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llvm / llvm-project / f15a8545672a643f2a3e0a9ad7d1958470ee488d / . / polly / lib / External / isl / isl_ast_codegen.c
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/*
* Copyright 2012-2014 Ecole Normale Superieure
* Copyright 2014 INRIA Rocquencourt
*
* Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege,
* Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
* and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
* B.P. 105 - 78153 Le Chesnay, France
*/
#include <limits.h>
#include <isl/id.h>
#include <isl/val.h>
#include <isl/space.h>
#include <isl/aff.h>
#include <isl/constraint.h>
#include <isl/set.h>
#include <isl/ilp.h>
#include <isl/union_set.h>
#include <isl/union_map.h>
#include <isl/schedule_node.h>
#include <isl/options.h>
#include <isl_sort.h>
#include <isl_tarjan.h>
#include <isl_ast_private.h>
#include <isl_ast_build_expr.h>
#include <isl_ast_build_private.h>
#include <isl_ast_graft_private.h>
/* Try and reduce the number of disjuncts in the representation of "set",
* without dropping explicit representations of local variables.
*/
static __isl_give isl_set *isl_set_coalesce_preserve(__isl_take isl_set *set)
{
isl_ctx *ctx;
int save_preserve;
if (!set)
return NULL;
ctx = isl_set_get_ctx(set);
save_preserve = isl_options_get_coalesce_preserve_locals(ctx);
isl_options_set_coalesce_preserve_locals(ctx, 1);
set = isl_set_coalesce(set);
isl_options_set_coalesce_preserve_locals(ctx, save_preserve);
return set;
}
/* Data used in generate_domain.
*
* "build" is the input build.
* "list" collects the results.
*/
struct isl_generate_domain_data {
isl_ast_build *build;
isl_ast_graft_list *list;
};
static __isl_give isl_ast_graft_list *generate_next_level(
__isl_take isl_union_map *executed,
__isl_take isl_ast_build *build);
static __isl_give isl_ast_graft_list *generate_code(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build,
int internal);
/* Generate an AST for a single domain based on
* the (non single valued) inverse schedule "executed".
*
* We extend the schedule with the iteration domain
* and continue generating through a call to generate_code.
*
* In particular, if executed has the form
*
* S -> D
*
* then we continue generating code on
*
* [S -> D] -> D
*
* The extended inverse schedule is clearly single valued
* ensuring that the nested generate_code will not reach this function,
* but will instead create calls to all elements of D that need
* to be executed from the current schedule domain.
*/
static isl_stat generate_non_single_valued(__isl_take isl_map *executed,
struct isl_generate_domain_data *data)
{
isl_map *identity;
isl_ast_build *build;
isl_ast_graft_list *list;
build = isl_ast_build_copy(data->build);
identity = isl_set_identity(isl_map_range(isl_map_copy(executed)));
executed = isl_map_domain_product(executed, identity);
build = isl_ast_build_set_single_valued(build, 1);
list = generate_code(isl_union_map_from_map(executed), build, 1);
data->list = isl_ast_graft_list_concat(data->list, list);
return isl_stat_ok;
}
/* Call the at_each_domain callback, if requested by the user,
* after recording the current inverse schedule in the build.
*/
static __isl_give isl_ast_graft *at_each_domain(__isl_take isl_ast_graft *graft,
__isl_keep isl_map *executed, __isl_keep isl_ast_build *build)
{
if (!graft || !build)
return isl_ast_graft_free(graft);
if (!build->at_each_domain)
return graft;
build = isl_ast_build_copy(build);
build = isl_ast_build_set_executed(build,
isl_union_map_from_map(isl_map_copy(executed)));
if (!build)
return isl_ast_graft_free(graft);
graft->node = build->at_each_domain(graft->node,
build, build->at_each_domain_user);
isl_ast_build_free(build);
if (!graft->node)
graft = isl_ast_graft_free(graft);
return graft;
}
/* Generate a call expression for the single executed
* domain element "map" and put a guard around it based its (simplified)
* domain. "executed" is the original inverse schedule from which "map"
* has been derived. In particular, "map" is either identical to "executed"
* or it is the result of gisting "executed" with respect to the build domain.
* "executed" is only used if there is an at_each_domain callback.
*
* At this stage, any pending constraints in the build can no longer
* be simplified with respect to any enforced constraints since
* the call node does not have any enforced constraints.
* Since all pending constraints not covered by any enforced constraints
* will be added as a guard to the graft in create_node_scaled,
* even in the eliminated case, the pending constraints
* can be considered to have been generated by outer constructs.
*
* If the user has set an at_each_domain callback, it is called
* on the constructed call expression node.
*/
static isl_stat add_domain(__isl_take isl_map *executed,
__isl_take isl_map *map, struct isl_generate_domain_data *data)
{
isl_ast_build *build;
isl_ast_graft *graft;
isl_ast_graft_list *list;
isl_set *guard, *pending;
build = isl_ast_build_copy(data->build);
pending = isl_ast_build_get_pending(build);
build = isl_ast_build_replace_pending_by_guard(build, pending);
guard = isl_map_domain(isl_map_copy(map));
guard = isl_set_compute_divs(guard);
guard = isl_set_coalesce_preserve(guard);
guard = isl_set_gist(guard, isl_ast_build_get_generated(build));
guard = isl_ast_build_specialize(build, guard);
graft = isl_ast_graft_alloc_domain(map, build);
graft = at_each_domain(graft, executed, build);
isl_ast_build_free(build);
isl_map_free(executed);
graft = isl_ast_graft_add_guard(graft, guard, data->build);
list = isl_ast_graft_list_from_ast_graft(graft);
data->list = isl_ast_graft_list_concat(data->list, list);
return isl_stat_ok;
}
/* Generate an AST for a single domain based on
* the inverse schedule "executed" and add it to data->list.
*
* If there is more than one domain element associated to the current
* schedule "time", then we need to continue the generation process
* in generate_non_single_valued.
* Note that the inverse schedule being single-valued may depend
* on constraints that are only available in the original context
* domain specified by the user. We therefore first introduce
* some of the constraints of data->build->domain. In particular,
* we intersect with a single-disjunct approximation of this set.
* We perform this approximation to avoid further splitting up
* the executed relation, possibly introducing a disjunctive guard
* on the statement.
*
* On the other hand, we only perform the test after having taken the gist
* of the domain as the resulting map is the one from which the call
* expression is constructed. Using this map to construct the call
* expression usually yields simpler results in cases where the original
* map is not obviously single-valued.
* If the original map is obviously single-valued, then the gist
* operation is skipped.
*
* Because we perform the single-valuedness test on the gisted map,
* we may in rare cases fail to recognize that the inverse schedule
* is single-valued. This becomes problematic if this happens
* from the recursive call through generate_non_single_valued
* as we would then end up in an infinite recursion.
* We therefore check if we are inside a call to generate_non_single_valued
* and revert to the ungisted map if the gisted map turns out not to be
* single-valued.
*
* Otherwise, call add_domain to generate a call expression (with guard) and
* to call the at_each_domain callback, if any.
*/
static isl_stat generate_domain(__isl_take isl_map *executed, void *user)
{
struct isl_generate_domain_data *data = user;
isl_set *domain;
isl_map *map = NULL;
int empty, sv;
domain = isl_ast_build_get_domain(data->build);
domain = isl_set_from_basic_set(isl_set_simple_hull(domain));
executed = isl_map_intersect_domain(executed, domain);
empty = isl_map_is_empty(executed);
if (empty < 0)
goto error;
if (empty) {
isl_map_free(executed);
return isl_stat_ok;
}
sv = isl_map_plain_is_single_valued(executed);
if (sv < 0)
goto error;
if (sv)
return add_domain(executed, isl_map_copy(executed), data);
executed = isl_map_coalesce(executed);
map = isl_map_copy(executed);
map = isl_ast_build_compute_gist_map_domain(data->build, map);
sv = isl_map_is_single_valued(map);
if (sv < 0)
goto error;
if (!sv) {
isl_map_free(map);
if (data->build->single_valued)
map = isl_map_copy(executed);
else
return generate_non_single_valued(executed, data);
}
return add_domain(executed, map, data);
error:
isl_map_free(map);
isl_map_free(executed);
return isl_stat_error;
}
/* Call build->create_leaf to a create "leaf" node in the AST,
* encapsulate the result in an isl_ast_graft and return the result
* as a 1-element list.
*
* Note that the node returned by the user may be an entire tree.
*
* Since the node itself cannot enforce any constraints, we turn
* all pending constraints into guards and add them to the resulting
* graft to ensure that they will be generated.
*
* Before we pass control to the user, we first clear some information
* from the build that is (presumbably) only meaningful
* for the current code generation.
* This includes the create_leaf callback itself, so we make a copy
* of the build first.
*/
static __isl_give isl_ast_graft_list *call_create_leaf(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
{
isl_set *guard;
isl_ast_node *node;
isl_ast_graft *graft;
isl_ast_build *user_build;
guard = isl_ast_build_get_pending(build);
user_build = isl_ast_build_copy(build);
user_build = isl_ast_build_replace_pending_by_guard(user_build,
isl_set_copy(guard));
user_build = isl_ast_build_set_executed(user_build, executed);
user_build = isl_ast_build_clear_local_info(user_build);
if (!user_build)
node = NULL;
else
node = build->create_leaf(user_build, build->create_leaf_user);
graft = isl_ast_graft_alloc(node, build);
graft = isl_ast_graft_add_guard(graft, guard, build);
isl_ast_build_free(build);
return isl_ast_graft_list_from_ast_graft(graft);
}
static __isl_give isl_ast_graft_list *build_ast_from_child(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed);
/* Generate an AST after having handled the complete schedule
* of this call to the code generator or the complete band
* if we are generating an AST from a schedule tree.
*
* If we are inside a band node, then move on to the child of the band.
*
* If the user has specified a create_leaf callback, control
* is passed to the user in call_create_leaf.
*
* Otherwise, we generate one or more calls for each individual
* domain in generate_domain.
*/
static __isl_give isl_ast_graft_list *generate_inner_level(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
{
isl_ctx *ctx;
struct isl_generate_domain_data data = { build };
if (!build || !executed)
goto error;
if (isl_ast_build_has_schedule_node(build)) {
isl_schedule_node *node;
node = isl_ast_build_get_schedule_node(build);
build = isl_ast_build_reset_schedule_node(build);
return build_ast_from_child(build, node, executed);
}
if (build->create_leaf)
return call_create_leaf(executed, build);
ctx = isl_union_map_get_ctx(executed);
data.list = isl_ast_graft_list_alloc(ctx, 0);
if (isl_union_map_foreach_map(executed, &generate_domain, &data) < 0)
data.list = isl_ast_graft_list_free(data.list);
if (0)
error: data.list = NULL;
isl_ast_build_free(build);
isl_union_map_free(executed);
return data.list;
}
/* Call the before_each_for callback, if requested by the user.
*/
static __isl_give isl_ast_node *before_each_for(__isl_take isl_ast_node *node,
__isl_keep isl_ast_build *build)
{
isl_id *id;
if (!node || !build)
return isl_ast_node_free(node);
if (!build->before_each_for)
return node;
id = build->before_each_for(build, build->before_each_for_user);
node = isl_ast_node_set_annotation(node, id);
return node;
}
/* Call the after_each_for callback, if requested by the user.
*/
static __isl_give isl_ast_graft *after_each_for(__isl_take isl_ast_graft *graft,
__isl_keep isl_ast_build *build)
{
if (!graft || !build)
return isl_ast_graft_free(graft);
if (!build->after_each_for)
return graft;
graft->node = build->after_each_for(graft->node, build,
build->after_each_for_user);
if (!graft->node)
return isl_ast_graft_free(graft);
return graft;
}
/* Plug in all the know values of the current and outer dimensions
* in the domain of "executed". In principle, we only need to plug
* in the known value of the current dimension since the values of
* outer dimensions have been plugged in already.
* However, it turns out to be easier to just plug in all known values.
*/
static __isl_give isl_union_map *plug_in_values(
__isl_take isl_union_map *executed, __isl_keep isl_ast_build *build)
{
return isl_ast_build_substitute_values_union_map_domain(build,
executed);
}
/* Check if the constraint "c" is a lower bound on dimension "pos",
* an upper bound, or independent of dimension "pos".
*/
static int constraint_type(isl_constraint *c, int pos)
{
if (isl_constraint_is_lower_bound(c, isl_dim_set, pos))
return 1;
if (isl_constraint_is_upper_bound(c, isl_dim_set, pos))
return 2;
return 0;
}
/* Compare the types of the constraints "a" and "b",
* resulting in constraints that are independent of "depth"
* to be sorted before the lower bounds on "depth", which in
* turn are sorted before the upper bounds on "depth".
*/
static int cmp_constraint(__isl_keep isl_constraint *a,
__isl_keep isl_constraint *b, void *user)
{
int *depth = user;
int t1 = constraint_type(a, *depth);
int t2 = constraint_type(b, *depth);
return t1 - t2;
}
/* Extract a lower bound on dimension "pos" from constraint "c".
*
* If the constraint is of the form
*
* a x + f(...) >= 0
*
* then we essentially return
*
* l = ceil(-f(...)/a)
*
* However, if the current dimension is strided, then we need to make
* sure that the lower bound we construct is of the form
*
* f + s a
*
* with f the offset and s the stride.
* We therefore compute
*
* f + s * ceil((l - f)/s)
*/
static __isl_give isl_aff *lower_bound(__isl_keep isl_constraint *c,
int pos, __isl_keep isl_ast_build *build)
{
isl_aff *aff;
aff = isl_constraint_get_bound(c, isl_dim_set, pos);
aff = isl_aff_ceil(aff);
if (isl_ast_build_has_stride(build, pos)) {
isl_aff *offset;
isl_val *stride;
offset = isl_ast_build_get_offset(build, pos);
stride = isl_ast_build_get_stride(build, pos);
aff = isl_aff_sub(aff, isl_aff_copy(offset));
aff = isl_aff_scale_down_val(aff, isl_val_copy(stride));
aff = isl_aff_ceil(aff);
aff = isl_aff_scale_val(aff, stride);
aff = isl_aff_add(aff, offset);
}
aff = isl_ast_build_compute_gist_aff(build, aff);
return aff;
}
/* Return the exact lower bound (or upper bound if "upper" is set)
* of "domain" as a piecewise affine expression.
*
* If we are computing a lower bound (of a strided dimension), then
* we need to make sure it is of the form
*
* f + s a
*
* where f is the offset and s is the stride.
* We therefore need to include the stride constraint before computing
* the minimum.
*/
static __isl_give isl_pw_aff *exact_bound(__isl_keep isl_set *domain,
__isl_keep isl_ast_build *build, int upper)
{
isl_set *stride;
isl_map *it_map;
isl_pw_aff *pa;
isl_pw_multi_aff *pma;
domain = isl_set_copy(domain);
if (!upper) {
stride = isl_ast_build_get_stride_constraint(build);
domain = isl_set_intersect(domain, stride);
}
it_map = isl_ast_build_map_to_iterator(build, domain);
if (upper)
pma = isl_map_lexmax_pw_multi_aff(it_map);
else
pma = isl_map_lexmin_pw_multi_aff(it_map);
pa = isl_pw_multi_aff_get_pw_aff(pma, 0);
isl_pw_multi_aff_free(pma);
pa = isl_ast_build_compute_gist_pw_aff(build, pa);
pa = isl_pw_aff_coalesce(pa);
return pa;
}
/* Callback for sorting the isl_pw_aff_list passed to reduce_list and
* remove_redundant_lower_bounds.
*/
static int reduce_list_cmp(__isl_keep isl_pw_aff *a, __isl_keep isl_pw_aff *b,
void *user)
{
return isl_pw_aff_plain_cmp(a, b);
}
/* Given a list of lower bounds "list", remove those that are redundant
* with respect to the other bounds in "list" and the domain of "build".
*
* We first sort the bounds in the same way as they would be sorted
* by set_for_node_expressions so that we can try and remove the last
* bounds first.
*
* For a lower bound to be effective, there needs to be at least
* one domain element for which it is larger than all other lower bounds.
* For each lower bound we therefore intersect the domain with
* the conditions that it is larger than all other bounds and
* check whether the result is empty. If so, the bound can be removed.
*/
static __isl_give isl_pw_aff_list *remove_redundant_lower_bounds(
__isl_take isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
{
int i, j;
isl_size n;
isl_set *domain;
list = isl_pw_aff_list_sort(list, &reduce_list_cmp, NULL);
n = isl_pw_aff_list_n_pw_aff(list);
if (n < 0)
return isl_pw_aff_list_free(list);
if (n <= 1)
return list;
domain = isl_ast_build_get_domain(build);
for (i = n - 1; i >= 0; --i) {
isl_pw_aff *pa_i;
isl_set *domain_i;
int empty;
domain_i = isl_set_copy(domain);
pa_i = isl_pw_aff_list_get_pw_aff(list, i);
for (j = 0; j < n; ++j) {
isl_pw_aff *pa_j;
isl_set *better;
if (j == i)
continue;
pa_j = isl_pw_aff_list_get_pw_aff(list, j);
better = isl_pw_aff_gt_set(isl_pw_aff_copy(pa_i), pa_j);
domain_i = isl_set_intersect(domain_i, better);
}
empty = isl_set_is_empty(domain_i);
isl_set_free(domain_i);
isl_pw_aff_free(pa_i);
if (empty < 0)
goto error;
if (!empty)
continue;
list = isl_pw_aff_list_drop(list, i, 1);
n--;
}
isl_set_free(domain);
return list;
error:
isl_set_free(domain);
return isl_pw_aff_list_free(list);
}
/* Extract a lower bound on dimension "pos" from each constraint
* in "constraints" and return the list of lower bounds.
* If "constraints" has zero elements, then we extract a lower bound
* from "domain" instead.
*
* If the current dimension is strided, then the lower bound
* is adjusted by lower_bound to match the stride information.
* This modification may make one or more lower bounds redundant
* with respect to the other lower bounds. We therefore check
* for this condition and remove the redundant lower bounds.
*/
static __isl_give isl_pw_aff_list *lower_bounds(
__isl_keep isl_constraint_list *constraints, int pos,
__isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
{
isl_ctx *ctx;
isl_pw_aff_list *list;
int i;
isl_size n;
if (!build)
return NULL;
n = isl_constraint_list_n_constraint(constraints);
if (n < 0)
return NULL;
if (n == 0) {
isl_pw_aff *pa;
pa = exact_bound(domain, build, 0);
return isl_pw_aff_list_from_pw_aff(pa);
}
ctx = isl_ast_build_get_ctx(build);
list = isl_pw_aff_list_alloc(ctx,n);
for (i = 0; i < n; ++i) {
isl_aff *aff;
isl_constraint *c;
c = isl_constraint_list_get_constraint(constraints, i);
aff = lower_bound(c, pos, build);
isl_constraint_free(c);
list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
}
if (isl_ast_build_has_stride(build, pos))
list = remove_redundant_lower_bounds(list, build);
return list;
}
/* Extract an upper bound on dimension "pos" from each constraint
* in "constraints" and return the list of upper bounds.
* If "constraints" has zero elements, then we extract an upper bound
* from "domain" instead.
*/
static __isl_give isl_pw_aff_list *upper_bounds(
__isl_keep isl_constraint_list *constraints, int pos,
__isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
{
isl_ctx *ctx;
isl_pw_aff_list *list;
int i;
isl_size n;
n = isl_constraint_list_n_constraint(constraints);
if (n < 0)
return NULL;
if (n == 0) {
isl_pw_aff *pa;
pa = exact_bound(domain, build, 1);
return isl_pw_aff_list_from_pw_aff(pa);
}
ctx = isl_ast_build_get_ctx(build);
list = isl_pw_aff_list_alloc(ctx,n);
for (i = 0; i < n; ++i) {
isl_aff *aff;
isl_constraint *c;
c = isl_constraint_list_get_constraint(constraints, i);
aff = isl_constraint_get_bound(c, isl_dim_set, pos);
isl_constraint_free(c);
aff = isl_aff_floor(aff);
list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
}
return list;
}
/* Return an isl_ast_expr that performs the reduction of type "type"
* on AST expressions corresponding to the elements in "list".
*
* The list is assumed to contain at least one element.
* If the list contains exactly one element, then the returned isl_ast_expr
* simply computes that affine expression.
* If the list contains more than one element, then we sort it
* using a fairly arbitrary but hopefully reasonably stable order.
*/
static __isl_give isl_ast_expr *reduce_list(enum isl_ast_expr_op_type type,
__isl_keep isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
{
int i;
isl_size n;
isl_ctx *ctx;
isl_ast_expr *expr;
n = isl_pw_aff_list_n_pw_aff(list);
if (n < 0)
return NULL;
if (n == 1)
return isl_ast_build_expr_from_pw_aff_internal(build,
isl_pw_aff_list_get_pw_aff(list, 0));
ctx = isl_pw_aff_list_get_ctx(list);
expr = isl_ast_expr_alloc_op(ctx, type, n);
if (!expr)
return NULL;
list = isl_pw_aff_list_copy(list);
list = isl_pw_aff_list_sort(list, &reduce_list_cmp, NULL);
if (!list)
return isl_ast_expr_free(expr);
for (i = 0; i < n; ++i) {
isl_ast_expr *expr_i;
expr_i = isl_ast_build_expr_from_pw_aff_internal(build,
isl_pw_aff_list_get_pw_aff(list, i));
if (!expr_i)
goto error;
expr->u.op.args[i] = expr_i;
}
isl_pw_aff_list_free(list);
return expr;
error:
isl_pw_aff_list_free(list);
isl_ast_expr_free(expr);
return NULL;
}
/* Add guards implied by the "generated constraints",
* but not (necessarily) enforced by the generated AST to "guard".
* In particular, if there is any stride constraints,
* then add the guard implied by those constraints.
* If we have generated a degenerate loop, then add the guard
* implied by "bounds" on the outer dimensions, i.e., the guard
* that ensures that the single value actually exists.
* Since there may also be guards implied by a combination
* of these constraints, we first combine them before
* deriving the implied constraints.
*/
static __isl_give isl_set *add_implied_guards(__isl_take isl_set *guard,
int degenerate, __isl_keep isl_basic_set *bounds,
__isl_keep isl_ast_build *build)
{
isl_size depth;
isl_bool has_stride;
isl_space *space;
isl_set *dom, *set;
depth = isl_ast_build_get_depth(build);
has_stride = isl_ast_build_has_stride(build, depth);
if (depth < 0 || has_stride < 0)
return isl_set_free(guard);
if (!has_stride && !degenerate)
return guard;
space = isl_basic_set_get_space(bounds);
dom = isl_set_universe(space);
if (degenerate) {
bounds = isl_basic_set_copy(bounds);
bounds = isl_basic_set_drop_constraints_not_involving_dims(
bounds, isl_dim_set, depth, 1);
set = isl_set_from_basic_set(bounds);
dom = isl_set_intersect(dom, set);
}
if (has_stride) {
set = isl_ast_build_get_stride_constraint(build);
dom = isl_set_intersect(dom, set);
}
dom = isl_set_eliminate(dom, isl_dim_set, depth, 1);
dom = isl_ast_build_compute_gist(build, dom);
guard = isl_set_intersect(guard, dom);
return guard;
}
/* Update "graft" based on "sub_build" for the degenerate case.
