2 * Copyright 2012-2014 Ecole Normale Superieure
3 * Copyright 2014 INRIA Rocquencourt
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege,
8 * Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
9 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
10 * B.P. 105 - 78153 Le Chesnay, France
15 #include <isl/constraint.h>
18 #include <isl/union_set.h>
19 #include <isl/union_map.h>
20 #include <isl/schedule_node.h>
22 #include <isl_tarjan.h>
23 #include <isl_ast_private.h>
24 #include <isl_ast_build_expr.h>
25 #include <isl_ast_build_private.h>
26 #include <isl_ast_graft_private.h>
28 /* Data used in generate_domain.
30 * "build" is the input build.
31 * "list" collects the results.
33 struct isl_generate_domain_data
{
36 isl_ast_graft_list
*list
;
39 static __isl_give isl_ast_graft_list
*generate_next_level(
40 __isl_take isl_union_map
*executed
,
41 __isl_take isl_ast_build
*build
);
42 static __isl_give isl_ast_graft_list
*generate_code(
43 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
46 /* Generate an AST for a single domain based on
47 * the (non single valued) inverse schedule "executed".
49 * We extend the schedule with the iteration domain
50 * and continue generating through a call to generate_code.
52 * In particular, if executed has the form
56 * then we continue generating code on
60 * The extended inverse schedule is clearly single valued
61 * ensuring that the nested generate_code will not reach this function,
62 * but will instead create calls to all elements of D that need
63 * to be executed from the current schedule domain.
65 static int generate_non_single_valued(__isl_take isl_map
*executed
,
66 struct isl_generate_domain_data
*data
)
70 isl_ast_graft_list
*list
;
72 build
= isl_ast_build_copy(data
->build
);
74 identity
= isl_set_identity(isl_map_range(isl_map_copy(executed
)));
75 executed
= isl_map_domain_product(executed
, identity
);
76 build
= isl_ast_build_set_single_valued(build
, 1);
78 list
= generate_code(isl_union_map_from_map(executed
), build
, 1);
80 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
85 /* Call the at_each_domain callback, if requested by the user,
86 * after recording the current inverse schedule in the build.
88 static __isl_give isl_ast_graft
*at_each_domain(__isl_take isl_ast_graft
*graft
,
89 __isl_keep isl_map
*executed
, __isl_keep isl_ast_build
*build
)
92 return isl_ast_graft_free(graft
);
93 if (!build
->at_each_domain
)
96 build
= isl_ast_build_copy(build
);
97 build
= isl_ast_build_set_executed(build
,
98 isl_union_map_from_map(isl_map_copy(executed
)));
100 return isl_ast_graft_free(graft
);
102 graft
->node
= build
->at_each_domain(graft
->node
,
103 build
, build
->at_each_domain_user
);
104 isl_ast_build_free(build
);
107 graft
= isl_ast_graft_free(graft
);
112 /* Generate an AST for a single domain based on
113 * the inverse schedule "executed" and add it to data->list.
115 * If there is more than one domain element associated to the current
116 * schedule "time", then we need to continue the generation process
117 * in generate_non_single_valued.
118 * Note that the inverse schedule being single-valued may depend
119 * on constraints that are only available in the original context
120 * domain specified by the user. We therefore first introduce
121 * some of the constraints of data->build->domain. In particular,
122 * we intersect with a single-disjunct approximation of this set.
123 * We perform this approximation to avoid further splitting up
124 * the executed relation, possibly introducing a disjunctive guard
127 * On the other hand, we only perform the test after having taken the gist
128 * of the domain as the resulting map is the one from which the call
129 * expression is constructed. Using this map to construct the call
130 * expression usually yields simpler results.
131 * Because we perform the single-valuedness test on the gisted map,
132 * we may in rare cases fail to recognize that the inverse schedule
133 * is single-valued. This becomes problematic if this happens
134 * from the recursive call through generate_non_single_valued
135 * as we would then end up in an infinite recursion.
136 * We therefore check if we are inside a call to generate_non_single_valued
137 * and revert to the ungisted map if the gisted map turns out not to be
140 * Otherwise, we generate a call expression for the single executed
141 * domain element and put a guard around it based on the (simplified)
142 * domain of "executed".
144 * At this stage, any pending constraints in the build can no longer
145 * be simplified with respect to any enforced constraints since
146 * the call node does not have any enforced constraints.
147 * We therefore turn all pending constraints into guards
148 * (after simplifying them with respect to the already generated
149 * constraints) and add them to both the generated constraints
150 * and the guard of the constructed graft. This guard will ensure
151 * that the constraints are effectively generated.
153 * If the user has set an at_each_domain callback, it is called
154 * on the constructed call expression node.
156 static int generate_domain(__isl_take isl_map
*executed
, void *user
)
158 struct isl_generate_domain_data
*data
= user
;
159 isl_ast_build
*build
;
160 isl_ast_graft
*graft
;
161 isl_ast_graft_list
*list
;
162 isl_set
*guard
, *domain
;
166 domain
= isl_ast_build_get_domain(data
->build
);
167 domain
= isl_set_from_basic_set(isl_set_simple_hull(domain
));
168 executed
= isl_map_intersect_domain(executed
, domain
);
169 empty
= isl_map_is_empty(executed
);
173 isl_map_free(executed
);
177 executed
= isl_map_coalesce(executed
);
178 map
= isl_map_copy(executed
);
179 map
= isl_ast_build_compute_gist_map_domain(data
->build
, map
);
180 sv
= isl_map_is_single_valued(map
);
185 if (data
->build
->single_valued
)
186 map
= isl_map_copy(executed
);
188 return generate_non_single_valued(executed
, data
);
190 guard
= isl_map_domain(isl_map_copy(map
));
191 guard
= isl_set_compute_divs(guard
);
192 guard
= isl_set_intersect(guard
,
193 isl_ast_build_get_pending(data
->build
));
194 guard
= isl_set_coalesce(guard
);
195 guard
= isl_ast_build_specialize(data
->build
, guard
);
196 guard
= isl_set_gist(guard
, isl_ast_build_get_generated(data
->build
));
198 build
= isl_ast_build_copy(data
->build
);
199 build
= isl_ast_build_replace_pending_by_guard(build
,
200 isl_set_copy(guard
));
201 graft
= isl_ast_graft_alloc_domain(map
, build
);
202 graft
= at_each_domain(graft
, executed
, build
);
203 isl_ast_build_free(build
);
204 isl_map_free(executed
);
205 graft
= isl_ast_graft_add_guard(graft
, guard
, data
->build
);
207 list
= isl_ast_graft_list_from_ast_graft(graft
);
208 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
213 isl_map_free(executed
);
217 /* Call build->create_leaf to a create "leaf" node in the AST,
218 * encapsulate the result in an isl_ast_graft and return the result
219 * as a 1-element list.
221 * Note that the node returned by the user may be an entire tree.
223 * Since the node itself cannot enforce any constraints, we turn
224 * all pending constraints into guards and add them to the resulting
225 * graft to ensure that they will be generated.
227 * Before we pass control to the user, we first clear some information
228 * from the build that is (presumbably) only meaningful
229 * for the current code generation.
230 * This includes the create_leaf callback itself, so we make a copy
231 * of the build first.
233 static __isl_give isl_ast_graft_list
*call_create_leaf(
234 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
238 isl_ast_graft
*graft
;
239 isl_ast_build
*user_build
;
241 guard
= isl_ast_build_get_pending(build
);
242 user_build
= isl_ast_build_copy(build
);
243 user_build
= isl_ast_build_replace_pending_by_guard(user_build
,
244 isl_set_copy(guard
));
245 user_build
= isl_ast_build_set_executed(user_build
, executed
);
246 user_build
= isl_ast_build_clear_local_info(user_build
);
250 node
= build
->create_leaf(user_build
, build
->create_leaf_user
);
251 graft
= isl_ast_graft_alloc(node
, build
);
252 graft
= isl_ast_graft_add_guard(graft
, guard
, build
);
253 isl_ast_build_free(build
);
254 return isl_ast_graft_list_from_ast_graft(graft
);
257 static __isl_give isl_ast_graft_list
*build_ast_from_child(
258 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
259 __isl_take isl_union_map
*executed
);
261 /* Generate an AST after having handled the complete schedule
262 * of this call to the code generator or the complete band
263 * if we are generating an AST from a schedule tree.
265 * If we are inside a band node, then move on to the child of the band.
267 * If the user has specified a create_leaf callback, control
268 * is passed to the user in call_create_leaf.
270 * Otherwise, we generate one or more calls for each individual
271 * domain in generate_domain.
273 static __isl_give isl_ast_graft_list
*generate_inner_level(
274 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
277 struct isl_generate_domain_data data
= { build
};
279 if (!build
|| !executed
)
282 if (isl_ast_build_has_schedule_node(build
)) {
283 isl_schedule_node
*node
;
284 node
= isl_ast_build_get_schedule_node(build
);
285 build
= isl_ast_build_reset_schedule_node(build
);
286 return build_ast_from_child(build
, node
, executed
);
289 if (build
->create_leaf
)
290 return call_create_leaf(executed
, build
);
292 ctx
= isl_union_map_get_ctx(executed
);
293 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
294 if (isl_union_map_foreach_map(executed
, &generate_domain
, &data
) < 0)
295 data
.list
= isl_ast_graft_list_free(data
.list
);
298 error
: data
.list
= NULL
;
299 isl_ast_build_free(build
);
300 isl_union_map_free(executed
);
304 /* Call the before_each_for callback, if requested by the user.
306 static __isl_give isl_ast_node
*before_each_for(__isl_take isl_ast_node
*node
,
307 __isl_keep isl_ast_build
*build
)
312 return isl_ast_node_free(node
);
313 if (!build
->before_each_for
)
315 id
= build
->before_each_for(build
, build
->before_each_for_user
);
316 node
= isl_ast_node_set_annotation(node
, id
);
320 /* Call the after_each_for callback, if requested by the user.
322 static __isl_give isl_ast_graft
*after_each_for(__isl_take isl_ast_graft
*graft
,
323 __isl_keep isl_ast_build
*build
)
325 if (!graft
|| !build
)
326 return isl_ast_graft_free(graft
);
327 if (!build
->after_each_for
)
329 graft
->node
= build
->after_each_for(graft
->node
, build
,
330 build
->after_each_for_user
);
332 return isl_ast_graft_free(graft
);
336 /* Plug in all the know values of the current and outer dimensions
337 * in the domain of "executed". In principle, we only need to plug
338 * in the known value of the current dimension since the values of
339 * outer dimensions have been plugged in already.
340 * However, it turns out to be easier to just plug in all known values.
342 static __isl_give isl_union_map
*plug_in_values(
343 __isl_take isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
345 return isl_ast_build_substitute_values_union_map_domain(build
,
349 /* Check if the constraint "c" is a lower bound on dimension "pos",
350 * an upper bound, or independent of dimension "pos".
352 static int constraint_type(isl_constraint
*c
, int pos
)
354 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, pos
))
356 if (isl_constraint_is_upper_bound(c
, isl_dim_set
, pos
))
361 /* Compare the types of the constraints "a" and "b",
362 * resulting in constraints that are independent of "depth"
363 * to be sorted before the lower bounds on "depth", which in
364 * turn are sorted before the upper bounds on "depth".
366 static int cmp_constraint(__isl_keep isl_constraint
*a
,
367 __isl_keep isl_constraint
*b
, void *user
)
370 int t1
= constraint_type(a
, *depth
);
371 int t2
= constraint_type(b
, *depth
);
376 /* Extract a lower bound on dimension "pos" from constraint "c".
378 * If the constraint is of the form
382 * then we essentially return
384 * l = ceil(-f(...)/a)
386 * However, if the current dimension is strided, then we need to make
387 * sure that the lower bound we construct is of the form
391 * with f the offset and s the stride.
392 * We therefore compute
394 * f + s * ceil((l - f)/s)
396 static __isl_give isl_aff
*lower_bound(__isl_keep isl_constraint
*c
,
397 int pos
, __isl_keep isl_ast_build
*build
)
401 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
402 aff
= isl_aff_ceil(aff
);
404 if (isl_ast_build_has_stride(build
, pos
)) {
408 offset
= isl_ast_build_get_offset(build
, pos
);
409 stride
= isl_ast_build_get_stride(build
, pos
);
411 aff
= isl_aff_sub(aff
, isl_aff_copy(offset
));
412 aff
= isl_aff_scale_down_val(aff
, isl_val_copy(stride
));
413 aff
= isl_aff_ceil(aff
);
414 aff
= isl_aff_scale_val(aff
, stride
);
415 aff
= isl_aff_add(aff
, offset
);
418 aff
= isl_ast_build_compute_gist_aff(build
, aff
);
423 /* Return the exact lower bound (or upper bound if "upper" is set)
424 * of "domain" as a piecewise affine expression.
426 * If we are computing a lower bound (of a strided dimension), then
427 * we need to make sure it is of the form
431 * where f is the offset and s is the stride.
432 * We therefore need to include the stride constraint before computing
435 static __isl_give isl_pw_aff
*exact_bound(__isl_keep isl_set
*domain
,
436 __isl_keep isl_ast_build
*build
, int upper
)
441 isl_pw_multi_aff
*pma
;
443 domain
= isl_set_copy(domain
);
445 stride
= isl_ast_build_get_stride_constraint(build
);
446 domain
= isl_set_intersect(domain
, stride
);
448 it_map
= isl_ast_build_map_to_iterator(build
, domain
);
450 pma
= isl_map_lexmax_pw_multi_aff(it_map
);
452 pma
= isl_map_lexmin_pw_multi_aff(it_map
);
453 pa
= isl_pw_multi_aff_get_pw_aff(pma
, 0);
454 isl_pw_multi_aff_free(pma
);
455 pa
= isl_ast_build_compute_gist_pw_aff(build
, pa
);
456 pa
= isl_pw_aff_coalesce(pa
);
461 /* Callback for sorting the isl_pw_aff_list passed to reduce_list and
462 * remove_redundant_lower_bounds.
464 static int reduce_list_cmp(__isl_keep isl_pw_aff
*a
, __isl_keep isl_pw_aff
*b
,
467 return isl_pw_aff_plain_cmp(a
, b
);
470 /* Given a list of lower bounds "list", remove those that are redundant
471 * with respect to the other bounds in "list" and the domain of "build".
473 * We first sort the bounds in the same way as they would be sorted
474 * by set_for_node_expressions so that we can try and remove the last
477 * For a lower bound to be effective, there needs to be at least
478 * one domain element for which it is larger than all other lower bounds.
479 * For each lower bound we therefore intersect the domain with
480 * the conditions that it is larger than all other bounds and
481 * check whether the result is empty. If so, the bound can be removed.
483 static __isl_give isl_pw_aff_list
*remove_redundant_lower_bounds(
484 __isl_take isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
489 list
= isl_pw_aff_list_sort(list
, &reduce_list_cmp
, NULL
);
493 n
= isl_pw_aff_list_n_pw_aff(list
);
497 domain
= isl_ast_build_get_domain(build
);
499 for (i
= n
- 1; i
>= 0; --i
) {
504 domain_i
= isl_set_copy(domain
);
505 pa_i
= isl_pw_aff_list_get_pw_aff(list
, i
);
507 for (j
= 0; j
< n
; ++j
) {
514 pa_j
= isl_pw_aff_list_get_pw_aff(list
, j
);
515 better
= isl_pw_aff_gt_set(isl_pw_aff_copy(pa_i
), pa_j
);
516 domain_i
= isl_set_intersect(domain_i
, better
);
519 empty
= isl_set_is_empty(domain_i
);
521 isl_set_free(domain_i
);
522 isl_pw_aff_free(pa_i
);
528 list
= isl_pw_aff_list_drop(list
, i
, 1);
532 isl_set_free(domain
);
536 isl_set_free(domain
);
537 return isl_pw_aff_list_free(list
);
540 /* Extract a lower bound on dimension "pos" from each constraint
541 * in "constraints" and return the list of lower bounds.
542 * If "constraints" has zero elements, then we extract a lower bound
543 * from "domain" instead.
545 * If the current dimension is strided, then the lower bound
546 * is adjusted by lower_bound to match the stride information.
547 * This modification may make one or more lower bounds redundant
548 * with respect to the other lower bounds. We therefore check
549 * for this condition and remove the redundant lower bounds.
551 static __isl_give isl_pw_aff_list
*lower_bounds(
552 __isl_keep isl_constraint_list
*constraints
, int pos
,
553 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
556 isl_pw_aff_list
*list
;
562 n
= isl_constraint_list_n_constraint(constraints
);
565 pa
= exact_bound(domain
, build
, 0);
566 return isl_pw_aff_list_from_pw_aff(pa
);
569 ctx
= isl_ast_build_get_ctx(build
);
570 list
= isl_pw_aff_list_alloc(ctx
,n
);
572 for (i
= 0; i
< n
; ++i
) {
576 c
= isl_constraint_list_get_constraint(constraints
, i
);
577 aff
= lower_bound(c
, pos
, build
);
578 isl_constraint_free(c
);
579 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
582 if (isl_ast_build_has_stride(build
, pos
))
583 list
= remove_redundant_lower_bounds(list
, build
);
588 /* Extract an upper bound on dimension "pos" from each constraint
589 * in "constraints" and return the list of upper bounds.
590 * If "constraints" has zero elements, then we extract an upper bound
591 * from "domain" instead.
593 static __isl_give isl_pw_aff_list
*upper_bounds(
594 __isl_keep isl_constraint_list
*constraints
, int pos
,
595 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
598 isl_pw_aff_list
*list
;
601 n
= isl_constraint_list_n_constraint(constraints
);
604 pa
= exact_bound(domain
, build
, 1);
605 return isl_pw_aff_list_from_pw_aff(pa
);
608 ctx
= isl_ast_build_get_ctx(build
);
609 list
= isl_pw_aff_list_alloc(ctx
,n
);
611 for (i
= 0; i
< n
; ++i
) {
615 c
= isl_constraint_list_get_constraint(constraints
, i
);
616 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
617 isl_constraint_free(c
);
618 aff
= isl_aff_floor(aff
);
619 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
625 /* Return an isl_ast_expr that performs the reduction of type "type"
626 * on AST expressions corresponding to the elements in "list".
628 * The list is assumed to contain at least one element.
629 * If the list contains exactly one element, then the returned isl_ast_expr
630 * simply computes that affine expression.
631 * If the list contains more than one element, then we sort it
632 * using a fairly abitrary but hopefully reasonably stable order.
634 static __isl_give isl_ast_expr
*reduce_list(enum isl_ast_op_type type
,
635 __isl_keep isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
644 n
= isl_pw_aff_list_n_pw_aff(list
);
647 return isl_ast_build_expr_from_pw_aff_internal(build
,
648 isl_pw_aff_list_get_pw_aff(list
, 0));
650 ctx
= isl_pw_aff_list_get_ctx(list
);
651 expr
= isl_ast_expr_alloc_op(ctx
, type
, n
);
655 list
= isl_pw_aff_list_copy(list
);
656 list
= isl_pw_aff_list_sort(list
, &reduce_list_cmp
, NULL
);
658 return isl_ast_expr_free(expr
);
660 for (i
= 0; i
< n
; ++i
) {
661 isl_ast_expr
*expr_i
;
663 expr_i
= isl_ast_build_expr_from_pw_aff_internal(build
,
664 isl_pw_aff_list_get_pw_aff(list
, i
));
667 expr
->u
.op
.args
[i
] = expr_i
;
670 isl_pw_aff_list_free(list
);
673 isl_pw_aff_list_free(list
);
674 isl_ast_expr_free(expr
);
678 /* Add guards implied by the "generated constraints",
679 * but not (necessarily) enforced by the generated AST to "guard".
680 * In particular, if there is any stride constraints,
681 * then add the guard implied by those constraints.
682 * If we have generated a degenerate loop, then add the guard
683 * implied by "bounds" on the outer dimensions, i.e., the guard
684 * that ensures that the single value actually exists.
685 * Since there may also be guards implied by a combination
686 * of these constraints, we first combine them before
687 * deriving the implied constraints.
689 static __isl_give isl_set
*add_implied_guards(__isl_take isl_set
*guard
,
690 int degenerate
, __isl_keep isl_basic_set
*bounds
,
691 __isl_keep isl_ast_build
*build
)
693 int depth
, has_stride
;
697 depth
= isl_ast_build_get_depth(build
);
698 has_stride
= isl_ast_build_has_stride(build
, depth
);
699 if (!has_stride
&& !degenerate
)
702 space
= isl_basic_set_get_space(bounds
);
703 dom
= isl_set_universe(space
);
706 bounds
= isl_basic_set_copy(bounds
);
707 bounds
= isl_basic_set_drop_constraints_not_involving_dims(
708 bounds
, isl_dim_set
, depth
, 1);
709 set
= isl_set_from_basic_set(bounds
);
710 dom
= isl_set_intersect(dom
, set
);
714 set
= isl_ast_build_get_stride_constraint(build
);
715 dom
= isl_set_intersect(dom
, set
);
718 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
719 dom
= isl_ast_build_compute_gist(build
, dom
);
720 guard
= isl_set_intersect(guard
, dom
);
725 /* Update "graft" based on "sub_build" for the degenerate case.
727 * "build" is the build in which graft->node was created
728 * "sub_build" contains information about the current level itself,
729 * including the single value attained.
731 * We set the initialization part of the for loop to the single
732 * value attained by the current dimension.
733 * The increment and condition are not strictly needed as the are known
734 * to be "1" and "iterator <= value" respectively.
736 static __isl_give isl_ast_graft
*refine_degenerate(
737 __isl_take isl_ast_graft
*graft
, __isl_keep isl_ast_build
*build
,
738 __isl_keep isl_ast_build
*sub_build
)
742 if (!graft
|| !sub_build
)
743 return isl_ast_graft_free(graft
);
745 value
= isl_pw_aff_copy(sub_build
->value
);
747 graft
->node
->u
.f
.init
= isl_ast_build_expr_from_pw_aff_internal(build
,
749 if (!graft
->node
->u
.f
.init
)
750 return isl_ast_graft_free(graft
);
755 /* Return the intersection of constraints in "list" as a set.
757 static __isl_give isl_set
*intersect_constraints(
758 __isl_keep isl_constraint_list
*list
)
763 n
= isl_constraint_list_n_constraint(list
);
765 isl_die(isl_constraint_list_get_ctx(list
), isl_error_internal
,
766 "expecting at least one constraint", return NULL
);
768 bset
= isl_basic_set_from_constraint(
769 isl_constraint_list_get_constraint(list
, 0));
770 for (i
= 1; i
< n
; ++i
) {
771 isl_basic_set
*bset_i
;
773 bset_i
= isl_basic_set_from_constraint(
774 isl_constraint_list_get_constraint(list
, i
));
775 bset
= isl_basic_set_intersect(bset
, bset_i
);
778 return isl_set_from_basic_set(bset
);
781 /* Compute the constraints on the outer dimensions enforced by
782 * graft->node and add those constraints to graft->enforced,
783 * in case the upper bound is expressed as a set "upper".
