/* * Copyright 2011 INRIA Saclay * Copyright 2012-2014 Ecole Normale Superieure * Copyright 2015 Sven Verdoolaege * * 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 */ #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". */ enum isl_edge_type { isl_edge_validity = 0, isl_edge_first = isl_edge_validity, isl_edge_coincidence, isl_edge_condition, isl_edge_conditional_validity, isl_edge_proximity, isl_edge_last = isl_edge_proximity, isl_edge_local }; /* The constraints that need to be satisfied by a schedule on "domain". * * "context" specifies extra constraints on the parameters. * * "validity" constraints map domain elements i to domain elements * that should be scheduled after i. (Hard constraint) * "proximity" constraints map domain elements i to domains elements * that should be scheduled as early as possible after i (or before i). * (Soft constraint) * * "condition" and "conditional_validity" constraints map possibly "tagged" * domain elements i -> s to "tagged" domain elements j -> t. * The elements of the "conditional_validity" constraints, but without the * tags (i.e., the elements i -> j) are treated as validity constraints, * except that during the construction of a tilable band, * the elements of the "conditional_validity" constraints may be violated * provided that all adjacent elements of the "condition" constraints * are local within the band. * A dependence is local within a band if domain and range are mapped * to the same schedule point by the band. */ struct isl_schedule_constraints { isl_union_set *domain; isl_set *context; isl_union_map *constraint[isl_edge_last + 1]; }; __isl_give isl_schedule_constraints *isl_schedule_constraints_copy( __isl_keep isl_schedule_constraints *sc) { isl_ctx *ctx; isl_schedule_constraints *sc_copy; enum isl_edge_type i; ctx = isl_union_set_get_ctx(sc->domain); sc_copy = isl_calloc_type(ctx, struct isl_schedule_constraints); if (!sc_copy) return NULL; sc_copy->domain = isl_union_set_copy(sc->domain); sc_copy->context = isl_set_copy(sc->context); if (!sc_copy->domain || !sc_copy->context) return isl_schedule_constraints_free(sc_copy); for (i = isl_edge_first; i <= isl_edge_last; ++i) { sc_copy->constraint[i] = isl_union_map_copy(sc->constraint[i]); if (!sc_copy->constraint[i]) return isl_schedule_constraints_free(sc_copy); } return sc_copy; } /* Construct an isl_schedule_constraints object for computing a schedule * on "domain". The initial object does not impose any constraints. */ __isl_give isl_schedule_constraints *isl_schedule_constraints_on_domain( __isl_take isl_union_set *domain) { isl_ctx *ctx; isl_space *space; isl_schedule_constraints *sc; isl_union_map *empty; enum isl_edge_type i; if (!domain) return NULL; ctx = isl_union_set_get_ctx(domain); sc = isl_calloc_type(ctx, struct isl_schedule_constraints); if (!sc) goto error; space = isl_union_set_get_space(domain); sc->domain = domain; sc->context = isl_set_universe(isl_space_copy(space)); empty = isl_union_map_empty(space); for (i = isl_edge_first; i <= isl_edge_last; ++i) { sc->constraint[i] = isl_union_map_copy(empty); if (!sc->constraint[i]) sc->domain = isl_union_set_free(sc->domain); } isl_union_map_free(empty); if (!sc->domain || !sc->context) return isl_schedule_constraints_free(sc); return sc; error: isl_union_set_free(domain); return NULL; } /* Replace the context of "sc" by "context". */ __isl_give isl_schedule_constraints *isl_schedule_constraints_set_context( __isl_take isl_schedule_constraints *sc, __isl_take isl_set *context) { if (!sc || !context) goto error; isl_set_free(sc->context); sc->context = context; return sc; error: isl_schedule_constraints_free(sc); isl_set_free(context); return NULL; } /* Replace the validity constraints of "sc" by "validity". */ __isl_give isl_schedule_constraints *isl_schedule_constraints_set_validity( __isl_take isl_schedule_constraints *sc, __isl_take isl_union_map *validity) { if (!sc || !validity) goto error; isl_union_map_free(sc->constraint[isl_edge_validity]); sc->constraint[isl_edge_validity] = validity; return sc; error: isl_schedule_constraints_free(sc); isl_union_map_free(validity); return NULL; } /* Replace the coincidence constraints of "sc" by "coincidence". */ __isl_give isl_schedule_constraints *isl_schedule_constraints_set_coincidence( __isl_take