/* * Copyright 2011 INRIA Saclay * Copyright 2012-2014 Ecole Normale Superieure * Copyright 2015-2016 Sven Verdoolaege * Copyright 2016 INRIA Paris * * Use of this software is governed by the MIT license * * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France, * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod, * 91893 Orsay, France * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12, * CS 42112, 75589 Paris Cedex 12, France */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include /* * The scheduling algorithm implemented in this file was inspired by * Bondhugula et al., "Automatic Transformations for Communication-Minimized * Parallelization and Locality Optimization in the Polyhedral Model". */ /* Internal information about a node that is used during the construction * of a schedule. * space represents the space in which the domain lives * sched is a matrix representation of the schedule being constructed * for this node; if compressed is set, then this schedule is * defined over the compressed domain space * sched_map is an isl_map representation of the same (partial) schedule * sched_map may be NULL; if compressed is set, then this map * is defined over the uncompressed domain space * rank is the number of linearly independent rows in the linear part * of sched * the columns of cmap represent a change of basis for the schedule * coefficients; the first rank columns span the linear part of * the schedule rows * cinv is the inverse of cmap. * ctrans is the transpose of cmap. * start is the first variable in the LP problem in the sequences that * represents the schedule coefficients of this node * nvar is the dimension of the domain * nparam is the number of parameters or 0 if we are not constructing * a parametric schedule * * If compressed is set, then hull represents the constraints * that were used to derive the compression, while compress and * decompress map the original space to the compressed space and * vice versa. * * scc is the index of SCC (or WCC) this node belongs to * * "cluster" is only used inside extract_clusters and identifies * the cluster of SCCs that the node belongs to. * * coincident contains a boolean for each of the rows of the schedule, * indicating whether the corresponding scheduling dimension satisfies * the coincidence constraints in the sense that the corresponding * dependence distances are zero. * * If the schedule_treat_coalescing option is set, then * "sizes" contains the sizes of the (compressed) instance set * in each direction. If there is no fixed size in a given direction, * then the corresponding size value is set to infinity. * If the schedule_treat_coalescing option or the schedule_max_coefficient * option is set, then "max" contains the maximal values for * schedule coefficients of the (compressed) variables. If no bound * needs to be imposed on a particular variable, then the corresponding * value is negative. */ struct isl_sched_node { isl_space *space; int compressed; isl_set *hull; isl_multi_aff *compress; isl_multi_aff *decompress; isl_mat *sched; isl_map *sched_map; int rank; isl_mat *cmap; isl_mat *cinv; isl_mat *ctrans; int start; int nvar; int nparam; int scc; int cluster; int *coincident; isl_multi_val *sizes; isl_vec *max; }; static int node_has_space(const void *entry, const void *val) { struct isl_sched_node *node = (struct isl_sched_node *)entry; isl_space *dim = (isl_space *)val; return isl_space_is_equal(node->space, dim); } static int node_scc_exactly(struct isl_sched_node *node, int scc) { return node->scc == scc; } static int node_scc_at_most(struct isl_sched_node *node, int scc) { return node->scc <= scc; } static int node_scc_at_least(struct isl_sched_node *node, int scc) { return node->scc >= scc; } /* An edge in the dependence graph. An edge may be used to * ensure validity of the generated schedule, to minimize the dependence * distance or both * * map is the dependence relation, with i -> j in the map if j depends on i * tagged_condition and tagged_validity contain the union of all tagged * condition or conditional validity dependence relations that * specialize the dependence relation "map"; that is, * if (i -> a) -> (j -> b) is an element of "tagged_condition" * or "tagged_validity", then i -> j is an element of "map". * If these fields are NULL, then they represent the empty relation. * src is the source node * dst is the sink node * * types is a bit vector containing the types of this edge. * validity is set if the edge is used to ensure correctness * coincidence is used to enforce zero dependence distances * proximity is set if the edge is used to minimize dependence distances * condition is set if the edge represents a condition * for a conditional validity schedule constraint * local can only be set for condition edges and indicates that * the dependence distance over the edge should be zero * conditional_validity is set if the edge is used to conditionally * ensure correctness * * For validity edges, start and end mark the sequence of inequality * constraints in the LP problem that encode the validity constraint * corresponding to this edge. * * During clustering, an edge may be marked "no_merge" if it should * not be used to merge clusters. * The weight is also only used during clustering and it is * an indication of how many schedule dimensions on either side * of the schedule constraints can be aligned. * If the weight is negative, then this means that this edge was postponed * by has_bounded_distances or any_no_merge. The original weight can * be retrieved by adding 1 + graph->max_weight, with "graph" * the graph containing this edge. */ struct isl_sched_edge { isl_map *map; isl_union_map *tagged_condition; isl_union_map *tagged_validity; struct isl_sched_node *src; struct isl_sched_node *dst; unsigned types; int start; int end; int no_merge; int weight; }; /* Is "edge" marked as being of type "type"? */ static int is_type(struct isl_sched_edge *edge, enum isl_edge_type type) { return ISL_FL_ISSET(edge->types, 1 << type); } /* Mark "edge" as being of type "type". */ static void set_type(struct isl_sched_edge *edge, enum isl_edge_type type) { ISL_FL_SET(edge->types, 1 << type); } /* No longer mark "edge" as being of type "type"? */ static void clear_type(struct isl_sched_edge *edge, enum isl_edge_type type) { ISL_FL_CLR(edge->types, 1 << type); } /* Is "edge" marked as a validity edge? */ static int is_validity(struct isl_sched_edge *edge) { return is_type(edge, isl_edge_validity); } /* Mark "edge" as a validity edge. */ static void set_validity(struct isl_sched_edge *edge) { set_type(edge, isl_edge_validity); } /* Is "edge" marked as a proximity edge? */ static int is_proximity(struct isl_sched_edge *edge) { return is_type(edge, isl_edge_proximity); } /* Is "edge" marked as a local edge? */ static int is_local(struct isl_sched_edge *edge) { return is_type(edge, isl_edge_local); } /* Mark "edge" as a local edge. */ static void set_local(struct isl_sched_edge *edge) { set_type(edge, isl_edge_local); } /* No longer mark "edge" as a local edge. */ static void clear_local(struct isl_sched_edge *edge) { clear_type(edge, isl_edge_local); } /* Is "edge" marked as a coincidence edge? */ static int is_coincidence(struct isl_sched_edge *edge) { return is_type(edge, isl_edge_coincidence); } /* Is "edge" marked as a condition edge? */ static int is_condition(struct isl_sched_edge *edge) { return is_type(edge, isl_edge_condition); } /* Is "edge" marked as a conditional validity edge? */ static int is_conditional_validity(struct isl_sched_edge *edge) { return is_type(edge, isl_edge_conditional_validity); } /* Internal information about the dependence graph used during * the construction of the schedule. * * intra_hmap is a cache, mapping dependence relations to their dual, * for dependences from a node to itself * inter_hmap is a cache, mapping dependence relations to their dual, * for dependences between distinct nodes * if compression is involved then the key for these maps * is the original, uncompressed dependence relation, while * the value is the dual of the compressed dependence relation. * * 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 * band_start is the starting row in the node schedules of the current band * root is set if this graph is the original dependence graph, * without any splitting * * sorted contains a list of node indices sorted according to the * SCC to which a node belongs * * 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; 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 one of the * sets of dependences; however, for each type there is only * a single edge between a given pair of source and sink space * in the entire graph * * node_table contains pointers into the node array, hashed on the space * * region contains a list of variable sequences that should be non-trivial * * lp contains the (I)LP problem used to obtain new schedule rows * * src_scc and dst_scc are the source and sink SCCs of an edge with * conflicting constraints * * scc represents the number of components * weak is set if the components are weakly connected * * max_weight is used during clustering and represents the maximal * weight of the relevant proximity edges. */ struct isl_sched_graph { isl_map_to_basic_set *intra_hmap; isl_map_to_basic_set *inter_hmap; struct isl_sched_node *node; int n; int maxvar; int max_row; int n_row; int *sorted; int n_total_row; int band_start; int root; struct isl_sched_edge *edge; int n_edge; 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; isl_basic_set *lp; int src_scc; int dst_scc; int scc; int weak; int max_weight; }; /* Initialize node_table based on the list of nodes. */ static int graph_init_table(isl_ctx *ctx, struct isl_sched_graph *graph) { int i; graph->node_table = isl_hash_table_alloc(ctx, graph->n); if (!graph->node_table) return -1; for (i = 0; i < graph->n; ++i) { struct isl_hash_table_entry *entry; uint32_t hash; hash = isl_space_get_hash(graph->node[i].space); entry = isl_hash_table_find(ctx, graph->node_table, hash, &node_has_space, graph->node[i].space, 1); if (!entry) return -1; entry->data = &graph->node[i]; } return 0; } /* Return a pointer to the node that lives within the given space, * 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_space *dim) { struct isl_hash_table_entry *entry; uint32_t hash; hash = isl_space_get_hash(dim); entry = isl_hash_table_find(ctx, graph->node_table, hash, &node_has_space, dim, 0); return entry ? entry->data : NULL; } static int edge_has_src_and_dst(const void *entry, const void *val) { const struct isl_sched_edge *edge = entry; const struct isl_sched_edge *temp = val; return edge->src == temp->src && edge->dst == temp->dst; } /* Add the given edge to graph->edge_table[type]. */ static isl_stat graph_edge_table_add(isl_ctx *ctx, struct isl_sched_graph *graph, enum isl_edge_type type, struct isl_sched_edge *edge) { struct isl_hash_table_entry *entry; uint32_t hash; 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 isl_stat_error; entry->data = edge; return isl_stat_ok; } /* 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; 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; } return 0; } /* 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 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->space); uint32_t hash; struct isl_sched_edge temp = { .src = src, .dst = dst }; hash = isl_hash_init(); hash = isl_hash_builtin(hash, temp.src); hash = isl_hash_builtin(hash, temp.dst); 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 given type * between the given two nodes. */ static isl_bool 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; isl_bool empty; edge = graph_find_edge(graph, type, src, dst); if (!edge) return 0; empty = isl_map_plain_is_empty(edge->map); if (empty < 0) return isl_bool_error; return !empty; } /* Look for any edge with the same src, dst and map fields as "model". * * Return the matching edge if one can be found. * Return "model" if no matching edge is found. * Return NULL on error. */ static struct isl_sched_edge *graph_find_matching_edge( struct isl_sched_graph *graph, struct isl_sched_edge *model) { enum isl_edge_type i; struct isl_sched_edge *edge; for (i = isl_edge_first; i <= isl_edge_last; ++i) { int is_equal; edge = graph_find_edge(graph, i, model->src, model->dst); if (!edge) continue; is_equal = isl_map_plain_is_equal(model->map, edge->map); if (is_equal < 0) return NULL; if (is_equal) return edge; } return model; } /* 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 isl_bool graph_has_any_edge(struct isl_sched_graph *graph, struct isl_sched_node *src, struct isl_sched_node *dst) { enum isl_edge_type i; isl_bool 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. * * Conditional validity edges are essentially validity edges that * can be ignored if the corresponding condition edges are iteration private. * Here, we are only checking for the presence of validity * edges, so we need to consider the conditional validity edges too. * In particular, this function is used during the detection * of strongly connected components and we cannot ignore * conditional validity edges during this detection. */ static isl_bool graph_has_validity_edge(struct isl_sched_graph *graph, struct isl_sched_node *src, struct isl_sched_node *dst) { isl_bool r; r = graph_has_edge(graph, isl_edge_validity, src, dst); if (r < 0 || r) return r; return graph_has_edge(graph, isl_edge_conditional_validity, src, dst); } static int graph_alloc(isl_ctx *ctx, struct isl_sched_graph *graph, int n_node, int n_edge) { int i; graph->n = n_node; graph->n_edge = n_edge; 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->edge = isl_calloc_array(ctx, struct isl_sched_edge, graph->n_edge); graph->intra_hmap = isl_map_to_basic_set_alloc(ctx, 2 * n_edge); graph->inter_hmap = isl_map_to_basic_set_alloc(ctx, 2 * n_edge); if (!graph->node || !graph->region || (graph->n_edge && !graph->edge) || !graph->sorted) return -1; for(i = 0; i < graph->n; ++i) graph->sorted[i] = i; return 0; } static void graph_free(isl_ctx *ctx, struct isl_sched_graph *graph) { int i; isl_map_to_basic_set_free(graph->intra_hmap); isl_map_to_basic_set_free(graph->inter_hmap); if (graph->node) for (i = 0; i < graph->n; ++i) { isl_space_free(graph->node[i].space); isl_set_free(graph->node[i].hull); isl_multi_aff_free(graph->node[i].compress); isl_multi_aff_free(graph->node[i].decompress); isl_mat_free(graph->node[i].sched); isl_map_free(graph->node[i].sched_map); isl_mat_free(graph->node[i].cmap); isl_mat_free(graph->node[i].cinv); isl_mat_free(graph->node[i].ctrans); if (graph->root) free(graph->node[i].coincident); isl_multi_val_free(graph->node[i].sizes); isl_vec_free(graph->node[i].max); } free(graph->node); free(graph->sorted); if (graph->edge) for (i = 0; i < graph->n_edge; ++i) { isl_map_free(graph->edge[i].map); isl_union_map_free(graph->edge[i].tagged_condition); isl_union_map_free(graph->edge[i].tagged_validity); } free(graph->edge); free(graph->region); 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 isl_stat 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 isl_stat_ok; } /* Compute the number of rows that should be allocated for the schedule. * In particular, we need one row for each variable or one row * for each basic map in the dependences. * Note that it is practically impossible to exhaust both * the number of dependences and the number of variables. */ static isl_stat compute_max_row(struct isl_sched_graph *graph, __isl_keep isl_schedule_constraints *sc) { int n_edge; isl_stat r; isl_union_set *domain; graph->n = 0; graph->maxvar = 0; domain = isl_schedule_constraints_get_domain(sc); r = isl_union_set_foreach_set(domain, &init_n_maxvar, graph); isl_union_set_free(domain); if (r < 0) return isl_stat_error; n_edge = isl_schedule_constraints_n_basic_map(sc); if (n_edge < 0) return isl_stat_error; graph->max_row = n_edge + graph->maxvar; return isl_stat_ok; } /* Does "bset" have any defining equalities for its set variables? */ static int has_any_defining_equality(__isl_keep isl_basic_set *bset) { int i, n; if (!bset) return -1; n = isl_basic_set_dim(bset, isl_dim_set); for (i = 0; i < n; ++i) { int has; has = isl_basic_set_has_defining_equality(bset, isl_dim_set, i, NULL); if (has < 0 || has) return has; } return 0; } /* Set the entries of node->max to the value of the schedule_max_coefficient * option, if set. */ static isl_stat set_max_coefficient(isl_ctx *ctx, struct isl_sched_node *node) { int max; max = isl_options_get_schedule_max_coefficient(ctx); if (max == -1) return isl_stat_ok; node->max = isl_vec_alloc(ctx, node->nvar); node->max = isl_vec_set_si(node->max, max); if (!node->max) return isl_stat_error; return isl_stat_ok; } /* Set the entries of node->max to the minimum of the schedule_max_coefficient * option (if set) and half of the minimum of the sizes in the other * dimensions. If the minimum of the sizes is one, half of the size * is zero and this value is reset to one. * If the global minimum is unbounded (i.e., if both * the schedule_max_coefficient is not set and the sizes in the other * dimensions are unbounded), then store a negative value. * If the schedule coefficient is close to the size of the instance set * in another dimension, then the schedule may represent a loop * coalescing transformation (especially if the coefficient * in that other dimension is one). Forcing the coefficient to be * smaller than or equal to half the minimal size should avoid this * situation. */ static isl_stat compute_max_coefficient(isl_ctx *ctx, struct isl_sched_node *node) { int max; int i, j; isl_vec *v; max = isl_options_get_schedule_max_coefficient(ctx); v = isl_vec_alloc(ctx, node->nvar); if (!v) return isl_stat_error; for (i = 0; i < node->nvar; ++i) { isl_int_set_si(v->el[i], max); isl_int_mul_si(v->el[i], v->el[i], 2); } for (i = 0; i < node->nvar; ++i) { isl_val *size; size = isl_multi_val_get_val(node->sizes, i); if (!size) goto error; if (!isl_val_is_int(size)) { isl_val_free(size); continue; } for (j = 0; j < node->nvar; ++j) { if (j == i) continue; if (isl_int_is_neg(v->el[j]) || isl_int_gt(v->el[j], size->n)) isl_int_set(v->el[j], size->n); } isl_val_free(size); } for (i = 0; i < node->nvar; ++i) { isl_int_fdiv_q_ui(v->el[i], v->el[i], 2); if (isl_int_is_zero(v->el[i])) isl_int_set_si(v->el[i], 1); } node->max = v; return isl_stat_ok; error: isl_vec_free(v); return isl_stat_error; } /* Compute and return the size of "set" in dimension "dim". * The size is taken to be the difference in values for that variable * for fixed values of the other variables. * In particular, the variable is first isolated from the other variables * in the range of a map * * [i_0, ..., i_dim-1, i_dim+1, ...] -> [i_dim] * * and then duplicated * * [i_0, ..., i_dim-1, i_dim+1, ...] -> [[i_dim] -> [i_dim']] * * The shared variables are then projected out and the maximal value * of i_dim' - i_dim is computed. */ static __isl_give isl_val *compute_size(__isl_take isl_set *set, int dim) { isl_map *map; isl_local_space *ls; isl_aff *obj; isl_val *v; map = isl_set_project_onto_map(set, isl_dim_set, dim, 1); map = isl_map_project_out(map, isl_dim_in, dim, 1); map = isl_map_range_product(map, isl_map_copy(map)); map = isl_set_unwrap(isl_map_range(map)); set = isl_map_deltas(map); ls = isl_local_space_from_space(isl_set_get_space(set)); obj = isl_aff_var_on_domain(ls, isl_dim_set, 0); v = isl_set_max_val(set, obj); isl_aff_free(obj); isl_set_free(set); return v; } /* Compute the size of the instance set "set" of "node", after compression, * as well as bounds on the corresponding coefficients, if needed. * * The sizes are needed when the schedule_treat_coalescing option is set. * The bounds are needed when the schedule_treat_coalescing option or * the schedule_max_coefficient option is set. * * If the schedule_treat_coalescing option is not set, then at most * the bounds need to be set and this is done in set_max_coefficient. * Otherwise, compress the domain if needed, compute the size * in each direction and store the results in node->size. * Finally, set the bounds on the coefficients based on the sizes * and the schedule_max_coefficient option in compute_max_coefficient. */ static isl_stat compute_sizes_and_max(isl_ctx *ctx, struct isl_sched_node *node, __isl_take isl_set *set) { int j, n; isl_multi_val *mv; if (!isl_options_get_schedule_treat_coalescing(ctx)) { isl_set_free(set); return set_max_coefficient(ctx, node); } if (node->compressed) set = isl_set_preimage_multi_aff(set, isl_multi_aff_copy(node->decompress)); mv = isl_multi_val_zero(isl_set_get_space(set)); n = isl_set_dim(set, isl_dim_set); for (j = 0; j < n; ++j) { isl_val *v; v = compute_size(isl_set_copy(set), j); mv = isl_multi_val_set_val(mv, j, v); } node->sizes = mv; isl_set_free(set); if (!node->sizes) return isl_stat_error; return compute_max_coefficient(ctx, node); } /* Add a new node to the graph representing the given instance set. * "nvar" is the (possibly compressed) number of variables and * may be smaller than then number of set variables in "set" * if "compressed" is set. * If "compressed" is set, then "hull" represents the constraints * that were used to derive the compression, while "compress" and * "decompress" map the original space to the compressed space and * vice versa. * If "compressed" is not set, then "hull", "compress" and "decompress" * should be NULL. * * Compute the size of the instance set and bounds on the coefficients, * if needed. */ static isl_stat add_node(struct isl_sched_graph *graph, __isl_take isl_set *set, int nvar, int compressed, __isl_take isl_set *hull, __isl_take isl_multi_aff *compress, __isl_take isl_multi_aff *decompress) { int nparam; isl_ctx *ctx; isl_mat *sched; isl_space *space; int *coincident; struct isl_sched_node *node; if (!set) return isl_stat_error; ctx = isl_set_get_ctx(set); nparam = isl_set_dim(set, isl_dim_param); if (!ctx->opt->schedule_parametric) nparam = 0; sched = isl_mat_alloc(ctx, 0, 1 + nparam + nvar); node = &graph->node[graph->n]; graph->n++; space = isl_set_get_space(set); node->space = space; node->nvar = nvar; node->nparam = nparam; node->sched = sched; node->sched_map = NULL; coincident = isl_calloc_array(ctx, int, graph->max_row); node->coincident = coincident; node->compressed = compressed; node->hull = hull; node->compress = compress; node->decompress = decompress; if (compute_sizes_and_max(ctx, node, set) < 0) return isl_stat_error; if (!space || !sched || (graph->max_row && !coincident)) return isl_stat_error; if (compressed && (!hull || !compress || !decompress)) return isl_stat_error; return isl_stat_ok; } /* Add a new node to the graph representing the given set. * * If any of the set variables is defined by an equality, then * we perform variable compression such that we can perform * the scheduling on the compressed domain. */ static isl_stat extract_node(__isl_take isl_set *set, void *user) { int nvar; int has_equality; isl_basic_set *hull; isl_set *hull_set; isl_morph *morph; isl_multi_aff *compress, *decompress; struct isl_sched_graph *graph = user; hull = isl_set_affine_hull(isl_set_copy(set)); hull = isl_basic_set_remove_divs(hull); nvar = isl_set_dim(set, isl_dim_set); has_equality = has_any_defining_equality(hull); if (has_equality < 0) goto error; if (!has_equality) { isl_basic_set_free(hull); return add_node(graph, set, nvar, 0, NULL, NULL, NULL); } morph = isl_basic_set_variable_compression(hull, isl_dim_set); nvar = isl_morph_ran_dim(morph, isl_dim_set); compress = isl_morph_get_var_multi_aff(morph); morph = isl_morph_inverse(morph); decompress = isl_morph_get_var_multi_aff(morph); isl_morph_free(morph); hull_set = isl_set_from_basic_set(hull); return add_node(graph, set, nvar, 1, hull_set, compress, decompress); error: isl_basic_set_free(hull); isl_set_free(set); return isl_stat_error; } struct isl_extract_edge_data { enum isl_edge_type type; struct isl_sched_graph *graph; }; /* Merge edge2 into edge1, freeing the contents of edge2. * Return 0 on success and -1 on failure. * * edge1 and edge2 are assumed to have the same value for the map field. */ static int merge_edge(struct isl_sched_edge *edge1, struct isl_sched_edge *edge2) { edge1->types |= edge2->types; isl_map_free(edge2->map); if (is_condition(edge2)) { if (!edge1->tagged_condition) edge1->tagged_condition = edge2->tagged_condition; else edge1->tagged_condition = isl_union_map_union(edge1->tagged_condition, edge2->tagged_condition); } if (is_conditional_validity(edge2)) { if (!edge1->tagged_validity) edge1->tagged_validity = edge2->tagged_validity; else edge1->tagged_validity = isl_union_map_union(edge1->tagged_validity, edge2->tagged_validity); } if (is_condition(edge2) && !edge1->tagged_condition) return -1; if (is_conditional_validity(edge2) && !edge1->tagged_validity) return -1; return 0; } /* Insert dummy tags in domain and range of "map". * * In particular, if "map" is of the form * * A -> B * * then return * * [A -> dummy_tag] -> [B -> dummy_tag] * * where the dummy_tags are identical and equal to any dummy tags * introduced by any other call to this function. */ static __isl_give isl_map *insert_dummy_tags(__isl_take isl_map *map) { static char dummy; isl_ctx *ctx; isl_id *id; isl_space *space; isl_set *domain, *range; ctx = isl_map_get_ctx(map); id = isl_id_alloc(ctx, NULL, &dummy); space = isl_space_params(isl_map_get_space(map)); space = isl_space_set_from_params(space); space = isl_space_set_tuple_id(space, isl_dim_set, id); space = isl_space_map_from_set(space); domain = isl_map_wrap(map); range = isl_map_wrap(isl_map_universe(space)); map = isl_map_from_domain_and_range(domain, range); map = isl_map_zip(map); return map; } /* Given that at least one of "src" or "dst" is compressed, return * a map between the spaces of these nodes restricted to the affine * hull that was used in the compression. */ static __isl_give isl_map *extract_hull(struct isl_sched_node *src, struct isl_sched_node *dst) { isl_set *dom, *ran; if (src->compressed) dom = isl_set_copy(src->hull); else dom = isl_set_universe(isl_space_copy(src->space)); if (dst->compressed) ran = isl_set_copy(dst->hull); else ran = isl_set_universe(isl_space_copy(dst->space)); return isl_map_from_domain_and_range(dom, ran); } /* Intersect the domains of the nested relations in domain and range * of "tagged" with "map". */ static __isl_give isl_map *map_intersect_domains(__isl_take isl_map *tagged, __isl_keep isl_map *map) { isl_set *set; tagged = isl_map_zip(tagged); set = isl_map_wrap(isl_map_copy(map)); tagged = isl_map_intersect_domain(tagged, set); tagged = isl_map_zip(tagged); return tagged; } /* Return a pointer to the node that lives in the domain space of "map" * or NULL if there is no such node. */ static struct isl_sched_node *find_domain_node(isl_ctx *ctx, struct isl_sched_graph *graph, __isl_keep isl_map *map) { struct isl_sched_node *node; isl_space *space; space = isl_space_domain(isl_map_get_space(map)); node = graph_find_node(ctx, graph, space); isl_space_free(space); return node; } /* Return a pointer to the node that lives in the range space of "map" * or NULL if there is no such node. */ static struct isl_sched_node *find_range_node(isl_ctx *ctx, struct isl_sched_graph *graph, __isl_keep isl_map *map) { struct isl_sched_node *node; isl_space *space; space = isl_space_range(isl_map_get_space(map)); node = graph_find_node(ctx, graph, space); isl_space_free(space); return node; } /* 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. * * Edges of type isl_edge_condition or isl_edge_conditional_validity * may be specified as "tagged" dependence relations. That is, "map" * may contain elements (i -> a) -> (j -> b), where i -> j denotes * the dependence on iterations and a and b are tags. * edge->map is set to the relation containing the elements i -> j, * while edge->tagged_condition and edge->tagged_validity contain * the union of all the "map" relations * for which extract_edge is called that result in the same edge->map. * * If the source or the destination node is compressed, then * intersect both "map" and "tagged" with the constraints that * were used to construct the compression. * This ensures that there are no schedule constraints defined * outside of these domains, while the scheduler no longer has * any control over those outside parts. */ static isl_stat extract_edge(__isl_take isl_map *map, void *user) { isl_ctx *ctx = isl_map_get_ctx(map); struct isl_extract_edge_data *data = user; struct isl_sched_graph *graph = data->graph; struct isl_sched_node *src, *dst; struct isl_sched_edge *edge; isl_map *tagged = NULL; if (data->type == isl_edge_condition || data->type == isl_edge_conditional_validity) { if (isl_map_can_zip(map)) { tagged = isl_map_copy(map); map = isl_set_unwrap(isl_map_domain(isl_map_zip(map))); } else { tagged = insert_dummy_tags(isl_map_copy(map)); } } src = find_domain_node(ctx, graph, map); dst = find_range_node(ctx, graph, map); if (!src || !dst) { isl_map_free(map); isl_map_free(tagged); return isl_stat_ok; } if (src->compressed || dst->compressed) { isl_map *hull; hull = extract_hull(src, dst); if (tagged) tagged = map_intersect_domains(tagged, hull); map = isl_map_intersect(map, hull); } 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].types = 0; graph->edge[graph->n_edge].tagged_condition = NULL; graph->edge[graph->n_edge].tagged_validity = NULL; set_type(&graph->edge[graph->n_edge], data->type); if (data->type == isl_edge_condition) graph->edge[graph->n_edge].tagged_condition = isl_union_map_from_map(tagged); if (data->type == isl_edge_conditional_validity) graph->edge[graph->n_edge].tagged_validity = isl_union_map_from_map(tagged); edge = graph_find_matching_edge(graph, &graph->edge[graph->n_edge]); if (!edge) { graph->n_edge++; return isl_stat_error; } if (edge == &graph->edge[graph->n_edge]) return graph_edge_table_add(ctx, graph, data->type, &graph->edge[graph->n_edge++]); if (merge_edge(edge, &graph->edge[graph->n_edge]) < 0) return -1; return graph_edge_table_add(ctx, graph, data->type, edge); } /* Initialize the schedule graph "graph" from the schedule constraints "sc". * * The context is included in the domain before the nodes of * the graphs are extracted in order to be able to exploit * any possible additional equalities. * Note that this intersection is only performed locally here. */ static isl_stat graph_init(struct isl_sched_graph *graph, __isl_keep isl_schedule_constraints *sc) { isl_ctx *ctx; isl_union_set *domain; isl_union_map *c; struct isl_extract_edge_data data; enum isl_edge_type i; isl_stat r; if (!sc) return isl_stat_error; ctx = isl_schedule_constraints_get_ctx(sc); domain = isl_schedule_constraints_get_domain(sc); graph->n = isl_union_set_n_set(domain); isl_union_set_free(domain); if (graph_alloc(ctx, graph, graph->n, isl_schedule_constraints_n_map(sc)) < 0) return isl_stat_error; if (compute_max_row(graph, sc) < 0) return isl_stat_error; graph->root = 1; graph->n = 0; domain = isl_schedule_constraints_get_domain(sc); domain = isl_union_set_intersect_params(domain, isl_schedule_constraints_get_context(sc)); r = isl_union_set_foreach_set(domain, &extract_node, graph); isl_union_set_free(domain); if (r < 0) return isl_stat_error; if (graph_init_table(ctx, graph) < 0) return isl_stat_error; for (i = isl_edge_first; i <= isl_edge_last; ++i) { c = isl_schedule_constraints_get(sc, i); graph->max_edge[i] = isl_union_map_n_map(c); isl_union_map_free(c); if (!c) return isl_stat_error; } if (graph_init_edge_tables(ctx, graph) < 0) return isl_stat_error; graph->n_edge = 0; data.graph = graph; for (i = isl_edge_first; i <= isl_edge_last; ++i) { isl_stat r; data.type = i; c = isl_schedule_constraints_get(sc, i); r = isl_union_map_foreach_map(c, &extract_edge, &data); isl_union_map_free(c); if (r < 0) return isl_stat_error; } return isl_stat_ok; } /* Check whether there is any dependence from node[j] to node[i] * or from node[i] to node[j]. */ static isl_bool node_follows_weak(int i, int j, void *user) { isl_bool 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]); } /* Check whether there is a (conditional) validity dependence from node[j] * to node[i], forcing node[i] to follow node[j]. */ static isl_bool node_follows_strong(int i, int j, void *user) { struct isl_sched_graph *graph = user; return graph_has_validity_edge(graph, &graph->node[j], &graph->node[i]); } /* Use Tarjan's algorithm for computing the strongly connected components * in the dependence graph only considering those edges defined by "follows". */ static int detect_ccs(isl_ctx *ctx, struct isl_sched_graph *graph, isl_bool (*follows)(int i, int j, void *user)) { int i, n; struct isl_tarjan_graph *g = NULL; g = isl_tarjan_graph_init(ctx, graph->n, follows, graph); if (!g) 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. * Only consider the (conditional) validity dependences and clear "weak". */ static int detect_sccs(isl_ctx *ctx, struct isl_sched_graph *graph) { graph->weak = 0; return detect_ccs(ctx, graph, &node_follows_strong); } /* Apply Tarjan's algorithm to detect the (weakly) connected components * in the dependence graph. * Consider all dependences and set "weak". */ static int detect_wccs(isl_ctx *ctx, struct isl_sched_graph *graph) { graph->weak = 1; return detect_ccs(ctx, graph, &node_follows_weak); } static int cmp_scc(const void *a, const void *b, void *data) { struct isl_sched_graph *graph = data; const int *i1 = a; const int *i2 = b; return graph->node[*i1].scc - graph->node[*i2].scc; } /* Sort the elements of graph->sorted according to the corresponding SCCs. */ static int sort_sccs(struct isl_sched_graph *graph) { return isl_sort(graph->sorted, graph->n, sizeof(int), &cmp_scc, graph); } /* Given a dependence relation R from "node" to itself, * construct the set of coefficients of valid constraints for elements * in that dependence relation. * In particular, the result contains tuples of coefficients * c_0, c_n, c_x such that * * c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R * * or, equivalently, * * c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R } * * We choose here to compute the dual of delta R. * Alternatively, we could have computed the dual of R, resulting * in a set of tuples c_0, c_n, c_x, c_y, and then * plugged in (c_0, c_n, c_x, -c_x). * * If "node" has been compressed, then the dependence relation * is also compressed before the set of coefficients is computed. */ static __isl_give isl_basic_set *intra_coefficients( struct isl_sched_graph *graph, struct isl_sched_node *node, __isl_take isl_map *map) { isl_set *delta; isl_map *key; isl_basic_set *coef; isl_maybe_isl_basic_set m; m = isl_map_to_basic_set_try_get(graph->intra_hmap, map); if (m.valid < 0 || m.valid) { isl_map_free(map); return m.value; } key = isl_map_copy(map); if (node->compressed) { map = isl_map_preimage_domain_multi_aff(map, isl_multi_aff_copy(node->decompress)); map = isl_map_preimage_range_multi_aff(map, isl_multi_aff_copy(node->decompress)); } delta = isl_set_remove_divs(isl_map_deltas(map)); coef = isl_set_coefficients(delta); graph->intra_hmap = isl_map_to_basic_set_set(graph->intra_hmap, key, isl_basic_set_copy(coef)); return coef; } /* Given a dependence relation R, construct the set of coefficients * of valid constraints for elements in that dependence relation. * In particular, the result contains tuples of coefficients * c_0, c_n, c_x, c_y such that * * c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R * * If the source or destination nodes of "edge" have been compressed, * then the dependence relation is also compressed before * the set of coefficients is computed. */ static __isl_give isl_basic_set *inter_coefficients( struct isl_sched_graph *graph, struct isl_sched_edge *edge, __isl_take isl_map *map) { isl_set *set; isl_map *key; isl_basic_set *coef; isl_maybe_isl_basic_set m; m = isl_map_to_basic_set_try_get(graph->inter_hmap, map); if (m.valid < 0 || m.valid) { isl_map_free(map); return m.value; } key = isl_map_copy(map); if (edge->src->compressed) map = isl_map_preimage_domain_multi_aff(map, isl_multi_aff_copy(edge->src->decompress)); if (edge->dst->compressed) map = isl_map_preimage_range_multi_aff(map, isl_multi_aff_copy(edge->dst->decompress)); set = isl_map_wrap(isl_map_remove_divs(map)); coef = isl_set_coefficients(set); graph->inter_hmap = isl_map_to_basic_set_set(graph->inter_hmap, key, isl_basic_set_copy(coef)); return coef; } /* Return the position of the coefficients of the variables in * the coefficients constraints "coef". * * The space of "coef" is of the form * * { coefficients[[cst, params] -> S] } * * Return the position of S. */ static int coef_var_offset(__isl_keep isl_basic_set *coef) { int offset; isl_space *space; space = isl_space_unwrap(isl_basic_set_get_space(coef)); offset = isl_space_dim(space, isl_dim_in); isl_space_free(space); return offset; } /* Return the offset of the coefficients of the variables of "node" * within the (I)LP. * * Within each node, the coefficients have the following order: * - c_i_0 * - c_i_n (if parametric) * - positive and negative parts of c_i_x */ static int node_var_coef_offset(struct isl_sched_node *node) { return node->start + 1 + node->nparam; } /* Construct an isl_dim_map for mapping constraints on coefficients * for "node" to the corresponding positions in graph->lp. * "offset" is the offset of the coefficients for the variables * in the input constraints. * "s" is the sign of the mapping. * * The input constraints are given in terms of the coefficients (c_0, c_n, c_x). * The mapping produced by this function essentially plugs in * (0, 0, c_i_x^+ - c_i_x^-) if s = 1 and * (0, 0, -c_i_x^+ + c_i_x^-) if s = -1. * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart. * * The caller can extend the mapping to also map the other coefficients * (and therefore not plug in 0). */ static __isl_give isl_dim_map *intra_dim_map(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_sched_node *node, int offset, int s) { int pos; unsigned total; isl_dim_map *dim_map; total = isl_basic_set_total_dim(graph->lp); pos = node_var_coef_offset(node); dim_map = isl_dim_map_alloc(ctx, total); isl_dim_map_range(dim_map, pos, 2, offset, 1, node->nvar, -s); isl_dim_map_range(dim_map, pos + 1, 2, offset, 1, node->nvar, s); return dim_map; } /* Construct an isl_dim_map for mapping constraints on coefficients * for "src" (node i) and "dst" (node j) to the corresponding positions * in graph->lp. * "offset" is the offset of the coefficients for the variables of "src" * in the input constraints. * "s" is the sign of the mapping. * * The input constraints are given in terms of the coefficients * (c_0, c_n, c_x, c_y). * The mapping produced by this function essentially plugs in * (c_j_0 - c_i_0, c_j_n - c_i_n, * c_j_x^+ - c_j_x^-, -(c_i_x^+ - c_i_x^-)) if s = 1 and * (-c_j_0 + c_i_0, -c_j_n + c_i_n, * - (c_j_x^+ - c_j_x^-), c_i_x^+ - c_i_x^-) if s = -1. * In graph->lp, the c_*^- appear before their c_*^+ counterpart. * * The caller can further extend the mapping. */ static __isl_give isl_dim_map *inter_dim_map(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_sched_node *src, struct isl_sched_node *dst, int offset, int s) { int pos; unsigned total; isl_dim_map *dim_map; total = isl_basic_set_total_dim(graph->lp); dim_map = isl_dim_map_alloc(ctx, total); isl_dim_map_range(dim_map, dst->start, 0, 0, 0, 1, s); isl_dim_map_range(dim_map, dst->start + 1, 1, 1, 1, dst->nparam, s); pos = node_var_coef_offset(dst); isl_dim_map_range(dim_map, pos, 2, offset + src->nvar, 1, dst->nvar, -s); isl_dim_map_range(dim_map, pos + 1, 2, offset + 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, 1, 1, 1, src->nparam, -s); pos = node_var_coef_offset(src); isl_dim_map_range(dim_map, pos, 2, offset, 1, src->nvar, s); isl_dim_map_range(dim_map, pos + 1, 2, offset, 1, src->nvar, -s); return dim_map; } /* Add constraints to graph->lp that force validity for the given * dependence from a node i to itself. * That is, add constraints that enforce * * (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x) * = c_i_x (y - x) >= 0 * * for each (x,y) in R. * We obtain general constraints on coefficients (c_0, c_n, c_x) * of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-), * where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative. * In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart. * * Actually, we do not construct constraints for the c_i_x themselves, * but for the coefficients of c_i_x written as a linear combination * of the columns in node->cmap. */ static isl_stat add_intra_validity_constraints(struct isl_sched_graph *graph, struct isl_sched_edge *edge) { int offset; isl_map *map = isl_map_copy(edge->map); isl_ctx *ctx = isl_map_get_ctx(map); isl_dim_map *dim_map; isl_basic_set *coef; struct isl_sched_node *node = edge->src; coef = intra_coefficients(graph, node, map); offset = coef_var_offset(coef); coef = isl_basic_set_transform_dims(coef, isl_dim_set, offset, isl_mat_copy(node->cmap)); if (!coef) return isl_stat_error; dim_map = intra_dim_map(ctx, graph, node, offset, 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); return isl_stat_ok; } /* Add constraints to graph->lp that force validity for the given * dependence from node i to node j. * That is, add constraints that enforce * * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0 * * for each (x,y) in R. * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y) * of valid constraints for R and then plug in * (c_j_0 - c_i_0, c_j_n - c_i_n, c_j_x^+ - c_j_x^- - (c_i_x^+ - c_i_x^-)), * where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative. * In graph->lp, the c_*^- appear before their c_*^+ counterpart. * * Actually, we do not construct constraints for the c_*_x themselves, * but for the coefficients of c_*_x written as a linear combination * of the columns in node->cmap. */ static isl_stat add_inter_validity_constraints(struct isl_sched_graph *graph, struct isl_sched_edge *edge) { int offset; isl_map *map = isl_map_copy(edge->map); isl_ctx *ctx = isl_map_get_ctx(map); 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, edge, map); offset = coef_var_offset(coef); coef = isl_basic_set_transform_dims(coef, isl_dim_set, offset, isl_mat_copy(src->cmap)); coef = isl_basic_set_transform_dims(coef, isl_dim_set, offset + src->nvar, isl_mat_copy(dst->cmap)); if (!coef) return isl_stat_error; dim_map = inter_dim_map(ctx, graph, src, dst, offset, 1); edge->start = graph->lp->n_ineq; 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); if (!graph->lp) return isl_stat_error; edge->end = graph->lp->n_ineq; return isl_stat_ok; } /* Add constraints to graph->lp that bound the dependence distance for the given * dependence from a node i to itself. * If s = 1, we add the constraint * * c_i_x (y - x) <= m_0 + m_n n * * or * * -c_i_x (y - x) + m_0 + m_n n >= 0 * * for each (x,y) in R. * If s = -1, we add the constraint * * -c_i_x (y - x) <= m_0 + m_n n * * or * * c_i_x (y - x) + m_0 + m_n n >= 0 * * for each (x,y) in R. * We obtain general constraints on coefficients (c_0, c_n, c_x) * of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x), * with each coefficient (except m_0) represented as a pair of non-negative * coefficients. * * Actually, we do not construct constraints for the c_i_x themselves, * but for the coefficients of c_i_x written as a linear combination * of the columns in node->cmap. * * * If "local" is set, then we add constraints * * c_i_x (y - x) <= 0 * * or * * -c_i_x (y - x) <= 0 * * instead, forcing the dependence distance to be (less than or) equal to 0. * That is, we plug in (0, 0, -s * c_i_x), * Note that dependences marked local are treated as validity constraints * by add_all_validity_constraints and therefore also have * their distances bounded by 0 from below. */ static isl_stat add_intra_proximity_constraints(struct isl_sched_graph *graph, struct isl_sched_edge *edge, int s, int local) { int offset; unsigned nparam; isl_map *map = isl_map_copy(edge->map); isl_ctx *ctx = isl_map_get_ctx(map); isl_dim_map *dim_map; isl_basic_set *coef; struct isl_sched_node *node = edge->src; coef = intra_coefficients(graph, node, map); offset = coef_var_offset(coef); coef = isl_basic_set_transform_dims(coef, isl_dim_set, offset, isl_mat_copy(node->cmap)); if (!coef) return isl_stat_error; nparam = isl_space_dim(node->space, isl_dim_param); dim_map = intra_dim_map(ctx, graph, node, offset, -s); if (!local) { 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); } 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); return isl_stat_ok; } /* Add constraints to graph->lp that bound the dependence distance for the given * dependence from node i to node j. * If s = 1, we add the constraint * * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) * <= m_0 + m_n n * * or * * -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) + * m_0 + m_n n >= 0 * * for each (x,y) in R. * If s = -1, we add the constraint * * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)) * <= m_0 + m_n n * * or * * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) + * m_0 + m_n n >= 0 * * for each (x,y) in R. * We obtain general constraints on coefficients (c_0, c_n, c_x, c_y) * of valid constraints for R and then plug in * (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n, * -s*c_j_x+s*c_i_x) * with each coefficient (except m_0, c_*_0 and c_*_n) * represented as a pair of non-negative coefficients. * * Actually, we do not construct constraints for the c_*_x themselves, * but for the coefficients of c_*_x written as a linear combination * of the columns in node->cmap. * * * If "local" is set, then we add constraints * * (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) <= 0 * * or * * -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)) <= 0 * * instead, forcing the dependence distance to be (less than or) equal to 0. * That is, we plug in * (-s*c_j_0 + s*c_i_0, -s*c_j_n + s*c_i_n, -s*c_j_x+s*c_i_x). * Note that dependences marked local are treated as validity constraints * by add_all_validity_constraints and therefore also have * their distances bounded by 0 from below. */ static isl_stat add_inter_proximity_constraints(struct isl_sched_graph *graph, struct isl_sched_edge *edge, int s, int local) { int offset; unsigned nparam; isl_map *map = isl_map_copy(edge->map); isl_ctx *ctx = isl_map_get_ctx(map); 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, edge, map); offset = coef_var_offset(coef); coef = isl_basic_set_transform_dims(coef, isl_dim_set, offset, isl_mat_copy(src->cmap)); coef = isl_basic_set_transform_dims(coef, isl_dim_set, offset + src->nvar, isl_mat_copy(dst->cmap)); if (!coef) return isl_stat_error; nparam = isl_space_dim(src->space, isl_dim_param); dim_map = inter_dim_map(ctx, graph, src, dst, offset, -s); if (!local) { 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); } 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); return isl_stat_ok; } /* Add all validity constraints to graph->lp. * * An edge that is forced to be local needs to have its dependence * distances equal to zero. We take care of bounding them by 0 from below * here. add_all_proximity_constraints takes care of bounding them by 0 * from above. * * If "use_coincidence" is set, then we treat coincidence edges as local edges. * Otherwise, we ignore them. */ static int add_all_validity_constraints(struct isl_sched_graph *graph, int use_coincidence) { int i; for (i = 0; i < graph->n_edge; ++i) { struct isl_sched_edge *edge= &graph->edge[i]; int local; local = is_local(edge) || (is_coincidence(edge) && use_coincidence); if (!is_validity(edge) && !local) continue; if (edge->src != edge->dst) continue; if (add_intra_validity_constraints(graph, edge) < 0) return -1; } for (i = 0; i < graph->n_edge; ++i) { struct isl_sched_edge *edge = &graph->edge[i]; int local; local = is_local(edge) || (is_coincidence(edge) && use_coincidence); if (!is_validity(edge) && !local) continue; if (edge->src == edge->dst) continue; if (add_inter_validity_constraints(graph, edge) < 0) return -1; } return 0; } /* Add constraints to graph->lp that bound the dependence distance * for all dependence relations. * If a given proximity dependence is identical to a validity * dependence, then the dependence distance is already bounded * from below (by zero), so we only need to bound the distance * from above. (This includes the case of "local" dependences * which are treated as validity dependence by add_all_validity_constraints.) * Otherwise, we need to bound the distance both from above and from below. * * If "use_coincidence" is set, then we treat coincidence edges as local edges. * Otherwise, we ignore them. */ static int add_all_proximity_constraints(struct isl_sched_graph *graph, int use_coincidence) { int i; for (i = 0; i < graph->n_edge; ++i) { struct isl_sched_edge *edge= &graph->edge[i]; int local; local = is_local(edge) || (is_coincidence(edge) && use_coincidence); if (!is_proximity(edge) && !local) continue; if (edge->src == edge->dst && add_intra_proximity_constraints(graph, edge, 1, local) < 0) return -1; if (edge->src != edge->dst && add_inter_proximity_constraints(graph, edge, 1, local) < 0) return -1; if (is_validity(edge) || local) continue; if (edge->src == edge->dst && add_intra_proximity_constraints(graph, edge, -1, 0) < 0) return -1; if (edge->src != edge->dst && add_inter_proximity_constraints(graph, edge, -1, 0) < 0) return -1; } return 0; } /* Compute a basis for the rows in the linear part of the schedule * and extend this basis to a full basis. The remaining rows * can then be used to force linear independence from the rows * in the schedule. * * In particular, given the schedule rows S, we compute * * S = H Q * S U = H * * with H the Hermite normal form of S. That is, all but the * first rank columns of H are zero and so each row in S is * a linear combination of the first rank rows of Q. * The matrix Q is then transposed because we will write the * coefficients of the next schedule row as a column vector s * and express this s as a linear combination s = Q c of the * computed basis. * Similarly, the matrix U is transposed such that we can * compute the coefficients c = U s from a schedule row s. */ static int node_update_cmap(struct isl_sched_node *node) { isl_mat *H, *U, *Q; int n_row = isl_mat_rows(node->sched); H = isl_mat_sub_alloc(node->sched, 0, n_row, 1 + node->nparam, node->nvar); H = isl_mat_left_hermite(H, 0, &U, &Q); isl_mat_free(node->cmap); isl_mat_free(node->cinv); isl_mat_free(node->ctrans); node->ctrans = isl_mat_copy(Q); node->cmap = isl_mat_transpose(Q); node->cinv = isl_mat_transpose(U); node->rank = isl_mat_initial_non_zero_cols(H); isl_mat_free(H); if (!node->cmap || !node->cinv || !node->ctrans || node->rank < 0) return -1; return 0; } /* Is "edge" marked as a validity or a conditional validity edge? */ static int is_any_validity(struct isl_sched_edge *edge) { return is_validity(edge) || is_conditional_validity(edge); } /* How many times should we count the constraints in "edge"? * * If carry is set, then we are counting the number of * (validity or conditional 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) * local(+any) -> 2 (>= 0 and <= 0) * * If an edge is only marked conditional_validity then it counts * as zero since it is only checked afterwards. * * If "use_coincidence" is set, then we treat coincidence edges as local edges. * Otherwise, we ignore them. */ static int edge_multiplicity(struct isl_sched_edge *edge, int carry, int use_coincidence) { if (carry) return 1; if (is_proximity(edge) || is_local(edge)) return 2; if (use_coincidence && is_coincidence(edge)) return 2; if (is_validity(edge)) return 1; return 0; } /* Count the number of equality and inequality constraints * that will be added for the given map. * * "use_coincidence" is set if we should take into account coincidence edges. */ 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, int use_coincidence) { isl_basic_set *coef; int f = edge_multiplicity(edge, carry, use_coincidence); if (f == 0) { isl_map_free(map); return 0; } if (edge->src == edge->dst) coef = intra_coefficients(graph, edge->src, map); else coef = inter_coefficients(graph, edge, 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) * local(+any) -> 2 (>= 0 and <= 0) * * If "use_coincidence" is set, then we treat coincidence edges as local edges. * Otherwise, we ignore them. */ static int count_constraints(struct isl_sched_graph *graph, int *n_eq, int *n_ineq, int use_coincidence) { int i; *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); if (count_map_constraints(graph, edge, map, n_eq, n_ineq, 0, use_coincidence) < 0) return -1; } return 0; } /* Count the number of constraints that will be added by * add_bound_constant_constraints to bound the values of the constant terms * and increment *n_eq and *n_ineq accordingly. * * In practice, add_bound_constant_constraints only adds inequalities. */ static isl_stat count_bound_constant_constraints(isl_ctx *ctx, struct isl_sched_graph *graph, int *n_eq, int *n_ineq) { if (isl_options_get_schedule_max_constant_term(ctx) == -1) return isl_stat_ok; *n_ineq += graph->n; return isl_stat_ok; } /* Add constraints to bound the values of the constant terms in the schedule, * if requested by the user. * * The maximal value of the constant terms is defined by the option * "schedule_max_constant_term". * * Within each node, the coefficients have the following order: * - c_i_0 * - c_i_n (if parametric) * - positive and negative parts of c_i_x */ static isl_stat add_bound_constant_constraints(isl_ctx *ctx, struct isl_sched_graph *graph) { int i, k; int max; int total; max = isl_options_get_schedule_max_constant_term(ctx); if (max == -1) return isl_stat_ok; total = isl_basic_set_dim(graph->lp, isl_dim_set); 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 isl_stat_error; 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); } return isl_stat_ok; } /* Count the number of constraints that will be added by * add_bound_coefficient_constraints and increment *n_eq and *n_ineq * accordingly. * * In practice, add_bound_coefficient_constraints only adds inequalities. */ static int count_bound_coefficient_constraints(isl_ctx *ctx, struct isl_sched_graph *graph, int *n_eq, int *n_ineq) { int i; if (isl_options_get_schedule_max_coefficient(ctx) == -1 && !isl_options_get_schedule_treat_coalescing(ctx)) return 0; for (i = 0; i < graph->n; ++i) *n_ineq += graph->node[i].nparam + 2 * graph->node[i].nvar; return 0; } /* Add constraints to graph->lp that bound the values of * the parameter schedule coefficients of "node" to "max" and * the variable schedule coefficients to the corresponding entry * in node->max. * In either case, a negative value means that no bound needs to be imposed. * * For parameter coefficients, this amounts to adding a constraint * * c_n <= max * * i.e., * * -c_n + max >= 0 * * The variables coefficients are, however, not represented directly. * Instead, the variables coefficients c_x are written as a linear * combination c_x = cmap c_z of some other coefficients c_z, * which are in turn encoded as c_z = c_z^+ - c_z^-. * Let a_j be the elements of row i of node->cmap, then * * -max_i <= c_x_i <= max_i * * is encoded as * * -max_i <= \sum_j a_j (c_z_j^+ - c_z_j^-) <= max_i * * or * * -\sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0 * \sum_j a_j (c_z_j^+ - c_z_j^-) + max_i >= 0 */ static isl_stat node_add_coefficient_constraints(isl_ctx *ctx, struct isl_sched_graph *graph, struct isl_sched_node *node, int max) { int i, j, k; int total; isl_vec *ineq; total = isl_basic_set_dim(graph->lp, isl_dim_set); for (j = 0; j < node->nparam; ++j) { int dim; if (max < 0) continue; k = isl_basic_set_alloc_inequality(graph->lp); if (k < 0) return isl_stat_error; 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); } ineq = isl_vec_alloc(ctx, 1 + total); ineq = isl_vec_clr(ineq); if (!ineq) return isl_stat_error; for (i = 0; i < node->nvar; ++i) { int pos = 1 + node_var_coef_offset(node); if (isl_int_is_neg(node->max->el[i])) continue; for (j = 0; j < node->nvar; ++j) { isl_int_set(ineq->el[pos + 2 * j], node->cmap->row[i][j]); isl_int_neg(ineq->el[pos + 2 * j + 1], node->cmap->row[i][j]); } isl_int_set(ineq->el[0], node->max->el[i]); k = isl_basic_set_alloc_inequality(graph->lp); if (k < 0) goto error; isl_seq_cpy(graph->lp->ineq[k], ineq->el, 1 + total); isl_seq_neg(ineq->el + pos, ineq->el + pos, 2 * node->nvar); k = isl_basic_set_alloc_inequality(graph->lp); if (k < 0) goto error; isl_seq_cpy(graph->lp->ineq[k], ineq->el, 1 + total); } isl_vec_free(ineq); return isl_stat_ok; error: isl_vec_free(ineq); return isl_stat_error; } /* 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' and the entries in node->max. * These latter entries are only set if either the schedule_max_coefficient * option or the schedule_treat_coalescing option is set. */ static isl_stat add_bound_coefficient_constraints(isl_ctx *ctx, struct isl_sched_graph *graph) { int i; int max; max = isl_options_get_schedule_max_coefficient(ctx); if (max == -1 && !isl_options_get_schedule_treat_coalescing(ctx)) return isl_stat_ok; for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; if (node_add_coefficient_constraints(ctx, graph, node, max) < 0) return isl_stat_error; } return isl_stat_ok; } /* Add a constraint to graph->lp that equates the value at position * "sum_pos" to the sum of the "n" values starting at "first". */ static isl_stat add_sum_constraint(struct isl_sched_graph *graph, int sum_pos, int first, int n) { int i, k; int total; total = isl_basic_set_dim(graph->lp, isl_dim_set); k = isl_basic_set_alloc_equality(graph->lp); if (k < 0) return isl_stat_error; isl_seq_clr(graph->lp->eq[k], 1 + total); isl_int_set_si(graph->lp->eq[k][1 + sum_pos], -1); for (i = 0; i < n; ++i) isl_int_set_si(graph->lp->eq[k][1 + first + i], 1); return isl_stat_ok; } /* Add a constraint to graph->lp that equates the value at position * "sum_pos" to the sum of the parameter coefficients of all nodes. * * Within each node, the coefficients have the following order: * - c_i_0 * - c_i_n (if parametric) * - positive and negative parts of c_i_x */ static isl_stat add_param_sum_constraint(struct isl_sched_graph *graph, int sum_pos) { int i, j, k; int total; total = isl_basic_set_dim(graph->lp, isl_dim_set); k = isl_basic_set_alloc_equality(graph->lp); if (k < 0) return isl_stat_error; isl_seq_clr(graph->lp->eq[k], 1 + total); isl_int_set_si(graph->lp->eq[k][1 + sum_pos], -1); for (i = 0; i < graph->n; ++i) { int pos = 1 + graph->node[i].start + 1; for (j = 0; j < graph->node[i].nparam; ++j) isl_int_set_si(graph->lp->eq[k][pos + j], 1); } return isl_stat_ok; } /* Add a constraint to graph->lp that equates the value at position * "sum_pos" to the sum of the variable coefficients of all nodes. * * Within each node, the coefficients have the following order: * - c_i_0 * - c_i_n (if parametric) * - positive and negative parts of c_i_x */ static isl_stat add_var_sum_constraint(struct isl_sched_graph *graph, int sum_pos) { int i, j, k; int total; total = isl_basic_set_dim(graph->lp, isl_dim_set); k = isl_basic_set_alloc_equality(graph->lp); if (k < 0) return isl_stat_error; isl_seq_clr(graph->lp->eq[k], 1 + total); isl_int_set_si(graph->lp->eq[k][1 + sum_pos], -1); for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; int pos = 1 + node_var_coef_offset(node); for (j = 0; j < 2 * node->nvar; ++j) isl_int_set_si(graph->lp->eq[k][pos + j], 1); } return isl_stat_ok; } /* Construct an ILP problem for finding schedule coefficients * that result in non-negative, but small dependence distances * over all dependences. * In particular, the dependence distances over proximity edges * are bounded by m_0 + m_n n and we compute schedule coefficients * with small values (preferably zero) of m_n and m_0. * * All variables of the ILP are non-negative. The actual coefficients * may be negative, so each coefficient is represented as the difference * of two non-negative variables. The negative part always appears * immediately before the positive part. * Other than that, the variables have the following order * * - sum of positive and negative parts of m_n coefficients * - m_0 * - sum of all c_n coefficients * (unconstrained when computing non-parametric schedules) * - sum of positive and negative parts of all c_x coefficients * - positive and negative parts of m_n coefficients * - for each node * - c_i_0 * - c_i_n (if parametric) * - positive and negative parts of c_i_x * * The c_i_x are not represented directly, but through the columns of * node->cmap. That is, the computed values are for variable t_i_x * such that c_i_x = Q t_i_x with Q equal to node->cmap. * * The constraints are those from the edges plus two or three equalities * to express the sums. * * If "use_coincidence" is set, then we treat coincidence edges as local edges. * Otherwise, we ignore them. */ static isl_stat setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph, int use_coincidence) { int i; unsigned nparam; unsigned total; isl_space *space; int parametric; int param_pos; int n_eq, n_ineq; parametric = ctx->opt->schedule_parametric; nparam = isl_space_dim(graph->node[0].space, isl_dim_param); param_pos = 4; total = param_pos + 2 * nparam; for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[graph->sorted[i]]; if (node_update_cmap(node) < 0) return isl_stat_error; node->start = total; total += 1 + node->nparam + 2 * node->nvar; } if (count_constraints(graph, &n_eq, &n_ineq, use_coincidence) < 0) return isl_stat_error; if (count_bound_constant_constraints(ctx, graph, &n_eq, &n_ineq) < 0) return isl_stat_error; if (count_bound_coefficient_constraints(ctx, graph, &n_eq, &n_ineq) < 0) return isl_stat_error; space = isl_space_set_alloc(ctx, 0, total); isl_basic_set_free(graph->lp); n_eq += 2 + parametric; graph->lp = isl_basic_set_alloc_space(space, 0, n_eq, n_ineq); if (add_sum_constraint(graph, 0, param_pos, 2 * nparam) < 0) return isl_stat_error; if (parametric && add_param_sum_constraint(graph, 2) < 0) return isl_stat_error; if (add_var_sum_constraint(graph, 3) < 0) return isl_stat_error; if (add_bound_constant_constraints(ctx, graph) < 0) return isl_stat_error; if (add_bound_coefficient_constraints(ctx, graph) < 0) return isl_stat_error; if (add_all_validity_constraints(graph, use_coincidence) < 0) return isl_stat_error; if (add_all_proximity_constraints(graph, use_coincidence) < 0) return isl_stat_error; return isl_stat_ok; } /* Analyze the conflicting constraint found by * isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity * constraint of one of the edges between distinct nodes, living, moreover * in distinct SCCs, then record the source and sink SCC as this may * be a good place to cut between SCCs. */ static int check_conflict(int con, void *user) { int i; struct isl_sched_graph *graph = user; if (graph->src_scc >= 0) return 0; con -= graph->lp->n_eq; if (con >= graph->lp->n_ineq) return 0; for (i = 0; i < graph->n_edge; ++i) { if (!is_validity(&graph->edge[i])) continue; if (graph->edge[i].src == graph->edge[i].dst) continue; if (graph->edge[i].src->scc == graph->edge[i].dst->scc) continue; if (graph->edge[i].start > con) continue; if (graph->edge[i].end <= con) continue; graph->src_scc = graph->edge[i].src->scc; graph->dst_scc = graph->edge[i].dst->scc; } return 0; } /* Check whether the next schedule row of the given node needs to be * non-trivial. Lower-dimensional domains may have some trivial rows, * but as soon as the number of remaining required non-trivial rows * is as large as the number or remaining rows to be computed, * all remaining rows need to be non-trivial. */ static int needs_row(struct isl_sched_graph *graph, struct isl_sched_node *node) { return node->nvar - node->rank >= graph->maxvar - graph->n_row; } /* Solve the ILP problem constructed in setup_lp. * For each node such that all the remaining rows of its schedule * need to be non-trivial, we construct a non-triviality region. * This region imposes that the next row is independent of previous rows. * In particular the coefficients c_i_x are represented by t_i_x * variables with c_i_x = Q t_i_x and Q a unimodular matrix such that * its first columns span the rows of the previously computed part * of the schedule. The non-triviality region enforces that at least * one of the remaining components of t_i_x is non-zero, i.e., * that the new schedule row depends on at least one of the remaining * columns of Q. */ static __isl_give isl_vec *solve_lp(struct isl_sched_graph *graph) { int i; isl_vec *sol; isl_basic_set *lp; for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; int skip = node->rank; graph->region[i].pos = node_var_coef_offset(node) + 2 * skip; if (needs_row(graph, node)) graph->region[i].len = 2 * (node->nvar - skip); else graph->region[i].len = 0; } lp = isl_basic_set_copy(graph->lp); sol = isl_tab_basic_set_non_trivial_lexmin(lp, 2, graph->n, graph->region, &check_conflict, graph); return sol; } /* Extract the coefficients for the variables of "node" from "sol". * * Within each node, the coefficients have the following order: * - c_i_0 * - c_i_n (if parametric) * - positive and negative parts of c_i_x * * The c_i_x^- appear before their c_i_x^+ counterpart. * * Return c_i_x = c_i_x^+ - c_i_x^- */ static __isl_give isl_vec *extract_var_coef(struct isl_sched_node *node, __isl_keep isl_vec *sol) { int i; int pos; isl_vec *csol; if (!sol) return NULL; csol = isl_vec_alloc(isl_vec_get_ctx(sol), node->nvar); if (!csol) return NULL; pos = 1 + node_var_coef_offset(node); for (i = 0; i < node->nvar; ++i) isl_int_sub(csol->el[i], sol->el[pos + 2 * i + 1], sol->el[pos + 2 * i]); return csol; } /* Update the schedules of all nodes based on the given solution * of the LP problem. * The new row is added to the current band. * All possibly negative coefficients are encoded as a difference * of two non-negative variables, so we need to perform the subtraction * here. Moreover, if use_cmap is set, then the solution does * not refer to the actual coefficients c_i_x, but instead to variables * 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 coincident is set, then the caller guarantees that the new * row satisfies the coincidence constraints. */ static int update_schedule(struct isl_sched_graph *graph, __isl_take isl_vec *sol, int use_cmap, int coincident) { int i, j; isl_vec *csol = NULL; if (!sol) goto error; 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); for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; int pos = node->start; int row = isl_mat_rows(node->sched); isl_vec_free(csol); csol = extract_var_coef(node, sol); if (!csol) goto error; isl_map_free(node->sched_map); node->sched_map = NULL; node->sched = isl_mat_add_rows(node->sched, 1); if (!node->sched) goto error; for (j = 0; j < 1 + node->nparam; ++j) node->sched = isl_mat_set_element(node->sched, row, j, sol->el[1 + pos + j]); if (use_cmap) csol = isl_mat_vec_product(isl_mat_copy(node->cmap), csol); if (!csol) goto error; for (j = 0; j < node->nvar; ++j) node->sched = isl_mat_set_element(node->sched, row, 1 + node->nparam + j, csol->el[j]); node->coincident[graph->n_total_row] = coincident; } isl_vec_free(sol); isl_vec_free(csol); graph->n_row++; graph->n_total_row++; return 0; error: isl_vec_free(sol); isl_vec_free(csol); return -1; } /* Convert row "row" of node->sched into an isl_aff living in "ls" * and return this isl_aff. */ static __isl_give isl_aff *extract_schedule_row(__isl_take isl_local_space *ls, struct isl_sched_node *node, int row) { int j; isl_int v; isl_aff *aff; isl_int_init(v); aff = isl_aff_zero_on_domain(ls); isl_mat_get_element(node->sched, row, 0, &v); aff = isl_aff_set_constant(aff, v); for (j = 0; j < node->nparam; ++j) { isl_mat_get_element(node->sched, row, 1 + 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, row, 1 + node->nparam + j, &v); aff = isl_aff_set_coefficient(aff, isl_dim_in, j, v); } isl_int_clear(v); return aff; } /* Convert the "n" rows starting at "first" of node->sched into a multi_aff * and return this multi_aff. * * The result is defined over the uncompressed node domain. */ static __isl_give isl_multi_aff *node_extract_partial_schedule_multi_aff( struct isl_sched_node *node, int first, int n) { int i; isl_space *space; isl_local_space *ls; isl_aff *aff; isl_multi_aff *ma; int nrow; if (!node) return NULL; nrow = isl_mat_rows(node->sched); if (node->compressed) space = isl_multi_aff_get_domain_space(node->decompress); else space = isl_space_copy(node->space); ls = isl_local_space_from_space(isl_space_copy(space)); space = isl_space_from_domain(space); space = isl_space_add_dims(space, isl_dim_out, n); ma = isl_multi_aff_zero(space); for (i = first; i < first + n; ++i) { aff = extract_schedule_row(isl_local_space_copy(ls), node, i); ma = isl_multi_aff_set_aff(ma, i - first, aff); } isl_local_space_free(ls); if (node->compressed) ma = isl_multi_aff_pullback_multi_aff(ma, isl_multi_aff_copy(node->compress)); return ma; } /* Convert node->sched into a multi_aff and return this multi_aff. * * The result is defined over the uncompressed node domain. */ static __isl_give isl_multi_aff *node_extract_schedule_multi_aff( struct isl_sched_node *node) { int nrow; nrow = isl_mat_rows(node->sched); return node_extract_partial_schedule_multi_aff(node, 0, nrow); } /* 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. * It is defined over the uncompressed node domain. */ 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); } /* Construct a map that can be used to update a dependence relation * based on the current schedule. * That is, construct a map expressing that source and sink * are executed within the same iteration of the current schedule. * This map can then be intersected with the dependence relation. * This is not the most efficient way, but this shouldn't be a critical * operation. */ static __isl_give isl_map *specializer(struct isl_sched_node *src, struct isl_sched_node *dst) { isl_map *src_sched, *dst_sched; src_sched = node_extract_schedule(src); dst_sched = node_extract_schedule(dst); return isl_map_apply_range(src_sched, isl_map_reverse(dst_sched)); } /* Intersect the domains of the nested relations in domain and range * of "umap" with "map". */ static __isl_give isl_union_map *intersect_domains( __isl_take isl_union_map *umap, __isl_keep isl_map *map) { isl_union_set *uset; umap = isl_union_map_zip(umap); uset = isl_union_set_from_set(isl_map_wrap(isl_map_copy(map))); umap = isl_union_map_intersect_domain(umap, uset); umap = isl_union_map_zip(umap); return umap; } /* Update the dependence relation of the given edge based * on the current schedule. * If the dependence is carried completely by the current schedule, then * 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_edge(struct isl_sched_graph *graph, struct isl_sched_edge *edge) { int empty; isl_map *id; id = specializer(edge->src, edge->dst); edge->map = isl_map_intersect(edge->map, isl_map_copy(id)); if (!edge->map) goto error; if (edge->tagged_condition) { edge->tagged_condition = intersect_domains(edge->tagged_condition, id); if (!edge->tagged_condition) goto error; } if (edge->tagged_validity) { edge->tagged_validity = intersect_domains(edge->tagged_validity, id); if (!edge->tagged_validity) goto error; } empty = isl_map_plain_is_empty(edge->map); if (empty < 0) goto error; if (empty) graph_remove_edge(graph, edge); isl_map_free(id); return 0; error: isl_map_free(id); return -1; } /* Does the domain of "umap" intersect "uset"? */ static int domain_intersects(__isl_keep isl_union_map *umap, __isl_keep isl_union_set *uset) { int empty; umap = isl_union_map_copy(umap); umap = isl_union_map_intersect_domain(umap, isl_union_set_copy(uset)); empty = isl_union_map_is_empty(umap); isl_union_map_free(umap); return empty < 0 ? -1 : !empty; } /* Does the range of "umap" intersect "uset"? */ static int range_intersects(__isl_keep isl_union_map *umap, __isl_keep isl_union_set *uset) { int empty; umap = isl_union_map_copy(umap); umap = isl_union_map_intersect_range(umap, isl_union_set_copy(uset)); empty = isl_union_map_is_empty(umap); isl_union_map_free(umap); return empty < 0 ? -1 : !empty; } /* Are the condition dependences of "edge" local with respect to * the current schedule? * * That is, are domain and range of the condition dependences mapped * to the same point? * * In other words, is the condition false? */ static int is_condition_false(struct isl_sched_edge *edge) { isl_union_map *umap; isl_map *map, *sched, *test; int empty, local; empty = isl_union_map_is_empty(edge->tagged_condition); if (empty < 0 || empty) return empty; umap = isl_union_map_copy(edge->tagged_condition); umap = isl_union_map_zip(umap); umap = isl_union_set_unwrap(isl_union_map_domain(umap)); map = isl_map_from_union_map(umap); sched = node_extract_schedule(edge->src); map = isl_map_apply_domain(map, sched); sched = node_extract_schedule(edge->dst); map = isl_map_apply_range(map, sched); test = isl_map_identity(isl_map_get_space(map)); local = isl_map_is_subset(map, test); isl_map_free(map); isl_map_free(test); return local; } /* For each conditional validity constraint that is adjacent * to a condition with domain in condition_source or range in condition_sink, * turn it into an unconditional validity constraint. */ static int unconditionalize_adjacent_validity(struct isl_sched_graph *graph, __isl_take isl_union_set *condition_source, __isl_take isl_union_set *condition_sink) { int i; condition_source = isl_union_set_coalesce(condition_source); condition_sink = isl_union_set_coalesce(condition_sink); for (i = 0; i < graph->n_edge; ++i) { int adjacent; isl_union_map *validity; if (!is_conditional_validity(&graph->edge[i])) continue; if (is_validity(&graph->edge[i])) continue; validity = graph->edge[i].tagged_validity; adjacent = domain_intersects(validity, condition_sink); if (adjacent >= 0 && !adjacent) adjacent = range_intersects(validity, condition_source); if (adjacent < 0) goto error; if (!adjacent) continue; set_validity(&graph->edge[i]); } isl_union_set_free(condition_source); isl_union_set_free(condition_sink); return 0; error: isl_union_set_free(condition_source); isl_union_set_free(condition_sink); return -1; } /* Update the dependence relations of all edges based on the current schedule * and enforce conditional validity constraints that are adjacent * to satisfied condition constraints. * * First check if any of the condition constraints are satisfied * (i.e., not local to the outer schedule) and keep track of * their domain and range. * Then update all dependence relations (which removes the non-local * constraints). * Finally, if any condition constraints turned out to be satisfied, * then turn all adjacent conditional validity constraints into * unconditional validity constraints. */ static int update_edges(isl_ctx *ctx, struct isl_sched_graph *graph) { int i; int any = 0; isl_union_set *source, *sink; source = isl_union_set_empty(isl_space_params_alloc(ctx, 0)); sink = isl_union_set_empty(isl_space_params_alloc(ctx, 0)); for (i = 0; i < graph->n_edge; ++i) { int local; isl_union_set *uset; isl_union_map *umap; if (!is_condition(&graph->edge[i])) continue; if (is_local(&graph->edge[i])) continue; local = is_condition_false(&graph->edge[i]); if (local < 0) goto error; if (local) continue; any = 1; umap = isl_union_map_copy(graph->edge[i].tagged_condition); uset = isl_union_map_domain(umap); source = isl_union_set_union(source, uset); umap = isl_union_map_copy(graph->edge[i].tagged_condition); uset = isl_union_map_range(umap); sink = isl_union_set_union(sink, uset); } for (i = graph->n_edge - 1; i >= 0; --i) { if (update_edge(graph, &graph->edge[i]) < 0) goto error; } if (any) return unconditionalize_adjacent_validity(graph, source, sink); isl_union_set_free(source); isl_union_set_free(sink); return 0; error: isl_union_set_free(source); isl_union_set_free(sink); return -1; } static void next_band(struct isl_sched_graph *graph) { graph->band_start = graph->n_total_row; } /* Return the union of the universe domains of the nodes in "graph" * that satisfy "pred". */ static __isl_give isl_union_set *isl_sched_graph_domain(isl_ctx *ctx, struct isl_sched_graph *graph, int (*pred)(struct isl_sched_node *node, int data), int data) { int i; isl_set *set; isl_union_set *dom; for (i = 0; i < graph->n; ++i) if (pred(&graph->node[i], data)) break; if (i >= graph->n) isl_die(ctx, isl_error_internal, "empty component", return NULL); set = isl_set_universe(isl_space_copy(graph->node[i].space)); dom = isl_union_set_from_set(set); for (i = i + 1; i < graph->n; ++i) { if (!pred(&graph->node[i], data)) continue; set = isl_set_universe(isl_space_copy(graph->node[i].space)); dom = isl_union_set_union(dom, isl_union_set_from_set(set)); } return dom; } /* Return a list of unions of universe domains, where each element * in the list corresponds to an SCC (or WCC) indexed by node->scc. */ static __isl_give isl_union_set_list *extract_sccs(isl_ctx *ctx, struct isl_sched_graph *graph) { int i; isl_union_set_list *filters; filters = isl_union_set_list_alloc(ctx, graph->scc); for (i = 0; i < graph->scc; ++i) { isl_union_set *dom; dom = isl_sched_graph_domain(ctx, graph, &node_scc_exactly, i); filters = isl_union_set_list_add(filters, dom); } return filters; } /* Return a list of two unions of universe domains, one for the SCCs up * to and including graph->src_scc and another for the other SCCs. */ static __isl_give isl_union_set_list *extract_split(isl_ctx *ctx, struct isl_sched_graph *graph) { isl_union_set *dom; isl_union_set_list *filters; filters = isl_union_set_list_alloc(ctx, 2); dom = isl_sched_graph_domain(ctx, graph, &node_scc_at_most, graph->src_scc); filters = isl_union_set_list_add(filters, dom); dom = isl_sched_graph_domain(ctx, graph, &node_scc_at_least, graph->src_scc + 1); filters = isl_union_set_list_add(filters, dom); return filters; } /* Copy nodes that satisfy node_pred from the src dependence graph * to the dst dependence graph. */ static int copy_nodes(struct isl_sched_graph *dst, struct isl_sched_graph *src, int (*node_pred)(struct isl_sched_node *node, int data), int data) { int i; dst->n = 0; for (i = 0; i < src->n; ++i) { int j; if (!node_pred(&src->node[i], data)) continue; j = dst->n; dst->node[j].space = isl_space_copy(src->node[i].space); dst->node[j].compressed = src->node[i].compressed; dst->node[j].hull = isl_set_copy(src->node[i].hull); dst->node[j].compress = isl_multi_aff_copy(src->node[i].compress); dst->node[j].decompress = isl_multi_aff_copy(src->node[i].decompress); dst->node[j].nvar = src->node[i].nvar; dst->node[j].nparam = src->node[i].nparam; dst->node[j].sched = isl_mat_copy(src->node[i].sched); dst->node[j].sched_map = isl_map_copy(src->node[i].sched_map); dst->node[j].coincident = src->node[i].coincident; dst->node[j].sizes = isl_multi_val_copy(src->node[i].sizes); dst->node[j].max = isl_vec_copy(src->node[i].max); dst->n++; if (!dst->node[j].space || !dst->node[j].sched) return -1; if (dst->node[j].compressed && (!dst->node[j].hull || !dst->node[j].compress || !dst->node[j].decompress)) return -1; } return 0; } /* 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; isl_union_map *tagged_condition; isl_union_map *tagged_validity; struct isl_sched_node *dst_src, *dst_dst; if (!edge_pred(edge, data)) continue; if (isl_map_plain_is_empty(edge->map)) continue; dst_src = graph_find_node(ctx, dst, edge->src->space); dst_dst = graph_find_node(ctx, dst, edge->dst->space); if (!dst_src || !dst_dst) { if (is_validity(edge) || is_conditional_validity(edge)) isl_die(ctx, isl_error_internal, "backward (conditional) validity edge", return -1); continue; } map = isl_map_copy(edge->map); tagged_condition = isl_union_map_copy(edge->tagged_condition); tagged_validity = isl_union_map_copy(edge->tagged_validity); 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].tagged_condition = tagged_condition; dst->edge[dst->n_edge].tagged_validity = tagged_validity; dst->edge[dst->n_edge].types = edge->types; dst->n_edge++; if (edge->tagged_condition && !tagged_condition) return -1; if (edge->tagged_validity && !tagged_validity) return -1; 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; } /* Compute the maximal number of variables over all nodes. * This is the maximal number of linearly independent schedule * rows that we need to compute. * Just in case we end up in a part of the dependence graph * with only lower-dimensional domains, we make sure we will * compute the required amount of extra linearly independent rows. */ static int compute_maxvar(struct isl_sched_graph *graph) { int i; graph->maxvar = 0; for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; int nvar; if (node_update_cmap(node) < 0) return -1; nvar = node->nvar + graph->n_row - node->rank; if (nvar > graph->maxvar) graph->maxvar = nvar; } return 0; } /* Extract the subgraph of "graph" that consists of the node satisfying * "node_pred" and the edges satisfying "edge_pred" and store * the result in "sub". */ static int extract_sub_graph(isl_ctx *ctx, struct isl_sched_graph *graph, int (*node_pred)(struct isl_sched_node *node, int data), int (*edge_pred)(struct isl_sched_edge *edge, int data), int data, struct isl_sched_graph *sub) { int i, n = 0, n_edge = 0; int t; for (i = 0; i < graph->n; ++i) if (node_pred(&graph->node[i], data)) ++n; for (i = 0; i < graph->n_edge; ++i) if (edge_pred(&graph->edge[i], data)) ++n_edge; if (graph_alloc(ctx, sub, n, n_edge) < 0) return -1; if (copy_nodes(sub, graph, node_pred, data) < 0) return -1; if (graph_init_table(ctx, sub) < 0) return -1; for (t = 0; t <= isl_edge_last; ++t) sub->max_edge[t] = graph->max_edge[t]; if (graph_init_edge_tables(ctx, sub) < 0) return -1; if (copy_edges(ctx, sub, graph, edge_pred, data) < 0) return -1; sub->n_row = graph->n_row; sub->max_row = graph->max_row; sub->n_total_row = graph->n_total_row; sub->band_start = graph->band_start; return 0; } static __isl_give isl_schedule_node *compute_schedule(isl_schedule_node *node, struct isl_sched_graph *graph); static __isl_give isl_schedule_node *compute_schedule_wcc( isl_schedule_node *node, struct isl_sched_graph *graph); /* Compute a schedule for a subgraph of "graph". In particular, for * the graph composed of nodes that satisfy node_pred and edges that * that satisfy edge_pred. * If the subgraph is known to consist of a single component, then wcc should * be set and then we call compute_schedule_wcc on the constructed subgraph. * Otherwise, we call compute_schedule, which will check whether the subgraph * is connected. * * The schedule is inserted at "node" and the updated schedule node * is returned. */ static __isl_give isl_schedule_node *compute_sub_schedule( __isl_take isl_schedule_node *node, isl_ctx *ctx, struct isl_sched_graph *graph, int (*node_pred)(struct isl_sched_node *node, int data), int (*edge_pred)(struct isl_sched_edge *edge, int data), int data, int wcc) { struct isl_sched_graph split = { 0 }; if (extract_sub_graph(ctx, graph, node_pred, edge_pred, data, &split) < 0) goto error; if (wcc) node = compute_schedule_wcc(node, &split); else node = compute_schedule(node, &split); graph_free(ctx, &split); return node; error: graph_free(ctx, &split); return isl_schedule_node_free(node); } static int edge_scc_exactly(struct isl_sched_edge *edge, int scc) { return edge->src->scc == scc && edge->dst->scc == scc; } static int edge_dst_scc_at_most(struct isl_sched_edge *edge, int scc) { return edge->dst->scc <= scc; } static int edge_src_scc_at_least(struct isl_sched_edge *edge, int scc) { return edge->src->scc >= scc; } /* Reset the current band by dropping all its schedule rows. */ static int reset_band(struct isl_sched_graph *graph) { int i; int drop; drop = graph->n_total_row - graph->band_start; graph->n_total_row -= drop; graph->n_row -= drop; 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_drop_rows(node->sched, graph->band_start, drop); if (!node->sched) return -1; } return 0; } /* Split the current graph into two parts and compute a schedule for each * part individually. In particular, one part consists of all SCCs up * to and including graph->src_scc, while the other part contains the other * SCCs. The split is enforced by a sequence node inserted at position "node" * in the schedule tree. Return the updated schedule node. * If either of these two parts consists of a sequence, then it is spliced * into the sequence containing the two parts. * * The current band is reset. It would be possible to reuse * the previously computed rows 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. */ static __isl_give isl_schedule_node *compute_split_schedule( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph) { int is_seq; isl_ctx *ctx; isl_union_set_list *filters; if (!node) return NULL; if (reset_band(graph) < 0) return isl_schedule_node_free(node); next_band(graph); ctx = isl_schedule_node_get_ctx(node); filters = extract_split(ctx, graph); node = isl_schedule_node_insert_sequence(node, filters); node = isl_schedule_node_child(node, 1); node = isl_schedule_node_child(node, 0); node = compute_sub_schedule(node, ctx, graph, &node_scc_at_least, &edge_src_scc_at_least, graph->src_scc + 1, 0); is_seq = isl_schedule_node_get_type(node) == isl_schedule_node_sequence; node = isl_schedule_node_parent(node); node = isl_schedule_node_parent(node); if (is_seq) node = isl_schedule_node_sequence_splice_child(node, 1); node = isl_schedule_node_child(node, 0); node = isl_schedule_node_child(node, 0); node = compute_sub_schedule(node, ctx, graph, &node_scc_at_most, &edge_dst_scc_at_most, graph->src_scc, 0); is_seq = isl_schedule_node_get_type(node) == isl_schedule_node_sequence; node = isl_schedule_node_parent(node); node = isl_schedule_node_parent(node); if (is_seq) node = isl_schedule_node_sequence_splice_child(node, 0); return node; } /* Insert a band node at position "node" in the schedule tree corresponding * to the current band in "graph". Mark the band node permutable * if "permutable" is set. * The partial schedules and the coincidence property are extracted * from the graph nodes. * Return the updated schedule node. */ static __isl_give isl_schedule_node *insert_current_band( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph, int permutable) { int i; int start, end, n; isl_multi_aff *ma; isl_multi_pw_aff *mpa; isl_multi_union_pw_aff *mupa; if (!node) return NULL; if (graph->n < 1) isl_die(isl_schedule_node_get_ctx(node), isl_error_internal, "graph should have at least one node", return isl_schedule_node_free(node)); start = graph->band_start; end = graph->n_total_row; n = end - start; ma = node_extract_partial_schedule_multi_aff(&graph->node[0], start, n); mpa = isl_multi_pw_aff_from_multi_aff(ma); mupa = isl_multi_union_pw_aff_from_multi_pw_aff(mpa); for (i = 1; i < graph->n; ++i) { isl_multi_union_pw_aff *mupa_i; ma = node_extract_partial_schedule_multi_aff(&graph->node[i], start, n); mpa = isl_multi_pw_aff_from_multi_aff(ma); mupa_i = isl_multi_union_pw_aff_from_multi_pw_aff(mpa); mupa = isl_multi_union_pw_aff_union_add(mupa, mupa_i); } node = isl_schedule_node_insert_partial_schedule(node, mupa); for (i = 0; i < n; ++i) node = isl_schedule_node_band_member_set_coincident(node, i, graph->node[0].coincident[start + i]); node = isl_schedule_node_band_set_permutable(node, permutable); return node; } /* Update the dependence relations based on the current schedule, * add the current band to "node" and then continue with the computation * of the next band. * Return the updated schedule node. */ static __isl_give isl_schedule_node *compute_next_band( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph, int permutable) { isl_ctx *ctx; if (!node) return NULL; ctx = isl_schedule_node_get_ctx(node); if (update_edges(ctx, graph) < 0) return isl_schedule_node_free(node); node = insert_current_band(node, graph, permutable); next_band(graph); node = isl_schedule_node_child(node, 0); node = compute_schedule(node, graph); node = isl_schedule_node_parent(node); return node; } /* 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) * = c_j_x (y - x) >= e_i * * for each (x,y) in R. * We obtain general constraints on coefficients (c_0, c_n, c_x) * of valid constraints for (y - x) and then plug in (-e_i, 0, c_j_x), * 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, struct isl_sched_edge *edge, __isl_take isl_map *map, int pos) { int offset; isl_ctx *ctx = isl_map_get_ctx(map); isl_dim_map *dim_map; isl_basic_set *coef; struct isl_sched_node *node = edge->src; coef = intra_coefficients(graph, node, map); if (!coef) return -1; offset = coef_var_offset(coef); dim_map = intra_dim_map(ctx, graph, node, offset, 1); isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -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); return 0; } /* 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 * * for each (x,y) in R. * We obtain general constraints on coefficients (c_0, c_n, c_x) * of valid constraints for R and then plug in * (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, c_k_x - c_j_x) * with each coefficient (except e_i, c_*_0 and c_*_n) * represented as a pair of non-negative coefficients. */ static int add_inter_constraints(struct isl_sched_graph *graph, struct isl_sched_edge *edge, __isl_take isl_map *map, int pos) { int offset; isl_ctx *ctx = isl_map_get_ctx(map); 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, edge, map); if (!coef) return -1; offset = coef_var_offset(coef); dim_map = inter_dim_map(ctx, graph, src, dst, offset, 1); isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -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); return 0; } /* Add constraints to graph->lp that force all (conditional) validity * dependences to be respected and attempt to carry them. */ static int add_all_constraints(struct isl_sched_graph *graph) { int i, j; int pos; pos = 0; for (i = 0; i < graph->n_edge; ++i) { struct isl_sched_edge *edge= &graph->edge[i]; if (!is_any_validity(edge)) 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]; if (!is_any_validity(edge)) 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 (count_map_constraints(graph, edge, map, n_eq, n_ineq, 1, 0) < 0) return -1; } } return 0; } /* Construct an LP problem for finding schedule coefficients * such that the schedule carries as many dependences as possible. * In particular, for each dependence i, we bound the dependence distance * from below by e_i, with 0 <= e_i <= 1 and then maximize the sum * of all e_i's. Dependences 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 of 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 * of two non-negative variables. The negative part always appears * immediately before the positive part. * Other than that, the