#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl_space_private.h>
+#include <isl/aff.h>
#include <isl/hash.h>
#include <isl/constraint.h>
#include <isl/schedule.h>
#include <isl_schedule_private.h>
#include <isl_band_private.h>
#include <isl_list_private.h>
+#include <isl_options_private.h>
/*
* The scheduling algorithm implemented in this file was inspired by
int end;
};
+enum isl_edge_type {
+ isl_edge_validity = 0,
+ isl_edge_proximity,
+ isl_edge_last = isl_edge_proximity
+};
+
/* Internal information about the dependence graph used during
* the construction of the schedule.
*
* 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
*
* n_edge is the number of edges
* edge is the list of edges
+ * max_edge contains the maximal number of edges of each type;
+ * in particular, it contains the number of edges in the inital graph.
* edge_table contains pointers into the edge array, hashed on the source
- * and sink spaces; the table only contains edges that represent
- * validity constraints (and that may or may not also represent proximity
- * constraints)
+ * and sink spaces; there is one such table for each type;
+ * a given edge may be referenced from more than one table
+ * if the corresponding relation appears in more than of the
+ * sets of dependences
*
* node_table contains pointers into the node array, hashed on the space
*
struct isl_sched_node *node;
int n;
int maxvar;
+ int max_row;
int n_row;
int *sorted;
struct isl_sched_edge *edge;
int n_edge;
- struct isl_hash_table *edge_table;
+ int max_edge[isl_edge_last + 1];
+ struct isl_hash_table *edge_table[isl_edge_last + 1];
struct isl_hash_table *node_table;
struct isl_region *region;
return edge->src == temp->src && edge->dst == temp->dst;
}
-/* Initialize edge_table based on the list of edges.
- * Only edges with validity set are added to the table.
+/* Add the given edge to graph->edge_table[type].
*/
-static int graph_init_edge_table(isl_ctx *ctx, struct isl_sched_graph *graph)
+static int graph_edge_table_add(isl_ctx *ctx, struct isl_sched_graph *graph,
+ enum isl_edge_type type, struct isl_sched_edge *edge)
{
- int i;
+ struct isl_hash_table_entry *entry;
+ uint32_t hash;
- graph->edge_table = isl_hash_table_alloc(ctx, graph->n_edge);
- if (!graph->edge_table)
+ hash = isl_hash_init();
+ hash = isl_hash_builtin(hash, edge->src);
+ hash = isl_hash_builtin(hash, edge->dst);
+ entry = isl_hash_table_find(ctx, graph->edge_table[type], hash,
+ &edge_has_src_and_dst, edge, 1);
+ if (!entry)
return -1;
+ entry->data = edge;
- for (i = 0; i < graph->n_edge; ++i) {
- struct isl_hash_table_entry *entry;
- uint32_t hash;
+ return 0;
+}
- if (!graph->edge[i].validity)
- continue;
+/* Allocate the edge_tables based on the maximal number of edges of
+ * each type.
+ */
+static int graph_init_edge_tables(isl_ctx *ctx, struct isl_sched_graph *graph)
+{
+ int i;
- hash = isl_hash_init();
- hash = isl_hash_builtin(hash, graph->edge[i].src);
- hash = isl_hash_builtin(hash, graph->edge[i].dst);
- entry = isl_hash_table_find(ctx, graph->edge_table, hash,
- &edge_has_src_and_dst,
- &graph->edge[i], 1);
- if (!entry)
+ for (i = 0; i <= isl_edge_last; ++i) {
+ graph->edge_table[i] = isl_hash_table_alloc(ctx,
+ graph->max_edge[i]);
+ if (!graph->edge_table[i])
return -1;
- entry->data = &graph->edge[i];
}
return 0;
}
-/* Check whether the dependence graph has a (validity) edge
- * between the given two nodes.
+/* If graph->edge_table[type] contains an edge from the given source
+ * to the given destination, then return the hash table entry of this edge.
+ * Otherwise, return NULL.
*/
-static int graph_has_edge(struct isl_sched_graph *graph,
+static struct isl_hash_table_entry *graph_find_edge_entry(
+ struct isl_sched_graph *graph,
+ enum isl_edge_type type,
struct isl_sched_node *src, struct isl_sched_node *dst)
{
isl_ctx *ctx = isl_space_get_ctx(src->dim);
- struct isl_hash_table_entry *entry;
uint32_t hash;
struct isl_sched_edge temp = { .src = src, .dst = dst };
- struct isl_sched_edge *edge;
- int empty;
hash = isl_hash_init();
hash = isl_hash_builtin(hash, temp.src);
hash = isl_hash_builtin(hash, temp.dst);
- entry = isl_hash_table_find(ctx, graph->edge_table, hash,
+ return isl_hash_table_find(ctx, graph->edge_table[type], hash,
&edge_has_src_and_dst, &temp, 0);
+}
+
+
+/* If graph->edge_table[type] contains an edge from the given source
+ * to the given destination, then return this edge.
+ * Otherwise, return NULL.
+ */
+static struct isl_sched_edge *graph_find_edge(struct isl_sched_graph *graph,
+ enum isl_edge_type type,
+ struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+ struct isl_hash_table_entry *entry;
+
+ entry = graph_find_edge_entry(graph, type, src, dst);
if (!entry)
+ return NULL;
+
+ return entry->data;
+}
+
+/* Check whether the dependence graph has an edge of the give type
+ * between the given two nodes.
+ */
+static int graph_has_edge(struct isl_sched_graph *graph,
+ enum isl_edge_type type,
+ struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+ struct isl_sched_edge *edge;
+ int empty;
+
+ edge = graph_find_edge(graph, type, src, dst);
+ if (!edge)
return 0;
- edge = entry->data;
empty = isl_map_plain_is_empty(edge->map);
if (empty < 0)
return -1;
return !empty;
}
+/* If there is an edge from the given source to the given destination
+ * of any type then return this edge.
