add isl_aff_mod_val
[platform/upstream/isl.git] / isl_flow.c
index e9752fc..8dca5c4 100644 (file)
@@ -2,8 +2,9 @@
  * Copyright 2005-2007 Universiteit Leiden
  * Copyright 2008-2009 Katholieke Universiteit Leuven
  * Copyright 2010      INRIA Saclay
+ * Copyright 2012      Universiteit Leiden
  *
- * 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, Leiden Institute of Advanced Computer Science,
  * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
  * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
  */
 
+#include <isl/set.h>
+#include <isl/map.h>
 #include <isl/flow.h>
+#include <isl_sort.h>
+
+enum isl_restriction_type {
+       isl_restriction_type_empty,
+       isl_restriction_type_none,
+       isl_restriction_type_input,
+       isl_restriction_type_output
+};
+
+struct isl_restriction {
+       enum isl_restriction_type type;
+
+       isl_set *source;
+       isl_set *sink;
+};
+
+/* Create a restriction of the given type.
+ */
+static __isl_give isl_restriction *isl_restriction_alloc(
+       __isl_take isl_map *source_map, enum isl_restriction_type type)
+{
+       isl_ctx *ctx;
+       isl_restriction *restr;
+
+       if (!source_map)
+               return NULL;
+
+       ctx = isl_map_get_ctx(source_map);
+       restr = isl_calloc_type(ctx, struct isl_restriction);
+       if (!restr)
+               goto error;
+
+       restr->type = type;
+
+       isl_map_free(source_map);
+       return restr;
+error:
+       isl_map_free(source_map);
+       return NULL;
+}
+
+/* Create a restriction that doesn't restrict anything.
+ */
+__isl_give isl_restriction *isl_restriction_none(__isl_take isl_map *source_map)
+{
+       return isl_restriction_alloc(source_map, isl_restriction_type_none);
+}
+
+/* Create a restriction that removes everything.
+ */
+__isl_give isl_restriction *isl_restriction_empty(
+       __isl_take isl_map *source_map)
+{
+       return isl_restriction_alloc(source_map, isl_restriction_type_empty);
+}
+
+/* Create a restriction on the input of the maximization problem
+ * based on the given source and sink restrictions.
+ */
+__isl_give isl_restriction *isl_restriction_input(
+       __isl_take isl_set *source_restr, __isl_take isl_set *sink_restr)
+{
+       isl_ctx *ctx;
+       isl_restriction *restr;
+
+       if (!source_restr || !sink_restr)
+               goto error;
+
+       ctx = isl_set_get_ctx(source_restr);
+       restr = isl_calloc_type(ctx, struct isl_restriction);
+       if (!restr)
+               goto error;
+
+       restr->type = isl_restriction_type_input;
+       restr->source = source_restr;
+       restr->sink = sink_restr;
+
+       return restr;
+error:
+       isl_set_free(source_restr);
+       isl_set_free(sink_restr);
+       return NULL;
+}
+
+/* Create a restriction on the output of the maximization problem
+ * based on the given source restriction.
+ */
+__isl_give isl_restriction *isl_restriction_output(
+       __isl_take isl_set *source_restr)
+{
+       isl_ctx *ctx;
+       isl_restriction *restr;
+
+       if (!source_restr)
+               return NULL;
+
+       ctx = isl_set_get_ctx(source_restr);
+       restr = isl_calloc_type(ctx, struct isl_restriction);
+       if (!restr)
+               goto error;
+
+       restr->type = isl_restriction_type_output;
+       restr->source = source_restr;
+
+       return restr;
+error:
+       isl_set_free(source_restr);
+       return NULL;
+}
+
+void *isl_restriction_free(__isl_take isl_restriction *restr)
+{
+       if (!restr)
+               return NULL;
+
+       isl_set_free(restr->source);
+       isl_set_free(restr->sink);
+       free(restr);
+       return NULL;
+}
+
+isl_ctx *isl_restriction_get_ctx(__isl_keep isl_restriction *restr)
+{
+       return restr ? isl_set_get_ctx(restr->source) : NULL;
+}
 
 /* A private structure to keep track of a mapping together with
  * a user-specified identifier and a boolean indicating whether
@@ -30,20 +158,31 @@ struct isl_labeled_map {
  * - n_must + n_may (<= max_source) sources
  * - a function for determining the relative order of sources and sink
  * The must sources are placed before the may sources.
+ *
+ * domain_map is an auxiliary map that maps the sink access relation
+ * to the domain of this access relation.
+ *
+ * restrict_fn is a callback that (if not NULL) will be called
+ * right before any lexicographical maximization.
  */
 struct isl_access_info {
-       struct isl_labeled_map  sink;
-       isl_access_level_before level_before;
-       int                     max_source;
-       int                     n_must;
-       int                     n_may;
-       struct isl_labeled_map  source[1];
+       isl_map                         *domain_map;
+       struct isl_labeled_map          sink;
+       isl_access_level_before         level_before;
+
+       isl_access_restrict             restrict_fn;
+       void                            *restrict_user;
+
+       int                             max_source;
+       int                             n_must;
+       int                             n_may;
+       struct isl_labeled_map          source[1];
 };
 
 /* A structure containing the output of dependence analysis:
  * - n_source dependences
- * - a subset of the sink for which definitely no source could be found
- * - a subset of the sink for which possibly no source could be found
+ * - a wrapped subset of the sink for which definitely no source could be found
+ * - a wrapped subset of the sink for which possibly no source could be found
  */
 struct isl_flow {
        isl_set                 *must_no_source;
@@ -58,14 +197,16 @@ struct isl_flow {
 __isl_give isl_access_info *isl_access_info_alloc(__isl_take isl_map *sink,
        void *sink_user, isl_access_level_before fn, int max_source)
 {
+       isl_ctx *ctx;
        struct isl_access_info *acc;
 
        if (!sink)
                return NULL;
 