*
* "build" is the build in which graft->node was created
* "sub_build" contains information about the current level itself,
* including the single value attained.
*
* We set the initialization part of the for loop to the single
* value attained by the current dimension.
* The increment and condition are not strictly needed as they are known
* to be "1" and "iterator <= value" respectively.
*/
static __isl_give isl_ast_graft *refine_degenerate(
__isl_take isl_ast_graft *graft, __isl_keep isl_ast_build *build,
__isl_keep isl_ast_build *sub_build)
{
isl_pw_aff *value;
if (!graft || !sub_build)
return isl_ast_graft_free(graft);
value = isl_pw_aff_copy(sub_build->value);
graft->node->u.f.init = isl_ast_build_expr_from_pw_aff_internal(build,
value);
if (!graft->node->u.f.init)
return isl_ast_graft_free(graft);
return graft;
}
/* Return the intersection of constraints in "list" as a set.
*/
static __isl_give isl_set *intersect_constraints(
__isl_keep isl_constraint_list *list)
{
int i;
isl_size n;
isl_basic_set *bset;
n = isl_constraint_list_n_constraint(list);
if (n < 0)
return NULL;
if (n < 1)
isl_die(isl_constraint_list_get_ctx(list), isl_error_internal,
"expecting at least one constraint", return NULL);
bset = isl_basic_set_from_constraint(
isl_constraint_list_get_constraint(list, 0));
for (i = 1; i < n; ++i) {
isl_basic_set *bset_i;
bset_i = isl_basic_set_from_constraint(
isl_constraint_list_get_constraint(list, i));
bset = isl_basic_set_intersect(bset, bset_i);
}
return isl_set_from_basic_set(bset);
}
/* Compute the constraints on the outer dimensions enforced by
* graft->node and add those constraints to graft->enforced,
* in case the upper bound is expressed as a set "upper".
*
* In particular, if l(...) is a lower bound in "lower", and
*
* -a i + f(...) >= 0 or a i <= f(...)
*
* is an upper bound ocnstraint on the current dimension i,
* then the for loop enforces the constraint
*
* -a l(...) + f(...) >= 0 or a l(...) <= f(...)
*
* We therefore simply take each lower bound in turn, plug it into
* the upper bounds and compute the intersection over all lower bounds.
*
* If a lower bound is a rational expression, then
* isl_basic_set_preimage_multi_aff will force this rational
* expression to have only integer values. However, the loop
* itself does not enforce this integrality constraint. We therefore
* use the ceil of the lower bounds instead of the lower bounds themselves.
* Other constraints will make sure that the for loop is only executed
* when each of the lower bounds attains an integral value.
* In particular, potentially rational values only occur in
* lower_bound if the offset is a (seemingly) rational expression,
* but then outer conditions will make sure that this rational expression
* only attains integer values.
*/
static __isl_give isl_ast_graft *set_enforced_from_set(
__isl_take isl_ast_graft *graft,
__isl_keep isl_pw_aff_list *lower, int pos, __isl_keep isl_set *upper)
{
isl_space *space;
isl_basic_set *enforced;
isl_pw_multi_aff *pma;
int i;
isl_size n;
n = isl_pw_aff_list_n_pw_aff(lower);
if (!graft || n < 0)
return isl_ast_graft_free(graft);
space = isl_set_get_space(upper);
enforced = isl_basic_set_universe(isl_space_copy(space));
space = isl_space_map_from_set(space);
pma = isl_pw_multi_aff_identity(space);
for (i = 0; i < n; ++i) {
isl_pw_aff *pa;
isl_set *enforced_i;
isl_basic_set *hull;
isl_pw_multi_aff *pma_i;
pa = isl_pw_aff_list_get_pw_aff(lower, i);
pa = isl_pw_aff_ceil(pa);
pma_i = isl_pw_multi_aff_copy(pma);
pma_i = isl_pw_multi_aff_set_pw_aff(pma_i, pos, pa);
enforced_i = isl_set_copy(upper);
enforced_i = isl_set_preimage_pw_multi_aff(enforced_i, pma_i);
hull = isl_set_simple_hull(enforced_i);
enforced = isl_basic_set_intersect(enforced, hull);
}
isl_pw_multi_aff_free(pma);
graft = isl_ast_graft_enforce(graft, enforced);
return graft;
}
/* Compute the constraints on the outer dimensions enforced by
* graft->node and add those constraints to graft->enforced,
* in case the upper bound is expressed as
* a list of affine expressions "upper".
*
* The enforced condition is that each lower bound expression is less
* than or equal to each upper bound expression.
*/
static __isl_give isl_ast_graft *set_enforced_from_list(
__isl_take isl_ast_graft *graft,
__isl_keep isl_pw_aff_list *lower, __isl_keep isl_pw_aff_list *upper)
{
isl_set *cond;
isl_basic_set *enforced;
lower = isl_pw_aff_list_copy(lower);
upper = isl_pw_aff_list_copy(upper);
cond = isl_pw_aff_list_le_set(lower, upper);
enforced = isl_set_simple_hull(cond);
graft = isl_ast_graft_enforce(graft, enforced);
return graft;
}
/* Does "aff" have a negative constant term?
*/
static isl_bool aff_constant_is_negative(__isl_keep isl_set *set,
__isl_keep isl_aff *aff, void *user)
{
isl_bool is_neg;
isl_val *v;
v = isl_aff_get_constant_val(aff);
is_neg = isl_val_is_neg(v);
isl_val_free(v);
return is_neg;
}
/* Does "pa" have a negative constant term over its entire domain?
*/
static isl_bool pw_aff_constant_is_negative(__isl_keep isl_pw_aff *pa,
void *user)
{
return isl_pw_aff_every_piece(pa, &aff_constant_is_negative, NULL);
}
/* Does each element in "list" have a negative constant term?
*/
static int list_constant_is_negative(__isl_keep isl_pw_aff_list *list)
{
return isl_pw_aff_list_every(list, &pw_aff_constant_is_negative, NULL);
}
/* Add 1 to each of the elements in "list", where each of these elements
* is defined over the internal schedule space of "build".
*/
static __isl_give isl_pw_aff_list *list_add_one(
__isl_take isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
{
int i;
isl_size n;
isl_space *space;
isl_aff *aff;
isl_pw_aff *one;
n = isl_pw_aff_list_n_pw_aff(list);
if (n < 0)
return isl_pw_aff_list_free(list);
space = isl_ast_build_get_space(build, 1);
aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
aff = isl_aff_add_constant_si(aff, 1);
one = isl_pw_aff_from_aff(aff);
for (i = 0; i < n; ++i) {
isl_pw_aff *pa;
pa = isl_pw_aff_list_get_pw_aff(list, i);
pa = isl_pw_aff_add(pa, isl_pw_aff_copy(one));
list = isl_pw_aff_list_set_pw_aff(list, i, pa);
}
isl_pw_aff_free(one);
return list;
}
/* Set the condition part of the for node graft->node in case
* the upper bound is represented as a list of piecewise affine expressions.
*
* In particular, set the condition to
*
* iterator <= min(list of upper bounds)
*
* If each of the upper bounds has a negative constant term, then
* set the condition to
*
* iterator < min(list of (upper bound + 1)s)
*
*/
static __isl_give isl_ast_graft *set_for_cond_from_list(
__isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *list,
__isl_keep isl_ast_build *build)
{
int neg;
isl_ast_expr *bound, *iterator, *cond;
enum isl_ast_expr_op_type type = isl_ast_expr_op_le;
if (!graft || !list)
return isl_ast_graft_free(graft);
neg = list_constant_is_negative(list);
if (neg < 0)
return isl_ast_graft_free(graft);
list = isl_pw_aff_list_copy(list);
if (neg) {
list = list_add_one(list, build);
type = isl_ast_expr_op_lt;
}
bound = reduce_list(isl_ast_expr_op_min, list, build);
iterator = isl_ast_expr_copy(graft->node->u.f.iterator);
cond = isl_ast_expr_alloc_binary(type, iterator, bound);
graft->node->u.f.cond = cond;
isl_pw_aff_list_free(list);
if (!graft->node->u.f.cond)
return isl_ast_graft_free(graft);
return graft;
}
/* Set the condition part of the for node graft->node in case
* the upper bound is represented as a set.
*/
static __isl_give isl_ast_graft *set_for_cond_from_set(
__isl_take isl_ast_graft *graft, __isl_keep isl_set *set,
__isl_keep isl_ast_build *build)
{
isl_ast_expr *cond;
if (!graft)
return NULL;
cond = isl_ast_build_expr_from_set_internal(build, isl_set_copy(set));
graft->node->u.f.cond = cond;
if (!graft->node->u.f.cond)
return isl_ast_graft_free(graft);
return graft;
}
/* Construct an isl_ast_expr for the increment (i.e., stride) of
* the current dimension.
*/
static __isl_give isl_ast_expr *for_inc(__isl_keep isl_ast_build *build)
{
isl_size depth;
isl_val *v;
isl_ctx *ctx;
depth = isl_ast_build_get_depth(build);
if (depth < 0)
return NULL;
ctx = isl_ast_build_get_ctx(build);
if (!isl_ast_build_has_stride(build, depth))
return isl_ast_expr_alloc_int_si(ctx, 1);
v = isl_ast_build_get_stride(build, depth);
return isl_ast_expr_from_val(v);
}
/* Should we express the loop condition as
*
* iterator <= min(list of upper bounds)
*
* or as a conjunction of constraints?
*
* The first is constructed from a list of upper bounds.
* The second is constructed from a set.
*
* If there are no upper bounds in "constraints", then this could mean
* that "domain" simply doesn't have an upper bound or that we didn't
* pick any upper bound. In the first case, we want to generate the
* loop condition as a(n empty) conjunction of constraints
* In the second case, we will compute
* a single upper bound from "domain" and so we use the list form.
*
* If there are upper bounds in "constraints",
* then we use the list form iff the atomic_upper_bound option is set.
*/
static int use_upper_bound_list(isl_ctx *ctx, int n_upper,
__isl_keep isl_set *domain, int depth)
{
if (n_upper > 0)
return isl_options_get_ast_build_atomic_upper_bound(ctx);
else
return isl_set_dim_has_upper_bound(domain, isl_dim_set, depth);
}
/* Fill in the expressions of the for node in graft->node.
*
* In particular,
* - set the initialization part of the loop to the maximum of the lower bounds
* - extract the increment from the stride of the current dimension
* - construct the for condition either based on a list of upper bounds
* or on a set of upper bound constraints.
*/
static __isl_give isl_ast_graft *set_for_node_expressions(
__isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *lower,
int use_list, __isl_keep isl_pw_aff_list *upper_list,
__isl_keep isl_set *upper_set, __isl_keep isl_ast_build *build)
{
isl_ast_node *node;
if (!graft)
return NULL;
build = isl_ast_build_copy(build);
node = graft->node;
node->u.f.init = reduce_list(isl_ast_expr_op_max, lower, build);
node->u.f.inc = for_inc(build);
if (!node->u.f.init || !node->u.f.inc)
graft = isl_ast_graft_free(graft);
if (use_list)
graft = set_for_cond_from_list(graft, upper_list, build);
else
graft = set_for_cond_from_set(graft, upper_set, build);
isl_ast_build_free(build);
return graft;
}
/* Update "graft" based on "bounds" and "domain" for the generic,
* non-degenerate, case.
*
* "c_lower" and "c_upper" contain the lower and upper bounds
* that the loop node should express.
* "domain" is the subset of the intersection of the constraints
* for which some code is executed.
*
* There may be zero lower bounds or zero upper bounds in "constraints"
* in case the list of constraints was created
* based on the atomic option or based on separation with explicit bounds.
* In that case, we use "domain" to derive lower and/or upper bounds.
*
* We first compute a list of one or more lower bounds.
*
* Then we decide if we want to express the condition as
*
* iterator <= min(list of upper bounds)
*
* or as a conjunction of constraints.
*
* The set of enforced constraints is then computed either based on
* a list of upper bounds or on a set of upper bound constraints.
* We do not compute any enforced constraints if we were forced
* to compute a lower or upper bound using exact_bound. The domains
* of the resulting expressions may imply some bounds on outer dimensions
* that we do not want to appear in the enforced constraints since
* they are not actually enforced by the corresponding code.
*
* Finally, we fill in the expressions of the for node.
*/
static __isl_give isl_ast_graft *refine_generic_bounds(
__isl_take isl_ast_graft *graft,
__isl_take isl_constraint_list *c_lower,
__isl_take isl_constraint_list *c_upper,
__isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
{
isl_size depth;
isl_ctx *ctx;
isl_pw_aff_list *lower;
int use_list;
isl_set *upper_set = NULL;
isl_pw_aff_list *upper_list = NULL;
isl_size n_lower, n_upper;
depth = isl_ast_build_get_depth(build);
if (!graft || !c_lower || !c_upper || depth < 0)
goto error;
ctx = isl_ast_graft_get_ctx(graft);
n_lower = isl_constraint_list_n_constraint(c_lower);
n_upper = isl_constraint_list_n_constraint(c_upper);
if (n_lower < 0 || n_upper < 0)
goto error;
use_list = use_upper_bound_list(ctx, n_upper, domain, depth);
lower = lower_bounds(c_lower, depth, domain, build);
if (use_list)
upper_list = upper_bounds(c_upper, depth, domain, build);
else if (n_upper > 0)
upper_set = intersect_constraints(c_upper);
else
upper_set = isl_set_universe(isl_set_get_space(domain));
if (n_lower == 0 || n_upper == 0)
;
else if (use_list)
graft = set_enforced_from_list(graft, lower, upper_list);
else
graft = set_enforced_from_set(graft, lower, depth, upper_set);
graft = set_for_node_expressions(graft, lower, use_list, upper_list,
upper_set, build);
isl_pw_aff_list_free(lower);
isl_pw_aff_list_free(upper_list);
isl_set_free(upper_set);
isl_constraint_list_free(c_lower);
isl_constraint_list_free(c_upper);
return graft;
error:
isl_constraint_list_free(c_lower);
isl_constraint_list_free(c_upper);
return isl_ast_graft_free(graft);
}
/* Internal data structure used inside count_constraints to keep
* track of the number of constraints that are independent of dimension "pos",
* the lower bounds in "pos" and the upper bounds in "pos".
*/
struct isl_ast_count_constraints_data {
int pos;
int n_indep;
int n_lower;
int n_upper;
};
/* Increment data->n_indep, data->lower or data->upper depending
* on whether "c" is independenct of dimensions data->pos,
* a lower bound or an upper bound.
*/
static isl_stat count_constraints(__isl_take isl_constraint *c, void *user)
{
struct isl_ast_count_constraints_data *data = user;
if (isl_constraint_is_lower_bound(c, isl_dim_set, data->pos))
data->n_lower++;
else if (isl_constraint_is_upper_bound(c, isl_dim_set, data->pos))
data->n_upper++;
else
data->n_indep++;
isl_constraint_free(c);
return isl_stat_ok;
}
/* Update "graft" based on "bounds" and "domain" for the generic,
* non-degenerate, case.
*
* "list" respresent the list of bounds that need to be encoded by
* the for loop. Only the constraints that involve the iterator
* are relevant here. The other constraints are taken care of by
* the caller and are included in the generated constraints of "build".
* "domain" is the subset of the intersection of the constraints
* for which some code is executed.
* "build" is the build in which graft->node was created.
*
* We separate lower bounds, upper bounds and constraints that
* are independent of the loop iterator.
*
* The actual for loop bounds are generated in refine_generic_bounds.
*/
static __isl_give isl_ast_graft *refine_generic_split(
__isl_take isl_ast_graft *graft, __isl_take isl_constraint_list *list,
__isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
{
struct isl_ast_count_constraints_data data;
isl_size depth;
isl_constraint_list *lower;
isl_constraint_list *upper;
depth = isl_ast_build_get_depth(build);
if (depth < 0)
list = isl_constraint_list_free(list);
if (!list)
return isl_ast_graft_free(graft);
data.pos = depth;
list = isl_constraint_list_sort(list, &cmp_constraint, &data.pos);
if (!list)
return isl_ast_graft_free(graft);
data.n_indep = data.n_lower = data.n_upper = 0;
if (isl_constraint_list_foreach(list, &count_constraints, &data) < 0) {
isl_constraint_list_free(list);
return isl_ast_graft_free(graft);
}
lower = isl_constraint_list_drop(list, 0, data.n_indep);
upper = isl_constraint_list_copy(lower);
lower = isl_constraint_list_drop(lower, data.n_lower, data.n_upper);
upper = isl_constraint_list_drop(upper, 0, data.n_lower);
return refine_generic_bounds(graft, lower, upper, domain, build);
}
/* Update "graft" based on "bounds" and "domain" for the generic,
* non-degenerate, case.
*
* "bounds" respresent the bounds that need to be encoded by
* the for loop (or a guard around the for loop).
* "domain" is the subset of "bounds" for which some code is executed.
* "build" is the build in which graft->node was created.
*
* We break up "bounds" into a list of constraints and continue with
* refine_generic_split.
*/
static __isl_give isl_ast_graft *refine_generic(
__isl_take isl_ast_graft *graft,
__isl_keep isl_basic_set *bounds, __isl_keep isl_set *domain,
__isl_keep isl_ast_build *build)
{
isl_constraint_list *list;
if (!build || !graft)
return isl_ast_graft_free(graft);
list = isl_basic_set_get_constraint_list(bounds);
graft = refine_generic_split(graft, list, domain, build);
return graft;
}
/* Create a for node for the current level.
*
* Mark the for node degenerate if "degenerate" is set.
*/
static __isl_give isl_ast_node *create_for(__isl_keep isl_ast_build *build,
int degenerate)
{
isl_size depth;
isl_id *id;
isl_ast_node *node;
depth = isl_ast_build_get_depth(build);
if (depth < 0)
return NULL;
id = isl_ast_build_get_iterator_id(build, depth);
node = isl_ast_node_alloc_for(id);
if (degenerate)
node = isl_ast_node_for_mark_degenerate(node);
return node;
}
/* If the ast_build_exploit_nested_bounds option is set, then return
* the constraints enforced by all elements in "list".
* Otherwise, return the universe.
*/
static __isl_give isl_basic_set *extract_shared_enforced(
__isl_keep isl_ast_graft_list *list, __isl_keep isl_ast_build *build)
{
isl_ctx *ctx;
isl_space *space;
if (!list)
return NULL;
ctx = isl_ast_graft_list_get_ctx(list);
if (isl_options_get_ast_build_exploit_nested_bounds(ctx))
return isl_ast_graft_list_extract_shared_enforced(list, build);
space = isl_ast_build_get_space(build, 1);
return isl_basic_set_universe(space);
}
/* Return the pending constraints of "build" that are not already taken
* care of (by a combination of "enforced" and the generated constraints
* of "build").
*/
static __isl_give isl_set *extract_pending(__isl_keep isl_ast_build *build,
__isl_keep isl_basic_set *enforced)
{
isl_set *guard, *context;
guard = isl_ast_build_get_pending(build);
context = isl_set_from_basic_set(isl_basic_set_copy(enforced));
context = isl_set_intersect(context,
isl_ast_build_get_generated(build));
return isl_set_gist(guard, context);
}
/* Create an AST node for the current dimension based on
* the schedule domain "bounds" and return the node encapsulated
* in an isl_ast_graft.
*
* "executed" is the current inverse schedule, taking into account
* the bounds in "bounds"
* "domain" is the domain of "executed", with inner dimensions projected out.
* It may be a strict subset of "bounds" in case "bounds" was created
* based on the atomic option or based on separation with explicit bounds.
*
* "domain" may satisfy additional equalities that result
* from intersecting "executed" with "bounds" in add_node.
* It may also satisfy some global constraints that were dropped out because
* we performed separation with explicit bounds.
* The very first step is then to copy these constraints to "bounds".
*
* Since we may be calling before_each_for and after_each_for
* callbacks, we record the current inverse schedule in the build.
*
* We consider three builds,
* "build" is the one in which the current level is created,
* "body_build" is the build in which the next level is created,
* "sub_build" is essentially the same as "body_build", except that
* the depth has not been increased yet.
*
* "build" already contains information (in strides and offsets)
* about the strides at the current level, but this information is not
* reflected in the build->domain.
* We first add this information and the "bounds" to the sub_build->domain.
* isl_ast_build_set_loop_bounds adds the stride information and
* checks whether the current dimension attains
* only a single value and whether this single value can be represented using
* a single affine expression.
* In the first case, the current level is considered "degenerate".
* In the second, sub-case, the current level is considered "eliminated".
* Eliminated levels don't need to be reflected in the AST since we can
* simply plug in the affine expression. For degenerate, but non-eliminated,
* levels, we do introduce a for node, but mark is as degenerate so that
* it can be printed as an assignment of the single value to the loop
* "iterator".
*
* If the current level is eliminated, we explicitly plug in the value
* for the current level found by isl_ast_build_set_loop_bounds in the
* inverse schedule. This ensures that if we are working on a slice
* of the domain based on information available in the inverse schedule
* and the build domain, that then this information is also reflected
* in the inverse schedule. This operation also eliminates the current
* dimension from the inverse schedule making sure no inner dimensions depend
* on the current dimension. Otherwise, we create a for node, marking
* it degenerate if appropriate. The initial for node is still incomplete
* and will be completed in either refine_degenerate or refine_generic.
*
* We then generate a sequence of grafts for the next level,
* create a surrounding graft for the current level and insert
* the for node we created (if the current level is not eliminated).
* Before creating a graft for the current level, we first extract
* hoistable constraints from the child guards and combine them
* with the pending constraints in the build. These constraints
* are used to simplify the child guards and then added to the guard
* of the current graft to ensure that they will be generated.
* If the hoisted guard is a disjunction, then we use it directly
* to gist the guards on the children before intersect it with the
* pending constraints. We do so because this disjunction is typically
* identical to the guards on the children such that these guards
* can be effectively removed completely. After the intersection,
* the gist operation would have a harder time figuring this out.
*
* Finally, we set the bounds of the for loop in either
* refine_degenerate or refine_generic.
* We do so in a context where the pending constraints of the build
* have been replaced by the guard of the current graft.