+ * Otherwise, return NULL.
+ */
+static struct isl_sched_edge *graph_find_any_edge(struct isl_sched_graph *graph,
+ struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+ int i;
+ struct isl_sched_edge *edge;
+
+ for (i = 0; i <= isl_edge_last; ++i) {
+ edge = graph_find_edge(graph, i, src, dst);
+ if (edge)
+ return edge;
+ }
+
+ return NULL;
+}
+
+/* Remove the given edge from all the edge_tables that refer to it.
+ */
+static void graph_remove_edge(struct isl_sched_graph *graph,
+ struct isl_sched_edge *edge)
+{
+ isl_ctx *ctx = isl_map_get_ctx(edge->map);
+ int i;
+
+ for (i = 0; i <= isl_edge_last; ++i) {
+ struct isl_hash_table_entry *entry;
+
+ entry = graph_find_edge_entry(graph, i, edge->src, edge->dst);
+ if (!entry)
+ continue;
+ if (entry->data != edge)
+ continue;
+ isl_hash_table_remove(ctx, graph->edge_table[i], entry);
+ }
+}
+
+/* Check whether the dependence graph has any edge
+ * between the given two nodes.
+ */
+static int graph_has_any_edge(struct isl_sched_graph *graph,
+ struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+ int i;
+ int r;
+
+ for (i = 0; i <= isl_edge_last; ++i) {
+ r = graph_has_edge(graph, i, src, dst);
+ if (r < 0 || r)
+ return r;
+ }
+
+ return r;
+}
+
+/* Check whether the dependence graph has a validity edge
+ * between the given two nodes.
+ */
+static int graph_has_validity_edge(struct isl_sched_graph *graph,
+ struct isl_sched_node *src, struct isl_sched_node *dst)
+{
+ return graph_has_edge(graph, isl_edge_validity, src, dst);
+}
+
static int graph_alloc(isl_ctx *ctx, struct isl_sched_graph *graph,
int n_node, int n_edge)
{
free(graph->edge);
free(graph->region);
free(graph->stack);
- isl_hash_table_free(ctx, graph->edge_table);
+ for (i = 0; i <= isl_edge_last; ++i)
+ isl_hash_table_free(ctx, graph->edge_table[i]);
isl_hash_table_free(ctx, graph->node_table);
isl_basic_set_free(graph->lp);
}
+/* For each "set" on which this function is called, increment
+ * graph->n by one and update graph->maxvar.
+ */
+static int init_n_maxvar(__isl_take isl_set *set, void *user)
+{
+ struct isl_sched_graph *graph = user;
+ int nvar = isl_set_dim(set, isl_dim_set);
+
+ graph->n++;
+ if (nvar > graph->maxvar)
+ graph->maxvar = nvar;
+
+ isl_set_free(set);
+
+ return 0;
+}
+
+/* Compute the number of rows that should be allocated for the schedule.
+ * The graph can be split at most "n - 1" times, there can be at most
+ * two rows for each dimension in the iteration domains (in particular,
+ * we usually have one row, but it may be split by split_scaled),
+ * and there can be one extra row for ordering the statements.
+ * Note that if we have actually split "n - 1" times, then no ordering
+ * is needed, so in principle we could use "graph->n + 2 * graph->maxvar - 1".
+ */
+static int compute_max_row(struct isl_sched_graph *graph,
+ __isl_keep isl_union_set *domain)
+{
+ graph->n = 0;
+ graph->maxvar = 0;
+ if (isl_union_set_foreach_set(domain, &init_n_maxvar, graph) < 0)
+ return -1;
+ graph->max_row = graph->n + 2 * graph->maxvar;
+
+ return 0;
+}
+
/* Add a new node to the graph representing the given set.
*/
static int extract_node(__isl_take isl_set *set, void *user)
graph->node[graph->n].nparam = nparam;
graph->node[graph->n].sched = sched;
graph->node[graph->n].sched_map = NULL;
- band = isl_alloc_array(ctx, int, graph->n_edge + nvar);
+ band = isl_alloc_array(ctx, int, graph->max_row);
graph->node[graph->n].band = band;
- band_id = isl_calloc_array(ctx, int, graph->n_edge + nvar);
+ band_id = isl_calloc_array(ctx, int, graph->max_row);
graph->node[graph->n].band_id = band_id;
- zero = isl_calloc_array(ctx, int, graph->n_edge + nvar);
+ zero = isl_calloc_array(ctx, int, graph->max_row);
graph->node[graph->n].zero = zero;
graph->n++;
return 0;
}
-/* Add a new edge to the graph based on the given map.
- * Edges are first extracted from the validity dependences,
- * from which the edge_table is constructed.
- * Afterwards, the proximity dependences are added. If a proximity
- * dependence relation happens to be identical to one of the
- * validity dependence relations added before, then we don't create
- * a new edge, but instead mark the original edge as also representing
- * a proximity dependence.
+struct isl_extract_edge_data {
+ enum isl_edge_type type;
+ struct isl_sched_graph *graph;
+};
+
+/* Add a new edge to the graph based on the given map
+ * and add it to data->graph->edge_table[data->type].
+ * If a dependence relation of a given type happens to be identical
+ * to one of the dependence relations of a type that was added before,
+ * then we don't create a new edge, but instead mark the original edge
+ * as also representing a dependence of the current type.