785 * In particular, if l(...) is a lower bound in "lower", and
787 * -a i + f(...) >= 0 or a i <= f(...)
789 * is an upper bound ocnstraint on the current dimension i,
790 * then the for loop enforces the constraint
792 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
794 * We therefore simply take each lower bound in turn, plug it into
795 * the upper bounds and compute the intersection over all lower bounds.
797 * If a lower bound is a rational expression, then
798 * isl_basic_set_preimage_multi_aff will force this rational
799 * expression to have only integer values. However, the loop
800 * itself does not enforce this integrality constraint. We therefore
801 * use the ceil of the lower bounds instead of the lower bounds themselves.
802 * Other constraints will make sure that the for loop is only executed
803 * when each of the lower bounds attains an integral value.
804 * In particular, potentially rational values only occur in
805 * lower_bound if the offset is a (seemingly) rational expression,
806 * but then outer conditions will make sure that this rational expression
807 * only attains integer values.
809 static __isl_give isl_ast_graft
*set_enforced_from_set(
810 __isl_take isl_ast_graft
*graft
,
811 __isl_keep isl_pw_aff_list
*lower
, int pos
, __isl_keep isl_set
*upper
)
814 isl_basic_set
*enforced
;
815 isl_pw_multi_aff
*pma
;
818 if (!graft
|| !lower
)
819 return isl_ast_graft_free(graft
);
821 space
= isl_set_get_space(upper
);
822 enforced
= isl_basic_set_universe(isl_space_copy(space
));
824 space
= isl_space_map_from_set(space
);
825 pma
= isl_pw_multi_aff_identity(space
);
827 n
= isl_pw_aff_list_n_pw_aff(lower
);
828 for (i
= 0; i
< n
; ++i
) {
832 isl_pw_multi_aff
*pma_i
;
834 pa
= isl_pw_aff_list_get_pw_aff(lower
, i
);
835 pa
= isl_pw_aff_ceil(pa
);
836 pma_i
= isl_pw_multi_aff_copy(pma
);
837 pma_i
= isl_pw_multi_aff_set_pw_aff(pma_i
, pos
, pa
);
838 enforced_i
= isl_set_copy(upper
);
839 enforced_i
= isl_set_preimage_pw_multi_aff(enforced_i
, pma_i
);
840 hull
= isl_set_simple_hull(enforced_i
);
841 enforced
= isl_basic_set_intersect(enforced
, hull
);
844 isl_pw_multi_aff_free(pma
);
846 graft
= isl_ast_graft_enforce(graft
, enforced
);
851 /* Compute the constraints on the outer dimensions enforced by
852 * graft->node and add those constraints to graft->enforced,
853 * in case the upper bound is expressed as
854 * a list of affine expressions "upper".
856 * The enforced condition is that each lower bound expression is less
857 * than or equal to each upper bound expression.
859 static __isl_give isl_ast_graft
*set_enforced_from_list(
860 __isl_take isl_ast_graft
*graft
,
861 __isl_keep isl_pw_aff_list
*lower
, __isl_keep isl_pw_aff_list
*upper
)
864 isl_basic_set
*enforced
;
866 lower
= isl_pw_aff_list_copy(lower
);
867 upper
= isl_pw_aff_list_copy(upper
);
868 cond
= isl_pw_aff_list_le_set(lower
, upper
);
869 enforced
= isl_set_simple_hull(cond
);
870 graft
= isl_ast_graft_enforce(graft
, enforced
);
875 /* Does "aff" have a negative constant term?
877 static int aff_constant_is_negative(__isl_take isl_set
*set
,
878 __isl_take isl_aff
*aff
, void *user
)
883 v
= isl_aff_get_constant_val(aff
);
884 *neg
= isl_val_is_neg(v
);
889 return *neg
? 0 : -1;
892 /* Does "pa" have a negative constant term over its entire domain?
894 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff
*pa
, void *user
)
899 r
= isl_pw_aff_foreach_piece(pa
, &aff_constant_is_negative
, user
);
902 return (*neg
&& r
>= 0) ? 0 : -1;
905 /* Does each element in "list" have a negative constant term?
907 * The callback terminates the iteration as soon an element has been
908 * found that does not have a negative constant term.
910 static int list_constant_is_negative(__isl_keep isl_pw_aff_list
*list
)
914 if (isl_pw_aff_list_foreach(list
,
915 &pw_aff_constant_is_negative
, &neg
) < 0 && neg
)
921 /* Add 1 to each of the elements in "list", where each of these elements
922 * is defined over the internal schedule space of "build".
924 static __isl_give isl_pw_aff_list
*list_add_one(
925 __isl_take isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
932 space
= isl_ast_build_get_space(build
, 1);
933 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(space
));
934 aff
= isl_aff_add_constant_si(aff
, 1);
935 one
= isl_pw_aff_from_aff(aff
);
937 n
= isl_pw_aff_list_n_pw_aff(list
);
938 for (i
= 0; i
< n
; ++i
) {
940 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
941 pa
= isl_pw_aff_add(pa
, isl_pw_aff_copy(one
));
942 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
945 isl_pw_aff_free(one
);
950 /* Set the condition part of the for node graft->node in case
951 * the upper bound is represented as a list of piecewise affine expressions.
953 * In particular, set the condition to
955 * iterator <= min(list of upper bounds)
957 * If each of the upper bounds has a negative constant term, then
958 * set the condition to
960 * iterator < min(list of (upper bound + 1)s)
963 static __isl_give isl_ast_graft
*set_for_cond_from_list(
964 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*list
,
965 __isl_keep isl_ast_build
*build
)
968 isl_ast_expr
*bound
, *iterator
, *cond
;
969 enum isl_ast_op_type type
= isl_ast_op_le
;
972 return isl_ast_graft_free(graft
);
974 neg
= list_constant_is_negative(list
);
976 return isl_ast_graft_free(graft
);
977 list
= isl_pw_aff_list_copy(list
);
979 list
= list_add_one(list
, build
);
980 type
= isl_ast_op_lt
;
983 bound
= reduce_list(isl_ast_op_min
, list
, build
);
984 iterator
= isl_ast_expr_copy(graft
->node
->u
.f
.iterator
);
985 cond
= isl_ast_expr_alloc_binary(type
, iterator
, bound
);
986 graft
->node
->u
.f
.cond
= cond
;
988 isl_pw_aff_list_free(list
);
989 if (!graft
->node
->u
.f
.cond
)
990 return isl_ast_graft_free(graft
);
994 /* Set the condition part of the for node graft->node in case
995 * the upper bound is represented as a set.
997 static __isl_give isl_ast_graft
*set_for_cond_from_set(
998 __isl_take isl_ast_graft
*graft
, __isl_keep isl_set
*set
,
999 __isl_keep isl_ast_build
*build
)
1006 cond
= isl_ast_build_expr_from_set_internal(build
, isl_set_copy(set
));
1007 graft
->node
->u
.f
.cond
= cond
;
1008 if (!graft
->node
->u
.f
.cond
)
1009 return isl_ast_graft_free(graft
);
1013 /* Construct an isl_ast_expr for the increment (i.e., stride) of
1014 * the current dimension.
1016 static __isl_give isl_ast_expr
*for_inc(__isl_keep isl_ast_build
*build
)
1024 ctx
= isl_ast_build_get_ctx(build
);
1025 depth
= isl_ast_build_get_depth(build
);
1027 if (!isl_ast_build_has_stride(build
, depth
))
1028 return isl_ast_expr_alloc_int_si(ctx
, 1);
1030 v
= isl_ast_build_get_stride(build
, depth
);
1031 return isl_ast_expr_from_val(v
);
1034 /* Should we express the loop condition as
1036 * iterator <= min(list of upper bounds)
1038 * or as a conjunction of constraints?
1040 * The first is constructed from a list of upper bounds.
1041 * The second is constructed from a set.
1043 * If there are no upper bounds in "constraints", then this could mean
1044 * that "domain" simply doesn't have an upper bound or that we didn't
1045 * pick any upper bound. In the first case, we want to generate the
1046 * loop condition as a(n empty) conjunction of constraints
1047 * In the second case, we will compute
1048 * a single upper bound from "domain" and so we use the list form.
1050 * If there are upper bounds in "constraints",
1051 * then we use the list form iff the atomic_upper_bound option is set.
1053 static int use_upper_bound_list(isl_ctx
*ctx
, int n_upper
,
1054 __isl_keep isl_set
*domain
, int depth
)
1057 return isl_options_get_ast_build_atomic_upper_bound(ctx
);
1059 return isl_set_dim_has_upper_bound(domain
, isl_dim_set
, depth
);
1062 /* Fill in the expressions of the for node in graft->node.
1065 * - set the initialization part of the loop to the maximum of the lower bounds
1066 * - extract the increment from the stride of the current dimension
1067 * - construct the for condition either based on a list of upper bounds
1068 * or on a set of upper bound constraints.
1070 static __isl_give isl_ast_graft
*set_for_node_expressions(
1071 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*lower
,
1072 int use_list
, __isl_keep isl_pw_aff_list
*upper_list
,
1073 __isl_keep isl_set
*upper_set
, __isl_keep isl_ast_build
*build
)
1080 build
= isl_ast_build_copy(build
);
1083 node
->u
.f
.init
= reduce_list(isl_ast_op_max
, lower
, build
);
1084 node
->u
.f
.inc
= for_inc(build
);
1087 graft
= set_for_cond_from_list(graft
, upper_list
, build
);
1089 graft
= set_for_cond_from_set(graft
, upper_set
, build
);
1091 isl_ast_build_free(build
);
1093 if (!node
->u
.f
.iterator
|| !node
->u
.f
.init
||
1094 !node
->u
.f
.cond
|| !node
->u
.f
.inc
)
1095 return isl_ast_graft_free(graft
);
1100 /* Update "graft" based on "bounds" and "domain" for the generic,
1101 * non-degenerate, case.
1103 * "c_lower" and "c_upper" contain the lower and upper bounds
1104 * that the loop node should express.
1105 * "domain" is the subset of the intersection of the constraints
1106 * for which some code is executed.
1108 * There may be zero lower bounds or zero upper bounds in "constraints"
1109 * in case the list of constraints was created
1110 * based on the atomic option or based on separation with explicit bounds.
1111 * In that case, we use "domain" to derive lower and/or upper bounds.
1113 * We first compute a list of one or more lower bounds.
1115 * Then we decide if we want to express the condition as
1117 * iterator <= min(list of upper bounds)
1119 * or as a conjunction of constraints.
1121 * The set of enforced constraints is then computed either based on
1122 * a list of upper bounds or on a set of upper bound constraints.
1123 * We do not compute any enforced constraints if we were forced
1124 * to compute a lower or upper bound using exact_bound. The domains
1125 * of the resulting expressions may imply some bounds on outer dimensions
1126 * that we do not want to appear in the enforced constraints since
1127 * they are not actually enforced by the corresponding code.
1129 * Finally, we fill in the expressions of the for node.
1131 static __isl_give isl_ast_graft
*refine_generic_bounds(
1132 __isl_take isl_ast_graft
*graft
,
1133 __isl_take isl_constraint_list
*c_lower
,
1134 __isl_take isl_constraint_list
*c_upper
,
1135 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1139 isl_pw_aff_list
*lower
;
1141 isl_set
*upper_set
= NULL
;
1142 isl_pw_aff_list
*upper_list
= NULL
;
1143 int n_lower
, n_upper
;
1145 if (!graft
|| !c_lower
|| !c_upper
|| !build
)
1148 depth
= isl_ast_build_get_depth(build
);
1149 ctx
= isl_ast_graft_get_ctx(graft
);
1151 n_lower
= isl_constraint_list_n_constraint(c_lower
);
1152 n_upper
= isl_constraint_list_n_constraint(c_upper
);
1154 use_list
= use_upper_bound_list(ctx
, n_upper
, domain
, depth
);
1156 lower
= lower_bounds(c_lower
, depth
, domain
, build
);
1159 upper_list
= upper_bounds(c_upper
, depth
, domain
, build
);
1160 else if (n_upper
> 0)
1161 upper_set
= intersect_constraints(c_upper
);
1163 upper_set
= isl_set_universe(isl_set_get_space(domain
));
1165 if (n_lower
== 0 || n_upper
== 0)
1168 graft
= set_enforced_from_list(graft
, lower
, upper_list
);
1170 graft
= set_enforced_from_set(graft
, lower
, depth
, upper_set
);
1172 graft
= set_for_node_expressions(graft
, lower
, use_list
, upper_list
,
1175 isl_pw_aff_list_free(lower
);
1176 isl_pw_aff_list_free(upper_list
);
1177 isl_set_free(upper_set
);
1178 isl_constraint_list_free(c_lower
);
1179 isl_constraint_list_free(c_upper
);
1183 isl_constraint_list_free(c_lower
);
1184 isl_constraint_list_free(c_upper
);
1185 return isl_ast_graft_free(graft
);
1188 /* Internal data structure used inside count_constraints to keep
1189 * track of the number of constraints that are independent of dimension "pos",
1190 * the lower bounds in "pos" and the upper bounds in "pos".
1192 struct isl_ast_count_constraints_data
{
1200 /* Increment data->n_indep, data->lower or data->upper depending
1201 * on whether "c" is independenct of dimensions data->pos,
1202 * a lower bound or an upper bound.
1204 static int count_constraints(__isl_take isl_constraint
*c
, void *user
)
1206 struct isl_ast_count_constraints_data
*data
= user
;
1208 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->pos
))
1210 else if (isl_constraint_is_upper_bound(c
, isl_dim_set
, data
->pos
))
1215 isl_constraint_free(c
);
1220 /* Update "graft" based on "bounds" and "domain" for the generic,
1221 * non-degenerate, case.
1223 * "list" respresent the list of bounds that need to be encoded by
1224 * the for loop. Only the constraints that involve the iterator
1225 * are relevant here. The other constraints are taken care of by
1226 * the caller and are included in the generated constraints of "build".
1227 * "domain" is the subset of the intersection of the constraints
1228 * for which some code is executed.
1229 * "build" is the build in which graft->node was created.
1231 * We separate lower bounds, upper bounds and constraints that
1232 * are independent of the loop iterator.
1234 * The actual for loop bounds are generated in refine_generic_bounds.
1236 static __isl_give isl_ast_graft
*refine_generic_split(
1237 __isl_take isl_ast_graft
*graft
, __isl_take isl_constraint_list
*list
,
1238 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1240 struct isl_ast_count_constraints_data data
;
1241 isl_constraint_list
*lower
;
1242 isl_constraint_list
*upper
;
1245 return isl_ast_graft_free(graft
);
1247 data
.pos
= isl_ast_build_get_depth(build
);
1249 list
= isl_constraint_list_sort(list
, &cmp_constraint
, &data
.pos
);
1251 return isl_ast_graft_free(graft
);
1253 data
.n_indep
= data
.n_lower
= data
.n_upper
= 0;
1254 if (isl_constraint_list_foreach(list
, &count_constraints
, &data
) < 0) {
1255 isl_constraint_list_free(list
);
1256 return isl_ast_graft_free(graft
);
1259 lower
= isl_constraint_list_drop(list
, 0, data
.n_indep
);
1260 upper
= isl_constraint_list_copy(lower
);
1261 lower
= isl_constraint_list_drop(lower
, data
.n_lower
, data
.n_upper
);
1262 upper
= isl_constraint_list_drop(upper
, 0, data
.n_lower
);
1264 return refine_generic_bounds(graft
, lower
, upper
, domain
, build
);
1267 /* Update "graft" based on "bounds" and "domain" for the generic,
1268 * non-degenerate, case.
1270 * "bounds" respresent the bounds that need to be encoded by
1271 * the for loop (or a guard around the for loop).
1272 * "domain" is the subset of "bounds" for which some code is executed.
1273 * "build" is the build in which graft->node was created.
1275 * We break up "bounds" into a list of constraints and continue with
1276 * refine_generic_split.
1278 static __isl_give isl_ast_graft
*refine_generic(
1279 __isl_take isl_ast_graft
*graft
,
1280 __isl_keep isl_basic_set
*bounds
, __isl_keep isl_set
*domain
,
1281 __isl_keep isl_ast_build
*build
)
1283 isl_constraint_list
*list
;
1285 if (!build
|| !graft
)
1286 return isl_ast_graft_free(graft
);
1288 list
= isl_basic_set_get_constraint_list(bounds
);
1290 graft
= refine_generic_split(graft
, list
, domain
, build
);
1295 /* Create a for node for the current level.
1297 * Mark the for node degenerate if "degenerate" is set.
1299 static __isl_give isl_ast_node
*create_for(__isl_keep isl_ast_build
*build
,
1309 depth
= isl_ast_build_get_depth(build
);
1310 id
= isl_ast_build_get_iterator_id(build
, depth
);
1311 node
= isl_ast_node_alloc_for(id
);
1313 node
= isl_ast_node_for_mark_degenerate(node
);
1318 /* If the ast_build_exploit_nested_bounds option is set, then return
1319 * the constraints enforced by all elements in "list".
1320 * Otherwise, return the universe.
1322 static __isl_give isl_basic_set
*extract_shared_enforced(
1323 __isl_keep isl_ast_graft_list
*list
, __isl_keep isl_ast_build
*build
)
1331 ctx
= isl_ast_graft_list_get_ctx(list
);
1332 if (isl_options_get_ast_build_exploit_nested_bounds(ctx
))
1333 return isl_ast_graft_list_extract_shared_enforced(list
, build
);
1335 space
= isl_ast_build_get_space(build
, 1);
1336 return isl_basic_set_universe(space
);
1339 /* Return the pending constraints of "build" that are not already taken
1340 * care of (by a combination of "enforced" and the generated constraints
1343 static __isl_give isl_set
*extract_pending(__isl_keep isl_ast_build
*build
,
1344 __isl_keep isl_basic_set
*enforced
)
1346 isl_set
*guard
, *context
;
1348 guard
= isl_ast_build_get_pending(build
);
1349 context
= isl_set_from_basic_set(isl_basic_set_copy(enforced
));
1350 context
= isl_set_intersect(context
,
1351 isl_ast_build_get_generated(build
));
1352 return isl_set_gist(guard
, context
);
1355 /* Create an AST node for the current dimension based on
1356 * the schedule domain "bounds" and return the node encapsulated
1357 * in an isl_ast_graft.
1359 * "executed" is the current inverse schedule, taking into account
1360 * the bounds in "bounds"
1361 * "domain" is the domain of "executed", with inner dimensions projected out.
1362 * It may be a strict subset of "bounds" in case "bounds" was created
1363 * based on the atomic option or based on separation with explicit bounds.
1365 * "domain" may satisfy additional equalities that result
1366 * from intersecting "executed" with "bounds" in add_node.
1367 * It may also satisfy some global constraints that were dropped out because
1368 * we performed separation with explicit bounds.
1369 * The very first step is then to copy these constraints to "bounds".
1371 * Since we may be calling before_each_for and after_each_for
1372 * callbacks, we record the current inverse schedule in the build.
1374 * We consider three builds,
1375 * "build" is the one in which the current level is created,
1376 * "body_build" is the build in which the next level is created,
1377 * "sub_build" is essentially the same as "body_build", except that
1378 * the depth has not been increased yet.
1380 * "build" already contains information (in strides and offsets)
1381 * about the strides at the current level, but this information is not
1382 * reflected in the build->domain.
1383 * We first add this information and the "bounds" to the sub_build->domain.
1384 * isl_ast_build_set_loop_bounds adds the stride information and
1385 * checks whether the current dimension attains
1386 * only a single value and whether this single value can be represented using
1387 * a single affine expression.
1388 * In the first case, the current level is considered "degenerate".
1389 * In the second, sub-case, the current level is considered "eliminated".
1390 * Eliminated levels don't need to be reflected in the AST since we can
1391 * simply plug in the affine expression. For degenerate, but non-eliminated,
1392 * levels, we do introduce a for node, but mark is as degenerate so that
1393 * it can be printed as an assignment of the single value to the loop
1396 * If the current level is eliminated, we explicitly plug in the value
1397 * for the current level found by isl_ast_build_set_loop_bounds in the
1398 * inverse schedule. This ensures that if we are working on a slice
1399 * of the domain based on information available in the inverse schedule
1400 * and the build domain, that then this information is also reflected
1401 * in the inverse schedule. This operation also eliminates the current
1402 * dimension from the inverse schedule making sure no inner dimensions depend
1403 * on the current dimension. Otherwise, we create a for node, marking
1404 * it degenerate if appropriate. The initial for node is still incomplete
1405 * and will be completed in either refine_degenerate or refine_generic.
1407 * We then generate a sequence of grafts for the next level,
1408 * create a surrounding graft for the current level and insert
1409 * the for node we created (if the current level is not eliminated).
1410 * Before creating a graft for the current level, we first extract
1411 * hoistable constraints from the child guards and combine them
1412 * with the pending constraints in the build. These constraints
1413 * are used to simplify the child guards and then added to the guard
1414 * of the current graft to ensure that they will be generated.
1415 * If the hoisted guard is a disjunction, then we use it directly
1416 * to gist the guards on the children before intersect it with the
1417 * pending constraints. We do so because this disjunction is typically
1418 * identical to the guards on the children such that these guards
1419 * can be effectively removed completely. After the intersection,
1420 * the gist operation would have a harder time figuring this out.
1422 * Finally, we set the bounds of the for loop in either
1423 * refine_degenerate or refine_generic.
1424 * We do so in a context where the pending constraints of the build
1425 * have been replaced by the guard of the current graft.
