isl_basic_set_opt: avoid invalid access on error path
[platform/upstream/isl.git] / isl_fold.c
index 036c296..ba93a69 100644 (file)
@@ -1,22 +1,40 @@
 /*
  * Copyright 2010      INRIA Saclay
  *
- * 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 
  */
 
+#define ISL_DIM_H
+#include <isl_map_private.h>
+#include <isl_union_map_private.h>
 #include <isl_polynomial_private.h>
 #include <isl_point_private.h>
-#include <isl_dim.h>
-#include <isl_map_private.h>
-#include <isl_lp.h>
-#include <isl_seq.h>
+#include <isl_space_private.h>
+#include <isl/lp.h>
+#include <isl/seq.h>
+#include <isl_mat_private.h>
+#include <isl_config.h>
+
+enum isl_fold isl_fold_type_negate(enum isl_fold type)
+{
+       switch (type) {
+       case isl_fold_min:
+               return isl_fold_max;
+       case isl_fold_max:
+               return isl_fold_min;
+       case isl_fold_list:
+               return isl_fold_list;
+       }
+
+       isl_die(NULL, isl_error_internal, "unhandled isl_fold type", abort());
+}
 
 static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
-       enum isl_fold type, __isl_take isl_dim *dim, int n)
+       enum isl_fold type, __isl_take isl_space *dim, int n)
 {
        isl_qpolynomial_fold *fold;
 
@@ -24,7 +42,7 @@ static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
                goto error;
 
        isl_assert(dim->ctx, n >= 0, goto error);
-       fold = isl_alloc(dim->ctx, struct isl_qpolynomial_fold,
+       fold = isl_calloc(dim->ctx, struct isl_qpolynomial_fold,
                        sizeof(struct isl_qpolynomial_fold) +
                        (n - 1) * sizeof(struct isl_qpolynomial *));
        if (!fold)
@@ -38,10 +56,71 @@ static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
 
        return fold;
 error:
-       isl_dim_free(dim);
+       isl_space_free(dim);
+       return NULL;
+}
+
+isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
+{
+       return fold ? fold->dim->ctx : NULL;
+}
+
+__isl_give isl_space *isl_qpolynomial_fold_get_domain_space(
+       __isl_keep isl_qpolynomial_fold *fold)
+{
+       return fold ? isl_space_copy(fold->dim) : NULL;
+}
+
+__isl_give isl_space *isl_qpolynomial_fold_get_space(
+       __isl_keep isl_qpolynomial_fold *fold)
+{
+       isl_space *space;
+       if (!fold)
+               return NULL;
+       space = isl_space_copy(fold->dim);
+       space = isl_space_from_domain(space);
+       space = isl_space_add_dims(space, isl_dim_out, 1);
+       return space;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_domain_space(
+       __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
+{
+       int i;
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold || !dim)
+               goto error;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_reset_domain_space(fold->qp[i],
+                                                       isl_space_copy(dim));
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       isl_space_free(fold->dim);
+       fold->dim = dim;
+
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       isl_space_free(dim);
        return NULL;
 }
 
+/* Reset the space of "fold".  This function is called from isl_pw_templ.c
+ * and doesn't know if the space of an element object is represented
+ * directly or through its domain.  It therefore passes along both.
+ */
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_space_and_domain(
+       __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space,
+       __isl_take isl_space *domain)
+{
+       isl_space_free(space);
+       return isl_qpolynomial_fold_reset_domain_space(fold, domain);
+}
+
 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
        enum isl_dim_type type, unsigned first, unsigned n)
 {
@@ -61,21 +140,50 @@ int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
        return 0;
 }
 
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
+       __isl_take isl_qpolynomial_fold *fold,
+       enum isl_dim_type type, unsigned pos, const char *s)
+{
+       int i;
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               return NULL;
+       fold->dim = isl_space_set_dim_name(fold->dim, type, pos, s);
+       if (!fold->dim)
+               goto error;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_set_dim_name(fold->qp[i],
+                                                           type, pos, s);
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       return NULL;
+}
+
 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
        __isl_take isl_qpolynomial_fold *fold,
        enum isl_dim_type type, unsigned first, unsigned n)
 {
        int i;
+       enum isl_dim_type set_type;
 
        if (!fold)
                return NULL;
        if (n == 0)
                return fold;
 