-       isl_assert(sink->ctx, max_source >= 0, goto error);
+       ctx = isl_map_get_ctx(sink);
+       isl_assert(ctx, max_source >= 0, goto error);
 
-       acc = isl_alloc(sink->ctx, struct isl_access_info,
+       acc = isl_calloc(ctx, struct isl_access_info,
                        sizeof(struct isl_access_info) +
                        (max_source - 1) * sizeof(struct isl_labeled_map));
        if (!acc)
@@ -86,16 +227,33 @@ error:
 
 /* Free the given isl_access_info structure.
  */
-void isl_access_info_free(__isl_take isl_access_info *acc)
+void *isl_access_info_free(__isl_take isl_access_info *acc)
 {
        int i;
 
        if (!acc)
-               return;
+               return NULL;
+       isl_map_free(acc->domain_map);
        isl_map_free(acc->sink.map);
        for (i = 0; i < acc->n_must + acc->n_may; ++i)
                isl_map_free(acc->source[i].map);
        free(acc);
+       return NULL;
+}
+
+isl_ctx *isl_access_info_get_ctx(__isl_keep isl_access_info *acc)
+{
+       return acc ? isl_map_get_ctx(acc->sink.map) : NULL;
+}
+
+__isl_give isl_access_info *isl_access_info_set_restrict(
+       __isl_take isl_access_info *acc, isl_access_restrict fn, void *user)
+{
+       if (!acc)
+               return NULL;
+       acc->restrict_fn = fn;
+       acc->restrict_user = user;
+       return acc;
 }
 
 /* Add another source to an isl_access_info structure, making
@@ -108,10 +266,12 @@ __isl_give isl_access_info *isl_access_info_add_source(
        __isl_take isl_access_info *acc, __isl_take isl_map *source,
        int must, void *source_user)
 {
+       isl_ctx *ctx;
+
        if (!acc)
-               return NULL;
-       isl_assert(acc->sink.map->ctx,
-                   acc->n_must + acc->n_may < acc->max_source, goto error);
+               goto error;
+       ctx = isl_map_get_ctx(acc->sink.map);
+       isl_assert(ctx, acc->n_must + acc->n_may < acc->max_source, goto error);
        
        if (must) {
                if (acc->n_may)
@@ -135,83 +295,70 @@ error:
        return NULL;
 }
 
-/* A temporary structure used while sorting the accesses in an isl_access_info.
- */
-struct isl_access_sort_info {
-       struct isl_map          *source_map;
-       void                    *source_data;
-       struct isl_access_info  *acc;
-};
-
 /* Return -n, 0 or n (with n a positive value), depending on whether
  * the source access identified by p1 should be sorted before, together
  * or after that identified by p2.
  *
- * If p1 and p2 share a different number of levels with the sink,
- * then the one with the lowest number of shared levels should be
- * sorted first.
- * If they both share no levels, then the order is irrelevant.
- * Otherwise, if p1 appears before p2, then it should be sorted first.
+ * If p1 appears before p2, then it should be sorted first.
+ * For more generic initial schedules, it is possible that neither
+ * p1 nor p2 appears before the other, or at least not in any obvious way.
+ * We therefore also check if p2 appears before p1, in which case p2
+ * should be sorted first.
+ * If not, we try to order the two statements based on the description
+ * of the iteration domains.  This results in an arbitrary, but fairly
+ * stable ordering.
  */
-static int access_sort_cmp(const void *p1, const void *p2)
+static int access_sort_cmp(const void *p1, const void *p2, void *user)
 {
-       const struct isl_access_sort_info *i1, *i2;
+       isl_access_info *acc = user;
+       const struct isl_labeled_map *i1, *i2;
        int level1, level2;
-       i1 = (const struct isl_access_sort_info *) p1;
-       i2 = (const struct isl_access_sort_info *) p2;
-
-       level1 = i1->acc->level_before(i1->source_data, i1->acc->sink.data);
-       level2 = i2->acc->level_before(i2->source_data, i2->acc->sink.data);
+       uint32_t h1, h2;
+       i1 = (const struct isl_labeled_map *) p1;
+       i2 = (const struct isl_labeled_map *) p2;
 
-       if (level1 != level2 || !level1)
-               return level1 - level2;
+       level1 = acc->level_before(i1->data, i2->data);
+       if (level1 % 2)
+               return -1;
 
-       level1 = i1->acc->level_before(i1->source_data, i2->source_data);
+       level2 = acc->level_before(i2->data, i1->data);
+       if (level2 % 2)
+               return 1;
 
-       return (level1 % 2) ? -1 : 1;
+       h1 = isl_map_get_hash(i1->map);
+       h2 = isl_map_get_hash(i2->map);
+       return h1 > h2 ? 1 : h1 < h2 ? -1 : 0;
 }
 
-/* Sort the must source accesses in order of increasing number of shared
- * levels with the sink access.
- * Source accesses with the same number of shared levels are sorted
- * in their textual order.
+/* Sort the must source accesses in their textual order.
  */
 static __isl_give isl_access_info *isl_access_info_sort_sources(
        __isl_take isl_access_info *acc)
 {
-       int i;
-       struct isl_access_sort_info *array;
-
        if (!acc)
                return NULL;
        if (acc->n_must <= 1)
                return acc;
 
-       array = isl_alloc_array(acc->sink.map->ctx,
-                               struct isl_access_sort_info, acc->n_must);
-       if (!array)
-               goto error;
+       if (isl_sort(acc->source, acc->n_must, sizeof(struct isl_labeled_map),
+                   access_sort_cmp, acc) < 0)
+               return isl_access_info_free(acc);
 