1427 static __isl_give isl_ast_graft
*create_node_scaled(
1428 __isl_take isl_union_map
*executed
,
1429 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1430 __isl_take isl_ast_build
*build
)
1433 int degenerate
, eliminated
;
1434 isl_basic_set
*hull
;
1435 isl_basic_set
*enforced
;
1436 isl_set
*guard
, *hoisted
;
1437 isl_ast_node
*node
= NULL
;
1438 isl_ast_graft
*graft
;
1439 isl_ast_graft_list
*children
;
1440 isl_ast_build
*sub_build
;
1441 isl_ast_build
*body_build
;
1443 domain
= isl_ast_build_eliminate_divs(build
, domain
);
1444 domain
= isl_set_detect_equalities(domain
);
1445 hull
= isl_set_unshifted_simple_hull(isl_set_copy(domain
));
1446 bounds
= isl_basic_set_intersect(bounds
, hull
);
1447 build
= isl_ast_build_set_executed(build
, isl_union_map_copy(executed
));
1449 depth
= isl_ast_build_get_depth(build
);
1450 sub_build
= isl_ast_build_copy(build
);
1451 sub_build
= isl_ast_build_set_loop_bounds(sub_build
,
1452 isl_basic_set_copy(bounds
));
1453 degenerate
= isl_ast_build_has_value(sub_build
);
1454 eliminated
= isl_ast_build_has_affine_value(sub_build
, depth
);
1455 if (degenerate
< 0 || eliminated
< 0)
1456 executed
= isl_union_map_free(executed
);
1458 executed
= plug_in_values(executed
, sub_build
);
1460 node
= create_for(build
, degenerate
);
1462 body_build
= isl_ast_build_copy(sub_build
);
1463 body_build
= isl_ast_build_increase_depth(body_build
);
1465 node
= before_each_for(node
, body_build
);
1466 children
= generate_next_level(executed
,
1467 isl_ast_build_copy(body_build
));
1469 enforced
= extract_shared_enforced(children
, build
);
1470 guard
= extract_pending(sub_build
, enforced
);
1471 hoisted
= isl_ast_graft_list_extract_hoistable_guard(children
, build
);
1472 if (isl_set_n_basic_set(hoisted
) > 1)
1473 children
= isl_ast_graft_list_gist_guards(children
,
1474 isl_set_copy(hoisted
));
1475 guard
= isl_set_intersect(guard
, hoisted
);
1477 guard
= add_implied_guards(guard
, degenerate
, bounds
, build
);
1479 graft
= isl_ast_graft_alloc_from_children(children
,
1480 isl_set_copy(guard
), enforced
, build
, sub_build
);
1483 bounds
= isl_ast_build_compute_gist_basic_set(build
, bounds
);
1485 isl_ast_build
*for_build
;
1487 graft
= isl_ast_graft_insert_for(graft
, node
);
1488 for_build
= isl_ast_build_copy(build
);
1489 for_build
= isl_ast_build_replace_pending_by_guard(for_build
,
1490 isl_set_copy(guard
));
1492 graft
= refine_degenerate(graft
, for_build
, sub_build
);
1494 graft
= refine_generic(graft
, bounds
,
1496 isl_ast_build_free(for_build
);
1498 isl_set_free(guard
);
1500 graft
= after_each_for(graft
, body_build
);
1502 isl_ast_build_free(body_build
);
1503 isl_ast_build_free(sub_build
);
1504 isl_ast_build_free(build
);
1505 isl_basic_set_free(bounds
);
1506 isl_set_free(domain
);
1511 /* Internal data structure for checking if all constraints involving
1512 * the input dimension "depth" are such that the other coefficients
1513 * are multiples of "m", reducing "m" if they are not.
1514 * If "m" is reduced all the way down to "1", then the check has failed
1515 * and we break out of the iteration.
1517 struct isl_check_scaled_data
{
1522 /* If constraint "c" involves the input dimension data->depth,
1523 * then make sure that all the other coefficients are multiples of data->m,
1524 * reducing data->m if needed.
1525 * Break out of the iteration if data->m has become equal to "1".
1527 static int constraint_check_scaled(__isl_take isl_constraint
*c
, void *user
)
1529 struct isl_check_scaled_data
*data
= user
;
1531 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_out
,
1534 if (!isl_constraint_involves_dims(c
, isl_dim_in
, data
->depth
, 1)) {
1535 isl_constraint_free(c
);
1539 for (i
= 0; i
< 4; ++i
) {
1540 n
= isl_constraint_dim(c
, t
[i
]);
1541 for (j
= 0; j
< n
; ++j
) {
1544 if (t
[i
] == isl_dim_in
&& j
== data
->depth
)
1546 if (!isl_constraint_involves_dims(c
, t
[i
], j
, 1))
1548 d
= isl_constraint_get_coefficient_val(c
, t
[i
], j
);
1549 data
->m
= isl_val_gcd(data
->m
, d
);
1550 if (isl_val_is_one(data
->m
))
1557 isl_constraint_free(c
);
1559 return i
< 4 ? -1 : 0;
1562 /* For each constraint of "bmap" that involves the input dimension data->depth,
1563 * make sure that all the other coefficients are multiples of data->m,
1564 * reducing data->m if needed.
1565 * Break out of the iteration if data->m has become equal to "1".
1567 static int basic_map_check_scaled(__isl_take isl_basic_map
*bmap
, void *user
)
1571 r
= isl_basic_map_foreach_constraint(bmap
,
1572 &constraint_check_scaled
, user
);
1573 isl_basic_map_free(bmap
);
1578 /* For each constraint of "map" that involves the input dimension data->depth,
1579 * make sure that all the other coefficients are multiples of data->m,
1580 * reducing data->m if needed.
1581 * Break out of the iteration if data->m has become equal to "1".
1583 static int map_check_scaled(__isl_take isl_map
*map
, void *user
)
1587 r
= isl_map_foreach_basic_map(map
, &basic_map_check_scaled
, user
);
1593 /* Create an AST node for the current dimension based on
1594 * the schedule domain "bounds" and return the node encapsulated
1595 * in an isl_ast_graft.
1597 * "executed" is the current inverse schedule, taking into account
1598 * the bounds in "bounds"
1599 * "domain" is the domain of "executed", with inner dimensions projected out.
1602 * Before moving on to the actual AST node construction in create_node_scaled,
1603 * we first check if the current dimension is strided and if we can scale
1604 * down this stride. Note that we only do this if the ast_build_scale_strides
1607 * In particular, let the current dimension take on values
1611 * with a an integer. We check if we can find an integer m that (obviously)
1612 * divides both f and s.
1614 * If so, we check if the current dimension only appears in constraints
1615 * where the coefficients of the other variables are multiples of m.
1616 * We perform this extra check to avoid the risk of introducing
1617 * divisions by scaling down the current dimension.
1619 * If so, we scale the current dimension down by a factor of m.
1620 * That is, we plug in
1624 * Note that in principle we could always scale down strided loops
1629 * but this may result in i' taking on larger values than the original i,
1630 * due to the shift by "f".
1631 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1633 static __isl_give isl_ast_graft
*create_node(__isl_take isl_union_map
*executed
,
1634 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1635 __isl_take isl_ast_build
*build
)
1637 struct isl_check_scaled_data data
;
1642 ctx
= isl_ast_build_get_ctx(build
);
1643 if (!isl_options_get_ast_build_scale_strides(ctx
))
1644 return create_node_scaled(executed
, bounds
, domain
, build
);
1646 data
.depth
= isl_ast_build_get_depth(build
);
1647 if (!isl_ast_build_has_stride(build
, data
.depth
))
1648 return create_node_scaled(executed
, bounds
, domain
, build
);
1650 offset
= isl_ast_build_get_offset(build
, data
.depth
);
1651 data
.m
= isl_ast_build_get_stride(build
, data
.depth
);
1653 offset
= isl_aff_free(offset
);
1654 offset
= isl_aff_scale_down_val(offset
, isl_val_copy(data
.m
));
1655 d
= isl_aff_get_denominator_val(offset
);
1657 executed
= isl_union_map_free(executed
);
1659 if (executed
&& isl_val_is_divisible_by(data
.m
, d
))
1660 data
.m
= isl_val_div(data
.m
, d
);
1662 data
.m
= isl_val_set_si(data
.m
, 1);
1666 if (!isl_val_is_one(data
.m
)) {
1667 if (isl_union_map_foreach_map(executed
, &map_check_scaled
,
1669 !isl_val_is_one(data
.m
))
1670 executed
= isl_union_map_free(executed
);
1673 if (!isl_val_is_one(data
.m
)) {
1678 isl_union_map
*umap
;
1680 space
= isl_ast_build_get_space(build
, 1);
1681 space
= isl_space_map_from_set(space
);
1682 ma
= isl_multi_aff_identity(space
);
1683 aff
= isl_multi_aff_get_aff(ma
, data
.depth
);
1684 aff
= isl_aff_scale_val(aff
, isl_val_copy(data
.m
));
1685 ma
= isl_multi_aff_set_aff(ma
, data
.depth
, aff
);
1687 bounds
= isl_basic_set_preimage_multi_aff(bounds
,
1688 isl_multi_aff_copy(ma
));
1689 domain
= isl_set_preimage_multi_aff(domain
,
1690 isl_multi_aff_copy(ma
));
1691 map
= isl_map_reverse(isl_map_from_multi_aff(ma
));
1692 umap
= isl_union_map_from_map(map
);
1693 executed
= isl_union_map_apply_domain(executed
,
1694 isl_union_map_copy(umap
));
1695 build
= isl_ast_build_scale_down(build
, isl_val_copy(data
.m
),
1698 isl_aff_free(offset
);
1699 isl_val_free(data
.m
);
1701 return create_node_scaled(executed
, bounds
, domain
, build
);
1704 /* Add the basic set to the list that "user" points to.
1706 static int collect_basic_set(__isl_take isl_basic_set
*bset
, void *user
)
1708 isl_basic_set_list
**list
= user
;
1710 *list
= isl_basic_set_list_add(*list
, bset
);
1715 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1717 static __isl_give isl_basic_set_list
*isl_basic_set_list_from_set(
1718 __isl_take isl_set
*set
)
1722 isl_basic_set_list
*list
;
1727 ctx
= isl_set_get_ctx(set
);
1729 n
= isl_set_n_basic_set(set
);
1730 list
= isl_basic_set_list_alloc(ctx
, n
);
1731 if (isl_set_foreach_basic_set(set
, &collect_basic_set
, &list
) < 0)
1732 list
= isl_basic_set_list_free(list
);
1738 /* Generate code for the schedule domain "bounds"
1739 * and add the result to "list".
1741 * We mainly detect strides here and check if the bounds do not
1742 * conflict with the current build domain
1743 * and then pass over control to create_node.
1745 * "bounds" reflects the bounds on the current dimension and possibly
1746 * some extra conditions on outer dimensions.
1747 * It does not, however, include any divs involving the current dimension,
1748 * so it does not capture any stride constraints.
1749 * We therefore need to compute that part of the schedule domain that
1750 * intersects with "bounds" and derive the strides from the result.
1752 static __isl_give isl_ast_graft_list
*add_node(
1753 __isl_take isl_ast_graft_list
*list
, __isl_take isl_union_map
*executed
,
1754 __isl_take isl_basic_set
*bounds
, __isl_take isl_ast_build
*build
)
1756 isl_ast_graft
*graft
;
1757 isl_set
*domain
= NULL
;
1758 isl_union_set
*uset
;
1759 int empty
, disjoint
;
1761 uset
= isl_union_set_from_basic_set(isl_basic_set_copy(bounds
));
1762 executed
= isl_union_map_intersect_domain(executed
, uset
);
1763 empty
= isl_union_map_is_empty(executed
);
1769 uset
= isl_union_map_domain(isl_union_map_copy(executed
));
1770 domain
= isl_set_from_union_set(uset
);
1771 domain
= isl_ast_build_specialize(build
, domain
);
1773 domain
= isl_set_compute_divs(domain
);
1774 domain
= isl_ast_build_eliminate_inner(build
, domain
);
1775 disjoint
= isl_set_is_disjoint(domain
, build
->domain
);
1781 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
1783 graft
= create_node(executed
, bounds
, domain
,
1784 isl_ast_build_copy(build
));
1785 list
= isl_ast_graft_list_add(list
, graft
);
1786 isl_ast_build_free(build
);
1789 list
= isl_ast_graft_list_free(list
);
1791 isl_set_free(domain
);
1792 isl_basic_set_free(bounds
);
1793 isl_union_map_free(executed
);
1794 isl_ast_build_free(build
);
1798 /* Does any element of i follow or coincide with any element of j
1799 * at the current depth for equal values of the outer dimensions?
1801 static int domain_follows_at_depth(__isl_keep isl_basic_set
*i
,
1802 __isl_keep isl_basic_set
*j
, void *user
)
1804 int depth
= *(int *) user
;
1805 isl_basic_map
*test
;
1809 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
1810 isl_basic_set_copy(j
));
1811 for (l
= 0; l
< depth
; ++l
)
1812 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1814 test
= isl_basic_map_order_ge(test
, isl_dim_in
, depth
,
1815 isl_dim_out
, depth
);
1816 empty
= isl_basic_map_is_empty(test
);
1817 isl_basic_map_free(test
);
1819 return empty
< 0 ? -1 : !empty
;
1822 /* Split up each element of "list" into a part that is related to "bset"
1823 * according to "gt" and a part that is not.
1824 * Return a list that consist of "bset" and all the pieces.
1826 static __isl_give isl_basic_set_list
*add_split_on(
1827 __isl_take isl_basic_set_list
*list
, __isl_take isl_basic_set
*bset
,
1828 __isl_keep isl_basic_map
*gt
)
1831 isl_basic_set_list
*res
;
1834 bset
= isl_basic_set_free(bset
);
1836 gt
= isl_basic_map_copy(gt
);
1837 gt
= isl_basic_map_intersect_domain(gt
, isl_basic_set_copy(bset
));
1838 n
= isl_basic_set_list_n_basic_set(list
);
1839 res
= isl_basic_set_list_from_basic_set(bset
);
1840 for (i
= 0; res
&& i
< n
; ++i
) {
1841 isl_basic_set
*bset
;
1842 isl_set
*set1
, *set2
;
1843 isl_basic_map
*bmap
;
1846 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1847 bmap
= isl_basic_map_copy(gt
);
1848 bmap
= isl_basic_map_intersect_range(bmap
, bset
);
1849 bset
= isl_basic_map_range(bmap
);
1850 empty
= isl_basic_set_is_empty(bset
);
1852 res
= isl_basic_set_list_free(res
);
1854 isl_basic_set_free(bset
);
1855 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1856 res
= isl_basic_set_list_add(res
, bset
);
1860 res
= isl_basic_set_list_add(res
, isl_basic_set_copy(bset
));
1861 set1
= isl_set_from_basic_set(bset
);
1862 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1863 set2
= isl_set_from_basic_set(bset
);
1864 set1
= isl_set_subtract(set2
, set1
);
1865 set1
= isl_set_make_disjoint(set1
);
1867 res
= isl_basic_set_list_concat(res
,
1868 isl_basic_set_list_from_set(set1
));
1870 isl_basic_map_free(gt
);
1871 isl_basic_set_list_free(list
);
1875 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1876 __isl_keep isl_basic_set_list
*domain_list
,
1877 __isl_keep isl_union_map
*executed
,
1878 __isl_keep isl_ast_build
*build
);
1880 /* Internal data structure for add_nodes.
1882 * "executed" and "build" are extra arguments to be passed to add_node.
1883 * "list" collects the results.
1885 struct isl_add_nodes_data
{
1886 isl_union_map
*executed
;
1887 isl_ast_build
*build
;
1889 isl_ast_graft_list
*list
;
1892 /* Generate code for the schedule domains in "scc"
1893 * and add the results to "list".
1895 * The domains in "scc" form a strongly connected component in the ordering.
1896 * If the number of domains in "scc" is larger than 1, then this means
1897 * that we cannot determine a valid ordering for the domains in the component.
1898 * This should be fairly rare because the individual domains
1899 * have been made disjoint first.
1900 * The problem is that the domains may be integrally disjoint but not
1901 * rationally disjoint. For example, we may have domains
1903 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1905 * These two domains have an empty intersection, but their rational
1906 * relaxations do intersect. It is impossible to order these domains
1907 * in the second dimension because the first should be ordered before
1908 * the second for outer dimension equal to 0, while it should be ordered
1909 * after for outer dimension equal to 1.
1911 * This may happen in particular in case of unrolling since the domain
1912 * of each slice is replaced by its simple hull.
1914 * For each basic set i in "scc" and for each of the following basic sets j,
1915 * we split off that part of the basic set i that shares the outer dimensions
1916 * with j and lies before j in the current dimension.
1917 * We collect all the pieces in a new list that replaces "scc".
1919 * While the elements in "scc" should be disjoint, we double-check
1920 * this property to avoid running into an infinite recursion in case
1921 * they intersect due to some internal error.
1923 static int add_nodes(__isl_take isl_basic_set_list
*scc
, void *user
)
1925 struct isl_add_nodes_data
*data
= user
;
1927 isl_basic_set
*bset
, *first
;
1928 isl_basic_set_list
*list
;
1932 n
= isl_basic_set_list_n_basic_set(scc
);
1933 bset
= isl_basic_set_list_get_basic_set(scc
, 0);
1935 isl_basic_set_list_free(scc
);
1936 data
->list
= add_node(data
->list
,
1937 isl_union_map_copy(data
->executed
), bset
,
1938 isl_ast_build_copy(data
->build
));
1939 return data
->list
? 0 : -1;
1942 depth
= isl_ast_build_get_depth(data
->build
);
1943 space
= isl_basic_set_get_space(bset
);
1944 space
= isl_space_map_from_set(space
);
1945 gt
= isl_basic_map_universe(space
);
1946 for (i
= 0; i
< depth
; ++i
)
1947 gt
= isl_basic_map_equate(gt
, isl_dim_in
, i
, isl_dim_out
, i
);
1948 gt
= isl_basic_map_order_gt(gt
, isl_dim_in
, depth
, isl_dim_out
, depth
);
1950 first
= isl_basic_set_copy(bset
);
1951 list
= isl_basic_set_list_from_basic_set(bset
);
1952 for (i
= 1; i
< n
; ++i
) {
1955 bset
= isl_basic_set_list_get_basic_set(scc
, i
);
1957 disjoint
= isl_basic_set_is_disjoint(bset
, first
);
1959 list
= isl_basic_set_list_free(list
);
1961 isl_die(isl_basic_set_list_get_ctx(scc
),
1963 "basic sets in scc are assumed to be disjoint",
1964 list
= isl_basic_set_list_free(list
));
1966 list
= add_split_on(list
, bset
, gt
);
1968 isl_basic_set_free(first
);
1969 isl_basic_map_free(gt
);
1970 isl_basic_set_list_free(scc
);
1972 data
->list
= isl_ast_graft_list_concat(data
->list
,
1973 generate_sorted_domains(scc
, data
->executed
, data
->build
));
1974 isl_basic_set_list_free(scc
);
1976 return data
->list
? 0 : -1;
1979 /* Sort the domains in "domain_list" according to the execution order
1980 * at the current depth (for equal values of the outer dimensions),
1981 * generate code for each of them, collecting the results in a list.
1982 * If no code is generated (because the intersection of the inverse schedule
1983 * with the domains turns out to be empty), then an empty list is returned.
1985 * The caller is responsible for ensuring that the basic sets in "domain_list"
1986 * are pair-wise disjoint. It can, however, in principle happen that
1987 * two basic sets should be ordered one way for one value of the outer
1988 * dimensions and the other way for some other value of the outer dimensions.
1989 * We therefore play safe and look for strongly connected components.
1990 * The function add_nodes takes care of handling non-trivial components.
1992 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1993 __isl_keep isl_basic_set_list
*domain_list
,
1994 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1997 struct isl_add_nodes_data data
;
2004 ctx
= isl_basic_set_list_get_ctx(domain_list
);
2005 n
= isl_basic_set_list_n_basic_set(domain_list
);
2006 data
.list
= isl_ast_graft_list_alloc(ctx
, n
);
2010 return add_node(data
.list
, isl_union_map_copy(executed
),
2011 isl_basic_set_list_get_basic_set(domain_list
, 0),
2012 isl_ast_build_copy(build
));
2014 depth
= isl_ast_build_get_depth(build
);
2015 data
.executed
= executed
;
2017 if (isl_basic_set_list_foreach_scc(domain_list
,
2018 &domain_follows_at_depth
, &depth
,
2019 &add_nodes
, &data
) < 0)
2020 data
.list
= isl_ast_graft_list_free(data
.list
);
2025 /* Do i and j share any values for the outer dimensions?
2027 static int shared_outer(__isl_keep isl_basic_set
*i
,
2028 __isl_keep isl_basic_set
*j
, void *user
)
2030 int depth
= *(int *) user
;
2031 isl_basic_map
*test
;
2035 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
2036 isl_basic_set_copy(j
));
2037 for (l
= 0; l
< depth
; ++l
)
2038 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
2040 empty
= isl_basic_map_is_empty(test
);
2041 isl_basic_map_free(test
);
2043 return empty
< 0 ? -1 : !empty
;
2046 /* Internal data structure for generate_sorted_domains_wrap.
2048 * "n" is the total number of basic sets
2049 * "executed" and "build" are extra arguments to be passed
2050 * to generate_sorted_domains.
2052 * "single" is set to 1 by generate_sorted_domains_wrap if there
2053 * is only a single component.
2054 * "list" collects the results.
2056 struct isl_ast_generate_parallel_domains_data
{
2058 isl_union_map
*executed
;
2059 isl_ast_build
*build
;
2062 isl_ast_graft_list
*list
;
2065 /* Call generate_sorted_domains on "scc", fuse the result into a list
2066 * with either zero or one graft and collect the these single element
2067 * lists into data->list.
2069 * If there is only one component, i.e., if the number of basic sets
2070 * in the current component is equal to the total number of basic sets,
2071 * then data->single is set to 1 and the result of generate_sorted_domains
2074 static int generate_sorted_domains_wrap(__isl_take isl_basic_set_list
*scc
,
2077 struct isl_ast_generate_parallel_domains_data
*data
= user
;
2078 isl_ast_graft_list
*list
;
2080 list
= generate_sorted_domains(scc
, data
->executed
, data
->build
);
2081 data
->single
= isl_basic_set_list_n_basic_set(scc
) == data
->n
;
2083 list
= isl_ast_graft_list_fuse(list
, data
->build
);
2087 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
2089 isl_basic_set_list_free(scc
);
2096 /* Look for any (weakly connected) components in the "domain_list"
2097 * of domains that share some values of the outer dimensions.
2098 * That is, domains in different components do not share any values
2099 * of the outer dimensions. This means that these components
2100 * can be freely reordered.
2101 * Within each of the components, we sort the domains according
2102 * to the execution order at the current depth.
2104 * If there is more than one component, then generate_sorted_domains_wrap
2105 * fuses the result of each call to generate_sorted_domains
2106 * into a list with either zero or one graft and collects these (at most)
2107 * single element lists into a bigger list. This means that the elements of the
2108 * final list can be freely reordered. In particular, we sort them
2109 * according to an arbitrary but fixed ordering to ease merging of
2110 * graft lists from different components.
