isl_basic_set_opt: avoid invalid access on error path
[platform/upstream/isl.git] / isl_schedule.c
index 3c79dcb..9760c62 100644 (file)
@@ -1,7 +1,7 @@
 /*
  * Copyright 2011      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,
@@ -10,7 +10,8 @@
 
 #include <isl_ctx_private.h>
 #include <isl_map_private.h>
-#include <isl_dim_private.h>
+#include <isl_space_private.h>
+#include <isl/aff.h>
 #include <isl/hash.h>
 #include <isl/constraint.h>
 #include <isl/schedule.h>
 #include <isl_tab.h>
 #include <isl_dim_map.h>
 #include <isl_hmap_map_basic_set.h>
-#include <isl_qsort.h>
+#include <isl_sort.h>
+#include <isl_schedule_private.h>
+#include <isl_band_private.h>
+#include <isl_list_private.h>
+#include <isl_options_private.h>
+#include <isl_tarjan.h>
 
 /*
  * The scheduling algorithm implemented in this file was inspired by
  */
 
 
-/* The schedule for an individual domain, plus information about the bands.
- * In particular, we keep track of the number of bands and for each
- * band, the starting position of the next band.  The first band starts at
- * position 0.
- */
-struct isl_schedule_node {
-       isl_map *sched;
-       int      n_band;
-       int     *band_end;
-};
-
-/* Information about the computed schedule.
- * n is the number of nodes/domains/statements.
- * n_band is the maximal number of bands.
- * n_total_row is the number of coordinates of the schedule.
- * dim contains a description of the parameters.
- */
-struct isl_schedule {
-       int n;
-       int n_band;
-       int n_total_row;
-       isl_dim *dim;
-
-       struct isl_schedule_node node[1];
-};
-
 /* Internal information about a node that is used during the construction
  * of a schedule.
  * dim represents the space in which the domain lives
@@ -75,15 +55,17 @@ struct isl_schedule {
  *
  * scc is the index of SCC (or WCC) this node belongs to
  *
- * band contains the band index for each of the rows of the schedule
- *
- * index, min_index and on_stack are used during the SCC detection
- * index represents the order in which nodes are visited.
- * min_index is the index of the root of a (sub)component.
- * on_stack indicates whether the node is currently on the stack.
+ * band contains the band index for each of the rows of the schedule.
+ * band_id is used to differentiate between separate bands at the same
+ * level within the same parent band, i.e., bands that are separated
+ * by the parent band or bands that are independent of each other.
+ * zero contains a boolean for each of the rows of the schedule,
+ * indicating whether the corresponding scheduling dimension results
+ * in zero dependence distances within its band and with respect
+ * to the proximity edges.
  */
 struct isl_sched_node {
-       isl_dim *dim;
+       isl_space *dim;
        isl_mat *sched;
        isl_map *sched_map;
        int      rank;
@@ -95,19 +77,16 @@ struct isl_sched_node {
        int      scc;
 
        int     *band;
-
-       /* scc detection */
-       int      index;
-       int      min_index;
-       int      on_stack;
+       int     *band_id;
+       int     *zero;
 };
 
 static int node_has_dim(const void *entry, const void *val)
 {
        struct isl_sched_node *node = (struct isl_sched_node *)entry;
-       isl_dim *dim = (isl_dim *)val;
+       isl_space *dim = (isl_space *)val;
 
-       return isl_dim_equal(node->dim, dim);
+       return isl_space_is_equal(node->dim, dim);
 }
 
 /* An edge in the dependence graph.  An edge may be used to
@@ -137,6 +116,13 @@ struct isl_sched_edge {
        int end;
 };
 
+enum isl_edge_type {
+       isl_edge_validity = 0,
+       isl_edge_first = isl_edge_validity,
+       isl_edge_proximity,
+       isl_edge_last = isl_edge_proximity
+};
+
 /* Internal information about the dependence graph used during
  * the construction of the schedule.
  *
@@ -148,6 +134,7 @@ struct isl_sched_edge {
  * n is the number of nodes
  * node is the list of nodes
  * maxvar is the maximal number of variables over all nodes
+ * max_row is the allocated number of rows in the schedule
  * n_row is the current (maximal) number of linearly independent
  *     rows in the node schedules
  * n_total_row is the current number of rows in the node schedules
@@ -161,10 +148,13 @@ struct isl_sched_edge {
  *
  * n_edge is the number of edges
  * edge is the list of edges
+ * max_edge contains the maximal number of edges of each type;
+ *     in particular, it contains the number of edges in the inital graph.
  * edge_table contains pointers into the edge array, hashed on the source
- *     and sink spaces; the table only contains edges that represent
- *     validity constraints (and that may or may not also represent proximity
- *     constraints)
+ *     and sink spaces; there is one such table for each type;
+ *     a given edge may be referenced from more than one table
+ *     if the corresponding relation appears in more than of the
+ *     sets of dependences
  *
  * node_table contains pointers into the node array, hashed on the space
  *
@@ -175,11 +165,7 @@ struct isl_sched_edge {
  * src_scc and dst_scc are the source and sink SCCs of an edge with
  *     conflicting constraints
  *
- * scc, sp, index and stack are used during the detection of SCCs
- * scc is the number of the next SCC
- * stack contains the nodes on the path from the root to the current node
- * sp is the stack pointer
- * index is the index of the last node visited
+ * scc represents the number of components
  */
 struct isl_sched_graph {
        isl_hmap_map_basic_set *intra_hmap;
@@ -188,6 +174,7 @@ struct isl_sched_graph {
        struct isl_sched_node *node;
        int n;
        int maxvar;
+       int max_row;
        int n_row;
 
        int *sorted;
@@ -200,7 +187,8 @@ struct isl_sched_graph {
 
        struct isl_sched_edge *edge;
        int n_edge;
-       struct isl_hash_table *edge_table;
+       int max_edge[isl_edge_last + 1];
+       struct isl_hash_table *edge_table[isl_edge_last + 1];
 
        struct isl_hash_table *node_table;
        struct isl_region *region;
@@ -210,11 +198,7 @@ struct isl_sched_graph {
        int src_scc;
        int dst_scc;
 
-       /* scc detection */
        int scc;
-       int sp;
-       int index;
-       int *stack;
 };
 
 /* Initialize node_table based on the list of nodes.
@@ -231,7 +215,7 @@ static int graph_init_table(isl_ctx *ctx, struct isl_sched_graph *graph)
                struct isl_hash_table_entry *entry;
                uint32_t hash;
 
-               hash = isl_dim_get_hash(graph->node[i].dim);
+               hash = isl_space_get_hash(graph->node[i].dim);
                entry = isl_hash_table_find(ctx, graph->node_table, hash,
                                            &node_has_dim,
                                            graph->node[i].dim, 1);
@@ -247,12 +231,12 @@ static int graph_init_table(isl_ctx *ctx, struct isl_sched_graph *graph)
  * or NULL if there is no such node.
  */
 static struct isl_sched_node *graph_find_node(isl_ctx *ctx,
-       struct isl_sched_graph *graph, __isl_keep isl_dim *dim)
+       struct isl_sched_graph *graph, __isl_keep isl_space *dim)
 {
        struct isl_hash_table_entry *entry;
        uint32_t hash;
 
-       hash = isl_dim_get_hash(dim);
+       hash = isl_space_get_hash(dim);
        entry = isl_hash_table_find(ctx, graph->node_table, hash,
                                    &node_has_dim, dim, 0);
 
@@ -267,67 +251,168 @@ static int edge_has_src_and_dst(const void *entry, const void *val)
        return edge->src == temp->src && edge->dst == temp->dst;
 }
 
-/* Initialize edge_table based on the list of edges.
- * Only edges with validity set are added to the table.
+/* Add the given edge to graph->edge_table[type].
  */
-static int graph_init_edge_table(isl_ctx *ctx, struct isl_sched_graph *graph)
+static int graph_edge_table_add(isl_ctx *ctx, struct isl_sched_graph *graph,
+       enum isl_edge_type type, struct isl_sched_edge *edge)
 {
-       int i;
+       struct isl_hash_table_entry *entry;
+       uint32_t hash;
 
-       graph->edge_table = isl_hash_table_alloc(ctx, graph->n_edge);
-       if (!graph->edge_table)
+       hash = isl_hash_init();
+       hash = isl_hash_builtin(hash, edge->src);
+       hash = isl_hash_builtin(hash, edge->dst);
+       entry = isl_hash_table_find(ctx, graph->edge_table[type], hash,
+                                   &edge_has_src_and_dst, edge, 1);
+       if (!entry)
                return -1;
+       entry->data = edge;
 
-       for (i = 0; i < graph->n_edge; ++i) {
-               struct isl_hash_table_entry *entry;
-               uint32_t hash;
+       return 0;
+}
 
-               if (!graph->edge[i].validity)
-                       continue;
+/* Allocate the edge_tables based on the maximal number of edges of
+ * each type.
+ */
+static int graph_init_edge_tables(isl_ctx *ctx, struct isl_sched_graph *graph)
+{
+       int i;
 
-               hash = isl_hash_init();
-               hash = isl_hash_builtin(hash, graph->edge[i].src);
-               hash = isl_hash_builtin(hash, graph->edge[i].dst);
-               entry = isl_hash_table_find(ctx, graph->edge_table, hash,
-                                           &edge_has_src_and_dst,
-                                           &graph->edge[i], 1);
-               if (!entry)
+       for (i = 0; i <= isl_edge_last; ++i) {
+               graph->edge_table[i] = isl_hash_table_alloc(ctx,
+                                                           graph->max_edge[i]);
+               if (!graph->edge_table[i])
                        return -1;
-               entry->data = &graph->edge[i];
        }
 
        return 0;
 }
 
-/* Check whether the dependence graph has a (validity) edge
- * between the given two nodes.
+/* If graph->edge_table[type] contains an edge from the given source
+ * to the given destination, then return the hash table entry of this edge.
+ * Otherwise, return NULL.
  */
-static int graph_has_edge(struct isl_sched_graph *graph,
+static struct isl_hash_table_entry *graph_find_edge_entry(
+       struct isl_sched_graph *graph,
+       enum isl_edge_type type,
        struct isl_sched_node *src, struct isl_sched_node *dst)
 {
-       isl_ctx *ctx = isl_dim_get_ctx(src->dim);
-       struct isl_hash_table_entry *entry;
+       isl_ctx *ctx = isl_space_get_ctx(src->dim);
        uint32_t hash;
        struct isl_sched_edge temp = { .src = src, .dst = dst };
-       struct isl_sched_edge *edge;
-       int empty;
 
        hash = isl_hash_init();
        hash = isl_hash_builtin(hash, temp.src);
        hash = isl_hash_builtin(hash, temp.dst);
-       entry = isl_hash_table_find(ctx, graph->edge_table, hash,
+       return isl_hash_table_find(ctx, graph->edge_table[type], hash,
                                    &edge_has_src_and_dst, &temp, 0);
+}
+
+
+/* If graph->edge_table[type] contains an edge from the given source
+ * to the given destination, then return this edge.
+ * Otherwise, return NULL.
+ */
+static struct isl_sched_edge *graph_find_edge(struct isl_sched_graph *graph,
+       enum isl_edge_type type,
+       struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+       struct isl_hash_table_entry *entry;
+
+       entry = graph_find_edge_entry(graph, type, src, dst);
        if (!entry)
+               return NULL;
+
+       return entry->data;
+}
+
+/* Check whether the dependence graph has an edge of the give type
+ * between the given two nodes.
+ */
+static int graph_has_edge(struct isl_sched_graph *graph,
+       enum isl_edge_type type,
+       struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+       struct isl_sched_edge *edge;
+       int empty;
+
+       edge = graph_find_edge(graph, type, src, dst);
+       if (!edge)
                return 0;
 
-       edge = entry->data;
-       empty = isl_map_fast_is_empty(edge->map);
+       empty = isl_map_plain_is_empty(edge->map);
        if (empty < 0)
                return -1;
 
        return !empty;
 }
 
+/* If there is an edge from the given source to the given destination
+ * of any type then return this edge.
+ * Otherwise, return NULL.
+ */
+static struct isl_sched_edge *graph_find_any_edge(struct isl_sched_graph *graph,
+       struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+       enum isl_edge_type i;
+       struct isl_sched_edge *edge;
+
+       for (i = isl_edge_first; i <= isl_edge_last; ++i) {
+               edge = graph_find_edge(graph, i, src, dst);
+               if (edge)
+                       return edge;
+       }
+
+       return NULL;
+}
+
+/* Remove the given edge from all the edge_tables that refer to it.
+ */
+static void graph_remove_edge(struct isl_sched_graph *graph,
+       struct isl_sched_edge *edge)
+{
+       isl_ctx *ctx = isl_map_get_ctx(edge->map);
+       enum isl_edge_type i;
+
+       for (i = isl_edge_first; i <= isl_edge_last; ++i) {
+               struct isl_hash_table_entry *entry;
+
+               entry = graph_find_edge_entry(graph, i, edge->src, edge->dst);
+               if (!entry)
+                       continue;
+               if (entry->data != edge)
+                       continue;
+               isl_hash_table_remove(ctx, graph->edge_table[i], entry);
+       }
+}
+
+/* Check whether the dependence graph has any edge
+ * between the given two nodes.
+ */
+static int graph_has_any_edge(struct isl_sched_graph *graph,
+       struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+       enum isl_edge_type i;
+       int r;
+
+       for (i = isl_edge_first; i <= isl_edge_last; ++i) {
+               r = graph_has_edge(graph, i, src, dst);
+               if (r < 0 || r)
+                       return r;
+       }
+
+       return r;
+}
+
+/* Check whether the dependence graph has a validity edge
+ * between the given two nodes.
+ */
+static int graph_has_validity_edge(struct isl_sched_graph *graph,
+       struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+       return graph_has_edge(graph, isl_edge_validity, src, dst);
+}
+
 static int graph_alloc(isl_ctx *ctx, struct isl_sched_graph *graph,
        int n_node, int n_edge)
 {
@@ -338,15 +423,13 @@ static int graph_alloc(isl_ctx *ctx, struct isl_sched_graph *graph,
        graph->node = isl_calloc_array(ctx, struct isl_sched_node, graph->n);
        graph->sorted = isl_calloc_array(ctx, int, graph->n);
        graph->region = isl_alloc_array(ctx, struct isl_region, graph->n);
-       graph->stack = isl_alloc_array(ctx, int, graph->n);
        graph->edge = isl_calloc_array(ctx,
                                        struct isl_sched_edge, graph->n_edge);
 
        graph->intra_hmap = isl_hmap_map_basic_set_alloc(ctx, 2 * n_edge);
        graph->inter_hmap = isl_hmap_map_basic_set_alloc(ctx, 2 * n_edge);
 