*/
static __isl_give isl_ast_graft *create_node_scaled(
__isl_take isl_union_map *executed,
__isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
__isl_take isl_ast_build *build)
{
isl_size depth;
int degenerate;
isl_bool eliminated;
isl_size n;
isl_basic_set *hull;
isl_basic_set *enforced;
isl_set *guard, *hoisted;
isl_ast_node *node = NULL;
isl_ast_graft *graft;
isl_ast_graft_list *children;
isl_ast_build *sub_build;
isl_ast_build *body_build;
domain = isl_ast_build_eliminate_divs(build, domain);
domain = isl_set_detect_equalities(domain);
hull = isl_set_unshifted_simple_hull(isl_set_copy(domain));
bounds = isl_basic_set_intersect(bounds, hull);
build = isl_ast_build_set_executed(build, isl_union_map_copy(executed));
depth = isl_ast_build_get_depth(build);
if (depth < 0)
build = isl_ast_build_free(build);
sub_build = isl_ast_build_copy(build);
bounds = isl_basic_set_remove_redundancies(bounds);
bounds = isl_ast_build_specialize_basic_set(sub_build, bounds);
sub_build = isl_ast_build_set_loop_bounds(sub_build,
isl_basic_set_copy(bounds));
degenerate = isl_ast_build_has_value(sub_build);
eliminated = isl_ast_build_has_affine_value(sub_build, depth);
if (degenerate < 0 || eliminated < 0)
executed = isl_union_map_free(executed);
if (!degenerate)
bounds = isl_ast_build_compute_gist_basic_set(build, bounds);
sub_build = isl_ast_build_set_pending_generated(sub_build,
isl_basic_set_copy(bounds));
if (eliminated)
executed = plug_in_values(executed, sub_build);
else
node = create_for(build, degenerate);
body_build = isl_ast_build_copy(sub_build);
body_build = isl_ast_build_increase_depth(body_build);
if (!eliminated)
node = before_each_for(node, body_build);
children = generate_next_level(executed,
isl_ast_build_copy(body_build));
enforced = extract_shared_enforced(children, build);
guard = extract_pending(sub_build, enforced);
hoisted = isl_ast_graft_list_extract_hoistable_guard(children, build);
n = isl_set_n_basic_set(hoisted);
if (n < 0)
children = isl_ast_graft_list_free(children);
if (n > 1)
children = isl_ast_graft_list_gist_guards(children,
isl_set_copy(hoisted));
guard = isl_set_intersect(guard, hoisted);
if (!eliminated)
guard = add_implied_guards(guard, degenerate, bounds, build);
graft = isl_ast_graft_alloc_from_children(children,
isl_set_copy(guard), enforced, build, sub_build);
if (!eliminated) {
isl_ast_build *for_build;
graft = isl_ast_graft_insert_for(graft, node);
for_build = isl_ast_build_copy(build);
for_build = isl_ast_build_replace_pending_by_guard(for_build,
isl_set_copy(guard));
if (degenerate)
graft = refine_degenerate(graft, for_build, sub_build);
else
graft = refine_generic(graft, bounds,
domain, for_build);
isl_ast_build_free(for_build);
}
isl_set_free(guard);
if (!eliminated)
graft = after_each_for(graft, body_build);
isl_ast_build_free(body_build);
isl_ast_build_free(sub_build);
isl_ast_build_free(build);
isl_basic_set_free(bounds);
isl_set_free(domain);
return graft;
}
/* Internal data structure for checking if all constraints involving
* the input dimension "depth" are such that the other coefficients
* are multiples of "m", reducing "m" if they are not.
* If "m" is reduced all the way down to "1", then the check has failed
* and we break out of the iteration.
*/
struct isl_check_scaled_data {
int depth;
isl_val *m;
};
/* If constraint "c" involves the input dimension data->depth,
* then make sure that all the other coefficients are multiples of data->m,
* reducing data->m if needed.
* Break out of the iteration if data->m has become equal to "1".
*/
static isl_stat constraint_check_scaled(__isl_take isl_constraint *c,
void *user)
{
struct isl_check_scaled_data *data = user;
int i, j;
isl_size n;
enum isl_dim_type t[] = { isl_dim_param, isl_dim_in, isl_dim_out,
isl_dim_div };
if (!isl_constraint_involves_dims(c, isl_dim_in, data->depth, 1)) {
isl_constraint_free(c);
return isl_stat_ok;
}
for (i = 0; i < 4; ++i) {
n = isl_constraint_dim(c, t[i]);
if (n < 0)
break;
for (j = 0; j < n; ++j) {
isl_val *d;
if (t[i] == isl_dim_in && j == data->depth)
continue;
if (!isl_constraint_involves_dims(c, t[i], j, 1))
continue;
d = isl_constraint_get_coefficient_val(c, t[i], j);
data->m = isl_val_gcd(data->m, d);
if (isl_val_is_one(data->m))
break;
}
if (j < n)
break;
}
isl_constraint_free(c);
return i < 4 ? isl_stat_error : isl_stat_ok;
}
/* For each constraint of "bmap" that involves the input dimension data->depth,
* make sure that all the other coefficients are multiples of data->m,
* reducing data->m if needed.
* Break out of the iteration if data->m has become equal to "1".
*/
static isl_stat basic_map_check_scaled(__isl_take isl_basic_map *bmap,
void *user)
{
isl_stat r;
r = isl_basic_map_foreach_constraint(bmap,
&constraint_check_scaled, user);
isl_basic_map_free(bmap);
return r;
}
/* For each constraint of "map" that involves the input dimension data->depth,
* make sure that all the other coefficients are multiples of data->m,
* reducing data->m if needed.
* Break out of the iteration if data->m has become equal to "1".
*/
static isl_stat map_check_scaled(__isl_take isl_map *map, void *user)
{
isl_stat r;
r = isl_map_foreach_basic_map(map, &basic_map_check_scaled, user);
isl_map_free(map);
return r;
}
/* Create an AST node for the current dimension based on
* the schedule domain "bounds" and return the node encapsulated
* in an isl_ast_graft.
*
* "executed" is the current inverse schedule, taking into account
* the bounds in "bounds"
* "domain" is the domain of "executed", with inner dimensions projected out.
*
*
* Before moving on to the actual AST node construction in create_node_scaled,
* we first check if the current dimension is strided and if we can scale
* down this stride. Note that we only do this if the ast_build_scale_strides
* option is set.
*
* In particular, let the current dimension take on values
*
* f + s a
*
* with a an integer. We check if we can find an integer m that (obviously)
* divides both f and s.
*
* If so, we check if the current dimension only appears in constraints
* where the coefficients of the other variables are multiples of m.
* We perform this extra check to avoid the risk of introducing
* divisions by scaling down the current dimension.
*
* If so, we scale the current dimension down by a factor of m.
* That is, we plug in
*
* i = m i' (1)
*
* Note that in principle we could always scale down strided loops
* by plugging in
*
* i = f + s i'
*
* but this may result in i' taking on larger values than the original i,
* due to the shift by "f".
* By constrast, the scaling in (1) can only reduce the (absolute) value "i".
*/
static __isl_give isl_ast_graft *create_node(__isl_take isl_union_map *executed,
__isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
__isl_take isl_ast_build *build)
{
struct isl_check_scaled_data data;
isl_size depth;
isl_ctx *ctx;
isl_aff *offset;
isl_val *d;
ctx = isl_ast_build_get_ctx(build);
if (!isl_options_get_ast_build_scale_strides(ctx))
return create_node_scaled(executed, bounds, domain, build);
depth = isl_ast_build_get_depth(build);
if (depth < 0)
build = isl_ast_build_free(build);
data.depth = depth;
if (!isl_ast_build_has_stride(build, data.depth))
return create_node_scaled(executed, bounds, domain, build);
offset = isl_ast_build_get_offset(build, data.depth);
data.m = isl_ast_build_get_stride(build, data.depth);
if (!data.m)
offset = isl_aff_free(offset);
offset = isl_aff_scale_down_val(offset, isl_val_copy(data.m));
d = isl_aff_get_denominator_val(offset);
if (!d)
executed = isl_union_map_free(executed);
if (executed && isl_val_is_divisible_by(data.m, d))
data.m = isl_val_div(data.m, d);
else {
data.m = isl_val_set_si(data.m, 1);
isl_val_free(d);
}
if (!isl_val_is_one(data.m)) {
if (isl_union_map_foreach_map(executed, &map_check_scaled,
&data) < 0 &&
!isl_val_is_one(data.m))
executed = isl_union_map_free(executed);
}
if (!isl_val_is_one(data.m)) {
isl_space *space;
isl_multi_aff *ma;
isl_aff *aff;
isl_map *map;
isl_union_map *umap;
space = isl_ast_build_get_space(build, 1);
space = isl_space_map_from_set(space);
ma = isl_multi_aff_identity(space);
aff = isl_multi_aff_get_aff(ma, data.depth);
aff = isl_aff_scale_val(aff, isl_val_copy(data.m));
ma = isl_multi_aff_set_aff(ma, data.depth, aff);
bounds = isl_basic_set_preimage_multi_aff(bounds,
isl_multi_aff_copy(ma));
domain = isl_set_preimage_multi_aff(domain,
isl_multi_aff_copy(ma));
map = isl_map_reverse(isl_map_from_multi_aff(ma));
umap = isl_union_map_from_map(map);
executed = isl_union_map_apply_domain(executed,
isl_union_map_copy(umap));
build = isl_ast_build_scale_down(build, isl_val_copy(data.m),
umap);
}
isl_aff_free(offset);
isl_val_free(data.m);
return create_node_scaled(executed, bounds, domain, build);
}
/* Add the basic set to the list that "user" points to.
*/
static isl_stat collect_basic_set(__isl_take isl_basic_set *bset, void *user)
{
isl_basic_set_list **list = user;
*list = isl_basic_set_list_add(*list, bset);
return isl_stat_ok;
}
/* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
*/
static __isl_give isl_basic_set_list *isl_basic_set_list_from_set(
__isl_take isl_set *set)
{
isl_size n;
isl_ctx *ctx;
isl_basic_set_list *list;
n = isl_set_n_basic_set(set);
if (n < 0)
set = isl_set_free(set);
if (!set)
return NULL;
ctx = isl_set_get_ctx(set);
list = isl_basic_set_list_alloc(ctx, n);
if (isl_set_foreach_basic_set(set, &collect_basic_set, &list) < 0)
list = isl_basic_set_list_free(list);
isl_set_free(set);
return list;
}
/* Generate code for the schedule domain "bounds"
* and add the result to "list".
*
* We mainly detect strides here and check if the bounds do not
* conflict with the current build domain
* and then pass over control to create_node.
*
* "bounds" reflects the bounds on the current dimension and possibly
* some extra conditions on outer dimensions.
* It does not, however, include any divs involving the current dimension,
* so it does not capture any stride constraints.
* We therefore need to compute that part of the schedule domain that
* intersects with "bounds" and derive the strides from the result.
*/
static __isl_give isl_ast_graft_list *add_node(
__isl_take isl_ast_graft_list *list, __isl_take isl_union_map *executed,
__isl_take isl_basic_set *bounds, __isl_take isl_ast_build *build)
{
isl_ast_graft *graft;
isl_set *domain = NULL;
isl_union_set *uset;
int empty, disjoint;
uset = isl_union_set_from_basic_set(isl_basic_set_copy(bounds));
executed = isl_union_map_intersect_domain(executed, uset);
empty = isl_union_map_is_empty(executed);
if (empty < 0)
goto error;
if (empty)
goto done;
uset = isl_union_map_domain(isl_union_map_copy(executed));
domain = isl_set_from_union_set(uset);
domain = isl_ast_build_specialize(build, domain);
domain = isl_set_compute_divs(domain);
domain = isl_ast_build_eliminate_inner(build, domain);
disjoint = isl_set_is_disjoint(domain, build->domain);
if (disjoint < 0)
goto error;
if (disjoint)
goto done;
build = isl_ast_build_detect_strides(build, isl_set_copy(domain));
graft = create_node(executed, bounds, domain,
isl_ast_build_copy(build));
list = isl_ast_graft_list_add(list, graft);
isl_ast_build_free(build);
return list;
error:
list = isl_ast_graft_list_free(list);
done:
isl_set_free(domain);
isl_basic_set_free(bounds);
isl_union_map_free(executed);
isl_ast_build_free(build);
return list;
}
/* Does any element of i follow or coincide with any element of j
* at the current depth for equal values of the outer dimensions?
*/
static isl_bool domain_follows_at_depth(__isl_keep isl_basic_set *i,
__isl_keep isl_basic_set *j, void *user)
{
int depth = *(int *) user;
isl_basic_map *test;
isl_bool empty;
int l;
test = isl_basic_map_from_domain_and_range(isl_basic_set_copy(i),
isl_basic_set_copy(j));
for (l = 0; l < depth; ++l)
test = isl_basic_map_equate(test, isl_dim_in, l,
isl_dim_out, l);
test = isl_basic_map_order_ge(test, isl_dim_in, depth,
isl_dim_out, depth);
empty = isl_basic_map_is_empty(test);
isl_basic_map_free(test);
return isl_bool_not(empty);
}
/* Split up each element of "list" into a part that is related to "bset"
* according to "gt" and a part that is not.
* Return a list that consist of "bset" and all the pieces.
*/
static __isl_give isl_basic_set_list *add_split_on(
__isl_take isl_basic_set_list *list, __isl_take isl_basic_set *bset,
__isl_keep isl_basic_map *gt)
{
int i;
isl_size n;
isl_basic_set_list *res;
n = isl_basic_set_list_n_basic_set(list);
if (n < 0)
bset = isl_basic_set_free(bset);
gt = isl_basic_map_copy(gt);
gt = isl_basic_map_intersect_domain(gt, isl_basic_set_copy(bset));
res = isl_basic_set_list_from_basic_set(bset);
for (i = 0; res && i < n; ++i) {
isl_basic_set *bset;
isl_set *set1, *set2;
isl_basic_map *bmap;
int empty;
bset = isl_basic_set_list_get_basic_set(list, i);
bmap = isl_basic_map_copy(gt);
bmap = isl_basic_map_intersect_range(bmap, bset);
bset = isl_basic_map_range(bmap);
empty = isl_basic_set_is_empty(bset);
if (empty < 0)
res = isl_basic_set_list_free(res);
if (empty) {
isl_basic_set_free(bset);
bset = isl_basic_set_list_get_basic_set(list, i);
res = isl_basic_set_list_add(res, bset);
continue;
}
res = isl_basic_set_list_add(res, isl_basic_set_copy(bset));
set1 = isl_set_from_basic_set(bset);
bset = isl_basic_set_list_get_basic_set(list, i);
set2 = isl_set_from_basic_set(bset);
set1 = isl_set_subtract(set2, set1);
set1 = isl_set_make_disjoint(set1);
res = isl_basic_set_list_concat(res,
isl_basic_set_list_from_set(set1));
}
isl_basic_map_free(gt);
isl_basic_set_list_free(list);
return res;
}
static __isl_give isl_ast_graft_list *generate_sorted_domains(
__isl_keep isl_basic_set_list *domain_list,
__isl_keep isl_union_map *executed,
__isl_keep isl_ast_build *build);
/* Internal data structure for add_nodes.
*
* "executed" and "build" are extra arguments to be passed to add_node.
* "list" collects the results.
*/
struct isl_add_nodes_data {
isl_union_map *executed;
isl_ast_build *build;
isl_ast_graft_list *list;
};
/* Generate code for the schedule domains in "scc"
* and add the results to "list".
*
* The domains in "scc" form a strongly connected component in the ordering.
* If the number of domains in "scc" is larger than 1, then this means
* that we cannot determine a valid ordering for the domains in the component.
* This should be fairly rare because the individual domains
* have been made disjoint first.
* The problem is that the domains may be integrally disjoint but not
* rationally disjoint. For example, we may have domains
*
* { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
*
* These two domains have an empty intersection, but their rational
* relaxations do intersect. It is impossible to order these domains
* in the second dimension because the first should be ordered before
* the second for outer dimension equal to 0, while it should be ordered
* after for outer dimension equal to 1.
*
* This may happen in particular in case of unrolling since the domain
* of each slice is replaced by its simple hull.
*
* For each basic set i in "scc" and for each of the following basic sets j,
* we split off that part of the basic set i that shares the outer dimensions
* with j and lies before j in the current dimension.
* We collect all the pieces in a new list that replaces "scc".
*
* While the elements in "scc" should be disjoint, we double-check
* this property to avoid running into an infinite recursion in case
* they intersect due to some internal error.
*/
static isl_stat add_nodes(__isl_take isl_basic_set_list *scc, void *user)
{
struct isl_add_nodes_data *data = user;
int i;
isl_size depth;
isl_size n;
isl_basic_set *bset, *first;
isl_basic_set_list *list;
isl_space *space;
isl_basic_map *gt;
n = isl_basic_set_list_n_basic_set(scc);
if (n < 0)
goto error;
bset = isl_basic_set_list_get_basic_set(scc, 0);
if (n == 1) {
isl_basic_set_list_free(scc);
data->list = add_node(data->list,
isl_union_map_copy(data->executed), bset,
isl_ast_build_copy(data->build));
return data->list ? isl_stat_ok : isl_stat_error;
}
depth = isl_ast_build_get_depth(data->build);
if (depth < 0)
bset = isl_basic_set_free(bset);
space = isl_basic_set_get_space(bset);
space = isl_space_map_from_set(space);
gt = isl_basic_map_universe(space);
for (i = 0; i < depth; ++i)
gt = isl_basic_map_equate(gt, isl_dim_in, i, isl_dim_out, i);
gt = isl_basic_map_order_gt(gt, isl_dim_in, depth, isl_dim_out, depth);
first = isl_basic_set_copy(bset);
list = isl_basic_set_list_from_basic_set(bset);
for (i = 1; i < n; ++i) {
int disjoint;
bset = isl_basic_set_list_get_basic_set(scc, i);
disjoint = isl_basic_set_is_disjoint(bset, first);
if (disjoint < 0)
list = isl_basic_set_list_free(list);
else if (!disjoint)
isl_die(isl_basic_set_list_get_ctx(scc),
isl_error_internal,
"basic sets in scc are assumed to be disjoint",
list = isl_basic_set_list_free(list));
list = add_split_on(list, bset, gt);
}
isl_basic_set_free(first);
isl_basic_map_free(gt);
isl_basic_set_list_free(scc);
scc = list;
data->list = isl_ast_graft_list_concat(data->list,
generate_sorted_domains(scc, data->executed, data->build));
isl_basic_set_list_free(scc);
return data->list ? isl_stat_ok : isl_stat_error;
error:
isl_basic_set_list_free(scc);
return isl_stat_error;
}
/* Sort the domains in "domain_list" according to the execution order
* at the current depth (for equal values of the outer dimensions),
* generate code for each of them, collecting the results in a list.
* If no code is generated (because the intersection of the inverse schedule
* with the domains turns out to be empty), then an empty list is returned.
*
* The caller is responsible for ensuring that the basic sets in "domain_list"
* are pair-wise disjoint. It can, however, in principle happen that
* two basic sets should be ordered one way for one value of the outer
* dimensions and the other way for some other value of the outer dimensions.
* We therefore play safe and look for strongly connected components.
* The function add_nodes takes care of handling non-trivial components.
*/
static __isl_give isl_ast_graft_list *generate_sorted_domains(
__isl_keep isl_basic_set_list *domain_list,
__isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
{
isl_ctx *ctx;
struct isl_add_nodes_data data;
isl_size depth;
isl_size n;
n = isl_basic_set_list_n_basic_set(domain_list);
if (n < 0)
return NULL;
ctx = isl_basic_set_list_get_ctx(domain_list);
data.list = isl_ast_graft_list_alloc(ctx, n);
if (n == 0)
return data.list;
if (n == 1)
return add_node(data.list, isl_union_map_copy(executed),
isl_basic_set_list_get_basic_set(domain_list, 0),
isl_ast_build_copy(build));
depth = isl_ast_build_get_depth(build);
data.executed = executed;
data.build = build;
if (depth < 0 || isl_basic_set_list_foreach_scc(domain_list,
&domain_follows_at_depth, &depth,
&add_nodes, &data) < 0)
data.list = isl_ast_graft_list_free(data.list);
return data.list;
}
/* Do i and j share any values for the outer dimensions?
*/
static isl_bool shared_outer(__isl_keep isl_basic_set *i,
__isl_keep isl_basic_set *j, void *user)
{
int depth = *(int *) user;
isl_basic_map *test;
isl_bool empty;
int l;
test = isl_basic_map_from_domain_and_range(isl_basic_set_copy(i),
isl_basic_set_copy(j));
for (l = 0; l < depth; ++l)
test = isl_basic_map_equate(test, isl_dim_in, l,
isl_dim_out, l);
empty = isl_basic_map_is_empty(test);
isl_basic_map_free(test);
return isl_bool_not(empty);
}
/* Internal data structure for generate_sorted_domains_wrap.
*
* "n" is the total number of basic sets
* "executed" and "build" are extra arguments to be passed
* to generate_sorted_domains.
*
* "single" is set to 1 by generate_sorted_domains_wrap if there
* is only a single component.
* "list" collects the results.
*/
struct isl_ast_generate_parallel_domains_data {
isl_size n;
isl_union_map *executed;
isl_ast_build *build;
int single;
isl_ast_graft_list *list;
};
/* Call generate_sorted_domains on "scc", fuse the result into a list
* with either zero or one graft and collect the these single element
* lists into data->list.
*
* If there is only one component, i.e., if the number of basic sets
* in the current component is equal to the total number of basic sets,
* then data->single is set to 1 and the result of generate_sorted_domains
* is not fused.
*/
static isl_stat generate_sorted_domains_wrap(__isl_take isl_basic_set_list *scc,
void *user)
{
struct isl_ast_generate_parallel_domains_data *data = user;
isl_ast_graft_list *list;
isl_size n;
n = isl_basic_set_list_n_basic_set(scc);
if (n < 0)
scc = isl_basic_set_list_free(scc);
list = generate_sorted_domains(scc, data->executed, data->build);
data->single = n == data->n;
if (!data->single)
list = isl_ast_graft_list_fuse(list, data->build);
if (!data->list)
data->list = list;
else
data->list = isl_ast_graft_list_concat(data->list, list);
isl_basic_set_list_free(scc);
if (!data->list)
return isl_stat_error;
return isl_stat_ok;
}
/* Look for any (weakly connected) components in the "domain_list"
* of domains that share some values of the outer dimensions.
* That is, domains in different components do not share any values
* of the outer dimensions. This means that these components
* can be freely reordered.
* Within each of the components, we sort the domains according
* to the execution order at the current depth.
