2 * Copyright 2012-2014 Ecole Normale Superieure
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege,
7 * Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 #include <isl/union_map.h>
16 #include <isl_tarjan.h>
17 #include <isl_ast_private.h>
18 #include <isl_ast_build_expr.h>
19 #include <isl_ast_build_private.h>
20 #include <isl_ast_graft_private.h>
22 /* Data used in generate_domain.
24 * "build" is the input build.
25 * "list" collects the results.
27 struct isl_generate_domain_data
{
30 isl_ast_graft_list
*list
;
33 static __isl_give isl_ast_graft_list
*generate_next_level(
34 __isl_take isl_union_map
*executed
,
35 __isl_take isl_ast_build
*build
);
36 static __isl_give isl_ast_graft_list
*generate_code(
37 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
40 /* Generate an AST for a single domain based on
41 * the (non single valued) inverse schedule "executed".
43 * We extend the schedule with the iteration domain
44 * and continue generating through a call to generate_code.
46 * In particular, if executed has the form
50 * then we continue generating code on
54 * The extended inverse schedule is clearly single valued
55 * ensuring that the nested generate_code will not reach this function,
56 * but will instead create calls to all elements of D that need
57 * to be executed from the current schedule domain.
59 static int generate_non_single_valued(__isl_take isl_map
*executed
,
60 struct isl_generate_domain_data
*data
)
64 isl_ast_graft_list
*list
;
66 build
= isl_ast_build_copy(data
->build
);
68 identity
= isl_set_identity(isl_map_range(isl_map_copy(executed
)));
69 executed
= isl_map_domain_product(executed
, identity
);
70 build
= isl_ast_build_set_single_valued(build
, 1);
72 list
= generate_code(isl_union_map_from_map(executed
), build
, 1);
74 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
79 /* Call the at_each_domain callback, if requested by the user,
80 * after recording the current inverse schedule in the build.
82 static __isl_give isl_ast_graft
*at_each_domain(__isl_take isl_ast_graft
*graft
,
83 __isl_keep isl_map
*executed
, __isl_keep isl_ast_build
*build
)
86 return isl_ast_graft_free(graft
);
87 if (!build
->at_each_domain
)
90 build
= isl_ast_build_copy(build
);
91 build
= isl_ast_build_set_executed(build
,
92 isl_union_map_from_map(isl_map_copy(executed
)));
94 return isl_ast_graft_free(graft
);
96 graft
->node
= build
->at_each_domain(graft
->node
,
97 build
, build
->at_each_domain_user
);
98 isl_ast_build_free(build
);
101 graft
= isl_ast_graft_free(graft
);
106 /* Generate an AST for a single domain based on
107 * the inverse schedule "executed" and add it to data->list.
109 * If there is more than one domain element associated to the current
110 * schedule "time", then we need to continue the generation process
111 * in generate_non_single_valued.
112 * Note that the inverse schedule being single-valued may depend
113 * on constraints that are only available in the original context
114 * domain specified by the user. We therefore first introduce
115 * the constraints from data->build->domain.
116 * On the other hand, we only perform the test after having taken the gist
117 * of the domain as the resulting map is the one from which the call
118 * expression is constructed. Using this map to construct the call
119 * expression usually yields simpler results.
120 * Because we perform the single-valuedness test on the gisted map,
121 * we may in rare cases fail to recognize that the inverse schedule
122 * is single-valued. This becomes problematic if this happens
123 * from the recursive call through generate_non_single_valued
124 * as we would then end up in an infinite recursion.
125 * We therefore check if we are inside a call to generate_non_single_valued
126 * and revert to the ungisted map if the gisted map turns out not to be
129 * Otherwise, we generate a call expression for the single executed
130 * domain element and put a guard around it based on the (simplified)
131 * domain of "executed".
133 * If the user has set an at_each_domain callback, it is called
134 * on the constructed call expression node.
136 static int generate_domain(__isl_take isl_map
*executed
, void *user
)
138 struct isl_generate_domain_data
*data
= user
;
139 isl_ast_graft
*graft
;
140 isl_ast_graft_list
*list
;
145 executed
= isl_map_intersect_domain(executed
,
146 isl_set_copy(data
->build
->domain
));
147 empty
= isl_map_is_empty(executed
);
151 isl_map_free(executed
);
155 executed
= isl_map_coalesce(executed
);
156 map
= isl_map_copy(executed
);
157 map
= isl_ast_build_compute_gist_map_domain(data
->build
, map
);
158 sv
= isl_map_is_single_valued(map
);
163 if (data
->build
->single_valued
)
164 map
= isl_map_copy(executed
);
166 return generate_non_single_valued(executed
, data
);
168 guard
= isl_map_domain(isl_map_copy(map
));
169 guard
= isl_set_compute_divs(guard
);
170 guard
= isl_set_coalesce(guard
);
171 guard
= isl_ast_build_compute_gist(data
->build
, guard
);
172 graft
= isl_ast_graft_alloc_domain(map
, data
->build
);
173 graft
= at_each_domain(graft
, executed
, data
->build
);
175 isl_map_free(executed
);
176 graft
= isl_ast_graft_add_guard(graft
, guard
, data
->build
);
178 list
= isl_ast_graft_list_from_ast_graft(graft
);
179 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
184 isl_map_free(executed
);
188 /* Call build->create_leaf to a create "leaf" node in the AST,
189 * encapsulate the result in an isl_ast_graft and return the result
190 * as a 1-element list.
192 * Note that the node returned by the user may be an entire tree.
194 * Before we pass control to the user, we first clear some information
195 * from the build that is (presumbably) only meaningful
196 * for the current code generation.
197 * This includes the create_leaf callback itself, so we make a copy
198 * of the build first.
200 static __isl_give isl_ast_graft_list
*call_create_leaf(
201 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
204 isl_ast_graft
*graft
;
205 isl_ast_build
*user_build
;
207 user_build
= isl_ast_build_copy(build
);
208 user_build
= isl_ast_build_set_executed(user_build
, executed
);
209 user_build
= isl_ast_build_clear_local_info(user_build
);
213 node
= build
->create_leaf(user_build
, build
->create_leaf_user
);
214 graft
= isl_ast_graft_alloc(node
, build
);
215 isl_ast_build_free(build
);
216 return isl_ast_graft_list_from_ast_graft(graft
);
219 /* Generate an AST after having handled the complete schedule
220 * of this call to the code generator.
222 * If the user has specified a create_leaf callback, control
223 * is passed to the user in call_create_leaf.
225 * Otherwise, we generate one or more calls for each individual
226 * domain in generate_domain.
228 static __isl_give isl_ast_graft_list
*generate_inner_level(
229 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
232 struct isl_generate_domain_data data
= { build
};
234 if (!build
|| !executed
)
237 if (build
->create_leaf
)
238 return call_create_leaf(executed
, build
);
240 ctx
= isl_union_map_get_ctx(executed
);
241 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
242 if (isl_union_map_foreach_map(executed
, &generate_domain
, &data
) < 0)
243 data
.list
= isl_ast_graft_list_free(data
.list
);
246 error
: data
.list
= NULL
;
247 isl_ast_build_free(build
);
248 isl_union_map_free(executed
);
252 /* Call the before_each_for callback, if requested by the user.
254 static __isl_give isl_ast_node
*before_each_for(__isl_take isl_ast_node
*node
,
255 __isl_keep isl_ast_build
*build
)
260 return isl_ast_node_free(node
);
261 if (!build
->before_each_for
)
263 id
= build
->before_each_for(build
, build
->before_each_for_user
);
264 node
= isl_ast_node_set_annotation(node
, id
);
268 /* Call the after_each_for callback, if requested by the user.
270 static __isl_give isl_ast_graft
*after_each_for(__isl_take isl_ast_graft
*graft
,
271 __isl_keep isl_ast_build
*build
)
273 if (!graft
|| !build
)
274 return isl_ast_graft_free(graft
);
275 if (!build
->after_each_for
)
277 graft
->node
= build
->after_each_for(graft
->node
, build
,
278 build
->after_each_for_user
);
280 return isl_ast_graft_free(graft
);
284 /* Plug in all the know values of the current and outer dimensions
285 * in the domain of "executed". In principle, we only need to plug
286 * in the known value of the current dimension since the values of
287 * outer dimensions have been plugged in already.
288 * However, it turns out to be easier to just plug in all known values.
290 static __isl_give isl_union_map
*plug_in_values(
291 __isl_take isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
293 return isl_ast_build_substitute_values_union_map_domain(build
,
297 /* Check if the constraint "c" is a lower bound on dimension "pos",
298 * an upper bound, or independent of dimension "pos".
300 static int constraint_type(isl_constraint
*c
, int pos
)
302 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, pos
))
304 if (isl_constraint_is_upper_bound(c
, isl_dim_set
, pos
))
309 /* Compare the types of the constraints "a" and "b",
310 * resulting in constraints that are independent of "depth"
311 * to be sorted before the lower bounds on "depth", which in
312 * turn are sorted before the upper bounds on "depth".
314 static int cmp_constraint(__isl_keep isl_constraint
*a
,
315 __isl_keep isl_constraint
*b
, void *user
)
318 int t1
= constraint_type(a
, *depth
);
319 int t2
= constraint_type(b
, *depth
);
324 /* Extract a lower bound on dimension "pos" from constraint "c".
326 * If the constraint is of the form
330 * then we essentially return
332 * l = ceil(-f(...)/a)
334 * However, if the current dimension is strided, then we need to make
335 * sure that the lower bound we construct is of the form
339 * with f the offset and s the stride.
340 * We therefore compute
342 * f + s * ceil((l - f)/s)
344 static __isl_give isl_aff
*lower_bound(__isl_keep isl_constraint
*c
,
345 int pos
, __isl_keep isl_ast_build
*build
)
349 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
350 aff
= isl_aff_ceil(aff
);
352 if (isl_ast_build_has_stride(build
, pos
)) {
356 offset
= isl_ast_build_get_offset(build
, pos
);
357 stride
= isl_ast_build_get_stride(build
, pos
);
359 aff
= isl_aff_sub(aff
, isl_aff_copy(offset
));
360 aff
= isl_aff_scale_down_val(aff
, isl_val_copy(stride
));
361 aff
= isl_aff_ceil(aff
);
362 aff
= isl_aff_scale_val(aff
, stride
);
363 aff
= isl_aff_add(aff
, offset
);
366 aff
= isl_ast_build_compute_gist_aff(build
, aff
);
371 /* Return the exact lower bound (or upper bound if "upper" is set)
372 * of "domain" as a piecewise affine expression.
374 * If we are computing a lower bound (of a strided dimension), then
375 * we need to make sure it is of the form
379 * where f is the offset and s is the stride.
380 * We therefore need to include the stride constraint before computing
383 static __isl_give isl_pw_aff
*exact_bound(__isl_keep isl_set
*domain
,
384 __isl_keep isl_ast_build
*build
, int upper
)
389 isl_pw_multi_aff
*pma
;
391 domain
= isl_set_copy(domain
);
393 stride
= isl_ast_build_get_stride_constraint(build
);
394 domain
= isl_set_intersect(domain
, stride
);
396 it_map
= isl_ast_build_map_to_iterator(build
, domain
);
398 pma
= isl_map_lexmax_pw_multi_aff(it_map
);
400 pma
= isl_map_lexmin_pw_multi_aff(it_map
);
401 pa
= isl_pw_multi_aff_get_pw_aff(pma
, 0);
402 isl_pw_multi_aff_free(pma
);
403 pa
= isl_ast_build_compute_gist_pw_aff(build
, pa
);
404 pa
= isl_pw_aff_coalesce(pa
);
409 /* Extract a lower bound on dimension "pos" from each constraint
410 * in "constraints" and return the list of lower bounds.
411 * If "constraints" has zero elements, then we extract a lower bound
412 * from "domain" instead.
414 static __isl_give isl_pw_aff_list
*lower_bounds(
415 __isl_keep isl_constraint_list
*constraints
, int pos
,
416 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
419 isl_pw_aff_list
*list
;
425 n
= isl_constraint_list_n_constraint(constraints
);
428 pa
= exact_bound(domain
, build
, 0);
429 return isl_pw_aff_list_from_pw_aff(pa
);
432 ctx
= isl_ast_build_get_ctx(build
);
433 list
= isl_pw_aff_list_alloc(ctx
,n
);
435 for (i
= 0; i
< n
; ++i
) {
439 c
= isl_constraint_list_get_constraint(constraints
, i
);
440 aff
= lower_bound(c
, pos
, build
);
441 isl_constraint_free(c
);
442 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
448 /* Extract an upper bound on dimension "pos" from each constraint
449 * in "constraints" and return the list of upper bounds.
450 * If "constraints" has zero elements, then we extract an upper bound
451 * from "domain" instead.
453 static __isl_give isl_pw_aff_list
*upper_bounds(
454 __isl_keep isl_constraint_list
*constraints
, int pos
,
455 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
458 isl_pw_aff_list
*list
;
461 n
= isl_constraint_list_n_constraint(constraints
);
464 pa
= exact_bound(domain
, build
, 1);
465 return isl_pw_aff_list_from_pw_aff(pa
);
468 ctx
= isl_ast_build_get_ctx(build
);
469 list
= isl_pw_aff_list_alloc(ctx
,n
);
471 for (i
= 0; i
< n
; ++i
) {
475 c
= isl_constraint_list_get_constraint(constraints
, i
);
476 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
477 isl_constraint_free(c
);
478 aff
= isl_aff_floor(aff
);
479 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
485 /* Callback for sorting the isl_pw_aff_list passed to reduce_list.
487 static int reduce_list_cmp(__isl_keep isl_pw_aff
*a
, __isl_keep isl_pw_aff
*b
,
490 return isl_pw_aff_plain_cmp(a
, b
);
493 /* Return an isl_ast_expr that performs the reduction of type "type"
494 * on AST expressions corresponding to the elements in "list".
496 * The list is assumed to contain at least one element.
497 * If the list contains exactly one element, then the returned isl_ast_expr
498 * simply computes that affine expression.
499 * If the list contains more than one element, then we sort it
500 * using a fairly abitrary but hopefully reasonably stable order.
502 static __isl_give isl_ast_expr
*reduce_list(enum isl_ast_op_type type
,
503 __isl_keep isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
512 n
= isl_pw_aff_list_n_pw_aff(list
);
515 return isl_ast_build_expr_from_pw_aff_internal(build
,
516 isl_pw_aff_list_get_pw_aff(list
, 0));
518 ctx
= isl_pw_aff_list_get_ctx(list
);
519 expr
= isl_ast_expr_alloc_op(ctx
, type
, n
);
523 list
= isl_pw_aff_list_copy(list
);
524 list
= isl_pw_aff_list_sort(list
, &reduce_list_cmp
, NULL
);
526 return isl_ast_expr_free(expr
);
528 for (i
= 0; i
< n
; ++i
) {
529 isl_ast_expr
*expr_i
;
531 expr_i
= isl_ast_build_expr_from_pw_aff_internal(build
,
532 isl_pw_aff_list_get_pw_aff(list
, i
));
535 expr
->u
.op
.args
[i
] = expr_i
;
538 isl_pw_aff_list_free(list
);
541 isl_pw_aff_list_free(list
);
542 isl_ast_expr_free(expr
);
546 /* Add a guard to "graft" based on "bound" in the case of a degenerate
547 * level (including the special case of an eliminated level).