-       if (!graph->node || !graph->region || !graph->stack || !graph->edge ||
-           !graph->sorted)
+       if (!graph->node || !graph->region || !graph->edge || !graph->sorted)
                return -1;
 
        for(i = 0; i < graph->n; ++i)
@@ -363,12 +446,15 @@ static void graph_free(isl_ctx *ctx, struct isl_sched_graph *graph)
        isl_hmap_map_basic_set_free(ctx, graph->inter_hmap);
 
        for (i = 0; i < graph->n; ++i) {
-               isl_dim_free(graph->node[i].dim);
+               isl_space_free(graph->node[i].dim);
                isl_mat_free(graph->node[i].sched);
                isl_map_free(graph->node[i].sched_map);
                isl_mat_free(graph->node[i].cmap);
-               if (graph->root)
+               if (graph->root) {
                        free(graph->node[i].band);
+                       free(graph->node[i].band_id);
+                       free(graph->node[i].zero);
+               }
        }
        free(graph->node);
        free(graph->sorted);
@@ -376,28 +462,65 @@ static void graph_free(isl_ctx *ctx, struct isl_sched_graph *graph)
                isl_map_free(graph->edge[i].map);
        free(graph->edge);
        free(graph->region);
-       free(graph->stack);
-       isl_hash_table_free(ctx, graph->edge_table);
+       for (i = 0; i <= isl_edge_last; ++i)
+               isl_hash_table_free(ctx, graph->edge_table[i]);
        isl_hash_table_free(ctx, graph->node_table);
        isl_basic_set_free(graph->lp);
 }
 
+/* For each "set" on which this function is called, increment
+ * graph->n by one and update graph->maxvar.
+ */
+static int init_n_maxvar(__isl_take isl_set *set, void *user)
+{
+       struct isl_sched_graph *graph = user;
+       int nvar = isl_set_dim(set, isl_dim_set);
+
+       graph->n++;
+       if (nvar > graph->maxvar)
+               graph->maxvar = nvar;
+
+       isl_set_free(set);
+
+       return 0;
+}
+
+/* Compute the number of rows that should be allocated for the schedule.
+ * The graph can be split at most "n - 1" times, there can be at most
+ * two rows for each dimension in the iteration domains (in particular,
+ * we usually have one row, but it may be split by split_scaled),
+ * and there can be one extra row for ordering the statements.
+ * Note that if we have actually split "n - 1" times, then no ordering
+ * is needed, so in principle we could use "graph->n + 2 * graph->maxvar - 1".
+ */
+static int compute_max_row(struct isl_sched_graph *graph,
+       __isl_keep isl_union_set *domain)
+{
+       graph->n = 0;
+       graph->maxvar = 0;
+       if (isl_union_set_foreach_set(domain, &init_n_maxvar, graph) < 0)
+               return -1;
+       graph->max_row = graph->n + 2 * graph->maxvar;
+
+       return 0;
+}
+
 /* Add a new node to the graph representing the given set.
  */
 static int extract_node(__isl_take isl_set *set, void *user)
 {
        int nvar, nparam;
        isl_ctx *ctx;
-       isl_dim *dim;
+       isl_space *dim;
        isl_mat *sched;
        struct isl_sched_graph *graph = user;
-       int *band;
+       int *band, *band_id, *zero;
 
        ctx = isl_set_get_ctx(set);
-       dim = isl_set_get_dim(set);
+       dim = isl_set_get_space(set);
        isl_set_free(set);
-       nvar = isl_dim_size(dim, isl_dim_set);
-       nparam = isl_dim_size(dim, isl_dim_param);
+       nvar = isl_space_dim(dim, isl_dim_set);
+       nparam = isl_space_dim(dim, isl_dim_param);
        if (!ctx->opt->schedule_parametric)
                nparam = 0;
        sched = isl_mat_alloc(ctx, 0, 1 + nparam + nvar);
@@ -406,38 +529,48 @@ static int extract_node(__isl_take isl_set *set, void *user)
        graph->node[graph->n].nparam = nparam;
        graph->node[graph->n].sched = sched;
        graph->node[graph->n].sched_map = NULL;
-       band = isl_alloc_array(ctx, int, graph->n_edge + nvar);
+       band = isl_alloc_array(ctx, int, graph->max_row);
        graph->node[graph->n].band = band;
+       band_id = isl_calloc_array(ctx, int, graph->max_row);
+       graph->node[graph->n].band_id = band_id;
+       zero = isl_calloc_array(ctx, int, graph->max_row);
+       graph->node[graph->n].zero = zero;
        graph->n++;
 
-       if (!sched || !band)
+       if (!sched || !band || !band_id || !zero)
                return -1;
 
        return 0;
 }
 
-/* Add a new edge to the graph based on the given map.
- * Edges are first extracted from the validity dependences,
- * from which the edge_table is constructed.
- * Afterwards, the proximity dependences are added.  If a proximity
- * dependence relation happens to be identical to one of the
- * validity dependence relations added before, then we don't create
- * a new edge, but instead mark the original edge as also representing
- * a proximity dependence.
+struct isl_extract_edge_data {
+       enum isl_edge_type type;
+       struct isl_sched_graph *graph;
+};
+
+/* Add a new edge to the graph based on the given map
+ * and add it to data->graph->edge_table[data->type].
+ * If a dependence relation of a given type happens to be identical
+ * to one of the dependence relations of a type that was added before,
+ * then we don't create a new edge, but instead mark the original edge
+ * as also representing a dependence of the current type.
  */
 static int extract_edge(__isl_take isl_map *map, void *user)
 {
        isl_ctx *ctx = isl_map_get_ctx(map);
-       struct isl_sched_graph *graph = user;
+       struct isl_extract_edge_data *data = user;
+       struct isl_sched_graph *graph = data->graph;
        struct isl_sched_node *src, *dst;
-       isl_dim *dim;
+       isl_space *dim;
+       struct isl_sched_edge *edge;
+       int is_equal;
 
-       dim = isl_dim_domain(isl_map_get_dim(map));
+       dim = isl_space_domain(isl_map_get_space(map));
        src = graph_find_node(ctx, graph, dim);
-       isl_dim_free(dim);
-       dim = isl_dim_range(isl_map_get_dim(map));
+       isl_space_free(dim);
+       dim = isl_space_range(isl_map_get_space(map));
        dst = graph_find_node(ctx, graph, dim);
-       isl_dim_free(dim);
+       isl_space_free(dim);
 
        if (!src || !dst) {
                isl_map_free(map);
@@ -447,138 +580,107 @@ static int extract_edge(__isl_take isl_map *map, void *user)
        graph->edge[graph->n_edge].src = src;
        graph->edge[graph->n_edge].dst = dst;
        graph->edge[graph->n_edge].map = map;
-       graph->edge[graph->n_edge].validity = !graph->edge_table;
-       graph->edge[graph->n_edge].proximity = !!graph->edge_table;
+       if (data->type == isl_edge_validity) {
+               graph->edge[graph->n_edge].validity = 1;
+               graph->edge[graph->n_edge].proximity = 0;
+       }
+       if (data->type == isl_edge_proximity) {
+               graph->edge[graph->n_edge].validity = 0;
+               graph->edge[graph->n_edge].proximity = 1;
+       }
        graph->n_edge++;
 
-       if (graph->edge_table) {
-               uint32_t hash;
-               struct isl_hash_table_entry *entry;
-               struct isl_sched_edge *edge;
-               int is_equal;
-
-               hash = isl_hash_init();
-               hash = isl_hash_builtin(hash, src);
-               hash = isl_hash_builtin(hash, dst);
-               entry = isl_hash_table_find(ctx, graph->edge_table, hash,
-                                           &edge_has_src_and_dst,
-                                           &graph->edge[graph->n_edge - 1], 0);
-               if (!entry)
-                       return 0;
-               edge = entry->data;
-               is_equal = isl_map_fast_is_equal(map, edge->map);
-               if (is_equal < 0)
-                       return -1;
-               if (!is_equal)
-                       return 0;
+       edge = graph_find_any_edge(graph, src, dst);
+       if (!edge)
+               return graph_edge_table_add(ctx, graph, data->type,
+                                   &graph->edge[graph->n_edge - 1]);
+       is_equal = isl_map_plain_is_equal(map, edge->map);
+       if (is_equal < 0)
+               return -1;
+       if (!is_equal)
+               return graph_edge_table_add(ctx, graph, data->type,
+                                   &graph->edge[graph->n_edge - 1]);
 
-               graph->n_edge--;
-               edge->proximity = 1;
-               isl_map_free(map);
-       }
+       graph->n_edge--;
+       edge->validity |= graph->edge[graph->n_edge].validity;
+       edge->proximity |= graph->edge[graph->n_edge].proximity;
+       isl_map_free(map);
 
-       return 0;
+       return graph_edge_table_add(ctx, graph, data->type, edge);
 }
 
-/* Check whether there is a validity dependence from src to dst,
- * forcing dst to follow src.
+/* Check whether there is any dependence from node[j] to node[i]
+ * or from node[i] to node[j].
  */
-static int node_follows(struct isl_sched_graph *graph, 
-       struct isl_sched_node *dst, struct isl_sched_node *src)
+static int node_follows_weak(int i, int j, void *user)
 {
-       return graph_has_edge(graph, src, dst);
+       int f;
+       struct isl_sched_graph *graph = user;
+
+       f = graph_has_any_edge(graph, &graph->node[j], &graph->node[i]);
+       if (f < 0 || f)
+               return f;
+       return graph_has_any_edge(graph, &graph->node[i], &graph->node[j]);
 }
 
-/* Perform Tarjan's algorithm for computing the strongly connected components
- * in the dependence graph (only validity edges).
- * If directed is not set, we consider the graph to be undirected and
- * we effectively compute the (weakly) connected components.
+/* Check whether there is a validity dependence from node[j] to node[i],
+ * forcing node[i] to follow node[j].
  */
-static int detect_sccs_tarjan(struct isl_sched_graph *g, int i, int directed)
+static int node_follows_strong(int i, int j, void *user)
 {
-       int j;
-
-       g->node[i].index = g->index;
-       g->node[i].min_index = g->index;
-       g->node[i].on_stack = 1;
-       g->index++;
-       g->stack[g->sp++] = i;
-
-       for (j = g->n - 1; j >= 0; --j) {
-               int f;
-
-               if (j == i)
-                       continue;
-               if (g->node[j].index >= 0 &&
-                       (!g->node[j].on_stack ||
-                        g->node[j].index > g->node[i].min_index))
-                       continue;
-               
-               f = node_follows(g, &g->node[i], &g->node[j]);
-               if (f < 0)
-                       return -1;
-               if (!f && !directed) {
-                       f = node_follows(g, &g->node[j], &g->node[i]);
-                       if (f < 0)
-                               return -1;
-               }
-               if (!f)
-                       continue;
-               if (g->node[j].index < 0) {
-                       detect_sccs_tarjan(g, j, directed);
-                       if (g->node[j].min_index < g->node[i].min_index)
-                               g->node[i].min_index = g->node[j].min_index;
-               } else if (g->node[j].index < g->node[i].min_index)
-                       g->node[i].min_index = g->node[j].index;
-       }
-
-       if (g->node[i].index != g->node[i].min_index)
-               return 0;
-
-       do {
-               j = g->stack[--g->sp];
-               g->node[j].on_stack = 0;
-               g->node[j].scc = g->scc;
-       } while (j != i);
-       g->scc++;
+       struct isl_sched_graph *graph = user;
 
-       return 0;
+       return graph_has_validity_edge(graph, &graph->node[j], &graph->node[i]);
 }
 
-static int detect_ccs(struct isl_sched_graph *graph, int directed)
+/* Use Tarjan's algorithm for computing the strongly connected components
+ * in the dependence graph (only validity edges).
+ * If weak is set, we consider the graph to be undirected and
+ * we effectively compute the (weakly) connected components.
+ * Additionally, we also consider other edges when weak is set.
+ */
+static int detect_ccs(isl_ctx *ctx, struct isl_sched_graph *graph, int weak)
 {
-       int i;
+       int i, n;
+       struct isl_tarjan_graph *g = NULL;
 
