(pw->dim, el_dim), goto error);
 	isl_assert(ctx, pw->n < pw->size, goto error);
 
 	pw->p[pw->n].set = set;
 	pw->p[pw->n].FIELD = el;
 	pw->n++;
 	
-	isl_dim_free(el_dim);
+	isl_space_free(el_dim);
 	return pw;
 error:
-	isl_dim_free(el_dim);
+	isl_space_free(el_dim);
 	FN(PW,free)(pw);
 	isl_set_free(set);
 	FN(EL,free)(el);
@@ -99,9 +101,9 @@ __isl_give PW *FN(PW,alloc)(__isl_take isl_set *set, __isl_take EL *el)
 		goto error;
 
 #ifdef HAS_TYPE
-	pw = FN(PW,alloc_)(isl_set_get_dim(set), type, 1);
+	pw = FN(PW,alloc_size)(FN(EL,get_space)(el), type, 1);
 #else
-	pw = FN(PW,alloc_)(isl_set_get_dim(set), 1);
+	pw = FN(PW,alloc_size)(FN(EL,get_space)(el), 1);
 #endif
 
 	return FN(PW,add_piece)(pw, set, el);
@@ -120,9 +122,9 @@ __isl_give PW *FN(PW,dup)(__isl_keep PW *pw)
 		return NULL;
 
 #ifdef HAS_TYPE
-	dup = FN(PW,alloc_)(isl_dim_copy(pw->dim), pw->type, pw->n);
+	dup = FN(PW,alloc_size)(isl_space_copy(pw->dim), pw->type, pw->n);
 #else
-	dup = FN(PW,alloc_)(isl_dim_copy(pw->dim), pw->n);
+	dup = FN(PW,alloc_size)(isl_space_copy(pw->dim), pw->n);
 #endif
 	if (!dup)
 		return NULL;
@@ -167,12 +169,49 @@ void *FN(PW,free)(__isl_take PW *pw)
 		isl_set_free(pw->p[i].set);
 		FN(EL,free)(pw->p[i].FIELD);
 	}
-	isl_dim_free(pw->dim);
+	isl_space_free(pw->dim);
 	free(pw);
 
 	return NULL;
 }
 
+const char *FN(PW,get_dim_name)(__isl_keep PW *pw, enum isl_dim_type type,
+	unsigned pos)
+{
+	return pw ? isl_space_get_dim_name(pw->dim, type, pos) : NULL;
+}
+
+int FN(PW,has_dim_id)(__isl_keep PW *pw, enum isl_dim_type type, unsigned pos)
+{
+	return pw ? isl_space_has_dim_id(pw->dim, type, pos) : -1;
+}
+
+__isl_give isl_id *FN(PW,get_dim_id)(__isl_keep PW *pw, enum isl_dim_type type,
+	unsigned pos)
+{
+	return pw ? isl_space_get_dim_id(pw->dim, type, pos) : NULL;
+}
+
+int FN(PW,has_tuple_name)(__isl_keep PW *pw, enum isl_dim_type type)
+{
+	return pw ? isl_space_has_tuple_name(pw->dim, type) : -1;
+}
+
+const char *FN(PW,get_tuple_name)(__isl_keep PW *pw, enum isl_dim_type type)
+{
+	return pw ? isl_space_get_tuple_name(pw->dim, type) : NULL;
+}
+
+int FN(PW,has_tuple_id)(__isl_keep PW *pw, enum isl_dim_type type)
+{
+	return pw ? isl_space_has_tuple_id(pw->dim, type) : -1;
+}
+
+__isl_give isl_id *FN(PW,get_tuple_id)(__isl_keep PW *pw, enum isl_dim_type type)
+{
+	return pw ? isl_space_get_tuple_id(pw->dim, type) : NULL;
+}
+
 int FN(PW,IS_ZERO)(__isl_keep PW *pw)
 {
 	if (!pw)
@@ -181,7 +220,125 @@ int FN(PW,IS_ZERO)(__isl_keep PW *pw)
 	return pw->n == 0;
 }
 
-__isl_give PW *FN(PW,add)(__isl_take PW *pw1, __isl_take PW *pw2)
+#ifndef NO_REALIGN
+__isl_give PW *FN(PW,realign_domain)(__isl_take PW *pw,
+	__isl_take isl_reordering *exp)
+{
+	int i;
+
+	pw = FN(PW,cow)(pw);
+	if (!pw || !exp)
+		goto error;
+
+	for (i = 0; i < pw->n; ++i) {
+		pw->p[i].set = isl_set_realign(pw->p[i].set,
+						    isl_reordering_copy(exp));
+		if (!pw->p[i].set)
+			goto error;
+		pw->p[i].FIELD = FN(EL,realign_domain)(pw->p[i].FIELD,
+						    isl_reordering_copy(exp));
+		if (!pw->p[i].FIELD)
+			goto error;
+	}
+
+	pw = FN(PW,reset_domain_space)(pw, isl_space_copy(exp->dim));
+
+	isl_reordering_free(exp);
+	return pw;
+error:
+	isl_reordering_free(exp);
+	FN(PW,free)(pw);
+	return NULL;
+}
+
+/* Align the parameters of "pw" to those of "model".
+ */
+__isl_give PW *FN(PW,align_params)(__isl_take PW *pw, __isl_take isl_space *model)
+{
+	isl_ctx *ctx;
+
+	if (!pw || !model)
+		goto error;
+
+	ctx = isl_space_get_ctx(model);
+	if (!isl_space_has_named_params(model))
+		isl_die(ctx, isl_error_invalid,
+			"model has unnamed parameters", goto error);
+	if (!isl_space_has_named_params(pw->dim))
+		isl_die(ctx, isl_error_invalid,
+			"input has unnamed parameters", goto error);
+	if (!isl_space_match(pw->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(pw->dim, model);
+		exp = isl_reordering_extend_space(exp,
+					FN(PW,get_domain_space)(pw));
+		pw = FN(PW,realign_domain)(pw, exp);
+	}
+
+	isl_space_free(model);
+	return pw;
+error:
+	isl_space_free(model);
+	FN(PW,free)(pw);
+	return NULL;
+}
+
+static __isl_give PW *FN(PW,align_params_pw_pw_and)(__isl_take PW *pw1,
+	__isl_take PW *pw2,
+	__isl_give PW *(*fn)(__isl_take PW *pw1, __isl_take PW *pw2))
+{
+	isl_ctx *ctx;
+
+	if (!pw1 || !pw2)
+		goto error;
+	if (isl_space_match(pw1->dim, isl_dim_param, pw2->dim, isl_dim_param))
+		return fn(pw1, pw2);
+	ctx = FN(PW,get_ctx)(pw1);
+	if (!isl_space_has_named_params(pw1->dim) ||
+	    !isl_space_has_named_params(pw2->dim))
+		isl_die(ctx, isl_error_invalid,
+			"unaligned unnamed parameters", goto error);
+	pw1 = FN(PW,align_params)(pw1, FN(PW,get_space)(pw2));
+	pw2 = FN(PW,align_params)(pw2, FN(PW,get_space)(pw1));
+	return fn(pw1, pw2);
+error:
+	FN(PW,free)(pw1);
+	FN(PW,free)(pw2);
+	return NULL;
+}
+
+static __isl_give PW *FN(PW,align_params_pw_set_and)(__isl_take PW *pw,
+	__isl_take isl_set *set,
+	__isl_give PW *(*fn)(__isl_take PW *pw, __isl_take isl_set *set))
+{
+	isl_ctx *ctx;
+
+	if (!pw || !set)
+		goto error;
+	if (isl_space_match(pw->dim, isl_dim_param, set->dim, isl_dim_param))
+		return fn(pw, set);
+	ctx = FN(PW,get_ctx)(pw);
+	if (!isl_space_has_named_params(pw->dim) ||
+	    !isl_space_has_named_params(set->dim))
+		isl_die(ctx, isl_error_invalid,
+			"unaligned unnamed parameters", goto error);
+	pw = FN(PW,align_params)(pw, isl_set_get_space(set));
+	set = isl_set_align_params(set, FN(PW,get_space)(pw));
+	return fn(pw, set);
+error:
+	FN(PW,free)(pw);
+	isl_set_free(set);
+	return NULL;
+}
+#endif
+
+static __isl_give PW *FN(PW,union_add_aligned)(__isl_take PW *pw1,
+	__isl_take PW *pw2)
 {
 	int i, j, n;
 	struct PW *res;
@@ -191,13 +348,13 @@ __isl_give PW *FN(PW,add)(__isl_take PW *pw1, __isl_take PW *pw2)
 	if (!pw1 || !pw2)
 		goto error;
 