+       set_type = type == isl_dim_in ? isl_dim_set : type;
+
        fold = isl_qpolynomial_fold_cow(fold);
        if (!fold)
                return NULL;
-       fold->dim = isl_dim_drop(fold->dim, type, first, n);
+       fold->dim = isl_space_drop_dims(fold->dim, set_type, first, n);
        if (!fold->dim)
                goto error;
 
@@ -92,6 +200,37 @@ error:
        return NULL;
 }
 
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
+       __isl_take isl_qpolynomial_fold *fold,
+       enum isl_dim_type type, unsigned first, unsigned n)
+{
+       int i;
+
+       if (!fold)
+               return NULL;
+       if (n == 0 && !isl_space_is_named_or_nested(fold->dim, type))
+               return fold;
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               return NULL;
+       fold->dim = isl_space_insert_dims(fold->dim, type, first, n);
+       if (!fold->dim)
+               goto error;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_insert_dims(fold->qp[i],
+                                                           type, first, n);
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       return NULL;
+}
+
 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
 {
        struct isl_upoly_cst *cst;
@@ -189,7 +328,7 @@ static int isl_qpolynomial_sign(__isl_keep isl_set *set,
        if (!rec)
                return 0;
 
-       d = isl_dim_total(qp->dim);
+       d = isl_space_dim(qp->dim, isl_dim_all);
        v = isl_vec_alloc(set->ctx, 2 + d);
        if (!v)
                return 0;
@@ -207,17 +346,17 @@ static int isl_qpolynomial_sign(__isl_keep isl_set *set,
                isl_qpolynomial *r, *q;
                isl_qpolynomial *t;
 
-               min = isl_qpolynomial_cst(isl_dim_copy(qp->dim), l);
-               base = isl_qpolynomial_pow(isl_dim_copy(qp->dim),
+               min = isl_qpolynomial_cst_on_domain(isl_space_copy(qp->dim), l);
+               base = isl_qpolynomial_var_pow_on_domain(isl_space_copy(qp->dim),
                                                qp->upoly->var, 1);
 
-               r = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), 0,
+               r = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
                                          isl_upoly_copy(rec->p[rec->n - 1]));
                q = isl_qpolynomial_copy(r);
 
                for (i = rec->n - 2; i >= 0; --i) {
                        r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
-                       t = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), 0,
+                       t = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
                                                  isl_upoly_copy(rec->p[i]));
                        r = isl_qpolynomial_add(r, t);
                        if (i == 0)
@@ -265,7 +404,7 @@ __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
                goto error;
 
        isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
-       isl_assert(fold1->dim->ctx, isl_dim_equal(fold1->dim, fold2->dim),
+       isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
                        goto error);
 
        better = fold1->type == isl_fold_max ? -1 : 1;
@@ -280,7 +419,7 @@ __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
                return fold1;
        }
 
-       res = qpolynomial_fold_alloc(fold1->type, isl_dim_copy(fold1->dim),
+       res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
                                        fold1->n + fold2->n);
        if (!res)
                goto error;
@@ -333,21 +472,188 @@ error:
        return NULL;
 }
 