549 * We eliminate the current dimension, simplify the result in the current
550 * build and add the result as guards to the graft.
552 * Note that we cannot simply drop the constraints on the current dimension
553 * even in the eliminated case, because the single affine expression may
554 * not be explicitly available in "bounds". Moreover, the single affine
555 * expression may only be defined on a subset of the build domain,
556 * so we do in some cases need to insert a guard even in the eliminated case.
558 static __isl_give isl_ast_graft
*add_degenerate_guard(
559 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
560 __isl_keep isl_ast_build
*build
)
565 depth
= isl_ast_build_get_depth(build
);
567 dom
= isl_set_from_basic_set(isl_basic_set_copy(bounds
));
568 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
569 dom
= isl_ast_build_compute_gist(build
, dom
);
571 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
576 /* Add the guard implied by the current stride constraint (if any),
577 * but not (necessarily) enforced by the generated AST to "graft".
579 static __isl_give isl_ast_graft
*add_stride_guard(
580 __isl_take isl_ast_graft
*graft
, __isl_keep isl_ast_build
*build
)
585 depth
= isl_ast_build_get_depth(build
);
586 if (!isl_ast_build_has_stride(build
, depth
))
589 dom
= isl_ast_build_get_stride_constraint(build
);
590 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
591 dom
= isl_ast_build_compute_gist(build
, dom
);
593 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
598 /* Update "graft" based on "bounds" for the eliminated case.
600 * In the eliminated case, no for node is created, so we only need
601 * to check if "bounds" imply any guards that need to be inserted.
603 static __isl_give isl_ast_graft
*refine_eliminated(
604 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
605 __isl_keep isl_ast_build
*build
)
607 return add_degenerate_guard(graft
, bounds
, build
);
610 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
612 * "build" is the build in which graft->node was created
613 * "sub_build" contains information about the current level itself,
614 * including the single value attained.
616 * We first set the initialization part of the for loop to the single
617 * value attained by the current dimension.
618 * The increment and condition are not strictly needed as the are known
619 * to be "1" and "iterator <= value" respectively.
620 * Then we check if "bounds" imply any guards that need to be inserted.
622 static __isl_give isl_ast_graft
*refine_degenerate(
623 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
624 __isl_keep isl_ast_build
*build
,
625 __isl_keep isl_ast_build
*sub_build
)
629 if (!graft
|| !sub_build
)
630 return isl_ast_graft_free(graft
);
632 value
= isl_pw_aff_copy(sub_build
->value
);
634 graft
->node
->u
.f
.init
= isl_ast_build_expr_from_pw_aff_internal(build
,
636 if (!graft
->node
->u
.f
.init
)
637 return isl_ast_graft_free(graft
);
639 graft
= add_degenerate_guard(graft
, bounds
, build
);
644 /* Return the intersection of constraints in "list" as a set.
646 static __isl_give isl_set
*intersect_constraints(
647 __isl_keep isl_constraint_list
*list
)
652 n
= isl_constraint_list_n_constraint(list
);
654 isl_die(isl_constraint_list_get_ctx(list
), isl_error_internal
,
655 "expecting at least one constraint", return NULL
);
657 bset
= isl_basic_set_from_constraint(
658 isl_constraint_list_get_constraint(list
, 0));
659 for (i
= 1; i
< n
; ++i
) {
660 isl_basic_set
*bset_i
;
662 bset_i
= isl_basic_set_from_constraint(
663 isl_constraint_list_get_constraint(list
, i
));
664 bset
= isl_basic_set_intersect(bset
, bset_i
);
667 return isl_set_from_basic_set(bset
);
670 /* Compute the constraints on the outer dimensions enforced by
671 * graft->node and add those constraints to graft->enforced,
672 * in case the upper bound is expressed as a set "upper".
674 * In particular, if l(...) is a lower bound in "lower", and
676 * -a i + f(...) >= 0 or a i <= f(...)
678 * is an upper bound ocnstraint on the current dimension i,
679 * then the for loop enforces the constraint
681 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
683 * We therefore simply take each lower bound in turn, plug it into
684 * the upper bounds and compute the intersection over all lower bounds.
686 * If a lower bound is a rational expression, then
687 * isl_basic_set_preimage_multi_aff will force this rational
688 * expression to have only integer values. However, the loop
689 * itself does not enforce this integrality constraint. We therefore
690 * use the ceil of the lower bounds instead of the lower bounds themselves.
691 * Other constraints will make sure that the for loop is only executed
692 * when each of the lower bounds attains an integral value.
693 * In particular, potentially rational values only occur in
694 * lower_bound if the offset is a (seemingly) rational expression,
695 * but then outer conditions will make sure that this rational expression
696 * only attains integer values.
698 static __isl_give isl_ast_graft
*set_enforced_from_set(
699 __isl_take isl_ast_graft
*graft
,
700 __isl_keep isl_pw_aff_list
*lower
, int pos
, __isl_keep isl_set
*upper
)
703 isl_basic_set
*enforced
;
704 isl_pw_multi_aff
*pma
;
707 if (!graft
|| !lower
)
708 return isl_ast_graft_free(graft
);
710 space
= isl_set_get_space(upper
);
711 enforced
= isl_basic_set_universe(isl_space_copy(space
));
713 space
= isl_space_map_from_set(space
);
714 pma
= isl_pw_multi_aff_identity(space
);
716 n
= isl_pw_aff_list_n_pw_aff(lower
);
717 for (i
= 0; i
< n
; ++i
) {
721 isl_pw_multi_aff
*pma_i
;
723 pa
= isl_pw_aff_list_get_pw_aff(lower
, i
);
724 pa
= isl_pw_aff_ceil(pa
);
725 pma_i
= isl_pw_multi_aff_copy(pma
);
726 pma_i
= isl_pw_multi_aff_set_pw_aff(pma_i
, pos
, pa
);
727 enforced_i
= isl_set_copy(upper
);
728 enforced_i
= isl_set_preimage_pw_multi_aff(enforced_i
, pma_i
);
729 hull
= isl_set_simple_hull(enforced_i
);
730 enforced
= isl_basic_set_intersect(enforced
, hull
);
733 isl_pw_multi_aff_free(pma
);
735 graft
= isl_ast_graft_enforce(graft
, enforced
);
740 /* Compute the constraints on the outer dimensions enforced by
741 * graft->node and add those constraints to graft->enforced,
742 * in case the upper bound is expressed as
743 * a list of affine expressions "upper".
745 * The enforced condition is that each lower bound expression is less
746 * than or equal to each upper bound expression.
748 static __isl_give isl_ast_graft
*set_enforced_from_list(
749 __isl_take isl_ast_graft
*graft
,
750 __isl_keep isl_pw_aff_list
*lower
, __isl_keep isl_pw_aff_list
*upper
)
753 isl_basic_set
*enforced
;
755 lower
= isl_pw_aff_list_copy(lower
);
756 upper
= isl_pw_aff_list_copy(upper
);
757 cond
= isl_pw_aff_list_le_set(lower
, upper
);
758 enforced
= isl_set_simple_hull(cond
);
759 graft
= isl_ast_graft_enforce(graft
, enforced
);
764 /* Does "aff" have a negative constant term?
766 static int aff_constant_is_negative(__isl_take isl_set
*set
,
767 __isl_take isl_aff
*aff
, void *user
)
772 v
= isl_aff_get_constant_val(aff
);
773 *neg
= isl_val_is_neg(v
);
778 return *neg
? 0 : -1;
781 /* Does "pa" have a negative constant term over its entire domain?
783 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff
*pa
, void *user
)
788 r
= isl_pw_aff_foreach_piece(pa
, &aff_constant_is_negative
, user
);
791 return *neg
? 0 : -1;
794 /* Does each element in "list" have a negative constant term?
796 * The callback terminates the iteration as soon an element has been
797 * found that does not have a negative constant term.
799 static int list_constant_is_negative(__isl_keep isl_pw_aff_list
*list
)
803 if (isl_pw_aff_list_foreach(list
,
804 &pw_aff_constant_is_negative
, &neg
) < 0 && neg
)
810 /* Add 1 to each of the elements in "list", where each of these elements
811 * is defined over the internal schedule space of "build".
813 static __isl_give isl_pw_aff_list
*list_add_one(
814 __isl_take isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
821 space
= isl_ast_build_get_space(build
, 1);
822 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(space
));
823 aff
= isl_aff_add_constant_si(aff
, 1);
824 one
= isl_pw_aff_from_aff(aff
);
826 n
= isl_pw_aff_list_n_pw_aff(list
);
827 for (i
= 0; i
< n
; ++i
) {
829 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
830 pa
= isl_pw_aff_add(pa
, isl_pw_aff_copy(one
));
831 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
834 isl_pw_aff_free(one
);
839 /* Set the condition part of the for node graft->node in case
840 * the upper bound is represented as a list of piecewise affine expressions.
842 * In particular, set the condition to
844 * iterator <= min(list of upper bounds)
846 * If each of the upper bounds has a negative constant term, then
847 * set the condition to
849 * iterator < min(list of (upper bound + 1)s)
852 static __isl_give isl_ast_graft
*set_for_cond_from_list(
853 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*list
,
854 __isl_keep isl_ast_build
*build
)
857 isl_ast_expr
*bound
, *iterator
, *cond
;
858 enum isl_ast_op_type type
= isl_ast_op_le
;
861 return isl_ast_graft_free(graft
);
863 neg
= list_constant_is_negative(list
);
865 return isl_ast_graft_free(graft
);
866 list
= isl_pw_aff_list_copy(list
);
868 list
= list_add_one(list
, build
);
869 type
= isl_ast_op_lt
;
872 bound
= reduce_list(isl_ast_op_min
, list
, build
);
873 iterator
= isl_ast_expr_copy(graft
->node
->u
.f
.iterator
);
874 cond
= isl_ast_expr_alloc_binary(type
, iterator
, bound
);
875 graft
->node
->u
.f
.cond
= cond
;
877 isl_pw_aff_list_free(list
);
878 if (!graft
->node
->u
.f
.cond
)
879 return isl_ast_graft_free(graft
);
883 /* Set the condition part of the for node graft->node in case
884 * the upper bound is represented as a set.
886 static __isl_give isl_ast_graft
*set_for_cond_from_set(
887 __isl_take isl_ast_graft
*graft
, __isl_keep isl_set
*set
,
888 __isl_keep isl_ast_build
*build
)
895 cond
= isl_ast_build_expr_from_set(build
, isl_set_copy(set
));
896 graft
->node
->u
.f
.cond
= cond
;
897 if (!graft
->node
->u
.f
.cond
)
898 return isl_ast_graft_free(graft
);
902 /* Construct an isl_ast_expr for the increment (i.e., stride) of
903 * the current dimension.
905 static __isl_give isl_ast_expr
*for_inc(__isl_keep isl_ast_build
*build
)
913 ctx
= isl_ast_build_get_ctx(build
);
914 depth
= isl_ast_build_get_depth(build
);
916 if (!isl_ast_build_has_stride(build
, depth
))
917 return isl_ast_expr_alloc_int_si(ctx
, 1);
919 v
= isl_ast_build_get_stride(build
, depth
);
920 return isl_ast_expr_from_val(v
);
923 /* Should we express the loop condition as
925 * iterator <= min(list of upper bounds)
927 * or as a conjunction of constraints?
929 * The first is constructed from a list of upper bounds.
930 * The second is constructed from a set.
932 * If there are no upper bounds in "constraints", then this could mean
933 * that "domain" simply doesn't have an upper bound or that we didn't
934 * pick any upper bound. In the first case, we want to generate the
935 * loop condition as a(n empty) conjunction of constraints
936 * In the second case, we will compute
937 * a single upper bound from "domain" and so we use the list form.
939 * If there are upper bounds in "constraints",
940 * then we use the list form iff the atomic_upper_bound option is set.
942 static int use_upper_bound_list(isl_ctx
*ctx
, int n_upper
,
943 __isl_keep isl_set
*domain
, int depth
)
946 return isl_options_get_ast_build_atomic_upper_bound(ctx
);
948 return isl_set_dim_has_upper_bound(domain
, isl_dim_set
, depth
);
951 /* Fill in the expressions of the for node in graft->node.
954 * - set the initialization part of the loop to the maximum of the lower bounds
955 * - extract the increment from the stride of the current dimension
956 * - construct the for condition either based on a list of upper bounds
957 * or on a set of upper bound constraints.
959 static __isl_give isl_ast_graft
*set_for_node_expressions(
960 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*lower
,
961 int use_list
, __isl_keep isl_pw_aff_list
*upper_list
,
962 __isl_keep isl_set
*upper_set
, __isl_keep isl_ast_build
*build
)
969 build
= isl_ast_build_copy(build
);
970 build
= isl_ast_build_set_enforced(build
,
971 isl_ast_graft_get_enforced(graft
));
974 node
->u
.f
.init
= reduce_list(isl_ast_op_max
, lower
, build
);
975 node
->u
.f
.inc
= for_inc(build
);
978 graft
= set_for_cond_from_list(graft
, upper_list
, build
);
980 graft
= set_for_cond_from_set(graft
, upper_set
, build
);
982 isl_ast_build_free(build
);
984 if (!node
->u
.f
.iterator
|| !node
->u
.f
.init
||
985 !node
->u
.f
.cond
|| !node
->u
.f
.inc
)
986 return isl_ast_graft_free(graft
);
991 /* Update "graft" based on "bounds" and "domain" for the generic,
992 * non-degenerate, case.
994 * "c_lower" and "c_upper" contain the lower and upper bounds
995 * that the loop node should express.
996 * "domain" is the subset of the intersection of the constraints
997 * for which some code is executed.
999 * There may be zero lower bounds or zero upper bounds in "constraints"
1000 * in case the list of constraints was created
1001 * based on the atomic option or based on separation with explicit bounds.
1002 * In that case, we use "domain" to derive lower and/or upper bounds.
1004 * We first compute a list of one or more lower bounds.
1006 * Then we decide if we want to express the condition as
1008 * iterator <= min(list of upper bounds)
1010 * or as a conjunction of constraints.
1012 * The set of enforced constraints is then computed either based on
1013 * a list of upper bounds or on a set of upper bound constraints.
1014 * We do not compute any enforced constraints if we were forced
1015 * to compute a lower or upper bound using exact_bound. The domains
1016 * of the resulting expressions may imply some bounds on outer dimensions
1017 * that we do not want to appear in the enforced constraints since
1018 * they are not actually enforced by the corresponding code.
1020 * Finally, we fill in the expressions of the for node.
