nexmon – Rev 1
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/*
* Copyright 2005-2007 Universiteit Leiden
* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2010 INRIA Saclay
* Copyright 2012 Universiteit Leiden
*
* Use of this software is governed by the GNU LGPLv2.1 license
*
* Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,
* Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
* and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,
* B-3001 Leuven, Belgium
* and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
* ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
*/
#include <isl/set.h>
#include <isl/map.h>
#include <isl/flow.h>
#include <isl_qsort.h>
enum isl_restriction_type {
isl_restriction_type_empty,
isl_restriction_type_none,
isl_restriction_type_input,
isl_restriction_type_output
};
struct isl_restriction {
enum isl_restriction_type type;
isl_set *source;
isl_set *sink;
};
/* Create a restriction that doesn't restrict anything.
*/
__isl_give isl_restriction *isl_restriction_none(__isl_take isl_map *source_map)
{
isl_ctx *ctx;
isl_restriction *restr;
if (!source_map)
return NULL;
ctx = isl_map_get_ctx(source_map);
restr = isl_calloc_type(ctx, struct isl_restriction);
if (!restr)
goto error;
restr->type = isl_restriction_type_none;
isl_map_free(source_map);
return restr;
error:
isl_map_free(source_map);
return NULL;
}
/* Create a restriction that removes everything.
*/
__isl_give isl_restriction *isl_restriction_empty(
__isl_take isl_map *source_map)
{
isl_ctx *ctx;
isl_restriction *restr;
if (!source_map)
return NULL;
ctx = isl_map_get_ctx(source_map);
restr = isl_calloc_type(ctx, struct isl_restriction);
if (!restr)
goto error;
restr->type = isl_restriction_type_empty;
isl_map_free(source_map);
return restr;
error:
isl_map_free(source_map);
return NULL;
}
/* Create a restriction on the input of the maximization problem
* based on the given source and sink restrictions.
*/
__isl_give isl_restriction *isl_restriction_input(
__isl_take isl_set *source_restr, __isl_take isl_set *sink_restr)
{
isl_ctx *ctx;
isl_restriction *restr;
if (!source_restr || !sink_restr)
goto error;
ctx = isl_set_get_ctx(source_restr);
restr = isl_calloc_type(ctx, struct isl_restriction);
if (!restr)
goto error;
restr->type = isl_restriction_type_input;
restr->source = source_restr;
restr->sink = sink_restr;
return restr;
error:
isl_set_free(source_restr);
isl_set_free(sink_restr);
return NULL;
}
/* Create a restriction on the output of the maximization problem
* based on the given source restriction.
*/
__isl_give isl_restriction *isl_restriction_output(
__isl_take isl_set *source_restr)
{
isl_ctx *ctx;
isl_restriction *restr;
if (!source_restr)
return NULL;
ctx = isl_set_get_ctx(source_restr);
restr = isl_calloc_type(ctx, struct isl_restriction);
if (!restr)
goto error;
restr->type = isl_restriction_type_output;
restr->source = source_restr;
return restr;
error:
isl_set_free(source_restr);
return NULL;
}
void *isl_restriction_free(__isl_take isl_restriction *restr)
{
if (!restr)
return NULL;
isl_set_free(restr->source);
isl_set_free(restr->sink);
free(restr);
return NULL;
}
isl_ctx *isl_restriction_get_ctx(__isl_keep isl_restriction *restr)
{
return restr ? isl_set_get_ctx(restr->source) : NULL;
}
/* A private structure to keep track of a mapping together with
* 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_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.
*
* domain_map is an auxiliary map that maps the sink access relation
* to the domain of this access relation.
*
* restrict_fn is a callback that (if not NULL) will be called
* right before any lexicographical maximization.
*/
struct isl_access_info {
isl_map *domain_map;
struct isl_labeled_map sink;
isl_access_level_before level_before;
isl_access_restrict restrict_fn;
void *restrict_user;
int max_source;
int n_must;
int n_may;
struct isl_labeled_map source[1];
};
/* A structure containing the output of dependence analysis:
* - n_source dependences
* - a wrapped subset of the sink for which definitely no source could be found
* - a wrapped subset of the sink for which possibly no source could be found
*/
struct isl_flow {
isl_set *must_no_source;
isl_set *may_no_source;
int n_source;
struct isl_labeled_map *dep;
};
/* Construct an isl_access_info structure and fill it up with
* the given data. The number of sources is set to 0.