-	ctx = isl_dim_get_ctx(pw1->dim);
+	ctx = isl_space_get_ctx(pw1->dim);
 #ifdef HAS_TYPE
 	if (pw1->type != pw2->type)
 		isl_die(ctx, isl_error_invalid,
 			"fold types don't match", goto error);
 #endif
-	isl_assert(ctx, isl_dim_equal(pw1->dim, pw2->dim), goto error);
+	isl_assert(ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
 
 	if (FN(PW,IS_ZERO)(pw1)) {
 		FN(PW,free)(pw1);
@@ -211,9 +368,9 @@ __isl_give PW *FN(PW,add)(__isl_take PW *pw1, __isl_take PW *pw2)
 
 	n = (pw1->n + 1) * (pw2->n + 1);
 #ifdef HAS_TYPE
-	res = FN(PW,alloc_)(isl_dim_copy(pw1->dim), pw1->type, n);
+	res = FN(PW,alloc_size)(isl_space_copy(pw1->dim), pw1->type, n);
 #else
-	res = FN(PW,alloc_)(isl_dim_copy(pw1->dim), n);
+	res = FN(PW,alloc_size)(isl_space_copy(pw1->dim), n);
 #endif
 
 	for (i = 0; i < pw1->n; ++i) {
@@ -221,14 +378,14 @@ __isl_give PW *FN(PW,add)(__isl_take PW *pw1, __isl_take PW *pw2)
 		for (j = 0; j < pw2->n; ++j) {
 			struct isl_set *common;
 			EL *sum;
-			set = isl_set_subtract(set,
-					isl_set_copy(pw2->p[j].set));
 			common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
 						isl_set_copy(pw2->p[j].set));
 			if (isl_set_plain_is_empty(common)) {
 				isl_set_free(common);
 				continue;
 			}
+			set = isl_set_subtract(set,
+					isl_set_copy(pw2->p[j].set));
 
 			sum = FN(EL,add_on_domain)(common,
 						   FN(EL,copy)(pw1->p[i].FIELD),
@@ -257,22 +414,73 @@ error:
 	return NULL;
 }
 
-__isl_give PW *FN(PW,add_disjoint)(__isl_take PW *pw1, __isl_take PW *pw2)
+/* Private version of "union_add".  For isl_pw_qpolynomial and
+ * isl_pw_qpolynomial_fold, we prefer to simply call it "add".
+ */
+static __isl_give PW *FN(PW,union_add_)(__isl_take PW *pw1, __isl_take PW *pw2)
+{
+	return FN(PW,align_params_pw_pw_and)(pw1, pw2,
+						&FN(PW,union_add_aligned));
+}
+
+/* Make sure "pw" has room for at least "n" more pieces.
+ *
+ * If there is only one reference to pw, we extend it in place.
+ * Otherwise, we create a new PW and copy the pieces.
+ */
+static __isl_give PW *FN(PW,grow)(__isl_take PW *pw, int n)
 {
 	int i;
 	isl_ctx *ctx;
 	PW *res;
 
+	if (!pw)
+		return NULL;
+	if (pw->n + n <= pw->size)
+		return pw;
+	ctx = FN(PW,get_ctx)(pw);
+	n += pw->n;
+	if (pw->ref == 1) {
+		res = isl_realloc(ctx, pw, struct PW,
+			    sizeof(struct PW) + (n - 1) * sizeof(S(PW,piece)));
+		if (!res)
+			return FN(PW,free)(pw);
+		res->size = n;
+		return res;
+	}
+#ifdef HAS_TYPE
+	res = FN(PW,alloc_size)(isl_space_copy(pw->dim), pw->type, n);
+#else
+	res = FN(PW,alloc_size)(isl_space_copy(pw->dim), n);
+#endif
+	if (!res)
+		return FN(PW,free)(pw);
+	for (i = 0; i < pw->n; ++i)
+		res = FN(PW,add_piece)(res, isl_set_copy(pw->p[i].set),
+					    FN(EL,copy)(pw->p[i].FIELD));
+	FN(PW,free)(pw);
+	return res;
+}
+
+static __isl_give PW *FN(PW,add_disjoint_aligned)(__isl_take PW *pw1,
+	__isl_take PW *pw2)
+{
+	int i;
+	isl_ctx *ctx;
+
 	if (!pw1 || !pw2)
 		goto error;
 
-	ctx = isl_dim_get_ctx(pw1->dim);
+	if (pw1->size < pw1->n + pw2->n && pw1->n < pw2->n)
+		return FN(PW,add_disjoint_aligned)(pw2, pw1);
+
+	ctx = isl_space_get_ctx(pw1->dim);
 #ifdef HAS_TYPE
 	if (pw1->type != pw2->type)
 		isl_die(ctx, isl_error_invalid,
 			"fold types don't match", goto error);
 #endif
-	isl_assert(ctx, isl_dim_equal(pw1->dim, pw2->dim), goto error);
+	isl_assert(ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
 
 	if (FN(PW,IS_ZERO)(pw1)) {
 		FN(PW,free)(pw1);
@@ -284,27 +492,116 @@ __isl_give PW *FN(PW,add_disjoint)(__isl_take PW *pw1, __isl_take PW *pw2)
 		return pw1;
 	}
 