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
+       __isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
+{
+       int i;
+
+       if (!fold || !qp)
+               goto error;
+
+       if (isl_qpolynomial_is_zero(qp)) {
+               isl_qpolynomial_free(qp);
+               return fold;
+       }
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               goto error;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_add(fold->qp[i],
+                                               isl_qpolynomial_copy(qp));
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       isl_qpolynomial_free(qp);
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       isl_qpolynomial_free(qp);
+       return NULL;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
+       __isl_keep isl_set *dom,
+       __isl_take isl_qpolynomial_fold *fold1,
+       __isl_take isl_qpolynomial_fold *fold2)
+{
+       int i;
+       isl_qpolynomial_fold *res = NULL;
+
+       if (!fold1 || !fold2)
+               goto error;
+
+       if (isl_qpolynomial_fold_is_empty(fold1)) {
+               isl_qpolynomial_fold_free(fold1);
+               return fold2;
+       }
+
+       if (isl_qpolynomial_fold_is_empty(fold2)) {
+               isl_qpolynomial_fold_free(fold2);
+               return fold1;
+       }
+
+       if (fold1->n == 1 && fold2->n != 1)
+               return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
+
+       if (fold2->n == 1) {
+               res = isl_qpolynomial_fold_add_qpolynomial(fold1,
+                                       isl_qpolynomial_copy(fold2->qp[0]));
+               isl_qpolynomial_fold_free(fold2);
+               return res;
+       }
+
+       res = isl_qpolynomial_fold_add_qpolynomial(
+                               isl_qpolynomial_fold_copy(fold1),
+                               isl_qpolynomial_copy(fold2->qp[0]));
+
+       for (i = 1; i < fold2->n; ++i) {
+               isl_qpolynomial_fold *res_i;
+               res_i = isl_qpolynomial_fold_add_qpolynomial(
+                                       isl_qpolynomial_fold_copy(fold1),
+                                       isl_qpolynomial_copy(fold2->qp[i]));
+               res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
+       }
+
+       isl_qpolynomial_fold_free(fold1);
+       isl_qpolynomial_fold_free(fold2);
+       return res;
+error:
+       isl_qpolynomial_fold_free(res);
+       isl_qpolynomial_fold_free(fold1);
+       isl_qpolynomial_fold_free(fold2);
+       return NULL;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
+       __isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
+{
+       int i;
+
+       if (!fold || !eq)
+               goto error;
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               return NULL;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_substitute_equalities(fold->qp[i],
+                                                       isl_basic_set_copy(eq));
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       isl_basic_set_free(eq);
+       return fold;
+error:
+       isl_basic_set_free(eq);
+       isl_qpolynomial_fold_free(fold);
+       return NULL;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
+       __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
+{
+       int i;
+
+       if (!fold || !context)
+               goto error;
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               return NULL;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_gist(fold->qp[i],
+                                                       isl_set_copy(context));
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       isl_set_free(context);
+       return fold;
+error:
+       isl_set_free(context);
+       isl_qpolynomial_fold_free(fold);
+       return NULL;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
+       __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
+{
+       isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
+       isl_set *dom_context = isl_set_universe(space);
+       dom_context = isl_set_intersect_params(dom_context, context);
+       return isl_qpolynomial_fold_gist(fold, dom_context);
+}
+
+#define HAS_TYPE
+
 #undef PW
 #define PW isl_pw_qpolynomial_fold
 #undef EL
 #define EL isl_qpolynomial_fold
+#undef EL_IS_ZERO
+#define EL_IS_ZERO is_empty
+#undef ZERO
+#define ZERO zero
 #undef IS_ZERO
-#define IS_ZERO is_empty
+#define IS_ZERO is_zero
 #undef FIELD
 #define FIELD fold
-#undef ADD
-#define ADD(d,e1,e2)   isl_qpolynomial_fold_fold_on_domain(d,e1,e2) 
+#undef DEFAULT_IS_ZERO
+#define DEFAULT_IS_ZERO 1
+
+#define NO_NEG
+#define NO_PULLBACK
 
 #include <isl_pw_templ.c>
 
+#undef UNION
+#define UNION isl_union_pw_qpolynomial_fold
+#undef PART
+#define PART isl_pw_qpolynomial_fold
+#undef PARTS
+#define PARTS pw_qpolynomial_fold
+#define ALIGN_DOMAIN
+
+#include <isl_union_templ.c>
+
 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
-       __isl_take isl_dim *dim)
+       __isl_take isl_space *dim)
 {
        return qpolynomial_fold_alloc(type, dim, 0);
 }
@@ -360,7 +666,7 @@ __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
        if (!qp)
                return NULL;
 
-       fold = qpolynomial_fold_alloc(type, isl_dim_copy(qp->dim), 1);
+       fold = qpolynomial_fold_alloc(type, isl_space_copy(qp->dim), 1);
        if (!fold)
                goto error;
 