*
* If there is more than one component, then generate_sorted_domains_wrap
* fuses the result of each call to generate_sorted_domains
* into a list with either zero or one graft and collects these (at most)
* single element lists into a bigger list. This means that the elements of the
* final list can be freely reordered. In particular, we sort them
* according to an arbitrary but fixed ordering to ease merging of
* graft lists from different components.
*/
static __isl_give isl_ast_graft_list *generate_parallel_domains(
__isl_keep isl_basic_set_list *domain_list,
__isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
{
isl_size depth;
struct isl_ast_generate_parallel_domains_data data;
data.n = isl_basic_set_list_n_basic_set(domain_list);
if (data.n < 0)
return NULL;
if (data.n <= 1)
return generate_sorted_domains(domain_list, executed, build);
depth = isl_ast_build_get_depth(build);
if (depth < 0)
return NULL;
data.list = NULL;
data.executed = executed;
data.build = build;
data.single = 0;
if (isl_basic_set_list_foreach_scc(domain_list, &shared_outer, &depth,
&generate_sorted_domains_wrap,
&data) < 0)
data.list = isl_ast_graft_list_free(data.list);
if (!data.single)
data.list = isl_ast_graft_list_sort_guard(data.list);
return data.list;
}
/* Internal data for separate_domain.
*
* "explicit" is set if we only want to use explicit bounds.
*
* "domain" collects the separated domains.
*/
struct isl_separate_domain_data {
isl_ast_build *build;
int explicit;
isl_set *domain;
};
/* Extract implicit bounds on the current dimension for the executed "map".
*
* The domain of "map" may involve inner dimensions, so we
* need to eliminate them.
*/
static __isl_give isl_set *implicit_bounds(__isl_take isl_map *map,
__isl_keep isl_ast_build *build)
{
isl_set *domain;
domain = isl_map_domain(map);
domain = isl_ast_build_eliminate(build, domain);
return domain;
}
/* Extract explicit bounds on the current dimension for the executed "map".
*
* Rather than eliminating the inner dimensions as in implicit_bounds,
* we simply drop any constraints involving those inner dimensions.
* The idea is that most bounds that are implied by constraints on the
* inner dimensions will be enforced by for loops and not by explicit guards.
* There is then no need to separate along those bounds.
*/
static __isl_give isl_set *explicit_bounds(__isl_take isl_map *map,
__isl_keep isl_ast_build *build)
{
isl_set *domain;
isl_size depth;
isl_size dim;
depth = isl_ast_build_get_depth(build);
dim = isl_map_dim(map, isl_dim_out);
if (depth < 0 || dim < 0)
return isl_map_domain(isl_map_free(map));
map = isl_map_drop_constraints_involving_dims(map, isl_dim_out, 0, dim);
domain = isl_map_domain(map);
dim = isl_set_dim(domain, isl_dim_set);
domain = isl_set_detect_equalities(domain);
domain = isl_set_drop_constraints_involving_dims(domain,
isl_dim_set, depth + 1, dim - (depth + 1));
domain = isl_set_remove_divs_involving_dims(domain,
isl_dim_set, depth, 1);
domain = isl_set_remove_unknown_divs(domain);
return domain;
}
/* Split data->domain into pieces that intersect with the range of "map"
* and pieces that do not intersect with the range of "map"
* and then add that part of the range of "map" that does not intersect
* with data->domain.
*/
static isl_stat separate_domain(__isl_take isl_map *map, void *user)
{
struct isl_separate_domain_data *data = user;
isl_set *domain;
isl_set *d1, *d2;
if (data->explicit)
domain = explicit_bounds(map, data->build);
else
domain = implicit_bounds(map, data->build);
domain = isl_set_coalesce(domain);
domain = isl_set_make_disjoint(domain);
d1 = isl_set_subtract(isl_set_copy(domain), isl_set_copy(data->domain));
d2 = isl_set_subtract(isl_set_copy(data->domain), isl_set_copy(domain));
data->domain = isl_set_intersect(data->domain, domain);
data->domain = isl_set_union(data->domain, d1);
data->domain = isl_set_union(data->domain, d2);
return isl_stat_ok;
}
/* Separate the schedule domains of "executed".
*
* That is, break up the domain of "executed" into basic sets,
* such that for each basic set S, every element in S is associated with
* the same domain spaces.
*
* "space" is the (single) domain space of "executed".
*/
static __isl_give isl_set *separate_schedule_domains(
__isl_take isl_space *space, __isl_take isl_union_map *executed,
__isl_keep isl_ast_build *build)
{
struct isl_separate_domain_data data = { build };
isl_ctx *ctx;
ctx = isl_ast_build_get_ctx(build);
data.explicit = isl_options_get_ast_build_separation_bounds(ctx) ==
ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT;
data.domain = isl_set_empty(space);
if (isl_union_map_foreach_map(executed, &separate_domain, &data) < 0)
data.domain = isl_set_free(data.domain);
isl_union_map_free(executed);
return data.domain;
}
/* Temporary data used during the search for a lower bound for unrolling.
*
* "build" is the build in which the unrolling will be performed
* "domain" is the original set for which to find a lower bound
* "depth" is the dimension for which to find a lower boudn
* "expansion" is the expansion that needs to be applied to "domain"
* in the unrolling that will be performed
*
* "lower" is the best lower bound found so far. It is NULL if we have not
* found any yet.
* "n" is the corresponding size. If lower is NULL, then the value of n
* is undefined.
* "n_div" is the maximal number of integer divisions in the first
* unrolled iteration (after expansion). It is set to -1 if it hasn't
* been computed yet.
*/
struct isl_find_unroll_data {
isl_ast_build *build;
isl_set *domain;
int depth;
isl_basic_map *expansion;
isl_aff *lower;
int *n;
int n_div;
};
/* Return the constraint
*
* i_"depth" = aff + offset
*/
static __isl_give isl_constraint *at_offset(int depth, __isl_keep isl_aff *aff,
int offset)
{
aff = isl_aff_copy(aff);
aff = isl_aff_add_coefficient_si(aff, isl_dim_in, depth, -1);
aff = isl_aff_add_constant_si(aff, offset);
return isl_equality_from_aff(aff);
}
/* Update *user to the number of integer divisions in the first element
* of "ma", if it is larger than the current value.
*/
static isl_stat update_n_div(__isl_take isl_set *set,
__isl_take isl_multi_aff *ma, void *user)
{
isl_aff *aff;
int *n = user;
isl_size n_div;
aff = isl_multi_aff_get_aff(ma, 0);
n_div = isl_aff_dim(aff, isl_dim_div);
isl_aff_free(aff);
isl_multi_aff_free(ma);
isl_set_free(set);
if (n_div > *n)
*n = n_div;
return n_div >= 0 ? isl_stat_ok : isl_stat_error;
}
/* Get the number of integer divisions in the expression for the iterator
* value at the first slice in the unrolling based on lower bound "lower",
* taking into account the expansion that needs to be performed on this slice.
*/
static int get_expanded_n_div(struct isl_find_unroll_data *data,
__isl_keep isl_aff *lower)
{
isl_constraint *c;
isl_set *set;
isl_map *it_map, *expansion;
isl_pw_multi_aff *pma;
int n;
c = at_offset(data->depth, lower, 0);
set = isl_set_copy(data->domain);
set = isl_set_add_constraint(set, c);
expansion = isl_map_from_basic_map(isl_basic_map_copy(data->expansion));
set = isl_set_apply(set, expansion);
it_map = isl_ast_build_map_to_iterator(data->build, set);
pma = isl_pw_multi_aff_from_map(it_map);
n = 0;
if (isl_pw_multi_aff_foreach_piece(pma, &update_n_div, &n) < 0)
n = -1;
isl_pw_multi_aff_free(pma);
return n;
}
/* Is the lower bound "lower" with corresponding iteration count "n"
* better than the one stored in "data"?
* If there is no upper bound on the iteration count ("n" is infinity) or
* if the count is too large, then we cannot use this lower bound.
* Otherwise, if there was no previous lower bound or
* if the iteration count of the new lower bound is smaller than
* the iteration count of the previous lower bound, then we consider
* the new lower bound to be better.
* If the iteration count is the same, then compare the number
* of integer divisions that would be needed to express
* the iterator value at the first slice in the unrolling
* according to the lower bound. If we end up computing this
* number, then store the lowest value in data->n_div.
*/
static int is_better_lower_bound(struct isl_find_unroll_data *data,
__isl_keep isl_aff *lower, __isl_keep isl_val *n)
{
int cmp;
int n_div;
if (!n)
return -1;
if (isl_val_is_infty(n))
return 0;
if (isl_val_cmp_si(n, INT_MAX) > 0)
return 0;
if (!data->lower)
return 1;
cmp = isl_val_cmp_si(n, *data->n);
if (cmp < 0)
return 1;
if (cmp > 0)
return 0;
if (data->n_div < 0)
data->n_div = get_expanded_n_div(data, data->lower);
if (data->n_div < 0)
return -1;
if (data->n_div == 0)
return 0;
n_div = get_expanded_n_div(data, lower);
if (n_div < 0)
return -1;
if (n_div >= data->n_div)
return 0;
data->n_div = n_div;
return 1;
}
/* Check if we can use "c" as a lower bound and if it is better than
* any previously found lower bound.
*
* If "c" does not involve the dimension at the current depth,
* then we cannot use it.
* Otherwise, let "c" be of the form
*
* i >= f(j)/a
*
* We compute the maximal value of
*
* -ceil(f(j)/a)) + i + 1
*
* over the domain. If there is such a value "n", then we know
*
* -ceil(f(j)/a)) + i + 1 <= n
*
* or
*
* i < ceil(f(j)/a)) + n
*
* meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
* We just need to check if we have found any lower bound before and
* if the new lower bound is better (smaller n or fewer integer divisions)
* than the previously found lower bounds.
*/
static isl_stat update_unrolling_lower_bound(struct isl_find_unroll_data *data,
__isl_keep isl_constraint *c)
{
isl_aff *aff, *lower;
isl_val *max;
int better;
if (!isl_constraint_is_lower_bound(c, isl_dim_set, data->depth))
return isl_stat_ok;
lower = isl_constraint_get_bound(c, isl_dim_set, data->depth);
lower = isl_aff_ceil(lower);
aff = isl_aff_copy(lower);
aff = isl_aff_neg(aff);
aff = isl_aff_add_coefficient_si(aff, isl_dim_in, data->depth, 1);
aff = isl_aff_add_constant_si(aff, 1);
max = isl_set_max_val(data->domain, aff);
isl_aff_free(aff);
better = is_better_lower_bound(data, lower, max);
if (better < 0 || !better) {
isl_val_free(max);
isl_aff_free(lower);
return better < 0 ? isl_stat_error : isl_stat_ok;
}
isl_aff_free(data->lower);
data->lower = lower;
*data->n = isl_val_get_num_si(max);
isl_val_free(max);
return isl_stat_ok;
}
/* Check if we can use "c" as a lower bound and if it is better than
* any previously found lower bound.
*/
static isl_stat constraint_find_unroll(__isl_take isl_constraint *c, void *user)
{
struct isl_find_unroll_data *data;
isl_stat r;
data = (struct isl_find_unroll_data *) user;
r = update_unrolling_lower_bound(data, c);
isl_constraint_free(c);
return r;
}
/* Look for a lower bound l(i) on the dimension at "depth"
* and a size n such that "domain" is a subset of
*
* { [i] : l(i) <= i_d < l(i) + n }
*
* where d is "depth" and l(i) depends only on earlier dimensions.
* Furthermore, try and find a lower bound such that n is as small as possible.
* In particular, "n" needs to be finite.
* "build" is the build in which the unrolling will be performed.
* "expansion" is the expansion that needs to be applied to "domain"
* in the unrolling that will be performed.
*
* Inner dimensions have been eliminated from "domain" by the caller.
*
* We first construct a collection of lower bounds on the input set
* by computing its simple hull. We then iterate through them,
* discarding those that we cannot use (either because they do not
* involve the dimension at "depth" or because they have no corresponding
* upper bound, meaning that "n" would be unbounded) and pick out the
* best from the remaining ones.
*
* If we cannot find a suitable lower bound, then we consider that
* to be an error.
*/
static __isl_give isl_aff *find_unroll_lower_bound(
__isl_keep isl_ast_build *build, __isl_keep isl_set *domain,
int depth, __isl_keep isl_basic_map *expansion, int *n)
{
struct isl_find_unroll_data data =
{ build, domain, depth, expansion, NULL, n, -1 };
isl_basic_set *hull;
hull = isl_set_simple_hull(isl_set_copy(domain));
if (isl_basic_set_foreach_constraint(hull,
&constraint_find_unroll, &data) < 0)
goto error;
isl_basic_set_free(hull);
if (!data.lower)
isl_die(isl_set_get_ctx(domain), isl_error_invalid,
"cannot find lower bound for unrolling", return NULL);
return data.lower;
error:
isl_basic_set_free(hull);
return isl_aff_free(data.lower);
}
/* Call "fn" on each iteration of the current dimension of "domain".
* If "init" is not NULL, then it is called with the number of
* iterations before any call to "fn".
* Return -1 on failure.
*
* Since we are going to be iterating over the individual values,
* we first check if there are any strides on the current dimension.
* If there is, we rewrite the current dimension i as
*
* i = stride i' + offset
*
* and then iterate over individual values of i' instead.
*
* We then look for a lower bound on i' and a size such that the domain
* is a subset of
*
* { [j,i'] : l(j) <= i' < l(j) + n }
*
* and then take slices of the domain at values of i'
* between l(j) and l(j) + n - 1.
*
* We compute the unshifted simple hull of each slice to ensure that
* we have a single basic set per offset. The slicing constraint
* may get simplified away before the unshifted simple hull is taken
* and may therefore in some rare cases disappear from the result.
* We therefore explicitly add the constraint back after computing
* the unshifted simple hull to ensure that the basic sets
* remain disjoint. The constraints that are dropped by taking the hull
* will be taken into account at the next level, as in the case of the
* atomic option.
*
* Finally, we map i' back to i and call "fn".
*/
static int foreach_iteration(__isl_take isl_set *domain,
__isl_keep isl_ast_build *build, int (*init)(int n, void *user),
int (*fn)(__isl_take isl_basic_set *bset, void *user), void *user)
{
int i, n;
isl_bool empty;
isl_size depth;
isl_multi_aff *expansion;
isl_basic_map *bmap;
isl_aff *lower = NULL;
isl_ast_build *stride_build;
depth = isl_ast_build_get_depth(build);
if (depth < 0)
domain = isl_set_free(domain);
domain = isl_ast_build_eliminate_inner(build, domain);
domain = isl_set_intersect(domain, isl_ast_build_get_domain(build));
stride_build = isl_ast_build_copy(build);
stride_build = isl_ast_build_detect_strides(stride_build,
isl_set_copy(domain));
expansion = isl_ast_build_get_stride_expansion(stride_build);
domain = isl_set_preimage_multi_aff(domain,
isl_multi_aff_copy(expansion));
domain = isl_ast_build_eliminate_divs(stride_build, domain);
isl_ast_build_free(stride_build);
bmap = isl_basic_map_from_multi_aff(expansion);
empty = isl_set_is_empty(domain);
if (empty < 0) {
n = -1;
} else if (empty) {
n = 0;
} else {
lower = find_unroll_lower_bound(build, domain, depth, bmap, &n);
if (!lower)
n = -1;
}
if (n >= 0 && init && init(n, user) < 0)
n = -1;
for (i = 0; i < n; ++i) {
isl_set *set;
isl_basic_set *bset;
isl_constraint *slice;
slice = at_offset(depth, lower, i);
set = isl_set_copy(domain);
set = isl_set_add_constraint(set, isl_constraint_copy(slice));
bset = isl_set_unshifted_simple_hull(set);
bset = isl_basic_set_add_constraint(bset, slice);
bset = isl_basic_set_apply(bset, isl_basic_map_copy(bmap));
if (fn(bset, user) < 0)
break;
}
isl_aff_free(lower);
isl_set_free(domain);
isl_basic_map_free(bmap);
return n < 0 || i < n ? -1 : 0;
}
/* Data structure for storing the results and the intermediate objects
* of compute_domains.
*
* "list" is the main result of the function and contains a list
* of disjoint basic sets for which code should be generated.
*
* "executed" and "build" are inputs to compute_domains.
* "schedule_domain" is the domain of "executed".
*
* "option" contains the domains at the current depth that should by
* atomic, separated or unrolled. These domains are as specified by
* the user, except that inner dimensions have been eliminated and
* that they have been made pair-wise disjoint.
*
* "sep_class" contains the user-specified split into separation classes
* specialized to the current depth.
* "done" contains the union of the separation domains that have already
* been handled.
*/
struct isl_codegen_domains {
isl_basic_set_list *list;
isl_union_map *executed;
isl_ast_build *build;
isl_set *schedule_domain;
isl_set *option[4];
isl_map *sep_class;
isl_set *done;
};
/* Internal data structure for do_unroll.
*
* "domains" stores the results of compute_domains.
* "class_domain" is the original class domain passed to do_unroll.
* "unroll_domain" collects the unrolled iterations.
*/
struct isl_ast_unroll_data {
struct isl_codegen_domains *domains;
isl_set *class_domain;
isl_set *unroll_domain;
};
/* Given an iteration of an unrolled domain represented by "bset",
* add it to data->domains->list.
* Since we may have dropped some constraints, we intersect with
* the class domain again to ensure that each element in the list
* is disjoint from the other class domains.
*/
static int do_unroll_iteration(__isl_take isl_basic_set *bset, void *user)
{
struct isl_ast_unroll_data *data = user;
isl_set *set;
isl_basic_set_list *list;
set = isl_set_from_basic_set(bset);
data->unroll_domain = isl_set_union(data->unroll_domain,
isl_set_copy(set));
set = isl_set_intersect(set, isl_set_copy(data->class_domain));
set = isl_set_make_disjoint(set);
list = isl_basic_set_list_from_set(set);
data->domains->list = isl_basic_set_list_concat(data->domains->list,
list);
return 0;
}
/* Extend domains->list with a list of basic sets, one for each value
* of the current dimension in "domain" and remove the corresponding
* sets from the class domain. Return the updated class domain.
* The divs that involve the current dimension have not been projected out
* from this domain.
*
* We call foreach_iteration to iterate over the individual values and
* in do_unroll_iteration we collect the individual basic sets in
* domains->list and their union in data->unroll_domain, which is then
* used to update the class domain.
*/
static __isl_give isl_set *do_unroll(struct isl_codegen_domains *domains,
__isl_take isl_set *domain, __isl_take isl_set *class_domain)
{
struct isl_ast_unroll_data data;
if (!domain)
return isl_set_free(class_domain);
if (!class_domain)
return isl_set_free(domain);
data.domains = domains;
data.class_domain = class_domain;
data.unroll_domain = isl_set_empty(isl_set_get_space(domain));
if (foreach_iteration(domain, domains->build, NULL,
&do_unroll_iteration, &data) < 0)
data.unroll_domain = isl_set_free(data.unroll_domain);
class_domain = isl_set_subtract(class_domain, data.unroll_domain);
return class_domain;
}
/* Add domains to domains->list for each individual value of the current
* dimension, for that part of the schedule domain that lies in the
* intersection of the option domain and the class domain.
* Remove the corresponding sets from the class domain and
* return the updated class domain.
*
* We first break up the unroll option domain into individual pieces
* and then handle each of them separately. The unroll option domain
* has been made disjoint in compute_domains_init_options,
*
* Note that we actively want to combine different pieces of the
* schedule domain that have the same value at the current dimension.
* We therefore need to break up the unroll option domain before
* intersecting with class and schedule domain, hoping that the
* unroll option domain specified by the user is relatively simple.
*/
static __isl_give isl_set *compute_unroll_domains(
struct isl_codegen_domains *domains, __isl_take isl_set *class_domain)
{
isl_set *unroll_domain;
isl_basic_set_list *unroll_list;
int i;
isl_size n;
isl_bool empty;
empty = isl_set_is_empty(domains->option[isl_ast_loop_unroll]);
if (empty < 0)
return isl_set_free(class_domain);
if (empty)
return class_domain;
unroll_domain = isl_set_copy(domains->option[isl_ast_loop_unroll]);
unroll_list = isl_basic_set_list_from_set(unroll_domain);
n = isl_basic_set_list_n_basic_set(unroll_list);
if (n < 0)
class_domain = isl_set_free(class_domain);
for (i = 0; i < n; ++i) {
isl_basic_set *bset;
bset = isl_basic_set_list_get_basic_set(unroll_list, i);
unroll_domain = isl_set_from_basic_set(bset);
unroll_domain = isl_set_intersect(unroll_domain,
isl_set_copy(class_domain));
unroll_domain = isl_set_intersect(unroll_domain,
isl_set_copy(domains->schedule_domain));
empty = isl_set_is_empty(unroll_domain);
if (empty >= 0 && empty) {
isl_set_free(unroll_domain);
continue;
}
class_domain = do_unroll(domains, unroll_domain, class_domain);
}
isl_basic_set_list_free(unroll_list);
return class_domain;
}
/* Try and construct a single basic set that includes the intersection of
* the schedule domain, the atomic option domain and the class domain.
* Add the resulting basic set(s) to domains->list and remove them
* from class_domain. Return the updated class domain.
*
* We construct a single domain rather than trying to combine
* the schedule domains of individual domains because we are working
* within a single component so that non-overlapping schedule domains
* should already have been separated.
* We do however need to make sure that this single domains is a subset
* of the class domain so that it would not intersect with any other
* class domains. This means that we may end up splitting up the atomic
* domain in case separation classes are being used.
*
* "domain" is the intersection of the schedule domain and the class domain,
* with inner dimensions projected out.
*/
static __isl_give isl_set *compute_atomic_domain(
struct isl_codegen_domains *domains, __isl_take isl_set *class_domain)
{
isl_basic_set *bset;
isl_basic_set_list *list;
isl_set *domain, *atomic_domain;
int empty;
domain = isl_set_copy(domains->option[isl_ast_loop_atomic]);
domain = isl_set_intersect(domain, isl_set_copy(class_domain));
domain = isl_set_intersect(domain,
isl_set_copy(domains->schedule_domain));
empty = isl_set_is_empty(domain);
if (empty < 0)
class_domain = isl_set_free(class_domain);
if (empty) {
isl_set_free(domain);
return class_domain;
}
domain = isl_ast_build_eliminate(domains->build, domain);
domain = isl_set_coalesce_preserve(domain);
bset = isl_set_unshifted_simple_hull(domain);
domain = isl_set_from_basic_set(bset);
atomic_domain = isl_set_copy(domain);
domain = isl_set_intersect(domain, isl_set_copy(class_domain));
class_domain = isl_set_subtract(class_domain, atomic_domain);
domain = isl_set_make_disjoint(domain);
list = isl_basic_set_list_from_set(domain);
domains->list = isl_basic_set_list_concat(domains->list, list);
return class_domain;
}
/* Split up the schedule domain into uniform basic sets,
* in the sense that each element in a basic set is associated to
* elements of the same domains, and add the result to domains->list.