-       for (i = 0; i < acc->n_must; ++i) {
-               array[i].source_map = acc->source[i].map;
-               array[i].source_data = acc->source[i].data;
-               array[i].acc = acc;
-       }
-
-       qsort(array, acc->n_must, sizeof(struct isl_access_sort_info),
-               access_sort_cmp);
-
-       for (i = 0; i < acc->n_must; ++i) {
-               acc->source[i].map = array[i].source_map;
-               acc->source[i].data = array[i].source_data;
-       }
+       return acc;
+}
 
-       free(array);
+/* Align the parameters of the two spaces if needed and then call
+ * isl_space_join.
+ */
+static __isl_give isl_space *space_align_and_join(__isl_take isl_space *left,
+       __isl_take isl_space *right)
+{
+       if (isl_space_match(left, isl_dim_param, right, isl_dim_param))
+               return isl_space_join(left, right);
 
-       return acc;
-error:
-       isl_access_info_free(acc);
-       return NULL;
+       left = isl_space_align_params(left, isl_space_copy(right));
+       right = isl_space_align_params(right, isl_space_copy(left));
+       return isl_space_join(left, right);
 }
 
 /* Initialize an empty isl_flow structure corresponding to a given
@@ -233,7 +380,7 @@ static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)
        if (!acc)
                return NULL;
 
-       ctx = acc->sink.map->ctx;
+       ctx = isl_map_get_ctx(acc->sink.map);
        dep = isl_calloc_type(ctx, struct isl_flow);
        if (!dep)
                return NULL;
@@ -245,9 +392,10 @@ static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)
 
        dep->n_source = 2 * acc->n_must + acc->n_may;
        for (i = 0; i < acc->n_must; ++i) {
-               struct isl_dim *dim;
-               dim = isl_dim_join(isl_map_get_dim(acc->source[i].map),
-                           isl_dim_reverse(isl_map_get_dim(acc->sink.map)));
+               isl_space *dim;
+               dim = space_align_and_join(
+                       isl_map_get_space(acc->source[i].map),
+                       isl_space_reverse(isl_map_get_space(acc->sink.map)));
                dep->dep[2 * i].map = isl_map_empty(dim);
                dep->dep[2 * i + 1].map = isl_map_copy(dep->dep[2 * i].map);
                dep->dep[2 * i].data = acc->source[i].data;
@@ -258,9 +406,10 @@ static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)
                        goto error;
        }
        for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {
-               struct isl_dim *dim;
-               dim = isl_dim_join(isl_map_get_dim(acc->source[i].map),
-                           isl_dim_reverse(isl_map_get_dim(acc->sink.map)));
+               isl_space *dim;
+               dim = space_align_and_join(
+                       isl_map_get_space(acc->source[i].map),
+                       isl_space_reverse(isl_map_get_space(acc->sink.map)));
                dep->dep[acc->n_must + i].map = isl_map_empty(dim);
                dep->dep[acc->n_must + i].data = acc->source[i].data;
                dep->dep[acc->n_must + i].must = 0;
@@ -290,7 +439,7 @@ int isl_flow_foreach(__isl_keep isl_flow *deps,
                return -1;
 
        for (i = 0; i < deps->n_source; ++i) {
-               if (isl_map_fast_is_empty(deps->dep[i].map))
+               if (isl_map_plain_is_empty(deps->dep[i].map))
                        continue;
                if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,
                                deps->dep[i].data, user) < 0)
@@ -302,15 +451,15 @@ int isl_flow_foreach(__isl_keep isl_flow *deps,
 
 /* Return a copy of the subset of the sink for which no source could be found.
  */
-__isl_give isl_set *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)
+__isl_give isl_map *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)
 {
        if (!deps)
                return NULL;
        
        if (must)
-               return isl_set_copy(deps->must_no_source);
+               return isl_set_unwrap(isl_set_copy(deps->must_no_source));
        else
-               return isl_set_copy(deps->may_no_source);
+               return isl_set_unwrap(isl_set_copy(deps->may_no_source));
 }
 
 void isl_flow_free(__isl_take isl_flow *deps)
@@ -329,6 +478,11 @@ void isl_flow_free(__isl_take isl_flow *deps)
        free(deps);
 }
 
+isl_ctx *isl_flow_get_ctx(__isl_keep isl_flow *deps)
+{
+       return deps ? isl_set_get_ctx(deps->must_no_source) : NULL;
+}
+
 /* Return a map that enforces that the domain iteration occurs after
  * the range iteration at the given level.
  * If level is odd, then the domain iteration should occur after
@@ -339,7 +493,7 @@ void isl_flow_free(__isl_take isl_flow *deps)
  * be greater than the loop iterator of the range at the last
  * of the level/2 shared loops, i.e., loop level/2 - 1.
  */
-static __isl_give isl_map *after_at_level(struct isl_dim *dim, int level)
+static __isl_give isl_map *after_at_level(__isl_take isl_space *dim, int level)
 {
        struct isl_basic_map *bmap;
 
@@ -351,6 +505,69 @@ static __isl_give isl_map *after_at_level(struct isl_dim *dim, int level)
        return isl_map_from_basic_map(bmap);
 }
 