isl_schedule_constraints *sc, __isl_take isl_union_map *coincidence) { if (!sc || !coincidence) goto error; isl_union_map_free(sc->constraint[isl_edge_coincidence]); sc->constraint[isl_edge_coincidence] = coincidence; return sc; error: isl_schedule_constraints_free(sc); isl_union_map_free(coincidence); return NULL; } /* Replace the proximity constraints of "sc" by "proximity". */ __isl_give isl_schedule_constraints *isl_schedule_constraints_set_proximity( __isl_take isl_schedule_constraints *sc, __isl_take isl_union_map *proximity) { if (!sc || !proximity) goto error; isl_union_map_free(sc->constraint[isl_edge_proximity]); sc->constraint[isl_edge_proximity] = proximity; return sc; error: isl_schedule_constraints_free(sc); isl_union_map_free(proximity); return NULL; } /* Replace the conditional validity constraints of "sc" by "condition" * and "validity". */ __isl_give isl_schedule_constraints * isl_schedule_constraints_set_conditional_validity( __isl_take isl_schedule_constraints *sc, __isl_take isl_union_map *condition, __isl_take isl_union_map *validity) { if (!sc || !condition || !validity) goto error; isl_union_map_free(sc->constraint[isl_edge_condition]); sc->constraint[isl_edge_condition] = condition; isl_union_map_free(sc->constraint[isl_edge_conditional_validity]); sc->constraint[isl_edge_conditional_validity] = validity; return sc; error: isl_schedule_constraints_free(sc); isl_union_map_free(condition); isl_union_map_free(validity); return NULL; } __isl_null isl_schedule_constraints *isl_schedule_constraints_free( __isl_take isl_schedule_constraints *sc) { enum isl_edge_type i; if (!sc) return NULL; isl_union_set_free(sc->domain); isl_set_free(sc->context); for (i = isl_edge_first; i <= isl_edge_last; ++i) isl_union_map_free(sc->constraint[i]); free(sc); return NULL; } isl_ctx *isl_schedule_constraints_get_ctx( __isl_keep isl_schedule_constraints *sc) { return sc ? isl_union_set_get_ctx(sc->domain) : NULL; } /* Return the domain of "sc". */ __isl_give isl_union_set *isl_schedule_constraints_get_domain( __isl_keep isl_schedule_constraints *sc) { if (!sc) return NULL; return isl_union_set_copy(sc->domain); } /* Return the validity constraints of "sc". */ __isl_give isl_union_map *isl_schedule_constraints_get_validity( __isl_keep isl_schedule_constraints *sc) { if (!sc) return NULL; return isl_union_map_copy(sc->constraint[isl_edge_validity]); } /* Return the coincidence constraints of "sc". */ __isl_give isl_union_map *isl_schedule_constraints_get_coincidence( __isl_keep isl_schedule_constraints *sc) { if (!sc) return NULL; return isl_union_map_copy(sc->constraint[isl_edge_coincidence]); } /* Return the conditional validity constraints of "sc". */ __isl_give isl_union_map *isl_schedule_constraints_get_conditional_validity( __isl_keep isl_schedule_constraints *sc) { if (!sc) return NULL; return isl_union_map_copy(sc->constraint[isl_edge_conditional_validity]); } /* Return the conditions for the conditional validity constraints of "sc". */ __isl_give isl_union_map * isl_schedule_constraints_get_conditional_validity_condition( __isl_keep isl_schedule_constraints *sc) { if (!sc) return NULL; return isl_union_map_copy(sc->constraint[isl_edge_condition]); } void isl_schedule_constraints_dump(__isl_keep isl_schedule_constraints *sc) { if (!sc) return; fprintf(stderr, "domain: "); isl_union_set_dump(sc->domain); fprintf(stderr, "context: "); isl_set_dump(sc->context); fprintf(stderr, "validity: "); isl_union_map_dump(sc->constraint[isl_edge_validity]); fprintf(stderr, "proximity: "); isl_union_map_dump(sc->constraint[isl_edge_proximity]); fprintf(stderr, "coincidence: "); isl_union_map_dump(sc->constraint[isl_edge_coincidence]); fprintf(stderr, "condition: "); isl_union_map_dump(sc->constraint[isl_edge_condition]); fprintf(stderr, "conditional_validity: "); isl_union_map_dump(sc->constraint[isl_edge_conditional_validity]); } /* Align the parameters of the fields of "sc". */ static __isl_give isl_schedule_constraints * isl_schedule_constraints_align_params(__isl_take isl_schedule_constraints *sc) { isl_space *space; enum isl_edge_type i; if (!sc) return NULL; space = isl_union_set_get_space(sc->domain); space = isl_space_align_params(space, isl_set_get_space(sc->context)); for (i = isl_edge_first; i <= isl_edge_last; ++i) space = isl_space_align_params(space, isl_union_map_get_space(sc->constraint[i])); for (i = isl_edge_first; i <= isl_edge_last; ++i) { sc->constraint[i] = isl_union_map_align_params( sc->constraint[i], isl_space_copy(space)); if (!sc->constraint[i]) space = isl_space_free(space); } sc->context = isl_set_align_params(sc->context, isl_space_copy(space)); sc->domain = isl_union_set_align_params(sc->domain, space); if (!sc->context || !sc->domain) return isl_schedule_constraints_free(sc); return sc; } /* Return the total number of isl_maps in the constraints of "sc". */ static __isl_give int isl_schedule_constraints_n_map( __isl_keep isl_schedule_constraints *sc) { enum isl_edge_type i; int n = 0; for (i = isl_edge_first; i <= isl_edge_last; ++i) n += isl_union_map_n_map(sc->constraint[i]); return n; } /* 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. * 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 * * 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. */ 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; int start; int nvar; int nparam; int scc; int *coincident; }; 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. */ 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; }; /* 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 * it 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 */ 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; }; /* 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); if (graph->root) free(graph->node[i].coincident); } 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; } /* Add the number of basic maps in "map" to *n. */ static isl_stat add_n_basic_map(__isl_take isl_map *map, void *user) { int *n = user; *n += isl_map_n_basic_map(map); isl_map_free(map); 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 int compute_max_row(struct isl_sched_graph *graph, __isl_keep isl_schedule_constraints *sc) { enum isl_edge_type i; int n_edge; graph->n = 0; graph->maxvar = 0; if (isl_union_set_foreach_set(sc->domain, &init_n_maxvar, graph) < 0) return -1; n_edge = 0; for (i = isl_edge_first; i <= isl_edge_last; ++i) if (isl_union_map_foreach_map(sc->constraint[i], &add_n_basic_map, &n_edge) < 0) return -1; graph->max_row = n_edge + graph->maxvar; return 0; } /* 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; } /* Add a new node to the graph representing the given space. * "nvar" is the (possibly compressed) number of variables and * may be smaller than then number of set variables in "space" * 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. */ static isl_stat add_node(struct isl_sched_graph *graph, __isl_take isl_space *space, 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; int *coincident; if (!space) return isl_stat_error; ctx = isl_space_get_ctx(space); nparam = isl_space_dim(space, isl_dim_param); if (!ctx->opt->schedule_parametric) nparam = 0; sched = isl_mat_alloc(ctx, 0, 1 + nparam + nvar); graph->node[graph->n].space = space; graph->node[graph->n].nvar = nvar; graph->node[graph->n].nparam = nparam; graph->node[graph->n].sched = sched; graph->node[graph->n].sched_map = NULL; coincident = isl_calloc_array(ctx, int, graph->max_row); graph->node[graph->n].coincident = coincident; graph->node[graph->n].compressed = compressed; graph->node[graph->n].hull = hull; graph->node[graph->n].compress = compress; graph->node[graph->n].decompress = decompress; graph->n++; 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_space *space; isl_basic_set *hull; isl_set *hull_set; isl_morph *morph; isl_multi_aff *compress, *decompress; struct isl_sched_graph *graph = user; space = isl_set_get_space(set); hull = isl_set_affine_hull(set); hull = isl_basic_set_remove_divs(hull); nvar = isl_space_dim(space, 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, space, 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, space, nvar, 1, hull_set, compress, decompress); error: isl_basic_set_free(hull); isl_space_free(space); 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; 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_set_copy(sc->context)); 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) graph->max_edge[i] = isl_union_map_n_map(sc->constraint[i]); 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) { data.type = i; if (isl_union_map_foreach_map(sc->constraint[i], &extract_edge, &data) < 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 validity edges). * If weak is set, we consider the graph to be undirected and * we effectively compute the (weakly) connected components. * Additionally, we also consider other edges when weak is set. */ static int detect_ccs(isl_ctx *ctx, struct isl_sched_graph *graph, int weak) { int i, n; struct isl_tarjan_graph *g = NULL; g = isl_tarjan_graph_init(ctx, graph->n, weak ? &node_follows_weak : &node_follows_strong, graph); if (!g) return -1; graph->weak = weak; graph->scc = 0; i = 0; n = graph->n; while (n) { while (g->order[i] != -1) { graph->node[g->order[i]].scc = graph->scc; --n; ++i; } ++i; graph->scc++; } isl_tarjan_graph_free(g); return 0; } /* Apply Tarjan's algorithm to detect the strongly connected components * in the dependence graph. */ static int detect_sccs(isl_ctx *ctx, struct isl_sched_graph *graph) { return detect_ccs(ctx, graph, 0); } /* Apply Tarjan's algorithm to detect the (weakly) connected components * in the dependence graph. */ static int detect_wccs(isl_ctx *ctx, struct isl_sched_graph *graph) { return detect_ccs(ctx, graph, 1); } 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; if (isl_map_to_basic_set_has(graph->intra_hmap, map)) return isl_map_to_basic_set_get(graph->intra_hmap, map); 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; if (isl_map_to_basic_set_has(graph->inter_hmap, map)) return isl_map_to_basic_set_get(graph->inter_hmap, map); 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; } /* 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 int add_intra_validity_constraints(struct isl_sched_graph *graph, struct isl_sched_edge *edge) { unsigned total; isl_map *map = isl_map_copy(edge->map); isl_ctx *ctx = isl_map_get_ctx(map); isl_space *dim; isl_dim_map *dim_map; isl_basic_set *coef; struct isl_sched_node *node = edge->src; coef = intra_coefficients(graph, node, map); dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef))); coef = isl_basic_set_transform_dims(coef, isl_dim_set, isl_space_dim(dim, isl_dim_set), isl_mat_copy(node->cmap)); if (!coef) goto error; total = isl_basic_set_total_dim(graph->lp); dim_map = isl_dim_map_alloc(ctx, total); isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 1, 2, isl_space_dim(dim, isl_dim_set), 1, node->nvar, -1); isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 2, 2, isl_space_dim(dim, isl_dim_set), 1, node->nvar, 1); graph->lp = isl_basic_set_extend_constraints(graph->lp, coef->n_eq, coef->n_ineq); graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp, coef, dim_map); isl_space_free(dim); return 0; error: isl_space_free(dim); return -1; } /* 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_j_n^- - (c_i_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 int add_inter_validity_constraints(struct isl_sched_graph *graph, struct isl_sched_edge *edge) { unsigned total; isl_map *map = isl_map_copy(edge->map); isl_ctx *ctx = isl_map_get_ctx(map); isl_space *dim; isl_dim_map *dim_map; isl_basic_set *coef; struct isl_sched_node *src = edge->src; struct isl_sched_node *dst = edge->dst; coef = inter_coefficients(graph, edge, map); dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef))); coef = isl_basic_set_transform_dims(coef, isl_dim_set, isl_space_dim(dim, isl_dim_set), isl_mat_copy(src->cmap)); coef = isl_basic_set_transform_dims(coef, isl_dim_set, isl_space_dim(dim, isl_dim_set) + src->nvar, isl_mat_copy(dst->cmap)); if (!coef) goto error; total = isl_basic_set_total_dim(graph->lp); dim_map = isl_dim_map_alloc(ctx, total); isl_dim_map_range(dim_map, dst->start, 0, 0, 0, 1, 1); isl_dim_map_range(dim_map, dst->start + 1, 2, 1, 1, dst->nparam, -1); isl_dim_map_range(dim_map, dst->start + 2, 2, 1, 1, dst->nparam, 1); isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 1, 2, isl_space_dim(dim, isl_dim_set) + src->nvar, 1, dst->nvar, -1); isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 2, 2, isl_space_dim(dim, isl_dim_set) + src->nvar, 1, dst->nvar, 1); isl_dim_map_range(dim_map, src->start, 0, 0, 0, 1, -1); isl_dim_map_range(dim_map, src->start + 1, 2, 1, 1, src->nparam, 1); isl_dim_map_range(dim_map, src->start + 2, 2, 1, 1, src->nparam, -1); isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 