1022 static __isl_give isl_ast_graft
*refine_generic_bounds(
1023 __isl_take isl_ast_graft
*graft
,
1024 __isl_take isl_constraint_list
*c_lower
,
1025 __isl_take isl_constraint_list
*c_upper
,
1026 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1030 isl_pw_aff_list
*lower
;
1032 isl_set
*upper_set
= NULL
;
1033 isl_pw_aff_list
*upper_list
= NULL
;
1034 int n_lower
, n_upper
;
1036 if (!graft
|| !c_lower
|| !c_upper
|| !build
)
1039 depth
= isl_ast_build_get_depth(build
);
1040 ctx
= isl_ast_graft_get_ctx(graft
);
1042 n_lower
= isl_constraint_list_n_constraint(c_lower
);
1043 n_upper
= isl_constraint_list_n_constraint(c_upper
);
1045 use_list
= use_upper_bound_list(ctx
, n_upper
, domain
, depth
);
1047 lower
= lower_bounds(c_lower
, depth
, domain
, build
);
1050 upper_list
= upper_bounds(c_upper
, depth
, domain
, build
);
1051 else if (n_upper
> 0)
1052 upper_set
= intersect_constraints(c_upper
);
1054 upper_set
= isl_set_universe(isl_set_get_space(domain
));
1056 if (n_lower
== 0 || n_upper
== 0)
1059 graft
= set_enforced_from_list(graft
, lower
, upper_list
);
1061 graft
= set_enforced_from_set(graft
, lower
, depth
, upper_set
);
1063 graft
= set_for_node_expressions(graft
, lower
, use_list
, upper_list
,
1066 isl_pw_aff_list_free(lower
);
1067 isl_pw_aff_list_free(upper_list
);
1068 isl_set_free(upper_set
);
1069 isl_constraint_list_free(c_lower
);
1070 isl_constraint_list_free(c_upper
);
1074 isl_constraint_list_free(c_lower
);
1075 isl_constraint_list_free(c_upper
);
1076 return isl_ast_graft_free(graft
);
1079 /* Internal data structure used inside count_constraints to keep
1080 * track of the number of constraints that are independent of dimension "pos",
1081 * the lower bounds in "pos" and the upper bounds in "pos".
1083 struct isl_ast_count_constraints_data
{
1091 /* Increment data->n_indep, data->lower or data->upper depending
1092 * on whether "c" is independenct of dimensions data->pos,
1093 * a lower bound or an upper bound.
1095 static int count_constraints(__isl_take isl_constraint
*c
, void *user
)
1097 struct isl_ast_count_constraints_data
*data
= user
;
1099 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->pos
))
1101 else if (isl_constraint_is_upper_bound(c
, isl_dim_set
, data
->pos
))
1106 isl_constraint_free(c
);
1111 /* Update "graft" based on "bounds" and "domain" for the generic,
1112 * non-degenerate, case.
1114 * "list" respresent the list of bounds that need to be encoded by
1115 * the for loop (or a guard around the for loop).
1116 * "domain" is the subset of the intersection of the constraints
1117 * for which some code is executed.
1118 * "build" is the build in which graft->node was created.
1120 * We separate lower bounds, upper bounds and constraints that
1121 * are independent of the loop iterator.
1123 * The actual for loop bounds are generated in refine_generic_bounds.
1124 * If there are any constraints that are independent of the loop iterator,
1125 * we need to put a guard around the for loop (which may get hoisted up
1126 * to higher levels) and we call refine_generic_bounds in a build
1127 * where this guard is enforced.
1129 static __isl_give isl_ast_graft
*refine_generic_split(
1130 __isl_take isl_ast_graft
*graft
, __isl_take isl_constraint_list
*list
,
1131 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1133 isl_ast_build
*for_build
;
1135 struct isl_ast_count_constraints_data data
;
1136 isl_constraint_list
*lower
;
1137 isl_constraint_list
*upper
;
1140 return isl_ast_graft_free(graft
);
1142 data
.pos
= isl_ast_build_get_depth(build
);
1144 list
= isl_constraint_list_sort(list
, &cmp_constraint
, &data
.pos
);
1146 return isl_ast_graft_free(graft
);
1148 data
.n_indep
= data
.n_lower
= data
.n_upper
= 0;
1149 if (isl_constraint_list_foreach(list
, &count_constraints
, &data
) < 0) {
1150 isl_constraint_list_free(list
);
1151 return isl_ast_graft_free(graft
);
1154 lower
= isl_constraint_list_copy(list
);
1155 lower
= isl_constraint_list_drop(lower
, 0, data
.n_indep
);
1156 upper
= isl_constraint_list_copy(lower
);
1157 lower
= isl_constraint_list_drop(lower
, data
.n_lower
, data
.n_upper
);
1158 upper
= isl_constraint_list_drop(upper
, 0, data
.n_lower
);
1160 if (data
.n_indep
== 0) {
1161 isl_constraint_list_free(list
);
1162 return refine_generic_bounds(graft
, lower
, upper
,
1166 list
= isl_constraint_list_drop(list
, data
.n_indep
,
1167 data
.n_lower
+ data
.n_upper
);
1168 guard
= intersect_constraints(list
);
1169 isl_constraint_list_free(list
);
1171 for_build
= isl_ast_build_copy(build
);
1172 for_build
= isl_ast_build_restrict_pending(for_build
,
1173 isl_set_copy(guard
));
1174 graft
= refine_generic_bounds(graft
, lower
, upper
, domain
, for_build
);
1175 isl_ast_build_free(for_build
);
1177 graft
= isl_ast_graft_add_guard(graft
, guard
, build
);
1182 /* Update "graft" based on "bounds" and "domain" for the generic,
1183 * non-degenerate, case.
1185 * "bounds" respresent the bounds that need to be encoded by
1186 * the for loop (or a guard around the for loop).
1187 * "domain" is the subset of "bounds" for which some code is executed.
1188 * "build" is the build in which graft->node was created.
1190 * We break up "bounds" into a list of constraints and continue with
1191 * refine_generic_split.
1193 static __isl_give isl_ast_graft
*refine_generic(
1194 __isl_take isl_ast_graft
*graft
,
1195 __isl_keep isl_basic_set
*bounds
, __isl_keep isl_set
*domain
,
1196 __isl_keep isl_ast_build
*build
)
1198 isl_constraint_list
*list
;
1200 if (!build
|| !graft
)
1201 return isl_ast_graft_free(graft
);
1203 bounds
= isl_basic_set_copy(bounds
);
1204 bounds
= isl_ast_build_compute_gist_basic_set(build
, bounds
);
1205 list
= isl_basic_set_get_constraint_list(bounds
);
1206 isl_basic_set_free(bounds
);
1208 graft
= refine_generic_split(graft
, list
, domain
, build
);
1213 /* Create a for node for the current level.
1215 * Mark the for node degenerate if "degenerate" is set.
1217 static __isl_give isl_ast_node
*create_for(__isl_keep isl_ast_build
*build
,
1227 depth
= isl_ast_build_get_depth(build
);
1228 id
= isl_ast_build_get_iterator_id(build
, depth
);
1229 node
= isl_ast_node_alloc_for(id
);
1231 node
= isl_ast_node_for_mark_degenerate(node
);
1236 /* If the ast_build_exploit_nested_bounds option is set, then return
1237 * the constraints enforced by all elements in "list".
1238 * Otherwise, return the universe.
1240 static __isl_give isl_basic_set
*extract_shared_enforced(
1241 __isl_keep isl_ast_graft_list
*list
, __isl_keep isl_ast_build
*build
)
1249 ctx
= isl_ast_graft_list_get_ctx(list
);
1250 if (isl_options_get_ast_build_exploit_nested_bounds(ctx
))
1251 return isl_ast_graft_list_extract_shared_enforced(list
, build
);
1253 space
= isl_ast_build_get_space(build
, 1);
1254 return isl_basic_set_universe(space
);
1257 /* Create an AST node for the current dimension based on
1258 * the schedule domain "bounds" and return the node encapsulated
1259 * in an isl_ast_graft.
1261 * "executed" is the current inverse schedule, taking into account
1262 * the bounds in "bounds"
1263 * "domain" is the domain of "executed", with inner dimensions projected out.
1264 * It may be a strict subset of "bounds" in case "bounds" was created
1265 * based on the atomic option or based on separation with explicit bounds.
1267 * "domain" may satisfy additional equalities that result
1268 * from intersecting "executed" with "bounds" in add_node.
1269 * It may also satisfy some global constraints that were dropped out because
1270 * we performed separation with explicit bounds.
1271 * The very first step is then to copy these constraints to "bounds".
1273 * Since we may be calling before_each_for and after_each_for
1274 * callbacks, we record the current inverse schedule in the build.
1276 * We consider three builds,
1277 * "build" is the one in which the current level is created,
1278 * "body_build" is the build in which the next level is created,
1279 * "sub_build" is essentially the same as "body_build", except that
1280 * the depth has not been increased yet.
1282 * "build" already contains information (in strides and offsets)
1283 * about the strides at the current level, but this information is not
1284 * reflected in the build->domain.
1285 * We first add this information and the "bounds" to the sub_build->domain.
1286 * isl_ast_build_set_loop_bounds adds the stride information and
1287 * checks whether the current dimension attains
1288 * only a single value and whether this single value can be represented using
1289 * a single affine expression.
1290 * In the first case, the current level is considered "degenerate".
1291 * In the second, sub-case, the current level is considered "eliminated".
1292 * Eliminated levels don't need to be reflected in the AST since we can
1293 * simply plug in the affine expression. For degenerate, but non-eliminated,
1294 * levels, we do introduce a for node, but mark is as degenerate so that
1295 * it can be printed as an assignment of the single value to the loop
1298 * If the current level is eliminated, we explicitly plug in the value
1299 * for the current level found by isl_ast_build_set_loop_bounds in the
1300 * inverse schedule. This ensures that if we are working on a slice
1301 * of the domain based on information available in the inverse schedule
1302 * and the build domain, that then this information is also reflected
1303 * in the inverse schedule. This operation also eliminates the current
1304 * dimension from the inverse schedule making sure no inner dimensions depend
1305 * on the current dimension. Otherwise, we create a for node, marking
1306 * it degenerate if appropriate. The initial for node is still incomplete
1307 * and will be completed in either refine_degenerate or refine_generic.
1309 * We then generate a sequence of grafts for the next level,
1310 * create a surrounding graft for the current level and insert
1311 * the for node we created (if the current level is not eliminated).
1312 * Before creating a graft for the current level, we first extract
1313 * hoistable constraints from the child guards. These constraints
1314 * are used to simplify the child guards and then added to the guard
1315 * of the current graft.
1317 * Finally, we set the bounds of the for loop and insert guards
1318 * (either in the AST or in the graft) in one of
1319 * refine_eliminated, refine_degenerate or refine_generic.
1321 static __isl_give isl_ast_graft
*create_node_scaled(
1322 __isl_take isl_union_map
*executed
,
1323 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1324 __isl_take isl_ast_build
*build
)
1327 int degenerate
, eliminated
;
1328 isl_basic_set
*hull
;
1329 isl_basic_set
*enforced
;
1331 isl_ast_node
*node
= NULL
;
1332 isl_ast_graft
*graft
;
1333 isl_ast_graft_list
*children
;
1334 isl_ast_build
*sub_build
;
1335 isl_ast_build
*body_build
;
1337 domain
= isl_ast_build_eliminate_divs(build
, domain
);
1338 domain
= isl_set_detect_equalities(domain
);
1339 hull
= isl_set_unshifted_simple_hull(isl_set_copy(domain
));
1340 bounds
= isl_basic_set_intersect(bounds
, hull
);
1341 build
= isl_ast_build_set_executed(build
, isl_union_map_copy(executed
));
1343 depth
= isl_ast_build_get_depth(build
);
1344 sub_build
= isl_ast_build_copy(build
);
1345 sub_build
= isl_ast_build_set_loop_bounds(sub_build
,
1346 isl_basic_set_copy(bounds
));
1347 degenerate
= isl_ast_build_has_value(sub_build
);
1348 eliminated
= isl_ast_build_has_affine_value(sub_build
, depth
);
1349 if (degenerate
< 0 || eliminated
< 0)
1350 executed
= isl_union_map_free(executed
);
1352 executed
= plug_in_values(executed
, sub_build
);
1354 node
= create_for(build
, degenerate
);
1356 body_build
= isl_ast_build_copy(sub_build
);
1357 body_build
= isl_ast_build_increase_depth(body_build
);
1359 node
= before_each_for(node
, body_build
);
1360 children
= generate_next_level(executed
,
1361 isl_ast_build_copy(body_build
));
1363 enforced
= extract_shared_enforced(children
, build
);
1364 hoisted
= isl_ast_graft_list_extract_hoistable_guard(children
, build
);
1365 graft
= isl_ast_graft_alloc_from_children(children
, hoisted
, enforced
,
1368 graft
= isl_ast_graft_insert_for(graft
, node
);
1370 graft
= refine_eliminated(graft
, bounds
, build
);
1371 else if (degenerate
)
1372 graft
= refine_degenerate(graft
, bounds
, build
, sub_build
);
1374 graft
= refine_generic(graft
, bounds
, domain
, build
);
1376 graft
= add_stride_guard(graft
, build
);
1377 graft
= after_each_for(graft
, body_build
);
1380 isl_ast_build_free(body_build
);
1381 isl_ast_build_free(sub_build
);
1382 isl_ast_build_free(build
);
1383 isl_basic_set_free(bounds
);
1384 isl_set_free(domain
);
1389 /* Internal data structure for checking if all constraints involving
1390 * the input dimension "depth" are such that the other coefficients
1391 * are multiples of "m", reducing "m" if they are not.
1392 * If "m" is reduced all the way down to "1", then the check has failed
1393 * and we break out of the iteration.
1395 struct isl_check_scaled_data
{
1400 /* If constraint "c" involves the input dimension data->depth,
1401 * then make sure that all the other coefficients are multiples of data->m,
1402 * reducing data->m if needed.
1403 * Break out of the iteration if data->m has become equal to "1".
1405 static int constraint_check_scaled(__isl_take isl_constraint
*c
, void *user
)
1407 struct isl_check_scaled_data
*data
= user
;
1409 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_out
,
1412 if (!isl_constraint_involves_dims(c
, isl_dim_in
, data
->depth
, 1)) {
1413 isl_constraint_free(c
);
1417 for (i
= 0; i
< 4; ++i
) {
1418 n
= isl_constraint_dim(c
, t
[i
]);
1419 for (j
= 0; j
< n
; ++j
) {
1422 if (t
[i
] == isl_dim_in
&& j
== data
->depth
)
1424 if (!isl_constraint_involves_dims(c
, t
[i
], j
, 1))
1426 d
= isl_constraint_get_coefficient_val(c
, t
[i
], j
);
1427 data
->m
= isl_val_gcd(data
->m
, d
);
1428 if (isl_val_is_one(data
->m
))
1435 isl_constraint_free(c
);
1437 return i
< 4 ? -1 : 0;
1440 /* For each constraint of "bmap" that involves the input dimension data->depth,
1441 * make sure that all the other coefficients are multiples of data->m,
1442 * reducing data->m if needed.
1443 * Break out of the iteration if data->m has become equal to "1".
1445 static int basic_map_check_scaled(__isl_take isl_basic_map
*bmap
, void *user
)
1449 r
= isl_basic_map_foreach_constraint(bmap
,
1450 &constraint_check_scaled
, user
);
1451 isl_basic_map_free(bmap
);
1456 /* For each constraint of "map" that involves the input dimension data->depth,
1457 * make sure that all the other coefficients are multiples of data->m,
1458 * reducing data->m if needed.