+/* Compute the partial lexicographic maximum of "dep" on domain "sink",
+ * but first check if the user has set acc->restrict_fn and if so
+ * update either the input or the output of the maximization problem
+ * with respect to the resulting restriction.
+ *
+ * Since the user expects a mapping from sink iterations to source iterations,
+ * whereas the domain of "dep" is a wrapped map, mapping sink iterations
+ * to accessed array elements, we first need to project out the accessed
+ * sink array elements by applying acc->domain_map.
+ * Similarly, the sink restriction specified by the user needs to be
+ * converted back to the wrapped map.
+ */
+static __isl_give isl_map *restricted_partial_lexmax(
+       __isl_keep isl_access_info *acc, __isl_take isl_map *dep,
+       int source, __isl_take isl_set *sink, __isl_give isl_set **empty)
+{
+       isl_map *source_map;
+       isl_restriction *restr;
+       isl_set *sink_domain;
+       isl_set *sink_restr;
+       isl_map *res;
+
+       if (!acc->restrict_fn)
+               return isl_map_partial_lexmax(dep, sink, empty);
+
+       source_map = isl_map_copy(dep);
+       source_map = isl_map_apply_domain(source_map,
+                                           isl_map_copy(acc->domain_map));
+       sink_domain = isl_set_copy(sink);
+       sink_domain = isl_set_apply(sink_domain, isl_map_copy(acc->domain_map));
+       restr = acc->restrict_fn(source_map, sink_domain,
+                               acc->source[source].data, acc->restrict_user);
+       isl_set_free(sink_domain);
+       isl_map_free(source_map);
+
+       if (!restr)
+               goto error;
+       if (restr->type == isl_restriction_type_input) {
+               dep = isl_map_intersect_range(dep, isl_set_copy(restr->source));
+               sink_restr = isl_set_copy(restr->sink);
+               sink_restr = isl_set_apply(sink_restr,
+                               isl_map_reverse(isl_map_copy(acc->domain_map)));
+               sink = isl_set_intersect(sink, sink_restr);
+       } else if (restr->type == isl_restriction_type_empty) {
+               isl_space *space = isl_map_get_space(dep);
+               isl_map_free(dep);
+               dep = isl_map_empty(space);
+       }
+
+       res = isl_map_partial_lexmax(dep, sink, empty);
+
+       if (restr->type == isl_restriction_type_output)
+               res = isl_map_intersect_range(res, isl_set_copy(restr->source));
+
+       isl_restriction_free(restr);
+       return res;
+error:
+       isl_map_free(dep);
+       isl_set_free(sink);
+       *empty = NULL;
+       return NULL;
+}
+
 /* Compute the last iteration of must source j that precedes the sink
  * at the given level for sink iterations in set_C.
  * The subset of set_C for which no such iteration can be found is returned
@@ -370,9 +587,9 @@ static struct isl_map *last_source(struct isl_access_info *acc,
        write_map = isl_map_copy(acc->source[j].map);
        write_map = isl_map_reverse(write_map);
        dep_map = isl_map_apply_range(read_map, write_map);
-       after = after_at_level(isl_map_get_dim(dep_map), level);
+       after = after_at_level(isl_map_get_space(dep_map), level);
        dep_map = isl_map_intersect(dep_map, after);
-       result = isl_map_partial_lexmax(dep_map, set_C, empty);
+       result = restricted_partial_lexmax(acc, dep_map, j, set_C, empty);
        result = isl_map_reverse(result);
 
        return result;
@@ -390,7 +607,7 @@ static struct isl_map *last_later_source(struct isl_access_info *acc,
                                         int k, int after_level,
                                         struct isl_set **empty)
 {
-       struct isl_dim *dim;
+       isl_space *dim;
        struct isl_set *set_C;
        struct isl_map *read_map;
        struct isl_map *write_map;
@@ -405,15 +622,15 @@ static struct isl_map *last_later_source(struct isl_access_info *acc,
 
        write_map = isl_map_reverse(write_map);
        dep_map = isl_map_apply_range(read_map, write_map);
-       dim = isl_dim_join(isl_map_get_dim(acc->source[k].map),
-                   isl_dim_reverse(isl_map_get_dim(acc->source[j].map)));
+       dim = space_align_and_join(isl_map_get_space(acc->source[k].map),
+                   isl_space_reverse(isl_map_get_space(acc->source[j].map)));
        after_write = after_at_level(dim, after_level);
        after_write = isl_map_apply_range(after_write, old_map);
        after_write = isl_map_reverse(after_write);
        dep_map = isl_map_intersect(dep_map, after_write);
-       before_read = after_at_level(isl_map_get_dim(dep_map), before_level);
+       before_read = after_at_level(isl_map_get_space(dep_map), before_level);
        dep_map = isl_map_intersect(dep_map, before_read);
-       result = isl_map_partial_lexmax(dep_map, set_C, empty);
+       result = restricted_partial_lexmax(acc, dep_map, k, set_C, empty);
        result = isl_map_reverse(result);
 
        return result;
@@ -454,7 +671,7 @@ static int intermediate_sources(__isl_keep isl_access_info *acc,
        int k, level;
        int depth = 2 * isl_map_dim(acc->source[j].map, isl_dim_in) + 1;
 
