isl_schedule.c: fix types of enum isl_edge_type iterators
[platform/upstream/isl.git] / isl_schedule.c
index 9a2d757..add0fa0 100644 (file)
@@ -11,6 +11,7 @@
 #include <isl_ctx_private.h>
 #include <isl_map_private.h>
 #include <isl_space_private.h>
+#include <isl/aff.h>
 #include <isl/hash.h>
 #include <isl/constraint.h>
 #include <isl/schedule.h>
@@ -124,6 +125,13 @@ 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.
  *
@@ -135,6 +143,7 @@ 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
@@ -148,10 +157,13 @@ 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
  *
@@ -175,6 +187,7 @@ struct isl_sched_graph {
        struct isl_sched_node *node;
        int n;
        int maxvar;
+       int max_row;
        int n_row;
 
        int *sorted;
@@ -187,7 +200,8 @@ 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;
@@ -254,60 +268,95 @@ 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_space_get_ctx(src->dim);
-       struct isl_hash_table_entry *entry;
        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_plain_is_empty(edge->map);
        if (empty < 0)
                return -1;
@@ -315,6 +364,72 @@ static int graph_has_edge(struct isl_sched_graph *graph,
        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)
 {
@@ -367,11 +482,49 @@ static void graph_free(isl_ctx *ctx, struct isl_sched_graph *graph)
        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)
@@ -396,11 +549,11 @@ 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->n_edge + nvar);
+       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->n_edge + nvar);
+       zero = isl_calloc_array(ctx, int, graph->max_row);
        graph->node[graph->n].zero = zero;
        graph->n++;
 
@@ -410,21 +563,27 @@ static int extract_node(__isl_take isl_set *set, void *user)
        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_space *dim;
+       struct isl_sched_edge *edge;
+       int is_equal;
 
        dim = isl_space_domain(isl_map_get_space(map));
        src = graph_find_node(ctx, graph, dim);
@@ -441,54 +600,55 @@ 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_plain_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.
+ * forcing dst to follow src (if weak is not set).
+ * If weak is set, then check if there is any dependence from src to dst.
  */
 static int node_follows(struct isl_sched_graph *graph, 
-       struct isl_sched_node *dst, struct isl_sched_node *src)
+       struct isl_sched_node *dst, struct isl_sched_node *src, int weak)
 {
-       return graph_has_edge(graph, src, dst);
+       if (weak)
+               return graph_has_any_edge(graph, src, dst);
+       else
+               return graph_has_validity_edge(graph, src, dst);
 }
 
 /* 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
+ * 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_sccs_tarjan(struct isl_sched_graph *g, int i, int directed)
+static int detect_sccs_tarjan(struct isl_sched_graph *g, int i, int weak)
 {
        int j;
 
@@ -508,18 +668,18 @@ static int detect_sccs_tarjan(struct isl_sched_graph *g, int i, int directed)
                         g->node[j].index > g->node[i].min_index))
                        continue;
                
-               f = node_follows(g, &g->node[i], &g->node[j]);
+               f = node_follows(g, &g->node[i], &g->node[j], weak);
                if (f < 0)
                        return -1;
-               if (!f && !directed) {
-                       f = node_follows(g, &g->node[j], &g->node[i]);
+               if (!f && weak) {
+                       f = node_follows(g, &g->node[j], &g->node[i], weak);
                        if (f < 0)
                                return -1;
                }
                if (!f)
                        continue;
                if (g->node[j].index < 0) {
-                       detect_sccs_tarjan(g, j, directed);
+                       detect_sccs_tarjan(g, j, weak);
                        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)
@@ -539,7 +699,7 @@ static int detect_sccs_tarjan(struct isl_sched_graph *g, int i, int directed)
        return 0;
 }
 
-static int detect_ccs(struct isl_sched_graph *graph, int directed)
+static int detect_ccs(struct isl_sched_graph *graph, int weak)
 {
        int i;
 
@@ -552,7 +712,7 @@ static int detect_ccs(struct isl_sched_graph *graph, int directed)
        for (i = graph->n - 1; i >= 0; --i) {
                if (graph->node[i].index >= 0)
                        continue;
-               if (detect_sccs_tarjan(graph, i, directed) < 0)
+               if (detect_sccs_tarjan(graph, i, weak) < 0)
                        return -1;
        }
 
@@ -564,7 +724,7 @@ static int detect_ccs(struct isl_sched_graph *graph, int directed)
  */
 static int detect_sccs(struct isl_sched_graph *graph)
 {
-       return detect_ccs(graph, 1);
+       return detect_ccs(graph, 0);
 }
 