1459 * Break out of the iteration if data->m has become equal to "1".
1461 static int map_check_scaled(__isl_take isl_map
*map
, void *user
)
1465 r
= isl_map_foreach_basic_map(map
, &basic_map_check_scaled
, user
);
1471 /* Create an AST node for the current dimension based on
1472 * the schedule domain "bounds" and return the node encapsulated
1473 * in an isl_ast_graft.
1475 * "executed" is the current inverse schedule, taking into account
1476 * the bounds in "bounds"
1477 * "domain" is the domain of "executed", with inner dimensions projected out.
1480 * Before moving on to the actual AST node construction in create_node_scaled,
1481 * we first check if the current dimension is strided and if we can scale
1482 * down this stride. Note that we only do this if the ast_build_scale_strides
1485 * In particular, let the current dimension take on values
1489 * with a an integer. We check if we can find an integer m that (obviously)
1490 * divides both f and s.
1492 * If so, we check if the current dimension only appears in constraints
1493 * where the coefficients of the other variables are multiples of m.
1494 * We perform this extra check to avoid the risk of introducing
1495 * divisions by scaling down the current dimension.
1497 * If so, we scale the current dimension down by a factor of m.
1498 * That is, we plug in
1502 * Note that in principle we could always scale down strided loops
1507 * but this may result in i' taking on larger values than the original i,
1508 * due to the shift by "f".
1509 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1511 static __isl_give isl_ast_graft
*create_node(__isl_take isl_union_map
*executed
,
1512 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1513 __isl_take isl_ast_build
*build
)
1515 struct isl_check_scaled_data data
;
1520 ctx
= isl_ast_build_get_ctx(build
);
1521 if (!isl_options_get_ast_build_scale_strides(ctx
))
1522 return create_node_scaled(executed
, bounds
, domain
, build
);
1524 data
.depth
= isl_ast_build_get_depth(build
);
1525 if (!isl_ast_build_has_stride(build
, data
.depth
))
1526 return create_node_scaled(executed
, bounds
, domain
, build
);
1528 offset
= isl_ast_build_get_offset(build
, data
.depth
);
1529 data
.m
= isl_ast_build_get_stride(build
, data
.depth
);
1531 offset
= isl_aff_free(offset
);
1532 offset
= isl_aff_scale_down_val(offset
, isl_val_copy(data
.m
));
1533 d
= isl_aff_get_denominator_val(offset
);
1535 executed
= isl_union_map_free(executed
);
1537 if (executed
&& isl_val_is_divisible_by(data
.m
, d
))
1538 data
.m
= isl_val_div(data
.m
, d
);
1540 data
.m
= isl_val_set_si(data
.m
, 1);
1544 if (!isl_val_is_one(data
.m
)) {
1545 if (isl_union_map_foreach_map(executed
, &map_check_scaled
,
1547 !isl_val_is_one(data
.m
))
1548 executed
= isl_union_map_free(executed
);
1551 if (!isl_val_is_one(data
.m
)) {
1556 isl_union_map
*umap
;
1558 space
= isl_ast_build_get_space(build
, 1);
1559 space
= isl_space_map_from_set(space
);
1560 ma
= isl_multi_aff_identity(space
);
1561 aff
= isl_multi_aff_get_aff(ma
, data
.depth
);
1562 aff
= isl_aff_scale_val(aff
, isl_val_copy(data
.m
));
1563 ma
= isl_multi_aff_set_aff(ma
, data
.depth
, aff
);
1565 bounds
= isl_basic_set_preimage_multi_aff(bounds
,
1566 isl_multi_aff_copy(ma
));
1567 domain
= isl_set_preimage_multi_aff(domain
,
1568 isl_multi_aff_copy(ma
));
1569 map
= isl_map_reverse(isl_map_from_multi_aff(ma
));
1570 umap
= isl_union_map_from_map(map
);
1571 executed
= isl_union_map_apply_domain(executed
,
1572 isl_union_map_copy(umap
));
1573 build
= isl_ast_build_scale_down(build
, isl_val_copy(data
.m
),
1576 isl_aff_free(offset
);
1577 isl_val_free(data
.m
);
1579 return create_node_scaled(executed
, bounds
, domain
, build
);
1582 /* Add the basic set to the list that "user" points to.
1584 static int collect_basic_set(__isl_take isl_basic_set
*bset
, void *user
)
1586 isl_basic_set_list
**list
= user
;
1588 *list
= isl_basic_set_list_add(*list
, bset
);
1593 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1595 static __isl_give isl_basic_set_list
*isl_basic_set_list_from_set(
1596 __isl_take isl_set
*set
)
1600 isl_basic_set_list
*list
;
1605 ctx
= isl_set_get_ctx(set
);
1607 n
= isl_set_n_basic_set(set
);
1608 list
= isl_basic_set_list_alloc(ctx
, n
);
1609 if (isl_set_foreach_basic_set(set
, &collect_basic_set
, &list
) < 0)
1610 list
= isl_basic_set_list_free(list
);
1616 /* Generate code for the schedule domain "bounds"
1617 * and add the result to "list".
1619 * We mainly detect strides here and check if the bounds do not
1620 * conflict with the current build domain
1621 * and then pass over control to create_node.
1623 * "bounds" reflects the bounds on the current dimension and possibly
1624 * some extra conditions on outer dimensions.
1625 * It does not, however, include any divs involving the current dimension,
1626 * so it does not capture any stride constraints.
1627 * We therefore need to compute that part of the schedule domain that
1628 * intersects with "bounds" and derive the strides from the result.
1630 static __isl_give isl_ast_graft_list
*add_node(
1631 __isl_take isl_ast_graft_list
*list
, __isl_take isl_union_map
*executed
,
1632 __isl_take isl_basic_set
*bounds
, __isl_take isl_ast_build
*build
)
1634 isl_ast_graft
*graft
;
1635 isl_set
*domain
= NULL
;
1636 isl_union_set
*uset
;
1637 int empty
, disjoint
;
1639 uset
= isl_union_set_from_basic_set(isl_basic_set_copy(bounds
));
1640 executed
= isl_union_map_intersect_domain(executed
, uset
);
1641 empty
= isl_union_map_is_empty(executed
);
1647 uset
= isl_union_map_domain(isl_union_map_copy(executed
));
1648 domain
= isl_set_from_union_set(uset
);
1649 domain
= isl_ast_build_specialize(build
, domain
);
1651 domain
= isl_set_compute_divs(domain
);
1652 domain
= isl_ast_build_eliminate_inner(build
, domain
);
1653 disjoint
= isl_set_is_disjoint(domain
, build
->domain
);
1659 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
1661 graft
= create_node(executed
, bounds
, domain
,
1662 isl_ast_build_copy(build
));
1663 list
= isl_ast_graft_list_add(list
, graft
);
1664 isl_ast_build_free(build
);
1667 list
= isl_ast_graft_list_free(list
);
1669 isl_set_free(domain
);
1670 isl_basic_set_free(bounds
);
1671 isl_union_map_free(executed
);
1672 isl_ast_build_free(build
);
1676 /* Does any element of i follow or coincide with any element of j
1677 * at the current depth for equal values of the outer dimensions?
1679 static int domain_follows_at_depth(__isl_keep isl_basic_set
*i
,
1680 __isl_keep isl_basic_set
*j
, void *user
)
1682 int depth
= *(int *) user
;
1683 isl_basic_map
*test
;
1687 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
1688 isl_basic_set_copy(j
));
1689 for (l
= 0; l
< depth
; ++l
)
1690 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1692 test
= isl_basic_map_order_ge(test
, isl_dim_in
, depth
,
1693 isl_dim_out
, depth
);
1694 empty
= isl_basic_map_is_empty(test
);
1695 isl_basic_map_free(test
);
1697 return empty
< 0 ? -1 : !empty
;
1700 /* Split up each element of "list" into a part that is related to "bset"
1701 * according to "gt" and a part that is not.
1702 * Return a list that consist of "bset" and all the pieces.
1704 static __isl_give isl_basic_set_list
*add_split_on(
1705 __isl_take isl_basic_set_list
*list
, __isl_take isl_basic_set
*bset
,
1706 __isl_keep isl_basic_map
*gt
)
1709 isl_basic_set_list
*res
;
1712 bset
= isl_basic_set_free(bset
);
1714 gt
= isl_basic_map_copy(gt
);
1715 gt
= isl_basic_map_intersect_domain(gt
, isl_basic_set_copy(bset
));
1716 n
= isl_basic_set_list_n_basic_set(list
);
1717 res
= isl_basic_set_list_from_basic_set(bset
);
1718 for (i
= 0; res
&& i
< n
; ++i
) {
1719 isl_basic_set
*bset
;
1720 isl_set
*set1
, *set2
;
1721 isl_basic_map
*bmap
;
1724 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1725 bmap
= isl_basic_map_copy(gt
);
1726 bmap
= isl_basic_map_intersect_range(bmap
, bset
);
1727 bset
= isl_basic_map_range(bmap
);
1728 empty
= isl_basic_set_is_empty(bset
);
1730 res
= isl_basic_set_list_free(res
);
1732 isl_basic_set_free(bset
);
1733 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1734 res
= isl_basic_set_list_add(res
, bset
);
1738 res
= isl_basic_set_list_add(res
, isl_basic_set_copy(bset
));
1739 set1
= isl_set_from_basic_set(bset
);
1740 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1741 set2
= isl_set_from_basic_set(bset
);
1742 set1
= isl_set_subtract(set2
, set1
);
1743 set1
= isl_set_make_disjoint(set1
);
1745 res
= isl_basic_set_list_concat(res
,
1746 isl_basic_set_list_from_set(set1
));
1748 isl_basic_map_free(gt
);
1749 isl_basic_set_list_free(list
);
1753 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1754 __isl_keep isl_basic_set_list
*domain_list
,
1755 __isl_keep isl_union_map
*executed
,
1756 __isl_keep isl_ast_build
*build
);
1758 /* Internal data structure for add_nodes.
1760 * "executed" and "build" are extra arguments to be passed to add_node.
1761 * "list" collects the results.
1763 struct isl_add_nodes_data
{
1764 isl_union_map
*executed
;
1765 isl_ast_build
*build
;
1767 isl_ast_graft_list
*list
;
1770 /* Generate code for the schedule domains in "scc"
1771 * and add the results to "list".
1773 * The domains in "scc" form a strongly connected component in the ordering.
1774 * If the number of domains in "scc" is larger than 1, then this means
1775 * that we cannot determine a valid ordering for the domains in the component.
1776 * This should be fairly rare because the individual domains
1777 * have been made disjoint first.
1778 * The problem is that the domains may be integrally disjoint but not
1779 * rationally disjoint. For example, we may have domains
1781 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1783 * These two domains have an empty intersection, but their rational
1784 * relaxations do intersect. It is impossible to order these domains
1785 * in the second dimension because the first should be ordered before
1786 * the second for outer dimension equal to 0, while it should be ordered
1787 * after for outer dimension equal to 1.
1789 * This may happen in particular in case of unrolling since the domain
1790 * of each slice is replaced by its simple hull.
1792 * For each basic set i in "scc" and for each of the following basic sets j,
1793 * we split off that part of the basic set i that shares the outer dimensions
1794 * with j and lies before j in the current dimension.
1795 * We collect all the pieces in a new list that replaces "scc".
1797 * While the elements in "scc" should be disjoint, we double-check
1798 * this property to avoid running into an infinite recursion in case
1799 * they intersect due to some internal error.
1801 static int add_nodes(__isl_take isl_basic_set_list
*scc
, void *user
)
1803 struct isl_add_nodes_data
*data
= user
;
1805 isl_basic_set
*bset
, *first
;
1806 isl_basic_set_list
*list
;
1810 n
= isl_basic_set_list_n_basic_set(scc
);
1811 bset
= isl_basic_set_list_get_basic_set(scc
, 0);
1813 isl_basic_set_list_free(scc
);
1814 data
->list
= add_node(data
->list
,
1815 isl_union_map_copy(data
->executed
), bset
,
1816 isl_ast_build_copy(data
->build
));
1817 return data
->list
? 0 : -1;
1820 depth
= isl_ast_build_get_depth(data
->build
);
1821 space
= isl_basic_set_get_space(bset
);
1822 space
= isl_space_map_from_set(space
);
1823 gt
= isl_basic_map_universe(space
);
1824 for (i
= 0; i
< depth
; ++i
)
1825 gt
= isl_basic_map_equate(gt
, isl_dim_in
, i
, isl_dim_out
, i
);
1826 gt
= isl_basic_map_order_gt(gt
, isl_dim_in
, depth
, isl_dim_out
, depth
);
1828 first
= isl_basic_set_copy(bset
);
1829 list
= isl_basic_set_list_from_basic_set(bset
);
1830 for (i
= 1; i
< n
; ++i
) {
1833 bset
= isl_basic_set_list_get_basic_set(scc
, i
);
1835 disjoint
= isl_basic_set_is_disjoint(bset
, first
);
1837 list
= isl_basic_set_list_free(list
);
1839 isl_die(isl_basic_set_list_get_ctx(scc
),
1841 "basic sets in scc are assumed to be disjoint",
1842 list
= isl_basic_set_list_free(list
));
1844 list
= add_split_on(list
, bset
, gt
);
1846 isl_basic_set_free(first
);
1847 isl_basic_map_free(gt
);
1848 isl_basic_set_list_free(scc
);
1850 data
->list
= isl_ast_graft_list_concat(data
->list
,
1851 generate_sorted_domains(scc
, data
->executed
, data
->build
));
1852 isl_basic_set_list_free(scc
);
1854 return data
->list
? 0 : -1;
1857 /* Sort the domains in "domain_list" according to the execution order
1858 * at the current depth (for equal values of the outer dimensions),
1859 * generate code for each of them, collecting the results in a list.
1860 * If no code is generated (because the intersection of the inverse schedule
1861 * with the domains turns out to be empty), then an empty list is returned.
1863 * The caller is responsible for ensuring that the basic sets in "domain_list"
1864 * are pair-wise disjoint. It can, however, in principle happen that
1865 * two basic sets should be ordered one way for one value of the outer
1866 * dimensions and the other way for some other value of the outer dimensions.
1867 * We therefore play safe and look for strongly connected components.
1868 * The function add_nodes takes care of handling non-trivial components.
1870 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1871 __isl_keep isl_basic_set_list
*domain_list
,
1872 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1875 struct isl_add_nodes_data data
;
1882 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1883 n
= isl_basic_set_list_n_basic_set(domain_list
);
1884 data
.list
= isl_ast_graft_list_alloc(ctx
, n
);
1888 return add_node(data
.list
, isl_union_map_copy(executed
),
1889 isl_basic_set_list_get_basic_set(domain_list
, 0),
1890 isl_ast_build_copy(build
));
1892 depth
= isl_ast_build_get_depth(build
);
1893 data
.executed
= executed
;
1895 if (isl_basic_set_list_foreach_scc(domain_list
,
1896 &domain_follows_at_depth
, &depth
,
1897 &add_nodes
, &data
) < 0)
1898 data
.list
= isl_ast_graft_list_free(data
.list
);
1903 /* Do i and j share any values for the outer dimensions?