*/
__isl_give isl_access_info *isl_access_info_alloc(__isl_take isl_map *sink,
void *sink_user, isl_access_level_before fn, int max_source)
{
isl_ctx *ctx;
struct isl_access_info *acc;
if (!sink)
return NULL;
ctx = isl_map_get_ctx(sink);
isl_assert(ctx, max_source >= 0, goto error);
acc = isl_calloc(ctx, struct isl_access_info,
sizeof(struct isl_access_info) +
(max_source - 1) * sizeof(struct isl_labeled_map));
if (!acc)
goto error;
acc->sink.map = sink;
acc->sink.data = sink_user;
acc->level_before = fn;
acc->max_source = max_source;
acc->n_must = 0;
acc->n_may = 0;
return acc;
error:
isl_map_free(sink);
return NULL;
}
/* Free the given isl_access_info structure.
*/
void isl_access_info_free(__isl_take isl_access_info *acc)
{
int i;
if (!acc)
return;
isl_map_free(acc->domain_map);
isl_map_free(acc->sink.map);
for (i = 0; i < acc->n_must + acc->n_may; ++i)
isl_map_free(acc->source[i].map);
free(acc);
}
isl_ctx *isl_access_info_get_ctx(__isl_keep isl_access_info *acc)
{
return acc ? isl_map_get_ctx(acc->sink.map) : NULL;
}
__isl_give isl_access_info *isl_access_info_set_restrict(
__isl_take isl_access_info *acc, isl_access_restrict fn, void *user)
{
if (!acc)
return NULL;
acc->restrict_fn = fn;
acc->restrict_user = user;
return acc;
}
/* 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,
int must, void *source_user)
{
isl_ctx *ctx;
if (!acc)
return NULL;
ctx = isl_map_get_ctx(acc->sink.map);
isl_assert(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:
isl_map_free(source);
isl_access_info_free(acc);
return NULL;
}
/* Return -n, 0 or n (with n a positive value), depending on whether
* the source access identified by p1 should be sorted before, together
* or after that identified by p2.
*
* If p1 appears before p2, then it should be sorted first.
* For more generic initial schedules, it is possible that neither
* p1 nor p2 appears before the other, or at least not in any obvious way.
* We therefore also check if p2 appears before p1, in which case p2
* should be sorted first.
* If not, we try to order the two statements based on the description
* of the iteration domains. This results in an arbitrary, but fairly
* stable ordering.
*/
static int access_sort_cmp(const void *p1, const void *p2, void *user)
{
isl_access_info *acc = user;
const struct isl_labeled_map *i1, *i2;
int level1, level2;
uint32_t h1, h2;
i1 = (const struct isl_labeled_map *) p1;
i2 = (const struct isl_labeled_map *) p2;
level1 = acc->level_before(i1->data, i2->data);
if (level1 % 2)
return -1;
level2 = acc->level_before(i2->data, i1->data);
if (level2 % 2)
return 1;
h1 = isl_map_get_hash(i1->map);
h2 = isl_map_get_hash(i2->map);
return h1 > h2 ? 1 : h1 < h2 ? -1 : 0;
}
/* Sort the must source accesses in their textual order.
*/
static __isl_give isl_access_info *isl_access_info_sort_sources(
__isl_take isl_access_info *acc)
{
if (!acc)
return NULL;
if (acc->n_must <= 1)
return acc;
isl_quicksort(acc->source, acc->n_must, sizeof(struct isl_labeled_map),
access_sort_cmp, acc);
return acc;
}
/* Align the parameters of the two spaces if needed and then call
* isl_space_join.
*/
static __isl_give isl_space *space_align_and_join(__isl_take isl_space *left,
__isl_take isl_space *right)
{
if (isl_space_match(left, isl_dim_param, right, isl_dim_param))
return isl_space_join(left, right);
left = isl_space_align_params(left, isl_space_copy(right));
right = isl_space_align_params(right, isl_space_copy(left));
return isl_space_join(left, right);
}
/* 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.