*/
static int extract_edge(__isl_take isl_map *map, void *user)
{
isl_ctx *ctx = isl_map_get_ctx(map);
- struct isl_sched_graph *graph = user;
+ struct isl_extract_edge_data *data = user;
+ struct isl_sched_graph *graph = data->graph;
struct isl_sched_node *src, *dst;
isl_space *dim;
+ struct isl_sched_edge *edge;
+ int is_equal;
dim = isl_space_domain(isl_map_get_space(map));
src = graph_find_node(ctx, graph, dim);
graph->edge[graph->n_edge].src = src;
graph->edge[graph->n_edge].dst = dst;
graph->edge[graph->n_edge].map = map;
- graph->edge[graph->n_edge].validity = !graph->edge_table;
- graph->edge[graph->n_edge].proximity = !!graph->edge_table;
+ if (data->type == isl_edge_validity) {
+ graph->edge[graph->n_edge].validity = 1;
+ graph->edge[graph->n_edge].proximity = 0;
+ }
+ if (data->type == isl_edge_proximity) {
+ graph->edge[graph->n_edge].validity = 0;
+ graph->edge[graph->n_edge].proximity = 1;
+ }
graph->n_edge++;
- if (graph->edge_table) {
- uint32_t hash;
- struct isl_hash_table_entry *entry;
- struct isl_sched_edge *edge;
- int is_equal;
-
- hash = isl_hash_init();
- hash = isl_hash_builtin(hash, src);
- hash = isl_hash_builtin(hash, dst);
- entry = isl_hash_table_find(ctx, graph->edge_table, hash,
- &edge_has_src_and_dst,
- &graph->edge[graph->n_edge - 1], 0);
- if (!entry)
- return 0;
- edge = entry->data;
- is_equal = isl_map_plain_is_equal(map, edge->map);
- if (is_equal < 0)
- return -1;
- if (!is_equal)
- return 0;
+ edge = graph_find_any_edge(graph, src, dst);
+ if (!edge)
+ return graph_edge_table_add(ctx, graph, data->type,
+ &graph->edge[graph->n_edge - 1]);
+ is_equal = isl_map_plain_is_equal(map, edge->map);
+ if (is_equal < 0)
+ return -1;
+ if (!is_equal)
+ return graph_edge_table_add(ctx, graph, data->type,
+ &graph->edge[graph->n_edge - 1]);
- graph->n_edge--;
- edge->proximity = 1;
- isl_map_free(map);
- }
+ graph->n_edge--;
+ edge->validity |= graph->edge[graph->n_edge].validity;
+ edge->proximity |= graph->edge[graph->n_edge].proximity;
+ isl_map_free(map);
- return 0;
+ return graph_edge_table_add(ctx, graph, data->type, edge);
}
/* Check whether there is a validity dependence from src to dst,
- * forcing dst to follow src.
+ * forcing dst to follow src (if weak is not set).
+ * If weak is set, then check if there is any dependence from src to dst.
*/
static int node_follows(struct isl_sched_graph *graph,
- struct isl_sched_node *dst, struct isl_sched_node *src)
+ struct isl_sched_node *dst, struct isl_sched_node *src, int weak)
{
- return graph_has_edge(graph, src, dst);
+ if (weak)
+ return graph_has_any_edge(graph, src, dst);
+ else
+ return graph_has_validity_edge(graph, src, dst);
}
/* Perform Tarjan's algorithm for computing the strongly connected components
* in the dependence graph (only validity edges).
- * If directed is not set, we consider the graph to be undirected and
+ * If weak is set, we consider the graph to be undirected and
* we effectively compute the (weakly) connected components.
+ * Additionally, we also consider other edges when weak is set.
*/
-static int detect_sccs_tarjan(struct isl_sched_graph *g, int i, int directed)
+static int detect_sccs_tarjan(struct isl_sched_graph *g, int i, int weak)
{
int j;
g->node[j].index > g->node[i].min_index))
continue;
- f = node_follows(g, &g->node[i], &g->node[j]);
+ f = node_follows(g, &g->node[i], &g->node[j], weak);
if (f < 0)
return -1;
- if (!f && !directed) {
- f = node_follows(g, &g->node[j], &g->node[i]);
+ if (!f && weak) {
+ f = node_follows(g, &g->node[j], &g->node[i], weak);
if (f < 0)
return -1;
}
if (!f)
continue;
if (g->node[j].index < 0) {
- detect_sccs_tarjan(g, j, directed);
+ detect_sccs_tarjan(g, j, weak);
if (g->node[j].min_index < g->node[i].min_index)
g->node[i].min_index = g->node[j].min_index;
} else if (g->node[j].index < g->node[i].min_index)
return 0;
}
-static int detect_ccs(struct isl_sched_graph *graph, int directed)
+static int detect_ccs(struct isl_sched_graph *graph, int weak)
{
int i;
for (i = graph->n - 1; i >= 0; --i) {
if (graph->node[i].index >= 0)
continue;
- if (detect_sccs_tarjan(graph, i, directed) < 0)
+ if (detect_sccs_tarjan(graph, i, weak) < 0)
return -1;
}
*/
static int detect_sccs(struct isl_sched_graph *graph)
{
- return detect_ccs(graph, 1);
+ return detect_ccs(graph, 0);
}
/* Apply Tarjan's algorithm to detect the (weakly) connected components
*/
static int detect_wccs(struct isl_sched_graph *graph)
{
- return detect_ccs(graph, 0);
+ return detect_ccs(graph, 1);
}
static int cmp_scc(const void *a, const void *b, void *data)
/* Count the number of equality and inequality constraints
* that will be added for the given map.
- * If once is set, then we count
+ * If carry is set, then we are counting the number of (validity)
+ * constraints that will be added in setup_carry_lp and we count
* each edge exactly once. Otherwise, we count as follows
* validity -> 1 (>= 0)
* validity+proximity -> 2 (>= 0 and upper bound)
*/
static int count_map_constraints(struct isl_sched_graph *graph,
struct isl_sched_edge *edge, __isl_take isl_map *map,
- int *n_eq, int *n_ineq, int once)
+ int *n_eq, int *n_ineq, int carry)
{
isl_basic_set *coef;
- int f = once ? 1 : edge->proximity ? 2 : 1;
+ int f = carry ? 1 : edge->proximity ? 2 : 1;
+
+ if (carry && !edge->validity) {
+ isl_map_free(map);
+ return 0;
+ }
if (edge->src == edge->dst)
coef = intra_coefficients(graph, map);
/* Count the number of equality and inequality constraints
* that will be added to the main lp problem.