-       graph->index = 0;
-       graph->sp = 0;
-       graph->scc = 0;
-       for (i = graph->n - 1; i >= 0; --i)
-               graph->node[i].index = -1;
+       g = isl_tarjan_graph_init(ctx, graph->n,
+               weak ? &node_follows_weak : &node_follows_strong, graph);
+       if (!g)
+               return -1;
 
-       for (i = graph->n - 1; i >= 0; --i) {
-               if (graph->node[i].index >= 0)
-                       continue;
-               if (detect_sccs_tarjan(graph, i, directed) < 0)
-                       return -1;
+       graph->scc = 0;
+       i = 0;
+       n = graph->n;
+       while (n) {
+               while (g->order[i] != -1) {
+                       graph->node[g->order[i]].scc = graph->scc;
+                       --n;
+                       ++i;
+               }
+               ++i;
+               graph->scc++;
        }
 
+       isl_tarjan_graph_free(g);
+
        return 0;
 }
 
 /* Apply Tarjan's algorithm to detect the strongly connected components
  * in the dependence graph.
  */
-static int detect_sccs(struct isl_sched_graph *graph)
+static int detect_sccs(isl_ctx *ctx, struct isl_sched_graph *graph)
 {
-       return detect_ccs(graph, 1);
+       return detect_ccs(ctx, graph, 0);
 }
 
 /* Apply Tarjan's algorithm to detect the (weakly) connected components
  * in the dependence graph.
  */
-static int detect_wccs(struct isl_sched_graph *graph)
+static int detect_wccs(isl_ctx *ctx, struct isl_sched_graph *graph)
 {
-       return detect_ccs(graph, 0);
+       return detect_ccs(ctx, graph, 1);
 }
 
 static int cmp_scc(const void *a, const void *b, void *data)
@@ -592,9 +694,9 @@ static int cmp_scc(const void *a, const void *b, void *data)
 
 /* Sort the elements of graph->sorted according to the corresponding SCCs.
  */
-static void sort_sccs(struct isl_sched_graph *graph)
+static int sort_sccs(struct isl_sched_graph *graph)
 {
-       isl_quicksort(graph->sorted, graph->n, sizeof(int), &cmp_scc, graph);
+       return isl_sort(graph->sorted, graph->n, sizeof(int), &cmp_scc, graph);
 }
 
 /* Given a dependence relation R from a node to itself,
@@ -681,33 +783,38 @@ static int add_intra_validity_constraints(struct isl_sched_graph *graph,
        unsigned total;
        isl_map *map = isl_map_copy(edge->map);
        isl_ctx *ctx = isl_map_get_ctx(map);
-       isl_dim *dim;
+       isl_space *dim;
        isl_dim_map *dim_map;
        isl_basic_set *coef;
        struct isl_sched_node *node = edge->src;
 
        coef = intra_coefficients(graph, map);
 
-       dim = isl_dim_domain(isl_dim_unwrap(isl_basic_set_get_dim(coef)));
+       dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
 
        coef = isl_basic_set_transform_dims(coef, isl_dim_set,
-                   isl_dim_size(dim, isl_dim_set), isl_mat_copy(node->cmap));
+                   isl_space_dim(dim, isl_dim_set), isl_mat_copy(node->cmap));
+       if (!coef)
+               goto error;
 
        total = isl_basic_set_total_dim(graph->lp);
        dim_map = isl_dim_map_alloc(ctx, total);
        isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 1, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          node->nvar, -1);
        isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 2, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          node->nvar, 1);
        graph->lp = isl_basic_set_extend_constraints(graph->lp,
                        coef->n_eq, coef->n_ineq);
        graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
                                                           coef, dim_map);
-       isl_dim_free(dim);
+       isl_space_free(dim);
 
        return 0;
+error:
+       isl_space_free(dim);
+       return -1;
 }
 
 /* Add constraints to graph->lp that force validity for the given
@@ -734,7 +841,7 @@ static int add_inter_validity_constraints(struct isl_sched_graph *graph,
        unsigned total;
        isl_map *map = isl_map_copy(edge->map);
        isl_ctx *ctx = isl_map_get_ctx(map);
-       isl_dim *dim;
+       isl_space *dim;
        isl_dim_map *dim_map;
        isl_basic_set *coef;
        struct isl_sched_node *src = edge->src;
@@ -742,13 +849,15 @@ static int add_inter_validity_constraints(struct isl_sched_graph *graph,
 
        coef = inter_coefficients(graph, map);
 
-       dim = isl_dim_domain(isl_dim_unwrap(isl_basic_set_get_dim(coef)));
+       dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
 
        coef = isl_basic_set_transform_dims(coef, isl_dim_set,
-                   isl_dim_size(dim, isl_dim_set), isl_mat_copy(src->cmap));
+                   isl_space_dim(dim, isl_dim_set), isl_mat_copy(src->cmap));
        coef = isl_basic_set_transform_dims(coef, isl_dim_set,
-                   isl_dim_size(dim, isl_dim_set) + src->nvar,
+                   isl_space_dim(dim, isl_dim_set) + src->nvar,
                    isl_mat_copy(dst->cmap));
+       if (!coef)
+               goto error;
 
        total = isl_basic_set_total_dim(graph->lp);
        dim_map = isl_dim_map_alloc(ctx, total);
@@ -757,20 +866,20 @@ static int add_inter_validity_constraints(struct isl_sched_graph *graph,
        isl_dim_map_range(dim_map, dst->start + 1, 2, 1, 1, dst->nparam, -1);
        isl_dim_map_range(dim_map, dst->start + 2, 2, 1, 1, dst->nparam, 1);
        isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 1, 2,
-                         isl_dim_size(dim, isl_dim_set) + src->nvar, 1,
+                         isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
                          dst->nvar, -1);
        isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 2, 2,
-                         isl_dim_size(dim, isl_dim_set) + src->nvar, 1,
+                         isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
                          dst->nvar, 1);
 
        isl_dim_map_range(dim_map, src->start, 0, 0, 0, 1, -1);
        isl_dim_map_range(dim_map, src->start + 1, 2, 1, 1, src->nparam, 1);
        isl_dim_map_range(dim_map, src->start + 2, 2, 1, 1, src->nparam, -1);
        isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 1, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          src->nvar, 1);
        isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 2, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          src->nvar, -1);
 
        edge->start = graph->lp->n_ineq;
@@ -778,10 +887,15 @@ static int add_inter_validity_constraints(struct isl_sched_graph *graph,
                        coef->n_eq, coef->n_ineq);
        graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
                                                           coef, dim_map);
-       isl_dim_free(dim);
+       if (!graph->lp)
+               goto error;
+       isl_space_free(dim);
        edge->end = graph->lp->n_ineq;
 
        return 0;
+error:
+       isl_space_free(dim);
+       return -1;
 }
 
 /* Add constraints to graph->lp that bound the dependence distance for the given
@@ -820,37 +934,42 @@ static int add_intra_proximity_constraints(struct isl_sched_graph *graph,
        unsigned nparam;
        isl_map *map = isl_map_copy(edge->map);
        isl_ctx *ctx = isl_map_get_ctx(map);
-       isl_dim *dim;
+       isl_space *dim;
        isl_dim_map *dim_map;
        isl_basic_set *coef;
        struct isl_sched_node *node = edge->src;
 
        coef = intra_coefficients(graph, map);
 
-       dim = isl_dim_domain(isl_dim_unwrap(isl_basic_set_get_dim(coef)));
+       dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
 
        coef = isl_basic_set_transform_dims(coef, isl_dim_set,
-                   isl_dim_size(dim, isl_dim_set), isl_mat_copy(node->cmap));
+                   isl_space_dim(dim, isl_dim_set), isl_mat_copy(node->cmap));
+       if (!coef)
+               goto error;
 
-       nparam = isl_dim_size(node->dim, isl_dim_param);
+       nparam = isl_space_dim(node->dim, isl_dim_param);
        total = isl_basic_set_total_dim(graph->lp);
        dim_map = isl_dim_map_alloc(ctx, total);
        isl_dim_map_range(dim_map, 1, 0, 0, 0, 1, 1);
        isl_dim_map_range(dim_map, 4, 2, 1, 1, nparam, -1);
        isl_dim_map_range(dim_map, 5, 2, 1, 1, nparam, 1);
        isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 1, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          node->nvar, s);
        isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 2, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          node->nvar, -s);
        graph->lp = isl_basic_set_extend_constraints(graph->lp,
                        coef->n_eq, coef->n_ineq);
        graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
                                                           coef, dim_map);
-       isl_dim_free(dim);
+       isl_space_free(dim);
 
        return 0;
+error:
+       isl_space_free(dim);
+       return -1;
 }
 
 /* Add constraints to graph->lp that bound the dependence distance for the given
@@ -895,7 +1014,7 @@ static int add_inter_proximity_constraints(struct isl_sched_graph *graph,
        unsigned nparam;
        isl_map *map = isl_map_copy(edge->map);
        isl_ctx *ctx = isl_map_get_ctx(map);
-       isl_dim *dim;
+       isl_space *dim;
        isl_dim_map *dim_map;
        isl_basic_set *coef;
        struct isl_sched_node *src = edge->src;
@@ -903,15 +1022,17 @@ static int add_inter_proximity_constraints(struct isl_sched_graph *graph,
 
        coef = inter_coefficients(graph, map);
 
-       dim = isl_dim_domain(isl_dim_unwrap(isl_basic_set_get_dim(coef)));
+       dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
 
        coef = isl_basic_set_transform_dims(coef, isl_dim_set,
-                   isl_dim_size(dim, isl_dim_set), isl_mat_copy(src->cmap));
+                   isl_space_dim(dim, isl_dim_set), isl_mat_copy(src->cmap));
        coef = isl_basic_set_transform_dims(coef, isl_dim_set,
-                   isl_dim_size(dim, isl_dim_set) + src->nvar,
+                   isl_space_dim(dim, isl_dim_set) + src->nvar,
                    isl_mat_copy(dst->cmap));
+       if (!coef)
+               goto error;
 
-       nparam = isl_dim_size(src->dim, isl_dim_param);
+       nparam = isl_space_dim(src->dim, isl_dim_param);
        total = isl_basic_set_total_dim(graph->lp);
        dim_map = isl_dim_map_alloc(ctx, total);
 
@@ -923,29 +1044,32 @@ static int add_inter_proximity_constraints(struct isl_sched_graph *graph,
        isl_dim_map_range(dim_map, dst->start + 1, 2, 1, 1, dst->nparam, s);
        isl_dim_map_range(dim_map, dst->start + 2, 2, 1, 1, dst->nparam, -s);
        isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 1, 2,
-                         isl_dim_size(dim, isl_dim_set) + src->nvar, 1,
+                         isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
                          dst->nvar, s);
        isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 2, 2,
-                         isl_dim_size(dim, isl_dim_set) + src->nvar, 1,
+                         isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
                          dst->nvar, -s);
 
        isl_dim_map_range(dim_map, src->start, 0, 0, 0, 1, s);
        isl_dim_map_range(dim_map, src->start + 1, 2, 1, 1, src->nparam, -s);
        isl_dim_map_range(dim_map, src->start + 2, 2, 1, 1, src->nparam, s);
        isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 1, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          src->nvar, -s);
        isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 2, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          src->nvar, s);
 
        graph->lp = isl_basic_set_extend_constraints(graph->lp,
                        coef->n_eq, coef->n_ineq);
        graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
                                                           coef, dim_map);
-       isl_dim_free(dim);
+       isl_space_free(dim);
 
        return 0;
+error:
+       isl_space_free(dim);
+       return -1;
 }
 
 static int add_all_validity_constraints(struct isl_sched_graph *graph)
@@ -1047,33 +1171,96 @@ static int node_update_cmap(struct isl_sched_node *node)
 }
 
 /* Count the number of equality and inequality constraints
- * that will be added.  If once is set, then we count
+ * that will be added for the given map.
+ * If carry is set, then we are counting the number of (validity)
+ * constraints that will be added in setup_carry_lp and we count
  * each edge exactly once.  Otherwise, we count as follows
  * validity            -> 1 (>= 0)
  * validity+proximity  -> 2 (>= 0 and upper bound)
  * proximity           -> 2 (lower and upper bound)
  */
+static int count_map_constraints(struct isl_sched_graph *graph,
+       struct isl_sched_edge *edge, __isl_take isl_map *map,
+       int *n_eq, int *n_ineq, int carry)
+{
+       isl_basic_set *coef;
+       int f = carry ? 1 : edge->proximity ? 2 : 1;
+
+       if (carry && !edge->validity) {
+               isl_map_free(map);
+               return 0;
+       }
+
+       if (edge->src == edge->dst)
+               coef = intra_coefficients(graph, map);
+       else
+               coef = inter_coefficients(graph, map);
+       if (!coef)
+               return -1;
+       *n_eq += f * coef->n_eq;
+       *n_ineq += f * coef->n_ineq;
+       isl_basic_set_free(coef);
+
+       return 0;
+}
+
+/* Count the number of equality and inequality constraints
+ * that will be added to the main lp problem.
+ * We count as follows
+ * validity            -> 1 (>= 0)
+ * validity+proximity  -> 2 (>= 0 and upper bound)
+ * proximity           -> 2 (lower and upper bound)
+ */
 static int count_constraints(struct isl_sched_graph *graph,
-       int *n_eq, int *n_ineq, int once)
+       int *n_eq, int *n_ineq)
 {
        int i;
-       isl_basic_set *coef;
 
        *n_eq = *n_ineq = 0;
        for (i = 0; i < graph->n_edge; ++i) {
                struct isl_sched_edge *edge= &graph->edge[i];
                isl_map *map = isl_map_copy(edge->map);
-               int f = once ? 1 : edge->proximity ? 2 : 1;
 