@@ -393,10 +699,11 @@ __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
        if (!fold)
                return NULL;
        dup = qpolynomial_fold_alloc(fold->type,
-                                       isl_dim_copy(fold->dim), fold->n);
+                                       isl_space_copy(fold->dim), fold->n);
        if (!dup)
                return NULL;
        
+       dup->n = fold->n;
        for (i = 0; i < fold->n; ++i) {
                dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
                if (!dup->qp[i])
@@ -432,7 +739,7 @@ void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
 
        for (i = 0; i < fold->n; ++i)
                isl_qpolynomial_free(fold->qp[i]);
-       isl_dim_free(fold->dim);
+       isl_space_free(fold->dim);
        free(fold);
 }
 
@@ -455,7 +762,7 @@ __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
                goto error;
 
        isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
-       isl_assert(fold1->dim->ctx, isl_dim_equal(fold1->dim, fold2->dim),
+       isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
                        goto error);
 
        if (isl_qpolynomial_fold_is_empty(fold1)) {
@@ -468,7 +775,7 @@ __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
                return fold1;
        }
 
-       res = qpolynomial_fold_alloc(fold1->type, isl_dim_copy(fold1->dim),
+       res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
                                        fold1->n + fold2->n);
        if (!res)
                goto error;
@@ -498,6 +805,149 @@ error:
        return NULL;
 }
 
+__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
+       __isl_take isl_pw_qpolynomial_fold *pw1,
+       __isl_take isl_pw_qpolynomial_fold *pw2)
+{
+       int i, j, n;
+       struct isl_pw_qpolynomial_fold *res;
+       isl_set *set;
+
+       if (!pw1 || !pw2)
+               goto error;
+
+       isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
+
+       if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
+               isl_pw_qpolynomial_fold_free(pw1);
+               return pw2;
+       }
+
+       if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
+               isl_pw_qpolynomial_fold_free(pw2);
+               return pw1;
+       }
+
+       if (pw1->type != pw2->type)
+               isl_die(pw1->dim->ctx, isl_error_invalid,
+                       "fold types don't match", goto error);
+
+       n = (pw1->n + 1) * (pw2->n + 1);
+       res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
+                                               pw1->type, n);
+
+       for (i = 0; i < pw1->n; ++i) {
+               set = isl_set_copy(pw1->p[i].set);
+               for (j = 0; j < pw2->n; ++j) {
+                       struct isl_set *common;
+                       isl_qpolynomial_fold *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;
+                       }
+
+                       sum = isl_qpolynomial_fold_fold_on_domain(common,
+                              isl_qpolynomial_fold_copy(pw1->p[i].fold),
+                              isl_qpolynomial_fold_copy(pw2->p[j].fold));
+
+                       res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
+               }
+               res = isl_pw_qpolynomial_fold_add_piece(res, set,
+                       isl_qpolynomial_fold_copy(pw1->p[i].fold));
+       }
+
+       for (j = 0; j < pw2->n; ++j) {
+               set = isl_set_copy(pw2->p[j].set);
+               for (i = 0; i < pw1->n; ++i)
+                       set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
+               res = isl_pw_qpolynomial_fold_add_piece(res, set,
+                                   isl_qpolynomial_fold_copy(pw2->p[j].fold));
+       }
+
+       isl_pw_qpolynomial_fold_free(pw1);
+       isl_pw_qpolynomial_fold_free(pw2);
+
+       return res;
+error:
+       isl_pw_qpolynomial_fold_free(pw1);
+       isl_pw_qpolynomial_fold_free(pw2);
+       return NULL;
+}
+
+__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
+       __isl_take isl_union_pw_qpolynomial_fold *u,
+       __isl_take isl_pw_qpolynomial_fold *part)
+{
+       uint32_t hash;
+       struct isl_hash_table_entry *entry;
+
+       u = isl_union_pw_qpolynomial_fold_cow(u);
+
+       if (!part || !u)
+               goto error;
+
+       isl_assert(u->dim->ctx, isl_space_match(part->dim, isl_dim_param, u->dim,
+                                             isl_dim_param), goto error);
+
+       hash = isl_space_get_hash(part->dim);
+       entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
+                                   &has_dim, part->dim, 1);
+       if (!entry)
+               goto error;
+
+       if (!entry->data)
+               entry->data = part;
+       else {
+               entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
+                                           isl_pw_qpolynomial_fold_copy(part));
+               if (!entry->data)
+                       goto error;
+               isl_pw_qpolynomial_fold_free(part);
+       }
+
+       return u;
+error:
+       isl_pw_qpolynomial_fold_free(part);
+       isl_union_pw_qpolynomial_fold_free(u);
+       return NULL;
+}
+
+static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
+{
+       isl_union_pw_qpolynomial_fold **u;
+       u = (isl_union_pw_qpolynomial_fold **)user;
+
+       *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
+
+       return 0;
+}
+
+__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
+       __isl_take isl_union_pw_qpolynomial_fold *u1,
+       __isl_take isl_union_pw_qpolynomial_fold *u2)
+{
+       u1 = isl_union_pw_qpolynomial_fold_cow(u1);
+
+       if (!u1 || !u2)
+               goto error;
+
+       if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
+                                                       &fold_part, &u1) < 0)
+               goto error;
+
+       isl_union_pw_qpolynomial_fold_free(u2);
+
+       return u1;
+error:
+       isl_union_pw_qpolynomial_fold_free(u1);
+       isl_union_pw_qpolynomial_fold_free(u2);
+       return NULL;
+}
+
 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
        enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
 {
@@ -507,7 +957,8 @@ __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
        if (!pwqp)
                return NULL;
        