* Do this for that part of the schedule domain that lies in the
* intersection of "class_domain" and the separate option domain.
*
* "class_domain" may or may not include the constraints
* of the schedule domain, but this does not make a difference
* since we are going to intersect it with the domain of the inverse schedule.
* If it includes schedule domain constraints, then they may involve
* inner dimensions, but we will eliminate them in separation_domain.
*/
static int compute_separate_domain(struct isl_codegen_domains *domains,
__isl_keep isl_set *class_domain)
{
isl_space *space;
isl_set *domain;
isl_union_map *executed;
isl_basic_set_list *list;
int empty;
domain = isl_set_copy(domains->option[isl_ast_loop_separate]);
domain = isl_set_intersect(domain, isl_set_copy(class_domain));
executed = isl_union_map_copy(domains->executed);
executed = isl_union_map_intersect_domain(executed,
isl_union_set_from_set(domain));
empty = isl_union_map_is_empty(executed);
if (empty < 0 || empty) {
isl_union_map_free(executed);
return empty < 0 ? -1 : 0;
}
space = isl_set_get_space(class_domain);
domain = separate_schedule_domains(space, executed, domains->build);
list = isl_basic_set_list_from_set(domain);
domains->list = isl_basic_set_list_concat(domains->list, list);
return 0;
}
/* Split up the domain at the current depth into disjoint
* basic sets for which code should be generated separately
* for the given separation class domain.
*
* If any separation classes have been defined, then "class_domain"
* is the domain of the current class and does not refer to inner dimensions.
* Otherwise, "class_domain" is the universe domain.
*
* We first make sure that the class domain is disjoint from
* previously considered class domains.
*
* The separate domains can be computed directly from the "class_domain".
*
* The unroll, atomic and remainder domains need the constraints
* from the schedule domain.
*
* For unrolling, the actual schedule domain is needed (with divs that
* may refer to the current dimension) so that stride detection can be
* performed.
*
* For atomic and remainder domains, inner dimensions and divs involving
* the current dimensions should be eliminated.
* In case we are working within a separation class, we need to intersect
* the result with the current "class_domain" to ensure that the domains
* are disjoint from those generated from other class domains.
*
* The domain that has been made atomic may be larger than specified
* by the user since it needs to be representable as a single basic set.
* This possibly larger domain is removed from class_domain by
* compute_atomic_domain. It is computed first so that the extended domain
* would not overlap with any domains computed before.
* Similary, the unrolled domains may have some constraints removed and
* may therefore also be larger than specified by the user.
*
* If anything is left after handling separate, unroll and atomic,
* we split it up into basic sets and append the basic sets to domains->list.
*/
static isl_stat compute_partial_domains(struct isl_codegen_domains *domains,
__isl_take isl_set *class_domain)
{
isl_basic_set_list *list;
isl_set *domain;
class_domain = isl_set_subtract(class_domain,
isl_set_copy(domains->done));
domains->done = isl_set_union(domains->done,
isl_set_copy(class_domain));
class_domain = compute_atomic_domain(domains, class_domain);
class_domain = compute_unroll_domains(domains, class_domain);
domain = isl_set_copy(class_domain);
if (compute_separate_domain(domains, domain) < 0)
goto error;
domain = isl_set_subtract(domain,
isl_set_copy(domains->option[isl_ast_loop_separate]));
domain = isl_set_intersect(domain,
isl_set_copy(domains->schedule_domain));
domain = isl_ast_build_eliminate(domains->build, domain);
domain = isl_set_intersect(domain, isl_set_copy(class_domain));
domain = isl_set_coalesce_preserve(domain);
domain = isl_set_make_disjoint(domain);
list = isl_basic_set_list_from_set(domain);
domains->list = isl_basic_set_list_concat(domains->list, list);
isl_set_free(class_domain);
return isl_stat_ok;
error:
isl_set_free(domain);
isl_set_free(class_domain);
return isl_stat_error;
}
/* Split up the domain at the current depth into disjoint
* basic sets for which code should be generated separately
* for the separation class identified by "pnt".
*
* We extract the corresponding class domain from domains->sep_class,
* eliminate inner dimensions and pass control to compute_partial_domains.
*/
static isl_stat compute_class_domains(__isl_take isl_point *pnt, void *user)
{
struct isl_codegen_domains *domains = user;
isl_set *class_set;
isl_set *domain;
int disjoint;
class_set = isl_set_from_point(pnt);
domain = isl_map_domain(isl_map_intersect_range(
isl_map_copy(domains->sep_class), class_set));
domain = isl_ast_build_compute_gist(domains->build, domain);
domain = isl_ast_build_eliminate(domains->build, domain);
disjoint = isl_set_plain_is_disjoint(domain, domains->schedule_domain);
if (disjoint < 0)
return isl_stat_error;
if (disjoint) {
isl_set_free(domain);
return isl_stat_ok;
}
return compute_partial_domains(domains, domain);
}
/* Extract the domains at the current depth that should be atomic,
* separated or unrolled and store them in option.
*
* The domains specified by the user might overlap, so we make
* them disjoint by subtracting earlier domains from later domains.
*/
static void compute_domains_init_options(isl_set *option[4],
__isl_keep isl_ast_build *build)
{
enum isl_ast_loop_type type, type2;
isl_set *unroll;
for (type = isl_ast_loop_atomic;
type <= isl_ast_loop_separate; ++type) {
option[type] = isl_ast_build_get_option_domain(build, type);
for (type2 = isl_ast_loop_atomic; type2 < type; ++type2)
option[type] = isl_set_subtract(option[type],
isl_set_copy(option[type2]));
}
unroll = option[isl_ast_loop_unroll];
unroll = isl_set_coalesce(unroll);
unroll = isl_set_make_disjoint(unroll);
option[isl_ast_loop_unroll] = unroll;
}
/* Split up the domain at the current depth into disjoint
* basic sets for which code should be generated separately,
* based on the user-specified options.
* Return the list of disjoint basic sets.
*
* There are three kinds of domains that we need to keep track of.
* - the "schedule domain" is the domain of "executed"
* - the "class domain" is the domain corresponding to the currrent
* separation class
* - the "option domain" is the domain corresponding to one of the options
* atomic, unroll or separate
*
* We first consider the individial values of the separation classes
* and split up the domain for each of them separately.
* Finally, we consider the remainder. If no separation classes were
* specified, then we call compute_partial_domains with the universe
* "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
* with inner dimensions removed. We do this because we want to
* avoid computing the complement of the class domains (i.e., the difference
* between the universe and domains->done).
*/
static __isl_give isl_basic_set_list *compute_domains(
__isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
{
struct isl_codegen_domains domains;
isl_ctx *ctx;
isl_set *domain;
isl_union_set *schedule_domain;
isl_set *classes;
isl_space *space;
int n_param;
enum isl_ast_loop_type type;
isl_bool empty;
if (!executed)
return NULL;
ctx = isl_union_map_get_ctx(executed);
domains.list = isl_basic_set_list_alloc(ctx, 0);
schedule_domain = isl_union_map_domain(isl_union_map_copy(executed));
domain = isl_set_from_union_set(schedule_domain);
compute_domains_init_options(domains.option, build);
domains.sep_class = isl_ast_build_get_separation_class(build);
classes = isl_map_range(isl_map_copy(domains.sep_class));
n_param = isl_set_dim(classes, isl_dim_param);
if (n_param < 0)
classes = isl_set_free(classes);
classes = isl_set_project_out(classes, isl_dim_param, 0, n_param);
space = isl_set_get_space(domain);
domains.build = build;
domains.schedule_domain = isl_set_copy(domain);
domains.executed = executed;
domains.done = isl_set_empty(space);
if (isl_set_foreach_point(classes, &compute_class_domains, &domains) < 0)
domains.list = isl_basic_set_list_free(domains.list);
isl_set_free(classes);
empty = isl_set_is_empty(domains.done);
if (empty < 0) {
domains.list = isl_basic_set_list_free(domains.list);
domain = isl_set_free(domain);
} else if (empty) {
isl_set_free(domain);
domain = isl_set_universe(isl_set_get_space(domains.done));
} else {
domain = isl_ast_build_eliminate(build, domain);
}
if (compute_partial_domains(&domains, domain) < 0)
domains.list = isl_basic_set_list_free(domains.list);
isl_set_free(domains.schedule_domain);
isl_set_free(domains.done);
isl_map_free(domains.sep_class);
for (type = isl_ast_loop_atomic; type <= isl_ast_loop_separate; ++type)
isl_set_free(domains.option[type]);
return domains.list;
}
/* Generate code for a single component, after shifting (if any)
* has been applied, in case the schedule was specified as a union map.
*
* We first split up the domain at the current depth into disjoint
* basic sets based on the user-specified options.
* Then we generated code for each of them and concatenate the results.
*/
static __isl_give isl_ast_graft_list *generate_shifted_component_flat(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
{
isl_basic_set_list *domain_list;
isl_ast_graft_list *list = NULL;
domain_list = compute_domains(executed, build);
list = generate_parallel_domains(domain_list, executed, build);
isl_basic_set_list_free(domain_list);
isl_union_map_free(executed);
isl_ast_build_free(build);
return list;
}
/* Generate code for a single component, after shifting (if any)
* has been applied, in case the schedule was specified as a schedule tree
* and the separate option was specified.
*
* We perform separation on the domain of "executed" and then generate
* an AST for each of the resulting disjoint basic sets.
*/
static __isl_give isl_ast_graft_list *generate_shifted_component_tree_separate(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
{
isl_space *space;
isl_set *domain;
isl_basic_set_list *domain_list;
isl_ast_graft_list *list;
space = isl_ast_build_get_space(build, 1);
domain = separate_schedule_domains(space,
isl_union_map_copy(executed), build);
domain_list = isl_basic_set_list_from_set(domain);
list = generate_parallel_domains(domain_list, executed, build);
isl_basic_set_list_free(domain_list);
isl_union_map_free(executed);
isl_ast_build_free(build);
return list;
}
/* Internal data structure for generate_shifted_component_tree_unroll.
*
* "executed" and "build" are inputs to generate_shifted_component_tree_unroll.
* "list" collects the constructs grafts.
*/
struct isl_ast_unroll_tree_data {
isl_union_map *executed;
isl_ast_build *build;
isl_ast_graft_list *list;
};
/* Initialize data->list to a list of "n" elements.
*/
static int init_unroll_tree(int n, void *user)
{
struct isl_ast_unroll_tree_data *data = user;
isl_ctx *ctx;
ctx = isl_ast_build_get_ctx(data->build);
data->list = isl_ast_graft_list_alloc(ctx, n);
return 0;
}
/* Given an iteration of an unrolled domain represented by "bset",
* generate the corresponding AST and add the result to data->list.
*/
static int do_unroll_tree_iteration(__isl_take isl_basic_set *bset, void *user)
{
struct isl_ast_unroll_tree_data *data = user;
data->list = add_node(data->list, isl_union_map_copy(data->executed),
bset, isl_ast_build_copy(data->build));
return 0;
}
/* Generate code for a single component, after shifting (if any)
* has been applied, in case the schedule was specified as a schedule tree
* and the unroll option was specified.
*
* We call foreach_iteration to iterate over the individual values and
* construct and collect the corresponding grafts in do_unroll_tree_iteration.
*/
static __isl_give isl_ast_graft_list *generate_shifted_component_tree_unroll(
__isl_take isl_union_map *executed, __isl_take isl_set *domain,
__isl_take isl_ast_build *build)
{
struct isl_ast_unroll_tree_data data = { executed, build, NULL };
if (foreach_iteration(domain, build, &init_unroll_tree,
&do_unroll_tree_iteration, &data) < 0)
data.list = isl_ast_graft_list_free(data.list);
isl_union_map_free(executed);
isl_ast_build_free(build);
return data.list;
}
/* Does "domain" involve a disjunction that is purely based on
* constraints involving only outer dimension?
*
* In particular, is there a disjunction such that the constraints
* involving the current and later dimensions are the same over
* all the disjuncts?
*/
static isl_bool has_pure_outer_disjunction(__isl_keep isl_set *domain,
__isl_keep isl_ast_build *build)
{
isl_basic_set *hull;
isl_set *shared, *inner;
isl_bool equal;
isl_size depth;
isl_size n;
isl_size dim;
n = isl_set_n_basic_set(domain);
if (n < 0)
return isl_bool_error;
if (n <= 1)
return isl_bool_false;
dim = isl_set_dim(domain, isl_dim_set);
depth = isl_ast_build_get_depth(build);
if (dim < 0 || depth < 0)
return isl_bool_error;
inner = isl_set_copy(domain);
inner = isl_set_drop_constraints_not_involving_dims(inner,
isl_dim_set, depth, dim - depth);
hull = isl_set_plain_unshifted_simple_hull(isl_set_copy(inner));
shared = isl_set_from_basic_set(hull);
equal = isl_set_plain_is_equal(inner, shared);
isl_set_free(inner);
isl_set_free(shared);
return equal;
}
/* Generate code for a single component, after shifting (if any)
* has been applied, in case the schedule was specified as a schedule tree.
* In particular, handle the base case where there is either no isolated
* set or we are within the isolated set (in which case "isolated" is set)
* or the iterations that precede or follow the isolated set.
*
* The schedule domain is broken up or combined into basic sets
* according to the AST generation option specified in the current
* schedule node, which may be either atomic, separate, unroll or
* unspecified. If the option is unspecified, then we currently simply
* split the schedule domain into disjoint basic sets.
*
* In case the separate option is specified, the AST generation is
* handled by generate_shifted_component_tree_separate.
* In the other cases, we need the global schedule domain.
* In the unroll case, the AST generation is then handled by
* generate_shifted_component_tree_unroll which needs the actual
* schedule domain (with divs that may refer to the current dimension)
* so that stride detection can be performed.
* In the atomic or unspecified case, inner dimensions and divs involving
* the current dimensions should be eliminated.
* The result is then either combined into a single basic set or
* split up into disjoint basic sets.
* Finally an AST is generated for each basic set and the results are
* concatenated.
*
* If the schedule domain involves a disjunction that is purely based on
* constraints involving only outer dimension, then it is treated as
* if atomic was specified. This ensures that only a single loop
* is generated instead of a sequence of identical loops with
* different guards.
*/
static __isl_give isl_ast_graft_list *generate_shifted_component_tree_base(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build,
int isolated)
{
isl_bool outer_disjunction;
isl_union_set *schedule_domain;
isl_set *domain;
isl_basic_set_list *domain_list;
isl_ast_graft_list *list;
enum isl_ast_loop_type type;
type = isl_ast_build_get_loop_type(build, isolated);
if (type < 0)
goto error;
if (type == isl_ast_loop_separate)
return generate_shifted_component_tree_separate(executed,
build);
schedule_domain = isl_union_map_domain(isl_union_map_copy(executed));
domain = isl_set_from_union_set(schedule_domain);
if (type == isl_ast_loop_unroll)
return generate_shifted_component_tree_unroll(executed, domain,
build);
domain = isl_ast_build_eliminate(build, domain);
domain = isl_set_coalesce_preserve(domain);
outer_disjunction = has_pure_outer_disjunction(domain, build);
if (outer_disjunction < 0)
domain = isl_set_free(domain);
if (outer_disjunction || type == isl_ast_loop_atomic) {
isl_basic_set *hull;
hull = isl_set_unshifted_simple_hull(domain);
domain_list = isl_basic_set_list_from_basic_set(hull);
} else {
domain = isl_set_make_disjoint(domain);
domain_list = isl_basic_set_list_from_set(domain);
}
list = generate_parallel_domains(domain_list, executed, build);
isl_basic_set_list_free(domain_list);
isl_union_map_free(executed);
isl_ast_build_free(build);
return list;
error:
isl_union_map_free(executed);
isl_ast_build_free(build);
return NULL;
}
/* Extract out the disjunction imposed by "domain" on the outer
* schedule dimensions.
*
* In particular, remove all inner dimensions from "domain" (including
* the current dimension) and then remove the constraints that are shared
* by all disjuncts in the result.
*/
static __isl_give isl_set *extract_disjunction(__isl_take isl_set *domain,
__isl_keep isl_ast_build *build)
{
isl_set *hull;
isl_size depth;
isl_size dim;
domain = isl_ast_build_specialize(build, domain);
depth = isl_ast_build_get_depth(build);
dim = isl_set_dim(domain, isl_dim_set);
if (depth < 0 || dim < 0)
return isl_set_free(domain);
domain = isl_set_eliminate(domain, isl_dim_set, depth, dim - depth);
domain = isl_set_remove_unknown_divs(domain);
hull = isl_set_copy(domain);
hull = isl_set_from_basic_set(isl_set_unshifted_simple_hull(hull));
domain = isl_set_gist(domain, hull);
return domain;
}
/* Add "guard" to the grafts in "list".
* "build" is the outer AST build, while "sub_build" includes "guard"
* in its generated domain.
*
* First combine the grafts into a single graft and then add the guard.
* If the list is empty, or if some error occurred, then simply return
* the list.
*/
static __isl_give isl_ast_graft_list *list_add_guard(
__isl_take isl_ast_graft_list *list, __isl_keep isl_set *guard,
__isl_keep isl_ast_build *build, __isl_keep isl_ast_build *sub_build)
{
isl_ast_graft *graft;
isl_size n;
list = isl_ast_graft_list_fuse(list, sub_build);
n = isl_ast_graft_list_n_ast_graft(list);
if (n < 0)
return isl_ast_graft_list_free(list);
if (n != 1)
return list;
graft = isl_ast_graft_list_get_ast_graft(list, 0);
graft = isl_ast_graft_add_guard(graft, isl_set_copy(guard), build);
list = isl_ast_graft_list_set_ast_graft(list, 0, graft);
return list;
}
/* Generate code for a single component, after shifting (if any)
* has been applied, in case the schedule was specified as a schedule tree.
* In particular, do so for the specified subset of the schedule domain.
*
* If we are outside of the isolated part, then "domain" may include
* a disjunction. Explicitly generate this disjunction at this point
* instead of relying on the disjunction getting hoisted back up
* to this level.
*/
static __isl_give isl_ast_graft_list *generate_shifted_component_tree_part(
__isl_keep isl_union_map *executed, __isl_take isl_set *domain,
__isl_keep isl_ast_build *build, int isolated)
{
isl_union_set *uset;
isl_ast_graft_list *list;
isl_ast_build *sub_build;
int empty;
uset = isl_union_set_from_set(isl_set_copy(domain));
executed = isl_union_map_copy(executed);
executed = isl_union_map_intersect_domain(executed, uset);
empty = isl_union_map_is_empty(executed);
if (empty < 0)
goto error;
if (empty) {
isl_ctx *ctx;
isl_union_map_free(executed);
isl_set_free(domain);
ctx = isl_ast_build_get_ctx(build);
return isl_ast_graft_list_alloc(ctx, 0);
}
sub_build = isl_ast_build_copy(build);
if (!isolated) {
domain = extract_disjunction(domain, build);
sub_build = isl_ast_build_restrict_generated(sub_build,
isl_set_copy(domain));
}
list = generate_shifted_component_tree_base(executed,
isl_ast_build_copy(sub_build), isolated);
if (!isolated)
list = list_add_guard(list, domain, build, sub_build);
isl_ast_build_free(sub_build);
isl_set_free(domain);
return list;
error:
isl_union_map_free(executed);
isl_set_free(domain);
return NULL;
}
/* Generate code for a single component, after shifting (if any)
* has been applied, in case the schedule was specified as a schedule tree.
* In particular, do so for the specified sequence of subsets
* of the schedule domain, "before", "isolated", "after" and "other",
* where only the "isolated" part is considered to be isolated.
*/
static __isl_give isl_ast_graft_list *generate_shifted_component_parts(
__isl_take isl_union_map *executed, __isl_take isl_set *before,
__isl_take isl_set *isolated, __isl_take isl_set *after,
__isl_take isl_set *other, __isl_take isl_ast_build *build)
{
isl_ast_graft_list *list, *res;
res = generate_shifted_component_tree_part(executed, before, build, 0);
list = generate_shifted_component_tree_part(executed, isolated,
build, 1);
res = isl_ast_graft_list_concat(res, list);
list = generate_shifted_component_tree_part(executed, after, build, 0);
res = isl_ast_graft_list_concat(res, list);
list = generate_shifted_component_tree_part(executed, other, build, 0);
res = isl_ast_graft_list_concat(res, list);
isl_union_map_free(executed);
isl_ast_build_free(build);
return res;
}
/* Does "set" intersect "first", but not "second"?
*/
static isl_bool only_intersects_first(__isl_keep isl_set *set,
__isl_keep isl_set *first, __isl_keep isl_set *second)
{
isl_bool disjoint;
disjoint = isl_set_is_disjoint(set, first);
if (disjoint < 0)
return isl_bool_error;
if (disjoint)
return isl_bool_false;
return isl_set_is_disjoint(set, second);
}
/* Generate code for a single component, after shifting (if any)
* has been applied, in case the schedule was specified as a schedule tree.
* In particular, do so in case of isolation where there is
* only an "isolated" part and an "after" part.
* "dead1" and "dead2" are freed by this function in order to simplify
* the caller.
*
* The "before" and "other" parts are set to empty sets.
*/
static __isl_give isl_ast_graft_list *generate_shifted_component_only_after(
__isl_take isl_union_map *executed, __isl_take isl_set *isolated,
__isl_take isl_set *after, __isl_take isl_ast_build *build,
__isl_take isl_set *dead1, __isl_take isl_set *dead2)
{
isl_set *empty;
empty = isl_set_empty(isl_set_get_space(after));
isl_set_free(dead1);
isl_set_free(dead2);
return generate_shifted_component_parts(executed, isl_set_copy(empty),
isolated, after, empty, build);
}
/* Generate code for a single component, after shifting (if any)
* has been applied, in case the schedule was specified as a schedule tree.
*
* We first check if the user has specified an isolated schedule domain
* and that we are not already outside of this isolated schedule domain.
* If so, we break up the schedule domain into iterations that
* precede the isolated domain, the isolated domain itself,
* the iterations that follow the isolated domain and
* the remaining iterations (those that are incomparable
* to the isolated domain).
* We generate an AST for each piece and concatenate the results.
*
* If the isolated domain is not convex, then it is replaced
* by a convex superset to ensure that the sets of preceding and
* following iterations are properly defined and, in particular,
* that there are no intermediate iterations that do not belong
* to the isolated domain.
*
* In the special case where at least one element of the schedule
* domain that does not belong to the isolated domain needs
* to be scheduled after this isolated domain, but none of those
* elements need to be scheduled before, break up the schedule domain
* in only two parts, the isolated domain, and a part that will be
* scheduled after the isolated domain.