1905 static int shared_outer(__isl_keep isl_basic_set
*i
,
1906 __isl_keep isl_basic_set
*j
, void *user
)
1908 int depth
= *(int *) user
;
1909 isl_basic_map
*test
;
1913 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
1914 isl_basic_set_copy(j
));
1915 for (l
= 0; l
< depth
; ++l
)
1916 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1918 empty
= isl_basic_map_is_empty(test
);
1919 isl_basic_map_free(test
);
1921 return empty
< 0 ? -1 : !empty
;
1924 /* Internal data structure for generate_sorted_domains_wrap.
1926 * "n" is the total number of basic sets
1927 * "executed" and "build" are extra arguments to be passed
1928 * to generate_sorted_domains.
1930 * "single" is set to 1 by generate_sorted_domains_wrap if there
1931 * is only a single component.
1932 * "list" collects the results.
1934 struct isl_ast_generate_parallel_domains_data
{
1936 isl_union_map
*executed
;
1937 isl_ast_build
*build
;
1940 isl_ast_graft_list
*list
;
1943 /* Call generate_sorted_domains on "scc", fuse the result into a list
1944 * with either zero or one graft and collect the these single element
1945 * lists into data->list.
1947 * If there is only one component, i.e., if the number of basic sets
1948 * in the current component is equal to the total number of basic sets,
1949 * then data->single is set to 1 and the result of generate_sorted_domains
1952 static int generate_sorted_domains_wrap(__isl_take isl_basic_set_list
*scc
,
1955 struct isl_ast_generate_parallel_domains_data
*data
= user
;
1956 isl_ast_graft_list
*list
;
1958 list
= generate_sorted_domains(scc
, data
->executed
, data
->build
);
1959 data
->single
= isl_basic_set_list_n_basic_set(scc
) == data
->n
;
1961 list
= isl_ast_graft_list_fuse(list
, data
->build
);
1965 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
1967 isl_basic_set_list_free(scc
);
1974 /* Look for any (weakly connected) components in the "domain_list"
1975 * of domains that share some values of the outer dimensions.
1976 * That is, domains in different components do not share any values
1977 * of the outer dimensions. This means that these components
1978 * can be freely reordered.
1979 * Within each of the components, we sort the domains according
1980 * to the execution order at the current depth.
1982 * If there is more than one component, then generate_sorted_domains_wrap
1983 * fuses the result of each call to generate_sorted_domains
1984 * into a list with either zero or one graft and collects these (at most)
1985 * single element lists into a bigger list. This means that the elements of the
1986 * final list can be freely reordered. In particular, we sort them
1987 * according to an arbitrary but fixed ordering to ease merging of
1988 * graft lists from different components.
1990 static __isl_give isl_ast_graft_list
*generate_parallel_domains(
1991 __isl_keep isl_basic_set_list
*domain_list
,
1992 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1995 struct isl_ast_generate_parallel_domains_data data
;
2000 data
.n
= isl_basic_set_list_n_basic_set(domain_list
);
2002 return generate_sorted_domains(domain_list
, executed
, build
);
2004 depth
= isl_ast_build_get_depth(build
);
2006 data
.executed
= executed
;
2009 if (isl_basic_set_list_foreach_scc(domain_list
, &shared_outer
, &depth
,
2010 &generate_sorted_domains_wrap
,
2012 data
.list
= isl_ast_graft_list_free(data
.list
);
2015 data
.list
= isl_ast_graft_list_sort_guard(data
.list
);
2020 /* Internal data for separate_domain.
2022 * "explicit" is set if we only want to use explicit bounds.
2024 * "domain" collects the separated domains.
2026 struct isl_separate_domain_data
{
2027 isl_ast_build
*build
;
2032 /* Extract implicit bounds on the current dimension for the executed "map".
2034 * The domain of "map" may involve inner dimensions, so we
2035 * need to eliminate them.
2037 static __isl_give isl_set
*implicit_bounds(__isl_take isl_map
*map
,
2038 __isl_keep isl_ast_build
*build
)
2042 domain
= isl_map_domain(map
);
2043 domain
= isl_ast_build_eliminate(build
, domain
);
2048 /* Extract explicit bounds on the current dimension for the executed "map".
2050 * Rather than eliminating the inner dimensions as in implicit_bounds,
2051 * we simply drop any constraints involving those inner dimensions.
2052 * The idea is that most bounds that are implied by constraints on the
2053 * inner dimensions will be enforced by for loops and not by explicit guards.
2054 * There is then no need to separate along those bounds.
2056 static __isl_give isl_set
*explicit_bounds(__isl_take isl_map
*map
,
2057 __isl_keep isl_ast_build
*build
)
2062 dim
= isl_map_dim(map
, isl_dim_out
);
2063 map
= isl_map_drop_constraints_involving_dims(map
, isl_dim_out
, 0, dim
);
2065 domain
= isl_map_domain(map
);
2066 depth
= isl_ast_build_get_depth(build
);
2067 dim
= isl_set_dim(domain
, isl_dim_set
);
2068 domain
= isl_set_detect_equalities(domain
);
2069 domain
= isl_set_drop_constraints_involving_dims(domain
,
2070 isl_dim_set
, depth
+ 1, dim
- (depth
+ 1));
2071 domain
= isl_set_remove_divs_involving_dims(domain
,
2072 isl_dim_set
, depth
, 1);
2073 domain
= isl_set_remove_unknown_divs(domain
);
2078 /* Split data->domain into pieces that intersect with the range of "map"
2079 * and pieces that do not intersect with the range of "map"
2080 * and then add that part of the range of "map" that does not intersect
2081 * with data->domain.
2083 static int separate_domain(__isl_take isl_map
*map
, void *user
)
2085 struct isl_separate_domain_data
*data
= user
;
2090 domain
= explicit_bounds(map
, data
->build
);
2092 domain
= implicit_bounds(map
, data
->build
);
2094 domain
= isl_set_coalesce(domain
);
2095 domain
= isl_set_make_disjoint(domain
);
2096 d1
= isl_set_subtract(isl_set_copy(domain
), isl_set_copy(data
->domain
));
2097 d2
= isl_set_subtract(isl_set_copy(data
->domain
), isl_set_copy(domain
));
2098 data
->domain
= isl_set_intersect(data
->domain
, domain
);
2099 data
->domain
= isl_set_union(data
->domain
, d1
);
2100 data
->domain
= isl_set_union(data
->domain
, d2
);
2105 /* Separate the schedule domains of "executed".
2107 * That is, break up the domain of "executed" into basic sets,
2108 * such that for each basic set S, every element in S is associated with
2109 * the same domain spaces.
2111 * "space" is the (single) domain space of "executed".
2113 static __isl_give isl_set
*separate_schedule_domains(
2114 __isl_take isl_space
*space
, __isl_take isl_union_map
*executed
,
2115 __isl_keep isl_ast_build
*build
)
2117 struct isl_separate_domain_data data
= { build
};
2120 ctx
= isl_ast_build_get_ctx(build
);
2121 data
.explicit = isl_options_get_ast_build_separation_bounds(ctx
) ==
2122 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
;
2123 data
.domain
= isl_set_empty(space
);
2124 if (isl_union_map_foreach_map(executed
, &separate_domain
, &data
) < 0)
2125 data
.domain
= isl_set_free(data
.domain
);
2127 isl_union_map_free(executed
);
2131 /* Temporary data used during the search for a lower bound for unrolling.
2133 * "domain" is the original set for which to find a lower bound
2134 * "depth" is the dimension for which to find a lower boudn
2136 * "lower" is the best lower bound found so far. It is NULL if we have not
2138 * "n" is the corresponding size. If lower is NULL, then the value of n
2141 struct isl_find_unroll_data
{
2149 /* Check if we can use "c" as a lower bound and if it is better than
2150 * any previously found lower bound.
2152 * If "c" does not involve the dimension at the current depth,
2153 * then we cannot use it.
2154 * Otherwise, let "c" be of the form
2158 * We compute the maximal value of
2160 * -ceil(f(j)/a)) + i + 1
2162 * over the domain. If there is such a value "n", then we know
2164 * -ceil(f(j)/a)) + i + 1 <= n
2168 * i < ceil(f(j)/a)) + n
2170 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2171 * We just need to check if we have found any lower bound before and
2172 * if the new lower bound is better (smaller n) than the previously found
2175 static int update_unrolling_lower_bound(struct isl_find_unroll_data
*data
,
2176 __isl_keep isl_constraint
*c
)
2178 isl_aff
*aff
, *lower
;
2181 if (!isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->depth
))
2184 lower
= isl_constraint_get_bound(c
, isl_dim_set
, data
->depth
);
2185 lower
= isl_aff_ceil(lower
);
2186 aff
= isl_aff_copy(lower
);
2187 aff
= isl_aff_neg(aff
);
2188 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, data
->depth
, 1);
2189 aff
= isl_aff_add_constant_si(aff
, 1);
2190 max
= isl_set_max_val(data
->domain
, aff
);
2195 if (isl_val_is_infty(max
)) {
2197 isl_aff_free(lower
);
2201 if (isl_val_cmp_si(max
, INT_MAX
) <= 0 &&
2202 (!data
->lower
|| isl_val_cmp_si(max
, *data
->n
) < 0)) {
2203 isl_aff_free(data
->lower
);
2204 data
->lower
= lower
;
2205 *data
->n
= isl_val_get_num_si(max
);
2207 isl_aff_free(lower
);
2212 isl_aff_free(lower
);
2216 /* Check if we can use "c" as a lower bound and if it is better than
2217 * any previously found lower bound.
2219 static int constraint_find_unroll(__isl_take isl_constraint
*c
, void *user
)
2221 struct isl_find_unroll_data
*data
;
2224 data
= (struct isl_find_unroll_data
*) user
;
2225 r
= update_unrolling_lower_bound(data
, c
);
2226 isl_constraint_free(c
);
2231 /* Look for a lower bound l(i) on the dimension at "depth"
2232 * and a size n such that "domain" is a subset of
2234 * { [i] : l(i) <= i_d < l(i) + n }
2236 * where d is "depth" and l(i) depends only on earlier dimensions.
2237 * Furthermore, try and find a lower bound such that n is as small as possible.
2238 * In particular, "n" needs to be finite.
2240 * Inner dimensions have been eliminated from "domain" by the caller.
2242 * We first construct a collection of lower bounds on the input set
2243 * by computing its simple hull. We then iterate through them,
2244 * discarding those that we cannot use (either because they do not
2245 * involve the dimension at "depth" or because they have no corresponding
2246 * upper bound, meaning that "n" would be unbounded) and pick out the
2247 * best from the remaining ones.
2249 * If we cannot find a suitable lower bound, then we consider that
2252 static __isl_give isl_aff
*find_unroll_lower_bound(__isl_keep isl_set
*domain
,
2255 struct isl_find_unroll_data data
= { domain
, depth
, NULL
, n
};
2256 isl_basic_set
*hull
;
2258 hull
= isl_set_simple_hull(isl_set_copy(domain
));
2260 if (isl_basic_set_foreach_constraint(hull
,
2261 &constraint_find_unroll
, &data
) < 0)
2264 isl_basic_set_free(hull
);
2267 isl_die(isl_set_get_ctx(domain
), isl_error_invalid
,
2268 "cannot find lower bound for unrolling", return NULL
);
2272 isl_basic_set_free(hull
);
2273 return isl_aff_free(data
.lower
);
2276 /* Return the constraint
2278 * i_"depth" = aff + offset
2280 static __isl_give isl_constraint
*at_offset(int depth
, __isl_keep isl_aff
*aff
,
2283 aff
= isl_aff_copy(aff
);
2284 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, depth
, -1);
2285 aff
= isl_aff_add_constant_si(aff
, offset
);
2286 return isl_equality_from_aff(aff
);
2289 /* Data structure for storing the results and the intermediate objects
2290 * of compute_domains.
2292 * "list" is the main result of the function and contains a list
2293 * of disjoint basic sets for which code should be generated.
2295 * "executed" and "build" are inputs to compute_domains.
2296 * "schedule_domain" is the domain of "executed".
2298 * "option" constains the domains at the current depth that should by
2299 * atomic, separated or unrolled. These domains are as specified by
2300 * the user, except that inner dimensions have been eliminated and
2301 * that they have been made pair-wise disjoint.
2303 * "sep_class" contains the user-specified split into separation classes
2304 * specialized to the current depth.
2305 * "done" contains the union of the separation domains that have already
2308 struct isl_codegen_domains
{
2309 isl_basic_set_list
*list
;
2311 isl_union_map
*executed
;
2312 isl_ast_build
*build
;
2313 isl_set
*schedule_domain
;
2321 /* Extend domains->list with a list of basic sets, one for each value
2322 * of the current dimension in "domain" and remove the corresponding
2323 * sets from the class domain. Return the updated class domain.
2324 * The divs that involve the current dimension have not been projected out
2327 * Since we are going to be iterating over the individual values,
2328 * we first check if there are any strides on the current dimension.
2329 * If there is, we rewrite the current dimension i as
2331 * i = stride i' + offset
2333 * and then iterate over individual values of i' instead.
2335 * We then look for a lower bound on i' and a size such that the domain
2338 * { [j,i'] : l(j) <= i' < l(j) + n }
2340 * and then take slices of the domain at values of i'
2341 * between l(j) and l(j) + n - 1.
2343 * We compute the unshifted simple hull of each slice to ensure that
2344 * we have a single basic set per offset. The slicing constraint
2345 * may get simplified away before the unshifted simple hull is taken
2346 * and may therefore in some rare cases disappear from the result.
2347 * We therefore explicitly add the constraint back after computing
2348 * the unshifted simple hull to ensure that the basic sets
2349 * remain disjoint. The constraints that are dropped by taking the hull
2350 * will be taken into account at the next level, as in the case of the
2353 * Finally, we map i' back to i and add each basic set to the list.
2354 * Since we may have dropped some constraints, we intersect with
2355 * the class domain again to ensure that each element in the list
2356 * is disjoint from the other class domains.