2112 static __isl_give isl_ast_graft_list
*generate_parallel_domains(
2113 __isl_keep isl_basic_set_list
*domain_list
,
2114 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
2117 struct isl_ast_generate_parallel_domains_data data
;
2122 data
.n
= isl_basic_set_list_n_basic_set(domain_list
);
2124 return generate_sorted_domains(domain_list
, executed
, build
);
2126 depth
= isl_ast_build_get_depth(build
);
2128 data
.executed
= executed
;
2131 if (isl_basic_set_list_foreach_scc(domain_list
, &shared_outer
, &depth
,
2132 &generate_sorted_domains_wrap
,
2134 data
.list
= isl_ast_graft_list_free(data
.list
);
2137 data
.list
= isl_ast_graft_list_sort_guard(data
.list
);
2142 /* Internal data for separate_domain.
2144 * "explicit" is set if we only want to use explicit bounds.
2146 * "domain" collects the separated domains.
2148 struct isl_separate_domain_data
{
2149 isl_ast_build
*build
;
2154 /* Extract implicit bounds on the current dimension for the executed "map".
2156 * The domain of "map" may involve inner dimensions, so we
2157 * need to eliminate them.
2159 static __isl_give isl_set
*implicit_bounds(__isl_take isl_map
*map
,
2160 __isl_keep isl_ast_build
*build
)
2164 domain
= isl_map_domain(map
);
2165 domain
= isl_ast_build_eliminate(build
, domain
);
2170 /* Extract explicit bounds on the current dimension for the executed "map".
2172 * Rather than eliminating the inner dimensions as in implicit_bounds,
2173 * we simply drop any constraints involving those inner dimensions.
2174 * The idea is that most bounds that are implied by constraints on the
2175 * inner dimensions will be enforced by for loops and not by explicit guards.
2176 * There is then no need to separate along those bounds.
2178 static __isl_give isl_set
*explicit_bounds(__isl_take isl_map
*map
,
2179 __isl_keep isl_ast_build
*build
)
2184 dim
= isl_map_dim(map
, isl_dim_out
);
2185 map
= isl_map_drop_constraints_involving_dims(map
, isl_dim_out
, 0, dim
);
2187 domain
= isl_map_domain(map
);
2188 depth
= isl_ast_build_get_depth(build
);
2189 dim
= isl_set_dim(domain
, isl_dim_set
);
2190 domain
= isl_set_detect_equalities(domain
);
2191 domain
= isl_set_drop_constraints_involving_dims(domain
,
2192 isl_dim_set
, depth
+ 1, dim
- (depth
+ 1));
2193 domain
= isl_set_remove_divs_involving_dims(domain
,
2194 isl_dim_set
, depth
, 1);
2195 domain
= isl_set_remove_unknown_divs(domain
);
2200 /* Split data->domain into pieces that intersect with the range of "map"
2201 * and pieces that do not intersect with the range of "map"
2202 * and then add that part of the range of "map" that does not intersect
2203 * with data->domain.
2205 static int separate_domain(__isl_take isl_map
*map
, void *user
)
2207 struct isl_separate_domain_data
*data
= user
;
2212 domain
= explicit_bounds(map
, data
->build
);
2214 domain
= implicit_bounds(map
, data
->build
);
2216 domain
= isl_set_coalesce(domain
);
2217 domain
= isl_set_make_disjoint(domain
);
2218 d1
= isl_set_subtract(isl_set_copy(domain
), isl_set_copy(data
->domain
));
2219 d2
= isl_set_subtract(isl_set_copy(data
->domain
), isl_set_copy(domain
));
2220 data
->domain
= isl_set_intersect(data
->domain
, domain
);
2221 data
->domain
= isl_set_union(data
->domain
, d1
);
2222 data
->domain
= isl_set_union(data
->domain
, d2
);
2227 /* Separate the schedule domains of "executed".
2229 * That is, break up the domain of "executed" into basic sets,
2230 * such that for each basic set S, every element in S is associated with
2231 * the same domain spaces.
2233 * "space" is the (single) domain space of "executed".
2235 static __isl_give isl_set
*separate_schedule_domains(
2236 __isl_take isl_space
*space
, __isl_take isl_union_map
*executed
,
2237 __isl_keep isl_ast_build
*build
)
2239 struct isl_separate_domain_data data
= { build
};
2242 ctx
= isl_ast_build_get_ctx(build
);
2243 data
.explicit = isl_options_get_ast_build_separation_bounds(ctx
) ==
2244 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
;
2245 data
.domain
= isl_set_empty(space
);
2246 if (isl_union_map_foreach_map(executed
, &separate_domain
, &data
) < 0)
2247 data
.domain
= isl_set_free(data
.domain
);
2249 isl_union_map_free(executed
);
2253 /* Temporary data used during the search for a lower bound for unrolling.
2255 * "build" is the build in which the unrolling will be performed
2256 * "domain" is the original set for which to find a lower bound
2257 * "depth" is the dimension for which to find a lower boudn
2258 * "expansion" is the expansion that needs to be applied to "domain"
2259 * in the unrolling that will be performed
2261 * "lower" is the best lower bound found so far. It is NULL if we have not
2263 * "n" is the corresponding size. If lower is NULL, then the value of n
2265 * "n_div" is the maximal number of integer divisions in the first
2266 * unrolled iteration (after expansion). It is set to -1 if it hasn't
2267 * been computed yet.
2269 struct isl_find_unroll_data
{
2270 isl_ast_build
*build
;
2273 isl_basic_map
*expansion
;
2280 /* Return the constraint
2282 * i_"depth" = aff + offset
2284 static __isl_give isl_constraint
*at_offset(int depth
, __isl_keep isl_aff
*aff
,
2287 aff
= isl_aff_copy(aff
);
2288 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, depth
, -1);
2289 aff
= isl_aff_add_constant_si(aff
, offset
);
2290 return isl_equality_from_aff(aff
);
2293 /* Update *user to the number of integer divsions in the first element
2294 * of "ma", if it is larger than the current value.
2296 static int update_n_div(__isl_take isl_set
*set
, __isl_take isl_multi_aff
*ma
,
2303 aff
= isl_multi_aff_get_aff(ma
, 0);
2304 n_div
= isl_aff_dim(aff
, isl_dim_div
);
2306 isl_multi_aff_free(ma
);
2312 return aff
? 0 : -1;
2315 /* Get the number of integer divisions in the expression for the iterator
2316 * value at the first slice in the unrolling based on lower bound "lower",
2317 * taking into account the expansion that needs to be performed on this slice.
2319 static int get_expanded_n_div(struct isl_find_unroll_data
*data
,
2320 __isl_keep isl_aff
*lower
)
2324 isl_map
*it_map
, *expansion
;
2325 isl_pw_multi_aff
*pma
;
2328 c
= at_offset(data
->depth
, lower
, 0);
2329 set
= isl_set_copy(data
->domain
);
2330 set
= isl_set_add_constraint(set
, c
);
2331 expansion
= isl_map_from_basic_map(isl_basic_map_copy(data
->expansion
));
2332 set
= isl_set_apply(set
, expansion
);
2333 it_map
= isl_ast_build_map_to_iterator(data
->build
, set
);
2334 pma
= isl_pw_multi_aff_from_map(it_map
);
2336 if (isl_pw_multi_aff_foreach_piece(pma
, &update_n_div
, &n
) < 0)
2338 isl_pw_multi_aff_free(pma
);
2343 /* Is the lower bound "lower" with corresponding iteration count "n"
2344 * better than the one stored in "data"?
2345 * If there is no upper bound on the iteration count ("n" is infinity) or
2346 * if the count is too large, then we cannot use this lower bound.
2347 * Otherwise, if there was no previous lower bound or
2348 * if the iteration count of the new lower bound is smaller than
2349 * the iteration count of the previous lower bound, then we consider
2350 * the new lower bound to be better.
2351 * If the iteration count is the same, then compare the number
2352 * of integer divisions that would be needed to express
2353 * the iterator value at the first slice in the unrolling
2354 * according to the lower bound. If we end up computing this
2355 * number, then store the lowest value in data->n_div.
2357 static int is_better_lower_bound(struct isl_find_unroll_data
*data
,
2358 __isl_keep isl_aff
*lower
, __isl_keep isl_val
*n
)
2365 if (isl_val_is_infty(n
))
2367 if (isl_val_cmp_si(n
, INT_MAX
) > 0)
2371 cmp
= isl_val_cmp_si(n
, *data
->n
);
2376 if (data
->n_div
< 0)
2377 data
->n_div
= get_expanded_n_div(data
, data
->lower
);
2378 if (data
->n_div
< 0)
2380 if (data
->n_div
== 0)
2382 n_div
= get_expanded_n_div(data
, lower
);
2385 if (n_div
>= data
->n_div
)
2387 data
->n_div
= n_div
;
2392 /* Check if we can use "c" as a lower bound and if it is better than
2393 * any previously found lower bound.
2395 * If "c" does not involve the dimension at the current depth,
2396 * then we cannot use it.
2397 * Otherwise, let "c" be of the form
2401 * We compute the maximal value of
2403 * -ceil(f(j)/a)) + i + 1
2405 * over the domain. If there is such a value "n", then we know
2407 * -ceil(f(j)/a)) + i + 1 <= n
2411 * i < ceil(f(j)/a)) + n
2413 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2414 * We just need to check if we have found any lower bound before and
2415 * if the new lower bound is better (smaller n or fewer integer divisions)
2416 * than the previously found lower bounds.
2418 static int update_unrolling_lower_bound(struct isl_find_unroll_data
*data
,
2419 __isl_keep isl_constraint
*c
)
2421 isl_aff
*aff
, *lower
;
2425 if (!isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->depth
))
2428 lower
= isl_constraint_get_bound(c
, isl_dim_set
, data
->depth
);
2429 lower
= isl_aff_ceil(lower
);
2430 aff
= isl_aff_copy(lower
);
2431 aff
= isl_aff_neg(aff
);
2432 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, data
->depth
, 1);
2433 aff
= isl_aff_add_constant_si(aff
, 1);
2434 max
= isl_set_max_val(data
->domain
, aff
);
2437 better
= is_better_lower_bound(data
, lower
, max
);
2438 if (better
< 0 || !better
) {
2440 isl_aff_free(lower
);
2441 return better
< 0 ? -1 : 0;
2444 isl_aff_free(data
->lower
);
2445 data
->lower
= lower
;
2446 *data
->n
= isl_val_get_num_si(max
);
2452 /* Check if we can use "c" as a lower bound and if it is better than
2453 * any previously found lower bound.
2455 static int constraint_find_unroll(__isl_take isl_constraint
*c
, void *user
)
2457 struct isl_find_unroll_data
*data
;
2460 data
= (struct isl_find_unroll_data
*) user
;
2461 r
= update_unrolling_lower_bound(data
, c
);
2462 isl_constraint_free(c
);
2467 /* Look for a lower bound l(i) on the dimension at "depth"
2468 * and a size n such that "domain" is a subset of
2470 * { [i] : l(i) <= i_d < l(i) + n }
2472 * where d is "depth" and l(i) depends only on earlier dimensions.
2473 * Furthermore, try and find a lower bound such that n is as small as possible.
2474 * In particular, "n" needs to be finite.
2475 * "build" is the build in which the unrolling will be performed.
2476 * "expansion" is the expansion that needs to be applied to "domain"
2477 * in the unrolling that will be performed.
2479 * Inner dimensions have been eliminated from "domain" by the caller.
2481 * We first construct a collection of lower bounds on the input set
2482 * by computing its simple hull. We then iterate through them,
2483 * discarding those that we cannot use (either because they do not
2484 * involve the dimension at "depth" or because they have no corresponding
2485 * upper bound, meaning that "n" would be unbounded) and pick out the
2486 * best from the remaining ones.
2488 * If we cannot find a suitable lower bound, then we consider that
2491 static __isl_give isl_aff
*find_unroll_lower_bound(
2492 __isl_keep isl_ast_build
*build
, __isl_keep isl_set
*domain
,
2493 int depth
, __isl_keep isl_basic_map
*expansion
, int *n
)
2495 struct isl_find_unroll_data data
=
2496 { build
, domain
, depth
, expansion
, NULL
, n
, -1 };
2497 isl_basic_set
*hull
;
2499 hull
= isl_set_simple_hull(isl_set_copy(domain
));
2501 if (isl_basic_set_foreach_constraint(hull
,
2502 &constraint_find_unroll
, &data
) < 0)
2505 isl_basic_set_free(hull
);
2508 isl_die(isl_set_get_ctx(domain
), isl_error_invalid
,
2509 "cannot find lower bound for unrolling", return NULL
);
2513 isl_basic_set_free(hull
);
2514 return isl_aff_free(data
.lower
);
2517 /* Call "fn" on each iteration of the current dimension of "domain".
2518 * If "init" is not NULL, then it is called with the number of
2519 * iterations before any call to "fn".
2520 * Return -1 on failure.
2522 * Since we are going to be iterating over the individual values,
2523 * we first check if there are any strides on the current dimension.
2524 * If there is, we rewrite the current dimension i as
2526 * i = stride i' + offset
2528 * and then iterate over individual values of i' instead.
2530 * We then look for a lower bound on i' and a size such that the domain
2533 * { [j,i'] : l(j) <= i' < l(j) + n }
2535 * and then take slices of the domain at values of i'
2536 * between l(j) and l(j) + n - 1.
2538 * We compute the unshifted simple hull of each slice to ensure that
2539 * we have a single basic set per offset. The slicing constraint
2540 * may get simplified away before the unshifted simple hull is taken
2541 * and may therefore in some rare cases disappear from the result.
2542 * We therefore explicitly add the constraint back after computing
2543 * the unshifted simple hull to ensure that the basic sets
2544 * remain disjoint. The constraints that are dropped by taking the hull
2545 * will be taken into account at the next level, as in the case of the
2548 * Finally, we map i' back to i and call "fn".
2550 static int foreach_iteration(__isl_take isl_set
*domain
,
2551 __isl_keep isl_ast_build
*build
, int (*init
)(int n
, void *user
),
2552 int (*fn
)(__isl_take isl_basic_set
*bset
, void *user
), void *user
)
2556 isl_multi_aff
*expansion
;
2557 isl_basic_map
*bmap
;
2559 isl_ast_build
*stride_build
;
2561 depth
= isl_ast_build_get_depth(build
);
2563 domain
= isl_ast_build_eliminate_inner(build
, domain
);
2564 domain
= isl_set_intersect(domain
, isl_ast_build_get_domain(build
));
2565 stride_build
= isl_ast_build_copy(build
);
2566 stride_build
= isl_ast_build_detect_strides(stride_build
,
2567 isl_set_copy(domain
));
2568 expansion
= isl_ast_build_get_stride_expansion(stride_build
);
2570 domain
= isl_set_preimage_multi_aff(domain
,
2571 isl_multi_aff_copy(expansion
));
2572 domain
= isl_ast_build_eliminate_divs(stride_build
, domain
);
2573 isl_ast_build_free(stride_build
);
2575 bmap
= isl_basic_map_from_multi_aff(expansion
);
2577 lower
= find_unroll_lower_bound(build
, domain
, depth
, bmap
, &n
);
2580 else if (init
&& init(n
, user
) < 0)
2582 for (i
= 0; i
< n
; ++i
) {
2584 isl_basic_set
*bset
;
2585 isl_constraint
*slice
;
2587 slice
= at_offset(depth
, lower
, i
);
2588 set
= isl_set_copy(domain
);
2589 set
= isl_set_add_constraint(set
, isl_constraint_copy(slice
));
2590 bset
= isl_set_unshifted_simple_hull(set
);
2591 bset
= isl_basic_set_add_constraint(bset
, slice
);
2592 bset
= isl_basic_set_apply(bset
, isl_basic_map_copy(bmap
));
2594 if (fn(bset
, user
) < 0)
2598 isl_aff_free(lower
);
2599 isl_set_free(domain
);
2600 isl_basic_map_free(bmap
);
2602 return n
< 0 || i
< n
? -1 : 0;
2605 /* Data structure for storing the results and the intermediate objects
2606 * of compute_domains.
2608 * "list" is the main result of the function and contains a list
2609 * of disjoint basic sets for which code should be generated.
2611 * "executed" and "build" are inputs to compute_domains.
2612 * "schedule_domain" is the domain of "executed".
2614 * "option" constains the domains at the current depth that should by
2615 * atomic, separated or unrolled. These domains are as specified by
2616 * the user, except that inner dimensions have been eliminated and
2617 * that they have been made pair-wise disjoint.
2619 * "sep_class" contains the user-specified split into separation classes
2620 * specialized to the current depth.
2621 * "done" contains the union of the separation domains that have already
2624 struct isl_codegen_domains
{
2625 isl_basic_set_list
*list
;
2627 isl_union_map
*executed
;
2628 isl_ast_build
*build
;
2629 isl_set
*schedule_domain
;
2637 /* Internal data structure for do_unroll.
2639 * "domains" stores the results of compute_domains.
2640 * "class_domain" is the original class domain passed to do_unroll.
2641 * "unroll_domain" collects the unrolled iterations.
2643 struct isl_ast_unroll_data
{
2644 struct isl_codegen_domains
*domains
;
2645 isl_set
*class_domain
;
2646 isl_set
*unroll_domain
;
2649 /* Given an iteration of an unrolled domain represented by "bset",
2650 * add it to data->domains->list.
2651 * Since we may have dropped some constraints, we intersect with
2652 * the class domain again to ensure that each element in the list
2653 * is disjoint from the other class domains.
2655 static int do_unroll_iteration(__isl_take isl_basic_set
*bset
, void *user
)
2657 struct isl_ast_unroll_data
*data
= user
;
2659 isl_basic_set_list
*list
;
2661 set
= isl_set_from_basic_set(bset
);
2662 data
->unroll_domain
= isl_set_union(data
->unroll_domain
,
2664 set
= isl_set_intersect(set
, isl_set_copy(data
->class_domain
));
2665 set
= isl_set_make_disjoint(set
);
2666 list
= isl_basic_set_list_from_set(set
);
2667 data
->domains
->list
= isl_basic_set_list_concat(data
->domains
->list
,
2673 /* Extend domains->list with a list of basic sets, one for each value
2674 * of the current dimension in "domain" and remove the corresponding
2675 * sets from the class domain. Return the updated class domain.
2676 * The divs that involve the current dimension have not been projected out
2679 * We call foreach_iteration to iterate over the individual values and
2680 * in do_unroll_iteration we collect the individual basic sets in
2681 * domains->list and their union in data->unroll_domain, which is then
2682 * used to update the class domain.
2684 static __isl_give isl_set
*do_unroll(struct isl_codegen_domains
*domains
,
2685 __isl_take isl_set
*domain
, __isl_take isl_set
*class_domain
)
2687 struct isl_ast_unroll_data data
;
2690 return isl_set_free(class_domain
);
2692 return isl_set_free(domain
);
2694 data
.domains
= domains
;
2695 data
.class_domain
= class_domain
;
2696 data
.unroll_domain
= isl_set_empty(isl_set_get_space(domain
));
2698 if (foreach_iteration(domain
, domains
->build
, NULL
,
2699 &do_unroll_iteration
, &data
) < 0)
2700 data
.unroll_domain
= isl_set_free(data
.unroll_domain
);
2702 class_domain
= isl_set_subtract(class_domain
, data
.unroll_domain
);
2704 return class_domain
;
2707 /* Add domains to domains->list for each individual value of the current
2708 * dimension, for that part of the schedule domain that lies in the
2709 * intersection of the option domain and the class domain.
2710 * Remove the corresponding sets from the class domain and
2711 * return the updated class domain.
2713 * We first break up the unroll option domain into individual pieces
2714 * and then handle each of them separately. The unroll option domain
2715 * has been made disjoint in compute_domains_init_options,
2717 * Note that we actively want to combine different pieces of the
2718 * schedule domain that have the same value at the current dimension.
2719 * We therefore need to break up the unroll option domain before
2720 * intersecting with class and schedule domain, hoping that the
2721 * unroll option domain specified by the user is relatively simple.
2723 static __isl_give isl_set
*compute_unroll_domains(
2724 struct isl_codegen_domains
*domains
, __isl_take isl_set
*class_domain
)
2726 isl_set
*unroll_domain
;
2727 isl_basic_set_list
*unroll_list
;
2731 empty
= isl_set_is_empty(domains
->option
[isl_ast_loop_unroll
]);
2733 return isl_set_free(class_domain
);
2735 return class_domain
;
2737 unroll_domain
= isl_set_copy(domains
->option
[isl_ast_loop_unroll
]);
2738 unroll_list
= isl_basic_set_list_from_set(unroll_domain
);
2740 n
= isl_basic_set_list_n_basic_set(unroll_list
);
2741 for (i
= 0; i
< n
; ++i
) {
2742 isl_basic_set
*bset
;
2744 bset
= isl_basic_set_list_get_basic_set(unroll_list
, i
);
2745 unroll_domain
= isl_set_from_basic_set(bset
);
2746 unroll_domain
= isl_set_intersect(unroll_domain
,
2747 isl_set_copy(class_domain
));
2748 unroll_domain
= isl_set_intersect(unroll_domain
,
2749 isl_set_copy(domains
->schedule_domain
));
2751 empty
= isl_set_is_empty(unroll_domain
);
2752 if (empty
>= 0 && empty
) {
2753 isl_set_free(unroll_domain
);
2757 class_domain
= do_unroll(domains
, unroll_domain
, class_domain
);
2760 isl_basic_set_list_free(unroll_list
);
2762 return class_domain
;
2765 /* Try and construct a single basic set that includes the intersection of
2766 * the schedule domain, the atomic option domain and the class domain.
2767 * Add the resulting basic set(s) to domains->list and remove them
2768 * from class_domain. Return the updated class domain.
2770 * We construct a single domain rather than trying to combine
2771 * the schedule domains of individual domains because we are working
2772 * within a single component so that non-overlapping schedule domains
2773 * should already have been separated.
2774 * We do however need to make sure that this single domains is a subset
2775 * of the class domain so that it would not intersect with any other
2776 * class domains. This means that we may end up splitting up the atomic
2777 * domain in case separation classes are being used.
2779 * "domain" is the intersection of the schedule domain and the class domain,
2780 * with inner dimensions projected out.