*/
static __isl_give isl_flow *isl_flow_alloc(__isl_keep isl_access_info *acc)
{
int i;
struct isl_ctx *ctx;
struct isl_flow *dep;
if (!acc)
return NULL;
ctx = isl_map_get_ctx(acc->sink.map);
dep = isl_calloc_type(ctx, struct isl_flow);
if (!dep)
return NULL;
dep->dep = isl_calloc_array(ctx, struct isl_labeled_map,
2 * acc->n_must + acc->n_may);
if (!dep->dep)
goto error;
dep->n_source = 2 * acc->n_must + acc->n_may;
for (i = 0; i < acc->n_must; ++i) {
isl_space *dim;
dim = space_align_and_join(
isl_map_get_space(acc->source[i].map),
isl_space_reverse(isl_map_get_space(acc->sink.map)));
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;
if (!dep->dep[2 * i].map || !dep->dep[2 * i + 1].map)
goto error;
}
for (i = acc->n_must; i < acc->n_must + acc->n_may; ++i) {
isl_space *dim;
dim = space_align_and_join(
isl_map_get_space(acc->source[i].map),
isl_space_reverse(isl_map_get_space(acc->sink.map)));
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;
if (!dep->dep[acc->n_must + i].map)
goto error;
}
return dep;
error:
isl_flow_free(dep);
return NULL;
}
/* Iterate over all sources and for each resulting flow dependence
* that is not empty, call the user specfied function.
* The second argument in this function call identifies the source,
* while the third argument correspond to the final argument of
* the isl_flow_foreach call.
*/
int isl_flow_foreach(__isl_keep isl_flow *deps,
int (*fn)(__isl_take isl_map *dep, int must, void *dep_user, void *user),
void *user)
{
int i;
if (!deps)
return -1;
for (i = 0; i < deps->n_source; ++i) {
if (isl_map_plain_is_empty(deps->dep[i].map))
continue;
if (fn(isl_map_copy(deps->dep[i].map), deps->dep[i].must,
deps->dep[i].data, user) < 0)
return -1;
}
return 0;
}
/* Return a copy of the subset of the sink for which no source could be found.
*/
__isl_give isl_map *isl_flow_get_no_source(__isl_keep isl_flow *deps, int must)
{
if (!deps)
return NULL;
if (must)
return isl_set_unwrap(isl_set_copy(deps->must_no_source));
else
return isl_set_unwrap(isl_set_copy(deps->may_no_source));
}
void isl_flow_free(__isl_take isl_flow *deps)
{
int i;
if (!deps)
return;
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);
free(deps->dep);
}
free(deps);
}
isl_ctx *isl_flow_get_ctx(__isl_keep isl_flow *deps)
{
return deps ? isl_set_get_ctx(deps->must_no_source) : NULL;
}
/* Return a map that enforces that the domain iteration occurs after
* the range iteration at the given level.
* If level is odd, then the domain iteration should occur after
* the target iteration in their shared level/2 outermost loops.
* In this case we simply need to enforce that these outermost
* loop iterations are the same.
* If level is even, then the loop iterator of the domain should
* be greater than the loop iterator of the range at the last
* of the level/2 shared loops, i.e., loop level/2 - 1.
*/
static __isl_give isl_map *after_at_level(__isl_take isl_space *dim, int level)
{
struct isl_basic_map *bmap;
if (level % 2)
bmap = isl_basic_map_equal(dim, level/2);
else
bmap = isl_basic_map_more_at(dim, level/2 - 1);
return isl_map_from_basic_map(bmap);
}
/* Compute the partial lexicographic maximum of "dep" on domain "sink",
* but first check if the user has set acc->restrict_fn and if so
* update either the input or the output of the maximization problem
* with respect to the resulting restriction.
*
* Since the user expects a mapping from sink iterations to source iterations,
* whereas the domain of "dep" is a wrapped map, mapping sink iterations
* to accessed array elements, we first need to project out the accessed
* sink array elements by applying acc->domain_map.
* Similarly, the sink restriction specified by the user needs to be
* converted back to the wrapped map.