- * If once is set, then we count
- * each edge exactly once. Otherwise, we count as follows
+ * We count as follows
* validity -> 1 (>= 0)
* validity+proximity -> 2 (>= 0 and upper bound)
* proximity -> 2 (lower and upper bound)
*/
static int count_constraints(struct isl_sched_graph *graph,
- int *n_eq, int *n_ineq, int once)
+ int *n_eq, int *n_ineq)
{
int i;
isl_map *map = isl_map_copy(edge->map);
if (count_map_constraints(graph, edge, map,
- n_eq, n_ineq, once) < 0)
+ n_eq, n_ineq, 0) < 0)
return -1;
}
return 0;
}
+/* Add constraints that bound the values of the variable and parameter
+ * coefficients of the schedule.
+ *
+ * The maximal value of the coefficients is defined by the option
+ * 'schedule_max_coefficient'.
+ */
+static int add_bound_coefficient_constraints(isl_ctx *ctx,
+ struct isl_sched_graph *graph)
+{
+ int i, j, k;
+ int max_coefficient;
+ int total;
+
+ max_coefficient = ctx->opt->schedule_max_coefficient;
+
+ if (max_coefficient == -1)
+ return 0;
+
+ total = isl_basic_set_total_dim(graph->lp);
+
+ for (i = 0; i < graph->n; ++i) {
+ struct isl_sched_node *node = &graph->node[i];
+ for (j = 0; j < 2 * node->nparam + 2 * node->nvar; ++j) {
+ int dim;
+ k = isl_basic_set_alloc_inequality(graph->lp);
+ if (k < 0)
+ return -1;
+ dim = 1 + node->start + 1 + j;
+ isl_seq_clr(graph->lp->ineq[k], 1 + total);
+ isl_int_set_si(graph->lp->ineq[k][dim], -1);
+ isl_int_set_si(graph->lp->ineq[k][0], max_coefficient);
+ }
+ }
+
+ return 0;
+}
+
/* Construct an ILP problem for finding schedule coefficients
* that result in non-negative, but small dependence distances
* over all dependences.
int parametric;
int param_pos;
int n_eq, n_ineq;
+ int max_constant_term;
+ int max_coefficient;
+
+ max_constant_term = ctx->opt->schedule_max_constant_term;
+ max_coefficient = ctx->opt->schedule_max_coefficient;
parametric = ctx->opt->schedule_parametric;
nparam = isl_space_dim(graph->node[0].dim, isl_dim_param);
total += 1 + 2 * (node->nparam + node->nvar);
}
- if (count_constraints(graph, &n_eq, &n_ineq, 0) < 0)
+ if (count_constraints(graph, &n_eq, &n_ineq) < 0)
return -1;
dim = isl_space_set_alloc(ctx, 0, total);
isl_basic_set_free(graph->lp);
n_eq += 2 + parametric + force_zero;
+ if (max_constant_term != -1)
+ n_ineq += graph->n;
+ if (max_coefficient != -1)
+ for (i = 0; i < graph->n; ++i)
+ n_ineq += 2 * graph->node[i].nparam +
+ 2 * graph->node[i].nvar;
+
graph->lp = isl_basic_set_alloc_space(dim, 0, n_eq, n_ineq);
k = isl_basic_set_alloc_equality(graph->lp);
isl_int_set_si(graph->lp->eq[k][pos + j], 1);
}
+ if (max_constant_term != -1)
+ for (i = 0; i < graph->n; ++i) {
+ struct isl_sched_node *node = &graph->node[i];
+ k = isl_basic_set_alloc_inequality(graph->lp);
+ if (k < 0)
+ return -1;
+ isl_seq_clr(graph->lp->ineq[k], 1 + total);
+ isl_int_set_si(graph->lp->ineq[k][1 + node->start], -1);
+ isl_int_set_si(graph->lp->ineq[k][0], max_constant_term);
+ }
+
+ if (add_bound_coefficient_constraints(ctx, graph) < 0)
+ return -1;
if (add_all_validity_constraints(graph) < 0)
return -1;
if (add_all_proximity_constraints(graph) < 0)
return -1;
}
-/* Convert node->sched into a map and return this map.
- * We simply add equality constraints that express each output variable
- * as the affine combination of parameters and input variables specified
- * by the schedule matrix.
- *
- * The result is cached in node->sched_map, which needs to be released
- * whenever node->sched is updated.
+/* Convert node->sched into a multi_aff and return this multi_aff.