-#ifdef HAS_TYPE
-	res = FN(PW,alloc_)(isl_dim_copy(pw1->dim), pw1->type, pw1->n + pw2->n);
-#else
-	res = FN(PW,alloc_)(isl_dim_copy(pw1->dim), pw1->n + pw2->n);
-#endif
-
-	for (i = 0; i < pw1->n; ++i)
-		res = FN(PW,add_piece)(res,
-				isl_set_copy(pw1->p[i].set),
-				FN(EL,copy)(pw1->p[i].FIELD));
+	pw1 = FN(PW,grow)(pw1, pw2->n);
+	if (!pw1)
+		goto error;
 
 	for (i = 0; i < pw2->n; ++i)
-		res = FN(PW,add_piece)(res,
+		pw1 = FN(PW,add_piece)(pw1,
 				isl_set_copy(pw2->p[i].set),
 				FN(EL,copy)(pw2->p[i].FIELD));
 
+	FN(PW,free)(pw2);
+
+	return pw1;
+error:
 	FN(PW,free)(pw1);
 	FN(PW,free)(pw2);
+	return NULL;
+}
+
+__isl_give PW *FN(PW,add_disjoint)(__isl_take PW *pw1, __isl_take PW *pw2)
+{
+	return FN(PW,align_params_pw_pw_and)(pw1, pw2,
+						&FN(PW,add_disjoint_aligned));
+}
+
+/* This function is currently only used from isl_aff.c
+ */
+static __isl_give PW *FN(PW,on_shared_domain_in)(__isl_take PW *pw1,
+	__isl_take PW *pw2, __isl_take isl_space *space,
+	__isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
+	__attribute__ ((unused));
+
+/* Apply "fn" to pairs of elements from pw1 and pw2 on shared domains.
+ * The result of "fn" (and therefore also of this function) lives in "space".
+ */
+static __isl_give PW *FN(PW,on_shared_domain_in)(__isl_take PW *pw1,
+	__isl_take PW *pw2, __isl_take isl_space *space,
+	__isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
+{
+	int i, j, n;
+	PW *res = NULL;
 
+	if (!pw1 || !pw2)
+		goto error;
+
+	n = pw1->n * pw2->n;
+#ifdef HAS_TYPE
+	res = FN(PW,alloc_size)(isl_space_copy(space), pw1->type, n);
+#else
+	res = FN(PW,alloc_size)(isl_space_copy(space), n);
+#endif
+
+	for (i = 0; i < pw1->n; ++i) {
+		for (j = 0; j < pw2->n; ++j) {
+			isl_set *common;
+			EL *res_ij;
+			int empty;
+
+			common = isl_set_intersect(
+					isl_set_copy(pw1->p[i].set),
+					isl_set_copy(pw2->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 = fn(FN(EL,copy)(pw1->p[i].FIELD),
+				    FN(EL,copy)(pw2->p[j].FIELD));
+			res_ij = FN(EL,gist)(res_ij, isl_set_copy(common));
+
+			res = FN(PW,add_piece)(res, common, res_ij);
+		}
+	}
+
+	isl_space_free(space);
+	FN(PW,free)(pw1);
+	FN(PW,free)(pw2);
 	return res;
 error:
+	isl_space_free(space);
+	FN(PW,free)(pw1);
+	FN(PW,free)(pw2);
+	FN(PW,free)(res);
+	return NULL;
+}
+
+/* This function is currently only used from isl_aff.c
+ */
+static __isl_give PW *FN(PW,on_shared_domain)(__isl_take PW *pw1,
+	__isl_take PW *pw2,
+	__isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
+	__attribute__ ((unused));
+
+/* Apply "fn" to pairs of elements from pw1 and pw2 on shared domains.
+ * The result of "fn" is assumed to live in the same space as "pw1" and "pw2".
+ */
+static __isl_give PW *FN(PW,on_shared_domain)(__isl_take PW *pw1,
+	__isl_take PW *pw2,
+	__isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
+{
+	isl_space *space;
+
+	if (!pw1 || !pw2)
+		goto error;
+
+	space = isl_space_copy(pw1->dim);
+	return FN(PW,on_shared_domain_in)(pw1, pw2, space, fn);
+error:
 	FN(PW,free)(pw1);
 	FN(PW,free)(pw2);
 	return NULL;
@@ -333,6 +630,11 @@ __isl_give PW *FN(PW,neg)(__isl_take PW *pw)
 
 	return pw;
 }
+
+__isl_give PW *FN(PW,sub)(__isl_take PW *pw1, __isl_take PW *pw2)
+{
+	return FN(PW,add)(pw1, FN(PW,neg)(pw2));
+}
 #endif
 
 #ifndef NO_EVAL
@@ -342,14 +644,15 @@ __isl_give isl_qpolynomial *FN(PW,eval)(__isl_take PW *pw,
 	int i;
 	int found = 0;
 	isl_ctx *ctx;
-	isl_dim *pnt_dim = NULL;
+	isl_space *pnt_dim = NULL;
 	isl_qpolynomial *qp;
 
 	if (!pw || !pnt)
 		goto error;
 	ctx = isl_point_get_ctx(pnt);
-	pnt_dim = isl_point_get_dim(pnt);
-	isl_assert(ctx, isl_dim_equal(pnt_dim, pw->dim), goto error);
+	pnt_dim = isl_point_get_space(pnt);
+	isl_assert(ctx, isl_space_is_domain_internal(pnt_dim, pw->dim),
+		    goto error);
 
 	for (i = 0; i < pw->n; ++i) {
 		found = isl_set_contains_point(pw->p[i].set, pnt);
@@ -362,14 +665,14 @@ __isl_give isl_qpolynomial *FN(PW,eval)(__isl_take PW *pw,
 		qp = FN(EL,eval)(FN(EL,copy)(pw->p[i].FIELD),
 					    isl_point_copy(pnt));
 	else
-		qp = isl_qpolynomial_zero(isl_dim_copy(pw->dim));
+		qp = isl_qpolynomial_zero_on_domain(FN(PW,get_domain_space)(pw));
 	FN(PW,free)(pw);
-	isl_dim_free(pnt_dim);
+	isl_space_free(pnt_dim);
 	isl_point_free(pnt);
 	return qp;
 error:
 	FN(PW,free)(pw);
-	isl_dim_free(pnt_dim);
+	isl_space_free(pnt_dim);
 	isl_point_free(pnt);
 	return NULL;
 }
@@ -383,7 +686,7 @@ __isl_give isl_set *FN(PW,domain)(__isl_take PW *pw)
 	if (!pw)
 		return NULL;
 
-	dom = isl_set_empty(isl_dim_copy(pw->dim));
+	dom = isl_set_empty(FN(PW,get_domain_space)(pw));
 	for (i = 0; i < pw->n; ++i)
 		dom = isl_set_union_disjoint(dom, isl_set_copy(pw->p[i].set));
 
@@ -392,7 +695,14 @@ __isl_give isl_set *FN(PW,domain)(__isl_take PW *pw)
 	return dom;
 }
 
