#include <isl_flow.h>
/* A private structure to keep track of a mapping together with
- * a user-specified identifier.
+ * a user-specified identifier and a boolean indicating whether
+ * the map represents a must or may access/dependence.
*/
struct isl_labeled_map {
struct isl_map *map;
void *data;
+ int must;
};
/* A structure containing the input for dependence analysis:
* - a sink
- * - n_source (<= max_source) sources
+ * - n_must + n_may (<= max_source) sources
* - a function for determining the relative order of sources and sink
+ * The must sources are placed before the may sources.
*/
struct isl_access_info {
struct isl_labeled_map sink;
isl_access_level_before level_before;
int max_source;
- int n_source;
+ int n_must;
+ int n_may;
struct isl_labeled_map source[1];
};
/* A structure containing the output of dependence analysis:
- * - n_source flow dependences
- * - a subset of the sink for which no source could be found
+ * - n_source dependences
+ * - a subset of the sink for which definitely no source could be found
+ * - a subset of the sink for which possibly no source could be found
*/
struct isl_flow {
- struct isl_set *no_source;
+ isl_set *must_no_source;
+ isl_set *may_no_source;
int n_source;
struct isl_labeled_map *dep;
};
acc->sink.data = sink_user;
acc->level_before = fn;
acc->max_source = max_source;
- acc->n_source = 0;
+ acc->n_must = 0;
+ acc->n_may = 0;
return acc;
error:
if (!acc)
return;
isl_map_free(acc->sink.map);
- for (i = 0; i < acc->n_source; ++i)
+ for (i = 0; i < acc->n_must + acc->n_may; ++i)
isl_map_free(acc->source[i].map);
free(acc);
}
-/* Add another source to an isl_access_info structure.
+/* Add another source to an isl_access_info structure, making
+ * sure the "must" sources are placed before the "may" sources.
* This function may be called at most max_source times on a
* given isl_access_info structure, with max_source as specified
* in the call to isl_access_info_alloc that constructed the structure.
*/
__isl_give isl_access_info *isl_access_info_add_source(
__isl_take isl_access_info *acc, __isl_take isl_map *source,
- void *source_user)
+ int must, void *source_user)
{
if (!acc)
return NULL;
- isl_assert(acc->sink.map->ctx, acc->n_source < acc->max_source, goto error);
-
- acc->source[acc->n_source].map = source;
- acc->source[acc->n_source].data = source_user;
- acc->n_source++;
+ isl_assert(acc->sink.map->ctx,
+ acc->n_must + acc->n_may < acc->max_source, goto error);
+
+ if (must) {
+ if (acc->n_may)
+ acc->source[acc->n_must + acc->n_may] =
+ acc->source[acc->n_must];
+ acc->source[acc->n_must].map = source;
+ acc->source[acc->n_must].data = source_user;
+ acc->source[acc->n_must].must = 1;
+ acc->n_must++;
+ } else {
+ acc->source[acc->n_must + acc->n_may].map = source;
+ acc->source[acc->n_must + acc->n_may].data = source_user;
+ acc->source[acc->n_must + acc->n_may].must = 0;
+ acc->n_may++;
+ }
return acc;
error:
return (level1 % 2) ? -1 : 1;
}
-/* Sort the source accesses in order of increasing number of shared
+/* Sort the must source accesses in order of increasing number of shared
* levels with the sink access.
* Source accesses with the same number of shared levels are sorted
* in their textual order.
if (!acc)
return NULL;
- if (acc->n_source <= 1)
+ if (acc->n_must <= 1)
return acc;
array = isl_alloc_array(acc->sink.map->ctx,
- struct isl_access_sort_info, acc->n_source);
+ struct isl_access_sort_info, acc->n_must);
if (!array)
goto error;
- for (i = 0; i < acc->n_source; ++i) {
+ for (i = 0; i < acc->n_must; ++i) {
array[i].source_map = acc->source[i].map;
array[i].source_data = acc->source[i].data;
array[i].acc = acc;
}
- qsort(array, acc->n_source, sizeof(struct isl_access_sort_info),
+ qsort(array, acc->n_must, sizeof(struct isl_access_sort_info),
access_sort_cmp);
- for (i = 0; i < acc->n_source; ++i) {
+ for (i = 0; i < acc->n_must; ++i) {
acc->source[i].map = array[i].source_map;
acc->source[i].data = array[i].source_data;
}
/* Initialize an empty isl_flow structure corresponding to a given
* isl_access_info structure.