*/
static __isl_give isl_map *restricted_partial_lexmax(
__isl_keep isl_access_info *acc, __isl_take isl_map *dep,
int source, __isl_take isl_set *sink, __isl_give isl_set **empty)
{
isl_map *source_map;
isl_restriction *restr;
isl_set *sink_domain;
isl_set *sink_restr;
isl_map *res;
if (!acc->restrict_fn)
return isl_map_partial_lexmax(dep, sink, empty);
source_map = isl_map_copy(dep);
source_map = isl_map_apply_domain(source_map,
isl_map_copy(acc->domain_map));
sink_domain = isl_set_copy(sink);
sink_domain = isl_set_apply(sink_domain, isl_map_copy(acc->domain_map));
restr = acc->restrict_fn(source_map, sink_domain,
acc->source[source].data, acc->restrict_user);
isl_set_free(sink_domain);
isl_map_free(source_map);
if (!restr)
goto error;
if (restr->type == isl_restriction_type_input) {
dep = isl_map_intersect_range(dep, isl_set_copy(restr->source));
sink_restr = isl_set_copy(restr->sink);
sink_restr = isl_set_apply(sink_restr,
isl_map_reverse(isl_map_copy(acc->domain_map)));
sink = isl_set_intersect(sink, sink_restr);
} else if (restr->type == isl_restriction_type_empty) {
isl_space *space = isl_map_get_space(dep);
isl_map_free(dep);
dep = isl_map_empty(space);
}
res = isl_map_partial_lexmax(dep, sink, empty);
if (restr->type == isl_restriction_type_output)
res = isl_map_intersect_range(res, isl_set_copy(restr->source));
isl_restriction_free(restr);
return res;
error:
isl_map_free(dep);
isl_set_free(sink);
*empty = NULL;
return NULL;
}
/* 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.
*/
static struct isl_map *last_source(struct isl_access_info *acc,
struct isl_set *set_C,
int j, int level, struct isl_set **empty)
{
struct isl_map *read_map;
struct isl_map *write_map;
struct isl_map *dep_map;
struct isl_map *after;
struct isl_map *result;
read_map = isl_map_copy(acc->sink.map);
write_map = isl_map_copy(acc->source[j].map);
write_map = isl_map_reverse(write_map);
dep_map = isl_map_apply_range(read_map, write_map);
after = after_at_level(isl_map_get_space(dep_map), level);
dep_map = isl_map_intersect(dep_map, after);
result = restricted_partial_lexmax(acc, dep_map, j, set_C, empty);
result = isl_map_reverse(result);
return result;
}
/* 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 must source j at level
* after_level.
*/
static struct isl_map *last_later_source(struct isl_access_info *acc,
struct isl_map *old_map,
int j, int before_level,
int k, int after_level,
struct isl_set **empty)
{
isl_space *dim;
struct isl_set *set_C;
struct isl_map *read_map;
struct isl_map *write_map;
struct isl_map *dep_map;
struct isl_map *after_write;
struct isl_map *before_read;
struct isl_map *result;
set_C = isl_map_range(isl_map_copy(old_map));
read_map = isl_map_copy(acc->sink.map);
write_map = isl_map_copy(acc->source[k].map);
write_map = isl_map_reverse(write_map);
dep_map = isl_map_apply_range(read_map, write_map);
dim = space_align_and_join(isl_map_get_space(acc->source[k].map),
isl_space_reverse(isl_map_get_space(acc->source[j].map)));
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_map_get_space(dep_map), before_level);
dep_map = isl_map_intersect(dep_map, before_read);
result = restricted_partial_lexmax(acc, dep_map, k, set_C, empty);
result = isl_map_reverse(result);
return result;
}
/* Given a shared_level between two accesses, return 1 if the
* the first can precede the second at the requested target_level.
* If the target level is odd, i.e., refers to a statement level
* dimension, then first needs to precede second at the requested
* level, i.e., shared_level must be equal to target_level.
* If the target level is odd, then the two loops should share
* at least the requested number of outer loops.
*/
static int can_precede_at_level(int shared_level, int target_level)
{
if (shared_level < target_level)
return 0;
if ((target_level % 2) && shared_level > target_level)
return 0;
return 1;
}
/* Given a possible flow dependence temp_rel[j] between source j and the sink
* at level sink_level, remove those elements for which
* there is an iteration of another source k < j that is closer to the sink.