-__isl_give PW *FN(PW,intersect_domain)(__isl_take PW *pw, __isl_take isl_set *set)
+/* Restrict the domain of "pw" by combining each cell
+ * with "set" through a call to "fn", where "fn" may be
+ * isl_set_intersect or isl_set_intersect_params.
+ */
+static __isl_give PW *FN(PW,intersect_aligned)(__isl_take PW *pw,
+	__isl_take isl_set *set,
+	__isl_give isl_set *(*fn)(__isl_take isl_set *set1,
+				    __isl_take isl_set *set2))
 {
 	int i;
 
@@ -410,12 +720,14 @@ __isl_give PW *FN(PW,intersect_domain)(__isl_take PW *pw, __isl_take isl_set *se
 
 	for (i = pw->n - 1; i >= 0; --i) {
 		isl_basic_set *aff;
-		pw->p[i].set = isl_set_intersect(pw->p[i].set, isl_set_copy(set));
+		pw->p[i].set = fn(pw->p[i].set, isl_set_copy(set));
 		if (!pw->p[i].set)
 			goto error;
 		aff = isl_set_affine_hull(isl_set_copy(pw->p[i].set));
 		pw->p[i].FIELD = FN(EL,substitute_equalities)(pw->p[i].FIELD,
 								aff);
+		if (!pw->p[i].FIELD)
+			goto error;
 		if (isl_set_plain_is_empty(pw->p[i].set)) {
 			isl_set_free(pw->p[i].set);
 			FN(EL,free)(pw->p[i].FIELD);
@@ -433,7 +745,40 @@ error:
 	return NULL;
 }
 
-__isl_give PW *FN(PW,gist)(__isl_take PW *pw, __isl_take isl_set *context)
+static __isl_give PW *FN(PW,intersect_domain_aligned)(__isl_take PW *pw,
+	__isl_take isl_set *set)
+{
+	return FN(PW,intersect_aligned)(pw, set, &isl_set_intersect);
+}
+
+__isl_give PW *FN(PW,intersect_domain)(__isl_take PW *pw,
+	__isl_take isl_set *context)
+{
+	return FN(PW,align_params_pw_set_and)(pw, context,
+					&FN(PW,intersect_domain_aligned));
+}
+
+static __isl_give PW *FN(PW,intersect_params_aligned)(__isl_take PW *pw,
+	__isl_take isl_set *set)
+{
+	return FN(PW,intersect_aligned)(pw, set, &isl_set_intersect_params);
+}
+
+/* Intersect the domain of "pw" with the parameter domain "context".
+ */
+__isl_give PW *FN(PW,intersect_params)(__isl_take PW *pw,
+	__isl_take isl_set *context)
+{
+	return FN(PW,align_params_pw_set_and)(pw, context,
+					&FN(PW,intersect_params_aligned));
+}
+
+static __isl_give PW *FN(PW,gist_aligned)(__isl_take PW *pw,
+	__isl_take isl_set *context,
+	__isl_give EL *(*fn_el)(__isl_take EL *el,
+				    __isl_take isl_set *set),
+	__isl_give isl_set *(*fn_dom)(__isl_take isl_set *set,
+				    __isl_take isl_basic_set *bset))
 {
 	int i;
 	isl_basic_set *hull = NULL;
@@ -446,6 +791,12 @@ __isl_give PW *FN(PW,gist)(__isl_take PW *pw, __isl_take isl_set *context)
 		return pw;
 	}
 
+	if (!isl_space_match(pw->dim, isl_dim_param,
+				context->dim, isl_dim_param)) {
+		pw = FN(PW,align_params)(pw, isl_set_get_space(context));
+		context = isl_set_align_params(context, FN(PW,get_space)(pw));
+	}
+
 	context = isl_set_compute_divs(context);
 	hull = isl_set_simple_hull(isl_set_copy(context));
 
@@ -454,17 +805,17 @@ __isl_give PW *FN(PW,gist)(__isl_take PW *pw, __isl_take isl_set *context)
 		goto error;
 
 	for (i = pw->n - 1; i >= 0; --i) {
-		pw->p[i].set = isl_set_intersect(pw->p[i].set,
+		isl_set *set_i;
+		int empty;
+
+		set_i = isl_set_intersect(isl_set_copy(pw->p[i].set),
 						 isl_set_copy(context));
-		if (!pw->p[i].set)
+		empty = isl_set_plain_is_empty(set_i);
+		pw->p[i].FIELD = fn_el(pw->p[i].FIELD, set_i);
+		pw->p[i].set = fn_dom(pw->p[i].set, isl_basic_set_copy(hull));
+		if (!pw->p[i].FIELD || !pw->p[i].set)
 			goto error;
-		pw->p[i].FIELD = FN(EL,gist)(pw->p[i].FIELD,
-					     isl_set_copy(pw->p[i].set));
-		pw->p[i].set = isl_set_gist_basic_set(pw->p[i].set,
-						isl_basic_set_copy(hull));
-		if (!pw->p[i].set)
-			goto error;
-		if (isl_set_plain_is_empty(pw->p[i].set)) {
+		if (empty) {
 			isl_set_free(pw->p[i].set);
 			FN(EL,free)(pw->p[i].FIELD);
 			if (i != pw->n - 1)
@@ -484,6 +835,33 @@ error:
 	return NULL;
 }
 
+static __isl_give PW *FN(PW,gist_domain_aligned)(__isl_take PW *pw,
+	__isl_take isl_set *set)
+{
+	return FN(PW,gist_aligned)(pw, set, &FN(EL,gist),
+					&isl_set_gist_basic_set);
+}
+
+__isl_give PW *FN(PW,gist)(__isl_take PW *pw, __isl_take isl_set *context)
+{
+	return FN(PW,align_params_pw_set_and)(pw, context,
+						&FN(PW,gist_domain_aligned));
+}
+
+static __isl_give PW *FN(PW,gist_params_aligned)(__isl_take PW *pw,
+	__isl_take isl_set *set)
+{
+	return FN(PW,gist_aligned)(pw, set, &FN(EL,gist_params),
+					&isl_set_gist_params_basic_set);
+}
+
+__isl_give PW *FN(PW,gist_params)(__isl_take PW *pw,
+	__isl_take isl_set *context)
+{
+	return FN(PW,align_params_pw_set_and)(pw, context,
+						&FN(PW,gist_params_aligned));
+}
+
 __isl_give PW *FN(PW,coalesce)(__isl_take PW *pw)
 {
 	int i, j;
@@ -521,7 +899,7 @@ error:
 
 isl_ctx *FN(PW,get_ctx)(__isl_keep PW *pw)
 {
-	return pw ? isl_dim_get_ctx(pw->dim) : NULL;
+	return pw ? isl_space_get_ctx(pw->dim) : NULL;
 }
 