+ * For each must access, two dependences are created (initialized
+ * to the empty relation), one for the resulting must dependences
+ * and one for the resulting may dependences. May accesses can
+ * only lead to may dependences, so only one dependence is created
+ * for each of them.
* This function is private as isl_flow structures are only supposed
* to be created by isl_access_info_compute_flow.
*/
if (!dep)
return NULL;
- dep->dep = isl_alloc_array(ctx, struct isl_labeled_map, acc->n_source);
+ dep->dep = isl_alloc_array(ctx, struct isl_labeled_map,
+ 2 * acc->n_must + acc->n_may);
if (!dep->dep)
goto error;
- dep->n_source = acc->n_source;
- for (i = 0; i < acc->n_source; ++i) {
+ dep->n_source = 2 * acc->n_must + acc->n_may;
+ for (i = 0; i < acc->n_must; ++i) {
struct isl_dim *dim;
dim = isl_dim_join(isl_dim_copy(acc->source[i].map->dim),
isl_dim_reverse(isl_dim_copy(acc->sink.map->dim)));
- dep->dep[i].map = isl_map_empty(dim);
- dep->dep[i].data = acc->source[i].data;
+ dep->dep[2 * i].map = isl_map_empty(dim);
+ dep->dep[2 * i + 1].map = isl_map_copy(dep->dep[2 * i].map);
+ dep->dep[2 * i].data = acc->source[i].data;
+ dep->dep[2 * i + 1].data = acc->source[i].data;
+ dep->dep[2 * i].must = 1;
+ dep->dep[2 * i + 1].must = 0;
+ }
+ for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {
+ struct isl_dim *dim;
+ dim = isl_dim_join(isl_dim_copy(acc->source[i].map->dim),
+ isl_dim_reverse(isl_dim_copy(acc->sink.map->dim)));
+ dep->dep[acc->n_must + i].map = isl_map_empty(dim);
+ dep->dep[acc->n_must + i].data = acc->source[i].data;
+ dep->dep[acc->n_must + i].must = 0;
}
return dep;
* the isl_flow_foreach call.
*/
int isl_flow_foreach(__isl_keep isl_flow *deps,
- int (*fn)(__isl_take isl_map *dep, void *dep_user, void *user),
+ int (*fn)(__isl_take isl_map *dep, int must, void *dep_user, void *user),
void *user)
{
int i;
for (i = 0; i < deps->n_source; ++i) {
if (isl_map_fast_is_empty(deps->dep[i].map))
continue;
- if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].data, user) < 0)
+ if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,
+ deps->dep[i].data, user) < 0)
return -1;
}
/* Return a copy of the subset of the sink for which no source could be found.
*/
-__isl_give isl_set *isl_flow_get_no_source(__isl_keep isl_flow *deps)
+__isl_give isl_set *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)
{
if (!deps)
return NULL;
- return isl_set_copy(deps->no_source);
+ if (must)
+ return isl_set_copy(deps->must_no_source);
+ else
+ return isl_set_copy(deps->may_no_source);
}
void isl_flow_free(__isl_take isl_flow *deps)
if (!deps)
return;
- isl_set_free(deps->no_source);
+ isl_set_free(deps->must_no_source);
+ isl_set_free(deps->may_no_source);
if (deps->dep) {
for (i = 0; i < deps->n_source; ++i)
isl_map_free(deps->dep[i].map);
return isl_map_from_basic_map(bmap);
}
-/* Compute the last iteration of source j that precedes the sink at the given
- * level for sink iterations in set_C.
+/* Compute the last iteration of must source j that precedes the sink
+ * at the given level for sink iterations in set_C.
* The subset of set_C for which no such iteration can be found is returned
* in *empty.
*/
return result;
}
-/* For a given mapping between iterations of source j and iterations
- * of the sink, compute the last iteration of source k preceding
+/* For a given mapping between iterations of must source j and iterations
+ * of the sink, compute the last iteration of must source k preceding
* the sink at level before_level for any of the sink iterations,
- * but following the corresponding iteration of source j at level
+ * but following the corresponding iteration of must source j at level
* after_level.