2782 static __isl_give isl_set
*compute_atomic_domain(
2783 struct isl_codegen_domains
*domains
, __isl_take isl_set
*class_domain
)
2785 isl_basic_set
*bset
;
2786 isl_basic_set_list
*list
;
2787 isl_set
*domain
, *atomic_domain
;
2790 domain
= isl_set_copy(domains
->option
[isl_ast_loop_atomic
]);
2791 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2792 domain
= isl_set_intersect(domain
,
2793 isl_set_copy(domains
->schedule_domain
));
2794 empty
= isl_set_is_empty(domain
);
2796 class_domain
= isl_set_free(class_domain
);
2798 isl_set_free(domain
);
2799 return class_domain
;
2802 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2803 domain
= isl_set_coalesce(domain
);
2804 bset
= isl_set_unshifted_simple_hull(domain
);
2805 domain
= isl_set_from_basic_set(bset
);
2806 atomic_domain
= isl_set_copy(domain
);
2807 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2808 class_domain
= isl_set_subtract(class_domain
, atomic_domain
);
2809 domain
= isl_set_make_disjoint(domain
);
2810 list
= isl_basic_set_list_from_set(domain
);
2811 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2813 return class_domain
;
2816 /* Split up the schedule domain into uniform basic sets,
2817 * in the sense that each element in a basic set is associated to
2818 * elements of the same domains, and add the result to domains->list.
2819 * Do this for that part of the schedule domain that lies in the
2820 * intersection of "class_domain" and the separate option domain.
2822 * "class_domain" may or may not include the constraints
2823 * of the schedule domain, but this does not make a difference
2824 * since we are going to intersect it with the domain of the inverse schedule.
2825 * If it includes schedule domain constraints, then they may involve
2826 * inner dimensions, but we will eliminate them in separation_domain.
2828 static int compute_separate_domain(struct isl_codegen_domains
*domains
,
2829 __isl_keep isl_set
*class_domain
)
2833 isl_union_map
*executed
;
2834 isl_basic_set_list
*list
;
2837 domain
= isl_set_copy(domains
->option
[isl_ast_loop_separate
]);
2838 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2839 executed
= isl_union_map_copy(domains
->executed
);
2840 executed
= isl_union_map_intersect_domain(executed
,
2841 isl_union_set_from_set(domain
));
2842 empty
= isl_union_map_is_empty(executed
);
2843 if (empty
< 0 || empty
) {
2844 isl_union_map_free(executed
);
2845 return empty
< 0 ? -1 : 0;
2848 space
= isl_set_get_space(class_domain
);
2849 domain
= separate_schedule_domains(space
, executed
, domains
->build
);
2851 list
= isl_basic_set_list_from_set(domain
);
2852 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2857 /* Split up the domain at the current depth into disjoint
2858 * basic sets for which code should be generated separately
2859 * for the given separation class domain.
2861 * If any separation classes have been defined, then "class_domain"
2862 * is the domain of the current class and does not refer to inner dimensions.
2863 * Otherwise, "class_domain" is the universe domain.
2865 * We first make sure that the class domain is disjoint from
2866 * previously considered class domains.
2868 * The separate domains can be computed directly from the "class_domain".
2870 * The unroll, atomic and remainder domains need the constraints
2871 * from the schedule domain.
2873 * For unrolling, the actual schedule domain is needed (with divs that
2874 * may refer to the current dimension) so that stride detection can be
2877 * For atomic and remainder domains, inner dimensions and divs involving
2878 * the current dimensions should be eliminated.
2879 * In case we are working within a separation class, we need to intersect
2880 * the result with the current "class_domain" to ensure that the domains
2881 * are disjoint from those generated from other class domains.
2883 * The domain that has been made atomic may be larger than specified
2884 * by the user since it needs to be representable as a single basic set.
2885 * This possibly larger domain is removed from class_domain by
2886 * compute_atomic_domain. It is computed first so that the extended domain
2887 * would not overlap with any domains computed before.
2888 * Similary, the unrolled domains may have some constraints removed and
2889 * may therefore also be larger than specified by the user.
2891 * If anything is left after handling separate, unroll and atomic,
2892 * we split it up into basic sets and append the basic sets to domains->list.
2894 static int compute_partial_domains(struct isl_codegen_domains
*domains
,
2895 __isl_take isl_set
*class_domain
)
2897 isl_basic_set_list
*list
;
2900 class_domain
= isl_set_subtract(class_domain
,
2901 isl_set_copy(domains
->done
));
2902 domains
->done
= isl_set_union(domains
->done
,
2903 isl_set_copy(class_domain
));
2905 class_domain
= compute_atomic_domain(domains
, class_domain
);
2906 class_domain
= compute_unroll_domains(domains
, class_domain
);
2908 domain
= isl_set_copy(class_domain
);
2910 if (compute_separate_domain(domains
, domain
) < 0)
2912 domain
= isl_set_subtract(domain
,
2913 isl_set_copy(domains
->option
[isl_ast_loop_separate
]));
2915 domain
= isl_set_intersect(domain
,
2916 isl_set_copy(domains
->schedule_domain
));
2918 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2919 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2921 domain
= isl_set_coalesce(domain
);
2922 domain
= isl_set_make_disjoint(domain
);
2924 list
= isl_basic_set_list_from_set(domain
);
2925 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2927 isl_set_free(class_domain
);
2931 isl_set_free(domain
);
2932 isl_set_free(class_domain
);
2936 /* Split up the domain at the current depth into disjoint
2937 * basic sets for which code should be generated separately
2938 * for the separation class identified by "pnt".
2940 * We extract the corresponding class domain from domains->sep_class,
2941 * eliminate inner dimensions and pass control to compute_partial_domains.
2943 static int compute_class_domains(__isl_take isl_point
*pnt
, void *user
)
2945 struct isl_codegen_domains
*domains
= user
;
2950 class_set
= isl_set_from_point(pnt
);
2951 domain
= isl_map_domain(isl_map_intersect_range(
2952 isl_map_copy(domains
->sep_class
), class_set
));
2953 domain
= isl_ast_build_compute_gist(domains
->build
, domain
);
2954 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2956 disjoint
= isl_set_plain_is_disjoint(domain
, domains
->schedule_domain
);
2960 isl_set_free(domain
);
2964 return compute_partial_domains(domains
, domain
);
2967 /* Extract the domains at the current depth that should be atomic,
2968 * separated or unrolled and store them in option.
2970 * The domains specified by the user might overlap, so we make
2971 * them disjoint by subtracting earlier domains from later domains.
2973 static void compute_domains_init_options(isl_set
*option
[4],
2974 __isl_keep isl_ast_build
*build
)
2976 enum isl_ast_loop_type type
, type2
;
2979 for (type
= isl_ast_loop_atomic
;
2980 type
<= isl_ast_loop_separate
; ++type
) {
2981 option
[type
] = isl_ast_build_get_option_domain(build
, type
);
2982 for (type2
= isl_ast_loop_atomic
; type2
< type
; ++type2
)
2983 option
[type
] = isl_set_subtract(option
[type
],
2984 isl_set_copy(option
[type2
]));
2987 unroll
= option
[isl_ast_loop_unroll
];
2988 unroll
= isl_set_coalesce(unroll
);
2989 unroll
= isl_set_make_disjoint(unroll
);
2990 option
[isl_ast_loop_unroll
] = unroll
;
2993 /* Split up the domain at the current depth into disjoint
2994 * basic sets for which code should be generated separately,
2995 * based on the user-specified options.
2996 * Return the list of disjoint basic sets.
2998 * There are three kinds of domains that we need to keep track of.
2999 * - the "schedule domain" is the domain of "executed"
3000 * - the "class domain" is the domain corresponding to the currrent
3002 * - the "option domain" is the domain corresponding to one of the options
3003 * atomic, unroll or separate
3005 * We first consider the individial values of the separation classes
3006 * and split up the domain for each of them separately.
3007 * Finally, we consider the remainder. If no separation classes were
3008 * specified, then we call compute_partial_domains with the universe
3009 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
3010 * with inner dimensions removed. We do this because we want to
3011 * avoid computing the complement of the class domains (i.e., the difference
3012 * between the universe and domains->done).
3014 static __isl_give isl_basic_set_list
*compute_domains(
3015 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
3017 struct isl_codegen_domains domains
;
3020 isl_union_set
*schedule_domain
;
3024 enum isl_ast_loop_type type
;
3030 ctx
= isl_union_map_get_ctx(executed
);
3031 domains
.list
= isl_basic_set_list_alloc(ctx
, 0);
3033 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
3034 domain
= isl_set_from_union_set(schedule_domain
);
3036 compute_domains_init_options(domains
.option
, build
);
3038 domains
.sep_class
= isl_ast_build_get_separation_class(build
);
3039 classes
= isl_map_range(isl_map_copy(domains
.sep_class
));
3040 n_param
= isl_set_dim(classes
, isl_dim_param
);
3041 classes
= isl_set_project_out(classes
, isl_dim_param
, 0, n_param
);
3043 space
= isl_set_get_space(domain
);
3044 domains
.build
= build
;
3045 domains
.schedule_domain
= isl_set_copy(domain
);
3046 domains
.executed
= executed
;
3047 domains
.done
= isl_set_empty(space
);
3049 if (isl_set_foreach_point(classes
, &compute_class_domains
, &domains
) < 0)
3050 domains
.list
= isl_basic_set_list_free(domains
.list
);
3051 isl_set_free(classes
);
3053 empty
= isl_set_is_empty(domains
.done
);
3055 domains
.list
= isl_basic_set_list_free(domains
.list
);
3056 domain
= isl_set_free(domain
);
3058 isl_set_free(domain
);
3059 domain
= isl_set_universe(isl_set_get_space(domains
.done
));
3061 domain
= isl_ast_build_eliminate(build
, domain
);
3063 if (compute_partial_domains(&domains
, domain
) < 0)
3064 domains
.list
= isl_basic_set_list_free(domains
.list
);
3066 isl_set_free(domains
.schedule_domain
);
3067 isl_set_free(domains
.done
);
3068 isl_map_free(domains
.sep_class
);
3069 for (type
= isl_ast_loop_atomic
; type
<= isl_ast_loop_separate
; ++type
)
3070 isl_set_free(domains
.option
[type
]);
3072 return domains
.list
;
3075 /* Generate code for a single component, after shifting (if any)
3076 * has been applied, in case the schedule was specified as a union map.
3078 * We first split up the domain at the current depth into disjoint
3079 * basic sets based on the user-specified options.
3080 * Then we generated code for each of them and concatenate the results.
3082 static __isl_give isl_ast_graft_list
*generate_shifted_component_flat(
3083 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3085 isl_basic_set_list
*domain_list
;
3086 isl_ast_graft_list
*list
= NULL
;
3088 domain_list
= compute_domains(executed
, build
);
3089 list
= generate_parallel_domains(domain_list
, executed
, build
);
3091 isl_basic_set_list_free(domain_list
);
3092 isl_union_map_free(executed
);
3093 isl_ast_build_free(build
);
3098 /* Generate code for a single component, after shifting (if any)
3099 * has been applied, in case the schedule was specified as a schedule tree
3100 * and the separate option was specified.
3102 * We perform separation on the domain of "executed" and then generate
3103 * an AST for each of the resulting disjoint basic sets.
3105 static __isl_give isl_ast_graft_list
*generate_shifted_component_tree_separate(
3106 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3110 isl_basic_set_list
*domain_list
;
3111 isl_ast_graft_list
*list
;
3113 space
= isl_ast_build_get_space(build
, 1);
3114 domain
= separate_schedule_domains(space
,
3115 isl_union_map_copy(executed
), build
);
3116 domain_list
= isl_basic_set_list_from_set(domain
);
3118 list
= generate_parallel_domains(domain_list
, executed
, build
);
3120 isl_basic_set_list_free(domain_list
);
3121 isl_union_map_free(executed
);
3122 isl_ast_build_free(build
);
3127 /* Internal data structure for generate_shifted_component_tree_unroll.
3129 * "executed" and "build" are inputs to generate_shifted_component_tree_unroll.
3130 * "list" collects the constructs grafts.
3132 struct isl_ast_unroll_tree_data
{
3133 isl_union_map
*executed
;
3134 isl_ast_build
*build
;
3135 isl_ast_graft_list
*list
;
3138 /* Initialize data->list to a list of "n" elements.
3140 static int init_unroll_tree(int n
, void *user
)
3142 struct isl_ast_unroll_tree_data
*data
= user
;
3145 ctx
= isl_ast_build_get_ctx(data
->build
);
3146 data
->list
= isl_ast_graft_list_alloc(ctx
, n
);
3151 /* Given an iteration of an unrolled domain represented by "bset",
3152 * generate the corresponding AST and add the result to data->list.
3154 static int do_unroll_tree_iteration(__isl_take isl_basic_set
*bset
, void *user
)
3156 struct isl_ast_unroll_tree_data
*data
= user
;
3158 data
->list
= add_node(data
->list
, isl_union_map_copy(data
->executed
),
3159 bset
, isl_ast_build_copy(data
->build
));
3164 /* Generate code for a single component, after shifting (if any)
3165 * has been applied, in case the schedule was specified as a schedule tree
3166 * and the unroll option was specified.
3168 * We call foreach_iteration to iterate over the individual values and
3169 * construct and collect the corresponding grafts in do_unroll_tree_iteration.
3171 static __isl_give isl_ast_graft_list
*generate_shifted_component_tree_unroll(
3172 __isl_take isl_union_map
*executed
, __isl_take isl_set
*domain
,
3173 __isl_take isl_ast_build
*build
)
3175 struct isl_ast_unroll_tree_data data
= { executed
, build
, NULL
};
3177 if (foreach_iteration(domain
, build
, &init_unroll_tree
,
3178 &do_unroll_tree_iteration
, &data
) < 0)
3179 data
.list
= isl_ast_graft_list_free(data
.list
);
3181 isl_union_map_free(executed
);
3182 isl_ast_build_free(build
);
3187 /* Generate code for a single component, after shifting (if any)
3188 * has been applied, in case the schedule was specified as a schedule tree.
3189 * In particular, handle the base case where there is either no isolated
3190 * set or we are within the isolated set (in which case "isolated" is set)
3191 * or the iterations that precede or follow the isolated set.
3193 * The schedule domain is broken up or combined into basic sets
3194 * according to the AST generation option specified in the current
3195 * schedule node, which may be either atomic, separate, unroll or
3196 * unspecified. If the option is unspecified, then we currently simply
3197 * split the schedule domain into disjoint basic sets.
3199 * In case the separate option is specified, the AST generation is
3200 * handled by generate_shifted_component_tree_separate.
3201 * In the other cases, we need the global schedule domain.
3202 * In the unroll case, the AST generation is then handled by
3203 * generate_shifted_component_tree_unroll which needs the actual
3204 * schedule domain (with divs that may refer to the current dimension)
3205 * so that stride detection can be performed.
3206 * In the atomic or unspecified case, inner dimensions and divs involving
3207 * the current dimensions should be eliminated.
3208 * The result is then either combined into a single basic set or
3209 * split up into disjoint basic sets.
3210 * Finally an AST is generated for each basic set and the results are
3213 static __isl_give isl_ast_graft_list
*generate_shifted_component_tree_base(
3214 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
3217 isl_union_set
*schedule_domain
;
3219 isl_basic_set_list
*domain_list
;
3220 isl_ast_graft_list
*list
;
3221 enum isl_ast_loop_type type
;
3223 type
= isl_ast_build_get_loop_type(build
, isolated
);
3227 if (type
== isl_ast_loop_separate
)
3228 return generate_shifted_component_tree_separate(executed
,
3231 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
3232 domain
= isl_set_from_union_set(schedule_domain
);
3234 if (type
== isl_ast_loop_unroll
)
3235 return generate_shifted_component_tree_unroll(executed
, domain
,
3238 domain
= isl_ast_build_eliminate(build
, domain
);
3239 domain
= isl_set_coalesce(domain
);
3241 if (type
== isl_ast_loop_atomic
) {
3242 isl_basic_set
*hull
;
3243 hull
= isl_set_unshifted_simple_hull(domain
);
3244 domain_list
= isl_basic_set_list_from_basic_set(hull
);
3246 domain
= isl_set_make_disjoint(domain
);
3247 domain_list
= isl_basic_set_list_from_set(domain
);
3250 list
= generate_parallel_domains(domain_list
, executed
, build
);
3252 isl_basic_set_list_free(domain_list
);
3253 isl_union_map_free(executed
);
3254 isl_ast_build_free(build
);
3258 isl_union_map_free(executed
);
3259 isl_ast_build_free(build
);
3263 /* Generate code for a single component, after shifting (if any)
3264 * has been applied, in case the schedule was specified as a schedule tree.
3265 * In particular, do so for the specified subset of the schedule domain.
3267 static __isl_give isl_ast_graft_list
*generate_shifted_component_tree_part(
3268 __isl_keep isl_union_map
*executed
, __isl_take isl_set
*domain
,
3269 __isl_keep isl_ast_build
*build
, int isolated
)
3271 isl_union_set
*uset
;
3274 uset
= isl_union_set_from_set(domain
);
3275 executed
= isl_union_map_copy(executed
);
3276 executed
= isl_union_map_intersect_domain(executed
, uset
);
3277 empty
= isl_union_map_is_empty(executed
);
3282 isl_union_map_free(executed
);
3283 ctx
= isl_ast_build_get_ctx(build
);
3284 return isl_ast_graft_list_alloc(ctx
, 0);
3287 build
= isl_ast_build_copy(build
);
3288 return generate_shifted_component_tree_base(executed
, build
, isolated
);
3290 isl_union_map_free(executed
);
3294 /* Generate code for a single component, after shifting (if any)
3295 * has been applied, in case the schedule was specified as a schedule tree.
3297 * We first check if the user has specified an isolated schedule domain
3298 * and that we are not already outside of this isolated schedule domain.
3299 * If so, we break up the schedule domain into iterations that
3300 * precede the isolated domain, the isolated domain itself,
3301 * the iterations that follow the isolated domain and
3302 * the remaining iterations (those that are incomparable
3303 * to the isolated domain).
3304 * We generate an AST for each piece and concatenate the results.
3305 * If no isolated set has been specified, then we generate an
3306 * AST for the entire inverse schedule.
3308 static __isl_give isl_ast_graft_list
*generate_shifted_component_tree(
3309 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3312 int empty
, has_isolate
;
3314 isl_union_set
*schedule_domain
;
3316 isl_basic_set
*hull
;
3317 isl_set
*isolated
, *before
, *after
, *test
;
3319 isl_ast_graft_list
*list
, *res
;
3321 build
= isl_ast_build_extract_isolated(build
);
3322 has_isolate
= isl_ast_build_has_isolated(build
);
3323 if (has_isolate
< 0)
3324 executed
= isl_union_map_free(executed
);
3325 else if (!has_isolate
)
3326 return generate_shifted_component_tree_base(executed
, build
, 0);
3328 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
3329 domain
= isl_set_from_union_set(schedule_domain
);
3331 isolated
= isl_ast_build_get_isolated(build
);
3332 isolated
= isl_set_intersect(isolated
, isl_set_copy(domain
));
3333 test
= isl_ast_build_specialize(build
, isl_set_copy(isolated
));
3334 empty
= isl_set_is_empty(test
);
3339 isl_set_free(isolated
);
3340 isl_set_free(domain
);
3341 return generate_shifted_component_tree_base(executed
, build
, 0);
3343 isolated
= isl_ast_build_eliminate(build
, isolated
);
3344 hull
= isl_set_unshifted_simple_hull(isolated
);
3345 isolated
= isl_set_from_basic_set(hull
);
3347 depth
= isl_ast_build_get_depth(build
);
3348 space
= isl_space_map_from_set(isl_set_get_space(isolated
));
3349 gt
= isl_map_universe(space
);
3350 for (i
= 0; i
< depth
; ++i
)
3351 gt
= isl_map_equate(gt
, isl_dim_in
, i
, isl_dim_out
, i
);
3352 gt
= isl_map_order_gt(gt
, isl_dim_in
, depth
, isl_dim_out
, depth
);
3353 lt
= isl_map_reverse(isl_map_copy(gt
));
3354 before
= isl_set_apply(isl_set_copy(isolated
), gt
);
3355 after
= isl_set_apply(isl_set_copy(isolated
), lt
);
3357 domain
= isl_set_subtract(domain
, isl_set_copy(isolated
));
3358 domain
= isl_set_subtract(domain
, isl_set_copy(before
));
3359 domain
= isl_set_subtract(domain
, isl_set_copy(after
));
3360 after
= isl_set_subtract(after
, isl_set_copy(isolated
));
3361 after
= isl_set_subtract(after
, isl_set_copy(before
));
3362 before
= isl_set_subtract(before
, isl_set_copy(isolated
));
3364 res
= generate_shifted_component_tree_part(executed
, before
, build
, 0);
3365 list
= generate_shifted_component_tree_part(executed
, isolated
,
3367 res
= isl_ast_graft_list_concat(res
, list
);
3368 list
= generate_shifted_component_tree_part(executed
, after
, build
, 0);
3369 res
= isl_ast_graft_list_concat(res
, list
);
3370 list
= generate_shifted_component_tree_part(executed
, domain
, build
, 0);
3371 res
= isl_ast_graft_list_concat(res
, list
);
3373 isl_union_map_free(executed
);
3374 isl_ast_build_free(build
);
3378 isl_set_free(domain
);
3379 isl_set_free(isolated
);
3380 isl_union_map_free(executed
);
3381 isl_ast_build_free(build
);
3385 /* Generate code for a single component, after shifting (if any)
3388 * Call generate_shifted_component_tree or generate_shifted_component_flat
3389 * depending on whether the schedule was specified as a schedule tree.
3391 static __isl_give isl_ast_graft_list
*generate_shifted_component(
3392 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3394 if (isl_ast_build_has_schedule_node(build
))
3395 return generate_shifted_component_tree(executed
, build
);
3397 return generate_shifted_component_flat(executed
, build
);
3400 struct isl_set_map_pair
{
3405 /* Given an array "domain" of isl_set_map_pairs and an array "order"
3406 * of indices into the "domain" array,
3407 * return the union of the "map" fields of the elements
3408 * indexed by the first "n" elements of "order".
3410 static __isl_give isl_union_map
*construct_component_executed(
3411 struct isl_set_map_pair
*domain
, int *order
, int n
)
3415 isl_union_map
*executed
;
3417 map
= isl_map_copy(domain
[order
[0]].map
);
3418 executed
= isl_union_map_from_map(map
);
3419 for (i
= 1; i
< n
; ++i
) {
3420 map
= isl_map_copy(domain
[order
[i
]].map
);
3421 executed
= isl_union_map_add_map(executed
, map
);
3427 /* Generate code for a single component, after shifting (if any)
3430 * The component inverse schedule is specified as the "map" fields
3431 * of the elements of "domain" indexed by the first "n" elements of "order".