 #ifndef NO_INVOLVES_DIMS
@@ -529,17 +907,22 @@ int FN(PW,involves_dims)(__isl_keep PW *pw, enum isl_dim_type type,
 	unsigned first, unsigned n)
 {
 	int i;
+	enum isl_dim_type set_type;
 
 	if (!pw)
 		return -1;
 	if (pw->n == 0 || n == 0)
 		return 0;
+
+	set_type = type == isl_dim_in ? isl_dim_set : type;
+
 	for (i = 0; i < pw->n; ++i) {
 		int involves = FN(EL,involves_dims)(pw->p[i].FIELD,
 							type, first, n);
 		if (involves < 0 || involves)
 			return involves;
-		involves = isl_set_involves_dims(pw->p[i].set, type, first, n);
+		involves = isl_set_involves_dims(pw->p[i].set,
+							set_type, first, n);
 		if (involves < 0 || involves)
 			return involves;
 	}
@@ -551,17 +934,21 @@ __isl_give PW *FN(PW,set_dim_name)(__isl_take PW *pw,
 	enum isl_dim_type type, unsigned pos, const char *s)
 {
 	int i;
+	enum isl_dim_type set_type;
 
 	pw = FN(PW,cow)(pw);
 	if (!pw)
 		return NULL;
 
-	pw->dim = isl_dim_set_name(pw->dim, type, pos, s);
+	set_type = type == isl_dim_in ? isl_dim_set : type;
+
+	pw->dim = isl_space_set_dim_name(pw->dim, type, pos, s);
 	if (!pw->dim)
 		goto error;
 
 	for (i = 0; i < pw->n; ++i) {
-		pw->p[i].set = isl_set_set_dim_name(pw->p[i].set, type, pos, s);
+		pw->p[i].set = isl_set_set_dim_name(pw->p[i].set,
+							set_type, pos, s);
 		if (!pw->p[i].set)
 			goto error;
 		pw->p[i].FIELD = FN(EL,set_dim_name)(pw->p[i].FIELD, type, pos, s);
@@ -580,20 +967,65 @@ __isl_give PW *FN(PW,drop_dims)(__isl_take PW *pw,
 	enum isl_dim_type type, unsigned first, unsigned n)
 {
 	int i;
+	enum isl_dim_type set_type;
 
 	if (!pw)
 		return NULL;
-	if (n == 0 && !isl_dim_get_tuple_name(pw->dim, type))
+	if (n == 0 && !isl_space_get_tuple_name(pw->dim, type))
 		return pw;
 
+	set_type = type == isl_dim_in ? isl_dim_set : type;
+
 	pw = FN(PW,cow)(pw);
 	if (!pw)
 		return NULL;
-	pw->dim = isl_dim_drop(pw->dim, type, first, n);
+	pw->dim = isl_space_drop_dims(pw->dim, type, first, n);
 	if (!pw->dim)
 		goto error;
 	for (i = 0; i < pw->n; ++i) {
-		pw->p[i].set = isl_set_drop(pw->p[i].set, type, first, n);
+		pw->p[i].FIELD = FN(EL,drop_dims)(pw->p[i].FIELD, type, first, n);
+		if (!pw->p[i].FIELD)
+			goto error;
+		if (type == isl_dim_out)
+			continue;
+		pw->p[i].set = isl_set_drop(pw->p[i].set, set_type, first, n);
+		if (!pw->p[i].set)
+			goto error;
+	}
+
+	return pw;
+error:
+	FN(PW,free)(pw);
+	return NULL;
+}
+
+/* This function is very similar to drop_dims.
+ * The only difference is that the cells may still involve
+ * the specified dimensions.  They are removed using
+ * isl_set_project_out instead of isl_set_drop.
+ */
+__isl_give PW *FN(PW,project_out)(__isl_take PW *pw,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	int i;
+	enum isl_dim_type set_type;
+
+	if (!pw)
+		return NULL;
+	if (n == 0 && !isl_space_get_tuple_name(pw->dim, type))
+		return pw;
+
+	set_type = type == isl_dim_in ? isl_dim_set : type;
+
+	pw = FN(PW,cow)(pw);
+	if (!pw)
+		return NULL;
+	pw->dim = isl_space_drop_dims(pw->dim, type, first, n);
+	if (!pw->dim)
+		goto error;
+	for (i = 0; i < pw->n; ++i) {
+		pw->p[i].set = isl_set_project_out(pw->p[i].set,
+							set_type, first, n);
 		if (!pw->p[i].set)
 			goto error;
 		pw->p[i].FIELD = FN(EL,drop_dims)(pw->p[i].FIELD, type, first, n);
@@ -606,6 +1038,21 @@ error:
 	FN(PW,free)(pw);
 	return NULL;
 }
+
+/* Project the domain of pw onto its parameter space.
+ */
+__isl_give PW *FN(PW,project_domain_on_params)(__isl_take PW *pw)
+{
+	isl_space *space;
+	unsigned n;
+
+	n = FN(PW,dim)(pw, isl_dim_in);
+	pw = FN(PW,project_out)(pw, isl_dim_in, 0, n);
+	space = FN(PW,get_domain_space)(pw);
+	space = isl_space_params(space);
+	pw = FN(PW,reset_domain_space)(pw, space);
+	return pw;
+}
 #endif
 
 #ifndef NO_INSERT_DIMS
@@ -613,22 +1060,26 @@ __isl_give PW *FN(PW,insert_dims)(__isl_take PW *pw, enum isl_dim_type type,
 	unsigned first, unsigned n)
 {
 	int i;
+	enum isl_dim_type set_type;
 
 	if (!pw)
 		return NULL;
-	if (n == 0 && !isl_dim_is_named_or_nested(pw->dim, type))
+	if (n == 0 && !isl_space_is_named_or_nested(pw->dim, type))
 		return pw;
 
+	set_type = type == isl_dim_in ? isl_dim_set : type;
+
 	pw = FN(PW,cow)(pw);
 	if (!pw)
 		return NULL;
 
-	pw->dim = isl_dim_insert(pw->dim, type, first, n);
+	pw->dim = isl_space_insert_dims(pw->dim, type, first, n);
 	if (!pw->dim)
 		goto error;
 
 	for (i = 0; i < pw->n; ++i) {
-		pw->p[i].set = isl_set_insert(pw->p[i].set, type, first, n);
+		pw->p[i].set = isl_set_insert_dims(pw->p[i].set,
+							    set_type, first, n);
 		if (!pw->p[i].set)
 			goto error;
 		pw->p[i].FIELD = FN(EL,insert_dims)(pw->p[i].FIELD,
@@ -652,6 +1103,9 @@ __isl_give PW *FN(PW,fix_dim)(__isl_take PW *pw,
 	if (!pw)
 		return NULL;
 
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+
 	pw = FN(PW,cow)(pw);
 	if (!pw)
 		return NULL;
@@ -669,7 +1123,7 @@ error:
 
 unsigned FN(PW,dim)(__isl_keep PW *pw, enum isl_dim_type type)
 {
-	return pw ? isl_dim_size(pw->dim, type) : 0;
+	return pw ? isl_space_dim(pw->dim, type) : 0;
 }
 