-               if (edge->src == edge->dst)
-                       coef = intra_coefficients(graph, map);
-               else
-                       coef = inter_coefficients(graph, map);
-               if (!coef)
+               if (count_map_constraints(graph, edge, map,
+                                         n_eq, n_ineq, 0) < 0)
                        return -1;
-               *n_eq += f * coef->n_eq;
-               *n_ineq += f * coef->n_ineq;
-               isl_basic_set_free(coef);
+       }
+
+       return 0;
+}
+
+/* Add constraints that bound the values of the variable and parameter
+ * coefficients of the schedule.
+ *
+ * The maximal value of the coefficients is defined by the option
+ * 'schedule_max_coefficient'.
+ */
+static int add_bound_coefficient_constraints(isl_ctx *ctx,
+       struct isl_sched_graph *graph)
+{
+       int i, j, k;
+       int max_coefficient;
+       int total;
+
+       max_coefficient = ctx->opt->schedule_max_coefficient;
+
+       if (max_coefficient == -1)
+               return 0;
+
+       total = isl_basic_set_total_dim(graph->lp);
+
+       for (i = 0; i < graph->n; ++i) {
+               struct isl_sched_node *node = &graph->node[i];
+               for (j = 0; j < 2 * node->nparam + 2 * node->nvar; ++j) {
+                       int dim;
+                       k = isl_basic_set_alloc_inequality(graph->lp);
+                       if (k < 0)
+                               return -1;
+                       dim = 1 + node->start + 1 + j;
+                       isl_seq_clr(graph->lp->ineq[k], 1 +  total);
+                       isl_int_set_si(graph->lp->ineq[k][dim], -1);
+                       isl_int_set_si(graph->lp->ineq[k][0], max_coefficient);
+               }
        }
 
        return 0;
@@ -1109,20 +1296,29 @@ static int count_constraints(struct isl_sched_graph *graph,
  *
  * The constraints are those from the edges plus two or three equalities
  * to express the sums.
+ *
+ * If force_zero is set, then we add equalities to ensure that
+ * the sum of the m_n coefficients and m_0 are both zero.
  */
-static int setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
+static int setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph,
+       int force_zero)
 {
        int i, j;
        int k;
        unsigned nparam;
        unsigned total;
-       isl_dim *dim;
+       isl_space *dim;
        int parametric;
        int param_pos;
        int n_eq, n_ineq;
+       int max_constant_term;
+       int max_coefficient;
+
+       max_constant_term = ctx->opt->schedule_max_constant_term;
+       max_coefficient = ctx->opt->schedule_max_coefficient;
 
        parametric = ctx->opt->schedule_parametric;
-       nparam = isl_dim_size(graph->node[0].dim, isl_dim_param);
+       nparam = isl_space_dim(graph->node[0].dim, isl_dim_param);
        param_pos = 4;
        total = param_pos + 2 * nparam;
        for (i = 0; i < graph->n; ++i) {
@@ -1133,22 +1329,38 @@ static int setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
                total += 1 + 2 * (node->nparam + node->nvar);
        }
 
-       if (count_constraints(graph, &n_eq, &n_ineq, 0) < 0)
+       if (count_constraints(graph, &n_eq, &n_ineq) < 0)
                return -1;
 
-       dim = isl_dim_set_alloc(ctx, 0, total);
+       dim = isl_space_set_alloc(ctx, 0, total);
        isl_basic_set_free(graph->lp);
-       n_eq += 2 + parametric;
-       graph->lp = isl_basic_set_alloc_dim(dim, 0, n_eq, n_ineq);
+       n_eq += 2 + parametric + force_zero;
+       if (max_constant_term != -1)
+               n_ineq += graph->n;
+       if (max_coefficient != -1)
+               for (i = 0; i < graph->n; ++i)
+                       n_ineq += 2 * graph->node[i].nparam +
+                                 2 * graph->node[i].nvar;
+
+       graph->lp = isl_basic_set_alloc_space(dim, 0, n_eq, n_ineq);
 
        k = isl_basic_set_alloc_equality(graph->lp);
        if (k < 0)
                return -1;
        isl_seq_clr(graph->lp->eq[k], 1 +  total);
-       isl_int_set_si(graph->lp->eq[k][1], -1);
+       if (!force_zero)
+               isl_int_set_si(graph->lp->eq[k][1], -1);
        for (i = 0; i < 2 * nparam; ++i)
                isl_int_set_si(graph->lp->eq[k][1 + param_pos + i], 1);
 
+       if (force_zero) {
+               k = isl_basic_set_alloc_equality(graph->lp);
+               if (k < 0)
+                       return -1;
+               isl_seq_clr(graph->lp->eq[k], 1 +  total);
+               isl_int_set_si(graph->lp->eq[k][2], -1);
+       }
+
        if (parametric) {
                k = isl_basic_set_alloc_equality(graph->lp);
                if (k < 0)
@@ -1176,6 +1388,19 @@ static int setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
                        isl_int_set_si(graph->lp->eq[k][pos + j], 1);
        }
 
+       if (max_constant_term != -1)
+               for (i = 0; i < graph->n; ++i) {
+                       struct isl_sched_node *node = &graph->node[i];
+                       k = isl_basic_set_alloc_inequality(graph->lp);
+                       if (k < 0)
+                               return -1;
+                       isl_seq_clr(graph->lp->ineq[k], 1 +  total);
+                       isl_int_set_si(graph->lp->ineq[k][1 + node->start], -1);
+                       isl_int_set_si(graph->lp->ineq[k][0], max_constant_term);
+               }
+
+       if (add_bound_coefficient_constraints(ctx, graph) < 0)
+               return -1;
        if (add_all_validity_constraints(graph) < 0)
                return -1;
        if (add_all_proximity_constraints(graph) < 0)
@@ -1275,11 +1500,17 @@ static __isl_give isl_vec *solve_lp(struct isl_sched_graph *graph)
  * t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
  * In this case, we then also need to perform this multiplication
  * to obtain the values of c_i_x.
+ *
+ * If check_zero is set, then the first two coordinates of sol are
+ * assumed to correspond to the dependence distance.  If these two
+ * coordinates are zero, then the corresponding scheduling dimension
+ * is marked as being zero distance.
  */
 static int update_schedule(struct isl_sched_graph *graph,
-       __isl_take isl_vec *sol, int use_cmap)
+       __isl_take isl_vec *sol, int use_cmap, int check_zero)
 {
        int i, j;
+       int zero = 0;
        isl_vec *csol = NULL;
 
        if (!sol)
@@ -1287,6 +1518,13 @@ static int update_schedule(struct isl_sched_graph *graph,
        if (sol->size == 0)
                isl_die(sol->ctx, isl_error_internal,
                        "no solution found", goto error);
+       if (graph->n_total_row >= graph->max_row)
+               isl_die(sol->ctx, isl_error_internal,
+                       "too many schedule rows", goto error);
+
+       if (check_zero)
+               zero = isl_int_is_zero(sol->el[1]) &&
+                          isl_int_is_zero(sol->el[2]);
 
        for (i = 0; i < graph->n; ++i) {
                struct isl_sched_node *node = &graph->node[i];
@@ -1324,6 +1562,7 @@ static int update_schedule(struct isl_sched_graph *graph,
                        node->sched = isl_mat_set_element(node->sched,
                                        row, 1 + node->nparam + j, csol->el[j]);
                node->band[graph->n_total_row] = graph->n_band;
+               node->zero[graph->n_total_row] = zero;
        }
        isl_vec_free(sol);
        isl_vec_free(csol);
@@ -1338,56 +1577,65 @@ error:
        return -1;
 }
 
-/* Convert node->sched into a map and return this map.
- * We simply add equality constraints that express each output variable
- * as the affine combination of parameters and input variables specified
- * by the schedule matrix.
- *
- * The result is cached in node->sched_map, which needs to be released
- * whenever node->sched is updated.
+/* Convert node->sched into a multi_aff and return this multi_aff.
  */
-static __isl_give isl_map *node_extract_schedule(struct isl_sched_node *node)
+static __isl_give isl_multi_aff *node_extract_schedule_multi_aff(
+       struct isl_sched_node *node)
 {
        int i, j;
-       isl_dim *dim;
-       isl_basic_map *bmap;
-       isl_constraint *c;
+       isl_space *space;
+       isl_local_space *ls;
+       isl_aff *aff;
+       isl_multi_aff *ma;
        int nrow, ncol;
        isl_int v;
 
-       if (node->sched_map)
-               return isl_map_copy(node->sched_map);
-
        nrow = isl_mat_rows(node->sched);
        ncol = isl_mat_cols(node->sched) - 1;
-       dim = isl_dim_from_domain(isl_dim_copy(node->dim));
-       dim = isl_dim_add(dim, isl_dim_out, nrow);
-       bmap = isl_basic_map_universe(isl_dim_copy(dim));
+       space = isl_space_from_domain(isl_space_copy(node->dim));
+       space = isl_space_add_dims(space, isl_dim_out, nrow);
+       ma = isl_multi_aff_zero(space);
+       ls = isl_local_space_from_space(isl_space_copy(node->dim));
 
        isl_int_init(v);
 
        for (i = 0; i < nrow; ++i) {
-               c = isl_equality_alloc(isl_dim_copy(dim));
-               isl_constraint_set_coefficient_si(c, isl_dim_out, i, -1);
+               aff = isl_aff_zero_on_domain(isl_local_space_copy(ls));
                isl_mat_get_element(node->sched, i, 0, &v);
-               isl_constraint_set_constant(c, v);
+               aff = isl_aff_set_constant(aff, v);
                for (j = 0; j < node->nparam; ++j) {
                        isl_mat_get_element(node->sched, i, 1 + j, &v);
-                       isl_constraint_set_coefficient(c, isl_dim_param, j, v);
+                       aff = isl_aff_set_coefficient(aff, isl_dim_param, j, v);
                }
                for (j = 0; j < node->nvar; ++j) {
                        isl_mat_get_element(node->sched,
                                            i, 1 + node->nparam + j, &v);
-                       isl_constraint_set_coefficient(c, isl_dim_in, j, v);
+                       aff = isl_aff_set_coefficient(aff, isl_dim_in, j, v);
                }
-               bmap = isl_basic_map_add_constraint(bmap, c);
+               ma = isl_multi_aff_set_aff(ma, i, aff);
        }
 
        isl_int_clear(v);
 
-       isl_dim_free(dim);
+       isl_local_space_free(ls);
+
+       return ma;
+}
+
+/* Convert node->sched into a map and return this map.
+ *
+ * The result is cached in node->sched_map, which needs to be released
+ * whenever node->sched is updated.
+ */
+static __isl_give isl_map *node_extract_schedule(struct isl_sched_node *node)
+{
+       if (!node->sched_map) {
+               isl_multi_aff *ma;
+
+               ma = node_extract_schedule_multi_aff(node);
+               node->sched_map = isl_map_from_multi_aff(ma);
+       }
 
-       node->sched_map = isl_map_from_basic_map(bmap);
        return isl_map_copy(node->sched_map);
 }
 
@@ -1411,12 +1659,12 @@ static __isl_give isl_map *specialize(__isl_take isl_map *map,
 
 /* Update the dependence relations of all edges based on the current schedule.
  * If a dependence is carried completely by the current schedule, then
- * it is removed and edge_table is updated accordingly.
+ * it is removed from the edge_tables.  It is kept in the list of edges
+ * as otherwise all edge_tables would have to be recomputed.
  */
 static int update_edges(isl_ctx *ctx, struct isl_sched_graph *graph)
 {
        int i;
-       int reset_table = 0;
 
        for (i = graph->n_edge - 1; i >= 0; --i) {
                struct isl_sched_edge *edge = &graph->edge[i];
@@ -1424,19 +1672,8 @@ static int update_edges(isl_ctx *ctx, struct isl_sched_graph *graph)
                if (!edge->map)
                        return -1;
 
-               if (isl_map_fast_is_empty(edge->map)) {
-                       reset_table = 1;
-                       isl_map_free(edge->map);
-                       if (i != graph->n_edge - 1)
-                               graph->edge[i] = graph->edge[graph->n_edge - 1];
-                       graph->n_edge--;
-               }
-       }
-
-       if (reset_table) {
-               isl_hash_table_free(ctx, graph->edge_table);
-               graph->edge_table = NULL;
-               return graph_init_edge_table(ctx, graph);
+               if (isl_map_plain_is_empty(edge->map))
+                       graph_remove_edge(graph, edge);
        }
 
        return 0;
@@ -1448,7 +1685,7 @@ static void next_band(struct isl_sched_graph *graph)
        graph->n_band++;
 }
 
-/* Topologically sort statements mapped to same schedule iteration
+/* Topologically sort statements mapped to the same schedule iteration
  * and add a row to the schedule corresponding to this order.
  */
 static int sort_statements(isl_ctx *ctx, struct isl_sched_graph *graph)
@@ -1464,9 +1701,13 @@ static int sort_statements(isl_ctx *ctx, struct isl_sched_graph *graph)
        if (graph->n_edge == 0)
                return 0;
 
-       if (detect_sccs(graph) < 0)
+       if (detect_sccs(ctx, graph) < 0)
                return -1;
 