*/
static struct isl_map *last_later_source(struct isl_access_info *acc,
return 0;
}
-/* Given a "sink" access, a list of n "source" accesses,
- * compute for each iteration of the sink access
- * and for each element accessed by that iteration,
- * the source access in the list that last accessed the
- * element accessed by the sink access before this sink access.
- * Each access is given as a map from the loop iterators
- * to the array indices.
- * The result is a list of n relations between source and sink
- * iterations and a subset of the domain of the sink access,
- * corresponding to those iterations that access an element
- * not previously accessed.
+/* Compute all iterations of may source j that precedes the sink at the given
+ * level for sink iterations in set_C.
+ */
+static __isl_give isl_map *all_sources(__isl_keep isl_access_info *acc,
+ __isl_take isl_set *set_C, int j, int level)
+{
+ isl_map *read_map;
+ isl_map *write_map;
+ isl_map *dep_map;
+ isl_map *after;
+
+ read_map = isl_map_copy(acc->sink.map);
+ read_map = isl_map_intersect_domain(read_map, set_C);
+ write_map = isl_map_copy(acc->source[acc->n_must + j].map);
+ write_map = isl_map_reverse(write_map);
+ dep_map = isl_map_apply_range(read_map, write_map);
+ after = after_at_level(isl_dim_copy(dep_map->dim), level);
+ dep_map = isl_map_intersect(dep_map, after);
+
+ return isl_map_reverse(dep_map);
+}
+
+/* For a given mapping between iterations of must source k and iterations
+ * of the sink, compute the all iteration of may source j preceding
+ * the sink at level before_level for any of the sink iterations,
+ * but following the corresponding iteration of must source k at level
+ * after_level.
+ */
+static __isl_give isl_map *all_later_sources(__isl_keep isl_access_info *acc,
+ __isl_keep isl_map *old_map,
+ int j, int before_level, int k, int after_level)
+{
+ isl_dim *dim;
+ isl_set *set_C;
+ isl_map *read_map;
+ isl_map *write_map;
+ isl_map *dep_map;
+ isl_map *after_write;
+ isl_map *before_read;
+
+ set_C = isl_map_range(isl_map_copy(old_map));
+ read_map = isl_map_copy(acc->sink.map);
+ read_map = isl_map_intersect_domain(read_map, set_C);
+ write_map = isl_map_copy(acc->source[acc->n_must + j].map);
+
+ write_map = isl_map_reverse(write_map);
+ dep_map = isl_map_apply_range(read_map, write_map);
+ dim = isl_dim_join(isl_dim_copy(acc->source[acc->n_must + j].map->dim),
+ isl_dim_reverse(isl_dim_copy(acc->source[k].map->dim)));
+ after_write = after_at_level(dim, after_level);
+ after_write = isl_map_apply_range(after_write, old_map);
+ after_write = isl_map_reverse(after_write);
+ dep_map = isl_map_intersect(dep_map, after_write);
+ before_read = after_at_level(isl_dim_copy(dep_map->dim), before_level);
+ dep_map = isl_map_intersect(dep_map, before_read);
+ return isl_map_reverse(dep_map);
+}
+
+/* Given the must and may dependence relations for the must accesses
+ * for level sink_level, check if there are any accesses of may access j
+ * that occur in between and return their union.
+ * If some of these accesses are intermediate with respect to
+ * (previously thought to be) must dependences, then these
+ * must dependences are turned into may dependences.
