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 if (isl_ast_build_has_stride(build
, depth
)) {
571 stride
= isl_ast_build_get_stride_constraint(build
);
572 dom
= isl_set_intersect(dom
, stride
);
574 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
575 dom
= isl_ast_build_compute_gist(build
, dom
);
577 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
582 /* Update "graft" based on "bounds" for the eliminated case.
584 * In the eliminated case, no for node is created, so we only need
585 * to check if "bounds" imply any guards that need to be inserted.
587 static __isl_give isl_ast_graft
*refine_eliminated(
588 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
589 __isl_keep isl_ast_build
*build
)
591 return add_degenerate_guard(graft
, bounds
, build
);
594 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
596 * "build" is the build in which graft->node was created
597 * "sub_build" contains information about the current level itself,
598 * including the single value attained.
600 * We first set the initialization part of the for loop to the single
601 * value attained by the current dimension.
602 * The increment and condition are not strictly needed as the are known
603 * to be "1" and "iterator <= value" respectively.
604 * Then we check if "bounds" imply any guards that need to be inserted.
606 static __isl_give isl_ast_graft
*refine_degenerate(
607 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
608 __isl_keep isl_ast_build
*build
,
609 __isl_keep isl_ast_build
*sub_build
)
613 if (!graft
|| !sub_build
)
614 return isl_ast_graft_free(graft
);
616 value
= isl_pw_aff_copy(sub_build
->value
);
618 graft
->node
->u
.f
.init
= isl_ast_build_expr_from_pw_aff_internal(build
,
620 if (!graft
->node
->u
.f
.init
)
621 return isl_ast_graft_free(graft
);
623 graft
= add_degenerate_guard(graft
, bounds
, build
);
628 /* Return the intersection of constraints in "list" as a set.
630 static __isl_give isl_set
*intersect_constraints(
631 __isl_keep isl_constraint_list
*list
)
636 n
= isl_constraint_list_n_constraint(list
);
638 isl_die(isl_constraint_list_get_ctx(list
), isl_error_internal
,
639 "expecting at least one constraint", return NULL
);
641 bset
= isl_basic_set_from_constraint(
642 isl_constraint_list_get_constraint(list
, 0));
643 for (i
= 1; i
< n
; ++i
) {
644 isl_basic_set
*bset_i
;
646 bset_i
= isl_basic_set_from_constraint(
647 isl_constraint_list_get_constraint(list
, i
));
648 bset
= isl_basic_set_intersect(bset
, bset_i
);
651 return isl_set_from_basic_set(bset
);
654 /* Compute the constraints on the outer dimensions enforced by
655 * graft->node and add those constraints to graft->enforced,
656 * in case the upper bound is expressed as a set "upper".
658 * In particular, if l(...) is a lower bound in "lower", and
660 * -a i + f(...) >= 0 or a i <= f(...)
662 * is an upper bound ocnstraint on the current dimension i,
663 * then the for loop enforces the constraint
665 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
667 * We therefore simply take each lower bound in turn, plug it into
668 * the upper bounds and compute the intersection over all lower bounds.
670 * If a lower bound is a rational expression, then
671 * isl_basic_set_preimage_multi_aff will force this rational
672 * expression to have only integer values. However, the loop
673 * itself does not enforce this integrality constraint. We therefore
674 * use the ceil of the lower bounds instead of the lower bounds themselves.
675 * Other constraints will make sure that the for loop is only executed
676 * when each of the lower bounds attains an integral value.
677 * In particular, potentially rational values only occur in
678 * lower_bound if the offset is a (seemingly) rational expression,
679 * but then outer conditions will make sure that this rational expression
680 * only attains integer values.