* The flow dependences temp_rel[k] are updated with the improved sources.
* Any improved source needs to precede the sink at the same level
* and needs to follow source j at the same or a deeper level.
* The lower this level, the later the execution date of source k.
* We therefore consider lower levels first.
*
* If temp_rel[j] is empty, then there can be no improvement and
* we return immediately.
*/
static int intermediate_sources(__isl_keep isl_access_info *acc,
struct isl_map **temp_rel, int j, int sink_level)
{
int k, level;
int depth = 2 * isl_map_dim(acc->source[j].map, isl_dim_in) + 1;
if (isl_map_plain_is_empty(temp_rel[j]))
return 0;
for (k = j - 1; k >= 0; --k) {
int plevel, plevel2;
plevel = acc->level_before(acc->source[k].data, acc->sink.data);
if (!can_precede_at_level(plevel, sink_level))
continue;
plevel2 = acc->level_before(acc->source[j].data,
acc->source[k].data);
for (level = sink_level; level <= depth; ++level) {
struct isl_map *T;
struct isl_set *trest;
struct isl_map *copy;
if (!can_precede_at_level(plevel2, level))
continue;
copy = isl_map_copy(temp_rel[j]);
T = last_later_source(acc, copy, j, sink_level, k,
level, &trest);
if (isl_map_plain_is_empty(T)) {
isl_set_free(trest);
isl_map_free(T);
continue;
}
temp_rel[j] = isl_map_intersect_range(temp_rel[j], trest);
temp_rel[k] = isl_map_union_disjoint(temp_rel[k], T);
}
}
return 0;
}
/* 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_map_get_space(dep_map), 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_space *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_space_join(isl_map_get_space(acc->source[acc->n_must + j].map),
isl_space_reverse(isl_map_get_space(acc->source[k].map)));
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_map_get_space(dep_map), 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_plain_is_empty(may_rel[k]) &&
isl_map_plain_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_space_domain(isl_map_get_space(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_keep isl_access_info *acc)
{
int i;
isl_set *mustdo;
isl_set *maydo;
isl_flow *res;
res = isl_flow_alloc(acc);
if (!res)
return NULL;
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_space *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_space(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;
return res;
}
/* Compute dependences for the case where there is at least one
* "must" access.
*
* 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
* for all sources w that may precede the sink access at that level
* compute the last iteration of the source that precedes the sink access
* at that level
* add result to possible last accesses at level l of source w
* for all sources w2 that we haven't considered yet at this level that may
* also precede the sink access
* for all levels l2 of w from l to innermost
* for all possible last accesses dep of w at l
* compute last iteration of w2 between the source and sink
* of dep
* add result to possible last accesses at level l of write w2
* and replace possible last accesses dep by the remainder
*
*
* 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.
*
*/
static __isl_give isl_flow *compute_val_based_dependences(
__isl_keep isl_access_info *acc)
{
isl_ctx *ctx;
isl_flow *res;
isl_set *mustdo = NULL;
isl_set *maydo = NULL;
int level, j;
int depth;
isl_map **must_rel = NULL;
isl_map **may_rel = NULL;
if (!acc)
return NULL;
res = isl_flow_alloc(acc);
if (!res)
goto error;
ctx = isl_map_get_ctx(acc->sink.map);
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 (!mustdo || !maydo)
goto error;
if (isl_set_plain_is_empty(mustdo))
goto done;
must_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
may_rel = isl_alloc_array(ctx, struct isl_map *, acc->n_must);
if (!must_rel || !may_rel)
goto error;
for (level = depth; level >= 1; --level) {
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_must - 1; j >= 0; --j) {
struct isl_map *T;
struct isl_set *rest;
int plevel;
plevel = acc->level_before(acc->source[j].data,
acc->sink.data);
if (!can_precede_at_level(plevel, level))
continue;
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, may_rel, j, level);