+ */
+static __isl_give isl_map *all_intermediate_sources(
+ __isl_keep isl_access_info *acc, __isl_take isl_map *map,
+ struct isl_map **must_rel, struct isl_map **may_rel,
+ int j, int sink_level)
+{
+ int k, level;
+ int depth = 2 * isl_map_dim(acc->source[acc->n_must + j].map,
+ isl_dim_in) + 1;
+
+ for (k = 0; k < acc->n_must; ++k) {
+ int plevel;
+
+ if (isl_map_fast_is_empty(may_rel[k]) &&
+ isl_map_fast_is_empty(must_rel[k]))
+ continue;
+
+ plevel = acc->level_before(acc->source[k].data,
+ acc->source[acc->n_must + j].data);
+
+ for (level = sink_level; level <= depth; ++level) {
+ isl_map *T;
+ isl_map *copy;
+ isl_set *ran;
+
+ if (!can_precede_at_level(plevel, level))
+ continue;
+
+ copy = isl_map_copy(may_rel[k]);
+ T = all_later_sources(acc, copy, j, sink_level, k, level);
+ map = isl_map_union(map, T);
+
+ copy = isl_map_copy(must_rel[k]);
+ T = all_later_sources(acc, copy, j, sink_level, k, level);
+ ran = isl_map_range(isl_map_copy(T));
+ map = isl_map_union(map, T);
+ may_rel[k] = isl_map_union_disjoint(may_rel[k],
+ isl_map_intersect_range(isl_map_copy(must_rel[k]),
+ isl_set_copy(ran)));
+ T = isl_map_from_domain_and_range(
+ isl_set_universe(
+ isl_dim_domain(isl_map_get_dim(must_rel[k]))),
+ ran);
+ must_rel[k] = isl_map_subtract(must_rel[k], T);
+ }
+ }
+
+ return map;
+}
+
+/* Compute dependences for the case where all accesses are "may"
+ * accesses, which boils down to computing memory based dependences.
+ * The generic algorithm would also work in this case, but it would
+ * be overkill to use it.
+ */
+static __isl_give isl_flow *compute_mem_based_dependences(
+ __isl_take isl_access_info *acc)
+{
+ int i;
+ isl_set *mustdo;
+ isl_set *maydo;
+ isl_flow *res;
+
+ res = isl_flow_alloc(acc);
+ if (!res)
+ goto error;
+
+ mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
+ maydo = isl_set_copy(mustdo);
+
+ for (i = 0; i < acc->n_may; ++i) {
+ int plevel;
+ int is_before;
+ isl_dim *dim;
+ isl_map *before;
+ isl_map *dep;
+
+ plevel = acc->level_before(acc->source[i].data, acc->sink.data);
+ is_before = plevel & 1;
+ plevel >>= 1;
+
+ dim = isl_map_get_dim(res->dep[i].map);
+ if (is_before)
+ before = isl_map_lex_le_first(dim, plevel);
+ else
+ before = isl_map_lex_lt_first(dim, plevel);
+ dep = isl_map_apply_range(isl_map_copy(acc->source[i].map),
+ isl_map_reverse(isl_map_copy(acc->sink.map)));
+ dep = isl_map_intersect(dep, before);
+ mustdo = isl_set_subtract(mustdo,
+ isl_map_range(isl_map_copy(dep)));
+ res->dep[i].map = isl_map_union(res->dep[i].map, dep);
+ }
+
+ res->may_no_source = isl_set_subtract(maydo, isl_set_copy(mustdo));
+ res->must_no_source = mustdo;
+
+ isl_access_info_free(acc);
+
+ return res;
+error:
+ isl_access_info_free(acc);
+ return NULL;
+}
+
+/* Compute dependences for the case where there is at least one
+ * "must" access.
*
- * The algorithm considers all levels in which a source may precede the sink,
- * where a level may either be a statement level or a loop level.
+ * The core algorithm considers all levels in which a source may precede
+ * the sink, where a level may either be a statement level or a loop level.
* The outermost statement level is 1, the first loop level is 2, etc...
* The algorithm basically does the following:
* for all levels l of the read access from innermost to outermost
* and replace possible last accesses dep by the remainder
*
*
- * To deal with multi-valued sink access relations, the sink iteration
- * domain is first extended with dimensions that correspond to the data
- * space. After the computation is finished, these extra dimensions are
- * projected out again.
+ * The above algorithm is applied to the must access. During the course
+ * of the algorithm, we keep track of sink iterations that still
+ * need to be considered. These iterations are split into those that
+ * haven't been matched to any source access (mustdo) and those that have only
+ * been matched to may accesses (maydo).
+ * At the end of each level, we also consider the may accesses.