2358 static __isl_give isl_set
*do_unroll(struct isl_codegen_domains
*domains
,
2359 __isl_take isl_set
*domain
, __isl_take isl_set
*class_domain
)
2365 isl_multi_aff
*expansion
;
2366 isl_basic_map
*bmap
;
2367 isl_set
*unroll_domain
;
2368 isl_ast_build
*build
;
2371 return isl_set_free(class_domain
);
2373 ctx
= isl_set_get_ctx(domain
);
2374 depth
= isl_ast_build_get_depth(domains
->build
);
2375 build
= isl_ast_build_copy(domains
->build
);
2376 domain
= isl_ast_build_eliminate_inner(build
, domain
);
2377 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
2378 expansion
= isl_ast_build_get_stride_expansion(build
);
2380 domain
= isl_set_preimage_multi_aff(domain
,
2381 isl_multi_aff_copy(expansion
));
2382 domain
= isl_ast_build_eliminate_divs(build
, domain
);
2384 isl_ast_build_free(build
);
2386 lower
= find_unroll_lower_bound(domain
, depth
, &n
);
2388 class_domain
= isl_set_free(class_domain
);
2390 bmap
= isl_basic_map_from_multi_aff(expansion
);
2392 unroll_domain
= isl_set_empty(isl_set_get_space(domain
));
2394 for (i
= 0; class_domain
&& i
< n
; ++i
) {
2396 isl_basic_set
*bset
;
2397 isl_constraint
*slice
;
2398 isl_basic_set_list
*list
;
2400 slice
= at_offset(depth
, lower
, i
);
2401 set
= isl_set_copy(domain
);
2402 set
= isl_set_add_constraint(set
, isl_constraint_copy(slice
));
2403 bset
= isl_set_unshifted_simple_hull(set
);
2404 bset
= isl_basic_set_add_constraint(bset
, slice
);
2405 bset
= isl_basic_set_apply(bset
, isl_basic_map_copy(bmap
));
2406 set
= isl_set_from_basic_set(bset
);
2407 unroll_domain
= isl_set_union(unroll_domain
, isl_set_copy(set
));
2408 set
= isl_set_intersect(set
, isl_set_copy(class_domain
));
2409 set
= isl_set_make_disjoint(set
);
2410 list
= isl_basic_set_list_from_set(set
);
2411 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2414 class_domain
= isl_set_subtract(class_domain
, unroll_domain
);
2416 isl_aff_free(lower
);
2417 isl_set_free(domain
);
2418 isl_basic_map_free(bmap
);
2420 return class_domain
;
2423 /* Add domains to domains->list for each individual value of the current
2424 * dimension, for that part of the schedule domain that lies in the
2425 * intersection of the option domain and the class domain.
2426 * Remove the corresponding sets from the class domain and
2427 * return the updated class domain.
2429 * We first break up the unroll option domain into individual pieces
2430 * and then handle each of them separately. The unroll option domain
2431 * has been made disjoint in compute_domains_init_options,
2433 * Note that we actively want to combine different pieces of the
2434 * schedule domain that have the same value at the current dimension.
2435 * We therefore need to break up the unroll option domain before
2436 * intersecting with class and schedule domain, hoping that the
2437 * unroll option domain specified by the user is relatively simple.
2439 static __isl_give isl_set
*compute_unroll_domains(
2440 struct isl_codegen_domains
*domains
, __isl_take isl_set
*class_domain
)
2442 isl_set
*unroll_domain
;
2443 isl_basic_set_list
*unroll_list
;
2447 empty
= isl_set_is_empty(domains
->option
[unroll
]);
2449 return isl_set_free(class_domain
);
2451 return class_domain
;
2453 unroll_domain
= isl_set_copy(domains
->option
[unroll
]);
2454 unroll_list
= isl_basic_set_list_from_set(unroll_domain
);
2456 n
= isl_basic_set_list_n_basic_set(unroll_list
);
2457 for (i
= 0; i
< n
; ++i
) {
2458 isl_basic_set
*bset
;
2460 bset
= isl_basic_set_list_get_basic_set(unroll_list
, i
);
2461 unroll_domain
= isl_set_from_basic_set(bset
);
2462 unroll_domain
= isl_set_intersect(unroll_domain
,
2463 isl_set_copy(class_domain
));
2464 unroll_domain
= isl_set_intersect(unroll_domain
,
2465 isl_set_copy(domains
->schedule_domain
));
2467 empty
= isl_set_is_empty(unroll_domain
);
2468 if (empty
>= 0 && empty
) {
2469 isl_set_free(unroll_domain
);
2473 class_domain
= do_unroll(domains
, unroll_domain
, class_domain
);
2476 isl_basic_set_list_free(unroll_list
);
2478 return class_domain
;
2481 /* Try and construct a single basic set that includes the intersection of
2482 * the schedule domain, the atomic option domain and the class domain.
2483 * Add the resulting basic set(s) to domains->list and remove them
2484 * from class_domain. Return the updated class domain.
2486 * We construct a single domain rather than trying to combine
2487 * the schedule domains of individual domains because we are working
2488 * within a single component so that non-overlapping schedule domains
2489 * should already have been separated.
2490 * We do however need to make sure that this single domains is a subset
2491 * of the class domain so that it would not intersect with any other
2492 * class domains. This means that we may end up splitting up the atomic
2493 * domain in case separation classes are being used.
2495 * "domain" is the intersection of the schedule domain and the class domain,
2496 * with inner dimensions projected out.
2498 static __isl_give isl_set
*compute_atomic_domain(
2499 struct isl_codegen_domains
*domains
, __isl_take isl_set
*class_domain
)
2501 isl_basic_set
*bset
;
2502 isl_basic_set_list
*list
;
2503 isl_set
*domain
, *atomic_domain
;
2506 domain
= isl_set_copy(domains
->option
[atomic
]);
2507 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2508 domain
= isl_set_intersect(domain
,
2509 isl_set_copy(domains
->schedule_domain
));
2510 empty
= isl_set_is_empty(domain
);
2512 class_domain
= isl_set_free(class_domain
);
2514 isl_set_free(domain
);
2515 return class_domain
;
2518 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2519 domain
= isl_set_coalesce(domain
);
2520 bset
= isl_set_unshifted_simple_hull(domain
);
2521 domain
= isl_set_from_basic_set(bset
);
2522 atomic_domain
= isl_set_copy(domain
);
2523 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2524 class_domain
= isl_set_subtract(class_domain
, atomic_domain
);
2525 domain
= isl_set_make_disjoint(domain
);
2526 list
= isl_basic_set_list_from_set(domain
);
2527 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2529 return class_domain
;
2532 /* Split up the schedule domain into uniform basic sets,
2533 * in the sense that each element in a basic set is associated to
2534 * elements of the same domains, and add the result to domains->list.
2535 * Do this for that part of the schedule domain that lies in the
2536 * intersection of "class_domain" and the separate option domain.
2538 * "class_domain" may or may not include the constraints
2539 * of the schedule domain, but this does not make a difference
2540 * since we are going to intersect it with the domain of the inverse schedule.
2541 * If it includes schedule domain constraints, then they may involve
2542 * inner dimensions, but we will eliminate them in separation_domain.
2544 static int compute_separate_domain(struct isl_codegen_domains
*domains
,
2545 __isl_keep isl_set
*class_domain
)
2549 isl_union_map
*executed
;
2550 isl_basic_set_list
*list
;
2553 domain
= isl_set_copy(domains
->option
[separate
]);
2554 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2555 executed
= isl_union_map_copy(domains
->executed
);
2556 executed
= isl_union_map_intersect_domain(executed
,
2557 isl_union_set_from_set(domain
));
2558 empty
= isl_union_map_is_empty(executed
);
2559 if (empty
< 0 || empty
) {
2560 isl_union_map_free(executed
);
2561 return empty
< 0 ? -1 : 0;
2564 space
= isl_set_get_space(class_domain
);
2565 domain
= separate_schedule_domains(space
, executed
, domains
->build
);
2567 list
= isl_basic_set_list_from_set(domain
);
2568 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2573 /* Split up the domain at the current depth into disjoint
2574 * basic sets for which code should be generated separately
2575 * for the given separation class domain.
2577 * If any separation classes have been defined, then "class_domain"
2578 * is the domain of the current class and does not refer to inner dimensions.
2579 * Otherwise, "class_domain" is the universe domain.
2581 * We first make sure that the class domain is disjoint from
2582 * previously considered class domains.
2584 * The separate domains can be computed directly from the "class_domain".
2586 * The unroll, atomic and remainder domains need the constraints
2587 * from the schedule domain.
2589 * For unrolling, the actual schedule domain is needed (with divs that
2590 * may refer to the current dimension) so that stride detection can be
2593 * For atomic and remainder domains, inner dimensions and divs involving
2594 * the current dimensions should be eliminated.
2595 * In case we are working within a separation class, we need to intersect
2596 * the result with the current "class_domain" to ensure that the domains
2597 * are disjoint from those generated from other class domains.
2599 * The domain that has been made atomic may be larger than specified
2600 * by the user since it needs to be representable as a single basic set.
2601 * This possibly larger domain is removed from class_domain by
2602 * compute_atomic_domain. It is computed first so that the extended domain
2603 * would not overlap with any domains computed before.
2604 * Similary, the unrolled domains may have some constraints removed and
2605 * may therefore also be larger than specified by the user.
2607 * If anything is left after handling separate, unroll and atomic,
2608 * we split it up into basic sets and append the basic sets to domains->list.
2610 static int compute_partial_domains(struct isl_codegen_domains
*domains
,
2611 __isl_take isl_set
*class_domain
)
2613 isl_basic_set_list
*list
;
2616 class_domain
= isl_set_subtract(class_domain
,
2617 isl_set_copy(domains
->done
));
2618 domains
->done
= isl_set_union(domains
->done
,
2619 isl_set_copy(class_domain
));
2621 class_domain
= compute_atomic_domain(domains
, class_domain
);
2622 class_domain
= compute_unroll_domains(domains
, class_domain
);
2624 domain
= isl_set_copy(class_domain
);
2626 if (compute_separate_domain(domains
, domain
) < 0)
2628 domain
= isl_set_subtract(domain
,
2629 isl_set_copy(domains
->option
[separate
]));
2631 domain
= isl_set_intersect(domain
,
2632 isl_set_copy(domains
->schedule_domain
));
2634 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2635 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2637 domain
= isl_set_coalesce(domain
);
2638 domain
= isl_set_make_disjoint(domain
);
2640 list
= isl_basic_set_list_from_set(domain
);
2641 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2643 isl_set_free(class_domain
);
2647 isl_set_free(domain
);
2648 isl_set_free(class_domain
);
2652 /* Split up the domain at the current depth into disjoint
2653 * basic sets for which code should be generated separately
2654 * for the separation class identified by "pnt".
2656 * We extract the corresponding class domain from domains->sep_class,
2657 * eliminate inner dimensions and pass control to compute_partial_domains.
2659 static int compute_class_domains(__isl_take isl_point
*pnt
, void *user
)
2661 struct isl_codegen_domains
*domains
= user
;
2666 class_set
= isl_set_from_point(pnt
);
2667 domain
= isl_map_domain(isl_map_intersect_range(
2668 isl_map_copy(domains
->sep_class
), class_set
));
2669 domain
= isl_ast_build_compute_gist(domains
->build
, domain
);
2670 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2672 disjoint
= isl_set_plain_is_disjoint(domain
, domains
->schedule_domain
);
2676 isl_set_free(domain
);
2680 return compute_partial_domains(domains
, domain
);
2683 /* Extract the domains at the current depth that should be atomic,
2684 * separated or unrolled and store them in option.
2686 * The domains specified by the user might overlap, so we make
2687 * them disjoint by subtracting earlier domains from later domains.
2689 static void compute_domains_init_options(isl_set
*option
[3],
2690 __isl_keep isl_ast_build
*build
)
2692 enum isl_ast_build_domain_type type
, type2
;
2694 for (type
= atomic
; type
<= separate
; ++type
) {
2695 option
[type
] = isl_ast_build_get_option_domain(build
, type
);
2696 for (type2
= atomic
; type2
< type
; ++type2
)
2697 option
[type
] = isl_set_subtract(option
[type
],
2698 isl_set_copy(option
[type2
]));
2701 option
[unroll
] = isl_set_coalesce(option
[unroll
]);
2702 option
[unroll
] = isl_set_make_disjoint(option
[unroll
]);
2705 /* Split up the domain at the current depth into disjoint
2706 * basic sets for which code should be generated separately,
2707 * based on the user-specified options.
2708 * Return the list of disjoint basic sets.
2710 * There are three kinds of domains that we need to keep track of.
2711 * - the "schedule domain" is the domain of "executed"
2712 * - the "class domain" is the domain corresponding to the currrent
2714 * - the "option domain" is the domain corresponding to one of the options
2715 * atomic, unroll or separate
2717 * We first consider the individial values of the separation classes
2718 * and split up the domain for each of them separately.
2719 * Finally, we consider the remainder. If no separation classes were
2720 * specified, then we call compute_partial_domains with the universe
2721 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2722 * with inner dimensions removed. We do this because we want to
2723 * avoid computing the complement of the class domains (i.e., the difference
2724 * between the universe and domains->done).
2726 static __isl_give isl_basic_set_list
*compute_domains(
2727 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
2729 struct isl_codegen_domains domains
;
2732 isl_union_set
*schedule_domain
;
2736 enum isl_ast_build_domain_type type
;
2742 ctx
= isl_union_map_get_ctx(executed
);
2743 domains
.list
= isl_basic_set_list_alloc(ctx
, 0);
2745 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
2746 domain
= isl_set_from_union_set(schedule_domain
);
2748 compute_domains_init_options(domains
.option
, build
);
2750 domains
.sep_class
= isl_ast_build_get_separation_class(build
);
2751 classes
= isl_map_range(isl_map_copy(domains
.sep_class
));
2752 n_param
= isl_set_dim(classes
, isl_dim_param
);
2753 classes
= isl_set_project_out(classes
, isl_dim_param
, 0, n_param
);
2755 space
= isl_set_get_space(domain
);
2756 domains
.build
= build
;
2757 domains
.schedule_domain
= isl_set_copy(domain
);
2758 domains
.executed
= executed
;
2759 domains
.done
= isl_set_empty(space
);
2761 if (isl_set_foreach_point(classes
, &compute_class_domains
, &domains
) < 0)
2762 domains
.list
= isl_basic_set_list_free(domains
.list
);
2763 isl_set_free(classes
);
2765 empty
= isl_set_is_empty(domains
.done
);
2767 domains
.list
= isl_basic_set_list_free(domains
.list
);
2768 domain
= isl_set_free(domain
);
2770 isl_set_free(domain
);
2771 domain
= isl_set_universe(isl_set_get_space(domains
.done
));
2773 domain
= isl_ast_build_eliminate(build
, domain
);
2775 if (compute_partial_domains(&domains
, domain
) < 0)
2776 domains
.list
= isl_basic_set_list_free(domains
.list
);
2778 isl_set_free(domains
.schedule_domain
);
2779 isl_set_free(domains
.done
);
2780 isl_map_free(domains
.sep_class
);
2781 for (type
= atomic
; type
<= separate
; ++type
)
2782 isl_set_free(domains
.option
[type
]);
2784 return domains
.list
;
2787 /* Generate code for a single component, after shifting (if any)
2790 * We first split up the domain at the current depth into disjoint
2791 * basic sets based on the user-specified options.
2792 * Then we generated code for each of them and concatenate the results.
2794 static __isl_give isl_ast_graft_list
*generate_shifted_component(
2795 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
2797 isl_basic_set_list
*domain_list
;
2798 isl_ast_graft_list
*list
= NULL
;
2800 domain_list
= compute_domains(executed
, build
);
2801 list
= generate_parallel_domains(domain_list
, executed
, build
);
2803 isl_basic_set_list_free(domain_list
);
2804 isl_union_map_free(executed
);
2805 isl_ast_build_free(build
);
2810 struct isl_set_map_pair
{
2815 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2816 * of indices into the "domain" array,
2817 * return the union of the "map" fields of the elements
2818 * indexed by the first "n" elements of "order".