 __isl_give PW *FN(PW,split_dims)(__isl_take PW *pw,
@@ -682,6 +1136,9 @@ __isl_give PW *FN(PW,split_dims)(__isl_take PW *pw,
 	if (n == 0)
 		return pw;
 
+	if (type == isl_dim_in)
+		type = isl_dim_set;
+
 	pw = FN(PW,cow)(pw);
 	if (!pw)
 		return NULL;
@@ -714,9 +1171,9 @@ __isl_give isl_qpolynomial *FN(PW,opt)(__isl_take PW *pw, int max)
 		return NULL;
 
 	if (pw->n == 0) {
-		isl_dim *dim = isl_dim_copy(pw->dim);
+		isl_space *dim = isl_space_copy(pw->dim);
 		FN(PW,free)(pw);
-		return isl_qpolynomial_zero(dim);
+		return isl_qpolynomial_zero_on_domain(isl_space_domain(dim));
 	}
 
 	opt = FN(EL,opt_on_domain)(FN(EL,copy)(pw->p[0].FIELD),
@@ -746,51 +1203,109 @@ __isl_give isl_qpolynomial *FN(PW,min)(__isl_take PW *pw)
 }
 #endif
 
-__isl_give isl_dim *FN(PW,get_dim)(__isl_keep PW *pw)
+__isl_give isl_space *FN(PW,get_space)(__isl_keep PW *pw)
 {
-	return pw ? isl_dim_copy(pw->dim) : NULL;
+	return pw ? isl_space_copy(pw->dim) : NULL;
+}
+
+__isl_give isl_space *FN(PW,get_domain_space)(__isl_keep PW *pw)
+{
+	return pw ? isl_space_domain(isl_space_copy(pw->dim)) : NULL;
 }
 
 #ifndef NO_RESET_DIM
-__isl_give PW *FN(PW,reset_dim)(__isl_take PW *pw, __isl_take isl_dim *dim)
+/* Reset the space of "pw".  Since we don't know if the elements
+ * represent the spaces themselves or their domains, we pass along
+ * both when we call their reset_space_and_domain.
+ */
+static __isl_give PW *FN(PW,reset_space_and_domain)(__isl_take PW *pw,
+	__isl_take isl_space *space, __isl_take isl_space *domain)
 {
 	int i;
 
 	pw = FN(PW,cow)(pw);
-	if (!pw || !dim)
+	if (!pw || !space || !domain)
 		goto error;
 
 	for (i = 0; i < pw->n; ++i) {
-		pw->p[i].set = isl_set_reset_dim(pw->p[i].set,
-						 isl_dim_copy(dim));
+		pw->p[i].set = isl_set_reset_space(pw->p[i].set,
+						 isl_space_copy(domain));
 		if (!pw->p[i].set)
 			goto error;
-		pw->p[i].FIELD = FN(EL,reset_dim)(pw->p[i].FIELD,
-						  isl_dim_copy(dim));
+		pw->p[i].FIELD = FN(EL,reset_space_and_domain)(pw->p[i].FIELD,
+			      isl_space_copy(space), isl_space_copy(domain));
 		if (!pw->p[i].FIELD)
 			goto error;
 	}
-	isl_dim_free(pw->dim);
-	pw->dim = dim;
+
+	isl_space_free(domain);
+
+	isl_space_free(pw->dim);
+	pw->dim = space;
 
 	return pw;
 error:
-	isl_dim_free(dim);
+	isl_space_free(domain);
+	isl_space_free(space);
 	FN(PW,free)(pw);
 	return NULL;
 }
+
+__isl_give PW *FN(PW,reset_domain_space)(__isl_take PW *pw,
+	__isl_take isl_space *domain)
+{
+	isl_space *space;
+
+	space = isl_space_extend_domain_with_range(isl_space_copy(domain),
+						   FN(PW,get_space)(pw));
+	return FN(PW,reset_space_and_domain)(pw, space, domain);
+}
+
+__isl_give PW *FN(PW,reset_space)(__isl_take PW *pw, __isl_take isl_space *dim)
+{
+	isl_space *domain;
+
+	domain = isl_space_domain(isl_space_copy(dim));
+	return FN(PW,reset_space_and_domain)(pw, dim, domain);
+}
+
+__isl_give PW *FN(PW,set_tuple_id)(__isl_keep PW *pw, enum isl_dim_type type,
+	__isl_take isl_id *id)
+{
+	isl_space *space;
+
+	pw = FN(PW,cow)(pw);
+	if (!pw)
+		return isl_id_free(id);
+
+	space = FN(PW,get_space)(pw);
+	space = isl_space_set_tuple_id(space, type, id);
+
+	return FN(PW,reset_space)(pw, space);
+}
+
+__isl_give PW *FN(PW,set_dim_id)(__isl_take PW *pw,
+	enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
+{
+	pw = FN(PW,cow)(pw);
+	if (!pw)
+		return isl_id_free(id);
+	pw->dim = isl_space_set_dim_id(pw->dim, type, pos, id);
+	return FN(PW,reset_space)(pw, isl_space_copy(pw->dim));
+}
 #endif
 
-int FN(PW,has_equal_dim)(__isl_keep PW *pw1, __isl_keep PW *pw2)
+int FN(PW,has_equal_space)(__isl_keep PW *pw1, __isl_keep PW *pw2)
 {
 	if (!pw1 || !pw2)
 		return -1;
 
-	return isl_dim_equal(pw1->dim, pw2->dim);
+	return isl_space_is_equal(pw1->dim, pw2->dim);
 }
 
 #ifndef NO_MORPH
-__isl_give PW *FN(PW,morph)(__isl_take PW *pw, __isl_take isl_morph *morph)
+__isl_give PW *FN(PW,morph_domain)(__isl_take PW *pw,
+	__isl_take isl_morph *morph)
 {
 	int i;
 	isl_ctx *ctx;
@@ -798,15 +1313,15 @@ __isl_give PW *FN(PW,morph)(__isl_take PW *pw, __isl_take isl_morph *morph)
 	if (!pw || !morph)
 		goto error;
 
-	ctx = isl_dim_get_ctx(pw->dim);
-	isl_assert(ctx, isl_dim_equal(pw->dim, morph->dom->dim),
+	ctx = isl_space_get_ctx(pw->dim);
+	isl_assert(ctx, isl_space_is_domain_internal(morph->dom->dim, pw->dim),
 		goto error);
 
 	pw = FN(PW,cow)(pw);
 	if (!pw)
 		goto error;
-	isl_dim_free(pw->dim);
-	pw->dim = isl_dim_copy(morph->ran->dim);
+	pw->dim = isl_space_extend_domain_with_range(
+			isl_space_copy(morph->ran->dim), pw->dim);
 	if (!pw->dim)
 		goto error;
 