*
* If no isolated set has been specified, then we generate an
* AST for the entire inverse schedule.
*/
static __isl_give isl_ast_graft_list *generate_shifted_component_tree(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
{
int i;
isl_size depth;
int empty, has_isolate;
isl_space *space;
isl_union_set *schedule_domain;
isl_set *domain;
isl_basic_set *hull;
isl_set *isolated, *before, *after, *test;
isl_map *gt, *lt;
isl_bool pure;
build = isl_ast_build_extract_isolated(build);
has_isolate = isl_ast_build_has_isolated(build);
if (has_isolate < 0)
executed = isl_union_map_free(executed);
else if (!has_isolate)
return generate_shifted_component_tree_base(executed, build, 0);
schedule_domain = isl_union_map_domain(isl_union_map_copy(executed));
domain = isl_set_from_union_set(schedule_domain);
isolated = isl_ast_build_get_isolated(build);
isolated = isl_set_intersect(isolated, isl_set_copy(domain));
test = isl_ast_build_specialize(build, isl_set_copy(isolated));
empty = isl_set_is_empty(test);
isl_set_free(test);
if (empty < 0)
goto error;
if (empty) {
isl_set_free(isolated);
isl_set_free(domain);
return generate_shifted_component_tree_base(executed, build, 0);
}
depth = isl_ast_build_get_depth(build);
if (depth < 0)
goto error;
isolated = isl_ast_build_eliminate(build, isolated);
hull = isl_set_unshifted_simple_hull(isolated);
isolated = isl_set_from_basic_set(hull);
space = isl_space_map_from_set(isl_set_get_space(isolated));
gt = isl_map_universe(space);
for (i = 0; i < depth; ++i)
gt = isl_map_equate(gt, isl_dim_in, i, isl_dim_out, i);
gt = isl_map_order_gt(gt, isl_dim_in, depth, isl_dim_out, depth);
lt = isl_map_reverse(isl_map_copy(gt));
before = isl_set_apply(isl_set_copy(isolated), gt);
after = isl_set_apply(isl_set_copy(isolated), lt);
domain = isl_set_subtract(domain, isl_set_copy(isolated));
pure = only_intersects_first(domain, after, before);
if (pure < 0)
executed = isl_union_map_free(executed);
else if (pure)
return generate_shifted_component_only_after(executed, isolated,
domain, build, before, after);
domain = isl_set_subtract(domain, isl_set_copy(before));
domain = isl_set_subtract(domain, isl_set_copy(after));
after = isl_set_subtract(after, isl_set_copy(isolated));
after = isl_set_subtract(after, isl_set_copy(before));
before = isl_set_subtract(before, isl_set_copy(isolated));
return generate_shifted_component_parts(executed, before, isolated,
after, domain, build);
error:
isl_set_free(domain);
isl_set_free(isolated);
isl_union_map_free(executed);
isl_ast_build_free(build);
return NULL;
}
/* Generate code for a single component, after shifting (if any)
* has been applied.
*
* Call generate_shifted_component_tree or generate_shifted_component_flat
* depending on whether the schedule was specified as a schedule tree.
*/
static __isl_give isl_ast_graft_list *generate_shifted_component(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
{
if (isl_ast_build_has_schedule_node(build))
return generate_shifted_component_tree(executed, build);
else
return generate_shifted_component_flat(executed, build);
}
struct isl_set_map_pair {
isl_set *set;
isl_map *map;
};
/* Given an array "domain" of isl_set_map_pairs and an array "order"
* of indices into the "domain" array,
* return the union of the "map" fields of the elements
* indexed by the first "n" elements of "order".
*/
static __isl_give isl_union_map *construct_component_executed(
struct isl_set_map_pair *domain, int *order, int n)
{
int i;
isl_map *map;
isl_union_map *executed;
map = isl_map_copy(domain[order[0]].map);
executed = isl_union_map_from_map(map);
for (i = 1; i < n; ++i) {
map = isl_map_copy(domain[order[i]].map);
executed = isl_union_map_add_map(executed, map);
}
return executed;
}
/* Generate code for a single component, after shifting (if any)
* has been applied.
*
* The component inverse schedule is specified as the "map" fields
* of the elements of "domain" indexed by the first "n" elements of "order".
*/
static __isl_give isl_ast_graft_list *generate_shifted_component_from_list(
struct isl_set_map_pair *domain, int *order, int n,
__isl_take isl_ast_build *build)
{
isl_union_map *executed;
executed = construct_component_executed(domain, order, n);
return generate_shifted_component(executed, build);
}
/* Does set dimension "pos" of "set" have an obviously fixed value?
*/
static int dim_is_fixed(__isl_keep isl_set *set, int pos)
{
int fixed;
isl_val *v;
v = isl_set_plain_get_val_if_fixed(set, isl_dim_set, pos);
if (!v)
return -1;
fixed = !isl_val_is_nan(v);
isl_val_free(v);
return fixed;
}
/* Given an array "domain" of isl_set_map_pairs and an array "order"
* of indices into the "domain" array,
* do all (except for at most one) of the "set" field of the elements
* indexed by the first "n" elements of "order" have a fixed value
* at position "depth"?
*/
static int at_most_one_non_fixed(struct isl_set_map_pair *domain,
int *order, int n, int depth)
{
int i;
int non_fixed = -1;
for (i = 0; i < n; ++i) {
int f;
f = dim_is_fixed(domain[order[i]].set, depth);
if (f < 0)
return -1;
if (f)
continue;
if (non_fixed >= 0)
return 0;
non_fixed = i;
}
return 1;
}
/* Given an array "domain" of isl_set_map_pairs and an array "order"
* of indices into the "domain" array,
* eliminate the inner dimensions from the "set" field of the elements
* indexed by the first "n" elements of "order", provided the current
* dimension does not have a fixed value.
*
* Return the index of the first element in "order" with a corresponding
* "set" field that does not have an (obviously) fixed value.
*/
static int eliminate_non_fixed(struct isl_set_map_pair *domain,
int *order, int n, int depth, __isl_keep isl_ast_build *build)
{
int i;
int base = -1;
for (i = n - 1; i >= 0; --i) {
int f;
f = dim_is_fixed(domain[order[i]].set, depth);
if (f < 0)
return -1;
if (f)
continue;
domain[order[i]].set = isl_ast_build_eliminate_inner(build,
domain[order[i]].set);
base = i;
}
return base;
}
/* Given an array "domain" of isl_set_map_pairs and an array "order"
* of indices into the "domain" array,
* find the element of "domain" (amongst those indexed by the first "n"
* elements of "order") with the "set" field that has the smallest
* value for the current iterator.
*
* Note that the domain with the smallest value may depend on the parameters
* and/or outer loop dimension. Since the result of this function is only
* used as heuristic, we only make a reasonable attempt at finding the best
* domain, one that should work in case a single domain provides the smallest
* value for the current dimension over all values of the parameters
* and outer dimensions.
*
* In particular, we compute the smallest value of the first domain
* and replace it by that of any later domain if that later domain
* has a smallest value that is smaller for at least some value
* of the parameters and outer dimensions.
*/
static int first_offset(struct isl_set_map_pair *domain, int *order, int n,
__isl_keep isl_ast_build *build)
{
int i;
isl_map *min_first;
int first = 0;
min_first = isl_ast_build_map_to_iterator(build,
isl_set_copy(domain[order[0]].set));
min_first = isl_map_lexmin(min_first);
for (i = 1; i < n; ++i) {
isl_map *min, *test;
int empty;
min = isl_ast_build_map_to_iterator(build,
isl_set_copy(domain[order[i]].set));
min = isl_map_lexmin(min);
test = isl_map_copy(min);
test = isl_map_apply_domain(isl_map_copy(min_first), test);
test = isl_map_order_lt(test, isl_dim_in, 0, isl_dim_out, 0);
empty = isl_map_is_empty(test);
isl_map_free(test);
if (empty >= 0 && !empty) {
isl_map_free(min_first);
first = i;
min_first = min;
} else
isl_map_free(min);
if (empty < 0)
break;
}
isl_map_free(min_first);
return i < n ? -1 : first;
}
/* Construct a shifted inverse schedule based on the original inverse schedule,
* the stride and the offset.
*
* The original inverse schedule is specified as the "map" fields
* of the elements of "domain" indexed by the first "n" elements of "order".
*
* "stride" and "offset" are such that the difference
* between the values of the current dimension of domain "i"
* and the values of the current dimension for some reference domain are
* equal to
*
* stride * integer + offset[i]
*
* Moreover, 0 <= offset[i] < stride.
*
* For each domain, we create a map
*
* { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
*
* where j refers to the current dimension and the other dimensions are
* unchanged, and apply this map to the original schedule domain.
*
* For example, for the original schedule
*
* { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
*
* and assuming the offset is 0 for the A domain and 1 for the B domain,
* we apply the mapping
*
* { [j] -> [j, 0] }
*
* to the schedule of the "A" domain and the mapping
*
* { [j - 1] -> [j, 1] }
*
* to the schedule of the "B" domain.
*
*
* Note that after the transformation, the differences between pairs
* of values of the current dimension over all domains are multiples
* of stride and that we have therefore exposed the stride.
*
*
* To see that the mapping preserves the lexicographic order,
* first note that each of the individual maps above preserves the order.
* If the value of the current iterator is j1 in one domain and j2 in another,
* then if j1 = j2, we know that the same map is applied to both domains
* and the order is preserved.
* Otherwise, let us assume, without loss of generality, that j1 < j2.
* If c1 >= c2 (with c1 and c2 the corresponding offsets), then
*
* j1 - c1 < j2 - c2
*
* and the order is preserved.
* If c1 < c2, then we know
*
* 0 <= c2 - c1 < s
*
* We also have
*
* j2 - j1 = n * s + r
*
* with n >= 0 and 0 <= r < s.
* In other words, r = c2 - c1.
* If n > 0, then
*
* j1 - c1 < j2 - c2
*
* If n = 0, then
*
* j1 - c1 = j2 - c2
*
* and so
*
* (j1 - c1, c1) << (j2 - c2, c2)
*
* with "<<" the lexicographic order, proving that the order is preserved
* in all cases.
*/
static __isl_give isl_union_map *construct_shifted_executed(
struct isl_set_map_pair *domain, int *order, int n,
__isl_keep isl_val *stride, __isl_keep isl_multi_val *offset,
__isl_keep isl_ast_build *build)
{
int i;
isl_union_map *executed;
isl_space *space;
isl_map *map;
isl_size depth;
isl_constraint *c;
depth = isl_ast_build_get_depth(build);
if (depth < 0)
return NULL;
space = isl_ast_build_get_space(build, 1);
executed = isl_union_map_empty(isl_space_copy(space));
space = isl_space_map_from_set(space);
map = isl_map_identity(isl_space_copy(space));
map = isl_map_eliminate(map, isl_dim_out, depth, 1);
map = isl_map_insert_dims(map, isl_dim_out, depth + 1, 1);
space = isl_space_insert_dims(space, isl_dim_out, depth + 1, 1);
c = isl_constraint_alloc_equality(isl_local_space_from_space(space));
c = isl_constraint_set_coefficient_si(c, isl_dim_in, depth, 1);
c = isl_constraint_set_coefficient_si(c, isl_dim_out, depth, -1);
for (i = 0; i < n; ++i) {
isl_map *map_i;
isl_val *v;
v = isl_multi_val_get_val(offset, i);
if (!v)
break;
map_i = isl_map_copy(map);
map_i = isl_map_fix_val(map_i, isl_dim_out, depth + 1,
isl_val_copy(v));
v = isl_val_neg(v);
c = isl_constraint_set_constant_val(c, v);
map_i = isl_map_add_constraint(map_i, isl_constraint_copy(c));
map_i = isl_map_apply_domain(isl_map_copy(domain[order[i]].map),
map_i);
executed = isl_union_map_add_map(executed, map_i);
}
isl_constraint_free(c);
isl_map_free(map);
if (i < n)
executed = isl_union_map_free(executed);
return executed;
}
/* Generate code for a single component, after exposing the stride,
* given that the schedule domain is "shifted strided".
*
* The component inverse schedule is specified as the "map" fields
* of the elements of "domain" indexed by the first "n" elements of "order".
*
* The schedule domain being "shifted strided" means that the differences
* between the values of the current dimension of domain "i"
* and the values of the current dimension for some reference domain are
* equal to
*
* stride * integer + offset[i]
*
* We first look for the domain with the "smallest" value for the current
* dimension and adjust the offsets such that the offset of the "smallest"
* domain is equal to zero. The other offsets are reduced modulo stride.
*
* Based on this information, we construct a new inverse schedule in
* construct_shifted_executed that exposes the stride.
* Since this involves the introduction of a new schedule dimension,
* the build needs to be changed accordingly.
* After computing the AST, the newly introduced dimension needs
* to be removed again from the list of grafts. We do this by plugging
* in a mapping that represents the new schedule domain in terms of the
* old schedule domain.
*/
static __isl_give isl_ast_graft_list *generate_shift_component(
struct isl_set_map_pair *domain, int *order, int n,
__isl_keep isl_val *stride, __isl_keep isl_multi_val *offset,
__isl_take isl_ast_build *build)
{
isl_ast_graft_list *list;
int first;
isl_size depth;
isl_val *val;
isl_multi_val *mv;
isl_space *space;
isl_multi_aff *ma, *zero;
isl_union_map *executed;
depth = isl_ast_build_get_depth(build);
first = first_offset(domain, order, n, build);
if (depth < 0 || first < 0)
goto error;
mv = isl_multi_val_copy(offset);
val = isl_multi_val_get_val(offset, first);
val = isl_val_neg(val);
mv = isl_multi_val_add_val(mv, val);
mv = isl_multi_val_mod_val(mv, isl_val_copy(stride));
executed = construct_shifted_executed(domain, order, n, stride, mv,
build);
space = isl_ast_build_get_space(build, 1);
space = isl_space_map_from_set(space);
ma = isl_multi_aff_identity(isl_space_copy(space));
space = isl_space_from_domain(isl_space_domain(space));
space = isl_space_add_dims(space, isl_dim_out, 1);
zero = isl_multi_aff_zero(space);
ma = isl_multi_aff_range_splice(ma, depth + 1, zero);
build = isl_ast_build_insert_dim(build, depth + 1);
list = generate_shifted_component(executed, build);
list = isl_ast_graft_list_preimage_multi_aff(list, ma);
isl_multi_val_free(mv);
return list;
error:
isl_ast_build_free(build);
return NULL;
}
/* Does any node in the schedule tree rooted at the current schedule node
* of "build" depend on outer schedule nodes?
*/
static int has_anchored_subtree(__isl_keep isl_ast_build *build)
{
isl_schedule_node *node;
int dependent = 0;
node = isl_ast_build_get_schedule_node(build);
dependent = isl_schedule_node_is_subtree_anchored(node);
isl_schedule_node_free(node);
return dependent;
}
/* Generate code for a single component.
*
* The component inverse schedule is specified as the "map" fields
* of the elements of "domain" indexed by the first "n" elements of "order".
*
* This function may modify the "set" fields of "domain".
*
* Before proceeding with the actual code generation for the component,
* we first check if there are any "shifted" strides, meaning that
* the schedule domains of the individual domains are all strided,
* but that they have different offsets, resulting in the union
* of schedule domains not being strided anymore.
*
* The simplest example is the schedule
*
* { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
*
* Both schedule domains are strided, but their union is not.
* This function detects such cases and then rewrites the schedule to
*
* { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
*
* In the new schedule, the schedule domains have the same offset (modulo
* the stride), ensuring that the union of schedule domains is also strided.
*
*
* If there is only a single domain in the component, then there is
* nothing to do. Similarly, if the current schedule dimension has
* a fixed value for almost all domains then there is nothing to be done.
* In particular, we need at least two domains where the current schedule
* dimension does not have a fixed value.
* Finally, in case of a schedule map input,
* if any of the options refer to the current schedule dimension,
* then we bail out as well. It would be possible to reformulate the options
* in terms of the new schedule domain, but that would introduce constraints
* that separate the domains in the options and that is something we would
* like to avoid.
* In the case of a schedule tree input, we bail out if any of
* the descendants of the current schedule node refer to outer
* schedule nodes in any way.
*
*
* To see if there is any shifted stride, we look at the differences
* between the values of the current dimension in pairs of domains
* for equal values of outer dimensions. These differences should be
* of the form
*
* m x + r
*
* with "m" the stride and "r" a constant. Note that we cannot perform
* this analysis on individual domains as the lower bound in each domain
* may depend on parameters or outer dimensions and so the current dimension
* itself may not have a fixed remainder on division by the stride.
*
* In particular, we compare the first domain that does not have an
* obviously fixed value for the current dimension to itself and all
* other domains and collect the offsets and the gcd of the strides.
* If the gcd becomes one, then we failed to find shifted strides.
* If the gcd is zero, then the differences were all fixed, meaning
* that some domains had non-obviously fixed values for the current dimension.
* If all the offsets are the same (for those domains that do not have
* an obviously fixed value for the current dimension), then we do not
* apply the transformation.
* If none of the domains were skipped, then there is nothing to do.
* If some of them were skipped, then if we apply separation, the schedule
* domain should get split in pieces with a (non-shifted) stride.
*
* Otherwise, we apply a shift to expose the stride in
* generate_shift_component.
*/
static __isl_give isl_ast_graft_list *generate_component(
struct isl_set_map_pair *domain, int *order, int n,
__isl_take isl_ast_build *build)
{
int i, d;
isl_size depth;
isl_ctx *ctx;
isl_map *map;
isl_set *deltas;
isl_val *gcd = NULL;
isl_multi_val *mv;
int fixed, skip;
int base;
isl_ast_graft_list *list;
int res = 0;
depth = isl_ast_build_get_depth(build);
if (depth < 0)
goto error;
skip = n == 1;
if (skip >= 0 && !skip)
skip = at_most_one_non_fixed(domain, order, n, depth);
if (skip >= 0 && !skip) {
if (isl_ast_build_has_schedule_node(build))
skip = has_anchored_subtree(build);
else
skip = isl_ast_build_options_involve_depth(build);
}
if (skip < 0)
goto error;
if (skip)
return generate_shifted_component_from_list(domain,
order, n, build);
base = eliminate_non_fixed(domain, order, n, depth, build);
if (base < 0)
goto error;
ctx = isl_ast_build_get_ctx(build);
mv = isl_multi_val_zero(isl_space_set_alloc(ctx, 0, n));
fixed = 1;
for (i = 0; i < n; ++i) {
isl_val *r, *m;
map = isl_map_from_domain_and_range(
isl_set_copy(domain[order[base]].set),
isl_set_copy(domain[order[i]].set));
for (d = 0; d < depth; ++d)
map = isl_map_equate(map, isl_dim_in, d,
isl_dim_out, d);
deltas = isl_map_deltas(map);
res = isl_set_dim_residue_class_val(deltas, depth, &m, &r);
isl_set_free(deltas);
if (res < 0)
break;
if (i == 0)
gcd = m;
else
gcd = isl_val_gcd(gcd, m);
if (isl_val_is_one(gcd)) {
isl_val_free(r);
break;
}
mv = isl_multi_val_set_val(mv, i, r);
res = dim_is_fixed(domain[order[i]].set, depth);
if (res < 0)
break;
if (res)
continue;
if (fixed && i > base) {
isl_val *a, *b;
a = isl_multi_val_get_val(mv, i);
b = isl_multi_val_get_val(mv, base);
if (isl_val_ne(a, b))
fixed = 0;
isl_val_free(a);
isl_val_free(b);
}
}
if (res < 0 || !gcd) {
isl_ast_build_free(build);
list = NULL;
} else if (i < n || fixed || isl_val_is_zero(gcd)) {
list = generate_shifted_component_from_list(domain,
order, n, build);
} else {
list = generate_shift_component(domain, order, n, gcd, mv,
build);
}
isl_val_free(gcd);
isl_multi_val_free(mv);
return list;
error:
isl_ast_build_free(build);
return NULL;
}
/* Store both "map" itself and its domain in the
* structure pointed to by *next and advance to the next array element.
*/
static isl_stat extract_domain(__isl_take isl_map *map, void *user)
{
struct isl_set_map_pair **next = user;
(*next)->map = isl_map_copy(map);
(*next)->set = isl_map_domain(map);
(*next)++;
return isl_stat_ok;
}
static isl_bool after_in_tree(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node);
/* Is any domain element of "umap" scheduled after any of
* the corresponding image elements by the tree rooted at
* the child of "node"?
*/
static isl_bool after_in_child(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node)
{
isl_schedule_node *child;
isl_bool after;
child = isl_schedule_node_get_child(node, 0);
after = after_in_tree(umap, child);
isl_schedule_node_free(child);
return after;
}
/* Is any domain element of "umap" scheduled after any of
* the corresponding image elements by the tree rooted at
* the band node "node"?
*
* We first check if any domain element is scheduled after any
* of the corresponding image elements by the band node itself.
* If not, we restrict "map" to those pairs of element that
* are scheduled together by the band node and continue with
* the child of the band node.
* If there are no such pairs then the map passed to after_in_child
* will be empty causing it to return 0.
*/
static isl_bool after_in_band(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node)
{
isl_multi_union_pw_aff *mupa;
isl_union_map *partial, *test, *gt, *universe, *umap1, *umap2;
isl_union_set *domain, *range;
isl_space *space;
isl_bool empty;
isl_bool after;
isl_size n;
n = isl_schedule_node_band_n_member(node);
if (n < 0)
return isl_bool_error;
if (n == 0)
return after_in_child(umap, node);
mupa = isl_schedule_node_band_get_partial_schedule(node);
space = isl_multi_union_pw_aff_get_space(mupa);
partial = isl_union_map_from_multi_union_pw_aff(mupa);
test = isl_union_map_copy(umap);
test = isl_union_map_apply_domain(test, isl_union_map_copy(partial));
test = isl_union_map_apply_range(test, isl_union_map_copy(partial));
gt = isl_union_map_from_map(isl_map_lex_gt(space));
test = isl_union_map_intersect(test, gt);
empty = isl_union_map_is_empty(test);
isl_union_map_free(test);
if (empty < 0 || !empty) {
isl_union_map_free(partial);
return isl_bool_not(empty);
}
universe = isl_union_map_universe(isl_union_map_copy(umap));
domain = isl_union_map_domain(isl_union_map_copy(universe));
range = isl_union_map_range(universe);
umap1 = isl_union_map_copy(partial);
umap1 = isl_union_map_intersect_domain(umap1, domain);
umap2 = isl_union_map_intersect_domain(partial, range);
test = isl_union_map_apply_range(umap1, isl_union_map_reverse(umap2));
test = isl_union_map_intersect(test, isl_union_map_copy(umap));
after = after_in_child(test, node);
isl_union_map_free(test);
return after;
}
/* Is any domain element of "umap" scheduled after any of
* the corresponding image elements by the tree rooted at
* the context node "node"?
