/* * Copyright 2015 Sven Verdoolaege * * Use of this software is governed by the MIT license * * Written by Sven Verdoolaege */ #include "isl_map_private.h" #include <isl/id.h> #include <isl/schedule_node.h> #include <isl/union_set.h> #include "isl_mat_private.h" #include "isl_scheduler_clustering.h" #include "isl_scheduler_scc.h" #include "isl_seq.h" #include "isl_tarjan.h" /* Initialize the clustering data structure "c" from "graph". * * In particular, allocate memory, extract the SCCs from "graph" * into c->scc, initialize scc_cluster and construct * a band of schedule rows for each SCC. * Within each SCC, there is only one SCC by definition. * Each SCC initially belongs to a cluster containing only that SCC. */ static isl_stat clustering_init(isl_ctx *ctx, struct isl_clustering *c, struct isl_sched_graph *graph) { … } /* Free all memory allocated for "c". */ static void clustering_free(isl_ctx *ctx, struct isl_clustering *c) { … } /* Should we refrain from merging the cluster in "graph" with * any other cluster? * In particular, is its current schedule band empty and incomplete. */ static int bad_cluster(struct isl_sched_graph *graph) { … } /* Is "edge" a proximity edge with a non-empty dependence relation? */ static isl_bool is_non_empty_proximity(struct isl_sched_edge *edge) { … } /* Return the index of an edge in "graph" that can be used to merge * two clusters in "c". * Return graph->n_edge if no such edge can be found. * Return -1 on error. * * In particular, return a proximity edge between two clusters * that is not marked "no_merge" and such that neither of the * two clusters has an incomplete, empty band. * * If there are multiple such edges, then try and find the most * appropriate edge to use for merging. In particular, pick the edge * with the greatest weight. If there are multiple of those, * then pick one with the shortest distance between * the two cluster representatives. */ static int find_proximity(struct isl_sched_graph *graph, struct isl_clustering *c) { … } /* Internal data structure used in mark_merge_sccs. * * "graph" is the dependence graph in which a strongly connected * component is constructed. * "scc_cluster" maps each SCC index to the cluster to which it belongs. * "src" and "dst" are the indices of the nodes that are being merged. */ struct isl_mark_merge_sccs_data { … }; /* Check whether the cluster containing node "i" depends on the cluster * containing node "j". If "i" and "j" belong to the same cluster, * then they are taken to depend on each other to ensure that * the resulting strongly connected component consists of complete * clusters. Furthermore, if "i" and "j" are the two nodes that * are being merged, then they are taken to depend on each other as well. * Otherwise, check if there is a (conditional) validity dependence * from node[j] to node[i], forcing node[i] to follow node[j]. */ static isl_bool cluster_follows(int i, int j, void *user) { … } /* Mark all SCCs that belong to either of the two clusters in "c" * connected by the edge in "graph" with index "edge", or to any * of the intermediate clusters. * The marking is recorded in c->scc_in_merge. * * The given edge has been selected for merging two clusters, * meaning that there is at least a proximity edge between the two nodes. * However, there may also be (indirect) validity dependences * between the two nodes. When merging the two clusters, all clusters * containing one or more of the intermediate nodes along the * indirect validity dependences need to be merged in as well. * * First collect all such nodes by computing the strongly connected * component (SCC) containing the two nodes connected by the edge, where * the two nodes are considered to depend on each other to make * sure they end up in the same SCC. Similarly, each node is considered * to depend on every other node in the same cluster to ensure * that the SCC consists of complete clusters. * * Then the original SCCs that contain any of these nodes are marked * in c->scc_in_merge. */ static isl_stat mark_merge_sccs(isl_ctx *ctx, struct isl_sched_graph *graph, int edge, struct isl_clustering *c) { … } /* Construct the identifier "cluster_i". */ static __isl_give isl_id *cluster_id(isl_ctx *ctx, int i) { … } /* Construct the space of the cluster with index "i" containing * the strongly connected component "scc". * * In particular, construct a space called cluster_i with dimension equal * to the number of schedule rows in the current band of "scc". */ static __isl_give isl_space *cluster_space(struct isl_sched_graph *scc, int i) { … } /* Collect the domain of the graph for merging clusters. * * In particular, for each cluster with first SCC "i", construct * a set in the space called cluster_i with dimension equal * to the number of schedule rows in the current band of the cluster. */ static __isl_give isl_union_set *collect_domain(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_clustering *c) { … } /* Construct a map from the original instances to the corresponding * cluster instance in the current bands of the clusters in "c". */ static __isl_give isl_union_map *collect_cluster_map(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_clustering *c) { … } /* Add "umap" to the schedule constraints "sc" of all types of "edge" * that are not isl_edge_condition or isl_edge_conditional_validity. */ static __isl_give isl_schedule_constraints *add_non_conditional_constraints( struct isl_sched_edge *edge, __isl_keep isl_union_map *umap, __isl_take isl_schedule_constraints *sc) { … } /* Add schedule constraints of types isl_edge_condition and * isl_edge_conditional_validity to "sc" by applying "umap" to * the domains of the wrapped relations in domain and range * of the corresponding tagged constraints of "edge". */ static __isl_give isl_schedule_constraints *add_conditional_constraints( struct isl_sched_edge *edge, __isl_keep isl_union_map *umap, __isl_take isl_schedule_constraints *sc) { … } /* Given a mapping "cluster_map" from the original instances to * the cluster instances, add schedule constraints on the clusters * to "sc" corresponding to the original constraints represented by "edge". * * For non-tagged dependence constraints, the cluster constraints * are obtained by applying "cluster_map" to the edge->map. * * For tagged dependence constraints, "cluster_map" needs to be applied * to the domains of the wrapped relations in domain and range * of the tagged dependence constraints. Pick out the mappings * from these domains from "cluster_map" and construct their product. * This mapping can then be applied to the pair of domains. */ static __isl_give isl_schedule_constraints *collect_edge_constraints( struct isl_sched_edge *edge, __isl_keep isl_union_map *cluster_map, __isl_take isl_schedule_constraints *sc) { … } /* Given a mapping "cluster_map" from the original instances to * the cluster instances, add schedule constraints on the clusters * to "sc" corresponding to all edges in "graph" between nodes that * belong to SCCs that are marked for merging in "scc_in_merge". */ static __isl_give isl_schedule_constraints *collect_constraints( struct isl_sched_graph *graph, int *scc_in_merge, __isl_keep isl_union_map *cluster_map, __isl_take isl_schedule_constraints *sc) { … } /* Construct a dependence graph for scheduling clusters with respect * to each other and store the result in "merge_graph". * In particular, the nodes of the graph correspond to the schedule * dimensions of the current bands of those clusters that have been * marked for merging in "c". * * First construct an isl_schedule_constraints object for this domain * by transforming the edges in "graph" to the domain. * Then initialize a dependence graph for scheduling from these * constraints. */ static isl_stat init_merge_graph(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_clustering *c, struct isl_sched_graph *merge_graph) { … } /* Compute the maximal number of remaining schedule rows that still need * to be computed for the nodes that belong to clusters with the maximal * dimension for the current band (i.e., the band that is to be merged). * Only clusters that are about to be merged are considered. * "maxvar" is the maximal dimension for the current band. * "c" contains information about the clusters. * * Return the maximal number of remaining schedule rows or * isl_size_error on error. */ static isl_size compute_maxvar_max_slack(int maxvar, struct isl_clustering *c) { … } /* If there are any clusters where the dimension of the current band * (i.e., the band that is to be merged) is smaller than "maxvar" and * if there are any nodes in such a cluster where the number * of remaining schedule rows that still need to be computed * is greater than "max_slack", then return the smallest current band * dimension of all these clusters. Otherwise return the original value * of "maxvar". Return isl_size_error in case of any error. * Only clusters that are about to be merged are considered. * "c" contains information about the clusters. */ static isl_size limit_maxvar_to_slack(int maxvar, int max_slack, struct isl_clustering *c) { … } /* Adjust merge_graph->maxvar based on the number of remaining schedule rows * that still need to be computed. In particular, if there is a node * in a cluster where the dimension of the current band is smaller * than merge_graph->maxvar, but the number of remaining schedule rows * is greater than that of any node in a cluster with the maximal * dimension for the current band (i.e., merge_graph->maxvar), * then adjust merge_graph->maxvar to the (smallest) current band dimension * of those clusters. Without this adjustment, the total number of * schedule dimensions would be increased, resulting in a skewed view * of the number of coincident dimensions. * "c" contains information about the clusters. * * If the maximize_band_depth option is set and merge_graph->maxvar is reduced, * then there is no point in attempting any merge since it will be rejected * anyway. Set merge_graph->maxvar to zero in such cases. */ static isl_stat adjust_maxvar_to_slack(isl_ctx *ctx, struct isl_sched_graph *merge_graph, struct isl_clustering *c) { … } /* Return the number of coincident dimensions in the current band of "graph", * where the nodes of "graph" are assumed to be scheduled by a single band. */ static int get_n_coincident(struct isl_sched_graph *graph) { … } /* Should the clusters be merged based on the cluster schedule * in the current (and only) band of "merge_graph", given that * coincidence should be maximized? * * If the number of coincident schedule dimensions in the merged band * would be less than the maximal number of coincident schedule dimensions * in any of the merged clusters, then the clusters should not be merged. */ static isl_bool ok_to_merge_coincident(struct isl_clustering *c, struct isl_sched_graph *merge_graph) { … } /* Return the transformation on "node" expressed by the current (and only) * band of "merge_graph" applied to the clusters in "c". * * First find the representation of "node" in its SCC in "c" and * extract the transformation expressed by the current band. * Then extract the transformation applied by "merge_graph" * to the cluster to which this SCC belongs. * Combine the two to obtain the complete transformation on the node. * * Note that the range of the first transformation is an anonymous space, * while the domain of the second is named "cluster_X". The range * of the former therefore needs to be adjusted before the two * can be combined. */ static __isl_give isl_map *extract_node_transformation(isl_ctx *ctx, struct isl_sched_node *node, struct isl_clustering *c, struct isl_sched_graph *merge_graph) { … } /* Give a set of distances "set", are they bounded by a small constant * in direction "pos"? * In practice, check if they are bounded by 2 by checking that there * are no elements with a value greater than or equal to 3 or * smaller than or equal to -3. */ static isl_bool distance_is_bounded(__isl_keep isl_set *set, int pos) { … } /* Does the set "set" have a fixed (but possible parametric) value * at dimension "pos"? */ static isl_bool has_single_value(__isl_keep isl_set *set, int pos) { … } /* Does "map" have a fixed (but possible parametric) value * at dimension "pos" of either its domain or its range? */ static isl_bool has_singular_src_or_dst(__isl_keep isl_map *map, int pos) { … } /* Does the edge "edge" from "graph" have bounded dependence distances * in the merged graph "merge_graph" of a selection of clusters in "c"? * * Extract the complete transformations of the source and destination * nodes of the edge, apply them to the edge constraints and * compute the differences. Finally, check if these differences are bounded * in each direction. * * If the dimension of the band is greater than the number of * dimensions that can be expected to be optimized by the edge * (based on its weight), then also allow the differences to be unbounded * in the remaining dimensions, but only if either the source or * the destination has a fixed value in that direction. * This allows a statement that produces values that are used by * several instances of another statement to be merged with that * other statement. * However, merging such clusters will introduce an inherently * large proximity distance inside the merged cluster, meaning * that proximity distances will no longer be optimized in * subsequent merges. These merges are therefore only allowed * after all other possible merges have been tried. * The first time such a merge is encountered, the weight of the edge * is replaced by a negative weight. The second time (i.e., after * all merges over edges with a non-negative weight have been tried), * the merge is allowed. */ static isl_bool has_bounded_distances(isl_ctx *ctx, struct isl_sched_edge *edge, struct isl_sched_graph *graph, struct isl_clustering *c, struct isl_sched_graph *merge_graph) { … } /* Should the clusters be merged based on the cluster schedule * in the current (and only) band of "merge_graph"? * "graph" is the original dependence graph, while "c" records * which SCCs are involved in the latest merge. * * In particular, is there at least one proximity constraint * that is optimized by the merge? * * A proximity constraint is considered to be optimized * if the dependence distances are small. */ static isl_bool ok_to_merge_proximity(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_clustering *c, struct isl_sched_graph *merge_graph) { … } /* Should the clusters be merged based on the cluster schedule * in the current (and only) band of "merge_graph"? * "graph" is the original dependence graph, while "c" records * which SCCs are involved in the latest merge. * * If the current band is empty, then the clusters should not be merged. * * If the band depth should be maximized and the merge schedule * is incomplete (meaning that the dimension of some of the schedule * bands in the original schedule will be reduced), then the clusters * should not be merged. * * If the schedule_maximize_coincidence option is set, then check that * the number of coincident schedule dimensions is not reduced. * * Finally, only allow the merge if at least one proximity * constraint is optimized. */ static isl_bool ok_to_merge(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_clustering *c, struct isl_sched_graph *merge_graph) { … } /* Apply the schedule in "t_node" to the "n" rows starting at "first" * of the schedule in "node" and return the result. * * That is, essentially compute * * T * N(first:first+n-1) * * taking into account the constant term and the parameter coefficients * in "t_node". */ static __isl_give isl_mat *node_transformation(isl_ctx *ctx, struct isl_sched_node *t_node, struct isl_sched_node *node, int first, int n) { … } /* Apply the cluster schedule in "t_node" to the current band * schedule of the nodes in "graph". * * In particular, replace the rows starting at band_start * by the result of applying the cluster schedule in "t_node" * to the original rows. * * The coincidence of the schedule is determined by the coincidence * of the cluster schedule. */ static isl_stat transform(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_sched_node *t_node) { … } /* Merge the clusters marked for merging in "c" into a single * cluster using the cluster schedule in the current band of "merge_graph". * The representative SCC for the new cluster is the SCC with * the smallest index. * * The current band schedule of each SCC in the new cluster is obtained * by applying the schedule of the corresponding original cluster * to the original band schedule. * All SCCs in the new cluster have the same number of schedule rows. */ static isl_stat merge(isl_ctx *ctx, struct isl_clustering *c, struct isl_sched_graph *merge_graph) { … } /* Try and merge the clusters of SCCs marked in c->scc_in_merge * by scheduling the current cluster bands with respect to each other. * * Construct a dependence graph with a space for each cluster and * with the coordinates of each space corresponding to the schedule * dimensions of the current band of that cluster. * Construct a cluster schedule in this cluster dependence graph and * apply it to the current cluster bands if it is applicable * according to ok_to_merge. * * If the number of remaining schedule dimensions in a cluster * with a non-maximal current schedule dimension is greater than * the number of remaining schedule dimensions in clusters * with a maximal current schedule dimension, then restrict * the number of rows to be computed in the cluster schedule * to the minimal such non-maximal current schedule dimension. * Do this by adjusting merge_graph.maxvar. * * Return isl_bool_true if the clusters have effectively been merged * into a single cluster. * * Note that since the standard scheduling algorithm minimizes the maximal * distance over proximity constraints, the proximity constraints between * the merged clusters may not be optimized any further than what is * sufficient to bring the distances within the limits of the internal * proximity constraints inside the individual clusters. * It may therefore make sense to perform an additional translation step * to bring the clusters closer to each other, while maintaining * the linear part of the merging schedule found using the standard * scheduling algorithm. */ static isl_bool try_merge(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_clustering *c) { … } /* Is there any edge marked "no_merge" between two SCCs that are * about to be merged (i.e., that are set in "scc_in_merge")? * "merge_edge" is the proximity edge along which the clusters of SCCs * are going to be merged. * * If there is any edge between two SCCs with a negative weight, * while the weight of "merge_edge" is non-negative, then this * means that the edge was postponed. "merge_edge" should then * also be postponed since merging along the edge with negative weight should * be postponed until all edges with non-negative weight have been tried. * Replace the weight of "merge_edge" by a negative weight as well and * tell the caller not to attempt a merge. */ static int any_no_merge(struct isl_sched_graph *graph, int *scc_in_merge, struct isl_sched_edge *merge_edge) { … } /* Merge the two clusters in "c" connected by the edge in "graph" * with index "edge" into a single cluster. * If it turns out to be impossible to merge these two clusters, * then mark the edge as "no_merge" such that it will not be * considered again. * * First mark all SCCs that need to be merged. This includes the SCCs * in the two clusters, but it may also include the SCCs * of intermediate clusters. * If there is already a no_merge edge between any pair of such SCCs, * then simply mark the current edge as no_merge as well. * Likewise, if any of those edges was postponed by has_bounded_distances, * then postpone the current edge as well. * Otherwise, try and merge the clusters and mark "edge" as "no_merge" * if the clusters did not end up getting merged, unless the non-merge * is due to the fact that the edge was postponed. This postponement * can be recognized by a change in weight (from non-negative to negative). */ static isl_stat merge_clusters_along_edge(isl_ctx *ctx, struct isl_sched_graph *graph, int edge, struct isl_clustering *c) { … } /* Does "node" belong to the cluster identified by "cluster"? */ static int node_cluster_exactly(struct isl_sched_node *node, int cluster) { … } /* Does "edge" connect two nodes belonging to the cluster * identified by "cluster"? */ static int edge_cluster_exactly(struct isl_sched_edge *edge, int cluster) { … } /* Swap the schedule of "node1" and "node2". * Both nodes have been derived from the same node in a common parent graph. * Since the "coincident" field is shared with that node * in the parent graph, there is no need to also swap this field. */ static void swap_sched(struct isl_sched_node *node1, struct isl_sched_node *node2) { … } /* Copy the current band schedule from the SCCs that form