if (isl_set_plain_is_empty(mustdo) &&
isl_set_plain_is_empty(maydo))
break;
}
for (j = j - 1; j >= 0; --j) {
int plevel;
plevel = acc->level_before(acc->source[j].data,
acc->sink.data);
if (!can_precede_at_level(plevel, level))
continue;
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_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_plain_is_empty(mustdo) &&
isl_set_plain_is_empty(maydo))
break;
}
free(must_rel);
free(may_rel);
done:
res->must_no_source = mustdo;
res->may_no_source = maydo;
return res;
error:
isl_flow_free(res);
isl_set_free(mustdo);
isl_set_free(maydo);
free(must_rel);
free(may_rel);
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 = NULL;
if (!acc)
return NULL;
acc->domain_map = isl_map_domain_map(isl_map_copy(acc->sink.map));
acc->sink.map = isl_map_range_map(acc->sink.map);
if (!acc->sink.map)
goto error;
if (acc->n_must == 0)
res = compute_mem_based_dependences(acc);
else {
acc = isl_access_info_sort_sources(acc);
res = compute_val_based_dependences(acc);
}
if (!res)
goto error;
for (j = 0; j < res->n_source; ++j) {
res->dep[j].map = isl_map_apply_range(res->dep[j].map,
isl_map_copy(acc->domain_map));
if (!res->dep[j].map)
goto error;
}
if (!res->must_no_source || !res->may_no_source)
goto error;
isl_access_info_free(acc);
return res;
error:
isl_access_info_free(acc);
isl_flow_free(res);
return NULL;
}
/* Keep track of some information about a schedule for a given
* access. In particular, keep track of which dimensions
* have a constant value and of the actual constant values.
*/
struct isl_sched_info {
int *is_cst;
isl_vec *cst;
};
static void sched_info_free(__isl_take struct isl_sched_info *info)
{
if (!info)
return;
isl_vec_free(info->cst);
free(info->is_cst);
free(info);
}
/* Extract information on the constant dimensions of the schedule
* for a given access. The "map" is of the form
*
* [S -> D] -> A
*
* with S the schedule domain, D the iteration domain and A the data domain.
*/
static __isl_give struct isl_sched_info *sched_info_alloc(
__isl_keep isl_map *map)
{
isl_ctx *ctx;
isl_space *dim;
struct isl_sched_info *info;
int i, n;
isl_int v;
if (!map)
return NULL;
dim = isl_space_unwrap(isl_space_domain(isl_map_get_space(map)));
if (!dim)
return NULL;
n = isl_space_dim(dim, isl_dim_in);
isl_space_free(dim);
ctx = isl_map_get_ctx(map);
info = isl_alloc_type(ctx, struct isl_sched_info);
if (!info)
return NULL;
info->is_cst = isl_alloc_array(ctx, int, n);
info->cst = isl_vec_alloc(ctx, n);
if (!info->is_cst || !info->cst)
goto error;
isl_int_init(v);
for (i = 0; i < n; ++i) {
info->is_cst[i] = isl_map_plain_is_fixed(map, isl_dim_in, i,
&v);
info->cst = isl_vec_set_element(info->cst, i, v);
}
isl_int_clear(v);
return info;
error:
sched_info_free(info);
return NULL;
}
struct isl_compute_flow_data {
isl_union_map *must_source;
isl_union_map *may_source;
isl_union_map *must_dep;
isl_union_map *may_dep;
isl_union_map *must_no_source;
isl_union_map *may_no_source;
int count;
int must;
isl_space *dim;
struct isl_sched_info *sink_info;
struct isl_sched_info **source_info;
isl_access_info *accesses;
};
static int count_matching_array(__isl_take isl_map *map, void *user)
{
int eq;
isl_space *dim;
struct isl_compute_flow_data *data;
data = (struct isl_compute_flow_data *)user;
dim = isl_space_range(isl_map_get_space(map));
eq = isl_space_is_equal(dim, data->dim);
isl_space_free(dim);
isl_map_free(map);
if (eq < 0)
return -1;
if (eq)
data->count++;
return 0;
}
static int collect_matching_array(__isl_take isl_map *map, void *user)
{
int eq;
isl_space *dim;
struct isl_sched_info *info;
struct isl_compute_flow_data *data;
data = (struct isl_compute_flow_data *)user;
dim = isl_space_range(isl_map_get_space(map));
eq = isl_space_is_equal(dim, data->dim);
isl_space_free(dim);
if (eq < 0)
goto error;
if (!eq) {
isl_map_free(map);
return 0;
}
info = sched_info_alloc(map);
data->source_info[data->count] = info;
data->accesses = isl_access_info_add_source(data->accesses,
map, data->must, info);
data->count++;
return 0;
error:
isl_map_free(map);
return -1;
}
/* Determine the shared nesting level and the "textual order" of
* the given accesses.