*/
-static __isl_give isl_map *node_extract_schedule(struct isl_sched_node *node)
+static __isl_give isl_multi_aff *node_extract_schedule_multi_aff(
+ struct isl_sched_node *node)
{
int i, j;
- isl_space *dim;
+ isl_space *space;
isl_local_space *ls;
- isl_basic_map *bmap;
- isl_constraint *c;
+ isl_aff *aff;
+ isl_multi_aff *ma;
int nrow, ncol;
isl_int v;
- if (node->sched_map)
- return isl_map_copy(node->sched_map);
-
nrow = isl_mat_rows(node->sched);
ncol = isl_mat_cols(node->sched) - 1;
- dim = isl_space_from_domain(isl_space_copy(node->dim));
- dim = isl_space_add_dims(dim, isl_dim_out, nrow);
- bmap = isl_basic_map_universe(isl_space_copy(dim));
- ls = isl_local_space_from_space(dim);
+ space = isl_space_from_domain(isl_space_copy(node->dim));
+ space = isl_space_add_dims(space, isl_dim_out, nrow);
+ ma = isl_multi_aff_zero(space);
+ ls = isl_local_space_from_space(isl_space_copy(node->dim));
isl_int_init(v);
for (i = 0; i < nrow; ++i) {
- c = isl_equality_alloc(isl_local_space_copy(ls));
- isl_constraint_set_coefficient_si(c, isl_dim_out, i, -1);
+ aff = isl_aff_zero_on_domain(isl_local_space_copy(ls));
isl_mat_get_element(node->sched, i, 0, &v);
- isl_constraint_set_constant(c, v);
+ aff = isl_aff_set_constant(aff, v);
for (j = 0; j < node->nparam; ++j) {
isl_mat_get_element(node->sched, i, 1 + j, &v);
- isl_constraint_set_coefficient(c, isl_dim_param, j, v);
+ aff = isl_aff_set_coefficient(aff, isl_dim_param, j, v);
}
for (j = 0; j < node->nvar; ++j) {
isl_mat_get_element(node->sched,
i, 1 + node->nparam + j, &v);
- isl_constraint_set_coefficient(c, isl_dim_in, j, v);
+ aff = isl_aff_set_coefficient(aff, isl_dim_in, j, v);
}
- bmap = isl_basic_map_add_constraint(bmap, c);
+ ma = isl_multi_aff_set_aff(ma, i, aff);
}
isl_int_clear(v);
isl_local_space_free(ls);
- node->sched_map = isl_map_from_basic_map(bmap);
+ return ma;
+}
+
+/* Convert node->sched into a map and return this map.
+ *
+ * The result is cached in node->sched_map, which needs to be released
+ * whenever node->sched is updated.
+ */
+static __isl_give isl_map *node_extract_schedule(struct isl_sched_node *node)
+{
+ if (!node->sched_map) {
+ isl_multi_aff *ma;
+
+ ma = node_extract_schedule_multi_aff(node);
+ node->sched_map = isl_map_from_multi_aff(ma);
+ }
+
return isl_map_copy(node->sched_map);
}
/* Update the dependence relations of all edges based on the current schedule.
* If a dependence is carried completely by the current schedule, then
- * it is removed and edge_table is updated accordingly.
+ * it is removed from the edge_tables. It is kept in the list of edges
+ * as otherwise all edge_tables would have to be recomputed.
*/
static int update_edges(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i;
- int reset_table = 0;
for (i = graph->n_edge - 1; i >= 0; --i) {
struct isl_sched_edge *edge = &graph->edge[i];
if (!edge->map)
return -1;
- if (isl_map_plain_is_empty(edge->map)) {
- reset_table = 1;
- isl_map_free(edge->map);
- if (i != graph->n_edge - 1)
- graph->edge[i] = graph->edge[graph->n_edge - 1];
- graph->n_edge--;
- }
- }
-
- if (reset_table) {
- isl_hash_table_free(ctx, graph->edge_table);
- graph->edge_table = NULL;
- return graph_init_edge_table(ctx, graph);
+ if (isl_map_plain_is_empty(edge->map))
+ graph_remove_edge(graph, edge);
}
return 0;
graph->n_band++;
}
-/* Topologically sort statements mapped to same schedule iteration
+/* Topologically sort statements mapped to the same schedule iteration
* and add a row to the schedule corresponding to this order.
*/
static int sort_statements(isl_ctx *ctx, struct isl_sched_graph *graph)
band_end = isl_alloc_array(ctx, int, graph->n_band);
band_id = isl_alloc_array(ctx, int, graph->n_band);
zero = isl_alloc_array(ctx, int, graph->n_total_row);
- sched->node[i].sched = node_extract_schedule(&graph->node[i]);
+ sched->node[i].sched =
+ node_extract_schedule_multi_aff(&graph->node[i]);
sched->node[i].band_end = band_end;
sched->node[i].band_id = band_id;
sched->node[i].zero = zero;
/* 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;
+ int t;
dst->n_edge = 0;
for (i = 0; i < src->n_edge; ++i) {
struct isl_sched_edge *edge = &src->edge[i];
isl_map *map;
+ struct isl_sched_node *dst_src, *dst_dst;
if (!edge_pred(edge, data))
continue;
if (isl_map_plain_is_empty(edge->map))
continue;
+ dst_src = graph_find_node(ctx, dst, edge->src->dim);
+ dst_dst = graph_find_node(ctx, dst, edge->dst->dim);
+ if (!dst_src || !dst_dst) {
+ if (edge->validity)
+ isl_die(ctx, isl_error_internal,
+ "backward validity edge", return -1);
+ continue;
+ }
+
map = isl_map_copy(edge->map);
- dst->edge[dst->n_edge].src =
- graph_find_node(ctx, dst, edge->src->dim);
- dst->edge[dst->n_edge].dst =
- graph_find_node(ctx, dst, edge->dst->dim);
+ dst->edge[dst->n_edge].src = dst_src;
+ dst->edge[dst->n_edge].dst = dst_dst;
dst->edge[dst->n_edge].map = map;
dst->edge[dst->n_edge].validity = edge->validity;
dst->edge[dst->n_edge].proximity = edge->proximity;
dst->n_edge++;
+
+ for (t = 0; 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;
int data, int wcc)
{
struct isl_sched_graph split = { 0 };
+ int t;
if (graph_alloc(ctx, &split, n, n_edge) < 0)
goto error;
goto error;
if (graph_init_table(ctx, &split) < 0)
goto error;
- if (copy_edges(ctx, &split, graph, edge_pred, data) < 0)
+ for (t = 0; t <= isl_edge_last; ++t)
+ split.max_edge[t] = graph->max_edge[t];
+ if (graph_init_edge_tables(ctx, &split) < 0)
goto error;
- if (graph_init_edge_table(ctx, &split) < 0)
+ if (copy_edges(ctx, &split, graph, edge_pred, data) < 0)
goto error;
split.n_row = graph->n_row;
split.n_total_row = graph->n_total_row;
return node->scc >= scc;
}
-static int edge_src_scc_exactly(struct isl_sched_edge *edge, int scc)
+static int edge_scc_exactly(struct isl_sched_edge *edge, int scc)
{
- return edge->src->scc == scc;
+ return edge->src->scc == scc && edge->dst->scc == scc;
}
static int edge_dst_scc_at_most(struct isl_sched_edge *edge, int scc)
* It would be possible to reuse them as the first rows in the next
* band, but recomputing them may result in better rows as we are looking
* at a smaller part of the dependence graph.