3433 static __isl_give isl_ast_graft_list
*generate_shifted_component_from_list(
3434 struct isl_set_map_pair
*domain
, int *order
, int n
,
3435 __isl_take isl_ast_build
*build
)
3437 isl_union_map
*executed
;
3439 executed
= construct_component_executed(domain
, order
, n
);
3440 return generate_shifted_component(executed
, build
);
3443 /* Does set dimension "pos" of "set" have an obviously fixed value?
3445 static int dim_is_fixed(__isl_keep isl_set
*set
, int pos
)
3450 v
= isl_set_plain_get_val_if_fixed(set
, isl_dim_set
, pos
);
3453 fixed
= !isl_val_is_nan(v
);
3459 /* Given an array "domain" of isl_set_map_pairs and an array "order"
3460 * of indices into the "domain" array,
3461 * do all (except for at most one) of the "set" field of the elements
3462 * indexed by the first "n" elements of "order" have a fixed value
3463 * at position "depth"?
3465 static int at_most_one_non_fixed(struct isl_set_map_pair
*domain
,
3466 int *order
, int n
, int depth
)
3471 for (i
= 0; i
< n
; ++i
) {
3474 f
= dim_is_fixed(domain
[order
[i
]].set
, depth
);
3487 /* Given an array "domain" of isl_set_map_pairs and an array "order"
3488 * of indices into the "domain" array,
3489 * eliminate the inner dimensions from the "set" field of the elements
3490 * indexed by the first "n" elements of "order", provided the current
3491 * dimension does not have a fixed value.
3493 * Return the index of the first element in "order" with a corresponding
3494 * "set" field that does not have an (obviously) fixed value.
3496 static int eliminate_non_fixed(struct isl_set_map_pair
*domain
,
3497 int *order
, int n
, int depth
, __isl_keep isl_ast_build
*build
)
3502 for (i
= n
- 1; i
>= 0; --i
) {
3504 f
= dim_is_fixed(domain
[order
[i
]].set
, depth
);
3509 domain
[order
[i
]].set
= isl_ast_build_eliminate_inner(build
,
3510 domain
[order
[i
]].set
);
3517 /* Given an array "domain" of isl_set_map_pairs and an array "order"
3518 * of indices into the "domain" array,
3519 * find the element of "domain" (amongst those indexed by the first "n"
3520 * elements of "order") with the "set" field that has the smallest
3521 * value for the current iterator.
3523 * Note that the domain with the smallest value may depend on the parameters
3524 * and/or outer loop dimension. Since the result of this function is only
3525 * used as heuristic, we only make a reasonable attempt at finding the best
3526 * domain, one that should work in case a single domain provides the smallest
3527 * value for the current dimension over all values of the parameters
3528 * and outer dimensions.
3530 * In particular, we compute the smallest value of the first domain
3531 * and replace it by that of any later domain if that later domain
3532 * has a smallest value that is smaller for at least some value
3533 * of the parameters and outer dimensions.
3535 static int first_offset(struct isl_set_map_pair
*domain
, int *order
, int n
,
3536 __isl_keep isl_ast_build
*build
)
3542 min_first
= isl_ast_build_map_to_iterator(build
,
3543 isl_set_copy(domain
[order
[0]].set
));
3544 min_first
= isl_map_lexmin(min_first
);
3546 for (i
= 1; i
< n
; ++i
) {
3547 isl_map
*min
, *test
;
3550 min
= isl_ast_build_map_to_iterator(build
,
3551 isl_set_copy(domain
[order
[i
]].set
));
3552 min
= isl_map_lexmin(min
);
3553 test
= isl_map_copy(min
);
3554 test
= isl_map_apply_domain(isl_map_copy(min_first
), test
);
3555 test
= isl_map_order_lt(test
, isl_dim_in
, 0, isl_dim_out
, 0);
3556 empty
= isl_map_is_empty(test
);
3558 if (empty
>= 0 && !empty
) {
3559 isl_map_free(min_first
);
3569 isl_map_free(min_first
);
3571 return i
< n
? -1 : first
;
3574 /* Construct a shifted inverse schedule based on the original inverse schedule,
3575 * the stride and the offset.
3577 * The original inverse schedule is specified as the "map" fields
3578 * of the elements of "domain" indexed by the first "n" elements of "order".
3580 * "stride" and "offset" are such that the difference
3581 * between the values of the current dimension of domain "i"
3582 * and the values of the current dimension for some reference domain are
3585 * stride * integer + offset[i]
3587 * Moreover, 0 <= offset[i] < stride.
3589 * For each domain, we create a map
3591 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
3593 * where j refers to the current dimension and the other dimensions are
3594 * unchanged, and apply this map to the original schedule domain.
3596 * For example, for the original schedule
3598 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3600 * and assuming the offset is 0 for the A domain and 1 for the B domain,
3601 * we apply the mapping
3605 * to the schedule of the "A" domain and the mapping
3607 * { [j - 1] -> [j, 1] }
3609 * to the schedule of the "B" domain.
3612 * Note that after the transformation, the differences between pairs
3613 * of values of the current dimension over all domains are multiples
3614 * of stride and that we have therefore exposed the stride.
3617 * To see that the mapping preserves the lexicographic order,
3618 * first note that each of the individual maps above preserves the order.
3619 * If the value of the current iterator is j1 in one domain and j2 in another,
3620 * then if j1 = j2, we know that the same map is applied to both domains
3621 * and the order is preserved.
3622 * Otherwise, let us assume, without loss of generality, that j1 < j2.
3623 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
3627 * and the order is preserved.
3628 * If c1 < c2, then we know
3634 * j2 - j1 = n * s + r
3636 * with n >= 0 and 0 <= r < s.
3637 * In other words, r = c2 - c1.
3648 * (j1 - c1, c1) << (j2 - c2, c2)
3650 * with "<<" the lexicographic order, proving that the order is preserved
3653 static __isl_give isl_union_map
*contruct_shifted_executed(
3654 struct isl_set_map_pair
*domain
, int *order
, int n
,
3655 __isl_keep isl_val
*stride
, __isl_keep isl_multi_val
*offset
,
3656 __isl_take isl_ast_build
*build
)
3659 isl_union_map
*executed
;
3665 depth
= isl_ast_build_get_depth(build
);
3666 space
= isl_ast_build_get_space(build
, 1);
3667 executed
= isl_union_map_empty(isl_space_copy(space
));
3668 space
= isl_space_map_from_set(space
);
3669 map
= isl_map_identity(isl_space_copy(space
));
3670 map
= isl_map_eliminate(map
, isl_dim_out
, depth
, 1);
3671 map
= isl_map_insert_dims(map
, isl_dim_out
, depth
+ 1, 1);
3672 space
= isl_space_insert_dims(space
, isl_dim_out
, depth
+ 1, 1);
3674 c
= isl_equality_alloc(isl_local_space_from_space(space
));
3675 c
= isl_constraint_set_coefficient_si(c
, isl_dim_in
, depth
, 1);
3676 c
= isl_constraint_set_coefficient_si(c
, isl_dim_out
, depth
, -1);
3678 for (i
= 0; i
< n
; ++i
) {
3682 v
= isl_multi_val_get_val(offset
, i
);
3685 map_i
= isl_map_copy(map
);
3686 map_i
= isl_map_fix_val(map_i
, isl_dim_out
, depth
+ 1,
3689 c
= isl_constraint_set_constant_val(c
, v
);
3690 map_i
= isl_map_add_constraint(map_i
, isl_constraint_copy(c
));
3692 map_i
= isl_map_apply_domain(isl_map_copy(domain
[order
[i
]].map
),
3694 executed
= isl_union_map_add_map(executed
, map_i
);
3697 isl_constraint_free(c
);
3701 executed
= isl_union_map_free(executed
);
3706 /* Generate code for a single component, after exposing the stride,
3707 * given that the schedule domain is "shifted strided".
3709 * The component inverse schedule is specified as the "map" fields
3710 * of the elements of "domain" indexed by the first "n" elements of "order".
3712 * The schedule domain being "shifted strided" means that the differences
3713 * between the values of the current dimension of domain "i"
3714 * and the values of the current dimension for some reference domain are
3717 * stride * integer + offset[i]
3719 * We first look for the domain with the "smallest" value for the current
3720 * dimension and adjust the offsets such that the offset of the "smallest"
3721 * domain is equal to zero. The other offsets are reduced modulo stride.
3723 * Based on this information, we construct a new inverse schedule in
3724 * contruct_shifted_executed that exposes the stride.
3725 * Since this involves the introduction of a new schedule dimension,
3726 * the build needs to be changed accodingly.
3727 * After computing the AST, the newly introduced dimension needs
3728 * to be removed again from the list of grafts. We do this by plugging
3729 * in a mapping that represents the new schedule domain in terms of the
3730 * old schedule domain.
3732 static __isl_give isl_ast_graft_list
*generate_shift_component(
3733 struct isl_set_map_pair
*domain
, int *order
, int n
,
3734 __isl_keep isl_val
*stride
, __isl_keep isl_multi_val
*offset
,
3735 __isl_take isl_ast_build
*build
)
3737 isl_ast_graft_list
*list
;
3743 isl_multi_aff
*ma
, *zero
;
3744 isl_union_map
*executed
;
3746 depth
= isl_ast_build_get_depth(build
);
3748 first
= first_offset(domain
, order
, n
, build
);
3752 mv
= isl_multi_val_copy(offset
);
3753 val
= isl_multi_val_get_val(offset
, first
);
3754 val
= isl_val_neg(val
);
3755 mv
= isl_multi_val_add_val(mv
, val
);
3756 mv
= isl_multi_val_mod_val(mv
, isl_val_copy(stride
));
3758 executed
= contruct_shifted_executed(domain
, order
, n
, stride
, mv
,
3760 space
= isl_ast_build_get_space(build
, 1);
3761 space
= isl_space_map_from_set(space
);
3762 ma
= isl_multi_aff_identity(isl_space_copy(space
));
3763 space
= isl_space_from_domain(isl_space_domain(space
));
3764 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
3765 zero
= isl_multi_aff_zero(space
);
3766 ma
= isl_multi_aff_range_splice(ma
, depth
+ 1, zero
);
3767 build
= isl_ast_build_insert_dim(build
, depth
+ 1);
3768 list
= generate_shifted_component(executed
, build
);
3770 list
= isl_ast_graft_list_preimage_multi_aff(list
, ma
);
3772 isl_multi_val_free(mv
);
3776 isl_ast_build_free(build
);
3780 /* Does any node in the schedule tree rooted at the current schedule node
3781 * of "build" depend on outer schedule nodes?
3783 static int has_anchored_subtree(__isl_keep isl_ast_build
*build
)
3785 isl_schedule_node
*node
;
3788 node
= isl_ast_build_get_schedule_node(build
);
3789 dependent
= isl_schedule_node_is_subtree_anchored(node
);
3790 isl_schedule_node_free(node
);
3795 /* Generate code for a single component.
3797 * The component inverse schedule is specified as the "map" fields
3798 * of the elements of "domain" indexed by the first "n" elements of "order".
3800 * This function may modify the "set" fields of "domain".
3802 * Before proceeding with the actual code generation for the component,
3803 * we first check if there are any "shifted" strides, meaning that
3804 * the schedule domains of the individual domains are all strided,
3805 * but that they have different offsets, resulting in the union
3806 * of schedule domains not being strided anymore.
3808 * The simplest example is the schedule
3810 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3812 * Both schedule domains are strided, but their union is not.
3813 * This function detects such cases and then rewrites the schedule to
3815 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3817 * In the new schedule, the schedule domains have the same offset (modulo
3818 * the stride), ensuring that the union of schedule domains is also strided.
3821 * If there is only a single domain in the component, then there is
3822 * nothing to do. Similarly, if the current schedule dimension has
3823 * a fixed value for almost all domains then there is nothing to be done.
3824 * In particular, we need at least two domains where the current schedule
3825 * dimension does not have a fixed value.
3826 * Finally, in case of a schedule map input,
3827 * if any of the options refer to the current schedule dimension,
3828 * then we bail out as well. It would be possible to reformulate the options
3829 * in terms of the new schedule domain, but that would introduce constraints
3830 * that separate the domains in the options and that is something we would
3832 * In the case of a schedule tree input, we bail out if any of
3833 * the descendants of the current schedule node refer to outer
3834 * schedule nodes in any way.
3837 * To see if there is any shifted stride, we look at the differences
3838 * between the values of the current dimension in pairs of domains
3839 * for equal values of outer dimensions. These differences should be
3844 * with "m" the stride and "r" a constant. Note that we cannot perform
3845 * this analysis on individual domains as the lower bound in each domain
3846 * may depend on parameters or outer dimensions and so the current dimension
3847 * itself may not have a fixed remainder on division by the stride.
3849 * In particular, we compare the first domain that does not have an
3850 * obviously fixed value for the current dimension to itself and all
3851 * other domains and collect the offsets and the gcd of the strides.
3852 * If the gcd becomes one, then we failed to find shifted strides.
3853 * If the gcd is zero, then the differences were all fixed, meaning
3854 * that some domains had non-obviously fixed values for the current dimension.
3855 * If all the offsets are the same (for those domains that do not have
3856 * an obviously fixed value for the current dimension), then we do not
3857 * apply the transformation.
3858 * If none of the domains were skipped, then there is nothing to do.
3859 * If some of them were skipped, then if we apply separation, the schedule
3860 * domain should get split in pieces with a (non-shifted) stride.
3862 * Otherwise, we apply a shift to expose the stride in
3863 * generate_shift_component.
3865 static __isl_give isl_ast_graft_list
*generate_component(
3866 struct isl_set_map_pair
*domain
, int *order
, int n
,
3867 __isl_take isl_ast_build
*build
)
3874 isl_val
*gcd
= NULL
;
3878 isl_ast_graft_list
*list
;
3881 depth
= isl_ast_build_get_depth(build
);
3884 if (skip
>= 0 && !skip
)
3885 skip
= at_most_one_non_fixed(domain
, order
, n
, depth
);
3886 if (skip
>= 0 && !skip
) {
3887 if (isl_ast_build_has_schedule_node(build
))
3888 skip
= has_anchored_subtree(build
);
3890 skip
= isl_ast_build_options_involve_depth(build
);
3895 return generate_shifted_component_from_list(domain
,
3898 base
= eliminate_non_fixed(domain
, order
, n
, depth
, build
);
3902 ctx
= isl_ast_build_get_ctx(build
);
3904 mv
= isl_multi_val_zero(isl_space_set_alloc(ctx
, 0, n
));
3907 for (i
= 0; i
< n
; ++i
) {
3910 map
= isl_map_from_domain_and_range(
3911 isl_set_copy(domain
[order
[base
]].set
),
3912 isl_set_copy(domain
[order
[i
]].set
));
3913 for (d
= 0; d
< depth
; ++d
)
3914 map
= isl_map_equate(map
, isl_dim_in
, d
,
3916 deltas
= isl_map_deltas(map
);
3917 res
= isl_set_dim_residue_class_val(deltas
, depth
, &m
, &r
);
3918 isl_set_free(deltas
);
3925 gcd
= isl_val_gcd(gcd
, m
);
3926 if (isl_val_is_one(gcd
)) {
3930 mv
= isl_multi_val_set_val(mv
, i
, r
);
3932 res
= dim_is_fixed(domain
[order
[i
]].set
, depth
);
3938 if (fixed
&& i
> base
) {
3940 a
= isl_multi_val_get_val(mv
, i
);
3941 b
= isl_multi_val_get_val(mv
, base
);
3942 if (isl_val_ne(a
, b
))
3949 if (res
< 0 || !gcd
) {
3950 isl_ast_build_free(build
);
3952 } else if (i
< n
|| fixed
|| isl_val_is_zero(gcd
)) {
3953 list
= generate_shifted_component_from_list(domain
,
3956 list
= generate_shift_component(domain
, order
, n
, gcd
, mv
,
3961 isl_multi_val_free(mv
);
3965 isl_ast_build_free(build
);
3969 /* Store both "map" itself and its domain in the
3970 * structure pointed to by *next and advance to the next array element.
3972 static int extract_domain(__isl_take isl_map
*map
, void *user
)
3974 struct isl_set_map_pair
**next
= user
;
3976 (*next
)->map
= isl_map_copy(map
);
3977 (*next
)->set
= isl_map_domain(map
);
3983 static int after_in_tree(__isl_keep isl_union_map
*umap
,
3984 __isl_keep isl_schedule_node
*node
);
3986 /* Is any domain element of "umap" scheduled after any of
3987 * the corresponding image elements by the tree rooted at
3988 * the child of "node"?
3990 static int after_in_child(__isl_keep isl_union_map
*umap
,
3991 __isl_keep isl_schedule_node
*node
)
3993 isl_schedule_node
*child
;
3996 child
= isl_schedule_node_get_child(node
, 0);
3997 after
= after_in_tree(umap
, child
);
3998 isl_schedule_node_free(child
);
4003 /* Is any domain element of "umap" scheduled after any of
4004 * the corresponding image elements by the tree rooted at
4005 * the band node "node"?
4007 * We first check if any domain element is scheduled after any
4008 * of the corresponding image elements by the band node itself.
4009 * If not, we restrict "map" to those pairs of element that
4010 * are scheduled together by the band node and continue with
4011 * the child of the band node.
4012 * If there are no such pairs then the map passed to after_in_child
4013 * will be empty causing it to return 0.
4015 static int after_in_band(__isl_keep isl_union_map
*umap
,
4016 __isl_keep isl_schedule_node
*node
)
4018 isl_multi_union_pw_aff
*mupa
;
4019 isl_union_map
*partial
, *test
, *gt
, *universe
, *umap1
, *umap2
;
4020 isl_union_set
*domain
, *range
;
4025 if (isl_schedule_node_band_n_member(node
) == 0)
4026 return after_in_child(umap
, node
);
4028 mupa
= isl_schedule_node_band_get_partial_schedule(node
);
4029 space
= isl_multi_union_pw_aff_get_space(mupa
);
4030 partial
= isl_union_map_from_multi_union_pw_aff(mupa
);
4031 test
= isl_union_map_copy(umap
);
4032 test
= isl_union_map_apply_domain(test
, isl_union_map_copy(partial
));
4033 test
= isl_union_map_apply_range(test
, isl_union_map_copy(partial
));
4034 gt
= isl_union_map_from_map(isl_map_lex_gt(space
));
4035 test
= isl_union_map_intersect(test
, gt
);
4036 empty
= isl_union_map_is_empty(test
);
4037 isl_union_map_free(test
);
4039 if (empty
< 0 || !empty
) {
4040 isl_union_map_free(partial
);
4041 return empty
< 0 ? -1 : 1;
4044 universe
= isl_union_map_universe(isl_union_map_copy(umap
));
4045 domain
= isl_union_map_domain(isl_union_map_copy(universe
));
4046 range
= isl_union_map_range(universe
);
4047 umap1
= isl_union_map_copy(partial
);
4048 umap1
= isl_union_map_intersect_domain(umap1
, domain
);
4049 umap2
= isl_union_map_intersect_domain(partial
, range
);
4050 test
= isl_union_map_apply_range(umap1
, isl_union_map_reverse(umap2
));
4051 test
= isl_union_map_intersect(test
, isl_union_map_copy(umap
));
4052 after
= after_in_child(test
, node
);
4053 isl_union_map_free(test
);
4057 /* Is any domain element of "umap" scheduled after any of
4058 * the corresponding image elements by the tree rooted at
4059 * the context node "node"?
4061 * The context constraints apply to the schedule domain,
4062 * so we cannot apply them directly to "umap", which contains
4063 * pairs of statement instances. Instead, we add them
4064 * to the range of the prefix schedule for both domain and
4067 static int after_in_context(__isl_keep isl_union_map
*umap
,
4068 __isl_keep isl_schedule_node
*node
)
4070 isl_union_map
*prefix
, *universe
, *umap1
, *umap2
;
4071 isl_union_set
*domain
, *range
;
4075 umap
= isl_union_map_copy(umap
);
4076 context
= isl_schedule_node_context_get_context(node
);
4077 prefix
= isl_schedule_node_get_prefix_schedule_union_map(node
);
4078 universe
= isl_union_map_universe(isl_union_map_copy(umap
));
4079 domain
= isl_union_map_domain(isl_union_map_copy(universe
));
4080 range
= isl_union_map_range(universe
);
4081 umap1
= isl_union_map_copy(prefix
);
4082 umap1
= isl_union_map_intersect_domain(umap1
, domain
);
4083 umap2
= isl_union_map_intersect_domain(prefix
, range
);
4084 umap1
= isl_union_map_intersect_range(umap1
,
4085 isl_union_set_from_set(context
));
4086 umap1
= isl_union_map_apply_range(umap1
, isl_union_map_reverse(umap2
));
4087 umap
= isl_union_map_intersect(umap
, umap1
);
4089 after
= after_in_child(umap
, node
);
4091 isl_union_map_free(umap
);
4096 /* Is any domain element of "umap" scheduled after any of
4097 * the corresponding image elements by the tree rooted at
4098 * the expansion node "node"?
4100 * We apply the expansion to domain and range of "umap" and
4101 * continue with its child.
4103 static int after_in_expansion(__isl_keep isl_union_map
*umap
,
4104 __isl_keep isl_schedule_node
*node
)
4106 isl_union_map
*expansion
;
4109 expansion
= isl_schedule_node_expansion_get_expansion(node
);
4110 umap
= isl_union_map_copy(umap
);
4111 umap
= isl_union_map_apply_domain(umap
, isl_union_map_copy(expansion
));
4112 umap
= isl_union_map_apply_range(umap
, expansion
);
4114 after
= after_in_child(umap
, node
);
4116 isl_union_map_free(umap
);
4121 /* Is any domain element of "umap" scheduled after any of
4122 * the corresponding image elements by the tree rooted at
4123 * the extension node "node"?
4125 * Since the extension node may add statement instances before or
4126 * after the pairs of statement instances in "umap", we return 1
4127 * to ensure that these pairs are not broken up.
4129 static int after_in_extension(__isl_keep isl_union_map
*umap
,
4130 __isl_keep isl_schedule_node
*node
)
4135 /* Is any domain element of "umap" scheduled after any of
4136 * the corresponding image elements by the tree rooted at
4137 * the filter node "node"?
4139 * We intersect domain and range of "umap" with the filter and
4140 * continue with its child.
4142 static int after_in_filter(__isl_keep isl_union_map
*umap
,
4143 __isl_keep isl_schedule_node
*node
)
4145 isl_union_set
*filter
;
4148 umap
= isl_union_map_copy(umap
);
4149 filter
= isl_schedule_node_filter_get_filter(node
);
4150 umap
= isl_union_map_intersect_domain(umap
, isl_union_set_copy(filter
));
4151 umap
= isl_union_map_intersect_range(umap
, filter
);
4153 after
= after_in_child(umap
, node
);
4155 isl_union_map_free(umap
);
4160 /* Is any domain element of "umap" scheduled after any of
4161 * the corresponding image elements by the tree rooted at
4162 * the set node "node"?