@@ -814,7 +1329,7 @@ __isl_give PW *FN(PW,morph)(__isl_take PW *pw, __isl_take isl_morph *morph)
 		pw->p[i].set = isl_morph_set(isl_morph_copy(morph), pw->p[i].set);
 		if (!pw->p[i].set)
 			goto error;
-		pw->p[i].FIELD = FN(EL,morph)(pw->p[i].FIELD,
+		pw->p[i].FIELD = FN(EL,morph_domain)(pw->p[i].FIELD,
 						isl_morph_copy(morph));
 		if (!pw->p[i].FIELD)
 			goto error;
@@ -830,6 +1345,11 @@ error:
 }
 #endif
 
+int FN(PW,n_piece)(__isl_keep PW *pw)
+{
+	return pw ? pw->n : 0;
+}
+
 int FN(PW,foreach_piece)(__isl_keep PW *pw,
 	int (*fn)(__isl_take isl_set *set, __isl_take EL *el, void *user),
 	void *user)
@@ -879,7 +1399,7 @@ static int foreach_lifted_subset(__isl_take isl_set *set, __isl_take EL *el,
 		lift = isl_set_lift(lift);
 
 		copy = FN(EL,copy)(el);
-		copy = FN(EL,lift)(copy, isl_set_get_dim(lift));
+		copy = FN(EL,lift)(copy, isl_set_get_space(lift));
 
 		if (fn(lift, copy, user) < 0)
 			goto error;
@@ -934,55 +1454,32 @@ __isl_give PW *FN(PW,move_dims)(__isl_take PW *pw,
 	if (!pw)
 		return NULL;
 
-	pw->dim = isl_dim_move(pw->dim, dst_type, dst_pos, src_type, src_pos, n);
+	pw->dim = isl_space_move_dims(pw->dim, dst_type, dst_pos, src_type, src_pos, n);
 	if (!pw->dim)
 		goto error;
 
 	for (i = 0; i < pw->n; ++i) {
-		pw->p[i].set = isl_set_move_dims(pw->p[i].set,
-						dst_type, dst_pos,
-						src_type, src_pos, n);
-		if (!pw->p[i].set)
-			goto error;
 		pw->p[i].FIELD = FN(EL,move_dims)(pw->p[i].FIELD,
 					dst_type, dst_pos, src_type, src_pos, n);
 		if (!pw->p[i].FIELD)
 			goto error;
 	}
 
-	return pw;
-error:
-	FN(PW,free)(pw);
-	return NULL;
-}
-#endif
-
-#ifndef NO_REALIGN
-__isl_give PW *FN(PW,realign)(__isl_take PW *pw, __isl_take isl_reordering *exp)
-{
-	int i;
-
-	pw = FN(PW,cow)(pw);
-	if (!pw || !exp)
-		return NULL;
+	if (dst_type == isl_dim_in)
+		dst_type = isl_dim_set;
+	if (src_type == isl_dim_in)
+		src_type = isl_dim_set;
 
 	for (i = 0; i < pw->n; ++i) {
-		pw->p[i].set = isl_set_realign(pw->p[i].set,
-						    isl_reordering_copy(exp));
+		pw->p[i].set = isl_set_move_dims(pw->p[i].set,
+						dst_type, dst_pos,
+						src_type, src_pos, n);
 		if (!pw->p[i].set)
 			goto error;
-		pw->p[i].FIELD = FN(EL,realign)(pw->p[i].FIELD,
-						    isl_reordering_copy(exp));
-		if (!pw->p[i].FIELD)
-			goto error;
 	}
 
-	pw = FN(PW,reset_dim)(pw, isl_dim_copy(exp->dim));
-
-	isl_reordering_free(exp);
 	return pw;
 error:
-	isl_reordering_free(exp);
 	FN(PW,free)(pw);
 	return NULL;
 }
@@ -994,9 +1491,9 @@ __isl_give PW *FN(PW,mul_isl_int)(__isl_take PW *pw, isl_int v)
 