+       if (graph->n_total_row >= graph->max_row)
+               isl_die(ctx, isl_error_internal,
+                       "too many schedule rows", return -1);
+
        for (i = 0; i < graph->n; ++i) {
                struct isl_sched_node *node = &graph->node[i];
                int row = isl_mat_rows(node->sched);
@@ -1495,7 +1736,7 @@ static int sort_statements(isl_ctx *ctx, struct isl_sched_graph *graph)
  * in graph and with parameters specified by dim.
  */
 static __isl_give isl_schedule *extract_schedule(struct isl_sched_graph *graph,
-       __isl_take isl_dim *dim)
+       __isl_take isl_space *dim)
 {
        int i;
        isl_ctx *ctx;
@@ -1504,29 +1745,44 @@ static __isl_give isl_schedule *extract_schedule(struct isl_sched_graph *graph,
        if (!dim)
                return NULL;
 
-       ctx = isl_dim_get_ctx(dim);
+       ctx = isl_space_get_ctx(dim);
        sched = isl_calloc(ctx, struct isl_schedule,
                           sizeof(struct isl_schedule) +
                           (graph->n - 1) * sizeof(struct isl_schedule_node));
        if (!sched)
                goto error;
 
+       sched->ref = 1;
        sched->n = graph->n;
        sched->n_band = graph->n_band;
        sched->n_total_row = graph->n_total_row;
 
        for (i = 0; i < sched->n; ++i) {
                int r, b;
-               int *band_end;
+               int *band_end, *band_id, *zero;
 
-               band_end = isl_alloc_array(ctx, int, graph->n_band);
-               if (!band_end)
+               sched->node[i].sched =
+                       node_extract_schedule_multi_aff(&graph->node[i]);
+               if (!sched->node[i].sched)
                        goto error;
-               sched->node[i].sched = node_extract_schedule(&graph->node[i]);
-               sched->node[i].band_end = band_end;
 
-               for (r = b = 0; r < graph->n_total_row; ++r) {
-                       if (graph->node[i].band[r] == b)
+               sched->node[i].n_band = graph->n_band;
+               if (graph->n_band == 0)
+                       continue;
+
+               band_end = isl_alloc_array(ctx, int, graph->n_band);
+               band_id = isl_alloc_array(ctx, int, graph->n_band);
+               zero = isl_alloc_array(ctx, int, graph->n_total_row);
+               sched->node[i].band_end = band_end;
+               sched->node[i].band_id = band_id;
+               sched->node[i].zero = zero;
+               if (!band_end || !band_id || !zero)
+                       goto error;
+
+               for (r = 0; r < graph->n_total_row; ++r)
+                       zero[r] = graph->node[i].zero[r];
+               for (r = b = 0; r < graph->n_total_row; ++r) {
+                       if (graph->node[i].band[r] == b)
                                continue;
                        band_end[b++] = r;
                        if (graph->node[i].band[r] == -1)
@@ -1535,13 +1791,15 @@ static __isl_give isl_schedule *extract_schedule(struct isl_sched_graph *graph,
                if (r == graph->n_total_row)
                        band_end[b++] = r;
                sched->node[i].n_band = b;
+               for (--b; b >= 0; --b)
+                       band_id[b] = graph->node[i].band_id[b];
        }
 
        sched->dim = dim;
 
        return sched;
 error:
-       isl_dim_free(dim);
+       isl_space_free(dim);
        isl_schedule_free(sched);
        return NULL;
 }
@@ -1558,13 +1816,15 @@ static int copy_nodes(struct isl_sched_graph *dst, struct isl_sched_graph *src,
        for (i = 0; i < src->n; ++i) {
                if (!node_pred(&src->node[i], data))
                        continue;
-               dst->node[dst->n].dim = isl_dim_copy(src->node[i].dim);
+               dst->node[dst->n].dim = isl_space_copy(src->node[i].dim);
                dst->node[dst->n].nvar = src->node[i].nvar;
                dst->node[dst->n].nparam = src->node[i].nparam;
                dst->node[dst->n].sched = isl_mat_copy(src->node[i].sched);
                dst->node[dst->n].sched_map =
                        isl_map_copy(src->node[i].sched_map);
                dst->node[dst->n].band = src->node[i].band;
+               dst->node[dst->n].band_id = src->node[i].band_id;
+               dst->node[dst->n].zero = src->node[i].zero;
                dst->n++;
        }
 
@@ -1573,34 +1833,55 @@ static int copy_nodes(struct isl_sched_graph *dst, struct isl_sched_graph *src,
 
 /* Copy non-empty edges that satisfy edge_pred from the src dependence graph
  * to the dst dependence graph.
+ * If the source or destination node of the edge is not in the destination
+ * graph, then it must be a backward proximity edge and it should simply
+ * be ignored.
  */
 static int copy_edges(isl_ctx *ctx, struct isl_sched_graph *dst,
        struct isl_sched_graph *src,
        int (*edge_pred)(struct isl_sched_edge *edge, int data), int data)
 {
        int i;
+       enum isl_edge_type t;
 
        dst->n_edge = 0;
        for (i = 0; i < src->n_edge; ++i) {
                struct isl_sched_edge *edge = &src->edge[i];
                isl_map *map;
+               struct isl_sched_node *dst_src, *dst_dst;
 
                if (!edge_pred(edge, data))
                        continue;
 
-               if (isl_map_fast_is_empty(edge->map))
+               if (isl_map_plain_is_empty(edge->map))
+                       continue;
+
+               dst_src = graph_find_node(ctx, dst, edge->src->dim);
+               dst_dst = graph_find_node(ctx, dst, edge->dst->dim);
+               if (!dst_src || !dst_dst) {
+                       if (edge->validity)
+                               isl_die(ctx, isl_error_internal,
+                                       "backward validity edge", return -1);
                        continue;
+               }
 
                map = isl_map_copy(edge->map);
 
-               dst->edge[dst->n_edge].src =
-                       graph_find_node(ctx, dst, edge->src->dim);
-               dst->edge[dst->n_edge].dst =
-                       graph_find_node(ctx, dst, edge->dst->dim);
+               dst->edge[dst->n_edge].src = dst_src;
+               dst->edge[dst->n_edge].dst = dst_dst;
                dst->edge[dst->n_edge].map = map;
                dst->edge[dst->n_edge].validity = edge->validity;
                dst->edge[dst->n_edge].proximity = edge->proximity;
                dst->n_edge++;
+
+               for (t = isl_edge_first; t <= isl_edge_last; ++t) {
+                       if (edge !=
+                           graph_find_edge(src, t, edge->src, edge->dst))
+                               continue;
+                       if (graph_edge_table_add(ctx, dst, t,
+                                           &dst->edge[dst->n_edge - 1]) < 0)
+                               return -1;
+               }
        }
 
        return 0;
@@ -1628,6 +1909,7 @@ static int copy_schedule(struct isl_sched_graph *dst,
                src->n++;
        }
 
+       dst->max_row = src->max_row;
        dst->n_total_row = src->n_total_row;
        dst->n_band = src->n_band;
 
@@ -1680,6 +1962,7 @@ static int compute_sub_schedule(isl_ctx *ctx,
        int data, int wcc)
 {
        struct isl_sched_graph split = { 0 };
+       int t;
 
        if (graph_alloc(ctx, &split, n, n_edge) < 0)
                goto error;
@@ -1687,11 +1970,14 @@ static int compute_sub_schedule(isl_ctx *ctx,
                goto error;
        if (graph_init_table(ctx, &split) < 0)
                goto error;
-       if (copy_edges(ctx, &split, graph, edge_pred, data) < 0)
+       for (t = 0; t <= isl_edge_last; ++t)
+               split.max_edge[t] = graph->max_edge[t];
+       if (graph_init_edge_tables(ctx, &split) < 0)
                goto error;
-       if (graph_init_edge_table(ctx, &split) < 0)
+       if (copy_edges(ctx, &split, graph, edge_pred, data) < 0)
                goto error;
        split.n_row = graph->n_row;
+       split.max_row = graph->max_row;
        split.n_total_row = graph->n_total_row;
        split.n_band = graph->n_band;
        split.band_start = graph->band_start;
@@ -1725,9 +2011,9 @@ static int node_scc_at_least(struct isl_sched_node *node, int scc)
        return node->scc >= scc;
 }
 
-static int edge_src_scc_exactly(struct isl_sched_edge *edge, int scc)
+static int edge_scc_exactly(struct isl_sched_edge *edge, int scc)
 {
-       return edge->src->scc == scc;
+       return edge->src->scc == scc && edge->dst->scc == scc;
 }
 
 static int edge_dst_scc_at_most(struct isl_sched_edge *edge, int scc)
@@ -1777,6 +2063,14 @@ static int pad_schedule(struct isl_sched_graph *graph)
  * It would be possible to reuse them as the first rows in the next
  * band, but recomputing them may result in better rows as we are looking
  * at a smaller part of the dependence graph.
+ * compute_split_schedule is only called when no zero-distance schedule row
+ * could be found on the entire graph, so we wark the splitting row as
+ * non zero-distance.
+ *
+ * The band_id of the second group is set to n, where n is the number
+ * of nodes in the first group.  This ensures that the band_ids over
+ * the two groups remain disjoint, even if either or both of the two
+ * groups contain independent components.
  */
 static int compute_split_schedule(isl_ctx *ctx, struct isl_sched_graph *graph)
 {
@@ -1785,6 +2079,10 @@ static int compute_split_schedule(isl_ctx *ctx, struct isl_sched_graph *graph)
        int n_band, orig_band;
        int drop;
 
+       if (graph->n_total_row >= graph->max_row)
+               isl_die(ctx, isl_error_internal,
+                       "too many schedule rows", return -1);
+
        drop = graph->n_total_row - graph->band_start;
        graph->n_total_row -= drop;
        graph->n_row -= drop;
@@ -1812,6 +2110,7 @@ static int compute_split_schedule(isl_ctx *ctx, struct isl_sched_graph *graph)
                        node->sched = isl_mat_set_element_si(node->sched,
                                                             row, j, 0);
                node->band[graph->n_total_row] = graph->n_band;
+               node->zero[graph->n_total_row] = 0;
        }
 
        e1 = e2 = 0;
@@ -1825,6 +2124,12 @@ static int compute_split_schedule(isl_ctx *ctx, struct isl_sched_graph *graph)
        graph->n_total_row++;
        next_band(graph);
 
+       for (i = 0; i < graph->n; ++i) {
+               struct isl_sched_node *node = &graph->node[i];
+               if (node->scc > graph->src_scc)
+                       node->band_id[graph->n_band] = n;
+       }
+
        orig_total_row = graph->n_total_row;
        orig_band = graph->n_band;
        if (compute_sub_schedule(ctx, graph, n, e1,
@@ -1859,9 +2164,10 @@ static int compute_next_band(isl_ctx *ctx, struct isl_sched_graph *graph)
        return compute_schedule(ctx, graph);
 }
 
-/* Add constraints to graph->lp that force the dependence of edge i
- * to be respected and attempt to carry it, where edge i is one from
- * a node j to itself.
+/* Add constraints to graph->lp that force the dependence "map" (which
+ * is part of the dependence relation of "edge")
+ * to be respected and attempt to carry it, where the edge is one from
+ * a node j to itself.  "pos" is the sequence number of the given map.
  * That is, add constraints that enforce
  *
  *     (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
@@ -1873,42 +2179,44 @@ static int compute_next_band(isl_ctx *ctx, struct isl_sched_graph *graph)
  * with each coefficient in c_j_x represented as a pair of non-negative
  * coefficients.
  */
-static int add_intra_constraints(struct isl_sched_graph *graph, int i)
+static int add_intra_constraints(struct isl_sched_graph *graph,
+       struct isl_sched_edge *edge, __isl_take isl_map *map, int pos)
 {
        unsigned total;
-       struct isl_sched_edge *edge= &graph->edge[i];
-       isl_map *map = isl_map_copy(edge->map);
        isl_ctx *ctx = isl_map_get_ctx(map);
-       isl_dim *dim;
+       isl_space *dim;
        isl_dim_map *dim_map;
        isl_basic_set *coef;
        struct isl_sched_node *node = edge->src;
 
        coef = intra_coefficients(graph, map);
+       if (!coef)
+               return -1;
 
-       dim = isl_dim_domain(isl_dim_unwrap(isl_basic_set_get_dim(coef)));
+       dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
 
        total = isl_basic_set_total_dim(graph->lp);
        dim_map = isl_dim_map_alloc(ctx, total);
-       isl_dim_map_range(dim_map, 3 + i, 0, 0, 0, 1, -1);
+       isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -1);
        isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 1, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          node->nvar, -1);
        isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 2, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          node->nvar, 1);
        graph->lp = isl_basic_set_extend_constraints(graph->lp,
                        coef->n_eq, coef->n_ineq);
        graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
                                                           coef, dim_map);
-       isl_dim_free(dim);
+       isl_space_free(dim);
 
        return 0;
 }
 
-/* Add constraints to graph->lp that force the dependence of edge i
- * to be respected and attempt to carry it, where edge i is one from
- * node j to node k.
+/* Add constraints to graph->lp that force the dependence "map" (which
+ * is part of the dependence relation of "edge")
+ * to be respected and attempt to carry it, where the edge is one from
+ * node j to node k.  "pos" is the sequence number of the given map.
  * That is, add constraints that enforce
  *
  *     (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
@@ -1920,71 +2228,115 @@ static int add_intra_constraints(struct isl_sched_graph *graph, int i)
  * with each coefficient (except e_i, c_k_0 and c_j_0)
  * represented as a pair of non-negative coefficients.
  */
-static int add_inter_constraints(struct isl_sched_graph *graph, int i)
+static int add_inter_constraints(struct isl_sched_graph *graph,
+       struct isl_sched_edge *edge, __isl_take isl_map *map, int pos)
 {
        unsigned total;
-       struct isl_sched_edge *edge= &graph->edge[i];
-       isl_map *map = isl_map_copy(edge->map);
        isl_ctx *ctx = isl_map_get_ctx(map);
-       isl_dim *dim;
+       isl_space *dim;
        isl_dim_map *dim_map;
        isl_basic_set *coef;
        struct isl_sched_node *src = edge->src;
        struct isl_sched_node *dst = edge->dst;
 
        coef = inter_coefficients(graph, map);
+       if (!coef)
+               return -1;
 