*
* We first determine the minimal schedule dimension for both accesses.
*
* If among those dimensions, we can find one where both have a fixed
* value and if moreover those values are different, then the previous
* dimension is the last shared nesting level and the textual order
* is determined based on the order of the fixed values.
* If no such fixed values can be found, then we set the shared
* nesting level to the minimal schedule dimension, with no textual ordering.
*/
static int before(void *first, void *second)
{
struct isl_sched_info *info1 = first;
struct isl_sched_info *info2 = second;
int n1, n2;
int i;
isl_int v1, v2;
n1 = isl_vec_size(info1->cst);
n2 = isl_vec_size(info2->cst);
if (n2 < n1)
n1 = n2;
isl_int_init(v1);
isl_int_init(v2);
for (i = 0; i < n1; ++i) {
int r;
if (!info1->is_cst[i])
continue;
if (!info2->is_cst[i])
continue;
isl_vec_get_element(info1->cst, i, &v1);
isl_vec_get_element(info2->cst, i, &v2);
if (isl_int_eq(v1, v2))
continue;
r = 2 * i + isl_int_lt(v1, v2);
isl_int_clear(v1);
isl_int_clear(v2);
return r;
}
isl_int_clear(v1);
isl_int_clear(v2);
return 2 * n1;
}
/* Given a sink access, look for all the source accesses that access
* the same array and perform dataflow analysis on them using
* isl_access_info_compute_flow.
*/
static int compute_flow(__isl_take isl_map *map, void *user)
{
int i;
isl_ctx *ctx;
struct isl_compute_flow_data *data;
isl_flow *flow;
data = (struct isl_compute_flow_data *)user;
ctx = isl_map_get_ctx(map);
data->accesses = NULL;
data->sink_info = NULL;
data->source_info = NULL;
data->count = 0;
data->dim = isl_space_range(isl_map_get_space(map));
if (isl_union_map_foreach_map(data->must_source,
&count_matching_array, data) < 0)
goto error;
if (isl_union_map_foreach_map(data->may_source,
&count_matching_array, data) < 0)
goto error;
data->sink_info = sched_info_alloc(map);
data->source_info = isl_calloc_array(ctx, struct isl_sched_info *,
data->count);
data->accesses = isl_access_info_alloc(isl_map_copy(map),
data->sink_info, &before, data->count);
if (!data->sink_info || !data->source_info || !data->accesses)
goto error;
data->count = 0;
data->must = 1;
if (isl_union_map_foreach_map(data->must_source,
&collect_matching_array, data) < 0)
goto error;
data->must = 0;
if (isl_union_map_foreach_map(data->may_source,
&collect_matching_array, data) < 0)
goto error;
flow = isl_access_info_compute_flow(data->accesses);
data->accesses = NULL;
if (!flow)
goto error;
data->must_no_source = isl_union_map_union(data->must_no_source,
isl_union_map_from_map(isl_flow_get_no_source(flow, 1)));
data->may_no_source = isl_union_map_union(data->may_no_source,
isl_union_map_from_map(isl_flow_get_no_source(flow, 0)));
for (i = 0; i < flow->n_source; ++i) {
isl_union_map *dep;
dep = isl_union_map_from_map(isl_map_copy(flow->dep[i].map));
if (flow->dep[i].must)
data->must_dep = isl_union_map_union(data->must_dep, dep);
else
data->may_dep = isl_union_map_union(data->may_dep, dep);
}
isl_flow_free(flow);
sched_info_free(data->sink_info);
if (data->source_info) {
for (i = 0; i < data->count; ++i)
sched_info_free(data->source_info[i]);
free(data->source_info);
}
isl_space_free(data->dim);
isl_map_free(map);
return 0;
error:
isl_access_info_free(data->accesses);
sched_info_free(data->sink_info);
if (data->source_info) {
for (i = 0; i < data->count; ++i)
sched_info_free(data->source_info[i]);
free(data->source_info);
}
isl_space_free(data->dim);
isl_map_free(map);
return -1;
}
/* Given a collection of "sink" and "source" accesses,
* compute for each iteration of a 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 relations between source and sink
* iterations and a subset of the domain of the sink accesses,
* corresponding to those iterations that access an element
* not previously accessed.