-       if (isl_map_fast_is_empty(temp_rel[j]))
+       if (isl_map_plain_is_empty(temp_rel[j]))
                return 0;
 
        for (k = j - 1; k >= 0; --k) {
@@ -477,7 +694,7 @@ static int intermediate_sources(__isl_keep isl_access_info *acc,
                        copy = isl_map_copy(temp_rel[j]);
                        T = last_later_source(acc, copy, j, sink_level, k,
                                              level, &trest);
-                       if (isl_map_fast_is_empty(T)) {
+                       if (isl_map_plain_is_empty(T)) {
                                isl_set_free(trest);
                                isl_map_free(T);
                                continue;
@@ -506,7 +723,7 @@ static __isl_give isl_map *all_sources(__isl_keep isl_access_info *acc,
        write_map = isl_map_copy(acc->source[acc->n_must + j].map);
        write_map = isl_map_reverse(write_map);
        dep_map = isl_map_apply_range(read_map, write_map);
-       after = after_at_level(isl_map_get_dim(dep_map), level);
+       after = after_at_level(isl_map_get_space(dep_map), level);
        dep_map = isl_map_intersect(dep_map, after);
 
        return isl_map_reverse(dep_map);
@@ -522,7 +739,7 @@ static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,
        __isl_keep isl_map *old_map,
        int j, int before_level, int k, int after_level)
 {
-       isl_dim *dim;
+       isl_space *dim;
        isl_set *set_C;
        isl_map *read_map;
        isl_map *write_map;
@@ -537,13 +754,13 @@ static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,
 
        write_map = isl_map_reverse(write_map);
        dep_map = isl_map_apply_range(read_map, write_map);
-       dim = isl_dim_join(isl_map_get_dim(acc->source[acc->n_must + j].map),
-                   isl_dim_reverse(isl_map_get_dim(acc->source[k].map)));
+       dim = isl_space_join(isl_map_get_space(acc->source[acc->n_must + j].map),
+                   isl_space_reverse(isl_map_get_space(acc->source[k].map)));
        after_write = after_at_level(dim, after_level);
        after_write = isl_map_apply_range(after_write, old_map);
        after_write = isl_map_reverse(after_write);
        dep_map = isl_map_intersect(dep_map, after_write);
-       before_read = after_at_level(isl_map_get_dim(dep_map), before_level);
+       before_read = after_at_level(isl_map_get_space(dep_map), before_level);
        dep_map = isl_map_intersect(dep_map, before_read);
        return isl_map_reverse(dep_map);
 }
@@ -567,8 +784,8 @@ static __isl_give isl_map *all_intermediate_sources(
        for (k = 0; k < acc->n_must; ++k) {
                int plevel;
 
-               if (isl_map_fast_is_empty(may_rel[k]) &&
-                   isl_map_fast_is_empty(must_rel[k]))
+               if (isl_map_plain_is_empty(may_rel[k]) &&
+                   isl_map_plain_is_empty(must_rel[k]))
                        continue;
 
                plevel = acc->level_before(acc->source[k].data,
@@ -595,7 +812,7 @@ static __isl_give isl_map *all_intermediate_sources(
                                                    isl_set_copy(ran)));
                        T = isl_map_from_domain_and_range(
                            isl_set_universe(
-                               isl_dim_domain(isl_map_get_dim(must_rel[k]))),
+                               isl_space_domain(isl_map_get_space(must_rel[k]))),
                            ran);
                        must_rel[k] = isl_map_subtract(must_rel[k], T);
                }
@@ -610,7 +827,7 @@ static __isl_give isl_map *all_intermediate_sources(
  * be overkill to use it.
  */
 static __isl_give isl_flow *compute_mem_based_dependences(
-       __isl_take isl_access_info *acc)
+       __isl_keep isl_access_info *acc)
 {
        int i;
        isl_set *mustdo;
@@ -619,7 +836,7 @@ static __isl_give isl_flow *compute_mem_based_dependences(
 
        res = isl_flow_alloc(acc);
        if (!res)
-               goto error;
+               return NULL;
 
        mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
        maydo = isl_set_copy(mustdo);
@@ -627,7 +844,7 @@ static __isl_give isl_flow *compute_mem_based_dependences(
        for (i = 0; i < acc->n_may; ++i) {
                int plevel;
                int is_before;
-               isl_dim *dim;
+               isl_space *dim;
                isl_map *before;
                isl_map *dep;
 
@@ -635,7 +852,7 @@ static __isl_give isl_flow *compute_mem_based_dependences(
                is_before = plevel & 1;
                plevel >>= 1;
 
-               dim = isl_map_get_dim(res->dep[i].map);
+               dim = isl_map_get_space(res->dep[i].map);
                if (is_before)
                        before = isl_map_lex_le_first(dim, plevel);
                else
@@ -651,12 +868,7 @@ static __isl_give isl_flow *compute_mem_based_dependences(
        res->may_no_source = isl_set_subtract(maydo, isl_set_copy(mustdo));
        res->must_no_source = mustdo;
 
-       isl_access_info_free(acc);
-
        return res;
-error:
-       isl_access_info_free(acc);
-       return NULL;
 }
 
 /* Compute dependences for the case where there is at least one
@@ -695,7 +907,7 @@ error:
  * 
  */
 static __isl_give isl_flow *compute_val_based_dependences(
-       __isl_take isl_access_info *acc)
+       __isl_keep isl_access_info *acc)
 {
        isl_ctx *ctx;
        isl_flow *res;
@@ -706,21 +918,20 @@ static __isl_give isl_flow *compute_val_based_dependences(
        isl_map **must_rel = NULL;
        isl_map **may_rel = NULL;
 
-       acc = isl_access_info_sort_sources(acc);
        if (!acc)
                return NULL;
 
        res = isl_flow_alloc(acc);
        if (!res)
                goto error;
-       ctx = acc->sink.map->ctx;
+       ctx = isl_map_get_ctx(acc->sink.map);
 
        depth = 2 * isl_map_dim(acc->sink.map, isl_dim_in) + 1;
        mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
        maydo = isl_set_empty_like(mustdo);
        if (!mustdo || !maydo)
                goto error;
-       if (isl_set_fast_is_empty(mustdo))
+       if (isl_set_plain_is_empty(mustdo))
                goto done;
 
        must_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
@@ -756,8 +967,8 @@ static __isl_give isl_flow *compute_val_based_dependences(
 
                        intermediate_sources(acc, may_rel, j, level);
 