 /* Apply Tarjan's algorithm to detect the (weakly) connected components
@@ -572,7 +732,7 @@ static int detect_sccs(struct isl_sched_graph *graph)
  */
 static int detect_wccs(struct isl_sched_graph *graph)
 {
-       return detect_ccs(graph, 0);
+       return detect_ccs(graph, 1);
 }
 
 static int cmp_scc(const void *a, const void *b, void *data)
@@ -1042,7 +1202,8 @@ static int node_update_cmap(struct isl_sched_node *node)
 
 /* Count the number of equality and inequality constraints
  * that will be added for the given map.
- * If once is set, then we count
+ * 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)
@@ -1050,10 +1211,15 @@ static int node_update_cmap(struct isl_sched_node *node)
  */
 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 once)
+       int *n_eq, int *n_ineq, int carry)
 {
        isl_basic_set *coef;
-       int f = once ? 1 : edge->proximity ? 2 : 1;
+       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);
@@ -1070,14 +1236,13 @@ static int count_map_constraints(struct isl_sched_graph *graph,
 
 /* Count the number of equality and inequality constraints
  * that will be added to the main lp problem.
- * If once is set, then we count
- * each edge exactly once.  Otherwise, we count as follows
+ * 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;
 
@@ -1087,13 +1252,50 @@ static int count_constraints(struct isl_sched_graph *graph,
                isl_map *map = isl_map_copy(edge->map);
 
                if (count_map_constraints(graph, edge, map,
-                                         n_eq, n_ineq, once) < 0)
+                                         n_eq, n_ineq, 0) < 0)
                        return -1;
        }
 
        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;
+}
+
 /* Construct an ILP problem for finding schedule coefficients
  * that result in non-negative, but small dependence distances
  * over all dependences.
@@ -1140,8 +1342,10 @@ static int setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph,
        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_space_dim(graph->node[0].dim, isl_dim_param);
@@ -1155,7 +1359,7 @@ 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_space_set_alloc(ctx, 0, total);
@@ -1163,6 +1367,10 @@ static int setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph,
        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);
 
@@ -1221,6 +1429,8 @@ static int setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph,
                        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)
@@ -1394,58 +1604,65 @@ 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_space *dim;
+       isl_space *space;
        isl_local_space *ls;
-       isl_basic_map *bmap;
-       isl_constraint *c;
+       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_space_from_domain(isl_space_copy(node->dim));
-       dim = isl_space_add_dims(dim, isl_dim_out, nrow);
-       bmap = isl_basic_map_universe(isl_space_copy(dim));
-       ls = isl_local_space_from_space(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_local_space_copy(ls));
-               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_local_space_free(ls);
 
-       node->sched_map = isl_map_from_basic_map(bmap);
+       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);
+       }
+
        return isl_map_copy(node->sched_map);
 }
 
@@ -1469,12 +1686,12 @@ 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];
@@ -1482,19 +1699,8 @@ static int update_edges(isl_ctx *ctx, struct isl_sched_graph *graph)
                if (!edge->map)
                        return -1;
 
-               if (isl_map_plain_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;
@@ -1506,7 +1712,7 @@ 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)
@@ -1581,7 +1787,8 @@ static __isl_give isl_schedule *extract_schedule(struct isl_sched_graph *graph,
                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].sched = node_extract_schedule(&graph->node[i]);
+               sched->node[i].sched =
+                       node_extract_schedule_multi_aff(&graph->node[i]);
                sched->node[i].band_end = band_end;
                sched->node[i].band_id = band_id;
                sched->node[i].zero = zero;
@@ -1642,17 +1849,22 @@ 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;
@@ -1660,16 +1872,32 @@ static int copy_edges(isl_ctx *ctx, struct isl_sched_graph *dst,
                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;
@@ -1749,6 +1977,7 @@ 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;
@@ -1756,9 +1985,11 @@ 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.n_total_row = graph->n_total_row;
@@ -2054,8 +2285,8 @@ static int add_inter_constraints(struct isl_sched_graph *graph,
        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)
 {
@@ -2065,6 +2296,10 @@ static int add_all_constraints(struct isl_sched_graph *graph)
        pos = 0;
        for (i = 0; i < graph->n_edge; ++i) {
                struct isl_sched_edge *edge= &graph->edge[i];
+
+               if (!edge->validity)
+                       continue;
+
                for (j = 0; j < edge->map->n; ++j) {
                        isl_basic_map *bmap;
                        isl_map *map;
@@ -2087,14 +2322,10 @@ static int add_all_constraints(struct isl_sched_graph *graph)
 
 /* Count the number of equality and inequality constraints
  * that will be added to the carry_lp problem.
- * If once is set, then 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)
+ * We count each edge exactly once.
  */
 static int count_all_constraints(struct isl_sched_graph *graph,
-       int *n_eq, int *n_ineq, int once)
+       int *n_eq, int *n_ineq)
 {
        int i, j;
 