*
* We first prepend the schedule dimensions to the domain
* of the accesses so that we can easily compare their relative order.
* Then we consider each sink access individually in compute_flow.
*/
int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
__isl_take isl_union_map *must_source,
__isl_take isl_union_map *may_source,
__isl_take isl_union_map *schedule,
__isl_give isl_union_map **must_dep, __isl_give isl_union_map **may_dep,
__isl_give isl_union_map **must_no_source,
__isl_give isl_union_map **may_no_source)
{
isl_space *dim;
isl_union_map *range_map = NULL;
struct isl_compute_flow_data data;
sink = isl_union_map_align_params(sink,
isl_union_map_get_space(must_source));
sink = isl_union_map_align_params(sink,
isl_union_map_get_space(may_source));
sink = isl_union_map_align_params(sink,
isl_union_map_get_space(schedule));
dim = isl_union_map_get_space(sink);
must_source = isl_union_map_align_params(must_source, isl_space_copy(dim));
may_source = isl_union_map_align_params(may_source, isl_space_copy(dim));
schedule = isl_union_map_align_params(schedule, isl_space_copy(dim));
schedule = isl_union_map_reverse(schedule);
range_map = isl_union_map_range_map(schedule);
schedule = isl_union_map_reverse(isl_union_map_copy(range_map));
sink = isl_union_map_apply_domain(sink, isl_union_map_copy(schedule));
must_source = isl_union_map_apply_domain(must_source,
isl_union_map_copy(schedule));
may_source = isl_union_map_apply_domain(may_source, schedule);
data.must_source = must_source;
data.may_source = may_source;
data.must_dep = must_dep ?
isl_union_map_empty(isl_space_copy(dim)) : NULL;
data.may_dep = may_dep ? isl_union_map_empty(isl_space_copy(dim)) : NULL;
data.must_no_source = must_no_source ?
isl_union_map_empty(isl_space_copy(dim)) : NULL;
data.may_no_source = may_no_source ?
isl_union_map_empty(isl_space_copy(dim)) : NULL;
isl_space_free(dim);
if (isl_union_map_foreach_map(sink, &compute_flow, &data) < 0)
goto error;
isl_union_map_free(sink);
isl_union_map_free(must_source);
isl_union_map_free(may_source);
if (must_dep) {
data.must_dep = isl_union_map_apply_domain(data.must_dep,
isl_union_map_copy(range_map));
data.must_dep = isl_union_map_apply_range(data.must_dep,
isl_union_map_copy(range_map));
*must_dep = data.must_dep;
}
if (may_dep) {
data.may_dep = isl_union_map_apply_domain(data.may_dep,
isl_union_map_copy(range_map));
data.may_dep = isl_union_map_apply_range(data.may_dep,
isl_union_map_copy(range_map));
*may_dep = data.may_dep;
}
if (must_no_source) {
data.must_no_source = isl_union_map_apply_domain(
data.must_no_source, isl_union_map_copy(range_map));
*must_no_source = data.must_no_source;
}
if (may_no_source) {
data.may_no_source = isl_union_map_apply_domain(
data.may_no_source, isl_union_map_copy(range_map));
*may_no_source = data.may_no_source;
}
isl_union_map_free(range_map);
return 0;
error:
isl_union_map_free(range_map);
isl_union_map_free(sink);
isl_union_map_free(must_source);
isl_union_map_free(may_source);
isl_union_map_free(data.must_dep);
isl_union_map_free(data.may_dep);
isl_union_map_free(data.must_no_source);
isl_union_map_free(data.may_no_source);
if (must_dep)
*must_dep = NULL;
if (may_dep)
*may_dep = NULL;
if (must_no_source)
*must_no_source = NULL;
if (may_no_source)
*may_no_source = NULL;
return -1;
}