682 static __isl_give isl_ast_graft
*set_enforced_from_set(
683 __isl_take isl_ast_graft
*graft
,
684 __isl_keep isl_pw_aff_list
*lower
, int pos
, __isl_keep isl_set
*upper
)
687 isl_basic_set
*enforced
;
688 isl_pw_multi_aff
*pma
;
691 if (!graft
|| !lower
)
692 return isl_ast_graft_free(graft
);
694 space
= isl_set_get_space(upper
);
695 enforced
= isl_basic_set_universe(isl_space_copy(space
));
697 space
= isl_space_map_from_set(space
);
698 pma
= isl_pw_multi_aff_identity(space
);
700 n
= isl_pw_aff_list_n_pw_aff(lower
);
701 for (i
= 0; i
< n
; ++i
) {
705 isl_pw_multi_aff
*pma_i
;
707 pa
= isl_pw_aff_list_get_pw_aff(lower
, i
);
708 pa
= isl_pw_aff_ceil(pa
);
709 pma_i
= isl_pw_multi_aff_copy(pma
);
710 pma_i
= isl_pw_multi_aff_set_pw_aff(pma_i
, pos
, pa
);
711 enforced_i
= isl_set_copy(upper
);
712 enforced_i
= isl_set_preimage_pw_multi_aff(enforced_i
, pma_i
);
713 hull
= isl_set_simple_hull(enforced_i
);
714 enforced
= isl_basic_set_intersect(enforced
, hull
);
717 isl_pw_multi_aff_free(pma
);
719 graft
= isl_ast_graft_enforce(graft
, enforced
);
724 /* Compute the constraints on the outer dimensions enforced by
725 * graft->node and add those constraints to graft->enforced,
726 * in case the upper bound is expressed as
727 * a list of affine expressions "upper".
729 * The enforced condition is that each lower bound expression is less
730 * than or equal to each upper bound expression.
732 static __isl_give isl_ast_graft
*set_enforced_from_list(
733 __isl_take isl_ast_graft
*graft
,
734 __isl_keep isl_pw_aff_list
*lower
, __isl_keep isl_pw_aff_list
*upper
)
737 isl_basic_set
*enforced
;
739 lower
= isl_pw_aff_list_copy(lower
);
740 upper
= isl_pw_aff_list_copy(upper
);
741 cond
= isl_pw_aff_list_le_set(lower
, upper
);
742 enforced
= isl_set_simple_hull(cond
);
743 graft
= isl_ast_graft_enforce(graft
, enforced
);
748 /* Does "aff" have a negative constant term?
750 static int aff_constant_is_negative(__isl_take isl_set
*set
,
751 __isl_take isl_aff
*aff
, void *user
)
756 v
= isl_aff_get_constant_val(aff
);
757 *neg
= isl_val_is_neg(v
);
762 return *neg
? 0 : -1;
765 /* Does "pa" have a negative constant term over its entire domain?
767 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff
*pa
, void *user
)
772 r
= isl_pw_aff_foreach_piece(pa
, &aff_constant_is_negative
, user
);
775 return *neg
? 0 : -1;
778 /* Does each element in "list" have a negative constant term?
780 * The callback terminates the iteration as soon an element has been
781 * found that does not have a negative constant term.
783 static int list_constant_is_negative(__isl_keep isl_pw_aff_list
*list
)
787 if (isl_pw_aff_list_foreach(list
,
788 &pw_aff_constant_is_negative
, &neg
) < 0 && neg
)
794 /* Add 1 to each of the elements in "list", where each of these elements
795 * is defined over the internal schedule space of "build".
797 static __isl_give isl_pw_aff_list
*list_add_one(
798 __isl_take isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
805 space
= isl_ast_build_get_space(build
, 1);
806 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(space
));
807 aff
= isl_aff_add_constant_si(aff
, 1);
808 one
= isl_pw_aff_from_aff(aff
);
810 n
= isl_pw_aff_list_n_pw_aff(list
);
811 for (i
= 0; i
< n
; ++i
) {
813 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
814 pa
= isl_pw_aff_add(pa
, isl_pw_aff_copy(one
));
815 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
818 isl_pw_aff_free(one
);
823 /* Set the condition part of the for node graft->node in case
824 * the upper bound is represented as a list of piecewise affine expressions.