+ * compute_split_schedule is only called when no zero-distance schedule row
+ * could be found on the entire graph, so we wark the splitting row as
+ * non zero-distance.
*
* The band_id of the second group is set to n, where n is the number
* of nodes in the first group. This ensures that the band_ids over
node->sched = isl_mat_set_element_si(node->sched,
row, j, 0);
node->band[graph->n_total_row] = graph->n_band;
+ node->zero[graph->n_total_row] = 0;
}
e1 = e2 = 0;
return 0;
}
-/* Add constraints to graph->lp that force all dependence
- * to be respected and attempt to carry it.
+/* Add constraints to graph->lp that force all validity dependences
+ * to be respected and attempt to carry them.
*/
static int add_all_constraints(struct isl_sched_graph *graph)
{
pos = 0;
for (i = 0; i < graph->n_edge; ++i) {
struct isl_sched_edge *edge= &graph->edge[i];
+
+ if (!edge->validity)
+ continue;
+
for (j = 0; j < edge->map->n; ++j) {
isl_basic_map *bmap;
isl_map *map;
/* Count the number of equality and inequality constraints
* that will be added to the carry_lp problem.
- * If once is set, then we count
- * each edge exactly once. Otherwise, we count as follows
- * validity -> 1 (>= 0)
- * validity+proximity -> 2 (>= 0 and upper bound)
- * proximity -> 2 (lower and upper bound)
+ * We count each edge exactly once.
*/
static int count_all_constraints(struct isl_sched_graph *graph,
- int *n_eq, int *n_ineq, int once)
+ int *n_eq, int *n_ineq)
{
int i, j;
map = isl_map_from_basic_map(bmap);
if (count_map_constraints(graph, edge, map,
- n_eq, n_ineq, once) < 0)
+ n_eq, n_ineq, 1) < 0)
return -1;
}
}
* - positive and negative parts of c_i_n (if parametric)
* - positive and negative parts of c_i_x
*
- * The constraints are those from the edges plus three equalities
+ * The constraints are those from the (validity) edges plus three equalities
* to express the sums and n_edge inequalities to express e_i <= 1.
*/
static int setup_carry_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
total += 1 + 2 * (node->nparam + node->nvar);
}
- if (count_all_constraints(graph, &n_eq, &n_ineq, 1) < 0)
+ if (count_all_constraints(graph, &n_eq, &n_ineq) < 0)
return -1;
dim = isl_space_set_alloc(ctx, 0, total);
return 0;
}
-/* If the schedule_split_parallel option is set and if the linear
- * parts of the scheduling rows for all nodes in the graphs are the same,
- * then split off the constant term from the linear part.
+/* If the schedule_split_scaled option is set and if the linear
+ * parts of the scheduling rows for all nodes in the graphs have
+ * non-trivial common divisor, then split off the constant term
+ * from the linear part.
* The constant term is then placed in a separate band and
- * the linear part is simplified.
+ * the linear part is reduced.
*/
-static int split_parallel(isl_ctx *ctx, struct isl_sched_graph *graph)
+static int split_scaled(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i;
- int equal = 1;
- int row, cols;
- struct isl_sched_node *node0;
+ int row;
+ isl_int gcd, gcd_i;
- if (!ctx->opt->schedule_split_parallel)
+ if (!ctx->opt->schedule_split_scaled)
return 0;
if (graph->n <= 1)
return 0;
- node0 = &graph->node[0];
- row = isl_mat_rows(node0->sched) - 1;
- cols = isl_mat_cols(node0->sched);
- for (i = 1; i < graph->n; ++i) {
+ 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);
- if (!isl_seq_eq(node0->sched->row[row] + 1,
- node->sched->row[row] + 1, cols - 1))
- return 0;
- if (equal &&
- isl_int_ne(node0->sched->row[row][0],
- node->sched->row[row][0]))
- equal = 0;
+ isl_seq_gcd(node->sched->row[row] + 1, cols - 1, &gcd_i);
+ isl_int_gcd(gcd, gcd, gcd_i);
}
- if (equal)
+
+ isl_int_clear(gcd_i);
+
+ if (isl_int_cmp_si(gcd, 1) <= 0) {
+ isl_int_clear(gcd);
return 0;
+ }
next_band(graph);
node->sched_map = NULL;
node->sched = isl_mat_add_zero_rows(node->sched, 1);
if (!node->sched)
- return -1;
- isl_int_set(node->sched->row[row + 1][0],
- node->sched->row[row][0]);
- isl_int_set_si(node->sched->row[row][0], 0);
- node->sched = isl_mat_normalize_row(node->sched, row);
+ goto error;
+ isl_int_fdiv_r(node->sched->row[row + 1][0],
+ node->sched->row[row][0], gcd);
+ isl_int_fdiv_q(node->sched->row[row][0],
+ node->sched->row[row][0], gcd);
+ isl_int_mul(node->sched->row[row][0],
+ node->sched->row[row][0], gcd);
+ node->sched = isl_mat_scale_down_row(node->sched, row, gcd);
if (!node->sched)
- return -1;
+ goto error;
node->band[graph->n_total_row] = graph->n_band;
}
graph->n_total_row++;
+ isl_int_clear(gcd);
return 0;
+error:
+ isl_int_clear(gcd);
+ return -1;
}
/* Construct a schedule row for each node such that as many dependences
if (update_schedule(graph, sol, 0, 0) < 0)
return -1;
- if (split_parallel(ctx, graph) < 0)
+ if (split_scaled(ctx, graph) < 0)
return -1;
return compute_next_band(ctx, graph);
}
+/* Are there any (non-empty) validity edges in the graph?