1, 2, isl_space_dim(dim, isl_dim_set), 1, src->nvar, 1); isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 2, 2, isl_space_dim(dim, isl_dim_set), 1, src->nvar, -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) goto error; isl_space_free(dim); edge->end = graph->lp->n_ineq; return 0; error: isl_space_free(dim); return -1; } /* Add constraints to graph->lp that bound the dependence distance for the given * 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 int add_intra_proximity_constraints(struct isl_sched_graph *graph, struct isl_sched_edge *edge, int s, int local) { unsigned total; unsigned nparam; isl_map *map = isl_map_copy(edge->map); isl_ctx *ctx = isl_map_get_ctx(map); isl_space *dim; isl_dim_map *dim_map; isl_basic_set *coef; struct isl_sched_node *node = edge->src; coef = intra_coefficients(graph, node, map); dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef))); coef = isl_basic_set_transform_dims(coef, isl_dim_set, isl_space_dim(dim, isl_dim_set), isl_mat_copy(node->cmap)); if (!coef) goto error; nparam = isl_space_dim(node->space, isl_dim_param); total = isl_basic_set_total_dim(graph->lp); dim_map = isl_dim_map_alloc(ctx, total); 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); } isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 1, 2, isl_space_dim(dim, isl_dim_set), 1, node->nvar, s); isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 2, 2, isl_space_dim(dim, isl_dim_set), 1, node->nvar, -s); graph->lp = isl_basic_set_extend_constraints(graph->lp, coef->n_eq, coef->n_ineq); graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp, coef, dim_map); isl_space_free(dim); return 0; error: isl_space_free(dim); return -1; } /* Add constraints to graph->lp that bound the dependence distance for the given * 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_j_0 and c_i_0) * 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 int add_inter_proximity_constraints(struct isl_sched_graph *graph, struct isl_sched_edge *edge, int s, int local) { unsigned total; unsigned nparam; isl_map *map = isl_map_copy(edge->map); isl_ctx *ctx = isl_map_get_ctx(map); isl_space *dim; isl_dim_map *dim_map; isl_basic_set *coef; struct isl_sched_node *src = edge->src; struct isl_sched_node *dst = edge->dst; coef = inter_coefficients(graph, edge, map); dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef))); coef = isl_basic_set_transform_dims(coef, isl_dim_set, isl_space_dim(dim, isl_dim_set), isl_mat_copy(src->cmap)); coef = isl_basic_set_transform_dims(coef, isl_dim_set, isl_space_dim(dim, isl_dim_set) + src->nvar, isl_mat_copy(dst->cmap)); if (!coef) goto error; nparam = isl_space_dim(src->space, isl_dim_param); total = isl_basic_set_total_dim(graph->lp); dim_map = isl_dim_map_alloc(ctx, total); 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); } isl_dim_map_range(dim_map, dst->start, 0, 0, 0, 1, -s); isl_dim_map_range(dim_map, dst->start + 1, 2, 1, 1, dst->nparam, s); isl_dim_map_range(dim_map, dst->start + 2, 2, 1, 1, dst->nparam, -s); isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 1, 2, isl_space_dim(dim, isl_dim_set) + src->nvar, 1, dst->nvar, s); isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 2, 2, isl_space_dim(dim, isl_dim_set) + src->nvar, 1, dst->nvar, -s); isl_dim_map_range(dim_map, src->start, 0, 0, 0, 1, s); isl_dim_map_range(dim_map, src->start + 1, 2, 1, 1, src->nparam, -s); isl_dim_map_range(dim_map, src->start + 2, 2, 1, 1, src->nparam, s); isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 1, 2, isl_space_dim(dim, isl_dim_set), 1, src->nvar, -s); isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 2, 2, isl_space_dim(dim, isl_dim_set), 1, src->nvar, s); graph->lp = isl_basic_set_extend_constraints(graph->lp, coef->n_eq, coef->n_ineq); graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp, coef, dim_map); isl_space_free(dim); return 0; error: isl_space_free(dim); return -1; } /* 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); 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->rank < 0) return -1; return 0; } /* 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 && !is_validity(edge) && !is_conditional_validity(edge)) return 0; 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_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 (ctx->opt->schedule_max_coefficient == -1) return 0; for (i = 0; i < graph->n; ++i) *n_ineq += 2 * graph->node[i].nparam + 2 * graph->node[i].nvar; return 0; } /* Add constraints that bound the values of the variable and parameter * coefficients of the schedule. * * The maximal value of the coefficients is defined by the option * 'schedule_max_coefficient'. */ static int add_bound_coefficient_constraints(isl_ctx *ctx, struct isl_sched_graph *graph) { int i, j, k; int max_coefficient; int total; max_coefficient = ctx->opt->schedule_max_coefficient; if (max_coefficient == -1) return 0; total = isl_basic_set_total_dim(graph->lp); for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; for (j = 0; j < 2 * node->nparam + 2 * node->nvar; ++j) { int dim; k = isl_basic_set_alloc_inequality(graph->lp); if (k < 0) return -1; dim = 1 + node->start + 1 + j; isl_seq_clr(graph->lp->ineq[k], 1 + total); isl_int_set_si(graph->lp->ineq[k][dim], -1); isl_int_set_si(graph->lp->ineq[k][0], max_coefficient); } } return 0; } /* Construct an ILP problem for finding schedule coefficients * that result in non-negative, but small dependence distances * over all dependences. * 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 positive and negative parts 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 * - positive and negative parts of 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 int setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph, int use_coincidence) { int i, j; int k; unsigned nparam; unsigned total; isl_space *dim; int parametric; int param_pos; int n_eq, n_ineq; int max_constant_term; max_constant_term = ctx->opt->schedule_max_constant_term; 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 -1; node->start = total; total += 1 + 2 * (node->nparam + node->nvar); } if (count_constraints(graph, &n_eq, &n_ineq, use_coincidence) < 0) return -1; if (count_bound_coefficient_constraints(ctx, graph, &n_eq, &n_ineq) < 0) return -1; dim = isl_space_set_alloc(ctx, 0, total); isl_basic_set_free(graph->lp); n_eq += 2 + parametric; if (max_constant_term != -1) n_ineq += graph->n; graph->lp = isl_basic_set_alloc_space(dim, 0, n_eq, n_ineq); k = isl_basic_set_alloc_equality(graph->lp); if (k < 0) return -1; isl_seq_clr(graph->lp->eq[k], 1 + total); isl_int_set_si(graph->lp->eq[k][1], -1); for (i = 0; i < 2 * nparam; ++i) isl_int_set_si(graph->lp->eq[k][1 + param_pos + i], 1); if (parametric) { k = isl_basic_set_alloc_equality(graph->lp); if (k < 0) return -1; isl_seq_clr(graph->lp->eq[k], 1 + total); isl_int_set_si(graph->lp->eq[k][3], -1); for (i = 0; i < graph->n; ++i) { int pos = 1 + graph->node[i].start + 1; for (j = 0; j < 2 * graph->node[i].nparam; ++j) isl_int_set_si(graph->lp->eq[k][pos + j], 1); } } k = isl_basic_set_alloc_equality(graph->lp); if (k < 0) return -1; isl_seq_clr(graph->lp->eq[k], 1 + total); isl_int_set_si(graph->lp->eq[k][4], -1); for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; int pos = 1 + node->start + 1 + 2 * node->nparam; for (j = 0; j < 2 * node->nvar; ++j) isl_int_set_si(graph->lp->eq[k][pos + j], 1); } if (max_constant_term != -1) for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; k = isl_basic_set_alloc_inequality(graph->lp); if (k < 0) return -1; isl_seq_clr(graph->lp->ineq[k], 1 + total); isl_int_set_si(graph->lp->ineq[k][1 + node->start], -1); isl_int_set_si(graph->lp->ineq[k][0], max_constant_term); } if (add_bound_coefficient_constraints(ctx, graph) < 0) return -1; if (add_all_validity_constraints(graph, use_coincidence) < 0) return -1; if (add_all_proximity_constraints(graph, use_coincidence) < 0) return -1; return 0; } /* 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->start + 1 + 2*(node->nparam+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; } /* 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 = isl_vec_alloc(sol->ctx, node->nvar); 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; node->sched = isl_mat_set_element(node->sched, row, 0, sol->el[1 + pos]); for (j = 0; j < node->nparam + node->nvar; ++j) isl_int_sub(sol->el[1 + pos + 1 + 2 * j + 1], sol->el[1 + pos + 1 + 2 * j + 1], sol->el[1 + pos + 1 + 2 * j]); for (j = 0; j < node->nparam; ++j) node->sched = isl_mat_set_element(node->sched, row, 