-       pwf = isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pwqp->dim), pwqp->n);
+       pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
+                                               type, pwqp->n);
 
        for (i = 0; i < pwqp->n; ++i)
                pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
@@ -520,8 +971,15 @@ __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
        return pwf;
 }
 
-int isl_qpolynomial_fold_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
-       __isl_keep isl_qpolynomial_fold *fold2)
+__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
+       __isl_take isl_pw_qpolynomial_fold *pwf1,
+       __isl_take isl_pw_qpolynomial_fold *pwf2)
+{
+       return isl_pw_qpolynomial_fold_union_add_(pwf1, pwf2);
+}
+
+int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
+       __isl_keep isl_qpolynomial_fold *fold2)
 {
        int i;
 
@@ -533,7 +991,7 @@ int isl_qpolynomial_fold_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
 
        /* We probably want to sort the qps first... */
        for (i = 0; i < fold1->n; ++i) {
-               int eq = isl_qpolynomial_is_equal(fold1->qp[i], fold2->qp[i]);
+               int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
                if (eq < 0 || !eq)
                        return eq;
        }
@@ -548,13 +1006,13 @@ __isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
 
        if (!fold || !pnt)
                goto error;
-       isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, fold->dim), goto error);
+       isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
        isl_assert(pnt->dim->ctx,
                fold->type == isl_fold_max || fold->type == isl_fold_min,
                goto error);
 
        if (fold->n == 0)
-               qp = isl_qpolynomial_zero(isl_dim_copy(fold->dim));
+               qp = isl_qpolynomial_zero_on_domain(isl_space_copy(fold->dim));
        else {
                int i;
                qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
@@ -601,10 +1059,10 @@ __isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
                goto error;
 
        if (fold->n == 0) {
-               isl_dim *dim = isl_dim_copy(fold->dim);
+               isl_space *dim = isl_space_copy(fold->dim);
                isl_set_free(set);
                isl_qpolynomial_fold_free(fold);
-               return isl_qpolynomial_zero(dim);
+               return isl_qpolynomial_zero_on_domain(dim);
        }
 
        opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
@@ -629,3 +1087,544 @@ error:
        isl_qpolynomial_fold_free(fold);
        return NULL;
 }
+
+/* Check whether for each quasi-polynomial in "fold2" there is
+ * a quasi-polynomial in "fold1" that dominates it on "set".
+ */
+static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
+       __isl_keep isl_qpolynomial_fold *fold1,
+       __isl_keep isl_qpolynomial_fold *fold2)
+{
+       int i, j;
+       int covers;
+
+       if (!set || !fold1 || !fold2)
+               return -1;
+
+       covers = fold1->type == isl_fold_max ? 1 : -1;
+
+       for (i = 0; i < fold2->n; ++i) {
+               for (j = 0; j < fold1->n; ++j) {
+                       isl_qpolynomial *d;
+                       int sgn;
+
+                       d = isl_qpolynomial_sub(
+                               isl_qpolynomial_copy(fold1->qp[j]),
+                               isl_qpolynomial_copy(fold2->qp[i]));
+                       sgn = isl_qpolynomial_sign(set, d);
+                       isl_qpolynomial_free(d);
+                       if (sgn == covers)
+                               break;
+               }
+               if (j >= fold1->n)
+                       return 0;
+       }
+
+       return 1;
+}
+
+/* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
+ * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
+ * that of pwf2.
+ */
+int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
+       __isl_keep isl_pw_qpolynomial_fold *pwf2)
+{
+       int i, j;
+       isl_set *dom1, *dom2;
+       int is_subset;
+
+       if (!pwf1 || !pwf2)
+               return -1;
+
+       if (pwf2->n == 0)
+               return 1;
+       if (pwf1->n == 0)
+               return 0;
+
+       dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
+       dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
+       is_subset = isl_set_is_subset(dom2, dom1);
+       isl_set_free(dom1);
+       isl_set_free(dom2);
+
+       if (is_subset < 0 || !is_subset)
+               return is_subset;
+
+       for (i = 0; i < pwf2->n; ++i) {
+               for (j = 0; j < pwf1->n; ++j) {
+                       int is_empty;
+                       isl_set *common;
+                       int covers;
+
+                       common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
+                                                  isl_set_copy(pwf2->p[i].set));
+                       is_empty = isl_set_is_empty(common);
+                       if (is_empty < 0 || is_empty) {
+                               isl_set_free(common);
+                               if (is_empty < 0)
+                                       return -1;
+                               continue;
+                       }
+                       covers = qpolynomial_fold_covers_on_domain(common,
+                                       pwf1->p[j].fold, pwf2->p[i].fold);
+                       isl_set_free(common);
+                       if (covers < 0 || !covers)
+                               return covers;
+               }
+       }
+
+       return 1;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
+       __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
+{
+       int i;
+       isl_ctx *ctx;
+
+       if (!fold || !morph)
+               goto error;
+
+       ctx = fold->dim->ctx;
+       isl_assert(ctx, isl_space_is_equal(fold->dim, morph->dom->dim), goto error);
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               goto error;
+
+       isl_space_free(fold->dim);
+       fold->dim = isl_space_copy(morph->ran->dim);
+       if (!fold->dim)
+               goto error;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_morph_domain(fold->qp[i],
+                                               isl_morph_copy(morph));
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       isl_morph_free(morph);
+
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       isl_morph_free(morph);
+       return NULL;
+}
+
+enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
+{
+       if (!fold)
+               return isl_fold_list;
+       return fold->type;
+}
+
+enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
+       __isl_keep isl_union_pw_qpolynomial_fold *upwf)
+{
+       if (!upwf)
+               return isl_fold_list;
+       return upwf->type;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
+       __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
+{
+       int i;
+
+       if (!fold || !dim)
+               goto error;
+
+       if (isl_space_is_equal(fold->dim, dim)) {
+               isl_space_free(dim);
+               return fold;
+       }
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               goto error;
+
+       isl_space_free(fold->dim);
+       fold->dim = isl_space_copy(dim);
+       if (!fold->dim)
+               goto error;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
+                                               isl_space_copy(dim));
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       isl_space_free(dim);
+
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       isl_space_free(dim);
+       return NULL;
+}
+
+int isl_qpolynomial_fold_foreach_qpolynomial(
+       __isl_keep isl_qpolynomial_fold *fold,
+       int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