+ * In particular, we consider may accesses that precede the remaining
+ * sink iterations, moving elements from mustdo to maydo when appropriate,
+ * and may accesses that occur between a must source and a sink of any
+ * dependences found at the current level, turning must dependences into
+ * may dependences when appropriate.
+ *
*/
-__isl_give isl_flow *isl_access_info_compute_flow(__isl_take isl_access_info *acc)
+static __isl_give isl_flow *compute_val_based_dependences(
+ __isl_take isl_access_info *acc)
{
- struct isl_ctx *ctx;
- struct isl_set *todo;
+ isl_ctx *ctx;
+ isl_flow *res;
+ isl_set *mustdo;
+ isl_set *maydo;
int level, j;
int depth;
- struct isl_map **temp_rel;
- struct isl_flow *res;
- isl_dim *dim;
- isl_map *id;
- unsigned n_sink;
- unsigned n_data;
+ isl_map **must_rel;
+ isl_map **may_rel;
acc = isl_access_info_sort_sources(acc);
-
- n_sink = isl_map_dim(acc->sink.map, isl_dim_in);
- n_data = isl_map_dim(acc->sink.map, isl_dim_out);
- dim = isl_dim_range(isl_map_get_dim(acc->sink.map));
- id = isl_map_identity(dim);
- id = isl_map_insert(id, isl_dim_in, 0, n_sink);
- acc->sink.map = isl_map_insert(acc->sink.map, isl_dim_in,
- n_sink, n_data);
- acc->sink.map = isl_map_intersect(acc->sink.map, id);
+ if (!acc)
+ return NULL;
res = isl_flow_alloc(acc);
if (!res)
goto error;
ctx = acc->sink.map->ctx;
- depth = 2 * n_sink + 1;
- todo = isl_map_domain(isl_map_copy(acc->sink.map));
- if (isl_set_fast_is_empty(todo))
+ depth = 2 * isl_map_dim(acc->sink.map, isl_dim_in) + 1;
+ mustdo = isl_map_domain(isl_map_copy(acc->sink.map));
+ maydo = isl_set_empty_like(mustdo);
+ if (isl_set_fast_is_empty(mustdo))
goto done;
- temp_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_source);
+ must_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
+ may_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
for (level = depth; level >= 1; --level) {
- for (j = acc->n_source-1; j >=0; --j)
- temp_rel[j] = isl_map_empty_like(res->dep[j].map);
+ for (j = acc->n_must-1; j >=0; --j) {
+ must_rel[j] = isl_map_empty_like(res->dep[j].map);
+ may_rel[j] = isl_map_copy(must_rel[j]);
+ }
- for (j = acc->n_source - 1; j >= 0; --j) {
+ for (j = acc->n_must - 1; j >= 0; --j) {
struct isl_map *T;
struct isl_set *rest;
int plevel;
if (!can_precede_at_level(plevel, level))
continue;
- T = last_source(acc, todo, j, level, &rest);
- temp_rel[j] = isl_map_union_disjoint(temp_rel[j], T);
- todo = rest;
+ T = last_source(acc, mustdo, j, level, &rest);
+ must_rel[j] = isl_map_union_disjoint(must_rel[j], T);
+ mustdo = rest;
+
+ intermediate_sources(acc, must_rel, j, level);
+
+ T = last_source(acc, maydo, j, level, &rest);
+ may_rel[j] = isl_map_union_disjoint(may_rel[j], T);
+ maydo = rest;
- intermediate_sources(acc, temp_rel, j, level);
+ intermediate_sources(acc, may_rel, j, level);
- if (isl_set_fast_is_empty(todo))
+ if (isl_set_fast_is_empty(mustdo) &&
+ isl_set_fast_is_empty(maydo))
break;
}
for (j = j - 1; j >= 0; --j) {
if (!can_precede_at_level(plevel, level))
continue;
- intermediate_sources(acc, temp_rel, j, level);
+ intermediate_sources(acc, must_rel, j, level);
+ intermediate_sources(acc, may_rel, j, level);
+ }
+
+ for (j = 0; j < acc->n_may; ++j) {
+ int plevel;
+ isl_map *T;
+ isl_set *ran;
+
+ plevel = acc->level_before(acc->source[acc->n_must + j].data,
+ acc->sink.data);