-       dim = isl_dim_domain(isl_dim_unwrap(isl_basic_set_get_dim(coef)));
+       dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
 
        total = isl_basic_set_total_dim(graph->lp);
        dim_map = isl_dim_map_alloc(ctx, total);
 
-       isl_dim_map_range(dim_map, 3 + i, 0, 0, 0, 1, -1);
+       isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -1);
 
        isl_dim_map_range(dim_map, dst->start, 0, 0, 0, 1, 1);
        isl_dim_map_range(dim_map, dst->start + 1, 2, 1, 1, dst->nparam, -1);
        isl_dim_map_range(dim_map, dst->start + 2, 2, 1, 1, dst->nparam, 1);
        isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 1, 2,
-                         isl_dim_size(dim, isl_dim_set) + src->nvar, 1,
+                         isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
                          dst->nvar, -1);
        isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 2, 2,
-                         isl_dim_size(dim, isl_dim_set) + src->nvar, 1,
+                         isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
                          dst->nvar, 1);
 
        isl_dim_map_range(dim_map, src->start, 0, 0, 0, 1, -1);
        isl_dim_map_range(dim_map, src->start + 1, 2, 1, 1, src->nparam, 1);
        isl_dim_map_range(dim_map, src->start + 2, 2, 1, 1, src->nparam, -1);
        isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 1, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          src->nvar, 1);
        isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 2, 2,
-                         isl_dim_size(dim, isl_dim_set), 1,
+                         isl_space_dim(dim, isl_dim_set), 1,
                          src->nvar, -1);
 
        graph->lp = isl_basic_set_extend_constraints(graph->lp,
                        coef->n_eq, coef->n_ineq);
        graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
                                                           coef, dim_map);
-       isl_dim_free(dim);
+       isl_space_free(dim);
 
        return 0;
 }
 
-/* Add constraints to graph->lp that force all dependence
- * to be respected and attempt to carry it.
+/* Add constraints to graph->lp that force all validity dependences
+ * to be respected and attempt to carry them.
  */
 static int add_all_constraints(struct isl_sched_graph *graph)
 {
-       int i;
+       int i, j;
+       int pos;
 
+       pos = 0;
        for (i = 0; i < graph->n_edge; ++i) {
                struct isl_sched_edge *edge= &graph->edge[i];
-               if (edge->src == edge->dst &&
-                   add_intra_constraints(graph, i) < 0)
-                       return -1;
-               if (edge->src != edge->dst &&
-                   add_inter_constraints(graph, i) < 0)
-                       return -1;
+
+               if (!edge->validity)
+                       continue;
+
+               for (j = 0; j < edge->map->n; ++j) {
+                       isl_basic_map *bmap;
+                       isl_map *map;
+
+                       bmap = isl_basic_map_copy(edge->map->p[j]);
+                       map = isl_map_from_basic_map(bmap);
+
+                       if (edge->src == edge->dst &&
+                           add_intra_constraints(graph, edge, map, pos) < 0)
+                               return -1;
+                       if (edge->src != edge->dst &&
+                           add_inter_constraints(graph, edge, map, pos) < 0)
+                               return -1;
+                       ++pos;
+               }
+       }
+
+       return 0;
+}
+
+/* Count the number of equality and inequality constraints
+ * that will be added to the carry_lp problem.
+ * We count each edge exactly once.
+ */
+static int count_all_constraints(struct isl_sched_graph *graph,
+       int *n_eq, int *n_ineq)
+{
+       int i, j;
+
+       *n_eq = *n_ineq = 0;
+       for (i = 0; i < graph->n_edge; ++i) {
+               struct isl_sched_edge *edge= &graph->edge[i];
+               for (j = 0; j < edge->map->n; ++j) {
+                       isl_basic_map *bmap;
+                       isl_map *map;
+
+                       bmap = isl_basic_map_copy(edge->map->p[j]);
+                       map = isl_map_from_basic_map(bmap);
+
+                       if (count_map_constraints(graph, edge, map,
+                                                 n_eq, n_ineq, 1) < 0)
+                                   return -1;
+               }
        }
 
        return 0;
@@ -1996,6 +2348,11 @@ static int add_all_constraints(struct isl_sched_graph *graph)
  * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
  * of all e_i's.  Dependence with e_i = 0 in the solution are simply
  * respected, while those with e_i > 0 (in practice e_i = 1) are carried.
+ * Note that if the dependence relation is a union of basic maps,
+ * then we have to consider each basic map individually as it may only
+ * be possible to carry the dependences expressed by some of those
+ * basic maps and not all off them.
+ * Below, we consider each of those basic maps as a separate "edge".
  *
  * All variables of the LP are non-negative.  The actual coefficients
  * may be negative, so each coefficient is represented as the difference
@@ -2014,41 +2371,46 @@ static int add_all_constraints(struct isl_sched_graph *graph)
  *             - positive and negative parts of c_i_n (if parametric)
  *             - positive and negative parts of c_i_x
  *
- * The constraints are those from the edges plus three equalities
+ * The constraints are those from the (validity) edges plus three equalities
  * to express the sums and n_edge inequalities to express e_i <= 1.
  */
 static int setup_carry_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
 {
        int i, j;
        int k;
-       isl_dim *dim;
+       isl_space *dim;
        unsigned total;
        int n_eq, n_ineq;
+       int n_edge;
+
+       n_edge = 0;
+       for (i = 0; i < graph->n_edge; ++i)
+               n_edge += graph->edge[i].map->n;
 
-       total = 3 + graph->n_edge;
+       total = 3 + n_edge;
        for (i = 0; i < graph->n; ++i) {
                struct isl_sched_node *node = &graph->node[graph->sorted[i]];
                node->start = total;
                total += 1 + 2 * (node->nparam + node->nvar);
        }
 
-       if (count_constraints(graph, &n_eq, &n_ineq, 1) < 0)
+       if (count_all_constraints(graph, &n_eq, &n_ineq) < 0)
                return -1;
 
-       dim = isl_dim_set_alloc(ctx, 0, total);
+       dim = isl_space_set_alloc(ctx, 0, total);
        isl_basic_set_free(graph->lp);
        n_eq += 3;
-       n_ineq += graph->n_edge;
-       graph->lp = isl_basic_set_alloc_dim(dim, 0, n_eq, n_ineq);
+       n_ineq += n_edge;
+       graph->lp = isl_basic_set_alloc_space(dim, 0, n_eq, n_ineq);
        graph->lp = isl_basic_set_set_rational(graph->lp);
 
        k = isl_basic_set_alloc_equality(graph->lp);
        if (k < 0)
                return -1;
        isl_seq_clr(graph->lp->eq[k], 1 +  total);
-       isl_int_set_si(graph->lp->eq[k][0], -graph->n_edge);
+       isl_int_set_si(graph->lp->eq[k][0], -n_edge);
        isl_int_set_si(graph->lp->eq[k][1], 1);
-       for (i = 0; i < graph->n_edge; ++i)
+       for (i = 0; i < n_edge; ++i)
                isl_int_set_si(graph->lp->eq[k][4 + i], 1);
 
        k = isl_basic_set_alloc_equality(graph->lp);
@@ -2076,7 +2438,7 @@ static int setup_carry_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
                        isl_int_set_si(graph->lp->eq[k][pos + j], 1);
        }
 
-       for (i = 0; i < graph->n_edge; ++i) {
+       for (i = 0; i < n_edge; ++i) {
                k = isl_basic_set_alloc_inequality(graph->lp);
                if (k < 0)
                        return -1;
@@ -2091,14 +2453,148 @@ static int setup_carry_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
        return 0;
 }
 
+/* If the schedule_split_scaled option is set and if the linear
+ * parts of the scheduling rows for all nodes in the graphs have
+ * non-trivial common divisor, then split off the constant term
+ * from the linear part.
+ * The constant term is then placed in a separate band and
+ * the linear part is reduced.
+ */
+static int split_scaled(isl_ctx *ctx, struct isl_sched_graph *graph)
+{
+       int i;
+       int row;
+       isl_int gcd, gcd_i;
+
+       if (!ctx->opt->schedule_split_scaled)
+               return 0;
+       if (graph->n <= 1)
+               return 0;
+
+       if (graph->n_total_row >= graph->max_row)
+               isl_die(ctx, isl_error_internal,
+                       "too many schedule rows", return -1);
+
+       isl_int_init(gcd);
+       isl_int_init(gcd_i);
+
+       isl_int_set_si(gcd, 0);
+
+       row = isl_mat_rows(graph->node[0].sched) - 1;
+
+       for (i = 0; i < graph->n; ++i) {
+               struct isl_sched_node *node = &graph->node[i];
+               int cols = isl_mat_cols(node->sched);
+
+               isl_seq_gcd(node->sched->row[row] + 1, cols - 1, &gcd_i);
+               isl_int_gcd(gcd, gcd, gcd_i);
+       }
+
+       isl_int_clear(gcd_i);
+
+       if (isl_int_cmp_si(gcd, 1) <= 0) {
+               isl_int_clear(gcd);
+               return 0;
+       }
+
+       next_band(graph);
+
+       for (i = 0; i < graph->n; ++i) {
+               struct isl_sched_node *node = &graph->node[i];
+
+               isl_map_free(node->sched_map);
+               node->sched_map = NULL;
+               node->sched = isl_mat_add_zero_rows(node->sched, 1);
+               if (!node->sched)
+                       goto error;
+               isl_int_fdiv_r(node->sched->row[row + 1][0],
+                              node->sched->row[row][0], gcd);
+               isl_int_fdiv_q(node->sched->row[row][0],
+                              node->sched->row[row][0], gcd);
+               isl_int_mul(node->sched->row[row][0],
+                           node->sched->row[row][0], gcd);
+               node->sched = isl_mat_scale_down_row(node->sched, row, gcd);
+               if (!node->sched)
+                       goto error;
+               node->band[graph->n_total_row] = graph->n_band;
+       }
+
+       graph->n_total_row++;
+
+       isl_int_clear(gcd);
+       return 0;
+error:
+       isl_int_clear(gcd);
+       return -1;
+}
+
+static int compute_component_schedule(isl_ctx *ctx,
+       struct isl_sched_graph *graph);
+
+/* Is the schedule row "sol" trivial on node "node"?
+ * That is, is the solution zero on the dimensions orthogonal to
+ * the previously found solutions?
+ * Each coefficient is represented as the difference between
+ * two non-negative values in "sol".  The coefficient is then
+ * zero if those two values are equal to each other.
+ */
+static int is_trivial(struct isl_sched_node *node, __isl_keep isl_vec *sol)
+{
+       int i;
+       int pos;
+       int len;
+
+       pos = 1 + node->start + 1 + 2 * (node->nparam + node->rank);
+       len = 2 * (node->nvar - node->rank);
+
+       if (len == 0)
+               return 0;
+
+       for (i = 0; i < len; i += 2)
+               if (isl_int_ne(sol->el[pos + i], sol->el[pos + i + 1]))
+                       return 0;
+
+       return 1;
+}
+
+/* Is the schedule row "sol" trivial on any node where it should
+ * not be trivial?
+ */
+static int is_any_trivial(struct isl_sched_graph *graph,
+       __isl_keep isl_vec *sol)
+{
+       int i;
+
+       for (i = 0; i < graph->n; ++i) {
+               struct isl_sched_node *node = &graph->node[i];
+
+               if (!needs_row(graph, node))
+                       continue;
+               if (is_trivial(node, sol))
+                       return 1;
+       }
+
+       return 0;
+}
+
 /* Construct a schedule row for each node such that as many dependences
  * as possible are carried and then continue with the next band.
+ *
+ * If the computed schedule row turns out to be trivial on one or
+ * more nodes where it should not be trivial, then we throw it away
+ * and try again on each component separately.
  */
 static int carry_dependences(isl_ctx *ctx, struct isl_sched_graph *graph)
 {
+       int i;
+       int n_edge;
        isl_vec *sol;
        isl_basic_set *lp;
 
+       n_edge = 0;
+       for (i = 0; i < graph->n_edge; ++i)
+               n_edge += graph->edge[i].map->n;
+
        if (setup_carry_lp(ctx, graph) < 0)
                return -1;
 
@@ -2113,18 +2609,79 @@ static int carry_dependences(isl_ctx *ctx, struct isl_sched_graph *graph)
                        "error in schedule construction", return -1);
        }
 
-       if (isl_int_cmp_si(sol->el[1], graph->n_edge) >= 0) {
+       isl_int_divexact(sol->el[1], sol->el[1], sol->el[0]);
+       if (isl_int_cmp_si(sol->el[1], n_edge) >= 0) {
                isl_vec_free(sol);
                isl_die(ctx, isl_error_unknown,
                        "unable to carry dependences", return -1);
        }
 