variables have the following order * * - sum of (1 - e_i) over all edges * - sum of all c_n coefficients * (unconstrained when computing non-parametric schedules) * - sum of positive and negative parts of all c_x coefficients * - for each edge * - e_i * - for each node * - c_i_0 * - c_i_n (if parametric) * - positive and negative parts of c_i_x * * 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 isl_stat setup_carry_lp(isl_ctx *ctx, struct isl_sched_graph *graph) { int i; int k; 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 + n_edge; for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[graph->sorted[i]]; node->start = total; total += 1 + node->nparam + 2 * node->nvar; } if (count_all_constraints(graph, &n_eq, &n_ineq) < 0) return isl_stat_error; dim = isl_space_set_alloc(ctx, 0, total); isl_basic_set_free(graph->lp); n_eq += 3; 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 isl_stat_error; isl_seq_clr(graph->lp->eq[k], 1 + total); 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 < n_edge; ++i) isl_int_set_si(graph->lp->eq[k][4 + i], 1); if (add_param_sum_constraint(graph, 1) < 0) return isl_stat_error; if (add_var_sum_constraint(graph, 2) < 0) return isl_stat_error; for (i = 0; i < n_edge; ++i) { k = isl_basic_set_alloc_inequality(graph->lp); if (k < 0) return isl_stat_error; isl_seq_clr(graph->lp->ineq[k], 1 + total); isl_int_set_si(graph->lp->ineq[k][4 + i], -1); isl_int_set_si(graph->lp->ineq[k][0], 1); } if (add_all_constraints(graph) < 0) return isl_stat_error; return isl_stat_ok; } static __isl_give isl_schedule_node *compute_component_schedule( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph, int wcc); /* Comparison function for sorting the statements based on * the corresponding value in "r". */ static int smaller_value(const void *a, const void *b, void *data) { isl_vec *r = data; const int *i1 = a; const int *i2 = b; return isl_int_cmp(r->el[*i1], r->el[*i2]); } /* If the schedule_split_scaled option is set and if the linear * parts of the scheduling rows for all nodes in the graphs have * a non-trivial common divisor, then split off the remainder of the * constant term modulo this common divisor from the linear part. * Otherwise, insert a band node directly and continue with * the construction of the schedule. * * If a non-trivial common divisor is found, then * the linear part is reduced and the remainder is enforced * by a sequence node with the children placed in the order * of this remainder. * In particular, we assign an scc index based on the remainder and * then rely on compute_component_schedule to insert the sequence and * to continue the schedule construction on each part. */ static __isl_give isl_schedule_node *split_scaled( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph) { int i; int row; int scc; isl_ctx *ctx; isl_int gcd, gcd_i; isl_vec *r; int *order; if (!node) return NULL; ctx = isl_schedule_node_get_ctx(node); if (!ctx->opt->schedule_split_scaled) return compute_next_band(node, graph, 0); if (graph->n <= 1) return compute_next_band(node, graph, 0); 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 compute_next_band(node, graph, 0); } r = isl_vec_alloc(ctx, graph->n); order = isl_calloc_array(ctx, int, graph->n); if (!r || !order) goto error; for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; order[i] = i; isl_int_fdiv_r(r->el[i], 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; } if (isl_sort(order, graph->n, sizeof(order[0]), &smaller_value, r) < 0) goto error; scc = 0; for (i = 0; i < graph->n; ++i) { if (i > 0 && isl_int_ne(r->el[order[i - 1]], r->el[order[i]])) ++scc; graph->node[order[i]].scc = scc; } graph->scc = ++scc; graph->weak = 0; isl_int_clear(gcd); isl_vec_free(r); free(order); if (update_edges(ctx, graph) < 0) return isl_schedule_node_free(node); node = insert_current_band(node, graph, 0); next_band(graph); node = isl_schedule_node_child(node, 0); node = compute_component_schedule(node, graph, 0); node = isl_schedule_node_parent(node); return node; error: isl_vec_free(r); free(order); isl_int_clear(gcd); return isl_schedule_node_free(node); } /* Is the schedule row "sol" trivial on node "node"? * That is, is the solution zero on the dimensions orthogonal to * the previously found solutions? * Return 1 if the solution is trivial, 0 if it is not and -1 on error. * * Each coefficient is represented as the difference between * two non-negative values in "sol". "sol" has been computed * in terms of the original iterators (i.e., without use of cmap). * We construct the schedule row s and write it as a linear * combination of (linear combinations of) previously computed schedule rows. * s = Q c or c = U s. * If the final entries of c are all zero, then the solution is trivial. */ static int is_trivial(struct isl_sched_node *node, __isl_keep isl_vec *sol) { int trivial; isl_vec *node_sol; if (!sol) return -1; if (node->nvar == node->rank) return 0; node_sol = extract_var_coef(node, sol); node_sol = isl_mat_vec_product(isl_mat_copy(node->cinv), node_sol); if (!node_sol) return -1; trivial = isl_seq_first_non_zero(node_sol->el + node->rank, node->nvar - node->rank) == -1; isl_vec_free(node_sol); return trivial; } /* Is the schedule row "sol" trivial on any node where it should * not be trivial? * "sol" has been computed in terms of the original iterators * (i.e., without use of cmap). * Return 1 if any solution is trivial, 0 if they are not and -1 on error. */ 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]; int trivial; if (!needs_row(graph, node)) continue; trivial = is_trivial(node, sol); if (trivial < 0 || trivial) return trivial; } return 0; } /* Does the schedule represented by "sol" perform loop coalescing on "node"? * If so, return the position of the coalesced dimension. * Otherwise, return node->nvar or -1 on error. * * In particular, look for pairs of coefficients c_i and c_j such that * |c_j/c_i| >= size_i, i.e., |c_j| >= |c_i * size_i|. * If any such pair is found, then return i. * If size_i is infinity, then no check on c_i needs to be performed. */ static int find_node_coalescing(struct isl_sched_node *node, __isl_keep isl_vec *sol) { int i, j; isl_int max; isl_vec *csol; if (node->nvar <= 1) return node->nvar; csol = extract_var_coef(node, sol); if (!csol) return -1; isl_int_init(max); for (i = 0; i < node->nvar; ++i) { isl_val *v; if (isl_int_is_zero(csol->el[i])) continue; v = isl_multi_val_get_val(node->sizes, i); if (!v) goto error; if (!isl_val_is_int(v)) { isl_val_free(v); continue; } isl_int_mul(max, v->n, csol->el[i]); isl_val_free(v); for (j = 0; j < node->nvar; ++j) { if (j == i) continue; if (isl_int_abs_ge(csol->el[j], max)) break; } if (j < node->nvar) break; } isl_int_clear(max); isl_vec_free(csol); return i; error: isl_int_clear(max); isl_vec_free(csol); return -1; } /* Force the schedule coefficient at position "pos" of "node" to be zero * in "tl". * The coefficient is encoded as the difference between two non-negative * variables. Force these two variables to have the same value. */ static __isl_give isl_tab_lexmin *zero_out_node_coef( __isl_take isl_tab_lexmin *tl, struct isl_sched_node *node, int pos) { int dim; isl_ctx *ctx; isl_vec *eq; ctx = isl_space_get_ctx(node->space); dim = isl_tab_lexmin_dim(tl); if (dim < 0) return isl_tab_lexmin_free(tl); eq = isl_vec_alloc(ctx, 1 + dim); eq = isl_vec_clr(eq); if (!eq) return isl_tab_lexmin_free(tl); pos = 1 + node_var_coef_offset(node) + 2 * pos; isl_int_set_si(eq->el[pos], 1); isl_int_set_si(eq->el[pos + 1], -1); tl = isl_tab_lexmin_add_eq(tl, eq->el); isl_vec_free(eq); return tl; } /* Return the lexicographically smallest rational point in the basic set * from which "tl" was constructed, double checking that this input set * was not empty. */ static __isl_give isl_vec *non_empty_solution(__isl_keep isl_tab_lexmin *tl) { isl_vec *sol; sol = isl_tab_lexmin_get_solution(tl); if (!sol) return NULL; if (sol->size == 0) isl_die(isl_vec_get_ctx(sol), isl_error_internal, "error in schedule construction", return isl_vec_free(sol)); return sol; } /* Does the solution "sol" of the LP problem constructed by setup_carry_lp * carry any of the "n_edge" groups of dependences? * The value in the first position is the sum of (1 - e_i) over all "n_edge" * edges, with 0 <= e_i <= 1 equal to 1 when the dependences represented * by the edge are carried by the solution. * If the sum of the (1 - e_i) is smaller than "n_edge" then at least * one of those is carried. * * Note that despite the fact that the problem is solved using a rational * solver, the solution is guaranteed to be integral. * Specifically, the dependence distance lower bounds e_i (and therefore * also their sum) are integers. See Lemma 5 of [1]. * * Any potential denominator of the sum is cleared by this function. * The denominator is not relevant for any of the other elements * in the solution. * * [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 carries_dependences(__isl_keep isl_vec *sol, int n_edge) { isl_int_divexact(sol->el[1], sol->el[1], sol->el[0]); isl_int_set_si(sol->el[0], 1); return isl_int_cmp_si(sol->el[1], n_edge) < 0; } /* Return the lexicographically smallest rational point in "lp", * assuming that all variables are non-negative and performing some * additional sanity checks. * In particular, "lp" should not be empty by construction. * Double check that this is the case. * Also, check that dependences are carried for at least one of * the "n_edge" edges. * * If the computed schedule performs loop coalescing on a given node, * i.e., if it is of the form * * c_i i + c_j j + ... * * with |c_j/c_i| >= size_i, then force the coefficient c_i to be zero * to cut out this solution. Repeat this process until no more loop * coalescing occurs or until no more dependences can be carried. * In the latter case, revert to the previously computed solution. */ static __isl_give isl_vec *non_neg_lexmin(struct isl_sched_graph *graph, __isl_take isl_basic_set *lp, int n_edge) { int i, pos; isl_ctx *ctx; isl_tab_lexmin *tl; isl_vec *sol, *prev = NULL; int treat_coalescing; if (!lp) return NULL; ctx = isl_basic_set_get_ctx(lp); treat_coalescing = isl_options_get_schedule_treat_coalescing(ctx); tl = isl_tab_lexmin_from_basic_set(lp); do { sol = non_empty_solution(tl); if (!sol) goto error; if (!carries_dependences(sol, n_edge)) { if (!prev) isl_die(ctx, isl_error_unknown, "unable to carry dependences", goto error); isl_vec_free(sol); sol = prev; break; } prev = isl_vec_free(prev); if (!treat_coalescing) break; for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; pos = find_node_coalescing(node, sol); if (pos < 0) goto error; if (pos < node->nvar) break; } if (i < graph->n) { prev = sol; tl = zero_out_node_coef(tl, &graph->node[i], pos); } } while (i < graph->n); isl_tab_lexmin_free(tl); return sol; error: isl_tab_lexmin_free(tl); isl_vec_free(prev); isl_vec_free(sol); return NULL; } /* 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. * * If there is only one component, then we accept the schedule row anyway, * but we do not consider it as a complete row and therefore do not * increment graph->n_row. Note that the ranks of the nodes that * do get a non-trivial schedule part will get updated regardless and * graph->maxvar is computed based on these ranks. The test for * whether more schedule rows are required in compute_schedule_wcc * is therefore not affected. * * Insert a band corresponding to the schedule row at position "node" * of the schedule tree and continue with the construction of the schedule. * This insertion and the continued construction is performed by split_scaled * after optionally checking for non-trivial common divisors. */ static __isl_give isl_schedule_node *carry_dependences( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph) { int i; int n_edge; int trivial; isl_ctx *ctx; isl_vec *sol; isl_basic_set *lp; if (!node) return NULL; n_edge = 0; for (i = 0; i < graph->n_edge; ++i) n_edge += graph->edge[i].map->n; ctx = isl_schedule_node_get_ctx(node); if (setup_carry_lp(ctx, graph) < 0) return isl_schedule_node_free(node); lp = isl_basic_set_copy(graph->lp); sol = non_neg_lexmin(graph, lp, n_edge); if (!sol) return isl_schedule_node_free(node); trivial = is_any_trivial(graph, sol); if (trivial < 0) { sol = isl_vec_free(sol); } else if (trivial && graph->scc > 1) { isl_vec_free(sol); return compute_component_schedule(node, graph, 1); } if (update_schedule(graph, sol, 0, 0) < 0) return isl_schedule_node_free(node); if (trivial) graph->n_row--; return split_scaled(node, graph); } /* Topologically sort statements mapped to the same schedule iteration * and add insert a sequence node in front of "node" * corresponding to this order. * If "initialized" is set, then it may be assumed that compute_maxvar * has been called on the current band. Otherwise, call * compute_maxvar if and before carry_dependences gets called. * * If it turns out to be impossible to sort the statements apart, * because different dependences impose different orderings * on the statements, then we extend the schedule such that * it carries at least one more dependence. */ static __isl_give isl_schedule_node *sort_statements( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph, int initialized) { isl_ctx *ctx; isl_union_set_list *filters; if (!node) return NULL; ctx = isl_schedule_node_get_ctx(node); if (graph->n < 1) isl_die(ctx, isl_error_internal, "graph should have at least one node", return isl_schedule_node_free(node)); if (graph->n == 1) return node; if (update_edges(ctx, graph) < 0) return isl_schedule_node_free(node); if (graph->n_edge == 0) return node; if (detect_sccs(ctx, graph) < 0) return isl_schedule_node_free(node); next_band(graph); if (graph->scc < graph->n) { if (!initialized && compute_maxvar(graph) < 0) return isl_schedule_node_free(node); return carry_dependences(node, graph); } filters = extract_sccs(ctx, graph); node = isl_schedule_node_insert_sequence(node, filters); return node; } /* Are there any (non-empty) (conditional) 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 (is_any_validity(&graph->edge[i])) 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 and return the updated schedule node. * * 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 __isl_give isl_schedule_node *compute_schedule_wcc_feautrier( isl_schedule_node *node, struct isl_sched_graph *graph) { return carry_dependences(node, graph); } /* Turn off the "local" bit on all (condition) edges. */ static void clear_local_edges(struct isl_sched_graph *graph) { int i; for (i = 0; i < graph->n_edge; ++i) if (is_condition(&graph->edge[i])) clear_local(&graph->edge[i]); } /* Does "graph" have both condition and conditional validity edges? */ static int need_condition_check(struct isl_sched_graph *graph) { int i; int any_condition = 0; int any_conditional_validity = 0; for (i = 0; i < graph->n_edge; ++i) { if (is_condition(&graph->edge[i])) any_condition = 1; if (is_conditional_validity(&graph->edge[i])) any_conditional_validity = 1; } return any_condition && any_conditional_validity; } /* Does "graph" contain any coincidence edge? */ static int has_any_coincidence(struct isl_sched_graph *graph) { int i; for (i = 0; i < graph->n_edge; ++i) if (is_coincidence(&graph->edge[i])) return 1; return 0; } /* Extract the final schedule row as a map with the iteration domain * of "node" as domain. */ static __isl_give isl_map *final_row(struct isl_sched_node *node) { isl_local_space *ls; isl_aff *aff; int row; row = isl_mat_rows(node->sched) - 1; ls = isl_local_space_from_space(isl_space_copy(node->space)); aff = extract_schedule_row(ls, node, row); return isl_map_from_aff(aff); } /* Is the conditional validity dependence in the edge with index "edge_index" * violated by the latest (i.e., final) row of the schedule? * That is, is i scheduled after j * for any conditional validity dependence i -> j? */ static int is_violated(struct isl_sched_graph *graph, int edge_index) { isl_map *src_sched, *dst_sched, *map; struct isl_sched_edge *edge = &graph->edge[edge_index]; int empty; src_sched = final_row(edge->src); dst_sched = final_row(edge->dst); map = isl_map_copy(edge->map); map = isl_map_apply_domain(map, src_sched); map = isl_map_apply_range(map, dst_sched); map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0); empty = isl_map_is_empty(map); isl_map_free(map); if (empty < 0) return -1; return !empty; } /* Does "graph" have any satisfied condition edges that * are adjacent to the conditional validity constraint with * domain "conditional_source" and range "conditional_sink"? * * A satisfied condition is one that is not local. * If a condition was forced to be local already (i.e., marked as local) * then there is no need to check if it is in fact local. * * Additionally, mark all adjacent condition edges found as local. */ static int has_adjacent_true_conditions(struct isl_sched_graph *graph, __isl_keep isl_union_set *conditional_source, __isl_keep isl_union_set *conditional_sink) { int i; int any = 0; for (i = 0; i < graph->n_edge; ++i) { int adjacent, local; isl_union_map *condition; if (!is_condition(&graph->edge[i])) continue; if (is_local(&graph->edge[i])) continue; condition = graph->edge[i].tagged_condition; adjacent = domain_intersects(condition, conditional_sink); if (adjacent >= 0 && !adjacent) adjacent = range_intersects(condition, conditional_source); if (adjacent < 0) return -1; if (!adjacent) continue; set_local(&graph->edge[i]); local = is_condition_false(&graph->edge[i]); if (local < 0) return -1; if (!local) any = 1; } return any; } /* Are there any violated conditional validity dependences with * adjacent condition dependences that are not local with respect * to the current schedule? * That is, is the conditional validity constraint violated? * * Additionally, mark all those adjacent condition dependences as local. * We also mark those adjacent condition dependences that were not marked * as local before, but just happened to be local already. This ensures * that they remain local if the schedule is recomputed. * * We first collect domain and range of all violated conditional validity * dependences and