-                       if (isl_set_fast_is_empty(mustdo) &&
-                           isl_set_fast_is_empty(maydo))
+                       if (isl_set_plain_is_empty(mustdo) &&
+                           isl_set_plain_is_empty(maydo))
                                break;
                }
                for (j = j - 1; j >= 0; --j) {
@@ -807,8 +1018,8 @@ static __isl_give isl_flow *compute_val_based_dependences(
                                                             may_rel[j]);
                }
 
-               if (isl_set_fast_is_empty(mustdo) &&
-                   isl_set_fast_is_empty(maydo))
+               if (isl_set_plain_is_empty(mustdo) &&
+                   isl_set_plain_is_empty(maydo))
                        break;
        }
 
@@ -817,10 +1028,8 @@ static __isl_give isl_flow *compute_val_based_dependences(
 done:
        res->must_no_source = mustdo;
        res->may_no_source = maydo;
-       isl_access_info_free(acc);
        return res;
 error:
-       isl_access_info_free(acc);
        isl_flow_free(res);
        isl_set_free(mustdo);
        isl_set_free(maydo);
@@ -849,79 +1058,138 @@ error:
 __isl_give isl_flow *isl_access_info_compute_flow(__isl_take isl_access_info *acc)
 {
        int j;
-       struct isl_flow *res;
-       isl_map *domain_map = NULL;
+       struct isl_flow *res = NULL;
 
        if (!acc)
                return NULL;
 
-       domain_map = isl_map_domain_map(isl_map_copy(acc->sink.map));
+       acc->domain_map = isl_map_domain_map(isl_map_copy(acc->sink.map));
        acc->sink.map = isl_map_range_map(acc->sink.map);
        if (!acc->sink.map)
                goto error;
 
        if (acc->n_must == 0)
                res = compute_mem_based_dependences(acc);
-       else
+       else {
+               acc = isl_access_info_sort_sources(acc);
                res = compute_val_based_dependences(acc);
+       }
        if (!res)
-               return NULL;
+               goto error;
 
        for (j = 0; j < res->n_source; ++j) {
                res->dep[j].map = isl_map_apply_range(res->dep[j].map,
-                                       isl_map_copy(domain_map));
+                                       isl_map_copy(acc->domain_map));
                if (!res->dep[j].map)
-                       goto error2;
+                       goto error;
        }
-       res->must_no_source = isl_set_apply(res->must_no_source,
-                                       isl_map_copy(domain_map));
-       res->may_no_source = isl_set_apply(res->may_no_source,
-                                       isl_map_copy(domain_map));
        if (!res->must_no_source || !res->may_no_source)
-               goto error2;
+               goto error;
 
-       isl_map_free(domain_map);
+       isl_access_info_free(acc);
        return res;
 error:
-       isl_map_free(domain_map);
        isl_access_info_free(acc);
-       return NULL;
-error2:
-       isl_map_free(domain_map);
        isl_flow_free(res);
        return NULL;
 }
 
 
+/* Keep track of some information about a schedule for a given
+ * access.  In particular, keep track of which dimensions
+ * have a constant value and of the actual constant values.
+ */
+struct isl_sched_info {
+       int *is_cst;
+       isl_vec *cst;
+};
+
+static void sched_info_free(__isl_take struct isl_sched_info *info)
+{
+       if (!info)
+               return;
+       isl_vec_free(info->cst);
+       free(info->is_cst);
+       free(info);
+}
+
+/* Extract information on the constant dimensions of the schedule
+ * for a given access.  The "map" is of the form
+ *
+ *     [S -> D] -> A
+ *
+ * with S the schedule domain, D the iteration domain and A the data domain.
+ */
+static __isl_give struct isl_sched_info *sched_info_alloc(
+       __isl_keep isl_map *map)
+{
+       isl_ctx *ctx;
+       isl_space *dim;
+       struct isl_sched_info *info;
+       int i, n;
+       isl_int v;
+
+       if (!map)
+               return NULL;
+
+       dim = isl_space_unwrap(isl_space_domain(isl_map_get_space(map)));
+       if (!dim)
+               return NULL;
+       n = isl_space_dim(dim, isl_dim_in);
+       isl_space_free(dim);
+
+       ctx = isl_map_get_ctx(map);
+       info = isl_alloc_type(ctx, struct isl_sched_info);
+       if (!info)
+               return NULL;
+       info->is_cst = isl_alloc_array(ctx, int, n);
+       info->cst = isl_vec_alloc(ctx, n);
+       if (!info->is_cst || !info->cst)
+               goto error;
+
+       isl_int_init(v);
+       for (i = 0; i < n; ++i) {
+               info->is_cst[i] = isl_map_plain_is_fixed(map, isl_dim_in, i,
+                                                        &v);
+               info->cst = isl_vec_set_element(info->cst, i, v);
+       }
+       isl_int_clear(v);
+
+       return info;
+error:
+       sched_info_free(info);
+       return NULL;
+}
+
 struct isl_compute_flow_data {
        isl_union_map *must_source;
        isl_union_map *may_source;
        isl_union_map *must_dep;
        isl_union_map *may_dep;
-       isl_union_set *must_no_source;
-       isl_union_set *may_no_source;
+       isl_union_map *must_no_source;
+       isl_union_map *may_no_source;
 
        int count;
        int must;
-       isl_dim *dim;
-       isl_dim *sink_dim;
-       isl_dim **source_dim;
+       isl_space *dim;
+       struct isl_sched_info *sink_info;
+       struct isl_sched_info **source_info;
        isl_access_info *accesses;
 };
 
 static int count_matching_array(__isl_take isl_map *map, void *user)
 {
        int eq;
-       isl_dim *dim;
+       isl_space *dim;
        struct isl_compute_flow_data *data;
 
        data = (struct isl_compute_flow_data *)user;
 