 	if (isl_int_is_one(v))
 		return pw;
-	if (pw && isl_int_is_zero(v)) {
+	if (pw && DEFAULT_IS_ZERO && isl_int_is_zero(v)) {
 		PW *zero;
-		isl_dim *dim = FN(PW,get_dim)(pw);
+		isl_space *dim = FN(PW,get_space)(pw);
 #ifdef HAS_TYPE
 		zero = FN(PW,ZERO)(dim, pw->type);
 #else
@@ -1026,3 +1523,256 @@ error:
 	FN(PW,free)(pw);
 	return NULL;
 }
+
+__isl_give PW *FN(PW,scale)(__isl_take PW *pw, isl_int v)
+{
+	return FN(PW,mul_isl_int)(pw, v);
+}
+
+static int FN(PW,qsort_set_cmp)(const void *p1, const void *p2)
+{
+	isl_set *set1 = *(isl_set * const *)p1;
+	isl_set *set2 = *(isl_set * const *)p2;
+
+	return isl_set_plain_cmp(set1, set2);
+}
+
+/* We normalize in place, but if anything goes wrong we need
+ * to return NULL, so we need to make sure we don't change the
+ * meaning of any possible other copies of map.
+ */
+__isl_give PW *FN(PW,normalize)(__isl_take PW *pw)
+{
+	int i, j;
+	isl_set *set;
+
+	if (!pw)
+		return NULL;
+	for (i = 0; i < pw->n; ++i) {
+		set = isl_set_normalize(isl_set_copy(pw->p[i].set));
+		if (!set)
+			return FN(PW,free)(pw);
+		isl_set_free(pw->p[i].set);
+		pw->p[i].set = set;
+	}
+	qsort(pw->p, pw->n, sizeof(pw->p[0]), &FN(PW,qsort_set_cmp));
+	for (i = pw->n - 1; i >= 1; --i) {
+		if (!isl_set_plain_is_equal(pw->p[i - 1].set, pw->p[i].set))
+			continue;
+		if (!FN(EL,plain_is_equal)(pw->p[i - 1].FIELD, pw->p[i].FIELD))
+			continue;
+		set = isl_set_union(isl_set_copy(pw->p[i - 1].set),
+				    isl_set_copy(pw->p[i].set));
+		if (!set)
+			return FN(PW,free)(pw);
+		isl_set_free(pw->p[i].set);
+		FN(EL,free)(pw->p[i].FIELD);
+		isl_set_free(pw->p[i - 1].set);
+		pw->p[i - 1].set = set;
+		for (j = i + 1; j < pw->n; ++j)
+			pw->p[j - 1] = pw->p[j];
+		pw->n--;
+	}
+
+	return pw;
+}
+
+/* Is pw1 obviously equal to pw2?
+ * That is, do they have obviously identical cells and obviously identical
+ * elements on each cell?
+ */
+int FN(PW,plain_is_equal)(__isl_keep PW *pw1, __isl_keep PW *pw2)
+{
+	int i;
+	int equal;
+
+	if (!pw1 || !pw2)
+		return -1;
+
+	if (pw1 == pw2)
+		return 1;
+	if (!isl_space_is_equal(pw1->dim, pw2->dim))
+		return 0;
+
+	pw1 = FN(PW,copy)(pw1);
+	pw2 = FN(PW,copy)(pw2);
+	pw1 = FN(PW,normalize)(pw1);
+	pw2 = FN(PW,normalize)(pw2);
+	if (!pw1 || !pw2)
+		goto error;
+
+	equal = pw1->n == pw2->n;
+	for (i = 0; equal && i < pw1->n; ++i) {
+		equal = isl_set_plain_is_equal(pw1->p[i].set, pw2->p[i].set);
+		if (equal < 0)
+			goto error;
+		if (!equal)
+			break;
+		equal = FN(EL,plain_is_equal)(pw1->p[i].FIELD, pw2->p[i].FIELD);
+		if (equal < 0)
+			goto error;
+	}
+
+	FN(PW,free)(pw1);
+	FN(PW,free)(pw2);
+	return equal;
+error:
+	FN(PW,free)(pw1);
+	FN(PW,free)(pw2);
+	return -1;
+}
+
+#ifndef NO_PULLBACK
+static __isl_give PW *FN(PW,align_params_pw_multi_aff_and)(__isl_take PW *pw,
+	__isl_take isl_multi_aff *ma,
+	__isl_give PW *(*fn)(__isl_take PW *pw, __isl_take isl_multi_aff *ma))
+{
+	isl_ctx *ctx;
+	isl_space *ma_space;
+
+	ma_space = isl_multi_aff_get_space(ma);
+	if (!pw || !ma || !ma_space)
+		goto error;
+	if (isl_space_match(pw->dim, isl_dim_param, ma_space, isl_dim_param)) {
+		isl_space_free(ma_space);
+		return fn(pw, ma);
+	}
+	ctx = FN(PW,get_ctx)(pw);
+	if (!isl_space_has_named_params(pw->dim) ||
+	    !isl_space_has_named_params(ma_space))
+		isl_die(ctx, isl_error_invalid,
+			"unaligned unnamed parameters", goto error);
+	pw = FN(PW,align_params)(pw, ma_space);
+	ma = isl_multi_aff_align_params(ma, FN(PW,get_space)(pw));
+	return fn(pw, ma);
+error:
+	isl_space_free(ma_space);
+	FN(PW,free)(pw);
+	isl_multi_aff_free(ma);
+	return NULL;
+}
+
+static __isl_give PW *FN(PW,align_params_pw_pw_multi_aff_and)(__isl_take PW *pw,
+	__isl_take isl_pw_multi_aff *pma,
+	__isl_give PW *(*fn)(__isl_take PW *pw,
+		__isl_take isl_pw_multi_aff *ma))
+{
+	isl_ctx *ctx;
+	isl_space *pma_space;
+
+	pma_space = isl_pw_multi_aff_get_space(pma);
+	if (!pw || !pma || !pma_space)
+		goto error;
+	if (isl_space_match(pw->dim, isl_dim_param, pma_space, isl_dim_param)) {
+		isl_space_free(pma_space);
+		return fn(pw, pma);
+	}
+	ctx = FN(PW,get_ctx)(pw);
+	if (!isl_space_has_named_params(pw->dim) ||
+	    !isl_space_has_named_params(pma_space))
+		isl_die(ctx, isl_error_invalid,
+			"unaligned unnamed parameters", goto error);
+	pw = FN(PW,align_params)(pw, pma_space);
+	pma = isl_pw_multi_aff_align_params(pma, FN(PW,get_space)(pw));
+	return fn(pw, pma);
+error:
+	isl_space_free(pma_space);
+	FN(PW,free)(pw);
+	isl_pw_multi_aff_free(pma);
+	return NULL;
+}
+
+/* Compute the pullback of "pw" by the function represented by "ma".
+ * In other words, plug in "ma" in "pw".
+ */
+static __isl_give PW *FN(PW,pullback_multi_aff_aligned)(__isl_take PW *pw,
+	__isl_take isl_multi_aff *ma)
+{
+	int i;
+	isl_space *space = NULL;
+
+	ma = isl_multi_aff_align_divs(ma);
+	pw = FN(PW,cow)(pw);
+	if (!pw || !ma)
+		goto error;
+
+	space = isl_space_join(isl_multi_aff_get_space(ma),
+				FN(PW,get_space)(pw));
+
+	for (i = 0; i < pw->n; ++i) {
+		pw->p[i].set = isl_set_preimage_multi_aff(pw->p[i].set,
+						    isl_multi_aff_copy(ma));
+		if (!pw->p[i].set)
+			goto error;
+		pw->p[i].FIELD = FN(EL,pullback_multi_aff)(pw->p[i].FIELD,
+						    isl_multi_aff_copy(ma));
+		if (!pw->p[i].FIELD)
+			goto error;
+	}
+
+	pw = FN(PW,reset_space)(pw, space);
+	isl_multi_aff_free(ma);
+	return pw;
+error:
+	isl_space_free(space);
+	isl_multi_aff_free(ma);
+	FN(PW,free)(pw);
+	return NULL;
+}
+
+__isl_give PW *FN(PW,pullback_multi_aff)(__isl_take PW *pw,
+	__isl_take isl_multi_aff *ma)
+{
+	return FN(PW,align_params_pw_multi_aff_and)(pw, ma,
+					&FN(PW,pullback_multi_aff_aligned));
+}
+
+/* Compute the pullback of "pw" by the function represented by "pma".
+ * In other words, plug in "pma" in "pw".
+ */
+static __isl_give PW *FN(PW,pullback_pw_multi_aff_aligned)(__isl_take PW *pw,
+	__isl_take isl_pw_multi_aff *pma)
+{
+	int i;
+	PW *res;
+
+	if (!pma)
+		goto error;
+
+	if (pma->n == 0) {
+		isl_pw_multi_aff_free(pma);
+		res = FN(PW,empty)(FN(PW,get_space)(pw));
+		FN(PW,free)(pw);
+		return res;
+	}
+
+	res = FN(PW,pullback_multi_aff)(FN(PW,copy)(pw),
+					isl_multi_aff_copy(pma->p[0].maff));
+	res = FN(PW,intersect_domain)(res, isl_set_copy(pma->p[0].set));
+
+	for (i = 1; i < pma->n; ++i) {
+		PW *res_i;
+
+		res_i = FN(PW,pullback_multi_aff)(FN(PW,copy)(pw),
+					isl_multi_aff_copy(pma->p[i].maff));
+		res_i = FN(PW,intersect_domain)(res_i,
+					isl_set_copy(pma->p[i].set));
+		res = FN(PW,add_disjoint)(res, res_i);
+	}
+
+	isl_pw_multi_aff_free(pma);
+	FN(PW,free)(pw);
+	return res;
+error:
+	isl_pw_multi_aff_free(pma);
+	FN(PW,free)(pw);
+	return NULL;
+}
+
+__isl_give PW *FN(PW,pullback_pw_multi_aff)(__isl_take PW *pw,
+	__isl_take isl_pw_multi_aff *pma)
+{
+	return FN(PW,align_params_pw_pw_multi_aff_and)(pw, pma,
+					&FN(PW,pullback_pw_multi_aff_aligned));
+}
+#endif