-       if (update_schedule(graph, sol, 0) < 0)
+       if (is_any_trivial(graph, sol)) {
+               isl_vec_free(sol);
+               if (graph->scc > 1)
+                       return compute_component_schedule(ctx, graph);
+               isl_die(ctx, isl_error_unknown,
+                       "unable to construct non-trivial solution", return -1);
+       }
+
+       if (update_schedule(graph, sol, 0, 0) < 0)
+               return -1;
+
+       if (split_scaled(ctx, graph) < 0)
                return -1;
 
        return compute_next_band(ctx, graph);
 }
 
+/* Are there any (non-empty) validity edges in the graph?
+ */
+static int has_validity_edges(struct isl_sched_graph *graph)
+{
+       int i;
+
+       for (i = 0; i < graph->n_edge; ++i) {
+               int empty;
+
+               empty = isl_map_plain_is_empty(graph->edge[i].map);
+               if (empty < 0)
+                       return -1;
+               if (empty)
+                       continue;
+               if (graph->edge[i].validity)
+                       return 1;
+       }
+
+       return 0;
+}
+
+/* Should we apply a Feautrier step?
+ * That is, did the user request the Feautrier algorithm and are
+ * there any validity dependences (left)?
+ */
+static int need_feautrier_step(isl_ctx *ctx, struct isl_sched_graph *graph)
+{
+       if (ctx->opt->schedule_algorithm != ISL_SCHEDULE_ALGORITHM_FEAUTRIER)
+               return 0;
+
+       return has_validity_edges(graph);
+}
+
+/* Compute a schedule for a connected dependence graph using Feautrier's
+ * multi-dimensional scheduling algorithm.
+ * The original algorithm is described in [1].
+ * The main idea is to minimize the number of scheduling dimensions, by
+ * trying to satisfy as many dependences as possible per scheduling dimension.
+ *
+ * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
+ *     Problem, Part II: Multi-Dimensional Time.
+ *     In Intl. Journal of Parallel Programming, 1992.
+ */
+static int compute_schedule_wcc_feautrier(isl_ctx *ctx,
+       struct isl_sched_graph *graph)
+{
+       return carry_dependences(ctx, graph);
+}
+
 /* Compute a schedule for a connected dependence graph.
  * We try to find a sequence of as many schedule rows as possible that result
  * in non-negative dependence distances (independent of the previous rows
@@ -2137,39 +2694,61 @@ static int carry_dependences(isl_ctx *ctx, struct isl_sched_graph *graph)
  * - try to carry as many dependences as possible and continue with the next
  *     band
  *
+ * If Feautrier's algorithm is selected, we first recursively try to satisfy
+ * as many validity dependences as possible. When all validity dependences
+ * are satisfied we extend the schedule to a full-dimensional schedule.
+ *
  * If we manage to complete the schedule, we finish off by topologically
  * sorting the statements based on the remaining dependences.
+ *
+ * If ctx->opt->schedule_outer_zero_distance is set, then we force the
+ * outermost dimension in the current band to be zero distance.  If this
+ * turns out to be impossible, we fall back on the general scheme above
+ * and try to carry as many dependences as possible.
  */
 static int compute_schedule_wcc(isl_ctx *ctx, struct isl_sched_graph *graph)
 {
-       if (detect_sccs(graph) < 0)
+       int force_zero = 0;
+
+       if (detect_sccs(ctx, graph) < 0)
+               return -1;
+       if (sort_sccs(graph) < 0)
                return -1;
-       sort_sccs(graph);
 
        if (compute_maxvar(graph) < 0)
                return -1;
 
+       if (need_feautrier_step(ctx, graph))
+               return compute_schedule_wcc_feautrier(ctx, graph);
+
+       if (ctx->opt->schedule_outer_zero_distance)
+               force_zero = 1;
+
        while (graph->n_row < graph->maxvar) {
                isl_vec *sol;
 
                graph->src_scc = -1;
                graph->dst_scc = -1;
 
-               if (setup_lp(ctx, graph) < 0)
+               if (setup_lp(ctx, graph, force_zero) < 0)
                        return -1;
                sol = solve_lp(graph);
                if (!sol)
                        return -1;
                if (sol->size == 0) {
                        isl_vec_free(sol);
+                       if (!ctx->opt->schedule_maximize_band_depth &&
+                           graph->n_total_row > graph->band_start)
+                               return compute_next_band(ctx, graph);
                        if (graph->src_scc >= 0)
                                return compute_split_schedule(ctx, graph);
                        if (graph->n_total_row > graph->band_start)
                                return compute_next_band(ctx, graph);
                        return carry_dependences(ctx, graph);
                }
-               if (update_schedule(graph, sol, 1) < 0)
+               if (update_schedule(graph, sol, 1, 1) < 0)
                        return -1;
+               force_zero = 0;
        }
 
        if (graph->n_total_row > graph->band_start)
@@ -2177,8 +2756,45 @@ static int compute_schedule_wcc(isl_ctx *ctx, struct isl_sched_graph *graph)
        return sort_statements(ctx, graph);
 }
 
+/* Add a row to the schedules that separates the SCCs and move
+ * to the next band.
+ */
+static int split_on_scc(isl_ctx *ctx, struct isl_sched_graph *graph)
+{
+       int i;
+
+       if (graph->n_total_row >= graph->max_row)
+               isl_die(ctx, isl_error_internal,
+                       "too many schedule rows", return -1);
+
+       for (i = 0; i < graph->n; ++i) {
+               struct isl_sched_node *node = &graph->node[i];
+               int row = isl_mat_rows(node->sched);
+
+               isl_map_free(node->sched_map);
+               node->sched_map = NULL;
+               node->sched = isl_mat_add_zero_rows(node->sched, 1);
+               node->sched = isl_mat_set_element_si(node->sched, row, 0,
+                                                    node->scc);
+               if (!node->sched)
+                       return -1;
+               node->band[graph->n_total_row] = graph->n_band;
+       }
+
+       graph->n_total_row++;
+       next_band(graph);
+
+       return 0;
+}
+
 /* Compute a schedule for each component (identified by node->scc)
  * of the dependence graph separately and then combine the results.
+ * Depending on the setting of schedule_fuse, a component may be
+ * either weakly or strongly connected.
+ *
+ * The band_id is adjusted such that each component has a separate id.
+ * Note that the band_id may have already been set to a value different
+ * from zero by compute_split_schedule.
  */
 static int compute_component_schedule(isl_ctx *ctx,
        struct isl_sched_graph *graph)
@@ -2188,10 +2804,17 @@ static int compute_component_schedule(isl_ctx *ctx,
        int n_total_row, orig_total_row;
        int n_band, orig_band;
 
+       if (ctx->opt->schedule_fuse == ISL_SCHEDULE_FUSE_MIN ||
+           ctx->opt->schedule_separate_components)
+               if (split_on_scc(ctx, graph) < 0)
+                       return -1;
+
        n_total_row = 0;
        orig_total_row = graph->n_total_row;
        n_band = 0;
        orig_band = graph->n_band;
+       for (i = 0; i < graph->n; ++i)
+               graph->node[i].band_id[graph->n_band] += graph->node[i].scc;
        for (wcc = 0; wcc < graph->scc; ++wcc) {
                n = 0;
                for (i = 0; i < graph->n; ++i)
@@ -2199,12 +2822,13 @@ static int compute_component_schedule(isl_ctx *ctx,
                                n++;
                n_edge = 0;
                for (i = 0; i < graph->n_edge; ++i)
-                       if (graph->edge[i].src->scc == wcc)
+                       if (graph->edge[i].src->scc == wcc &&
+                           graph->edge[i].dst->scc == wcc)
                                n_edge++;
 
                if (compute_sub_schedule(ctx, graph, n, n_edge,
                                    &node_scc_exactly,
-                                   &edge_src_scc_exactly, wcc, 1) < 0)
+                                   &edge_scc_exactly, wcc, 1) < 0)
                        return -1;
                if (graph->n_total_row > n_total_row)
                        n_total_row = graph->n_total_row;
@@ -2222,12 +2846,20 @@ static int compute_component_schedule(isl_ctx *ctx,
 
 /* Compute a schedule for the given dependence graph.
  * We first check if the graph is connected (through validity dependences)
- * and if so compute a schedule for each component separately.
+ * and, if not, compute a schedule for each component separately.
+ * If schedule_fuse is set to minimal fusion, then we check for strongly
+ * connected components instead and compute a separate schedule for
+ * each such strongly connected component.
  */
 static int compute_schedule(isl_ctx *ctx, struct isl_sched_graph *graph)
 {
-       if (detect_wccs(graph) < 0)
-               return -1;
+       if (ctx->opt->schedule_fuse == ISL_SCHEDULE_FUSE_MIN) {
+               if (detect_sccs(ctx, graph) < 0)
+                       return -1;
+       } else {
+               if (detect_wccs(ctx, graph) < 0)
+                       return -1;
+       }
 
        if (graph->scc > 1)
                return compute_component_schedule(ctx, graph);
@@ -2236,8 +2868,12 @@ static int compute_schedule(isl_ctx *ctx, struct isl_sched_graph *graph)
 }
 
 /* Compute a schedule for the given union of domains that respects
- * all the validity dependences and tries to minimize the dependence
- * distances over the proximity dependences.
+ * all the validity dependences.
+ * If the default isl scheduling algorithm is used, it tries to minimize
+ * the dependence distances over the proximity dependences.
+ * If Feautrier's scheduling algorithm is used, the proximity dependence
+ * distances are only minimized during the extension to a full-dimensional
+ * schedule.
  */
 __isl_give isl_schedule *isl_union_set_compute_schedule(
        __isl_take isl_union_set *domain,
@@ -2245,16 +2881,17 @@ __isl_give isl_schedule *isl_union_set_compute_schedule(
        __isl_take isl_union_map *proximity)
 {
        isl_ctx *ctx = isl_union_set_get_ctx(domain);
-       isl_dim *dim;
+       isl_space *dim;
        struct isl_sched_graph graph = { 0 };
        isl_schedule *sched;
+       struct isl_extract_edge_data data;
 
        domain = isl_union_set_align_params(domain,
-                                           isl_union_map_get_dim(validity));
+                                           isl_union_map_get_space(validity));
        domain = isl_union_set_align_params(domain,
-                                           isl_union_map_get_dim(proximity));
-       dim = isl_union_set_get_dim(domain);
-       validity = isl_union_map_align_params(validity, isl_dim_copy(dim));
+                                           isl_union_map_get_space(proximity));
+       dim = isl_union_set_get_space(domain);
+       validity = isl_union_map_align_params(validity, isl_space_copy(dim));
        proximity = isl_union_map_align_params(proximity, dim);
 
        if (!domain)
@@ -2266,25 +2903,32 @@ __isl_give isl_schedule *isl_union_set_compute_schedule(
        if (graph_alloc(ctx, &graph, graph.n,
            isl_union_map_n_map(validity) + isl_union_map_n_map(proximity)) < 0)
                goto error;
+       if (compute_max_row(&graph, domain) < 0)
+               goto error;
        graph.root = 1;
        graph.n = 0;
        if (isl_union_set_foreach_set(domain, &extract_node, &graph) < 0)
                goto error;
        if (graph_init_table(ctx, &graph) < 0)
                goto error;
-       graph.n_edge = 0;
-       if (isl_union_map_foreach_map(validity, &extract_edge, &graph) < 0)
+       graph.max_edge[isl_edge_validity] = isl_union_map_n_map(validity);
+       graph.max_edge[isl_edge_proximity] = isl_union_map_n_map(proximity);
+       if (graph_init_edge_tables(ctx, &graph) < 0)
                goto error;
-       if (graph_init_edge_table(ctx, &graph) < 0)
+       graph.n_edge = 0;
+       data.graph = &graph;
+       data.type = isl_edge_validity;
+       if (isl_union_map_foreach_map(validity, &extract_edge, &data) < 0)
                goto error;
-       if (isl_union_map_foreach_map(proximity, &extract_edge, &graph) < 0)
+       data.type = isl_edge_proximity;
+       if (isl_union_map_foreach_map(proximity, &extract_edge, &data) < 0)
                goto error;
 
        if (compute_schedule(ctx, &graph) < 0)
                goto error;
 
 empty:
-       sched = extract_schedule(&graph, isl_union_set_get_dim(domain));
+       sched = extract_schedule(&graph, isl_union_set_get_space(domain));
 
        graph_free(ctx, &graph);
        isl_union_set_free(domain);
@@ -2305,15 +2949,105 @@ void *isl_schedule_free(__isl_take isl_schedule *sched)
        int i;
        if (!sched)
                return NULL;
+
+       if (--sched->ref > 0)
+               return NULL;
+
        for (i = 0; i < sched->n; ++i) {
-               isl_map_free(sched->node[i].sched);
+               isl_multi_aff_free(sched->node[i].sched);
                free(sched->node[i].band_end);
+               free(sched->node[i].band_id);
+               free(sched->node[i].zero);
        }
-       isl_dim_free(sched->dim);
+       isl_space_free(sched->dim);
+       isl_band_list_free(sched->band_forest);
        free(sched);
        return NULL;
 }
 