1 + j, sol->el[1+pos+1+2*j+1]); for (j = 0; j < node->nvar; ++j) isl_int_set(csol->el[j], sol->el[1+pos+1+2*(node->nparam+j)+1]); 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; 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->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; } 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 }; 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, &split, n, n_edge) < 0) goto error; if (copy_nodes(&split, graph, node_pred, data) < 0) goto error; if (graph_init_table(ctx, &split) < 0) goto error; for (t = 0; t <= isl_edge_last; ++t) split.max_edge[t] = graph->max_edge[t]; if (graph_init_edge_tables(ctx, &split) < 0) goto error; if (copy_edges(ctx, &split, graph, edge_pred, data) < 0) goto error; split.n_row = graph->n_row; split.max_row = graph->max_row; split.n_total_row = graph->n_total_row; split.band_start = graph->band_start; 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) { unsigned total; isl_ctx *ctx = isl_map_get_ctx(map); isl_space *dim; 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; dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef))); total = isl_basic_set_total_dim(graph->lp); dim_map = isl_dim_map_alloc(ctx, total); isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -1); isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 1, 2, isl_space_dim(dim, isl_dim_set), 1, node->nvar, -1); isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 2, 2, isl_space_dim(dim, isl_dim_set), 1, node->nvar, 1); graph->lp = isl_basic_set_extend_constraints(graph->lp, coef->n_eq, coef->n_ineq); graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp, coef, dim_map); isl_space_free(dim); 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_k_0 and c_j_0) * 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) { unsigned total; isl_ctx *ctx = isl_map_get_ctx(map); isl_space *dim; isl_dim_map *dim_map; isl_basic_set *coef; struct isl_sched_node *src = edge->src; struct isl_sched_node *dst = edge->dst; coef = inter_coefficients(graph, edge, map); if (!coef) return -1; dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef))); total = isl_basic_set_total_dim(graph->lp); dim_map = isl_dim_map_alloc(ctx, total); isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -1); isl_dim_map_range(dim_map, dst->start, 0, 0, 0, 1, 1); isl_dim_map_range(dim_map, dst->start + 1, 2, 1, 1, dst->nparam, -1); isl_dim_map_range(dim_map, dst->start + 2, 2, 1, 1, dst->nparam, 1); isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 1, 2, isl_space_dim(dim, isl_dim_set) + src->nvar, 1, dst->nvar, -1); isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 2, 2, isl_space_dim(dim, isl_dim_set) + src->nvar, 1, dst->nvar, 1); isl_dim_map_range(dim_map, src->start, 0, 0, 0, 1, -1); isl_dim_map_range(dim_map, src->start + 1, 2, 1, 1, src->nparam, 1); isl_dim_map_range(dim_map, src->start + 2, 2, 1, 1, src->nparam, -1); isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 1, 2, isl_space_dim(dim, isl_dim_set), 1, src->nvar, 1); isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 2, 2, isl_space_dim(dim, isl_dim_set), 1, src->nvar, -1); graph->lp = isl_basic_set_extend_constraints(graph->lp, coef->n_eq, coef->n_ineq); graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp, coef, dim_map); isl_space_free(dim); 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_validity(edge) && !is_conditional_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]; 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 positive and negative parts 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 * - positive and negative parts of 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 int setup_carry_lp(isl_ctx *ctx, struct isl_sched_graph *graph) { int i, j; 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 + 2 * (node->nparam + node->nvar); } if (count_all_constraints(graph, &n_eq, &n_ineq) < 0) return -1; 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 -1; 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); k = isl_basic_set_alloc_equality(graph->lp); if (k < 0) return -1; isl_seq_clr(graph->lp->eq[k], 1 + total); isl_int_set_si(graph->lp->eq[k][2], -1); for (i = 0; i < graph->n; ++i) { int pos = 1 + graph->node[i].start + 1; for (j = 0; j < 2 * graph->node[i].nparam; ++j) isl_int_set_si(graph->lp->eq[k][pos + j], 1); } k = isl_basic_set_alloc_equality(graph->lp); if (k < 0) return -1; isl_seq_clr(graph->lp->eq[k], 1 + total); isl_int_set_si(graph->lp->eq[k][3], -1); for (i = 0; i < graph->n; ++i) { struct isl_sched_node *node = &graph->node[i]; int pos = 1 + node->start + 1 + 2 * node->nparam; for (j = 0; j < 2 * node->nvar; ++j) isl_int_set_si(graph->lp->eq[k][pos + j], 1); } for (i = 0; i < n_edge; ++i) { k = isl_basic_set_alloc_inequality(graph->lp); if (k < 0) return -1; isl_seq_clr(graph->lp->ineq[k], 1 + total); isl_int_set_si(graph->lp->ineq[k][4 + i], -1); isl_int_set_si(graph->lp->ineq[k][0], 1); } if (add_all_constraints(graph) < 0) return -1; return 0; } 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 i; int pos; int trivial; isl_ctx *ctx; isl_vec *node_sol; if (!sol) return -1; if (node->nvar == node->rank) return 0; ctx = isl_vec_get_ctx(sol); node_sol = isl_vec_alloc(ctx, node->nvar); if (!node_sol) return -1; pos = 1 + node->start + 1 + 2 * node->nparam; for (i = 0; i < node->nvar; ++i) isl_int_sub(node_sol->el[i], sol->el[pos + 2 * i + 1], sol->el[pos + 2 * i]); 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; } /* Construct a schedule row for each node such that as many dependences * as possible are carried and then continue with the next band. * * 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]. * * 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. * * [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 *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 = isl_tab_basic_set_non_neg_lexmin(lp); if (!sol) return isl_schedule_node_free(node); if (sol->size == 0) { isl_vec_free(sol); isl_die(ctx, isl_error_internal, "error in schedule construction", return isl_schedule_node_free(node)); } isl_int_divexact(sol->el[1], sol->el[1], sol->el[0]); if (isl_int_cmp_si(sol->el[1], n_edge) >= 0) { isl_vec_free(sol); isl_die(ctx, isl_error_unknown, "unable to carry dependences", return 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 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) { 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) 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_validity(&graph->edge[i]) || is_conditional_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; } /* Compute a schedule for a connected dependence graph and return * the updated schedule node. * * 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. * If we can't find any more rows 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 Feautrier's algorithm is selected, we first recursively try to satisfy * as many validity dependences as possible. When all validity dependences * are satisfied we extend the schedule to a full-dimensional schedule. * * If we manage to complete the schedule, we insert a band node * (if any schedule rows were computed) and we finish off by topologically * sorting the statements based on the remaining dependences. * * 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_give isl_schedule_node *compute_schedule_wcc( __isl_take isl_schedule_node *node, struct isl_sched_graph *graph) { int has_coincidence; int use_coincidence; int force_coincidence = 0; int check_conditional; int insert; 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 (sort_sccs(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); 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_schedule_node_free(node); sol = solve_lp(graph); if (!sol) return isl_schedule_node_free(node); 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; } 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); return carry_dependences(node, graph); } coincident = !has_coincidence || use_coincidence; if (update_schedule(graph, sol, 1, coincident) < 0) return isl_schedule_node_free(node); if (!check_conditional) continue; violated = has_violated_conditional_constraint(ctx, graph); if (violated < 0) return isl_schedule_node_free(node); if (!violated) continue; if (reset_band(graph) < 0) return isl_schedule_node_free(node); use_coincidence = has_coincidence; } 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); if (insert) node = isl_schedule_node_parent(node); return node; } /* 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); }