then check if there are any adjacent non-local * condition dependences. */ static int has_violated_conditional_constraint(isl_ctx *ctx, struct isl_sched_graph *graph) { int i; int any = 0; isl_union_set *source, *sink; source = isl_union_set_empty(isl_space_params_alloc(ctx, 0)); sink = isl_union_set_empty(isl_space_params_alloc(ctx, 0)); for (i = 0; i < graph->n_edge; ++i) { isl_union_set *uset; isl_union_map *umap; int violated; if (!is_conditional_validity(&graph->edge[i])) continue; violated = is_violated(graph, i); if (violated < 0) goto error; if (!violated) continue; any = 1; umap = isl_union_map_copy(graph->edge[i].tagged_validity); uset = isl_union_map_domain(umap); source = isl_union_set_union(source, uset); source = isl_union_set_coalesce(source); umap = isl_union_map_copy(graph->edge[i].tagged_validity); uset = isl_union_map_range(umap); sink = isl_union_set_union(sink, uset); sink = isl_union_set_coalesce(sink); } if (any) any = has_adjacent_true_conditions(graph, source, sink); isl_union_set_free(source); isl_union_set_free(sink); return any; error: isl_union_set_free(source); isl_union_set_free(sink); return -1; } /* Examine the current band (the rows between graph->band_start and * graph->n_total_row), deciding whether to drop it or add it to "node" * and then continue with the computation of the next band, if any. * If "initialized" is set, then it may be assumed that compute_maxvar * has been called on the current band. Otherwise, call * compute_maxvar if and before carry_dependences gets called. * * The caller keeps looking for a new row as long as * graph->n_row < graph->maxvar. If the latest attempt to find * such a row failed (i.e., we still have graph->n_row < graph->maxvar), * then we either * - split between SCCs and start over (assuming we found an interesting * pair of SCCs between which to split) * - continue with the next band (assuming the current band has at least * one row) * - try to carry as many dependences as possible and continue with the next * band * In each case, we first insert a band node in the schedule tree * if any rows have been computed. * * If the caller managed to complete the schedule, we insert a band node * (if any schedule rows were computed) and we finish off by topologically * sorting the statements based on the remaining dependences. */ static __isl_give isl_schedule_node *compute_schedule_finish_band( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph, int initialized) { int insert; if (!node) return NULL; if (graph->n_row < graph->maxvar) { isl_ctx *ctx; int empty = graph->n_total_row == graph->band_start; ctx = isl_schedule_node_get_ctx(node); if (!ctx->opt->schedule_maximize_band_depth && !empty) return compute_next_band(node, graph, 1); if (graph->src_scc >= 0) return compute_split_schedule(node, graph); if (!empty) return compute_next_band(node, graph, 1); if (!initialized && compute_maxvar(graph) < 0) return isl_schedule_node_free(node); return carry_dependences(node, graph); } insert = graph->n_total_row > graph->band_start; if (insert) { node = insert_current_band(node, graph, 1); node = isl_schedule_node_child(node, 0); } node = sort_statements(node, graph, initialized); if (insert) node = isl_schedule_node_parent(node); return node; } /* Construct a band of schedule rows for a connected dependence graph. * The caller is responsible for determining the strongly connected * components and calling compute_maxvar first. * * 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 * in the sequence, i.e., such that the sequence is tilable), with as * many of the initial rows as possible satisfying the coincidence constraints. * The computation stops if we can't find any more rows or if we have found * all the rows we wanted to find. * * If ctx->opt->schedule_outer_coincidence is set, then we force the * outermost dimension to satisfy the coincidence constraints. If this * turns out to be impossible, we fall back on the general scheme above * and try to carry as many dependences as possible. * * If "graph" contains both condition and conditional validity dependences, * then we need to check that that the conditional schedule constraint * is satisfied, i.e., there are no violated conditional validity dependences * that are adjacent to any non-local condition dependences. * If there are, then we mark all those adjacent condition dependences * as local and recompute the current band. Those dependences that * are marked local will then be forced to be local. * The initial computation is performed with no dependences marked as local. * If we are lucky, then there will be no violated conditional validity * dependences adjacent to any non-local condition dependences. * Otherwise, we mark some additional condition dependences as local and * recompute. We continue this process until there are no violations left or * until we are no longer able to compute a schedule. * Since there are only a finite number of dependences, * there will only be a finite number of iterations. */ static isl_stat compute_schedule_wcc_band(isl_ctx *ctx, struct isl_sched_graph *graph) { int has_coincidence; int use_coincidence; int force_coincidence = 0; int check_conditional; if (sort_sccs(graph) < 0) return isl_stat_error; clear_local_edges(graph); check_conditional = need_condition_check(graph); has_coincidence = has_any_coincidence(graph); if (ctx->opt->schedule_outer_coincidence) force_coincidence = 1; use_coincidence = has_coincidence; while (graph->n_row < graph->maxvar) { isl_vec *sol; int violated; int coincident; graph->src_scc = -1; graph->dst_scc = -1; if (setup_lp(ctx, graph, use_coincidence) < 0) return isl_stat_error; sol = solve_lp(graph); if (!sol) return isl_stat_error; if (sol->size == 0) { int empty = graph->n_total_row == graph->band_start; isl_vec_free(sol); if (use_coincidence && (!force_coincidence || !empty)) { use_coincidence = 0; continue; } return isl_stat_ok; } coincident = !has_coincidence || use_coincidence; if (update_schedule(graph, sol, 1, coincident) < 0) return isl_stat_error; if (!check_conditional) continue; violated = has_violated_conditional_constraint(ctx, graph); if (violated < 0) return isl_stat_error; if (!violated) continue; if (reset_band(graph) < 0) return isl_stat_error; use_coincidence = has_coincidence; } return isl_stat_ok; } /* Compute a schedule for a connected dependence graph by considering * the graph as a whole and return the updated schedule node. * * The actual schedule rows of the current band are computed by * compute_schedule_wcc_band. compute_schedule_finish_band takes * care of integrating the band into "node" and continuing * the computation. */ static __isl_give isl_schedule_node *compute_schedule_wcc_whole( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph) { isl_ctx *ctx; if (!node) return NULL; ctx = isl_schedule_node_get_ctx(node); if (compute_schedule_wcc_band(ctx, graph) < 0) return isl_schedule_node_free(node); return compute_schedule_finish_band(node, graph, 1); } /* Clustering information used by compute_schedule_wcc_clustering. * * "n" is the number of SCCs in the original dependence graph * "scc" is an array of "n" elements, each representing an SCC * of the original dependence graph. All entries in the same cluster * have the same number of schedule rows. * "scc_cluster" maps each SCC index to the cluster to which it belongs, * where each cluster is represented by the index of the first SCC * in the cluster. Initially, each SCC belongs to a cluster containing * only that SCC. * * "scc_in_merge" is used by merge_clusters_along_edge to keep * track of which SCCs need to be merged. * * "cluster" contains the merged clusters of SCCs after the clustering * has completed. * * "scc_node" is a temporary data structure used inside copy_partial. * For each SCC, it keeps track of the number of nodes in the SCC * that have already been copied. */ struct isl_clustering { int n; struct isl_sched_graph *scc; struct isl_sched_graph *cluster; int *scc_cluster; int *scc_node; int *scc_in_merge; }; /* 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) { int i; c->n = graph->scc; c->scc = isl_calloc_array(ctx, struct isl_sched_graph, c->n); c->cluster = isl_calloc_array(ctx, struct isl_sched_graph, c->n); c->scc_cluster = isl_calloc_array(ctx, int, c->n); c->scc_node = isl_calloc_array(ctx, int, c->n); c->scc_in_merge = isl_calloc_array(ctx, int, c->n); if (!c->scc || !c->cluster || !c->scc_cluster || !c->scc_node || !c->scc_in_merge) return isl_stat_error; for (i = 0; i < c->n; ++i) { if (extract_sub_graph(ctx, graph, &node_scc_exactly, &edge_scc_exactly, i, &c->scc[i]) < 0) return isl_stat_error; c->scc[i].scc = 1; if (compute_maxvar(&c->scc[i]) < 0) return isl_stat_error; if (compute_schedule_wcc_band(ctx, &c->scc[i]) < 0) return isl_stat_error; c->scc_cluster[i] = i; } return isl_stat_ok; } /* Free all memory allocated for "c". */ static void clustering_free(isl_ctx *ctx, struct isl_clustering *c) { int i; if (c->scc) for (i = 0; i < c->n; ++i) graph_free(ctx, &c->scc[i]); free(c->scc); if (c->cluster) for (i = 0; i < c->n; ++i) graph_free(ctx, &c->cluster[i]); free(c->cluster); free(c->scc_cluster); free(c->scc_node); free(c->scc_in_merge); } /* 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) { return graph->n_row < graph->maxvar && graph->n_total_row == graph->band_start; } /* 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) { int i, best = graph->n_edge, best_dist, best_weight; for (i = 0; i < graph->n_edge; ++i) { struct isl_sched_edge *edge = &graph->edge[i]; int dist, weight; if (!is_proximity(edge)) continue; if (edge->no_merge) continue; if (bad_cluster(&c->scc[edge->src->scc]) || bad_cluster(&c->scc[edge->dst->scc])) continue; dist = c->scc_cluster[edge->dst->scc] - c->scc_cluster[edge->src->scc]; if (dist == 0) continue; weight = edge->weight; if (best < graph->n_edge) { if (best_weight > weight) continue; if (best_weight == weight && best_dist <= dist) continue; } best = i; best_dist = dist; best_weight = weight; } return best; } /* 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 { struct isl_sched_graph *graph; int *scc_cluster; int src; int dst; }; /* 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) { struct isl_mark_merge_sccs_data *data = user; struct isl_sched_graph *graph = data->graph; int *scc_cluster = data->scc_cluster; if (data->src == i && data->dst == j) return isl_bool_true; if (data->src == j && data->dst == i) return isl_bool_true; if (scc_cluster[graph->node[i].scc] == scc_cluster[graph->node[j].scc]) return isl_bool_true; return graph_has_validity_edge(graph, &graph->node[j], &graph->node[i]); } /* 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) { struct isl_mark_merge_sccs_data data; struct isl_tarjan_graph *g; int i; for (i = 0; i < c->n; ++i) c->scc_in_merge[i] = 0; data.graph = graph; data.scc_cluster = c->scc_cluster; data.src = graph->edge[edge].src - graph->node; data.dst = graph->edge[edge].dst - graph->node; g = isl_tarjan_graph_component(ctx, graph->n, data.dst, &cluster_follows, &data); if (!g) goto error; i = g->op; if (i < 3) isl_die(ctx, isl_error_internal, "expecting at least two nodes in component", goto error); if (g->order[--i] != -1) isl_die(ctx, isl_error_internal, "expecting end of component marker", goto error); for (--i; i >= 0 && g->order[i] != -1; --i) { int scc = graph->node[g->order[i]].scc; c->scc_in_merge[scc] = 1; } isl_tarjan_graph_free(g); return isl_stat_ok; error: isl_tarjan_graph_free(g); return isl_stat_error; } /* Construct the identifier "cluster_i". */ static __isl_give isl_id *cluster_id(isl_ctx *ctx, int i) { char name[40]; snprintf(name, sizeof(name), "cluster_%d", i); return isl_id_alloc(ctx, name, NULL); } /* 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) { int nvar; isl_space *space; isl_id *id; nvar = scc->n_total_row - scc->band_start; space = isl_space_copy(scc->node[0].space); space = isl_space_params(space); space = isl_space_set_from_params(space); space = isl_space_add_dims(space, isl_dim_set, nvar); id = cluster_id(isl_space_get_ctx(space), i); space = isl_space_set_tuple_id(space, isl_dim_set, id); return space; } /* 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) { int i; isl_space *space; isl_union_set *domain; space = isl_space_params_alloc(ctx, 0); domain = isl_union_set_empty(space); for (i = 0; i < graph->scc; ++i) { isl_space *space; if (!c->scc_in_merge[i]) continue; if (c->scc_cluster[i] != i) continue; space = cluster_space(&c->scc[i], i); domain = isl_union_set_add_set(domain, isl_set_universe(space)); } return domain; } /* 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) { int i, j; isl_space *space; isl_union_map *cluster_map; space = isl_space_params_alloc(ctx, 0); cluster_map = isl_union_map_empty(space); for (i = 0; i < graph->scc; ++i) { int start, n; isl_id *id; if (!c->scc_in_merge[i]) continue; id = cluster_id(ctx, c->scc_cluster[i]); start = c->scc[i].band_start; n = c->scc[i].n_total_row - start; for (j = 0; j < c->scc[i].n; ++j) { isl_multi_aff *ma; isl_map *map; struct isl_sched_node *node = &c->scc[i].node[j]; ma = node_extract_partial_schedule_multi_aff(node, start, n); ma = isl_multi_aff_set_tuple_id(ma, isl_dim_out, isl_id_copy(id)); map = isl_map_from_multi_aff(ma); cluster_map = isl_union_map_add_map(cluster_map, map); } isl_id_free(id); } return cluster_map; } /* 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) { enum isl_edge_type t; if (!sc) return NULL; for (t = isl_edge_first; t <= isl_edge_last; ++t) { if (t == isl_edge_condition || t == isl_edge_conditional_validity) continue; if (!is_type(edge, t)) continue; sc = isl_schedule_constraints_add(sc, t, isl_union_map_copy(umap)); } return 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) { enum isl_edge_type t; isl_union_map *tagged; for (t = isl_edge_condition; t <= isl_edge_conditional_validity; ++t) { if (!is_type(edge, t)) continue; if (t == isl_edge_condition) tagged = isl_union_map_copy(edge->tagged_condition); else tagged = isl_union_map_copy(edge->tagged_validity); tagged = isl_union_map_zip(tagged); tagged = isl_union_map_apply_domain(tagged, isl_union_map_copy(umap)); tagged = isl_union_map_zip(tagged); sc = isl_schedule_constraints_add(sc, t, tagged); if (!sc) return NULL; } return 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) { isl_union_map *umap; isl_space *space; isl_union_set *uset; isl_union_map *umap1, *umap2; if (!sc) return NULL; umap = isl_union_map_from_map(isl_map_copy(edge->map)); umap = isl_union_map_apply_domain(umap, isl_union_map_copy(cluster_map)); umap = isl_union_map_apply_range(umap, isl_union_map_copy(cluster_map)); sc = add_non_conditional_constraints(edge, umap, sc); isl_union_map_free(umap); if (!sc || (!is_condition(edge) && !is_conditional_validity(edge))) return sc; space = isl_space_domain(isl_map_get_space(edge->map)); uset = isl_union_set_from_set(isl_set_universe(space)); umap1 = isl_union_map_copy(cluster_map); umap1 = isl_union_map_intersect_domain(umap1, uset); space = isl_space_range(isl_map_get_space(edge->map)); uset = isl_union_set_from_set(isl_set_universe(space)); umap2 = isl_union_map_copy(cluster_map); umap2 = isl_union_map_intersect_domain(umap2, uset); umap = isl_union_map_product(umap1, umap2); sc = add_conditional_constraints(edge, umap, sc); isl_union_map_free(umap); return 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) { int i; for (i = 0; i < graph->n_edge; ++i) { struct isl_sched_edge *edge = &graph->edge[i]; if (!scc_in_merge[edge->src->scc]) continue; if (!scc_in_merge[edge->dst->scc]) continue; sc = collect_edge_constraints(edge, cluster_map, sc); } return 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) { isl_union_set *domain; isl_union_map *cluster_map; isl_schedule_constraints *sc; isl_stat r; domain = collect_domain(ctx, graph, c); sc = isl_schedule_constraints_on_domain(domain); if (!sc) return isl_stat_error; cluster_map = collect_cluster_map(ctx, graph, c); sc = collect_constraints(graph, c->scc_in_merge, cluster_map, sc); isl_union_map_free(cluster_map); r = graph_init(merge_graph, sc); isl_schedule_constraints_free(sc); return r; } /* 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 -1 on error. */ static int compute_maxvar_max_slack(int maxvar, struct isl_clustering *c) { int i, j; int max_slack; max_slack = 0; for (i = 0; i < c->n; ++i) { int nvar; struct isl_sched_graph *scc; if (!c->scc_in_merge[i]) continue; scc = &c->scc[i]; nvar = scc->n_total_row - scc->band_start; if (nvar != maxvar) continue; for (j = 0; j < scc->n; ++j) { struct isl_sched_node *node = &scc->node[j]; int slack; if (node_update_cmap(node) < 0) return -1; slack = node->nvar - node->rank; if (slack > max_slack) max_slack = slack; } } return max_slack; } /* 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 -1 in case of any error. * Only clusters that are about to be merged are considered. * "c" contains information about the clusters. */ static int limit_maxvar_to_slack(int maxvar, int max_slack, struct isl_clustering *c) { int i, j; for (i = 0; i < c->n; ++i) { int nvar; struct isl_sched_graph *scc; if (!c->scc_in_merge[i]) continue; scc = &c->scc[i]; nvar = scc->n_total_row - scc->band_start; if (nvar >= maxvar) continue; for (j = 0; j < scc->n; ++j) { struct isl_sched_node *node = &scc->node[j]; int slack; if (node_update_cmap(node) < 0) return -1; slack = node->nvar - node->rank; if (slack > max_slack) { maxvar = nvar; break; } } } return maxvar; } /* 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) { int max_slack, maxvar; max_slack = compute_maxvar_max_slack(merge_graph->maxvar, c); if (max_slack < 0) return isl_stat_error; maxvar = limit_maxvar_to_slack(merge_graph->maxvar, max_slack, c); if (maxvar < 0) return isl_stat_error; if (maxvar < merge_graph->maxvar) { if (isl_options_get_schedule_maximize_band_depth(ctx)) merge_graph->maxvar = 0; else merge_graph->maxvar = maxvar; } return isl_stat_ok; } /* 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) { int i; for (i = graph->band_start; i < graph->n_total_row; ++i) if (!graph->node[0].coincident[i]) break; return i - graph->band_start; } /* 