+ if (!can_precede_at_level(plevel, level))
+ continue;
+
+ T = all_sources(acc, isl_set_copy(maydo), j, level);
+ res->dep[2 * acc->n_must + j].map =
+ isl_map_union(res->dep[2 * acc->n_must + j].map, T);
+ T = all_sources(acc, isl_set_copy(mustdo), j, level);
+ ran = isl_map_range(isl_map_copy(T));
+ res->dep[2 * acc->n_must + j].map =
+ isl_map_union(res->dep[2 * acc->n_must + j].map, T);
+ mustdo = isl_set_subtract(mustdo, isl_set_copy(ran));
+ maydo = isl_set_union_disjoint(maydo, ran);
+
+ T = res->dep[2 * acc->n_must + j].map;
+ T = all_intermediate_sources(acc, T, must_rel, may_rel,
+ j, level);
+ res->dep[2 * acc->n_must + j].map = T;
}
- for (j = acc->n_source - 1; j >= 0; --j)
- res->dep[j].map = isl_map_union_disjoint(res->dep[j].map,
- temp_rel[j]);
- if (isl_set_fast_is_empty(todo))
+ for (j = acc->n_must - 1; j >= 0; --j) {
+ res->dep[2 * j].map =
+ isl_map_union_disjoint(res->dep[2 * j].map,
+ must_rel[j]);
+ res->dep[2 * j + 1].map =
+ isl_map_union_disjoint(res->dep[2 * j + 1].map,
+ may_rel[j]);
+ }
+
+ if (isl_set_fast_is_empty(mustdo) &&
+ isl_set_fast_is_empty(maydo))
break;
}
- free(temp_rel);
+ free(must_rel);
+ free(may_rel);
done:
- for (j = 0; j < res->n_source; ++j)
- res->dep[j].map = isl_map_project_out(res->dep[j].map,
- isl_dim_out, n_sink, n_data);
- res->no_source = todo;
+ res->must_no_source = mustdo;
+ res->may_no_source = maydo;
isl_access_info_free(acc);
return res;
error:
isl_access_info_free(acc);
return NULL;
}
+
+/* Given a "sink" access, a list of n "source" accesses,
+ * compute for each iteration of the sink access
+ * and for each element accessed by that iteration,
+ * the source access in the list that last accessed the
+ * element accessed by the sink access before this sink access.
+ * Each access is given as a map from the loop iterators
+ * to the array indices.
+ * The result is a list of n relations between source and sink
+ * iterations and a subset of the domain of the sink access,
+ * corresponding to those iterations that access an element
+ * not previously accessed.
+ *
+ * To deal with multi-valued sink access relations, the sink iteration
+ * domain is first extended with dimensions that correspond to the data
+ * space. After the computation is finished, these extra dimensions are
+ * projected out again.
+ */
+__isl_give isl_flow *isl_access_info_compute_flow(__isl_take isl_access_info *acc)
+{
+ int j;
+ struct isl_flow *res;
+ isl_dim *dim;
+ isl_map *id;
+ unsigned n_sink;
+ unsigned n_data;
+
+ if (!acc)
+ return NULL;
+
+ n_sink = isl_map_dim(acc->sink.map, isl_dim_in);
+ n_data = isl_map_dim(acc->sink.map, isl_dim_out);
+ dim = isl_dim_range(isl_map_get_dim(acc->sink.map));
+ id = isl_map_identity(dim);
+ id = isl_map_insert(id, isl_dim_in, 0, n_sink);
+ acc->sink.map = isl_map_insert(acc->sink.map, isl_dim_in,
+ n_sink, n_data);
+ acc->sink.map = isl_map_intersect(acc->sink.map, id);
+
+ if (acc->n_must == 0)
+ res = compute_mem_based_dependences(acc);
+ else
+ res = compute_val_based_dependences(acc);
+
+ for (j = 0; j < res->n_source; ++j)
+ res->dep[j].map = isl_map_project_out(res->dep[j].map,
+ isl_dim_out, n_sink, n_data);
+ res->must_no_source = isl_set_project_out(res->must_no_source, isl_dim_set, n_sink, n_data);
+ res->may_no_source = isl_set_project_out(res->may_no_source, isl_dim_set, n_sink, n_data);
+
+ return res;
+}