+{
+       int i;
+
+       if (!fold)
+               return -1;
+
+       for (i = 0; i < fold->n; ++i)
+               if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
+                       return -1;
+
+       return 0;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
+       __isl_take isl_qpolynomial_fold *fold,
+       enum isl_dim_type dst_type, unsigned dst_pos,
+       enum isl_dim_type src_type, unsigned src_pos, unsigned n)
+{
+       int i;
+
+       if (n == 0)
+               return fold;
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               return NULL;
+
+       fold->dim = isl_space_move_dims(fold->dim, dst_type, dst_pos,
+                                               src_type, src_pos, n);
+       if (!fold->dim)
+               goto error;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
+                               dst_type, dst_pos, src_type, src_pos, n);
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       return NULL;
+}
+
+/* For each 0 <= i < "n", replace variable "first" + i of type "type"
+ * in fold->qp[k] by subs[i].
+ */
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
+       __isl_take isl_qpolynomial_fold *fold,
+       enum isl_dim_type type, unsigned first, unsigned n,
+       __isl_keep isl_qpolynomial **subs)
+{
+       int i;
+
+       if (n == 0)
+               return fold;
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               return NULL;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
+                               type, first, n, subs);
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       return NULL;
+}
+
+static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
+{
+       isl_ctx *ctx;
+       isl_pw_qpolynomial_fold *pwf;
+       isl_union_pw_qpolynomial_fold **upwf;
+       uint32_t hash;
+       struct isl_hash_table_entry *entry;
+
+       upwf = (isl_union_pw_qpolynomial_fold **)user;
+
+       ctx = pwqp->dim->ctx;
+       hash = isl_space_get_hash(pwqp->dim);
+       entry = isl_hash_table_find(ctx, &(*upwf)->table,
+                                    hash, &has_dim, pwqp->dim, 1);
+       if (!entry)
+               goto error;
+
+       pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
+       if (!entry->data)
+               entry->data = pwf;
+       else {
+               entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
+               if (!entry->data)
+                       return -1;
+               if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
+                       isl_pw_qpolynomial_fold_free(entry->data);
+                       isl_hash_table_remove(ctx, &(*upwf)->table, entry);
+               }
+       }
+
+       return 0;
+error:
+       isl_pw_qpolynomial_free(pwqp);
+       return -1;
+}
+
+__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
+       __isl_take isl_union_pw_qpolynomial_fold *upwf,
+       __isl_take isl_union_pw_qpolynomial *upwqp)
+{
+       upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
+                               isl_union_pw_qpolynomial_get_space(upwqp));
+       upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
+                               isl_union_pw_qpolynomial_fold_get_space(upwf));
+
+       upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
+       if (!upwf || !upwqp)
+               goto error;
+
+       if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
+                                                        &upwf) < 0)
+               goto error;
+
+       isl_union_pw_qpolynomial_free(upwqp);
+
+       return upwf;
+error:
+       isl_union_pw_qpolynomial_fold_free(upwf);
+       isl_union_pw_qpolynomial_free(upwqp);
+       return NULL;
+}
+
+static int join_compatible(__isl_keep isl_space *dim1, __isl_keep isl_space *dim2)
+{
+       int m;
+       m = isl_space_match(dim1, isl_dim_param, dim2, isl_dim_param);
+       if (m < 0 || !m)
+               return m;
+       return isl_space_tuple_match(dim1, isl_dim_out, dim2, isl_dim_in);
+}
+
+/* Compute the intersection of the range of the map and the domain
+ * of the piecewise quasipolynomial reduction and then compute a bound
+ * on the associated quasipolynomial reduction over all elements
+ * in this intersection.
+ *
+ * We first introduce some unconstrained dimensions in the
+ * piecewise quasipolynomial, intersect the resulting domain
+ * with the wrapped map and the compute the sum.
+ */
+__isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
+       __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
+       int *tight)
+{
+       isl_ctx *ctx;
+       isl_set *dom;
+       isl_space *map_dim;
+       isl_space *pwf_dim;
+       unsigned n_in;
+       int ok;
+
+       ctx = isl_map_get_ctx(map);
+       if (!ctx)
+               goto error;
+
+       map_dim = isl_map_get_space(map);
+       pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
+       ok = join_compatible(map_dim, pwf_dim);
+       isl_space_free(map_dim);
+       isl_space_free(pwf_dim);
+       if (!ok)
+               isl_die(ctx, isl_error_invalid, "incompatible dimensions",
+                       goto error);
+
+       n_in = isl_map_dim(map, isl_dim_in);
+       pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);
+
+       dom = isl_map_wrap(map);