+ */
+static int has_validity_edges(struct isl_sched_graph *graph)
+{
+ int i;
+
+ for (i = 0; i < graph->n_edge; ++i) {
+ int empty;
+
+ empty = isl_map_plain_is_empty(graph->edge[i].map);
+ if (empty < 0)
+ return -1;
+ if (empty)
+ continue;
+ if (graph->edge[i].validity)
+ return 1;
+ }
+
+ return 0;
+}
+
+/* Should we apply a Feautrier step?
+ * That is, did the user request the Feautrier algorithm and are
+ * there any validity dependences (left)?
+ */
+static int need_feautrier_step(isl_ctx *ctx, struct isl_sched_graph *graph)
+{
+ if (ctx->opt->schedule_algorithm != ISL_SCHEDULE_ALGORITHM_FEAUTRIER)
+ return 0;
+
+ return has_validity_edges(graph);
+}
+
+/* Compute a schedule for a connected dependence graph using Feautrier's
+ * multi-dimensional scheduling algorithm.
+ * The original algorithm is described in [1].
+ * The main idea is to minimize the number of scheduling dimensions, by
+ * trying to satisfy as many dependences as possible per scheduling dimension.
+ *
+ * [1] P. Feautrier, Some Efficient Solutions to the Affine Scheduling
+ * Problem, Part II: Multi-Dimensional Time.
+ * In Intl. Journal of Parallel Programming, 1992.
+ */
+static int compute_schedule_wcc_feautrier(isl_ctx *ctx,
+ struct isl_sched_graph *graph)
+{
+ return carry_dependences(ctx, graph);
+}
+
/* Compute a schedule for a connected dependence graph.
* We try to find a sequence of as many schedule rows as possible that result
* in non-negative dependence distances (independent of the previous rows
* - try to carry as many dependences as possible and continue with the next
* band
*
+ * If Feautrier's algorithm is selected, we first recursively try to satisfy
+ * as many validity dependences as possible. When all validity dependences
+ * are satisfied we extend the schedule to a full-dimensional schedule.
+ *
* If we manage to complete the schedule, we finish off by topologically
* sorting the statements based on the remaining dependences.
*
if (compute_maxvar(graph) < 0)
return -1;
+ if (need_feautrier_step(ctx, graph))
+ return compute_schedule_wcc_feautrier(ctx, graph);
+
if (ctx->opt->schedule_outer_zero_distance)
force_zero = 1;
return sort_statements(ctx, graph);
}
+/* Add a row to the schedules that separates the SCCs and move
+ * to the next band.
+ */
+static int split_on_scc(struct isl_sched_graph *graph)
+{
+ int i;
+
+ for (i = 0; i < graph->n; ++i) {
+ struct isl_sched_node *node = &graph->node[i];
+ int row = isl_mat_rows(node->sched);
+
+ isl_map_free(node->sched_map);
+ node->sched_map = NULL;
+ node->sched = isl_mat_add_zero_rows(node->sched, 1);
+ node->sched = isl_mat_set_element_si(node->sched, row, 0,
+ node->scc);
+ if (!node->sched)
+ return -1;
+ node->band[graph->n_total_row] = graph->n_band;
+ }
+
+ graph->n_total_row++;
+ next_band(graph);
+
+ return 0;
+}
+
/* Compute a schedule for each component (identified by node->scc)
* of the dependence graph separately and then combine the results.
+ * Depending on the setting of schedule_fuse, a component may be
+ * either weakly or strongly connected.
*
* The band_id is adjusted such that each component has a separate id.
* Note that the band_id may have already been set to a value different
int n_total_row, orig_total_row;
int n_band, orig_band;
+ if (ctx->opt->schedule_fuse == ISL_SCHEDULE_FUSE_MIN ||
+ ctx->opt->schedule_separate_components)
+ split_on_scc(graph);
+
n_total_row = 0;
orig_total_row = graph->n_total_row;
n_band = 0;
n++;
n_edge = 0;
for (i = 0; i < graph->n_edge; ++i)
- if (graph->edge[i].src->scc == wcc)
+ if (graph->edge[i].src->scc == wcc &&
+ graph->edge[i].dst->scc == wcc)
n_edge++;
if (compute_sub_schedule(ctx, graph, n, n_edge,
&node_scc_exactly,
- &edge_src_scc_exactly, wcc, 1) < 0)
+ &edge_scc_exactly, wcc, 1) < 0)
return -1;
if (graph->n_total_row > n_total_row)
n_total_row = graph->n_total_row;
/* Compute a schedule for the given dependence graph.
* We first check if the graph is connected (through validity dependences)
- * and if so compute a schedule for each component separately.
+ * and, if not, compute a schedule for each component separately.
+ * If schedule_fuse is set to minimal fusion, then we check for strongly
+ * connected components instead and compute a separate schedule for
+ * each such strongly connected component.
*/
static int compute_schedule(isl_ctx *ctx, struct isl_sched_graph *graph)
{
- if (detect_wccs(graph) < 0)
- return -1;
+ if (ctx->opt->schedule_fuse == ISL_SCHEDULE_FUSE_MIN) {
+ if (detect_sccs(graph) < 0)
+ return -1;
+ } else {
+ if (detect_wccs(graph) < 0)
+ return -1;
+ }
if (graph->scc > 1)
return compute_component_schedule(ctx, graph);
}
/* Compute a schedule for the given union of domains that respects
- * all the validity dependences and tries to minimize the dependence
- * distances over the proximity dependences.
+ * all the validity dependences.
+ * If the default isl scheduling algorithm is used, it tries to minimize
+ * the dependence distances over the proximity dependences.