the cluster * with index "pos" to the actual cluster at position "pos". * By construction, the index of the first SCC that belongs to the cluster * is also "pos". * * The order of the nodes inside both the SCCs and the cluster * is assumed to be same as the order in the original "graph". * * Since the SCC graphs will no longer be used after this function, * the schedules are actually swapped rather than copied. */ static isl_stat copy_partial(struct isl_sched_graph *graph, struct isl_clustering *c, int pos) { … } /* Is there a (conditional) validity dependence from node[j] to node[i], * forcing node[i] to follow node[j] or do the nodes belong to the same * cluster? */ static isl_bool node_follows_strong_or_same_cluster(int i, int j, void *user) { … } /* Extract the merged clusters of SCCs in "graph", sort them, and * store them in c->clusters. Update c->scc_cluster accordingly. * * First keep track of the cluster containing the SCC to which a node * belongs in the node itself. * Then extract the clusters into c->clusters, copying the current * band schedule from the SCCs that belong to the cluster. * Do this only once per cluster. * * Finally, topologically sort the clusters and update c->scc_cluster * to match the new scc numbering. While the SCCs were originally * sorted already, some SCCs that depend on some other SCCs may * have been merged with SCCs that appear before these other SCCs. * A reordering may therefore be required. */ static isl_stat extract_clusters(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_clustering *c) { … } /* Compute weights on the proximity edges of "graph" that can * be used by find_proximity to find the most appropriate * proximity edge to use to merge two clusters in "c". * The weights are also used by has_bounded_distances to determine * whether the merge should be allowed. * Store the maximum of the computed weights in graph->max_weight. * * The computed weight is a measure for the number of remaining schedule * dimensions that can still be completely aligned. * In particular, compute the number of equalities between * input dimensions and output dimensions in the proximity constraints. * The directions that are already handled by outer schedule bands * are projected out prior to determining this number. * * Edges that will never be considered by find_proximity are ignored. */ static isl_stat compute_weights(struct isl_sched_graph *graph, struct isl_clustering *c) { … } /* Call isl_schedule_node_compute_finish_band on each of the clusters in "c" and * update "node" to arrange for them to be executed in an order * possibly involving set nodes that generalizes the topological order * determined by the scc fields of the nodes in "graph". * * Note that at this stage, there are graph->scc clusters and * their positions in c->cluster are determined by the values * of c->scc_cluster. * * Construct an isl_scc_graph and perform the decomposition * using this graph. */ static __isl_give isl_schedule_node *finish_bands_decompose( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph, struct isl_clustering *c) { … } /* Call isl_schedule_node_compute_finish_band on each of the clusters in "c" * in their topological order. This order is determined by the scc * fields of the nodes in "graph". * Combine the results in a sequence expressing the topological order. * * If there is only one cluster left, then there is no need to introduce * a sequence node. Also, in this case, the cluster necessarily contains * the SCC at position 0 in the original graph and is therefore also * stored in the first cluster of "c". * * If there are more than two clusters left, then some subsets of the clusters * may still be independent of each other. These could then still * be reordered with respect to each other. Call finish_bands_decompose * to try and construct an ordering involving set and sequence nodes * that generalizes the topological order. * Note that at the outermost level there can be no independent components * because isl_schedule_node_compute_wcc_clustering is called * on a (weakly) connected component. */ static __isl_give isl_schedule_node *finish_bands_clustering( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph, struct isl_clustering *c) { … } /* Compute a schedule for a connected dependence graph by first considering * each strongly connected component (SCC) in the graph separately and then * incrementally combining them into clusters. * Return the updated schedule node. * * Initially, each cluster consists of a single SCC, each with its * own band schedule. The algorithm then tries to merge pairs * of clusters along a proximity edge until no more suitable * proximity edges can be found. During this merging, the schedule * is maintained in the individual SCCs. * After the merging is completed, the full resulting clusters * are extracted and in finish_bands_clustering, * isl_schedule_node_compute_finish_band is called on each of them to integrate * the band into "node" and to continue the computation. * * compute_weights initializes the weights that are used by find_proximity. */ __isl_give isl_schedule_node *isl_schedule_node_compute_wcc_clustering( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph) { … }
Codebase Browser
llvm