+       pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
+                                               isl_set_get_space(dom));
+
+       pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
+       pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
+       
+       return pwf;
+error:
+       isl_map_free(map);
+       isl_pw_qpolynomial_fold_free(pwf);
+       return NULL;
+}
+
+__isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
+       __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
+       int *tight)
+{
+       return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
+}
+
+struct isl_apply_fold_data {
+       isl_union_pw_qpolynomial_fold *upwf;
+       isl_union_pw_qpolynomial_fold *res;
+       isl_map *map;
+       int tight;
+};
+
+static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
+       void *user)
+{
+       isl_space *map_dim;
+       isl_space *pwf_dim;
+       struct isl_apply_fold_data *data = user;
+       int ok;
+
+       map_dim = isl_map_get_space(data->map);
+       pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
+       ok = join_compatible(map_dim, pwf_dim);
+       isl_space_free(map_dim);
+       isl_space_free(pwf_dim);
+
+       if (ok) {
+               pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
+                                   pwf, data->tight ? &data->tight : NULL);
+               data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
+                                                       data->res, pwf);
+       } else
+               isl_pw_qpolynomial_fold_free(pwf);
+
+       return 0;
+}
+
+static int map_apply(__isl_take isl_map *map, void *user)
+{
+       struct isl_apply_fold_data *data = user;
+       int r;
+
+       data->map = map;
+       r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
+                               data->upwf, &pw_qpolynomial_fold_apply, data);
+
+       isl_map_free(map);
+       return r;
+}
+
+__isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
+       __isl_take isl_union_map *umap,
+       __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
+{
+       isl_space *dim;
+       enum isl_fold type;
+       struct isl_apply_fold_data data;
+
+       upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
+                               isl_union_map_get_space(umap));
+       umap = isl_union_map_align_params(umap,
+                               isl_union_pw_qpolynomial_fold_get_space(upwf));
+
+       data.upwf = upwf;
+       data.tight = tight ? 1 : 0;
+       dim = isl_union_pw_qpolynomial_fold_get_space(upwf);
+       type = isl_union_pw_qpolynomial_fold_get_type(upwf);
+       data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
+       if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
+               goto error;
+
+       isl_union_map_free(umap);
+       isl_union_pw_qpolynomial_fold_free(upwf);
+
+       if (tight)
+               *tight = data.tight;
+
+       return data.res;
+error:
+       isl_union_map_free(umap);
+       isl_union_pw_qpolynomial_fold_free(upwf);
+       isl_union_pw_qpolynomial_fold_free(data.res);
+       return NULL;
+}
+
+__isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
+       __isl_take isl_union_set *uset,
+       __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
+{
+       return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
+}
+
+/* Reorder the dimension of "fold" according to the given reordering.
+ */
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
+       __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
+{
+       int i;
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold || !r)
+               goto error;
+
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_realign_domain(fold->qp[i],
+                                                   isl_reordering_copy(r));
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       fold = isl_qpolynomial_fold_reset_domain_space(fold,
+                                                   isl_space_copy(r->dim));
+
+       isl_reordering_free(r);
+
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       isl_reordering_free(r);
+       return NULL;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
+       __isl_take isl_qpolynomial_fold *fold, isl_int v)
+{
+       int i;
+
+       if (isl_int_is_one(v))
+               return fold;
+       if (fold && isl_int_is_zero(v)) {
+               isl_qpolynomial_fold *zero;
+               isl_space *dim = isl_space_copy(fold->dim);
+               zero = isl_qpolynomial_fold_empty(fold->type, dim);
+               isl_qpolynomial_fold_free(fold);
+               return zero;
+       }
+
+       fold = isl_qpolynomial_fold_cow(fold);
+       if (!fold)
+               return NULL;
+
+       if (isl_int_is_neg(v))
+               fold->type = isl_fold_type_negate(fold->type);
+       for (i = 0; i < fold->n; ++i) {
+               fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
+               if (!fold->qp[i])
+                       goto error;
+       }
+
+       return fold;
+error:
+       isl_qpolynomial_fold_free(fold);
+       return NULL;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
+       __isl_take isl_qpolynomial_fold *fold, isl_int v)
+{
+       return isl_qpolynomial_fold_mul_isl_int(fold, v);
+}