2820 static __isl_give isl_union_map
*construct_component_executed(
2821 struct isl_set_map_pair
*domain
, int *order
, int n
)
2825 isl_union_map
*executed
;
2827 map
= isl_map_copy(domain
[order
[0]].map
);
2828 executed
= isl_union_map_from_map(map
);
2829 for (i
= 1; i
< n
; ++i
) {
2830 map
= isl_map_copy(domain
[order
[i
]].map
);
2831 executed
= isl_union_map_add_map(executed
, map
);
2837 /* Generate code for a single component, after shifting (if any)
2840 * The component inverse schedule is specified as the "map" fields
2841 * of the elements of "domain" indexed by the first "n" elements of "order".
2843 static __isl_give isl_ast_graft_list
*generate_shifted_component_from_list(
2844 struct isl_set_map_pair
*domain
, int *order
, int n
,
2845 __isl_take isl_ast_build
*build
)
2847 isl_union_map
*executed
;
2849 executed
= construct_component_executed(domain
, order
, n
);
2850 return generate_shifted_component(executed
, build
);
2853 /* Does set dimension "pos" of "set" have an obviously fixed value?
2855 static int dim_is_fixed(__isl_keep isl_set
*set
, int pos
)
2860 v
= isl_set_plain_get_val_if_fixed(set
, isl_dim_set
, pos
);
2863 fixed
= !isl_val_is_nan(v
);
2869 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2870 * of indices into the "domain" array,
2871 * do all (except for at most one) of the "set" field of the elements
2872 * indexed by the first "n" elements of "order" have a fixed value
2873 * at position "depth"?
2875 static int at_most_one_non_fixed(struct isl_set_map_pair
*domain
,
2876 int *order
, int n
, int depth
)
2881 for (i
= 0; i
< n
; ++i
) {
2884 f
= dim_is_fixed(domain
[order
[i
]].set
, depth
);
2897 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2898 * of indices into the "domain" array,
2899 * eliminate the inner dimensions from the "set" field of the elements
2900 * indexed by the first "n" elements of "order", provided the current
2901 * dimension does not have a fixed value.
2903 * Return the index of the first element in "order" with a corresponding
2904 * "set" field that does not have an (obviously) fixed value.
2906 static int eliminate_non_fixed(struct isl_set_map_pair
*domain
,
2907 int *order
, int n
, int depth
, __isl_keep isl_ast_build
*build
)
2912 for (i
= n
- 1; i
>= 0; --i
) {
2914 f
= dim_is_fixed(domain
[order
[i
]].set
, depth
);
2919 domain
[order
[i
]].set
= isl_ast_build_eliminate_inner(build
,
2920 domain
[order
[i
]].set
);
2927 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2928 * of indices into the "domain" array,
2929 * find the element of "domain" (amongst those indexed by the first "n"
2930 * elements of "order") with the "set" field that has the smallest
2931 * value for the current iterator.
2933 * Note that the domain with the smallest value may depend on the parameters
2934 * and/or outer loop dimension. Since the result of this function is only
2935 * used as heuristic, we only make a reasonable attempt at finding the best
2936 * domain, one that should work in case a single domain provides the smallest
2937 * value for the current dimension over all values of the parameters
2938 * and outer dimensions.
2940 * In particular, we compute the smallest value of the first domain
2941 * and replace it by that of any later domain if that later domain
2942 * has a smallest value that is smaller for at least some value
2943 * of the parameters and outer dimensions.
2945 static int first_offset(struct isl_set_map_pair
*domain
, int *order
, int n
,
2946 __isl_keep isl_ast_build
*build
)
2952 min_first
= isl_ast_build_map_to_iterator(build
,
2953 isl_set_copy(domain
[order
[0]].set
));
2954 min_first
= isl_map_lexmin(min_first
);
2956 for (i
= 1; i
< n
; ++i
) {
2957 isl_map
*min
, *test
;
2960 min
= isl_ast_build_map_to_iterator(build
,
2961 isl_set_copy(domain
[order
[i
]].set
));
2962 min
= isl_map_lexmin(min
);
2963 test
= isl_map_copy(min
);
2964 test
= isl_map_apply_domain(isl_map_copy(min_first
), test
);
2965 test
= isl_map_order_lt(test
, isl_dim_in
, 0, isl_dim_out
, 0);
2966 empty
= isl_map_is_empty(test
);
2968 if (empty
>= 0 && !empty
) {
2969 isl_map_free(min_first
);
2979 isl_map_free(min_first
);
2981 return i
< n
? -1 : first
;
2984 /* Construct a shifted inverse schedule based on the original inverse schedule,
2985 * the stride and the offset.
2987 * The original inverse schedule is specified as the "map" fields
2988 * of the elements of "domain" indexed by the first "n" elements of "order".
2990 * "stride" and "offset" are such that the difference
2991 * between the values of the current dimension of domain "i"
2992 * and the values of the current dimension for some reference domain are
2995 * stride * integer + offset[i]
2997 * Moreover, 0 <= offset[i] < stride.
2999 * For each domain, we create a map
3001 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
3003 * where j refers to the current dimension and the other dimensions are
3004 * unchanged, and apply this map to the original schedule domain.
3006 * For example, for the original schedule
3008 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3010 * and assuming the offset is 0 for the A domain and 1 for the B domain,
3011 * we apply the mapping
3015 * to the schedule of the "A" domain and the mapping
3017 * { [j - 1] -> [j, 1] }
3019 * to the schedule of the "B" domain.
3022 * Note that after the transformation, the differences between pairs
3023 * of values of the current dimension over all domains are multiples
3024 * of stride and that we have therefore exposed the stride.
3027 * To see that the mapping preserves the lexicographic order,
3028 * first note that each of the individual maps above preserves the order.
3029 * If the value of the current iterator is j1 in one domain and j2 in another,
3030 * then if j1 = j2, we know that the same map is applied to both domains
3031 * and the order is preserved.
3032 * Otherwise, let us assume, without loss of generality, that j1 < j2.
3033 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
3037 * and the order is preserved.
3038 * If c1 < c2, then we know
3044 * j2 - j1 = n * s + r
3046 * with n >= 0 and 0 <= r < s.
3047 * In other words, r = c2 - c1.
3058 * (j1 - c1, c1) << (j2 - c2, c2)
3060 * with "<<" the lexicographic order, proving that the order is preserved
3063 static __isl_give isl_union_map
*contruct_shifted_executed(
3064 struct isl_set_map_pair
*domain
, int *order
, int n
,
3065 __isl_keep isl_val
*stride
, __isl_keep isl_multi_val
*offset
,
3066 __isl_take isl_ast_build
*build
)
3069 isl_union_map
*executed
;
3075 depth
= isl_ast_build_get_depth(build
);
3076 space
= isl_ast_build_get_space(build
, 1);
3077 executed
= isl_union_map_empty(isl_space_copy(space
));
3078 space
= isl_space_map_from_set(space
);
3079 map
= isl_map_identity(isl_space_copy(space
));
3080 map
= isl_map_eliminate(map
, isl_dim_out
, depth
, 1);
3081 map
= isl_map_insert_dims(map
, isl_dim_out
, depth
+ 1, 1);
3082 space
= isl_space_insert_dims(space
, isl_dim_out
, depth
+ 1, 1);
3084 c
= isl_equality_alloc(isl_local_space_from_space(space
));
3085 c
= isl_constraint_set_coefficient_si(c
, isl_dim_in
, depth
, 1);
3086 c
= isl_constraint_set_coefficient_si(c
, isl_dim_out
, depth
, -1);
3088 for (i
= 0; i
< n
; ++i
) {
3092 v
= isl_multi_val_get_val(offset
, i
);
3095 map_i
= isl_map_copy(map
);
3096 map_i
= isl_map_fix_val(map_i
, isl_dim_out
, depth
+ 1,
3099 c
= isl_constraint_set_constant_val(c
, v
);
3100 map_i
= isl_map_add_constraint(map_i
, isl_constraint_copy(c
));
3102 map_i
= isl_map_apply_domain(isl_map_copy(domain
[order
[i
]].map
),
3104 executed
= isl_union_map_add_map(executed
, map_i
);
3107 isl_constraint_free(c
);
3111 executed
= isl_union_map_free(executed
);
3116 /* Generate code for a single component, after exposing the stride,
3117 * given that the schedule domain is "shifted strided".
3119 * The component inverse schedule is specified as the "map" fields
3120 * of the elements of "domain" indexed by the first "n" elements of "order".
3122 * The schedule domain being "shifted strided" means that the differences
3123 * between the values of the current dimension of domain "i"
3124 * and the values of the current dimension for some reference domain are
3127 * stride * integer + offset[i]
3129 * We first look for the domain with the "smallest" value for the current
3130 * dimension and adjust the offsets such that the offset of the "smallest"
3131 * domain is equal to zero. The other offsets are reduced modulo stride.
3133 * Based on this information, we construct a new inverse schedule in
3134 * contruct_shifted_executed that exposes the stride.
3135 * Since this involves the introduction of a new schedule dimension,
3136 * the build needs to be changed accodingly.
3137 * After computing the AST, the newly introduced dimension needs
3138 * to be removed again from the list of grafts. We do this by plugging
3139 * in a mapping that represents the new schedule domain in terms of the
3140 * old schedule domain.
3142 static __isl_give isl_ast_graft_list
*generate_shift_component(
3143 struct isl_set_map_pair
*domain
, int *order
, int n
,
3144 __isl_keep isl_val
*stride
, __isl_keep isl_multi_val
*offset
,
3145 __isl_take isl_ast_build
*build
)
3147 isl_ast_graft_list
*list
;
3154 isl_multi_aff
*ma
, *zero
;
3155 isl_union_map
*executed
;
3157 ctx
= isl_ast_build_get_ctx(build
);
3158 depth
= isl_ast_build_get_depth(build
);
3160 first
= first_offset(domain
, order
, n
, build
);
3164 mv
= isl_multi_val_copy(offset
);
3165 val
= isl_multi_val_get_val(offset
, first
);
3166 val
= isl_val_neg(val
);
3167 mv
= isl_multi_val_add_val(mv
, val
);
3168 mv
= isl_multi_val_mod_val(mv
, isl_val_copy(stride
));
3170 executed
= contruct_shifted_executed(domain
, order
, n
, stride
, mv
,
3172 space
= isl_ast_build_get_space(build
, 1);
3173 space
= isl_space_map_from_set(space
);
3174 ma
= isl_multi_aff_identity(isl_space_copy(space
));
3175 space
= isl_space_from_domain(isl_space_domain(space
));
3176 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
3177 zero
= isl_multi_aff_zero(space
);
3178 ma
= isl_multi_aff_range_splice(ma
, depth
+ 1, zero
);
3179 build
= isl_ast_build_insert_dim(build
, depth
+ 1);
3180 list
= generate_shifted_component(executed
, build
);
3182 list
= isl_ast_graft_list_preimage_multi_aff(list
, ma
);
3184 isl_multi_val_free(mv
);
3188 isl_ast_build_free(build
);
3192 /* Generate code for a single component.
3194 * The component inverse schedule is specified as the "map" fields
3195 * of the elements of "domain" indexed by the first "n" elements of "order".
3197 * This function may modify the "set" fields of "domain".
3199 * Before proceeding with the actual code generation for the component,
3200 * we first check if there are any "shifted" strides, meaning that
3201 * the schedule domains of the individual domains are all strided,
3202 * but that they have different offsets, resulting in the union
3203 * of schedule domains not being strided anymore.
3205 * The simplest example is the schedule
3207 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3209 * Both schedule domains are strided, but their union is not.
3210 * This function detects such cases and then rewrites the schedule to
3212 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3214 * In the new schedule, the schedule domains have the same offset (modulo
3215 * the stride), ensuring that the union of schedule domains is also strided.
3218 * If there is only a single domain in the component, then there is
3219 * nothing to do. Similarly, if the current schedule dimension has
3220 * a fixed value for almost all domains then there is nothing to be done.
3221 * In particular, we need at least two domains where the current schedule
3222 * dimension does not have a fixed value.
3223 * Finally, if any of the options refer to the current schedule dimension,
3224 * then we bail out as well. It would be possible to reformulate the options
3225 * in terms of the new schedule domain, but that would introduce constraints
3226 * that separate the domains in the options and that is something we would
3230 * To see if there is any shifted stride, we look at the differences
3231 * between the values of the current dimension in pairs of domains
3232 * for equal values of outer dimensions. These differences should be
3237 * with "m" the stride and "r" a constant. Note that we cannot perform
3238 * this analysis on individual domains as the lower bound in each domain
3239 * may depend on parameters or outer dimensions and so the current dimension
3240 * itself may not have a fixed remainder on division by the stride.
3242 * In particular, we compare the first domain that does not have an
3243 * obviously fixed value for the current dimension to itself and all
3244 * other domains and collect the offsets and the gcd of the strides.
3245 * If the gcd becomes one, then we failed to find shifted strides.
3246 * If the gcd is zero, then the differences were all fixed, meaning
3247 * that some domains had non-obviously fixed values for the current dimension.
3248 * If all the offsets are the same (for those domains that do not have
3249 * an obviously fixed value for the current dimension), then we do not
3250 * apply the transformation.
3251 * If none of the domains were skipped, then there is nothing to do.
3252 * If some of them were skipped, then if we apply separation, the schedule
3253 * domain should get split in pieces with a (non-shifted) stride.
3255 * Otherwise, we apply a shift to expose the stride in
3256 * generate_shift_component.
3258 static __isl_give isl_ast_graft_list
*generate_component(
3259 struct isl_set_map_pair
*domain
, int *order
, int n
,
3260 __isl_take isl_ast_build
*build
)
3267 isl_val
*gcd
= NULL
;
3271 isl_ast_graft_list
*list
;
3274 depth
= isl_ast_build_get_depth(build
);
3277 if (skip
>= 0 && !skip
)
3278 skip
= at_most_one_non_fixed(domain
, order
, n
, depth
);
3279 if (skip
>= 0 && !skip
)
3280 skip
= isl_ast_build_options_involve_depth(build
);
3284 return generate_shifted_component_from_list(domain
,
3287 base
= eliminate_non_fixed(domain
, order
, n
, depth
, build
);
3291 ctx
= isl_ast_build_get_ctx(build
);
3293 mv
= isl_multi_val_zero(isl_space_set_alloc(ctx
, 0, n
));
3296 for (i
= 0; i
< n
; ++i
) {
3299 map
= isl_map_from_domain_and_range(
3300 isl_set_copy(domain
[order
[base
]].set
),
3301 isl_set_copy(domain
[order
[i
]].set
));
3302 for (d
= 0; d
< depth
; ++d
)
3303 map
= isl_map_equate(map
, isl_dim_in
, d
,
3305 deltas
= isl_map_deltas(map
);
3306 res
= isl_set_dim_residue_class_val(deltas
, depth
, &m
, &r
);
3307 isl_set_free(deltas
);
3314 gcd
= isl_val_gcd(gcd
, m
);
3315 if (isl_val_is_one(gcd
)) {
3319 mv
= isl_multi_val_set_val(mv
, i
, r
);
3321 res
= dim_is_fixed(domain
[order
[i
]].set
, depth
);
3327 if (fixed
&& i
> base
) {
3329 a
= isl_multi_val_get_val(mv
, i
);
3330 b
= isl_multi_val_get_val(mv
, base
);
3331 if (isl_val_ne(a
, b
))
3338 if (res
< 0 || !gcd
) {
3339 isl_ast_build_free(build
);
3341 } else if (i
< n
|| fixed
|| isl_val_is_zero(gcd
)) {
3342 list
= generate_shifted_component_from_list(domain
,
3345 list
= generate_shift_component(domain
, order
, n
, gcd
, mv
,
3350 isl_multi_val_free(mv
);
3354 isl_ast_build_free(build
);
3358 /* Store both "map" itself and its domain in the
3359 * structure pointed to by *next and advance to the next array element.