4164 * This is only the case if this condition holds in any
4165 * of the (filter) children of the set node.
4166 * In particular, if the domain and the range of "umap"
4167 * are contained in different children, then the condition
4170 static int after_in_set(__isl_keep isl_union_map
*umap
,
4171 __isl_keep isl_schedule_node
*node
)
4175 n
= isl_schedule_node_n_children(node
);
4176 for (i
= 0; i
< n
; ++i
) {
4177 isl_schedule_node
*child
;
4180 child
= isl_schedule_node_get_child(node
, i
);
4181 after
= after_in_tree(umap
, child
);
4182 isl_schedule_node_free(child
);
4184 if (after
< 0 || after
)
4191 /* Return the filter of child "i" of "node".
4193 static __isl_give isl_union_set
*child_filter(
4194 __isl_keep isl_schedule_node
*node
, int i
)
4196 isl_schedule_node
*child
;
4197 isl_union_set
*filter
;
4199 child
= isl_schedule_node_get_child(node
, i
);
4200 filter
= isl_schedule_node_filter_get_filter(child
);
4201 isl_schedule_node_free(child
);
4206 /* Is any domain element of "umap" scheduled after any of
4207 * the corresponding image elements by the tree rooted at
4208 * the sequence node "node"?
4210 * This happens in particular if any domain element is
4211 * contained in a later child than one containing a range element or
4212 * if the condition holds within a given child in the sequence.
4213 * The later part of the condition is checked by after_in_set.
4215 static int after_in_sequence(__isl_keep isl_union_map
*umap
,
4216 __isl_keep isl_schedule_node
*node
)
4219 isl_union_map
*umap_i
;
4220 int empty
, after
= 0;
4222 n
= isl_schedule_node_n_children(node
);
4223 for (i
= 1; i
< n
; ++i
) {
4224 isl_union_set
*filter_i
;
4226 umap_i
= isl_union_map_copy(umap
);
4227 filter_i
= child_filter(node
, i
);
4228 umap_i
= isl_union_map_intersect_domain(umap_i
, filter_i
);
4229 empty
= isl_union_map_is_empty(umap_i
);
4233 isl_union_map_free(umap_i
);
4237 for (j
= 0; j
< i
; ++j
) {
4238 isl_union_set
*filter_j
;
4239 isl_union_map
*umap_ij
;
4241 umap_ij
= isl_union_map_copy(umap_i
);
4242 filter_j
= child_filter(node
, j
);
4243 umap_ij
= isl_union_map_intersect_range(umap_ij
,
4245 empty
= isl_union_map_is_empty(umap_ij
);
4246 isl_union_map_free(umap_ij
);
4256 isl_union_map_free(umap_i
);
4261 if (after
< 0 || after
)
4264 return after_in_set(umap
, node
);
4266 isl_union_map_free(umap_i
);
4270 /* Is any domain element of "umap" scheduled after any of
4271 * the corresponding image elements by the tree rooted at "node"?
4273 * If "umap" is empty, then clearly there is no such element.
4274 * Otherwise, consider the different types of nodes separately.
4276 static int after_in_tree(__isl_keep isl_union_map
*umap
,
4277 __isl_keep isl_schedule_node
*node
)
4280 enum isl_schedule_node_type type
;
4282 empty
= isl_union_map_is_empty(umap
);
4290 type
= isl_schedule_node_get_type(node
);
4292 case isl_schedule_node_error
:
4294 case isl_schedule_node_leaf
:
4296 case isl_schedule_node_band
:
4297 return after_in_band(umap
, node
);
4298 case isl_schedule_node_domain
:
4299 isl_die(isl_schedule_node_get_ctx(node
), isl_error_internal
,
4300 "unexpected internal domain node", return -1);
4301 case isl_schedule_node_context
:
4302 return after_in_context(umap
, node
);
4303 case isl_schedule_node_expansion
:
4304 return after_in_expansion(umap
, node
);
4305 case isl_schedule_node_extension
:
4306 return after_in_extension(umap
, node
);
4307 case isl_schedule_node_filter
:
4308 return after_in_filter(umap
, node
);
4309 case isl_schedule_node_guard
:
4310 case isl_schedule_node_mark
:
4311 return after_in_child(umap
, node
);
4312 case isl_schedule_node_set
:
4313 return after_in_set(umap
, node
);
4314 case isl_schedule_node_sequence
:
4315 return after_in_sequence(umap
, node
);
4321 /* Is any domain element of "map1" scheduled after any domain
4322 * element of "map2" by the subtree underneath the current band node,
4323 * while at the same time being scheduled together by the current
4324 * band node, i.e., by "map1" and "map2?
4326 * If the child of the current band node is a leaf, then
4327 * no element can be scheduled after any other element.
4329 * Otherwise, we construct a relation between domain elements
4330 * of "map1" and domain elements of "map2" that are scheduled
4331 * together and then check if the subtree underneath the current
4332 * band node determines their relative order.
4334 static int after_in_subtree(__isl_keep isl_ast_build
*build
,
4335 __isl_keep isl_map
*map1
, __isl_keep isl_map
*map2
)
4337 isl_schedule_node
*node
;
4339 isl_union_map
*umap
;
4342 node
= isl_ast_build_get_schedule_node(build
);
4345 node
= isl_schedule_node_child(node
, 0);
4346 if (isl_schedule_node_get_type(node
) == isl_schedule_node_leaf
) {
4347 isl_schedule_node_free(node
);
4350 map
= isl_map_copy(map2
);
4351 map
= isl_map_apply_domain(map
, isl_map_copy(map1
));
4352 umap
= isl_union_map_from_map(map
);
4353 after
= after_in_tree(umap
, node
);
4354 isl_union_map_free(umap
);
4355 isl_schedule_node_free(node
);
4359 /* Internal data for any_scheduled_after.
4361 * "build" is the build in which the AST is constructed.
4362 * "depth" is the number of loops that have already been generated
4363 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
4364 * "domain" is an array of set-map pairs corresponding to the different
4365 * iteration domains. The set is the schedule domain, i.e., the domain
4366 * of the inverse schedule, while the map is the inverse schedule itself.
4368 struct isl_any_scheduled_after_data
{
4369 isl_ast_build
*build
;
4371 int group_coscheduled
;
4372 struct isl_set_map_pair
*domain
;
4375 /* Is any element of domain "i" scheduled after any element of domain "j"
4376 * (for a common iteration of the first data->depth loops)?
4378 * data->domain[i].set contains the domain of the inverse schedule
4379 * for domain "i", i.e., elements in the schedule domain.
4381 * If we are inside a band of a schedule tree and there is a pair
4382 * of elements in the two domains that is schedule together by
4383 * the current band, then we check if any element of "i" may be schedule
4384 * after element of "j" by the descendants of the band node.
4386 * If data->group_coscheduled is set, then we also return 1 if there
4387 * is any pair of elements in the two domains that are scheduled together.
4389 static int any_scheduled_after(int i
, int j
, void *user
)
4391 struct isl_any_scheduled_after_data
*data
= user
;
4392 int dim
= isl_set_dim(data
->domain
[i
].set
, isl_dim_set
);
4395 for (pos
= data
->depth
; pos
< dim
; ++pos
) {
4398 follows
= isl_set_follows_at(data
->domain
[i
].set
,
4399 data
->domain
[j
].set
, pos
);
4409 if (isl_ast_build_has_schedule_node(data
->build
)) {
4412 after
= after_in_subtree(data
->build
, data
->domain
[i
].map
,
4413 data
->domain
[j
].map
);
4414 if (after
< 0 || after
)
4418 return data
->group_coscheduled
;
4421 /* Look for independent components at the current depth and generate code
4422 * for each component separately. The resulting lists of grafts are
4423 * merged in an attempt to combine grafts with identical guards.
4425 * Code for two domains can be generated separately if all the elements
4426 * of one domain are scheduled before (or together with) all the elements
4427 * of the other domain. We therefore consider the graph with as nodes
4428 * the domains and an edge between two nodes if any element of the first
4429 * node is scheduled after any element of the second node.
4430 * If the ast_build_group_coscheduled is set, then we also add an edge if
4431 * there is any pair of elements in the two domains that are scheduled
4433 * Code is then generated (by generate_component)
4434 * for each of the strongly connected components in this graph
4435 * in their topological order.
4437 * Since the test is performed on the domain of the inverse schedules of
4438 * the different domains, we precompute these domains and store
4439 * them in data.domain.
4441 static __isl_give isl_ast_graft_list
*generate_components(
4442 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
4445 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
4446 int n
= isl_union_map_n_map(executed
);
4447 struct isl_any_scheduled_after_data data
;
4448 struct isl_set_map_pair
*next
;
4449 struct isl_tarjan_graph
*g
= NULL
;
4450 isl_ast_graft_list
*list
= NULL
;
4453 data
.domain
= isl_calloc_array(ctx
, struct isl_set_map_pair
, n
);
4459 if (isl_union_map_foreach_map(executed
, &extract_domain
, &next
) < 0)
4465 data
.depth
= isl_ast_build_get_depth(build
);
4466 data
.group_coscheduled
= isl_options_get_ast_build_group_coscheduled(ctx
);
4467 g
= isl_tarjan_graph_init(ctx
, n
, &any_scheduled_after
, &data
);
4471 list
= isl_ast_graft_list_alloc(ctx
, 0);
4475 isl_ast_graft_list
*list_c
;
4478 if (g
->order
[i
] == -1)
4479 isl_die(ctx
, isl_error_internal
, "cannot happen",
4482 while (g
->order
[i
] != -1) {
4486 list_c
= generate_component(data
.domain
,
4487 g
->order
+ first
, i
- first
,
4488 isl_ast_build_copy(build
));
4489 list
= isl_ast_graft_list_merge(list
, list_c
, build
);
4495 error
: list
= isl_ast_graft_list_free(list
);
4496 isl_tarjan_graph_free(g
);
4497 for (i
= 0; i
< n_domain
; ++i
) {
4498 isl_map_free(data
.domain
[i
].map
);
4499 isl_set_free(data
.domain
[i
].set
);
4502 isl_union_map_free(executed
);
4503 isl_ast_build_free(build
);
4508 /* Generate code for the next level (and all inner levels).
4510 * If "executed" is empty, i.e., no code needs to be generated,
4511 * then we return an empty list.
4513 * If we have already generated code for all loop levels, then we pass
4514 * control to generate_inner_level.
4516 * If "executed" lives in a single space, i.e., if code needs to be
4517 * generated for a single domain, then there can only be a single
4518 * component and we go directly to generate_shifted_component.
4519 * Otherwise, we call generate_components to detect the components
4520 * and to call generate_component on each of them separately.
4522 static __isl_give isl_ast_graft_list
*generate_next_level(
4523 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
4527 if (!build
|| !executed
)
4530 if (isl_union_map_is_empty(executed
)) {
4531 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
4532 isl_union_map_free(executed
);
4533 isl_ast_build_free(build
);
4534 return isl_ast_graft_list_alloc(ctx
, 0);
4537 depth
= isl_ast_build_get_depth(build
);
4538 if (depth
>= isl_ast_build_dim(build
, isl_dim_set
))
4539 return generate_inner_level(executed
, build
);
4541 if (isl_union_map_n_map(executed
) == 1)
4542 return generate_shifted_component(executed
, build
);
4544 return generate_components(executed
, build
);
4546 isl_union_map_free(executed
);
4547 isl_ast_build_free(build
);
4551 /* Internal data structure used by isl_ast_build_node_from_schedule_map.
4552 * internal, executed and build are the inputs to generate_code.
4553 * list collects the output.
4555 struct isl_generate_code_data
{
4557 isl_union_map
*executed
;
4558 isl_ast_build
*build
;
4560 isl_ast_graft_list
*list
;
4563 /* Given an inverse schedule in terms of the external build schedule, i.e.,
4567 * with E the external build schedule and S the additional schedule "space",
4568 * reformulate the inverse schedule in terms of the internal schedule domain,
4573 * We first obtain a mapping
4577 * take the inverse and the product with S -> S, resulting in
4579 * [I -> S] -> [E -> S]
4581 * Applying the map to the input produces the desired result.
4583 static __isl_give isl_union_map
*internal_executed(
4584 __isl_take isl_union_map
*executed
, __isl_keep isl_space
*space
,
4585 __isl_keep isl_ast_build
*build
)
4589 proj
= isl_ast_build_get_schedule_map(build
);
4590 proj
= isl_map_reverse(proj
);
4591 space
= isl_space_map_from_set(isl_space_copy(space
));
4592 id
= isl_map_identity(space
);
4593 proj
= isl_map_product(proj
, id
);
4594 executed
= isl_union_map_apply_domain(executed
,
4595 isl_union_map_from_map(proj
));
4599 /* Generate an AST that visits the elements in the range of data->executed
4600 * in the relative order specified by the corresponding domain element(s)
4601 * for those domain elements that belong to "set".
4602 * Add the result to data->list.
4604 * The caller ensures that "set" is a universe domain.
4605 * "space" is the space of the additional part of the schedule.
4606 * It is equal to the space of "set" if build->domain is parametric.
4607 * Otherwise, it is equal to the range of the wrapped space of "set".
4609 * If the build space is not parametric and
4610 * if isl_ast_build_node_from_schedule_map
4611 * was called from an outside user (data->internal not set), then
4612 * the (inverse) schedule refers to the external build domain and needs to
4613 * be transformed to refer to the internal build domain.
4615 * If the build space is parametric, then we add some of the parameter
4616 * constraints to the executed relation. Adding these constraints
4617 * allows for an earlier detection of conflicts in some cases.
4618 * However, we do not want to divide the executed relation into
4619 * more disjuncts than necessary. We therefore approximate
4620 * the constraints on the parameters by a single disjunct set.
4622 * The build is extended to include the additional part of the schedule.
4623 * If the original build space was not parametric, then the options
4624 * in data->build refer only to the additional part of the schedule
4625 * and they need to be adjusted to refer to the complete AST build
4628 * After having adjusted inverse schedule and build, we start generating
4629 * code with the outer loop of the current code generation
4630 * in generate_next_level.
4632 * If the original build space was not parametric, we undo the embedding
4633 * on the resulting isl_ast_node_list so that it can be used within
4634 * the outer AST build.
4636 static int generate_code_in_space(struct isl_generate_code_data
*data
,
4637 __isl_take isl_set
*set
, __isl_take isl_space
*space
)
4639 isl_union_map
*executed
;
4640 isl_ast_build
*build
;
4641 isl_ast_graft_list
*list
;
4644 executed
= isl_union_map_copy(data
->executed
);
4645 executed
= isl_union_map_intersect_domain(executed
,
4646 isl_union_set_from_set(set
));
4648 embed
= !isl_set_is_params(data
->build
->domain
);
4649 if (embed
&& !data
->internal
)
4650 executed
= internal_executed(executed
, space
, data
->build
);
4653 domain
= isl_ast_build_get_domain(data
->build
);
4654 domain
= isl_set_from_basic_set(isl_set_simple_hull(domain
));
4655 executed
= isl_union_map_intersect_params(executed
, domain
);
4658 build
= isl_ast_build_copy(data
->build
);
4659 build
= isl_ast_build_product(build
, space
);
4661 list
= generate_next_level(executed
, build
);
4663 list
= isl_ast_graft_list_unembed(list
, embed
);
4665 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
4670 /* Generate an AST that visits the elements in the range of data->executed
4671 * in the relative order specified by the corresponding domain element(s)
4672 * for those domain elements that belong to "set".
4673 * Add the result to data->list.
4675 * The caller ensures that "set" is a universe domain.
4677 * If the build space S is not parametric, then the space of "set"
4678 * need to be a wrapped relation with S as domain. That is, it needs
4683 * Check this property and pass control to generate_code_in_space
4685 * If the build space is not parametric, then T is the space of "set".
4687 static int generate_code_set(__isl_take isl_set
*set
, void *user
)
4689 struct isl_generate_code_data
*data
= user
;
4690 isl_space
*space
, *build_space
;
4693 space
= isl_set_get_space(set
);
4695 if (isl_set_is_params(data
->build
->domain
))
4696 return generate_code_in_space(data
, set
, space
);
4698 build_space
= isl_ast_build_get_space(data
->build
, data
->internal
);
4699 space
= isl_space_unwrap(space
);
4700 is_domain
= isl_space_is_domain(build_space
, space
);
4701 isl_space_free(build_space
);
4702 space
= isl_space_range(space
);
4707 isl_die(isl_set_get_ctx(set
), isl_error_invalid
,
4708 "invalid nested schedule space", goto error
);
4710 return generate_code_in_space(data
, set
, space
);
4713 isl_space_free(space
);
4717 /* Generate an AST that visits the elements in the range of "executed"
4718 * in the relative order specified by the corresponding domain element(s).
4720 * "build" is an isl_ast_build that has either been constructed by
4721 * isl_ast_build_from_context or passed to a callback set by
4722 * isl_ast_build_set_create_leaf.
4723 * In the first case, the space of the isl_ast_build is typically
4724 * a parametric space, although this is currently not enforced.
4725 * In the second case, the space is never a parametric space.
4726 * If the space S is not parametric, then the domain space(s) of "executed"
4727 * need to be wrapped relations with S as domain.
4729 * If the domain of "executed" consists of several spaces, then an AST
4730 * is generated for each of them (in arbitrary order) and the results
4733 * If "internal" is set, then the domain "S" above refers to the internal
4734 * schedule domain representation. Otherwise, it refers to the external
4735 * representation, as returned by isl_ast_build_get_schedule_space.
4737 * We essentially run over all the spaces in the domain of "executed"
4738 * and call generate_code_set on each of them.
4740 static __isl_give isl_ast_graft_list
*generate_code(
4741 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
4745 struct isl_generate_code_data data
= { 0 };
4747 isl_union_set
*schedule_domain
;
4748 isl_union_map
*universe
;
4752 space
= isl_ast_build_get_space(build
, 1);
4753 space
= isl_space_align_params(space
,
4754 isl_union_map_get_space(executed
));
4755 space
= isl_space_align_params(space
,
4756 isl_union_map_get_space(build
->options
));
4757 build
= isl_ast_build_align_params(build
, isl_space_copy(space
));
4758 executed
= isl_union_map_align_params(executed
, space
);
4759 if (!executed
|| !build
)
4762 ctx
= isl_ast_build_get_ctx(build
);
4764 data
.internal
= internal
;
4765 data
.executed
= executed
;
4767 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
4769 universe
= isl_union_map_universe(isl_union_map_copy(executed
));
4770 schedule_domain
= isl_union_map_domain(universe
);
4771 if (isl_union_set_foreach_set(schedule_domain
, &generate_code_set
,
4773 data
.list
= isl_ast_graft_list_free(data
.list
);
4775 isl_union_set_free(schedule_domain
);
4776 isl_union_map_free(executed
);
4778 isl_ast_build_free(build
);
4781 isl_union_map_free(executed
);
4782 isl_ast_build_free(build
);
4786 /* Generate an AST that visits the elements in the domain of "schedule"
4787 * in the relative order specified by the corresponding image element(s).
4789 * "build" is an isl_ast_build that has either been constructed by
4790 * isl_ast_build_from_context or passed to a callback set by
4791 * isl_ast_build_set_create_leaf.
4792 * In the first case, the space of the isl_ast_build is typically
4793 * a parametric space, although this is currently not enforced.
4794 * In the second case, the space is never a parametric space.
4795 * If the space S is not parametric, then the range space(s) of "schedule"
4796 * need to be wrapped relations with S as domain.
4798 * If the range of "schedule" consists of several spaces, then an AST
4799 * is generated for each of them (in arbitrary order) and the results
4802 * We first initialize the local copies of the relevant options.
4803 * We do this here rather than when the isl_ast_build is created
4804 * because the options may have changed between the construction
4805 * of the isl_ast_build and the call to isl_generate_code.
4807 * The main computation is performed on an inverse schedule (with
4808 * the schedule domain in the domain and the elements to be executed
4809 * in the range) called "executed".
4811 __isl_give isl_ast_node
*isl_ast_build_node_from_schedule_map(
4812 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
4814 isl_ast_graft_list
*list
;
4816 isl_union_map
*executed
;
4818 build
= isl_ast_build_copy(build
);
4819 build
= isl_ast_build_set_single_valued(build
, 0);
4820 schedule
= isl_union_map_coalesce(schedule
);
4821 schedule
= isl_union_map_remove_redundancies(schedule
);
4822 executed
= isl_union_map_reverse(schedule
);
4823 list
= generate_code(executed
, isl_ast_build_copy(build
), 0);
4824 node
= isl_ast_node_from_graft_list(list
, build
);
4825 isl_ast_build_free(build
);
4830 /* The old name for isl_ast_build_node_from_schedule_map.
4831 * It is being kept for backward compatibility, but
4832 * it will be removed in the future.
4834 __isl_give isl_ast_node
*isl_ast_build_ast_from_schedule(
4835 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
4837 return isl_ast_build_node_from_schedule_map(build
, schedule
);
4840 /* Generate an AST that visits the elements in the domain of "executed"
4841 * in the relative order specified by the band node "node" and its descendants.
4843 * The relation "executed" maps the outer generated loop iterators
4844 * to the domain elements executed by those iterations.
4846 * If the band is empty, we continue with its descendants.
4847 * Otherwise, we extend the build and the inverse schedule with
4848 * the additional space/partial schedule and continue generating
4849 * an AST in generate_next_level.
4850 * As soon as we have extended the inverse schedule with the additional
4851 * partial schedule, we look for equalities that may exists between
4852 * the old and the new part.