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) { int i; int n_coincident; int max_coincident; max_coincident = 0; for (i = 0; i < c->n; ++i) { if (!c->scc_in_merge[i]) continue; n_coincident = get_n_coincident(&c->scc[i]); if (n_coincident > max_coincident) max_coincident = n_coincident; } n_coincident = get_n_coincident(merge_graph); return n_coincident >= max_coincident; } /* 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) { struct isl_sched_node *scc_node, *cluster_node; int start, n; isl_id *id; isl_space *space; isl_multi_aff *ma, *ma2; scc_node = graph_find_node(ctx, &c->scc[node->scc], node->space); start = c->scc[node->scc].band_start; n = c->scc[node->scc].n_total_row - start; ma = node_extract_partial_schedule_multi_aff(scc_node, start, n); space = cluster_space(&c->scc[node->scc], c->scc_cluster[node->scc]); cluster_node = graph_find_node(ctx, merge_graph, space); if (space && !cluster_node) isl_die(ctx, isl_error_internal, "unable to find cluster", space = isl_space_free(space)); id = isl_space_get_tuple_id(space, isl_dim_set); ma = isl_multi_aff_set_tuple_id(ma, isl_dim_out, id); isl_space_free(space); n = merge_graph->n_total_row; ma2 = node_extract_partial_schedule_multi_aff(cluster_node, 0, n); ma = isl_multi_aff_pullback_multi_aff(ma2, ma); return isl_map_from_multi_aff(ma); } /* 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) { isl_bool bounded; isl_set *test; if (!set) return isl_bool_error; test = isl_set_copy(set); test = isl_set_lower_bound_si(test, isl_dim_set, pos, 3); bounded = isl_set_is_empty(test); isl_set_free(test); if (bounded < 0 || !bounded) return bounded; test = isl_set_copy(set); test = isl_set_upper_bound_si(test, isl_dim_set, pos, -3); bounded = isl_set_is_empty(test); isl_set_free(test); return bounded; } /* 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) { int n; isl_bool single; if (!set) return isl_bool_error; set = isl_set_copy(set); n = isl_set_dim(set, isl_dim_set); set = isl_set_project_out(set, isl_dim_set, pos + 1, n - (pos + 1)); set = isl_set_project_out(set, isl_dim_set, 0, pos); single = isl_set_is_singleton(set); isl_set_free(set); return single; } /* 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) { isl_set *set; isl_bool single; set = isl_map_domain(isl_map_copy(map)); single = has_single_value(set, pos); isl_set_free(set); if (single < 0 || single) return single; set = isl_map_range(isl_map_copy(map)); single = has_single_value(set, pos); isl_set_free(set); return single; } /* 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) { int i, n, n_slack; isl_bool bounded; isl_map *map, *t; isl_set *dist; map = isl_map_copy(edge->map); t = extract_node_transformation(ctx, edge->src, c, merge_graph); map = isl_map_apply_domain(map, t); t = extract_node_transformation(ctx, edge->dst, c, merge_graph); map = isl_map_apply_range(map, t); dist = isl_map_deltas(isl_map_copy(map)); bounded = isl_bool_true; n = isl_set_dim(dist, isl_dim_set); n_slack = n - edge->weight; if (edge->weight < 0) n_slack -= graph->max_weight + 1; for (i = 0; i < n; ++i) { isl_bool bounded_i, singular_i; bounded_i = distance_is_bounded(dist, i); if (bounded_i < 0) goto error; if (bounded_i) continue; if (edge->weight >= 0) bounded = isl_bool_false; n_slack--; if (n_slack < 0) break; singular_i = has_singular_src_or_dst(map, i); if (singular_i < 0) goto error; if (singular_i) continue; bounded = isl_bool_false; break; } if (!bounded && i >= n && edge->weight >= 0) edge->weight -= graph->max_weight + 1; isl_map_free(map); isl_set_free(dist); return bounded; error: isl_map_free(map); isl_set_free(dist); return isl_bool_error; } /* 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) { int i; for (i = 0; i < graph->n_edge; ++i) { struct isl_sched_edge *edge = &graph->edge[i]; isl_bool bounded; if (!is_proximity(edge)) continue; if (!c->scc_in_merge[edge->src->scc]) continue; if (!c->scc_in_merge[edge->dst->scc]) continue; if (c->scc_cluster[edge->dst->scc] == c->scc_cluster[edge->src->scc]) continue; bounded = has_bounded_distances(ctx, edge, graph, c, merge_graph); if (bounded < 0 || bounded) return bounded; } return isl_bool_false; } /* 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) { if (merge_graph->n_total_row == merge_graph->band_start) return isl_bool_false; if (isl_options_get_schedule_maximize_band_depth(ctx) && merge_graph->n_total_row < merge_graph->maxvar) return isl_bool_false; if (isl_options_get_schedule_maximize_coincidence(ctx)) { isl_bool ok; ok = ok_to_merge_coincident(c, merge_graph); if (ok < 0 || !ok) return ok; } return ok_to_merge_proximity(ctx, graph, c, 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) { int i, j; isl_mat *t; int n_row, n_col, n_param, n_var; n_param = node->nparam; n_var = node->nvar; n_row = isl_mat_rows(t_node->sched); n_col = isl_mat_cols(node->sched); t = isl_mat_alloc(ctx, n_row, n_col); if (!t) return NULL; for (i = 0; i < n_row; ++i) { isl_seq_cpy(t->row[i], t_node->sched->row[i], 1 + n_param); isl_seq_clr(t->row[i] + 1 + n_param, n_var); for (j = 0; j < n; ++j) isl_seq_addmul(t->row[i], t_node->sched->row[i][1 + n_param + j], node->sched->row[first + j], 1 + n_param + n_var); } return t; } /* 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) { int i, j; int n_new; int start, n; start = graph->band_start; n = graph->n_total_row - start; n_new = isl_mat_rows(t_node->sched); for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; isl_mat *t; t = node_transformation(ctx, t_node, node, start, n); node->sched = isl_mat_drop_rows(node->sched, start, n); node->sched = isl_mat_concat(node->sched, t); node->sched_map = isl_map_free(node->sched_map); if (!node->sched) return isl_stat_error; for (j = 0; j < n_new; ++j) node->coincident[start + j] = t_node->coincident[j]; } graph->n_total_row -= n; graph->n_row -= n; graph->n_total_row += n_new; graph->n_row += n_new; return isl_stat_ok; } /* 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) { int i; int cluster = -1; isl_space *space; for (i = 0; i < c->n; ++i) { struct isl_sched_node *node; if (!c->scc_in_merge[i]) continue; if (cluster < 0) cluster = i; space = cluster_space(&c->scc[i], c->scc_cluster[i]); if (!space) return isl_stat_error; node = graph_find_node(ctx, merge_graph, space); isl_space_free(space); if (!node) isl_die(ctx, isl_error_internal, "unable to find cluster", return isl_stat_error); if (transform(ctx, &c->scc[i], node) < 0) return isl_stat_error; c->scc_cluster[i] = cluster; } return isl_stat_ok; } /* 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) { struct isl_sched_graph merge_graph = { 0 }; isl_bool merged; if (init_merge_graph(ctx, graph, c, &merge_graph) < 0) goto error; if (compute_maxvar(&merge_graph) < 0) goto error; if (adjust_maxvar_to_slack(ctx, &merge_graph,c) < 0) goto error; if (compute_schedule_wcc_band(ctx, &merge_graph) < 0) goto error; merged = ok_to_merge(ctx, graph, c, &merge_graph); if (merged && merge(ctx, c, &merge_graph) < 0) goto error; graph_free(ctx, &merge_graph); return merged; error: graph_free(ctx, &merge_graph); return isl_bool_error; } /* 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) { int i; for (i = 0; i < graph->n_edge; ++i) { struct isl_sched_edge *edge = &graph->edge[i]; if (!scc_in_merge[edge->src->scc]) continue; if (!scc_in_merge[edge->dst->scc]) continue; if (edge->no_merge) return 1; if (merge_edge->weight >= 0 && edge->weight < 0) { merge_edge->weight -= graph->max_weight + 1; return 1; } } return 0; } /* 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) { isl_bool merged; int edge_weight = graph->edge[edge].weight; if (mark_merge_sccs(ctx, graph, edge, c) < 0) return isl_stat_error; if (any_no_merge(graph, c->scc_in_merge, &graph->edge[edge])) merged = isl_bool_false; else merged = try_merge(ctx, graph, c); if (merged < 0) return isl_stat_error; if (!merged && edge_weight == graph->edge[edge].weight) graph->edge[edge].no_merge = 1; return isl_stat_ok; } /* Does "node" belong to the cluster identified by "cluster"? */ static int node_cluster_exactly(struct isl_sched_node *node, int cluster) { return node->cluster == 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) { return edge->src->cluster == cluster && edge->dst->cluster == 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) { isl_mat *sched; isl_map *sched_map; sched = node1->sched; node1->sched = node2->sched; node2->sched = sched; sched_map = node1->sched_map; node1->sched_map = node2->sched_map; node2->sched_map = sched_map; } /* 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) { int i, j; c->cluster[pos].n_total_row = c->scc[pos].n_total_row; c->cluster[pos].n_row = c->scc[pos].n_row; c->cluster[pos].maxvar = c->scc[pos].maxvar; j = 0; for (i = 0; i < graph->n; ++i) { int k; int s; if (graph->node[i].cluster != pos) continue; s = graph->node[i].scc; k = c->scc_node[s]++; swap_sched(&c->cluster[pos].node[j], &c->scc[s].node[k]); if (c->scc[s].maxvar > c->cluster[pos].maxvar) c->cluster[pos].maxvar = c->scc[s].maxvar; ++j; } return isl_stat_ok; } /* 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) { struct isl_sched_graph *graph = user; if (graph->node[i].cluster == graph->node[j].cluster) return isl_bool_true; return graph_has_validity_edge(graph, &graph->node[j], &graph->node[i]); } /* 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) { int i; for (i = 0; i < graph->n; ++i) graph->node[i].cluster = c->scc_cluster[graph->node[i].scc]; for (i = 0; i < graph->scc; ++i) { if (c->scc_cluster[i] != i) continue; if (extract_sub_graph(ctx, graph, &node_cluster_exactly, &edge_cluster_exactly, i, &c->cluster[i]) < 0) return isl_stat_error; c->cluster[i].src_scc = -1; c->cluster[i].dst_scc = -1; if (copy_partial(graph, c, i) < 0) return isl_stat_error; } if (detect_ccs(ctx, graph, &node_follows_strong_or_same_cluster) < 0) return isl_stat_error; for (i = 0; i < graph->n; ++i) c->scc_cluster[graph->node[i].scc] = graph->node[i].cluster; return isl_stat_ok; } /* 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) { int i; graph->max_weight = 0; for (i = 0; i < graph->n_edge; ++i) { struct isl_sched_edge *edge = &graph->edge[i]; struct isl_sched_node *src = edge->src; struct isl_sched_node *dst = edge->dst; isl_basic_map *hull; int n_in, n_out; if (!is_proximity(edge)) continue; if (bad_cluster(&c->scc[edge->src->scc]) || bad_cluster(&c->scc[edge->dst->scc])) continue; if (c->scc_cluster[edge->dst->scc] == c->scc_cluster[edge->src->scc]) continue; hull = isl_map_affine_hull(isl_map_copy(edge->map)); hull = isl_basic_map_transform_dims(hull, isl_dim_in, 0, isl_mat_copy(src->ctrans)); hull = isl_basic_map_transform_dims(hull, isl_dim_out, 0, isl_mat_copy(dst->ctrans)); hull = isl_basic_map_project_out(hull, isl_dim_in, 0, src->rank); hull = isl_basic_map_project_out(hull, isl_dim_out, 0, dst->rank); hull = isl_basic_map_remove_divs(hull); n_in = isl_basic_map_dim(hull, isl_dim_in); n_out = isl_basic_map_dim(hull, isl_dim_out); hull = isl_basic_map_drop_constraints_not_involving_dims(hull, isl_dim_in, 0, n_in); hull = isl_basic_map_drop_constraints_not_involving_dims(hull, isl_dim_out, 0, n_out); if (!hull) return isl_stat_error; edge->weight = hull->n_eq; isl_basic_map_free(hull); if (edge->weight > graph->max_weight) graph->max_weight = edge->weight; } return isl_stat_ok; } /* Call compute_schedule_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". */ static __isl_give isl_schedule_node *finish_bands_clustering( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph, struct isl_clustering *c) { int i; isl_ctx *ctx; isl_union_set_list *filters; if (graph->scc == 1) return compute_schedule_finish_band(node, &c->cluster[0], 0); ctx = isl_schedule_node_get_ctx(node); filters = extract_sccs(ctx, graph); node = isl_schedule_node_insert_sequence(node, filters); for (i = 0; i < graph->scc; ++i) { int j = c->scc_cluster[i]; node = isl_schedule_node_child(node, i); node = isl_schedule_node_child(node, 0); node = compute_schedule_finish_band(node, &c->cluster[j], 0); node = isl_schedule_node_parent(node); node = isl_schedule_node_parent(node); } return node; } /* 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, * compute_schedule_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. */ static __isl_give isl_schedule_node *compute_schedule_wcc_clustering( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph) { isl_ctx *ctx; struct isl_clustering c; int i; ctx = isl_schedule_node_get_ctx(node); if (clustering_init(ctx, &c, graph) < 0) goto error; if (compute_weights(graph, &c) < 0) goto error; for (;;) { i = find_proximity(graph, &c); if (i < 0) goto error; if (i >= graph->n_edge) break; if (merge_clusters_along_edge(ctx, graph, i, &c) < 0) goto error; } if (extract_clusters(ctx, graph, &c) < 0) goto error; node = finish_bands_clustering(node, graph, &c); clustering_free(ctx, &c); return node; error: clustering_free(ctx, &c); return isl_schedule_node_free(node); } /* Compute a schedule for a connected dependence graph and return * the updated schedule node. * * 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. * * Call compute_schedule_wcc_whole or compute_schedule_wcc_clustering * depending on whether the user has selected the option to try and * compute a schedule for the entire (weakly connected) component first. * If there is only a single strongly connected component (SCC), then * there is no point in trying to combine SCCs * in compute_schedule_wcc_clustering, so compute_schedule_wcc_whole * is called instead. */ static __isl_give isl_schedule_node *compute_schedule_wcc( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph) { isl_ctx *ctx; if (!node) return NULL; ctx = isl_schedule_node_get_ctx(node); if (detect_sccs(ctx, graph) < 0) return isl_schedule_node_free(node); if (compute_maxvar(graph) < 0) return isl_schedule_node_free(node); if (need_feautrier_step(ctx, graph)) return compute_schedule_wcc_feautrier(node, graph); if (graph->scc <= 1 || isl_options_get_schedule_whole_component(ctx)) return compute_schedule_wcc_whole(node, graph); else return compute_schedule_wcc_clustering(node, graph); } /* Compute a schedule for each group of nodes identified by node->scc * separately and then combine them in a sequence node (or as set node * if graph->weak is set) inserted at position "node" of the schedule tree. * Return the updated schedule node. * * If "wcc" is set then each of the groups belongs to a single * weakly connected component in the dependence graph so that * there is no need for compute_sub_schedule to look for weakly * connected components. */ static __isl_give isl_schedule_node *compute_component_schedule( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph, int wcc) { int component; isl_ctx *ctx; isl_union_set_list *filters; if (!node) return NULL; ctx = isl_schedule_node_get_ctx(node); filters = extract_sccs(ctx, graph); if (graph->weak) node = isl_schedule_node_insert_set(node, filters); else node = isl_schedule_node_insert_sequence(node, filters); for (component = 0; component < graph->scc; ++component) { node = isl_schedule_node_child(node, component); node = isl_schedule_node_child(node, 0); node = compute_sub_schedule(node, ctx, graph, &node_scc_exactly, &edge_scc_exactly, component, wcc); node = isl_schedule_node_parent(node); node = isl_schedule_node_parent(node); } return node; } /* Compute a schedule for the given dependence graph and insert it at "node". * Return the updated schedule node. * * We first check if the graph is connected (through validity and conditional * validity dependences) and, if not, compute a schedule * for each component separately. * If the schedule_serialize_sccs option is set, then we check for strongly * connected components instead and compute a separate schedule for * each such strongly connected component. */ static __isl_give isl_schedule_node *compute_schedule(isl_schedule_node *node, struct isl_sched_graph *graph) { isl_ctx *ctx; if (!node) return NULL; ctx = isl_schedule_node_get_ctx(node); if (isl_options_get_schedule_serialize_sccs(ctx)) { if (detect_sccs(ctx, graph) < 0) return isl_schedule_node_free(node); } else { if (detect_wccs(ctx, graph) < 0) return isl_schedule_node_free(node); } if (graph->scc > 1) return compute_component_schedule(node, graph, 1); return compute_schedule_wcc(node, graph); } /* Compute a schedule on sc->domain that respects the given schedule * constraints. * * In particular, the schedule respects 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. * * If there are any condition and conditional validity dependences, * then the conditional validity dependences may be violated inside * a tilable band, provided they have no adjacent non-local * condition dependences. */ __isl_give isl_schedule *isl_schedule_constraints_compute_schedule( __isl_take isl_schedule_constraints *sc) { isl_ctx *ctx = isl_schedule_constraints_get_ctx(sc); struct isl_sched_graph graph = { 0 }; isl_schedule *sched; isl_schedule_node *node; isl_union_set *domain; sc = isl_schedule_constraints_align_params(sc); domain = isl_schedule_constraints_get_domain(sc); if (isl_union_set_n_set(domain) == 0) { isl_schedule_constraints_free(sc); return isl_schedule_from_domain(domain); } if (graph_init(&graph, sc) < 0) domain = isl_union_set_free(domain); node = isl_schedule_node_from_domain(domain); node = isl_schedule_node_child(node, 0); if (graph.n > 0) node = compute_schedule(node, &graph); sched = isl_schedule_node_get_schedule(node); isl_schedule_node_free(node); graph_free(ctx, &graph); isl_schedule_constraints_free(sc); return sched; } /* Compute a schedule for the given union of domains that respects * all the validity dependences and minimizes * the dependence distances over the proximity dependences. * * This function is kept for backward compatibility. */ __isl_give isl_schedule *isl_union_set_compute_schedule( __isl_take isl_union_set *domain, __isl_take isl_union_map *validity, __isl_take isl_union_map *proximity) { isl_schedule_constraints *sc; sc = isl_schedule_constraints_on_domain(domain); sc = isl_schedule_constraints_set_validity(sc, validity); sc = isl_schedule_constraints_set_proximity(sc, proximity); return isl_schedule_constraints_compute_schedule(sc); }