-       dim = isl_dim_range(isl_map_get_dim(map));
+       dim = isl_space_range(isl_map_get_space(map));
 
-       eq = isl_dim_equal(dim, data->dim);
+       eq = isl_space_is_equal(dim, data->dim);
 
-       isl_dim_free(dim);
+       isl_space_free(dim);
        isl_map_free(map);
 
        if (eq < 0)
@@ -935,16 +1203,17 @@ static int count_matching_array(__isl_take isl_map *map, void *user)
 static int collect_matching_array(__isl_take isl_map *map, void *user)
 {
        int eq;
-       isl_dim *dim;
+       isl_space *dim;
+       struct isl_sched_info *info;
        struct isl_compute_flow_data *data;
 
        data = (struct isl_compute_flow_data *)user;
 
-       dim = isl_dim_range(isl_map_get_dim(map));
+       dim = isl_space_range(isl_map_get_space(map));
 
-       eq = isl_dim_equal(dim, data->dim);
+       eq = isl_space_is_equal(dim, data->dim);
 
-       isl_dim_free(dim);
+       isl_space_free(dim);
 
        if (eq < 0)
                goto error;
@@ -953,11 +1222,11 @@ static int collect_matching_array(__isl_take isl_map *map, void *user)
                return 0;
        }
 
-       dim = isl_dim_unwrap(isl_dim_domain(isl_map_get_dim(map)));
-       data->source_dim[data->count] = dim;
+       info = sched_info_alloc(map);
+       data->source_info[data->count] = info;
 
        data->accesses = isl_access_info_add_source(data->accesses,
-                                                   map, data->must, dim);
+                                                   map, data->must, info);
 
        data->count++;
 
@@ -967,19 +1236,56 @@ error:
        return -1;
 }
 
+/* Determine the shared nesting level and the "textual order" of
+ * the given accesses.
+ *
+ * We first determine the minimal schedule dimension for both accesses.
+ *
+ * If among those dimensions, we can find one where both have a fixed
+ * value and if moreover those values are different, then the previous
+ * dimension is the last shared nesting level and the textual order
+ * is determined based on the order of the fixed values.
+ * If no such fixed values can be found, then we set the shared
+ * nesting level to the minimal schedule dimension, with no textual ordering.
+ */
 static int before(void *first, void *second)
 {
-       isl_dim *dim1 = first;
-       isl_dim *dim2 = second;
+       struct isl_sched_info *info1 = first;
+       struct isl_sched_info *info2 = second;
        int n1, n2;
+       int i;
+       isl_int v1, v2;
 
-       n1 = isl_dim_size(dim1, isl_dim_in);
-       n2 = isl_dim_size(dim2, isl_dim_in);
+       n1 = isl_vec_size(info1->cst);
+       n2 = isl_vec_size(info2->cst);
 
        if (n2 < n1)
                n1 = n2;
 
-       return 2 * n1 + (dim1 < dim2);
+       isl_int_init(v1);
+       isl_int_init(v2);
+       for (i = 0; i < n1; ++i) {
+               int r;
+
+               if (!info1->is_cst[i])
+                       continue;
+               if (!info2->is_cst[i])
+                       continue;
+               isl_vec_get_element(info1->cst, i, &v1);
+               isl_vec_get_element(info2->cst, i, &v2);
+               if (isl_int_eq(v1, v2))
+                       continue;
+
+               r = 2 * i + isl_int_lt(v1, v2);
+
+               isl_int_clear(v1);
+               isl_int_clear(v2);
+               return r;
+       }
+       isl_int_clear(v1);
+       isl_int_clear(v2);
+
+       return 2 * n1;
 }
 
 /* Given a sink access, look for all the source accesses that access
@@ -998,10 +1304,10 @@ static int compute_flow(__isl_take isl_map *map, void *user)
        ctx = isl_map_get_ctx(map);
 
        data->accesses = NULL;
-       data->sink_dim = NULL;
-       data->source_dim = NULL;
+       data->sink_info = NULL;
+       data->source_info = NULL;
        data->count = 0;
-       data->dim = isl_dim_range(isl_map_get_dim(map));
+       data->dim = isl_space_range(isl_map_get_space(map));
 
        if (isl_union_map_foreach_map(data->must_source,
                                        &count_matching_array, data) < 0)
@@ -1010,11 +1316,14 @@ static int compute_flow(__isl_take isl_map *map, void *user)
                                        &count_matching_array, data) < 0)
                goto error;
 
-       data->sink_dim = isl_dim_unwrap(isl_dim_domain(isl_map_get_dim(map)));
-       data->source_dim = isl_calloc_array(ctx, isl_dim *, data->count);
+       data->sink_info = sched_info_alloc(map);
+       data->source_info = isl_calloc_array(ctx, struct isl_sched_info *,
+                                            data->count);
 
        data->accesses = isl_access_info_alloc(isl_map_copy(map),
-                               data->sink_dim, &before, data->count);
+                               data->sink_info, &before, data->count);
+       if (!data->sink_info || !data->source_info || !data->accesses)
+               goto error;
        data->count = 0;
        data->must = 1;
        if (isl_union_map_foreach_map(data->must_source,
@@ -1031,10 +1340,10 @@ static int compute_flow(__isl_take isl_map *map, void *user)
        if (!flow)
                goto error;
 