*
* The context constraints apply to the schedule domain,
* so we cannot apply them directly to "umap", which contains
* pairs of statement instances. Instead, we add them
* to the range of the prefix schedule for both domain and
* range of "umap".
*/
static isl_bool after_in_context(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node)
{
isl_union_map *prefix, *universe, *umap1, *umap2;
isl_union_set *domain, *range;
isl_set *context;
isl_bool after;
umap = isl_union_map_copy(umap);
context = isl_schedule_node_context_get_context(node);
prefix = isl_schedule_node_get_prefix_schedule_union_map(node);
universe = isl_union_map_universe(isl_union_map_copy(umap));
domain = isl_union_map_domain(isl_union_map_copy(universe));
range = isl_union_map_range(universe);
umap1 = isl_union_map_copy(prefix);
umap1 = isl_union_map_intersect_domain(umap1, domain);
umap2 = isl_union_map_intersect_domain(prefix, range);
umap1 = isl_union_map_intersect_range(umap1,
isl_union_set_from_set(context));
umap1 = isl_union_map_apply_range(umap1, isl_union_map_reverse(umap2));
umap = isl_union_map_intersect(umap, umap1);
after = after_in_child(umap, node);
isl_union_map_free(umap);
return after;
}
/* Is any domain element of "umap" scheduled after any of
* the corresponding image elements by the tree rooted at
* the expansion node "node"?
*
* We apply the expansion to domain and range of "umap" and
* continue with its child.
*/
static isl_bool after_in_expansion(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node)
{
isl_union_map *expansion;
isl_bool after;
expansion = isl_schedule_node_expansion_get_expansion(node);
umap = isl_union_map_copy(umap);
umap = isl_union_map_apply_domain(umap, isl_union_map_copy(expansion));
umap = isl_union_map_apply_range(umap, expansion);
after = after_in_child(umap, node);
isl_union_map_free(umap);
return after;
}
/* Is any domain element of "umap" scheduled after any of
* the corresponding image elements by the tree rooted at
* the extension node "node"?
*
* Since the extension node may add statement instances before or
* after the pairs of statement instances in "umap", we return isl_bool_true
* to ensure that these pairs are not broken up.
*/
static isl_bool after_in_extension(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node)
{
return isl_bool_true;
}
/* Is any domain element of "umap" scheduled after any of
* the corresponding image elements by the tree rooted at
* the filter node "node"?
*
* We intersect domain and range of "umap" with the filter and
* continue with its child.
*/
static isl_bool after_in_filter(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node)
{
isl_union_set *filter;
isl_bool after;
umap = isl_union_map_copy(umap);
filter = isl_schedule_node_filter_get_filter(node);
umap = isl_union_map_intersect_domain(umap, isl_union_set_copy(filter));
umap = isl_union_map_intersect_range(umap, filter);
after = after_in_child(umap, node);
isl_union_map_free(umap);
return after;
}
/* Is any domain element of "umap" scheduled after any of
* the corresponding image elements by the tree rooted at
* the set node "node"?
*
* This is only the case if this condition holds in any
* of the (filter) children of the set node.
* In particular, if the domain and the range of "umap"
* are contained in different children, then the condition
* does not hold.
*/
static isl_bool after_in_set(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node)
{
int i;
isl_size n;
n = isl_schedule_node_n_children(node);
if (n < 0)
return isl_bool_error;
for (i = 0; i < n; ++i) {
isl_schedule_node *child;
isl_bool after;
child = isl_schedule_node_get_child(node, i);
after = after_in_tree(umap, child);
isl_schedule_node_free(child);
if (after < 0 || after)
return after;
}
return isl_bool_false;
}
/* Return the filter of child "i" of "node".
*/
static __isl_give isl_union_set *child_filter(
__isl_keep isl_schedule_node *node, int i)
{
isl_schedule_node *child;
isl_union_set *filter;
child = isl_schedule_node_get_child(node, i);
filter = isl_schedule_node_filter_get_filter(child);
isl_schedule_node_free(child);
return filter;
}
/* Is any domain element of "umap" scheduled after any of
* the corresponding image elements by the tree rooted at
* the sequence node "node"?
*
* This happens in particular if any domain element is
* contained in a later child than one containing a range element or
* if the condition holds within a given child in the sequence.
* The later part of the condition is checked by after_in_set.
*/
static isl_bool after_in_sequence(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node)
{
int i, j;
isl_size n;
isl_union_map *umap_i;
isl_bool empty;
isl_bool after = isl_bool_false;
n = isl_schedule_node_n_children(node);
if (n < 0)
return isl_bool_error;
for (i = 1; i < n; ++i) {
isl_union_set *filter_i;
umap_i = isl_union_map_copy(umap);
filter_i = child_filter(node, i);
umap_i = isl_union_map_intersect_domain(umap_i, filter_i);
empty = isl_union_map_is_empty(umap_i);
if (empty < 0)
goto error;
if (empty) {
isl_union_map_free(umap_i);
continue;
}
for (j = 0; j < i; ++j) {
isl_union_set *filter_j;
isl_union_map *umap_ij;
umap_ij = isl_union_map_copy(umap_i);
filter_j = child_filter(node, j);
umap_ij = isl_union_map_intersect_range(umap_ij,
filter_j);
empty = isl_union_map_is_empty(umap_ij);
isl_union_map_free(umap_ij);
if (empty < 0)
goto error;
if (!empty)
after = isl_bool_true;
if (after)
break;
}
isl_union_map_free(umap_i);
if (after)
break;
}
if (after < 0 || after)
return after;
return after_in_set(umap, node);
error:
isl_union_map_free(umap_i);
return isl_bool_error;
}
/* Is any domain element of "umap" scheduled after any of
* the corresponding image elements by the tree rooted at "node"?
*
* If "umap" is empty, then clearly there is no such element.
* Otherwise, consider the different types of nodes separately.
*/
static isl_bool after_in_tree(__isl_keep isl_union_map *umap,
__isl_keep isl_schedule_node *node)
{
isl_bool empty;
enum isl_schedule_node_type type;
empty = isl_union_map_is_empty(umap);
if (empty < 0)
return isl_bool_error;
if (empty)
return isl_bool_false;
if (!node)
return isl_bool_error;
type = isl_schedule_node_get_type(node);
switch (type) {
case isl_schedule_node_error:
return isl_bool_error;
case isl_schedule_node_leaf:
return isl_bool_false;
case isl_schedule_node_band:
return after_in_band(umap, node);
case isl_schedule_node_domain:
isl_die(isl_schedule_node_get_ctx(node), isl_error_internal,
"unexpected internal domain node",
return isl_bool_error);
case isl_schedule_node_context:
return after_in_context(umap, node);
case isl_schedule_node_expansion:
return after_in_expansion(umap, node);
case isl_schedule_node_extension:
return after_in_extension(umap, node);
case isl_schedule_node_filter:
return after_in_filter(umap, node);
case isl_schedule_node_guard:
case isl_schedule_node_mark:
return after_in_child(umap, node);
case isl_schedule_node_set:
return after_in_set(umap, node);
case isl_schedule_node_sequence:
return after_in_sequence(umap, node);
}
return isl_bool_true;
}
/* Is any domain element of "map1" scheduled after any domain
* element of "map2" by the subtree underneath the current band node,
* while at the same time being scheduled together by the current
* band node, i.e., by "map1" and "map2?
*
* If the child of the current band node is a leaf, then
* no element can be scheduled after any other element.
*
* Otherwise, we construct a relation between domain elements
* of "map1" and domain elements of "map2" that are scheduled
* together and then check if the subtree underneath the current
* band node determines their relative order.
*/
static isl_bool after_in_subtree(__isl_keep isl_ast_build *build,
__isl_keep isl_map *map1, __isl_keep isl_map *map2)
{
isl_schedule_node *node;
isl_map *map;
isl_union_map *umap;
isl_bool after;
node = isl_ast_build_get_schedule_node(build);
if (!node)
return isl_bool_error;
node = isl_schedule_node_child(node, 0);
if (isl_schedule_node_get_type(node) == isl_schedule_node_leaf) {
isl_schedule_node_free(node);
return isl_bool_false;
}
map = isl_map_copy(map2);
map = isl_map_apply_domain(map, isl_map_copy(map1));
umap = isl_union_map_from_map(map);
after = after_in_tree(umap, node);
isl_union_map_free(umap);
isl_schedule_node_free(node);
return after;
}
/* Internal data for any_scheduled_after.
*
* "build" is the build in which the AST is constructed.
* "depth" is the number of loops that have already been generated
* "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
* "domain" is an array of set-map pairs corresponding to the different
* iteration domains. The set is the schedule domain, i.e., the domain
* of the inverse schedule, while the map is the inverse schedule itself.
*/
struct isl_any_scheduled_after_data {
isl_ast_build *build;
int depth;
int group_coscheduled;
struct isl_set_map_pair *domain;
};
/* Is any element of domain "i" scheduled after any element of domain "j"
* (for a common iteration of the first data->depth loops)?
*
* data->domain[i].set contains the domain of the inverse schedule
* for domain "i", i.e., elements in the schedule domain.
*
* If we are inside a band of a schedule tree and there is a pair
* of elements in the two domains that is schedule together by
* the current band, then we check if any element of "i" may be schedule
* after element of "j" by the descendants of the band node.
*
* If data->group_coscheduled is set, then we also return 1 if there
* is any pair of elements in the two domains that are scheduled together.
*/
static isl_bool any_scheduled_after(int i, int j, void *user)
{
struct isl_any_scheduled_after_data *data = user;
isl_size dim = isl_set_dim(data->domain[i].set, isl_dim_set);
int pos;
if (dim < 0)
return isl_bool_error;
for (pos = data->depth; pos < dim; ++pos) {
int follows;
follows = isl_set_follows_at(data->domain[i].set,
data->domain[j].set, pos);
if (follows < -1)
return isl_bool_error;
if (follows > 0)
return isl_bool_true;
if (follows < 0)
return isl_bool_false;
}
if (isl_ast_build_has_schedule_node(data->build)) {
isl_bool after;
after = after_in_subtree(data->build, data->domain[i].map,
data->domain[j].map);
if (after < 0 || after)
return after;
}
return isl_bool_ok(data->group_coscheduled);
}
/* Look for independent components at the current depth and generate code
* for each component separately. The resulting lists of grafts are
* merged in an attempt to combine grafts with identical guards.
*
* Code for two domains can be generated separately if all the elements
* of one domain are scheduled before (or together with) all the elements
* of the other domain. We therefore consider the graph with as nodes
* the domains and an edge between two nodes if any element of the first
* node is scheduled after any element of the second node.
* If the ast_build_group_coscheduled is set, then we also add an edge if
* there is any pair of elements in the two domains that are scheduled
* together.
* Code is then generated (by generate_component)
* for each of the strongly connected components in this graph
* in their topological order.
*
* Since the test is performed on the domain of the inverse schedules of
* the different domains, we precompute these domains and store
* them in data.domain.
*/
static __isl_give isl_ast_graft_list *generate_components(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
{
int i;
isl_ctx *ctx = isl_ast_build_get_ctx(build);
isl_size n = isl_union_map_n_map(executed);
isl_size depth;
struct isl_any_scheduled_after_data data;
struct isl_set_map_pair *next;
struct isl_tarjan_graph *g = NULL;
isl_ast_graft_list *list = NULL;
int n_domain = 0;
data.domain = NULL;
if (n < 0)
goto error;
data.domain = isl_calloc_array(ctx, struct isl_set_map_pair, n);
if (!data.domain)
goto error;
n_domain = n;
next = data.domain;
if (isl_union_map_foreach_map(executed, &extract_domain, &next) < 0)
goto error;
depth = isl_ast_build_get_depth(build);
if (depth < 0)
goto error;
data.build = build;
data.depth = depth;
data.group_coscheduled = isl_options_get_ast_build_group_coscheduled(ctx);
g = isl_tarjan_graph_init(ctx, n, &any_scheduled_after, &data);
if (!g)
goto error;
list = isl_ast_graft_list_alloc(ctx, 0);
i = 0;
while (list && n) {
isl_ast_graft_list *list_c;
int first = i;
if (g->order[i] == -1)
isl_die(ctx, isl_error_internal, "cannot happen",
goto error);
++i; --n;
while (g->order[i] != -1) {
++i; --n;
}
list_c = generate_component(data.domain,
g->order + first, i - first,
isl_ast_build_copy(build));
list = isl_ast_graft_list_merge(list, list_c, build);
++i;
}
if (0)
error: list = isl_ast_graft_list_free(list);
isl_tarjan_graph_free(g);
for (i = 0; i < n_domain; ++i) {
isl_map_free(data.domain[i].map);
isl_set_free(data.domain[i].set);
}
free(data.domain);
isl_union_map_free(executed);
isl_ast_build_free(build);
return list;
}
/* Generate code for the next level (and all inner levels).
*
* If "executed" is empty, i.e., no code needs to be generated,
* then we return an empty list.
*
* If we have already generated code for all loop levels, then we pass
* control to generate_inner_level.
*
* If "executed" lives in a single space, i.e., if code needs to be
* generated for a single domain, then there can only be a single
* component and we go directly to generate_shifted_component.
* Otherwise, we call generate_components to detect the components
* and to call generate_component on each of them separately.
*/
static __isl_give isl_ast_graft_list *generate_next_level(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
{
isl_size depth;
isl_size dim;
isl_size n;
if (!build || !executed)
goto error;
if (isl_union_map_is_empty(executed)) {
isl_ctx *ctx = isl_ast_build_get_ctx(build);
isl_union_map_free(executed);
isl_ast_build_free(build);
return isl_ast_graft_list_alloc(ctx, 0);
}
depth = isl_ast_build_get_depth(build);
dim = isl_ast_build_dim(build, isl_dim_set);
if (depth < 0 || dim < 0)
goto error;
if (depth >= dim)
return generate_inner_level(executed, build);
n = isl_union_map_n_map(executed);
if (n < 0)
goto error;
if (n == 1)
return generate_shifted_component(executed, build);
return generate_components(executed, build);
error:
isl_union_map_free(executed);
isl_ast_build_free(build);
return NULL;
}
/* Internal data structure used by isl_ast_build_node_from_schedule_map.
* internal, executed and build are the inputs to generate_code.
* list collects the output.
*/
struct isl_generate_code_data {
int internal;
isl_union_map *executed;
isl_ast_build *build;
isl_ast_graft_list *list;
};
/* Given an inverse schedule in terms of the external build schedule, i.e.,
*
* [E -> S] -> D
*
* with E the external build schedule and S the additional schedule "space",
* reformulate the inverse schedule in terms of the internal schedule domain,
* i.e., return
*
* [I -> S] -> D
*
* We first obtain a mapping
*
* I -> E
*
* take the inverse and the product with S -> S, resulting in
*
* [I -> S] -> [E -> S]
*
* Applying the map to the input produces the desired result.
*/
static __isl_give isl_union_map *internal_executed(
__isl_take isl_union_map *executed, __isl_keep isl_space *space,
__isl_keep isl_ast_build *build)
{
isl_map *id, *proj;
proj = isl_ast_build_get_schedule_map(build);
proj = isl_map_reverse(proj);
space = isl_space_map_from_set(isl_space_copy(space));
id = isl_map_identity(space);
proj = isl_map_product(proj, id);
executed = isl_union_map_apply_domain(executed,
isl_union_map_from_map(proj));
return executed;
}
/* Generate an AST that visits the elements in the range of data->executed
* in the relative order specified by the corresponding domain element(s)
* for those domain elements that belong to "set".
* Add the result to data->list.
*
* The caller ensures that "set" is a universe domain.
* "space" is the space of the additional part of the schedule.
* It is equal to the space of "set" if build->domain is parametric.
* Otherwise, it is equal to the range of the wrapped space of "set".
*
* If the build space is not parametric and
* if isl_ast_build_node_from_schedule_map
* was called from an outside user (data->internal not set), then
* the (inverse) schedule refers to the external build domain and needs to
* be transformed to refer to the internal build domain.
*
* If the build space is parametric, then we add some of the parameter
* constraints to the executed relation. Adding these constraints
* allows for an earlier detection of conflicts in some cases.
* However, we do not want to divide the executed relation into
* more disjuncts than necessary. We therefore approximate
* the constraints on the parameters by a single disjunct set.
*
* The build is extended to include the additional part of the schedule.
* If the original build space was not parametric, then the options
* in data->build refer only to the additional part of the schedule
* and they need to be adjusted to refer to the complete AST build
* domain.
*
* After having adjusted inverse schedule and build, we start generating
* code with the outer loop of the current code generation
* in generate_next_level.
*
* If the original build space was not parametric, we undo the embedding
* on the resulting isl_ast_node_list so that it can be used within
* the outer AST build.
*/
static isl_stat generate_code_in_space(struct isl_generate_code_data *data,
__isl_take isl_set *set, __isl_take isl_space *space)
{
isl_union_map *executed;
isl_ast_build *build;
isl_ast_graft_list *list;
int embed;
executed = isl_union_map_copy(data->executed);
executed = isl_union_map_intersect_domain(executed,
isl_union_set_from_set(set));
embed = !isl_set_is_params(data->build->domain);
if (embed && !data->internal)
executed = internal_executed(executed, space, data->build);
if (!embed) {
isl_set *domain;
domain = isl_ast_build_get_domain(data->build);
domain = isl_set_from_basic_set(isl_set_simple_hull(domain));
executed = isl_union_map_intersect_params(executed, domain);
}
build = isl_ast_build_copy(data->build);
build = isl_ast_build_product(build, space);
list = generate_next_level(executed, build);
list = isl_ast_graft_list_unembed(list, embed);
data->list = isl_ast_graft_list_concat(data->list, list);
return isl_stat_ok;
}
/* Generate an AST that visits the elements in the range of data->executed
* in the relative order specified by the corresponding domain element(s)
* for those domain elements that belong to "set".
* Add the result to data->list.
*
* The caller ensures that "set" is a universe domain.
*
* If the build space S is not parametric, then the space of "set"
* need to be a wrapped relation with S as domain. That is, it needs
* to be of the form
*
* [S -> T]
*
* Check this property and pass control to generate_code_in_space
* passing along T.
* If the build space is not parametric, then T is the space of "set".
*/
static isl_stat generate_code_set(__isl_take isl_set *set, void *user)
{
struct isl_generate_code_data *data = user;
isl_space *space, *build_space;
int is_domain;
space = isl_set_get_space(set);
if (isl_set_is_params(data->build->domain))
return generate_code_in_space(data, set, space);
build_space = isl_ast_build_get_space(data->build, data->internal);
space = isl_space_unwrap(space);
is_domain = isl_space_is_domain(build_space, space);
isl_space_free(build_space);
space = isl_space_range(space);
if (is_domain < 0)
goto error;
if (!is_domain)
isl_die(isl_set_get_ctx(set), isl_error_invalid,
"invalid nested schedule space", goto error);
return generate_code_in_space(data, set, space);
error:
isl_set_free(set);
isl_space_free(space);
return isl_stat_error;
}
/* Generate an AST that visits the elements in the range of "executed"
* in the relative order specified by the corresponding domain element(s).
*
* "build" is an isl_ast_build that has either been constructed by
* isl_ast_build_from_context or passed to a callback set by
* isl_ast_build_set_create_leaf.
* In the first case, the space of the isl_ast_build is typically
* a parametric space, although this is currently not enforced.
* In the second case, the space is never a parametric space.
* If the space S is not parametric, then the domain space(s) of "executed"
* need to be wrapped relations with S as domain.
*
* If the domain of "executed" consists of several spaces, then an AST
* is generated for each of them (in arbitrary order) and the results
* are concatenated.
*
* If "internal" is set, then the domain "S" above refers to the internal
* schedule domain representation. Otherwise, it refers to the external
* representation, as returned by isl_ast_build_get_schedule_space.
*
* We essentially run over all the spaces in the domain of "executed"
* and call generate_code_set on each of them.
*/
static __isl_give isl_ast_graft_list *generate_code(
__isl_take isl_union_map *executed, __isl_take isl_ast_build *build,
int internal)
{
isl_ctx *ctx;
struct isl_generate_code_data data = { 0 };
isl_space *space;
isl_union_set *schedule_domain;
isl_union_map *universe;
if (!build)
goto error;
space = isl_ast_build_get_space(build, 1);
space = isl_space_align_params(space,
isl_union_map_get_space(executed));
space = isl_space_align_params(space,
isl_union_map_get_space(build->options));
build = isl_ast_build_align_params(build, isl_space_copy(space));
executed = isl_union_map_align_params(executed, space);
if (!executed || !build)
goto error;
ctx = isl_ast_build_get_ctx(build);
data.internal = internal;
data.executed = executed;
data.build = build;
data.list = isl_ast_graft_list_alloc(ctx, 0);
universe = isl_union_map_universe(isl_union_map_copy(executed));
schedule_domain = isl_union_map_domain(universe);
if (isl_union_set_foreach_set(schedule_domain, &generate_code_set,
&data) < 0)
data.list = isl_ast_graft_list_free(data.list);
isl_union_set_free(schedule_domain);
isl_union_map_free(executed);
isl_ast_build_free(build);
return data.list;
error:
isl_union_map_free(executed);
isl_ast_build_free(build);
return NULL;
}
/* Generate an AST that visits the elements in the domain of "schedule"
* in the relative order specified by the corresponding image element(s).
*
* "build" is an isl_ast_build that has either been constructed by
* isl_ast_build_from_context or passed to a callback set by
* isl_ast_build_set_create_leaf.
* In the first case, the space of the isl_ast_build is typically
* a parametric space, although this is currently not enforced.
* In the second case, the space is never a parametric space.
* If the space S is not parametric, then the range space(s) of "schedule"
* need to be wrapped relations with S as domain.
*
* If the range of "schedule" consists of several spaces, then an AST
* is generated for each of them (in arbitrary order) and the results
* are concatenated.
*
* We first initialize the local copies of the relevant options.
* We do this here rather than when the isl_ast_build is created
* because the options may have changed between the construction
* of the isl_ast_build and the call to isl_generate_code.
*
* The main computation is performed on an inverse schedule (with
* the schedule domain in the domain and the elements to be executed
* in the range) called "executed".