@@ -2109,7 +2340,7 @@ static int count_all_constraints(struct isl_sched_graph *graph,
                        map = isl_map_from_basic_map(bmap);
 
                        if (count_map_constraints(graph, edge, map,
-                                                 n_eq, n_ineq, once) < 0)
+                                                 n_eq, n_ineq, 1) < 0)
                                    return -1;
                }
        }
@@ -2146,7 +2377,7 @@ static int count_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)
@@ -2169,7 +2400,7 @@ static int setup_carry_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
                total += 1 + 2 * (node->nparam + node->nvar);
        }
 
-       if (count_all_constraints(graph, &n_eq, &n_ineq, 1) < 0)
+       if (count_all_constraints(graph, &n_eq, &n_ineq) < 0)
                return -1;
 
        dim = isl_space_set_alloc(ctx, 0, total);
@@ -2342,15 +2573,23 @@ static int carry_dependences(isl_ctx *ctx, struct isl_sched_graph *graph)
        return compute_next_band(ctx, graph);
 }
 
-/* Are there any validity edges in the 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)
+       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;
 }
@@ -2500,7 +2739,8 @@ 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)
+       if (ctx->opt->schedule_fuse == ISL_SCHEDULE_FUSE_MIN ||
+           ctx->opt->schedule_separate_components)
                split_on_scc(graph);
 
        n_total_row = 0;
@@ -2578,6 +2818,7 @@ __isl_give isl_schedule *isl_union_set_compute_schedule(
        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_space(validity));
@@ -2596,18 +2837,25 @@ __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)
@@ -2640,7 +2888,7 @@ void *isl_schedule_free(__isl_take isl_schedule *sched)
                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);
@@ -2656,6 +2904,11 @@ isl_ctx *isl_schedule_get_ctx(__isl_keep isl_schedule *schedule)
        return schedule ? isl_space_get_ctx(schedule->dim) : NULL;
 }
 
+/* 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.
+ */
 __isl_give isl_union_map *isl_schedule_get_map(__isl_keep isl_schedule *sched)
 {
        int i;
@@ -2664,10 +2917,16 @@ __isl_give isl_union_map *isl_schedule_get_map(__isl_keep isl_schedule *sched)
        if (!sched)
                return NULL;
 
+       if (sched->band_forest)
+               return isl_band_list_get_suffix_schedule(sched->band_forest);
+
        umap = isl_union_map_empty(isl_space_copy(sched->dim));
-       for (i = 0; i < sched->n; ++i)
-               umap = isl_union_map_add_map(umap,
-                                           isl_map_copy(sched->node[i].sched));
+       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;
 }
@@ -2694,11 +2953,10 @@ static __isl_give isl_band *construct_band(__isl_keep isl_schedule *schedule,
        isl_band *band;
        unsigned start, end;
 
-       band = isl_calloc_type(ctx, isl_band);
+       band = isl_band_alloc(ctx);
        if (!band)
                return NULL;
 
-       band->ref = 1;
        band->schedule = schedule;
        band->parent = parent;
 
@@ -2733,22 +2991,24 @@ static __isl_give isl_band *construct_band(__isl_keep isl_schedule *schedule,
        for (j = 0; j < band->n; ++j)
                band->zero[j] = schedule->node[i].zero[start + j];
 
-       band->map = isl_union_map_empty(isl_space_copy(schedule->dim));
+       band->pma = isl_union_pw_multi_aff_empty(isl_space_copy(schedule->dim));
        for (i = 0; i < schedule->n; ++i) {
-               isl_map *map;
+               isl_multi_aff *ma;
+               isl_pw_multi_aff *pma;
                unsigned n_out;
 
                if (!active[i])
                        continue;
 
-               map = isl_map_copy(schedule->node[i].sched);
-               n_out = isl_map_dim(map, isl_dim_out);
-               map = isl_map_project_out(map, isl_dim_out, end, n_out - end);
-               map = isl_map_project_out(map, isl_dim_out, 0, start);
-               band->map = isl_union_map_union(band->map,
-                                               isl_union_map_from_map(map));
+               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->map)
+       if (!band->pma)
                goto error;
 
        return band;
@@ -2881,6 +3141,24 @@ __isl_give isl_band_list *isl_schedule_get_band_forest(
        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);
 
@@ -2890,7 +3168,7 @@ static __isl_give isl_printer *print_band(__isl_take isl_printer *p,
        isl_band_list *children;
 
        p = isl_printer_start_line(p);
-       p = isl_printer_print_union_map(p, band->map);
+       p = isl_printer_print_union_pw_multi_aff(p, band->pma);
        p = isl_printer_end_line(p);
 
        if (!isl_band_has_children(band))