-       data->must_no_source = isl_union_set_union(data->must_no_source,
-                   isl_union_set_from_set(isl_set_copy(flow->must_no_source)));
-       data->may_no_source = isl_union_set_union(data->may_no_source,
-                   isl_union_set_from_set(isl_set_copy(flow->may_no_source)));
+       data->must_no_source = isl_union_map_union(data->must_no_source,
+                   isl_union_map_from_map(isl_flow_get_no_source(flow, 1)));
+       data->may_no_source = isl_union_map_union(data->may_no_source,
+                   isl_union_map_from_map(isl_flow_get_no_source(flow, 0)));
 
        for (i = 0; i < flow->n_source; ++i) {
                isl_union_map *dep;
@@ -1047,25 +1356,25 @@ static int compute_flow(__isl_take isl_map *map, void *user)
 
        isl_flow_free(flow);
 
-       isl_dim_free(data->sink_dim);
-       if (data->source_dim) {
+       sched_info_free(data->sink_info);
+       if (data->source_info) {
                for (i = 0; i < data->count; ++i)
-                       isl_dim_free(data->source_dim[i]);
-               free(data->source_dim);
+                       sched_info_free(data->source_info[i]);
+               free(data->source_info);
        }
-       isl_dim_free(data->dim);
+       isl_space_free(data->dim);
        isl_map_free(map);
 
        return 0;
 error:
        isl_access_info_free(data->accesses);
-       isl_dim_free(data->sink_dim);
-       if (data->source_dim) {
+       sched_info_free(data->sink_info);
+       if (data->source_info) {
                for (i = 0; i < data->count; ++i)
-                       isl_dim_free(data->source_dim[i]);
-               free(data->source_dim);
+                       sched_info_free(data->source_info[i]);
+               free(data->source_info);
        }
-       isl_dim_free(data->dim);
+       isl_space_free(data->dim);
        isl_map_free(map);
 
        return -1;
@@ -1092,23 +1401,23 @@ int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
        __isl_take isl_union_map *may_source,
        __isl_take isl_union_map *schedule,
        __isl_give isl_union_map **must_dep, __isl_give isl_union_map **may_dep,
-       __isl_give isl_union_set **must_no_source,
-       __isl_give isl_union_set **may_no_source)
+       __isl_give isl_union_map **must_no_source,
+       __isl_give isl_union_map **may_no_source)
 {
-       isl_dim *dim;
+       isl_space *dim;
        isl_union_map *range_map = NULL;
        struct isl_compute_flow_data data;
 
        sink = isl_union_map_align_params(sink,
-                                           isl_union_map_get_dim(must_source));
+                                           isl_union_map_get_space(must_source));
        sink = isl_union_map_align_params(sink,
-                                           isl_union_map_get_dim(may_source));
+                                           isl_union_map_get_space(may_source));
        sink = isl_union_map_align_params(sink,
-                                           isl_union_map_get_dim(schedule));
-       dim = isl_union_map_get_dim(sink);
-       must_source = isl_union_map_align_params(must_source, isl_dim_copy(dim));
-       may_source = isl_union_map_align_params(may_source, isl_dim_copy(dim));
-       schedule = isl_union_map_align_params(schedule, isl_dim_copy(dim));
+                                           isl_union_map_get_space(schedule));
+       dim = isl_union_map_get_space(sink);
+       must_source = isl_union_map_align_params(must_source, isl_space_copy(dim));
+       may_source = isl_union_map_align_params(may_source, isl_space_copy(dim));
+       schedule = isl_union_map_align_params(schedule, isl_space_copy(dim));
 
        schedule = isl_union_map_reverse(schedule);
        range_map = isl_union_map_range_map(schedule);
@@ -1121,14 +1430,14 @@ int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
        data.must_source = must_source;
        data.may_source = may_source;
        data.must_dep = must_dep ?
-               isl_union_map_empty(isl_dim_copy(dim)) : NULL;
-       data.may_dep = may_dep ? isl_union_map_empty(isl_dim_copy(dim)) : NULL;
+               isl_union_map_empty(isl_space_copy(dim)) : NULL;
+       data.may_dep = may_dep ? isl_union_map_empty(isl_space_copy(dim)) : NULL;
        data.must_no_source = must_no_source ?
-               isl_union_set_empty(isl_dim_copy(dim)) : NULL;
+               isl_union_map_empty(isl_space_copy(dim)) : NULL;
        data.may_no_source = may_no_source ?
-               isl_union_set_empty(isl_dim_copy(dim)) : NULL;
+               isl_union_map_empty(isl_space_copy(dim)) : NULL;
 
-       isl_dim_free(dim);
+       isl_space_free(dim);
 
        if (isl_union_map_foreach_map(sink, &compute_flow, &data) < 0)
                goto error;
@@ -1152,13 +1461,13 @@ int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
                *may_dep = data.may_dep;
        }
        if (must_no_source) {
-               data.must_no_source = isl_union_set_apply(data.must_no_source,
-                                       isl_union_map_copy(range_map));
+               data.must_no_source = isl_union_map_apply_domain(
+                       data.must_no_source, isl_union_map_copy(range_map));
                *must_no_source = data.must_no_source;
        }
        if (may_no_source) {
-               data.may_no_source = isl_union_set_apply(data.may_no_source,
-                                       isl_union_map_copy(range_map));
+               data.may_no_source = isl_union_map_apply_domain(
+                       data.may_no_source, isl_union_map_copy(range_map));
                *may_no_source = data.may_no_source;
        }
 
@@ -1172,8 +1481,8 @@ error:
        isl_union_map_free(may_source);
        isl_union_map_free(data.must_dep);
        isl_union_map_free(data.may_dep);
-       isl_union_set_free(data.must_no_source);
-       isl_union_set_free(data.may_no_source);
+       isl_union_map_free(data.must_no_source);
+       isl_union_map_free(data.may_no_source);
 
        if (must_dep)
                *must_dep = NULL;