4854 static __isl_give isl_ast_graft_list
*build_ast_from_band(
4855 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
4856 __isl_take isl_union_map
*executed
)
4859 isl_multi_union_pw_aff
*extra
;
4860 isl_union_map
*extra_umap
;
4861 isl_ast_graft_list
*list
;
4864 if (!build
|| !node
|| !executed
)
4867 if (isl_schedule_node_band_n_member(node
) == 0)
4868 return build_ast_from_child(build
, node
, executed
);
4870 extra
= isl_schedule_node_band_get_partial_schedule(node
);
4871 extra
= isl_multi_union_pw_aff_align_params(extra
,
4872 isl_ast_build_get_space(build
, 1));
4873 space
= isl_multi_union_pw_aff_get_space(extra
);
4875 extra_umap
= isl_union_map_from_multi_union_pw_aff(extra
);
4876 extra_umap
= isl_union_map_reverse(extra_umap
);
4878 executed
= isl_union_map_domain_product(executed
, extra_umap
);
4879 executed
= isl_union_map_detect_equalities(executed
);
4881 n1
= isl_ast_build_dim(build
, isl_dim_param
);
4882 build
= isl_ast_build_product(build
, space
);
4883 n2
= isl_ast_build_dim(build
, isl_dim_param
);
4885 isl_die(isl_ast_build_get_ctx(build
), isl_error_invalid
,
4886 "band node is not allowed to introduce new parameters",
4887 build
= isl_ast_build_free(build
));
4888 build
= isl_ast_build_set_schedule_node(build
, node
);
4890 list
= generate_next_level(executed
, build
);
4892 list
= isl_ast_graft_list_unembed(list
, 1);
4896 isl_schedule_node_free(node
);
4897 isl_union_map_free(executed
);
4898 isl_ast_build_free(build
);
4902 /* Hoist a list of grafts (in practice containing a single graft)
4903 * from "sub_build" (which includes extra context information)
4906 * In particular, project out all additional parameters introduced
4907 * by the context node from the enforced constraints and the guard
4908 * of the single graft.
4910 static __isl_give isl_ast_graft_list
*hoist_out_of_context(
4911 __isl_take isl_ast_graft_list
*list
, __isl_keep isl_ast_build
*build
,
4912 __isl_keep isl_ast_build
*sub_build
)
4914 isl_ast_graft
*graft
;
4915 isl_basic_set
*enforced
;
4917 unsigned n_param
, extra_param
;
4919 if (!build
|| !sub_build
)
4920 return isl_ast_graft_list_free(list
);
4922 n_param
= isl_ast_build_dim(build
, isl_dim_param
);
4923 extra_param
= isl_ast_build_dim(sub_build
, isl_dim_param
);
4925 if (extra_param
== n_param
)
4928 extra_param
-= n_param
;
4929 enforced
= isl_ast_graft_list_extract_shared_enforced(list
, sub_build
);
4930 enforced
= isl_basic_set_project_out(enforced
, isl_dim_param
,
4931 n_param
, extra_param
);
4932 enforced
= isl_basic_set_remove_unknown_divs(enforced
);
4933 guard
= isl_ast_graft_list_extract_hoistable_guard(list
, sub_build
);
4934 guard
= isl_set_remove_divs_involving_dims(guard
, isl_dim_param
,
4935 n_param
, extra_param
);
4936 guard
= isl_set_project_out(guard
, isl_dim_param
, n_param
, extra_param
);
4937 guard
= isl_set_compute_divs(guard
);
4938 graft
= isl_ast_graft_alloc_from_children(list
, guard
, enforced
,
4940 list
= isl_ast_graft_list_from_ast_graft(graft
);
4945 /* Generate an AST that visits the elements in the domain of "executed"
4946 * in the relative order specified by the context node "node"
4947 * and its descendants.
4949 * The relation "executed" maps the outer generated loop iterators
4950 * to the domain elements executed by those iterations.
4952 * The context node may introduce additional parameters as well as
4953 * constraints on the outer schedule dimenions or original parameters.
4955 * We add the extra parameters to a new build and the context
4956 * constraints to both the build and (as a single disjunct)
4957 * to the domain of "executed". Since the context constraints
4958 * are specified in terms of the input schedule, we first need
4959 * to map them to the internal schedule domain.
4961 * After constructing the AST from the descendants of "node",
4962 * we combine the list of grafts into a single graft within
4963 * the new build, in order to be able to exploit the additional
4964 * context constraints during this combination.
4966 * Additionally, if the current node is the outermost node in
4967 * the schedule tree (apart from the root domain node), we generate
4968 * all pending guards, again to be able to exploit the additional
4969 * context constraints. We currently do not do this for internal
4970 * context nodes since we may still want to hoist conditions
4971 * to outer AST nodes.
4973 * If the context node introduced any new parameters, then they
4974 * are removed from the set of enforced constraints and guard
4975 * in hoist_out_of_context.
4977 static __isl_give isl_ast_graft_list
*build_ast_from_context(
4978 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
4979 __isl_take isl_union_map
*executed
)
4983 isl_multi_aff
*internal2input
;
4984 isl_ast_build
*sub_build
;
4985 isl_ast_graft_list
*list
;
4988 depth
= isl_schedule_node_get_tree_depth(node
);
4989 space
= isl_ast_build_get_space(build
, 1);
4990 context
= isl_schedule_node_context_get_context(node
);
4991 context
= isl_set_align_params(context
, space
);
4992 sub_build
= isl_ast_build_copy(build
);
4993 space
= isl_set_get_space(context
);
4994 sub_build
= isl_ast_build_align_params(sub_build
, space
);
4995 internal2input
= isl_ast_build_get_internal2input(sub_build
);
4996 context
= isl_set_preimage_multi_aff(context
, internal2input
);
4997 sub_build
= isl_ast_build_restrict_generated(sub_build
,
4998 isl_set_copy(context
));
4999 context
= isl_set_from_basic_set(isl_set_simple_hull(context
));
5000 executed
= isl_union_map_intersect_domain(executed
,
5001 isl_union_set_from_set(context
));
5003 list
= build_ast_from_child(isl_ast_build_copy(sub_build
),
5005 n
= isl_ast_graft_list_n_ast_graft(list
);
5007 list
= isl_ast_graft_list_free(list
);
5009 list
= isl_ast_graft_list_fuse(list
, sub_build
);
5011 list
= isl_ast_graft_list_insert_pending_guard_nodes(list
,
5014 list
= hoist_out_of_context(list
, build
, sub_build
);
5016 isl_ast_build_free(build
);
5017 isl_ast_build_free(sub_build
);
5022 /* Generate an AST that visits the elements in the domain of "executed"
5023 * in the relative order specified by the expansion node "node" and
5026 * The relation "executed" maps the outer generated loop iterators
5027 * to the domain elements executed by those iterations.
5029 * We expand the domain elements by the expansion and
5030 * continue with the descendants of the node.
5032 static __isl_give isl_ast_graft_list
*build_ast_from_expansion(
5033 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
5034 __isl_take isl_union_map
*executed
)
5036 isl_union_map
*expansion
;
5039 expansion
= isl_schedule_node_expansion_get_expansion(node
);
5040 expansion
= isl_union_map_align_params(expansion
,
5041 isl_union_map_get_space(executed
));
5043 n1
= isl_union_map_dim(executed
, isl_dim_param
);
5044 executed
= isl_union_map_apply_range(executed
, expansion
);
5045 n2
= isl_union_map_dim(executed
, isl_dim_param
);
5047 isl_die(isl_ast_build_get_ctx(build
), isl_error_invalid
,
5048 "expansion node is not allowed to introduce "
5049 "new parameters", goto error
);
5051 return build_ast_from_child(build
, node
, executed
);
5053 isl_ast_build_free(build
);
5054 isl_schedule_node_free(node
);
5055 isl_union_map_free(executed
);
5059 /* Generate an AST that visits the elements in the domain of "executed"
5060 * in the relative order specified by the extension node "node" and
5063 * The relation "executed" maps the outer generated loop iterators
5064 * to the domain elements executed by those iterations.
5066 * Extend the inverse schedule with the extension applied to current
5067 * set of generated constraints. Since the extension if formulated
5068 * in terms of the input schedule, it first needs to be transformed
5069 * to refer to the internal schedule.
5071 static __isl_give isl_ast_graft_list
*build_ast_from_extension(
5072 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
5073 __isl_take isl_union_map
*executed
)
5075 isl_union_set
*schedule_domain
;
5076 isl_union_map
*extension
;
5079 set
= isl_ast_build_get_generated(build
);
5080 schedule_domain
= isl_union_set_from_set(set
);
5082 extension
= isl_schedule_node_extension_get_extension(node
);
5084 extension
= isl_union_map_preimage_domain_multi_aff(extension
,
5085 isl_multi_aff_copy(build
->internal2input
));
5086 extension
= isl_union_map_intersect_domain(extension
, schedule_domain
);
5087 extension
= isl_ast_build_substitute_values_union_map_domain(build
,
5089 executed
= isl_union_map_union(executed
, extension
);
5091 return build_ast_from_child(build
, node
, executed
);
5094 /* Generate an AST that visits the elements in the domain of "executed"
5095 * in the relative order specified by the filter node "node" and
5098 * The relation "executed" maps the outer generated loop iterators
5099 * to the domain elements executed by those iterations.
5101 * We simply intersect the iteration domain (i.e., the range of "executed")
5102 * with the filter and continue with the descendants of the node,
5103 * unless the resulting inverse schedule is empty, in which
5104 * case we return an empty list.
5106 static __isl_give isl_ast_graft_list
*build_ast_from_filter(
5107 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
5108 __isl_take isl_union_map
*executed
)
5111 isl_union_set
*filter
;
5112 isl_ast_graft_list
*list
;
5116 if (!build
|| !node
|| !executed
)
5119 filter
= isl_schedule_node_filter_get_filter(node
);
5120 filter
= isl_union_set_align_params(filter
,
5121 isl_union_map_get_space(executed
));
5122 n1
= isl_union_map_dim(executed
, isl_dim_param
);
5123 executed
= isl_union_map_intersect_range(executed
, filter
);
5124 n2
= isl_union_map_dim(executed
, isl_dim_param
);
5126 isl_die(isl_ast_build_get_ctx(build
), isl_error_invalid
,
5127 "filter node is not allowed to introduce "
5128 "new parameters", goto error
);
5130 empty
= isl_union_map_is_empty(executed
);
5134 return build_ast_from_child(build
, node
, executed
);
5136 ctx
= isl_ast_build_get_ctx(build
);
5137 list
= isl_ast_graft_list_alloc(ctx
, 0);
5138 isl_ast_build_free(build
);
5139 isl_schedule_node_free(node
);
5140 isl_union_map_free(executed
);
5143 isl_ast_build_free(build
);
5144 isl_schedule_node_free(node
);
5145 isl_union_map_free(executed
);
5149 /* Generate an AST that visits the elements in the domain of "executed"
5150 * in the relative order specified by the guard node "node" and
5153 * The relation "executed" maps the outer generated loop iterators
5154 * to the domain elements executed by those iterations.
5156 * Ensure that the associated guard is enforced by the outer AST
5157 * constructs by adding it to the guard of the graft.
5158 * Since we know that we will enforce the guard, we can also include it
5159 * in the generated constraints used to construct an AST for
5160 * the descendant nodes.
5162 static __isl_give isl_ast_graft_list
*build_ast_from_guard(
5163 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
5164 __isl_take isl_union_map
*executed
)
5167 isl_set
*guard
, *hoisted
;
5168 isl_basic_set
*enforced
;
5169 isl_ast_build
*sub_build
;
5170 isl_ast_graft
*graft
;
5171 isl_ast_graft_list
*list
;
5174 space
= isl_ast_build_get_space(build
, 1);
5175 guard
= isl_schedule_node_guard_get_guard(node
);
5176 n1
= isl_space_dim(space
, isl_dim_param
);
5177 guard
= isl_set_align_params(guard
, space
);
5178 n2
= isl_set_dim(guard
, isl_dim_param
);
5180 isl_die(isl_ast_build_get_ctx(build
), isl_error_invalid
,
5181 "guard node is not allowed to introduce "
5182 "new parameters", guard
= isl_set_free(guard
));
5183 guard
= isl_set_preimage_multi_aff(guard
,
5184 isl_multi_aff_copy(build
->internal2input
));
5185 guard
= isl_ast_build_specialize(build
, guard
);
5186 guard
= isl_set_gist(guard
, isl_set_copy(build
->generated
));
5188 sub_build
= isl_ast_build_copy(build
);
5189 sub_build
= isl_ast_build_restrict_generated(sub_build
,
5190 isl_set_copy(guard
));
5192 list
= build_ast_from_child(isl_ast_build_copy(sub_build
),
5195 hoisted
= isl_ast_graft_list_extract_hoistable_guard(list
, sub_build
);
5196 if (isl_set_n_basic_set(hoisted
) > 1)
5197 list
= isl_ast_graft_list_gist_guards(list
,
5198 isl_set_copy(hoisted
));
5199 guard
= isl_set_intersect(guard
, hoisted
);
5200 enforced
= extract_shared_enforced(list
, build
);
5201 graft
= isl_ast_graft_alloc_from_children(list
, guard
, enforced
,
5204 isl_ast_build_free(sub_build
);
5205 isl_ast_build_free(build
);
5206 return isl_ast_graft_list_from_ast_graft(graft
);
5209 /* Call the before_each_mark callback, if requested by the user.
5211 * Return 0 on success and -1 on error.
5213 * The caller is responsible for recording the current inverse schedule
5216 static int before_each_mark(__isl_keep isl_id
*mark
,
5217 __isl_keep isl_ast_build
*build
)
5221 if (!build
->before_each_mark
)
5223 return build
->before_each_mark(mark
, build
,
5224 build
->before_each_mark_user
);
5227 /* Call the after_each_mark callback, if requested by the user.
5229 * The caller is responsible for recording the current inverse schedule
5232 static __isl_give isl_ast_graft
*after_each_mark(
5233 __isl_take isl_ast_graft
*graft
, __isl_keep isl_ast_build
*build
)
5235 if (!graft
|| !build
)
5236 return isl_ast_graft_free(graft
);
5237 if (!build
->after_each_mark
)
5239 graft
->node
= build
->after_each_mark(graft
->node
, build
,
5240 build
->after_each_mark_user
);
5242 return isl_ast_graft_free(graft
);
5247 /* Generate an AST that visits the elements in the domain of "executed"
5248 * in the relative order specified by the mark node "node" and
5251 * The relation "executed" maps the outer generated loop iterators
5252 * to the domain elements executed by those iterations.
5254 * Since we may be calling before_each_mark and after_each_mark
5255 * callbacks, we record the current inverse schedule in the build.
5257 * We generate an AST for the child of the mark node, combine
5258 * the graft list into a single graft and then insert the mark
5259 * in the AST of that single graft.
5261 static __isl_give isl_ast_graft_list
*build_ast_from_mark(
5262 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
5263 __isl_take isl_union_map
*executed
)
5266 isl_ast_graft
*graft
;
5267 isl_ast_graft_list
*list
;
5270 build
= isl_ast_build_set_executed(build
, isl_union_map_copy(executed
));
5272 mark
= isl_schedule_node_mark_get_id(node
);
5273 if (before_each_mark(mark
, build
) < 0)
5274 node
= isl_schedule_node_free(node
);
5276 list
= build_ast_from_child(isl_ast_build_copy(build
), node
, executed
);
5277 list
= isl_ast_graft_list_fuse(list
, build
);
5278 n
= isl_ast_graft_list_n_ast_graft(list
);
5280 list
= isl_ast_graft_list_free(list
);
5284 graft
= isl_ast_graft_list_get_ast_graft(list
, 0);
5285 graft
= isl_ast_graft_insert_mark(graft
, mark
);
5286 graft
= after_each_mark(graft
, build
);
5287 list
= isl_ast_graft_list_set_ast_graft(list
, 0, graft
);
5289 isl_ast_build_free(build
);
5294 static __isl_give isl_ast_graft_list
*build_ast_from_schedule_node(
5295 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
5296 __isl_take isl_union_map
*executed
);
5298 /* Generate an AST that visits the elements in the domain of "executed"
5299 * in the relative order specified by the sequence (or set) node "node" and
5302 * The relation "executed" maps the outer generated loop iterators
5303 * to the domain elements executed by those iterations.
5305 * We simply generate an AST for each of the children and concatenate
5308 static __isl_give isl_ast_graft_list
*build_ast_from_sequence(
5309 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
5310 __isl_take isl_union_map
*executed
)
5314 isl_ast_graft_list
*list
;
5316 ctx
= isl_ast_build_get_ctx(build
);
5317 list
= isl_ast_graft_list_alloc(ctx
, 0);
5319 n
= isl_schedule_node_n_children(node
);
5320 for (i
= 0; i
< n
; ++i
) {
5321 isl_schedule_node
*child
;
5322 isl_ast_graft_list
*list_i
;
5324 child
= isl_schedule_node_get_child(node
, i
);
5325 list_i
= build_ast_from_schedule_node(isl_ast_build_copy(build
),
5326 child
, isl_union_map_copy(executed
));
5327 list
= isl_ast_graft_list_concat(list
, list_i
);
5329 isl_ast_build_free(build
);
5330 isl_schedule_node_free(node
);
5331 isl_union_map_free(executed
);
5336 /* Generate an AST that visits the elements in the domain of "executed"
5337 * in the relative order specified by the node "node" and its descendants.
5339 * The relation "executed" maps the outer generated loop iterators
5340 * to the domain elements executed by those iterations.
5342 * If the node is a leaf, then we pass control to generate_inner_level.
5343 * Note that the current build does not refer to any band node, so
5344 * that generate_inner_level will not try to visit the child of
5347 * The other node types are handled in separate functions.
5348 * Set nodes are currently treated in the same way as sequence nodes.
5349 * The children of a set node may be executed in any order,
5350 * including the order of the children.
5352 static __isl_give isl_ast_graft_list
*build_ast_from_schedule_node(
5353 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
5354 __isl_take isl_union_map
*executed
)
5356 enum isl_schedule_node_type type
;
5358 type
= isl_schedule_node_get_type(node
);
5361 case isl_schedule_node_error
:
5363 case isl_schedule_node_leaf
:
5364 isl_schedule_node_free(node
);
5365 return generate_inner_level(executed
, build
);
5366 case isl_schedule_node_band
:
5367 return build_ast_from_band(build
, node
, executed
);
5368 case isl_schedule_node_context
:
5369 return build_ast_from_context(build
, node
, executed
);
5370 case isl_schedule_node_domain
:
5371 isl_die(isl_schedule_node_get_ctx(node
), isl_error_unsupported
,
5372 "unexpected internal domain node", goto error
);
5373 case isl_schedule_node_expansion
:
5374 return build_ast_from_expansion(build
, node
, executed
);
5375 case isl_schedule_node_extension
:
5376 return build_ast_from_extension(build
, node
, executed
);
5377 case isl_schedule_node_filter
:
5378 return build_ast_from_filter(build
, node
, executed
);
5379 case isl_schedule_node_guard
:
5380 return build_ast_from_guard(build
, node
, executed
);
5381 case isl_schedule_node_mark
:
5382 return build_ast_from_mark(build
, node
, executed
);
5383 case isl_schedule_node_sequence
:
5384 case isl_schedule_node_set
:
5385 return build_ast_from_sequence(build
, node
, executed
);
5388 isl_die(isl_ast_build_get_ctx(build
), isl_error_internal
,
5389 "unhandled type", goto error
);
5391 isl_union_map_free(executed
);
5392 isl_schedule_node_free(node
);
5393 isl_ast_build_free(build
);
5398 /* Generate an AST that visits the elements in the domain of "executed"
5399 * in the relative order specified by the (single) child of "node" and
5402 * The relation "executed" maps the outer generated loop iterators
5403 * to the domain elements executed by those iterations.
5405 * This function is never called on a leaf, set or sequence node,
5406 * so the node always has exactly one child.
5408 static __isl_give isl_ast_graft_list
*build_ast_from_child(
5409 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
,
5410 __isl_take isl_union_map
*executed
)
5412 node
= isl_schedule_node_child(node
, 0);
5413 return build_ast_from_schedule_node(build
, node
, executed
);
5416 /* Generate an AST that visits the elements in the domain of the domain
5417 * node "node" in the relative order specified by its descendants.
5419 * An initial inverse schedule is created that maps a zero-dimensional
5420 * schedule space to the node domain.
5421 * The input "build" is assumed to have a parametric domain and
5422 * is replaced by the same zero-dimensional schedule space.
5424 * We also add some of the parameter constraints in the build domain
5425 * to the executed relation. Adding these constraints
5426 * allows for an earlier detection of conflicts in some cases.
5427 * However, we do not want to divide the executed relation into
5428 * more disjuncts than necessary. We therefore approximate
5429 * the constraints on the parameters by a single disjunct set.
5431 static __isl_give isl_ast_node
*build_ast_from_domain(
5432 __isl_take isl_ast_build
*build
, __isl_take isl_schedule_node
*node
)
5435 isl_union_set
*domain
, *schedule_domain
;
5436 isl_union_map
*executed
;
5439 isl_ast_graft_list
*list
;
5446 ctx
= isl_ast_build_get_ctx(build
);
5447 space
= isl_ast_build_get_space(build
, 1);
5448 is_params
= isl_space_is_params(space
);
5449 isl_space_free(space
);
5453 isl_die(ctx
, isl_error_unsupported
,
5454 "expecting parametric initial context", goto error
);
5456 domain
= isl_schedule_node_domain_get_domain(node
);
5457 domain
= isl_union_set_coalesce(domain
);
5459 space
= isl_union_set_get_space(domain
);
5460 space
= isl_space_set_from_params(space
);
5461 build
= isl_ast_build_product(build
, space
);
5463 set
= isl_ast_build_get_domain(build
);
5464 set
= isl_set_from_basic_set(isl_set_simple_hull(set
));
5465 schedule_domain
= isl_union_set_from_set(set
);
5467 executed
= isl_union_map_from_domain_and_range(schedule_domain
, domain
);
5468 list
= build_ast_from_child(isl_ast_build_copy(build
), node
, executed
);
5469 ast
= isl_ast_node_from_graft_list(list
, build
);
5470 isl_ast_build_free(build
);
5474 isl_schedule_node_free(node
);
5475 isl_ast_build_free(build
);
5479 /* Generate an AST that visits the elements in the domain of "schedule"
5480 * in the relative order specified by the schedule tree.
5482 * "build" is an isl_ast_build that has been created using
5483 * isl_ast_build_alloc or isl_ast_build_from_context based
5484 * on a parametric set.
5486 * The construction starts at the root node of the schedule,
5487 * which is assumed to be a domain node.
5489 __isl_give isl_ast_node
*isl_ast_build_node_from_schedule(
5490 __isl_keep isl_ast_build
*build
, __isl_take isl_schedule
*schedule
)
5493 isl_schedule_node
*node
;
5495 if (!build
|| !schedule
)
5498 ctx
= isl_ast_build_get_ctx(build
);
5500 node
= isl_schedule_get_root(schedule
);
5501 isl_schedule_free(schedule
);
5503 build
= isl_ast_build_copy(build
);
5504 build
= isl_ast_build_set_single_valued(build
, 0);
5505 if (isl_schedule_node_get_type(node
) != isl_schedule_node_domain
)
5506 isl_die(ctx
, isl_error_unsupported
,
5507 "expecting root domain node",
5508 build
= isl_ast_build_free(build
));
5509 return build_ast_from_domain(build
, node
);
5511 isl_schedule_free(schedule
);