+ * If Feautrier's scheduling algorithm is used, the proximity dependence
+ * distances are only minimized during the extension to a full-dimensional
+ * schedule.
*/
__isl_give isl_schedule *isl_union_set_compute_schedule(
__isl_take isl_union_set *domain,
isl_space *dim;
struct isl_sched_graph graph = { 0 };
isl_schedule *sched;
+ struct isl_extract_edge_data data;
domain = isl_union_set_align_params(domain,
isl_union_map_get_space(validity));
if (graph_alloc(ctx, &graph, graph.n,
isl_union_map_n_map(validity) + isl_union_map_n_map(proximity)) < 0)
goto error;
+ if (compute_max_row(&graph, domain) < 0)
+ goto error;
graph.root = 1;
graph.n = 0;
if (isl_union_set_foreach_set(domain, &extract_node, &graph) < 0)
goto error;
if (graph_init_table(ctx, &graph) < 0)
goto error;
- graph.n_edge = 0;
- if (isl_union_map_foreach_map(validity, &extract_edge, &graph) < 0)
+ graph.max_edge[isl_edge_validity] = isl_union_map_n_map(validity);
+ graph.max_edge[isl_edge_proximity] = isl_union_map_n_map(proximity);
+ if (graph_init_edge_tables(ctx, &graph) < 0)
goto error;
- if (graph_init_edge_table(ctx, &graph) < 0)
+ graph.n_edge = 0;
+ data.graph = &graph;
+ data.type = isl_edge_validity;
+ if (isl_union_map_foreach_map(validity, &extract_edge, &data) < 0)
goto error;
- if (isl_union_map_foreach_map(proximity, &extract_edge, &graph) < 0)
+ data.type = isl_edge_proximity;
+ if (isl_union_map_foreach_map(proximity, &extract_edge, &data) < 0)
goto error;
if (compute_schedule(ctx, &graph) < 0)
return NULL;
for (i = 0; i < sched->n; ++i) {
- isl_map_free(sched->node[i].sched);
+ isl_multi_aff_free(sched->node[i].sched);
free(sched->node[i].band_end);
free(sched->node[i].band_id);
free(sched->node[i].zero);
return schedule ? isl_space_get_ctx(schedule->dim) : NULL;
}
+/* Return an isl_union_map of the schedule. If we have already constructed
+ * a band forest, then this band forest may have been modified so we need
+ * to extract the isl_union_map from the forest rather than from
+ * the originally computed schedule.
+ */
__isl_give isl_union_map *isl_schedule_get_map(__isl_keep isl_schedule *sched)
{
int i;
if (!sched)
return NULL;
+ if (sched->band_forest)
+ return isl_band_list_get_suffix_schedule(sched->band_forest);
+
umap = isl_union_map_empty(isl_space_copy(sched->dim));
- for (i = 0; i < sched->n; ++i)
- umap = isl_union_map_add_map(umap,
- isl_map_copy(sched->node[i].sched));
+ for (i = 0; i < sched->n; ++i) {
+ isl_multi_aff *ma;
+
+ ma = isl_multi_aff_copy(sched->node[i].sched);
+ umap = isl_union_map_add_map(umap, isl_map_from_multi_aff(ma));
+ }
return umap;
}
isl_band *band;
unsigned start, end;
- band = isl_calloc_type(ctx, isl_band);
+ band = isl_band_alloc(ctx);
if (!band)
return NULL;
- band->ref = 1;
band->schedule = schedule;
band->parent = parent;
for (j = 0; j < band->n; ++j)
band->zero[j] = schedule->node[i].zero[start + j];
- band->map = isl_union_map_empty(isl_space_copy(schedule->dim));
+ band->pma = isl_union_pw_multi_aff_empty(isl_space_copy(schedule->dim));
for (i = 0; i < schedule->n; ++i) {
- isl_map *map;
+ isl_multi_aff *ma;
+ isl_pw_multi_aff *pma;
unsigned n_out;
if (!active[i])
continue;
- map = isl_map_copy(schedule->node[i].sched);
- n_out = isl_map_dim(map, isl_dim_out);
- map = isl_map_project_out(map, isl_dim_out, end, n_out - end);
- map = isl_map_project_out(map, isl_dim_out, 0, start);
- band->map = isl_union_map_union(band->map,
- isl_union_map_from_map(map));
+ ma = isl_multi_aff_copy(schedule->node[i].sched);
+ n_out = isl_multi_aff_dim(ma, isl_dim_out);
+ ma = isl_multi_aff_drop_dims(ma, isl_dim_out, end, n_out - end);
+ ma = isl_multi_aff_drop_dims(ma, isl_dim_out, 0, start);
+ pma = isl_pw_multi_aff_from_multi_aff(ma);
+ band->pma = isl_union_pw_multi_aff_add_pw_multi_aff(band->pma,
+ pma);
}
- if (!band->map)
+ if (!band->pma)
goto error;
return band;
return isl_band_list_dup(schedule->band_forest);
}
+/* Call "fn" on each band in the schedule in depth-first post-order.
+ */
+int isl_schedule_foreach_band(__isl_keep isl_schedule *sched,
+ int (*fn)(__isl_keep isl_band *band, void *user), void *user)
+{
+ int r;
+ isl_band_list *forest;
+
+ if (!sched)
+ return -1;
+
+ forest = isl_schedule_get_band_forest(sched);
+ r = isl_band_list_foreach_band(forest, fn, user);
+ isl_band_list_free(forest);
+
+ return r;
+}
+
static __isl_give isl_printer *print_band_list(__isl_take isl_printer *p,
__isl_keep isl_band_list *list);
isl_band_list *children;
p = isl_printer_start_line(p);
- p = isl_printer_print_union_map(p, band->map);
+ p = isl_printer_print_union_pw_multi_aff(p, band->pma);
p = isl_printer_end_line(p);
if (!isl_band_has_children(band))
projects / platform / upstream / isl.git / blobdiff