*/
__isl_give isl_ast_node *isl_ast_build_node_from_schedule_map(
__isl_keep isl_ast_build *build, __isl_take isl_union_map *schedule)
{
isl_ast_graft_list *list;
isl_ast_node *node;
isl_union_map *executed;
build = isl_ast_build_copy(build);
build = isl_ast_build_set_single_valued(build, 0);
schedule = isl_union_map_coalesce(schedule);
schedule = isl_union_map_remove_redundancies(schedule);
executed = isl_union_map_reverse(schedule);
list = generate_code(executed, isl_ast_build_copy(build), 0);
node = isl_ast_node_from_graft_list(list, build);
isl_ast_build_free(build);
return node;
}
/* The old name for isl_ast_build_node_from_schedule_map.
* It is being kept for backward compatibility, but
* it will be removed in the future.
*/
__isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
__isl_keep isl_ast_build *build, __isl_take isl_union_map *schedule)
{
return isl_ast_build_node_from_schedule_map(build, schedule);
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the leaf node "node".
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* Simply pass control to generate_inner_level.
* Note that the current build does not refer to any band node, so
* that generate_inner_level will not try to visit the child of
* the leaf node.
*
* If multiple statement instances reach a leaf,
* then they can be executed in any order.
* Group the list of grafts based on shared guards
* such that identical guards are only generated once
* when the list is eventually passed on to isl_ast_graft_list_fuse.
*/
static __isl_give isl_ast_graft_list *build_ast_from_leaf(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
isl_ast_graft_list *list;
isl_schedule_node_free(node);
list = generate_inner_level(executed, isl_ast_build_copy(build));
list = isl_ast_graft_list_group_on_guard(list, build);
isl_ast_build_free(build);
return list;
}
/* Check that the band partial schedule "partial" does not filter out
* any statement instances, as specified by the range of "executed".
*/
static isl_stat check_band_schedule_total_on_instances(
__isl_keep isl_multi_union_pw_aff *partial,
__isl_keep isl_union_map *executed)
{
isl_bool subset;
isl_union_set *domain, *instances;
instances = isl_union_map_range(isl_union_map_copy(executed));
partial = isl_multi_union_pw_aff_copy(partial);
domain = isl_multi_union_pw_aff_domain(partial);
subset = isl_union_set_is_subset(instances, domain);
isl_union_set_free(domain);
isl_union_set_free(instances);
if (subset < 0)
return isl_stat_error;
if (!subset)
isl_die(isl_union_map_get_ctx(executed), isl_error_invalid,
"band node is not allowed to drop statement instances",
return isl_stat_error);
return isl_stat_ok;
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the band node "node" and its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* If the band is empty, we continue with its descendants.
* Otherwise, we extend the build and the inverse schedule with
* the additional space/partial schedule and continue generating
* an AST in generate_next_level.
* As soon as we have extended the inverse schedule with the additional
* partial schedule, we look for equalities that may exists between
* the old and the new part.
*/
static __isl_give isl_ast_graft_list *build_ast_from_band(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
isl_space *space;
isl_multi_union_pw_aff *extra;
isl_union_map *extra_umap;
isl_ast_graft_list *list;
isl_size n1, n2;
isl_size n;
n = isl_schedule_node_band_n_member(node);
if (!build || n < 0 || !executed)
goto error;
if (n == 0)
return build_ast_from_child(build, node, executed);
extra = isl_schedule_node_band_get_partial_schedule(node);
extra = isl_multi_union_pw_aff_align_params(extra,
isl_ast_build_get_space(build, 1));
space = isl_multi_union_pw_aff_get_space(extra);
if (check_band_schedule_total_on_instances(extra, executed) < 0)
executed = isl_union_map_free(executed);
extra_umap = isl_union_map_from_multi_union_pw_aff(extra);
extra_umap = isl_union_map_reverse(extra_umap);
executed = isl_union_map_domain_product(executed, extra_umap);
executed = isl_union_map_detect_equalities(executed);
n1 = isl_ast_build_dim(build, isl_dim_param);
build = isl_ast_build_product(build, space);
n2 = isl_ast_build_dim(build, isl_dim_param);
if (n1 < 0 || n2 < 0)
build = isl_ast_build_free(build);
else if (n2 > n1)
isl_die(isl_ast_build_get_ctx(build), isl_error_invalid,
"band node is not allowed to introduce new parameters",
build = isl_ast_build_free(build));
build = isl_ast_build_set_schedule_node(build, node);
list = generate_next_level(executed, build);
list = isl_ast_graft_list_unembed(list, 1);
return list;
error:
isl_schedule_node_free(node);
isl_union_map_free(executed);
isl_ast_build_free(build);
return NULL;
}
/* Hoist a list of grafts (in practice containing a single graft)
* from "sub_build" (which includes extra context information)
* to "build".
*
* In particular, project out all additional parameters introduced
* by the context node from the enforced constraints and the guard
* of the single graft.
*/
static __isl_give isl_ast_graft_list *hoist_out_of_context(
__isl_take isl_ast_graft_list *list, __isl_keep isl_ast_build *build,
__isl_keep isl_ast_build *sub_build)
{
isl_ast_graft *graft;
isl_basic_set *enforced;
isl_set *guard;
isl_size n_param, extra_param;
n_param = isl_ast_build_dim(build, isl_dim_param);
extra_param = isl_ast_build_dim(sub_build, isl_dim_param);
if (n_param < 0 || extra_param < 0)
return isl_ast_graft_list_free(list);
if (extra_param == n_param)
return list;
extra_param -= n_param;
enforced = isl_ast_graft_list_extract_shared_enforced(list, sub_build);
enforced = isl_basic_set_project_out(enforced, isl_dim_param,
n_param, extra_param);
enforced = isl_basic_set_remove_unknown_divs(enforced);
guard = isl_ast_graft_list_extract_hoistable_guard(list, sub_build);
guard = isl_set_remove_divs_involving_dims(guard, isl_dim_param,
n_param, extra_param);
guard = isl_set_project_out(guard, isl_dim_param, n_param, extra_param);
guard = isl_set_compute_divs(guard);
graft = isl_ast_graft_alloc_from_children(list, guard, enforced,
build, sub_build);
list = isl_ast_graft_list_from_ast_graft(graft);
return list;
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the context node "node"
* and its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* The context node may introduce additional parameters as well as
* constraints on the outer schedule dimensions or original parameters.
*
* We add the extra parameters to a new build and the context
* constraints to both the build and (as a single disjunct)
* to the domain of "executed". Since the context constraints
* are specified in terms of the input schedule, we first need
* to map them to the internal schedule domain.
*
* After constructing the AST from the descendants of "node",
* we combine the list of grafts into a single graft within
* the new build, in order to be able to exploit the additional
* context constraints during this combination.
*
* Additionally, if the current node is the outermost node in
* the schedule tree (apart from the root domain node), we generate
* all pending guards, again to be able to exploit the additional
* context constraints. We currently do not do this for internal
* context nodes since we may still want to hoist conditions
* to outer AST nodes.
*
* If the context node introduced any new parameters, then they
* are removed from the set of enforced constraints and guard
* in hoist_out_of_context.
*/
static __isl_give isl_ast_graft_list *build_ast_from_context(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
isl_set *context;
isl_space *space;
isl_multi_aff *internal2input;
isl_ast_build *sub_build;
isl_ast_graft_list *list;
isl_size n;
isl_size depth;
depth = isl_schedule_node_get_tree_depth(node);
if (depth < 0)
build = isl_ast_build_free(build);
space = isl_ast_build_get_space(build, 1);
context = isl_schedule_node_context_get_context(node);
context = isl_set_align_params(context, space);
sub_build = isl_ast_build_copy(build);
space = isl_set_get_space(context);
sub_build = isl_ast_build_align_params(sub_build, space);
internal2input = isl_ast_build_get_internal2input(sub_build);
context = isl_set_preimage_multi_aff(context, internal2input);
sub_build = isl_ast_build_restrict_generated(sub_build,
isl_set_copy(context));
context = isl_set_from_basic_set(isl_set_simple_hull(context));
executed = isl_union_map_intersect_domain(executed,
isl_union_set_from_set(context));
list = build_ast_from_child(isl_ast_build_copy(sub_build),
node, executed);
n = isl_ast_graft_list_n_ast_graft(list);
if (n < 0)
list = isl_ast_graft_list_free(list);
list = isl_ast_graft_list_fuse(list, sub_build);
if (depth == 1)
list = isl_ast_graft_list_insert_pending_guard_nodes(list,
sub_build);
if (n >= 1)
list = hoist_out_of_context(list, build, sub_build);
isl_ast_build_free(build);
isl_ast_build_free(sub_build);
return list;
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the expansion node "node" and
* its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* We expand the domain elements by the expansion and
* continue with the descendants of the node.
*/
static __isl_give isl_ast_graft_list *build_ast_from_expansion(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
isl_union_map *expansion;
isl_size n1, n2;
expansion = isl_schedule_node_expansion_get_expansion(node);
expansion = isl_union_map_align_params(expansion,
isl_union_map_get_space(executed));
n1 = isl_union_map_dim(executed, isl_dim_param);
executed = isl_union_map_apply_range(executed, expansion);
n2 = isl_union_map_dim(executed, isl_dim_param);
if (n1 < 0 || n2 < 0)
goto error;
if (n2 > n1)
isl_die(isl_ast_build_get_ctx(build), isl_error_invalid,
"expansion node is not allowed to introduce "
"new parameters", goto error);
return build_ast_from_child(build, node, executed);
error:
isl_ast_build_free(build);
isl_schedule_node_free(node);
isl_union_map_free(executed);
return NULL;
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the extension node "node" and
* its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* Extend the inverse schedule with the extension applied to current
* set of generated constraints. Since the extension if formulated
* in terms of the input schedule, it first needs to be transformed
* to refer to the internal schedule.
*/
static __isl_give isl_ast_graft_list *build_ast_from_extension(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
isl_union_set *schedule_domain;
isl_union_map *extension;
isl_set *set;
set = isl_ast_build_get_generated(build);
set = isl_set_from_basic_set(isl_set_simple_hull(set));
schedule_domain = isl_union_set_from_set(set);
extension = isl_schedule_node_extension_get_extension(node);
extension = isl_union_map_preimage_domain_multi_aff(extension,
isl_multi_aff_copy(build->internal2input));
extension = isl_union_map_intersect_domain(extension, schedule_domain);
extension = isl_ast_build_substitute_values_union_map_domain(build,
extension);
executed = isl_union_map_union(executed, extension);
return build_ast_from_child(build, node, executed);
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the filter node "node" and
* its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* We simply intersect the iteration domain (i.e., the range of "executed")
* with the filter and continue with the descendants of the node,
* unless the resulting inverse schedule is empty, in which
* case we return an empty list.
*
* If the result of the intersection is equal to the original "executed"
* relation, then keep the original representation since the intersection
* may have unnecessarily broken up the relation into a greater number
* of disjuncts.
*/
static __isl_give isl_ast_graft_list *build_ast_from_filter(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
isl_ctx *ctx;
isl_union_set *filter;
isl_union_map *orig;
isl_ast_graft_list *list;
int empty;
isl_bool unchanged;
isl_size n1, n2;
orig = isl_union_map_copy(executed);
if (!build || !node || !executed)
goto error;
filter = isl_schedule_node_filter_get_filter(node);
filter = isl_union_set_align_params(filter,
isl_union_map_get_space(executed));
n1 = isl_union_map_dim(executed, isl_dim_param);
executed = isl_union_map_intersect_range(executed, filter);
n2 = isl_union_map_dim(executed, isl_dim_param);
if (n1 < 0 || n2 < 0)
goto error;
if (n2 > n1)
isl_die(isl_ast_build_get_ctx(build), isl_error_invalid,
"filter node is not allowed to introduce "
"new parameters", goto error);
unchanged = isl_union_map_is_subset(orig, executed);
empty = isl_union_map_is_empty(executed);
if (unchanged < 0 || empty < 0)
goto error;
if (unchanged) {
isl_union_map_free(executed);
return build_ast_from_child(build, node, orig);
}
isl_union_map_free(orig);
if (!empty)
return build_ast_from_child(build, node, executed);
ctx = isl_ast_build_get_ctx(build);
list = isl_ast_graft_list_alloc(ctx, 0);
isl_ast_build_free(build);
isl_schedule_node_free(node);
isl_union_map_free(executed);
return list;
error:
isl_ast_build_free(build);
isl_schedule_node_free(node);
isl_union_map_free(executed);
isl_union_map_free(orig);
return NULL;
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the guard node "node" and
* its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* Ensure that the associated guard is enforced by the outer AST
* constructs by adding it to the guard of the graft.
* Since we know that we will enforce the guard, we can also include it
* in the generated constraints used to construct an AST for
* the descendant nodes.
*/
static __isl_give isl_ast_graft_list *build_ast_from_guard(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
isl_space *space;
isl_set *guard, *hoisted;
isl_basic_set *enforced;
isl_ast_build *sub_build;
isl_ast_graft *graft;
isl_ast_graft_list *list;
isl_size n1, n2, n;
space = isl_ast_build_get_space(build, 1);
guard = isl_schedule_node_guard_get_guard(node);
n1 = isl_space_dim(space, isl_dim_param);
guard = isl_set_align_params(guard, space);
n2 = isl_set_dim(guard, isl_dim_param);
if (n1 < 0 || n2 < 0)
guard = isl_set_free(guard);
else if (n2 > n1)
isl_die(isl_ast_build_get_ctx(build), isl_error_invalid,
"guard node is not allowed to introduce "
"new parameters", guard = isl_set_free(guard));
guard = isl_set_preimage_multi_aff(guard,
isl_multi_aff_copy(build->internal2input));
guard = isl_ast_build_specialize(build, guard);
guard = isl_set_gist(guard, isl_set_copy(build->generated));
sub_build = isl_ast_build_copy(build);
sub_build = isl_ast_build_restrict_generated(sub_build,
isl_set_copy(guard));
list = build_ast_from_child(isl_ast_build_copy(sub_build),
node, executed);
hoisted = isl_ast_graft_list_extract_hoistable_guard(list, sub_build);
n = isl_set_n_basic_set(hoisted);
if (n < 0)
list = isl_ast_graft_list_free(list);
if (n > 1)
list = isl_ast_graft_list_gist_guards(list,
isl_set_copy(hoisted));
guard = isl_set_intersect(guard, hoisted);
enforced = extract_shared_enforced(list, build);
graft = isl_ast_graft_alloc_from_children(list, guard, enforced,
build, sub_build);
isl_ast_build_free(sub_build);
isl_ast_build_free(build);
return isl_ast_graft_list_from_ast_graft(graft);
}
/* Call the before_each_mark callback, if requested by the user.
*
* Return 0 on success and -1 on error.
*
* The caller is responsible for recording the current inverse schedule
* in "build".
*/
static isl_stat before_each_mark(__isl_keep isl_id *mark,
__isl_keep isl_ast_build *build)
{
if (!build)
return isl_stat_error;
if (!build->before_each_mark)
return isl_stat_ok;
return build->before_each_mark(mark, build,
build->before_each_mark_user);
}
/* Call the after_each_mark callback, if requested by the user.
*
* The caller is responsible for recording the current inverse schedule
* in "build".
*/
static __isl_give isl_ast_graft *after_each_mark(
__isl_take isl_ast_graft *graft, __isl_keep isl_ast_build *build)
{
if (!graft || !build)
return isl_ast_graft_free(graft);
if (!build->after_each_mark)
return graft;
graft->node = build->after_each_mark(graft->node, build,
build->after_each_mark_user);
if (!graft->node)
return isl_ast_graft_free(graft);
return graft;
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the mark node "node" and
* its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
* Since we may be calling before_each_mark and after_each_mark
* callbacks, we record the current inverse schedule in the build.
*
* We generate an AST for the child of the mark node, combine
* the graft list into a single graft and then insert the mark
* in the AST of that single graft.
*/
static __isl_give isl_ast_graft_list *build_ast_from_mark(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
isl_id *mark;
isl_ast_graft *graft;
isl_ast_graft_list *list;
isl_size n;
build = isl_ast_build_set_executed(build, isl_union_map_copy(executed));
mark = isl_schedule_node_mark_get_id(node);
if (before_each_mark(mark, build) < 0)
node = isl_schedule_node_free(node);
list = build_ast_from_child(isl_ast_build_copy(build), node, executed);
list = isl_ast_graft_list_fuse(list, build);
n = isl_ast_graft_list_n_ast_graft(list);
if (n < 0)
list = isl_ast_graft_list_free(list);
if (n == 0) {
isl_id_free(mark);
} else {
graft = isl_ast_graft_list_get_ast_graft(list, 0);
graft = isl_ast_graft_insert_mark(graft, mark);
graft = after_each_mark(graft, build);
list = isl_ast_graft_list_set_ast_graft(list, 0, graft);
}
isl_ast_build_free(build);
return list;
}
static __isl_give isl_ast_graft_list *build_ast_from_schedule_node(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed);
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the sequence (or set) node "node" and
* its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* We simply generate an AST for each of the children and concatenate
* the results.
*/
static __isl_give isl_ast_graft_list *build_ast_from_sequence(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
int i;
isl_size n;
isl_ctx *ctx;
isl_ast_graft_list *list;
ctx = isl_ast_build_get_ctx(build);
list = isl_ast_graft_list_alloc(ctx, 0);
n = isl_schedule_node_n_children(node);
if (n < 0)
list = isl_ast_graft_list_free(list);
for (i = 0; i < n; ++i) {
isl_schedule_node *child;
isl_ast_graft_list *list_i;
child = isl_schedule_node_get_child(node, i);
list_i = build_ast_from_schedule_node(isl_ast_build_copy(build),
child, isl_union_map_copy(executed));
list = isl_ast_graft_list_concat(list, list_i);
}
isl_ast_build_free(build);
isl_schedule_node_free(node);
isl_union_map_free(executed);
return list;
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the node "node" and its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* The node types are handled in separate functions.
* Set nodes are currently treated in the same way as sequence nodes.
* The children of a set node may be executed in any order,
* including the order of the children.
*/
static __isl_give isl_ast_graft_list *build_ast_from_schedule_node(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
enum isl_schedule_node_type type;
type = isl_schedule_node_get_type(node);
switch (type) {
case isl_schedule_node_error:
goto error;
case isl_schedule_node_leaf:
return build_ast_from_leaf(build, node, executed);
case isl_schedule_node_band:
return build_ast_from_band(build, node, executed);
case isl_schedule_node_context:
return build_ast_from_context(build, node, executed);
case isl_schedule_node_domain:
isl_die(isl_schedule_node_get_ctx(node), isl_error_unsupported,
"unexpected internal domain node", goto error);
case isl_schedule_node_expansion:
return build_ast_from_expansion(build, node, executed);
case isl_schedule_node_extension:
return build_ast_from_extension(build, node, executed);
case isl_schedule_node_filter:
return build_ast_from_filter(build, node, executed);
case isl_schedule_node_guard:
return build_ast_from_guard(build, node, executed);
case isl_schedule_node_mark:
return build_ast_from_mark(build, node, executed);
case isl_schedule_node_sequence:
case isl_schedule_node_set:
return build_ast_from_sequence(build, node, executed);
}
isl_die(isl_ast_build_get_ctx(build), isl_error_internal,
"unhandled type", goto error);
error:
isl_union_map_free(executed);
isl_schedule_node_free(node);
isl_ast_build_free(build);
return NULL;
}
/* Generate an AST that visits the elements in the domain of "executed"
* in the relative order specified by the (single) child of "node" and
* its descendants.
*
* The relation "executed" maps the outer generated loop iterators
* to the domain elements executed by those iterations.
*
* This function is never called on a leaf, set or sequence node,
* so the node always has exactly one child.
*/
static __isl_give isl_ast_graft_list *build_ast_from_child(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node,
__isl_take isl_union_map *executed)
{
node = isl_schedule_node_child(node, 0);
return build_ast_from_schedule_node(build, node, executed);
}
/* Generate an AST that visits the elements in the domain of the domain
* node "node" in the relative order specified by its descendants.
*
* An initial inverse schedule is created that maps a zero-dimensional
* schedule space to the node domain.
* The input "build" is assumed to have a parametric domain and
* is replaced by the same zero-dimensional schedule space.
*
* We also add some of the parameter constraints in the build domain
* to the executed relation. Adding these constraints
* allows for an earlier detection of conflicts in some cases.
* However, we do not want to divide the executed relation into
* more disjuncts than necessary. We therefore approximate
* the constraints on the parameters by a single disjunct set.
*/
static __isl_give isl_ast_node *build_ast_from_domain(
__isl_take isl_ast_build *build, __isl_take isl_schedule_node *node)
{
isl_ctx *ctx;
isl_union_set *domain, *schedule_domain;
isl_union_map *executed;
isl_space *space;
isl_set *set;
isl_ast_graft_list *list;
isl_ast_node *ast;
int is_params;
if (!build)
goto error;
ctx = isl_ast_build_get_ctx(build);
space = isl_ast_build_get_space(build, 1);
is_params = isl_space_is_params(space);
isl_space_free(space);
if (is_params < 0)
goto error;
if (!is_params)
isl_die(ctx, isl_error_unsupported,
"expecting parametric initial context", goto error);
domain = isl_schedule_node_domain_get_domain(node);
domain = isl_union_set_coalesce(domain);
space = isl_union_set_get_space(domain);
space = isl_space_set_from_params(space);
build = isl_ast_build_product(build, space);
set = isl_ast_build_get_domain(build);
set = isl_set_from_basic_set(isl_set_simple_hull(set));
schedule_domain = isl_union_set_from_set(set);
executed = isl_union_map_from_domain_and_range(schedule_domain, domain);
list = build_ast_from_child(isl_ast_build_copy(build), node, executed);
ast = isl_ast_node_from_graft_list(list, build);
isl_ast_build_free(build);
return ast;
error:
isl_schedule_node_free(node);
isl_ast_build_free(build);
return NULL;
}
/* Generate an AST that visits the elements in the domain of "schedule"
* in the relative order specified by the schedule tree.
*
* "build" is an isl_ast_build that has been created using
* isl_ast_build_alloc or isl_ast_build_from_context based
* on a parametric set.
*
* The construction starts at the root node of the schedule,
* which is assumed to be a domain node.
*/
__isl_give isl_ast_node *isl_ast_build_node_from_schedule(
__isl_keep isl_ast_build *build, __isl_take isl_schedule *schedule)
{
isl_ctx *ctx;
isl_schedule_node *node;
if (!build || !schedule)
goto error;
ctx = isl_ast_build_get_ctx(build);
node = isl_schedule_get_root(schedule);
if (!node)
goto error;
isl_schedule_free(schedule);
build = isl_ast_build_copy(build);
build = isl_ast_build_set_single_valued(build, 0);
if (isl_schedule_node_get_type(node) != isl_schedule_node_domain)
isl_die(ctx, isl_error_unsupported,
"expecting root domain node",
build = isl_ast_build_free(build));
return build_ast_from_domain(build, node);
error:
isl_schedule_free(schedule);
return NULL;
}