+isl_ctx *isl_schedule_get_ctx(__isl_keep isl_schedule *schedule)
+{
+       return schedule ? isl_space_get_ctx(schedule->dim) : NULL;
+}
+
+/* Set max_out to the maximal number of output dimensions over
+ * all maps.
+ */
+static int update_max_out(__isl_take isl_map *map, void *user)
+{
+       int *max_out = user;
+       int n_out = isl_map_dim(map, isl_dim_out);
+
+       if (n_out > *max_out)
+               *max_out = n_out;
+
+       isl_map_free(map);
+       return 0;
+}
+
+/* Internal data structure for map_pad_range.
+ *
+ * "max_out" is the maximal schedule dimension.
+ * "res" collects the results.
+ */
+struct isl_pad_schedule_map_data {
+       int max_out;
+       isl_union_map *res;
+};
+
+/* Pad the range of the given map with zeros to data->max_out and
+ * then add the result to data->res.
+ */
+static int map_pad_range(__isl_take isl_map *map, void *user)
+{
+       struct isl_pad_schedule_map_data *data = user;
+       int i;
+       int n_out = isl_map_dim(map, isl_dim_out);
+
+       map = isl_map_add_dims(map, isl_dim_out, data->max_out - n_out);
+       for (i = n_out; i < data->max_out; ++i)
+               map = isl_map_fix_si(map, isl_dim_out, i, 0);
+
+       data->res = isl_union_map_add_map(data->res, map);
+       if (!data->res)
+               return -1;
+
+       return 0;
+}
+
+/* Pad the ranges of the maps in the union map with zeros such they all have
+ * the same dimension.
+ */
+static __isl_give isl_union_map *pad_schedule_map(
+       __isl_take isl_union_map *umap)
+{
+       struct isl_pad_schedule_map_data data;
+
+       if (!umap)
+               return NULL;
+       if (isl_union_map_n_map(umap) <= 1)
+               return umap;
+
+       data.max_out = 0;
+       if (isl_union_map_foreach_map(umap, &update_max_out, &data.max_out) < 0)
+               return isl_union_map_free(umap);
+
+       data.res = isl_union_map_empty(isl_union_map_get_space(umap));
+       if (isl_union_map_foreach_map(umap, &map_pad_range, &data) < 0)
+               data.res = isl_union_map_free(data.res);
+
+       isl_union_map_free(umap);
+       return data.res;
+}
+
+/* Return an isl_union_map of the schedule.  If we have already constructed
+ * a band forest, then this band forest may have been modified so we need
+ * to extract the isl_union_map from the forest rather than from
+ * the originally computed schedule.  This reconstructed schedule map
+ * then needs to be padded with zeros to unify the schedule space
+ * since the result of isl_band_list_get_suffix_schedule may not have
+ * a unified schedule space.
+ */
 __isl_give isl_union_map *isl_schedule_get_map(__isl_keep isl_schedule *sched)
 {
        int i;
@@ -2322,51 +3056,315 @@ __isl_give isl_union_map *isl_schedule_get_map(__isl_keep isl_schedule *sched)
        if (!sched)
                return NULL;
 
-       umap = isl_union_map_empty(isl_dim_copy(sched->dim));
-       for (i = 0; i < sched->n; ++i)
-               umap = isl_union_map_add_map(umap,
-                                           isl_map_copy(sched->node[i].sched));
+       if (sched->band_forest) {
+               umap = isl_band_list_get_suffix_schedule(sched->band_forest);
+               return pad_schedule_map(umap);
+       }
+
+       umap = isl_union_map_empty(isl_space_copy(sched->dim));
+       for (i = 0; i < sched->n; ++i) {
+               isl_multi_aff *ma;
+
+               ma = isl_multi_aff_copy(sched->node[i].sched);
+               umap = isl_union_map_add_map(umap, isl_map_from_multi_aff(ma));
+       }
 
        return umap;
 }
 
-int isl_schedule_n_band(__isl_keep isl_schedule *sched)
+static __isl_give isl_band_list *construct_band_list(
+       __isl_keep isl_schedule *schedule, __isl_keep isl_band *parent,
+       int band_nr, int *parent_active, int n_active);
+
+/* Construct an isl_band structure for the band in the given schedule
+ * with sequence number band_nr for the n_active nodes marked by active.
+ * If the nodes don't have a band with the given sequence number,
+ * then a band without members is created.
+ *
+ * Because of the way the schedule is constructed, we know that
+ * the position of the band inside the schedule of a node is the same
+ * for all active nodes.
+ */
+static __isl_give isl_band *construct_band(__isl_keep isl_schedule *schedule,
+       __isl_keep isl_band *parent,
+       int band_nr, int *active, int n_active)
+{
+       int i, j;
+       isl_ctx *ctx = isl_schedule_get_ctx(schedule);
+       isl_band *band;
+       unsigned start, end;
+
+       band = isl_band_alloc(ctx);
+       if (!band)
+               return NULL;
+
+       band->schedule = schedule;
+       band->parent = parent;
+
+       for (i = 0; i < schedule->n; ++i)
+               if (active[i] && schedule->node[i].n_band > band_nr + 1)
+                       break;
+
+       if (i < schedule->n) {
+               band->children = construct_band_list(schedule, band,
+                                               band_nr + 1, active, n_active);
+               if (!band->children)
+                       goto error;
+       }
+
+       for (i = 0; i < schedule->n; ++i)
+               if (active[i])
+                       break;
+
+       if (i >= schedule->n)
+               isl_die(ctx, isl_error_internal,
+                       "band without active statements", goto error);
+
+       start = band_nr ? schedule->node[i].band_end[band_nr - 1] : 0;
+       end = band_nr < schedule->node[i].n_band ?
+               schedule->node[i].band_end[band_nr] : start;
+       band->n = end - start;
+
+       band->zero = isl_alloc_array(ctx, int, band->n);
+       if (!band->zero)
+               goto error;
+
+       for (j = 0; j < band->n; ++j)
+               band->zero[j] = schedule->node[i].zero[start + j];
+
+       band->pma = isl_union_pw_multi_aff_empty(isl_space_copy(schedule->dim));
+       for (i = 0; i < schedule->n; ++i) {
+               isl_multi_aff *ma;
+               isl_pw_multi_aff *pma;
+               unsigned n_out;
+
+               if (!active[i])
+                       continue;
+
+               ma = isl_multi_aff_copy(schedule->node[i].sched);
+               n_out = isl_multi_aff_dim(ma, isl_dim_out);
+               ma = isl_multi_aff_drop_dims(ma, isl_dim_out, end, n_out - end);
+               ma = isl_multi_aff_drop_dims(ma, isl_dim_out, 0, start);
+               pma = isl_pw_multi_aff_from_multi_aff(ma);
+               band->pma = isl_union_pw_multi_aff_add_pw_multi_aff(band->pma,
+                                                                   pma);
+       }
+       if (!band->pma)
+               goto error;
+
+       return band;
+error:
+       isl_band_free(band);
+       return NULL;
+}
+
+/* Construct a list of bands that start at the same position (with
+ * sequence number band_nr) in the schedules of the nodes that
+ * were active in the parent band.
+ *
+ * A separate isl_band structure is created for each band_id
+ * and for each node that does not have a band with sequence
+ * number band_nr.  In the latter case, a band without members
+ * is created.
+ * This ensures that if a band has any children, then each node
+ * that was active in the band is active in exactly one of the children.
+ */
+static __isl_give isl_band_list *construct_band_list(
+       __isl_keep isl_schedule *schedule, __isl_keep isl_band *parent,
+       int band_nr, int *parent_active, int n_active)
 {
-       return sched ? sched->n_band : 0;
+       int i, j;
+       isl_ctx *ctx = isl_schedule_get_ctx(schedule);
+       int *active;
+       int n_band;
+       isl_band_list *list;
+
+       n_band = 0;
+       for (i = 0; i < n_active; ++i) {
+               for (j = 0; j < schedule->n; ++j) {
+                       if (!parent_active[j])
+                               continue;
+                       if (schedule->node[j].n_band <= band_nr)
+                               continue;
+                       if (schedule->node[j].band_id[band_nr] == i) {
+                               n_band++;
+                               break;
+                       }
+               }
+       }
+       for (j = 0; j < schedule->n; ++j)
+               if (schedule->node[j].n_band <= band_nr)
+                       n_band++;
+
+       if (n_band == 1) {
+               isl_band *band;
+               list = isl_band_list_alloc(ctx, n_band);
+               band = construct_band(schedule, parent, band_nr,
+                                       parent_active, n_active);
+               return isl_band_list_add(list, band);
+       }
+
+       active = isl_alloc_array(ctx, int, schedule->n);
+       if (!active)
+               return NULL;
+
+       list = isl_band_list_alloc(ctx, n_band);
+
+       for (i = 0; i < n_active; ++i) {
+               int n = 0;
+               isl_band *band;
+
+               for (j = 0; j < schedule->n; ++j) {
+                       active[j] = parent_active[j] &&
+                                       schedule->node[j].n_band > band_nr &&
+                                       schedule->node[j].band_id[band_nr] == i;
+                       if (active[j])
+                               n++;
+               }
+               if (n == 0)
+                       continue;
+
+               band = construct_band(schedule, parent, band_nr, active, n);
+
+               list = isl_band_list_add(list, band);
+       }
+       for (i = 0; i < schedule->n; ++i) {
+               isl_band *band;
+               if (!parent_active[i])
+                       continue;
+               if (schedule->node[i].n_band > band_nr)
+                       continue;
+               for (j = 0; j < schedule->n; ++j)
+                       active[j] = j == i;
+               band = construct_band(schedule, parent, band_nr, active, 1);
+               list = isl_band_list_add(list, band);
+       }
+
+       free(active);
+
+       return list;
 }
 
-/* Construct a mapping that maps each domain to the band in its schedule
- * with the specified band index.  Note that bands with the same index
- * but for different domains do not need to be related.
+/* Construct a band forest representation of the schedule and
+ * return the list of roots.
  */
-__isl_give isl_union_map *isl_schedule_get_band(__isl_keep isl_schedule *sched,
-       unsigned band)
+static __isl_give isl_band_list *construct_forest(
+       __isl_keep isl_schedule *schedule)
 {
        int i;
-       isl_union_map *umap;
+       isl_ctx *ctx = isl_schedule_get_ctx(schedule);
+       isl_band_list *forest;
+       int *active;
 
-       if (!sched)
+       active = isl_alloc_array(ctx, int, schedule->n);
+       if (!active)
                return NULL;
 
-       umap = isl_union_map_empty(isl_dim_copy(sched->dim));
-       for (i = 0; i < sched->n; ++i) {
-               int start, end;
-               isl_map *map;
+       for (i = 0; i < schedule->n; ++i)
+               active[i] = 1;
 
-               if (band >= sched->node[i].n_band)
-                       continue;
+       forest = construct_band_list(schedule, NULL, 0, active, schedule->n);
+
+       free(active);
+
+       return forest;
+}
+
+/* Return the roots of a band forest representation of the schedule.
+ */
+__isl_give isl_band_list *isl_schedule_get_band_forest(
+       __isl_keep isl_schedule *schedule)
+{
+       if (!schedule)
+               return NULL;
+       if (!schedule->band_forest)
+               schedule->band_forest = construct_forest(schedule);
+       return isl_band_list_dup(schedule->band_forest);
+}
+
+/* Call "fn" on each band in the schedule in depth-first post-order.
+ */
+int isl_schedule_foreach_band(__isl_keep isl_schedule *sched,
+       int (*fn)(__isl_keep isl_band *band, void *user), void *user)
+{
+       int r;
+       isl_band_list *forest;
+
+       if (!sched)
+               return -1;
+
+       forest = isl_schedule_get_band_forest(sched);
+       r = isl_band_list_foreach_band(forest, fn, user);
+       isl_band_list_free(forest);
+
+       return r;
+}
+
+static __isl_give isl_printer *print_band_list(__isl_take isl_printer *p,
+       __isl_keep isl_band_list *list);
 
-               start = band > 0 ? sched->node[i].band_end[band - 1] : 0;
-               end = sched->node[i].band_end[band];
+static __isl_give isl_printer *print_band(__isl_take isl_printer *p,
+       __isl_keep isl_band *band)
+{
+       isl_band_list *children;
+
+       p = isl_printer_start_line(p);
+       p = isl_printer_print_union_pw_multi_aff(p, band->pma);
+       p = isl_printer_end_line(p);
+
+       if (!isl_band_has_children(band))
+               return p;
 
-               map = isl_map_copy(sched->node[i].sched);
+       children = isl_band_get_children(band);
 
-               map = isl_map_project_out(map, isl_dim_out, end,
-                                         sched->n_total_row - end);
-               map = isl_map_project_out(map, isl_dim_out, 0, start);
+       p = isl_printer_indent(p, 4);
+       p = print_band_list(p, children);
+       p = isl_printer_indent(p, -4);
+
+       isl_band_list_free(children);
+
+       return p;
+}
 
-               umap = isl_union_map_add_map(umap, map);
+static __isl_give isl_printer *print_band_list(__isl_take isl_printer *p,
+       __isl_keep isl_band_list *list)
+{
+       int i, n;
+
+       n = isl_band_list_n_band(list);
+       for (i = 0; i < n; ++i) {
+               isl_band *band;
+               band = isl_band_list_get_band(list, i);
+               p = print_band(p, band);
+               isl_band_free(band);
        }
 
-       return umap;
+       return p;
+}
+
+__isl_give isl_printer *isl_printer_print_schedule(__isl_take isl_printer *p,
+       __isl_keep isl_schedule *schedule)
+{
+       isl_band_list *forest;
+
+       forest = isl_schedule_get_band_forest(schedule);
+
+       p = print_band_list(p, forest);
+
+       isl_band_list_free(forest);
+
+       return p;
+}
+
+void isl_schedule_dump(__isl_keep isl_schedule *schedule)
+{
+       isl_printer *printer;
+
+       if (!schedule)
+               return;
+
+       printer = isl_printer_to_file(isl_schedule_get_ctx(schedule), stderr);
+       printer = isl_printer_print_schedule(printer, schedule);
+
+       isl_printer_free(printer);
 }