3361 static int extract_domain(__isl_take isl_map
*map
, void *user
)
3363 struct isl_set_map_pair
**next
= user
;
3365 (*next
)->map
= isl_map_copy(map
);
3366 (*next
)->set
= isl_map_domain(map
);
3372 /* Internal data for any_scheduled_after.
3374 * "depth" is the number of loops that have already been generated
3375 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3376 * "domain" is an array of set-map pairs corresponding to the different
3377 * iteration domains. The set is the schedule domain, i.e., the domain
3378 * of the inverse schedule, while the map is the inverse schedule itself.
3380 struct isl_any_scheduled_after_data
{
3382 int group_coscheduled
;
3383 struct isl_set_map_pair
*domain
;
3386 /* Is any element of domain "i" scheduled after any element of domain "j"
3387 * (for a common iteration of the first data->depth loops)?
3389 * data->domain[i].set contains the domain of the inverse schedule
3390 * for domain "i", i.e., elements in the schedule domain.
3392 * If data->group_coscheduled is set, then we also return 1 if there
3393 * is any pair of elements in the two domains that are scheduled together.
3395 static int any_scheduled_after(int i
, int j
, void *user
)
3397 struct isl_any_scheduled_after_data
*data
= user
;
3398 int dim
= isl_set_dim(data
->domain
[i
].set
, isl_dim_set
);
3401 for (pos
= data
->depth
; pos
< dim
; ++pos
) {
3404 follows
= isl_set_follows_at(data
->domain
[i
].set
,
3405 data
->domain
[j
].set
, pos
);
3415 return data
->group_coscheduled
;
3418 /* Look for independent components at the current depth and generate code
3419 * for each component separately. The resulting lists of grafts are
3420 * merged in an attempt to combine grafts with identical guards.
3422 * Code for two domains can be generated separately if all the elements
3423 * of one domain are scheduled before (or together with) all the elements
3424 * of the other domain. We therefore consider the graph with as nodes
3425 * the domains and an edge between two nodes if any element of the first
3426 * node is scheduled after any element of the second node.
3427 * If the ast_build_group_coscheduled is set, then we also add an edge if
3428 * there is any pair of elements in the two domains that are scheduled
3430 * Code is then generated (by generate_component)
3431 * for each of the strongly connected components in this graph
3432 * in their topological order.
3434 * Since the test is performed on the domain of the inverse schedules of
3435 * the different domains, we precompute these domains and store
3436 * them in data.domain.
3438 static __isl_give isl_ast_graft_list
*generate_components(
3439 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3442 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3443 int n
= isl_union_map_n_map(executed
);
3444 struct isl_any_scheduled_after_data data
;
3445 struct isl_set_map_pair
*next
;
3446 struct isl_tarjan_graph
*g
= NULL
;
3447 isl_ast_graft_list
*list
= NULL
;
3450 data
.domain
= isl_calloc_array(ctx
, struct isl_set_map_pair
, n
);
3456 if (isl_union_map_foreach_map(executed
, &extract_domain
, &next
) < 0)
3461 data
.depth
= isl_ast_build_get_depth(build
);
3462 data
.group_coscheduled
= isl_options_get_ast_build_group_coscheduled(ctx
);
3463 g
= isl_tarjan_graph_init(ctx
, n
, &any_scheduled_after
, &data
);
3467 list
= isl_ast_graft_list_alloc(ctx
, 0);
3471 isl_ast_graft_list
*list_c
;
3474 if (g
->order
[i
] == -1)
3475 isl_die(ctx
, isl_error_internal
, "cannot happen",
3478 while (g
->order
[i
] != -1) {
3482 list_c
= generate_component(data
.domain
,
3483 g
->order
+ first
, i
- first
,
3484 isl_ast_build_copy(build
));
3485 list
= isl_ast_graft_list_merge(list
, list_c
, build
);
3491 error
: list
= isl_ast_graft_list_free(list
);
3492 isl_tarjan_graph_free(g
);
3493 for (i
= 0; i
< n_domain
; ++i
) {
3494 isl_map_free(data
.domain
[i
].map
);
3495 isl_set_free(data
.domain
[i
].set
);
3498 isl_union_map_free(executed
);
3499 isl_ast_build_free(build
);
3504 /* Generate code for the next level (and all inner levels).
3506 * If "executed" is empty, i.e., no code needs to be generated,
3507 * then we return an empty list.
3509 * If we have already generated code for all loop levels, then we pass
3510 * control to generate_inner_level.
3512 * If "executed" lives in a single space, i.e., if code needs to be
3513 * generated for a single domain, then there can only be a single
3514 * component and we go directly to generate_shifted_component.
3515 * Otherwise, we call generate_components to detect the components
3516 * and to call generate_component on each of them separately.
3518 static __isl_give isl_ast_graft_list
*generate_next_level(
3519 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3523 if (!build
|| !executed
)
3526 if (isl_union_map_is_empty(executed
)) {
3527 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3528 isl_union_map_free(executed
);
3529 isl_ast_build_free(build
);
3530 return isl_ast_graft_list_alloc(ctx
, 0);
3533 depth
= isl_ast_build_get_depth(build
);
3534 if (depth
>= isl_ast_build_dim(build
, isl_dim_set
))
3535 return generate_inner_level(executed
, build
);
3537 if (isl_union_map_n_map(executed
) == 1)
3538 return generate_shifted_component(executed
, build
);
3540 return generate_components(executed
, build
);
3542 isl_union_map_free(executed
);
3543 isl_ast_build_free(build
);
3547 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3548 * internal, executed and build are the inputs to generate_code.
3549 * list collects the output.
3551 struct isl_generate_code_data
{
3553 isl_union_map
*executed
;
3554 isl_ast_build
*build
;
3556 isl_ast_graft_list
*list
;
3559 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3563 * with E the external build schedule and S the additional schedule "space",
3564 * reformulate the inverse schedule in terms of the internal schedule domain,
3569 * We first obtain a mapping
3573 * take the inverse and the product with S -> S, resulting in
3575 * [I -> S] -> [E -> S]
3577 * Applying the map to the input produces the desired result.
3579 static __isl_give isl_union_map
*internal_executed(
3580 __isl_take isl_union_map
*executed
, __isl_keep isl_space
*space
,
3581 __isl_keep isl_ast_build
*build
)
3585 proj
= isl_ast_build_get_schedule_map(build
);
3586 proj
= isl_map_reverse(proj
);
3587 space
= isl_space_map_from_set(isl_space_copy(space
));
3588 id
= isl_map_identity(space
);
3589 proj
= isl_map_product(proj
, id
);
3590 executed
= isl_union_map_apply_domain(executed
,
3591 isl_union_map_from_map(proj
));
3595 /* Generate an AST that visits the elements in the range of data->executed
3596 * in the relative order specified by the corresponding domain element(s)
3597 * for those domain elements that belong to "set".
3598 * Add the result to data->list.
3600 * The caller ensures that "set" is a universe domain.
3601 * "space" is the space of the additional part of the schedule.
3602 * It is equal to the space of "set" if build->domain is parametric.
3603 * Otherwise, it is equal to the range of the wrapped space of "set".
3605 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3606 * was called from an outside user (data->internal not set), then
3607 * the (inverse) schedule refers to the external build domain and needs to
3608 * be transformed to refer to the internal build domain.
3610 * If the build space is parametric, then we add some of the parameter
3611 * constraints to the executed relation. Adding these constraints
3612 * allows for an earlier detection of conflicts in some cases.
3613 * However, we do not want to divide the executed relation into
3614 * more disjuncts than necessary. We therefore approximate
3615 * the constraints on the parameters by a single disjunct set.
3617 * The build is extended to include the additional part of the schedule.
3618 * If the original build space was not parametric, then the options
3619 * in data->build refer only to the additional part of the schedule
3620 * and they need to be adjusted to refer to the complete AST build
3623 * After having adjusted inverse schedule and build, we start generating
3624 * code with the outer loop of the current code generation
3625 * in generate_next_level.
3627 * If the original build space was not parametric, we undo the embedding
3628 * on the resulting isl_ast_node_list so that it can be used within
3629 * the outer AST build.
3631 static int generate_code_in_space(struct isl_generate_code_data
*data
,
3632 __isl_take isl_set
*set
, __isl_take isl_space
*space
)
3634 isl_union_map
*executed
;
3635 isl_ast_build
*build
;
3636 isl_ast_graft_list
*list
;
3639 executed
= isl_union_map_copy(data
->executed
);
3640 executed
= isl_union_map_intersect_domain(executed
,
3641 isl_union_set_from_set(set
));
3643 embed
= !isl_set_is_params(data
->build
->domain
);
3644 if (embed
&& !data
->internal
)
3645 executed
= internal_executed(executed
, space
, data
->build
);
3648 domain
= isl_ast_build_get_domain(data
->build
);
3649 domain
= isl_set_from_basic_set(isl_set_simple_hull(domain
));
3650 executed
= isl_union_map_intersect_params(executed
, domain
);
3653 build
= isl_ast_build_copy(data
->build
);
3654 build
= isl_ast_build_product(build
, space
);
3656 list
= generate_next_level(executed
, build
);
3658 list
= isl_ast_graft_list_unembed(list
, embed
);
3660 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
3665 /* Generate an AST that visits the elements in the range of data->executed
3666 * in the relative order specified by the corresponding domain element(s)
3667 * for those domain elements that belong to "set".
3668 * Add the result to data->list.
3670 * The caller ensures that "set" is a universe domain.
3672 * If the build space S is not parametric, then the space of "set"
3673 * need to be a wrapped relation with S as domain. That is, it needs
3678 * Check this property and pass control to generate_code_in_space
3680 * If the build space is not parametric, then T is the space of "set".
3682 static int generate_code_set(__isl_take isl_set
*set
, void *user
)
3684 struct isl_generate_code_data
*data
= user
;
3685 isl_space
*space
, *build_space
;
3688 space
= isl_set_get_space(set
);
3690 if (isl_set_is_params(data
->build
->domain
))
3691 return generate_code_in_space(data
, set
, space
);
3693 build_space
= isl_ast_build_get_space(data
->build
, data
->internal
);
3694 space
= isl_space_unwrap(space
);
3695 is_domain
= isl_space_is_domain(build_space
, space
);
3696 isl_space_free(build_space
);
3697 space
= isl_space_range(space
);
3702 isl_die(isl_set_get_ctx(set
), isl_error_invalid
,
3703 "invalid nested schedule space", goto error
);
3705 return generate_code_in_space(data
, set
, space
);
3708 isl_space_free(space
);
3712 /* Generate an AST that visits the elements in the range of "executed"
3713 * in the relative order specified by the corresponding domain element(s).
3715 * "build" is an isl_ast_build that has either been constructed by
3716 * isl_ast_build_from_context or passed to a callback set by
3717 * isl_ast_build_set_create_leaf.
3718 * In the first case, the space of the isl_ast_build is typically
3719 * a parametric space, although this is currently not enforced.
3720 * In the second case, the space is never a parametric space.
3721 * If the space S is not parametric, then the domain space(s) of "executed"
3722 * need to be wrapped relations with S as domain.
3724 * If the domain of "executed" consists of several spaces, then an AST
3725 * is generated for each of them (in arbitrary order) and the results
3728 * If "internal" is set, then the domain "S" above refers to the internal
3729 * schedule domain representation. Otherwise, it refers to the external
3730 * representation, as returned by isl_ast_build_get_schedule_space.
3732 * We essentially run over all the spaces in the domain of "executed"
3733 * and call generate_code_set on each of them.
3735 static __isl_give isl_ast_graft_list
*generate_code(
3736 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
3740 struct isl_generate_code_data data
= { 0 };
3742 isl_union_set
*schedule_domain
;
3743 isl_union_map
*universe
;
3747 space
= isl_ast_build_get_space(build
, 1);
3748 space
= isl_space_align_params(space
,
3749 isl_union_map_get_space(executed
));
3750 space
= isl_space_align_params(space
,
3751 isl_union_map_get_space(build
->options
));
3752 build
= isl_ast_build_align_params(build
, isl_space_copy(space
));
3753 executed
= isl_union_map_align_params(executed
, space
);
3754 if (!executed
|| !build
)
3757 ctx
= isl_ast_build_get_ctx(build
);
3759 data
.internal
= internal
;
3760 data
.executed
= executed
;
3762 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
3764 universe
= isl_union_map_universe(isl_union_map_copy(executed
));
3765 schedule_domain
= isl_union_map_domain(universe
);
3766 if (isl_union_set_foreach_set(schedule_domain
, &generate_code_set
,
3768 data
.list
= isl_ast_graft_list_free(data
.list
);
3770 isl_union_set_free(schedule_domain
);
3771 isl_union_map_free(executed
);
3773 isl_ast_build_free(build
);
3776 isl_union_map_free(executed
);
3777 isl_ast_build_free(build
);
3781 /* Generate an AST that visits the elements in the domain of "schedule"
3782 * in the relative order specified by the corresponding image element(s).
3784 * "build" is an isl_ast_build that has either been constructed by
3785 * isl_ast_build_from_context or passed to a callback set by
3786 * isl_ast_build_set_create_leaf.
3787 * In the first case, the space of the isl_ast_build is typically
3788 * a parametric space, although this is currently not enforced.
3789 * In the second case, the space is never a parametric space.
3790 * If the space S is not parametric, then the range space(s) of "schedule"
3791 * need to be wrapped relations with S as domain.
3793 * If the range of "schedule" consists of several spaces, then an AST
3794 * is generated for each of them (in arbitrary order) and the results
3797 * We first initialize the local copies of the relevant options.
3798 * We do this here rather than when the isl_ast_build is created
3799 * because the options may have changed between the construction
3800 * of the isl_ast_build and the call to isl_generate_code.
3802 * The main computation is performed on an inverse schedule (with
3803 * the schedule domain in the domain and the elements to be executed
3804 * in the range) called "executed".
3806 __isl_give isl_ast_node
*isl_ast_build_ast_from_schedule(
3807 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
3809 isl_ast_graft_list
*list
;
3811 isl_union_map
*executed
;
3813 build
= isl_ast_build_copy(build
);
3814 build
= isl_ast_build_set_single_valued(build
, 0);
3815 schedule
= isl_union_map_coalesce(schedule
);
3816 executed
= isl_union_map_reverse(schedule
);
3817 list
= generate_code(executed
, isl_ast_build_copy(build
), 0);
3818 node
= isl_ast_node_from_graft_list(list
, build
);
3819 isl_ast_build_free(build
);