826 * In particular, set the condition to
828 * iterator <= min(list of upper bounds)
830 * If each of the upper bounds has a negative constant term, then
831 * set the condition to
833 * iterator < min(list of (upper bound + 1)s)
836 static __isl_give isl_ast_graft
*set_for_cond_from_list(
837 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*list
,
838 __isl_keep isl_ast_build
*build
)
841 isl_ast_expr
*bound
, *iterator
, *cond
;
842 enum isl_ast_op_type type
= isl_ast_op_le
;
845 return isl_ast_graft_free(graft
);
847 neg
= list_constant_is_negative(list
);
849 return isl_ast_graft_free(graft
);
850 list
= isl_pw_aff_list_copy(list
);
852 list
= list_add_one(list
, build
);
853 type
= isl_ast_op_lt
;
856 bound
= reduce_list(isl_ast_op_min
, list
, build
);
857 iterator
= isl_ast_expr_copy(graft
->node
->u
.f
.iterator
);
858 cond
= isl_ast_expr_alloc_binary(type
, iterator
, bound
);
859 graft
->node
->u
.f
.cond
= cond
;
861 isl_pw_aff_list_free(list
);
862 if (!graft
->node
->u
.f
.cond
)
863 return isl_ast_graft_free(graft
);
867 /* Set the condition part of the for node graft->node in case
868 * the upper bound is represented as a set.
870 static __isl_give isl_ast_graft
*set_for_cond_from_set(
871 __isl_take isl_ast_graft
*graft
, __isl_keep isl_set
*set
,
872 __isl_keep isl_ast_build
*build
)
879 cond
= isl_ast_build_expr_from_set(build
, isl_set_copy(set
));
880 graft
->node
->u
.f
.cond
= cond
;
881 if (!graft
->node
->u
.f
.cond
)
882 return isl_ast_graft_free(graft
);
886 /* Construct an isl_ast_expr for the increment (i.e., stride) of
887 * the current dimension.
889 static __isl_give isl_ast_expr
*for_inc(__isl_keep isl_ast_build
*build
)
897 ctx
= isl_ast_build_get_ctx(build
);
898 depth
= isl_ast_build_get_depth(build
);
900 if (!isl_ast_build_has_stride(build
, depth
))
901 return isl_ast_expr_alloc_int_si(ctx
, 1);
903 v
= isl_ast_build_get_stride(build
, depth
);
904 return isl_ast_expr_from_val(v
);
907 /* Should we express the loop condition as
909 * iterator <= min(list of upper bounds)
911 * or as a conjunction of constraints?
913 * The first is constructed from a list of upper bounds.
914 * The second is constructed from a set.
916 * If there are no upper bounds in "constraints", then this could mean
917 * that "domain" simply doesn't have an upper bound or that we didn't
918 * pick any upper bound. In the first case, we want to generate the
919 * loop condition as a(n empty) conjunction of constraints
920 * In the second case, we will compute
921 * a single upper bound from "domain" and so we use the list form.
923 * If there are upper bounds in "constraints",
924 * then we use the list form iff the atomic_upper_bound option is set.
926 static int use_upper_bound_list(isl_ctx
*ctx
, int n_upper
,
927 __isl_keep isl_set
*domain
, int depth
)
930 return isl_options_get_ast_build_atomic_upper_bound(ctx
);
932 return isl_set_dim_has_upper_bound(domain
, isl_dim_set
, depth
);
935 /* Fill in the expressions of the for node in graft->node.
938 * - set the initialization part of the loop to the maximum of the lower bounds
939 * - extract the increment from the stride of the current dimension
940 * - construct the for condition either based on a list of upper bounds
941 * or on a set of upper bound constraints.
943 static __isl_give isl_ast_graft
*set_for_node_expressions(
944 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*lower
,
945 int use_list
, __isl_keep isl_pw_aff_list
*upper_list
,
946 __isl_keep isl_set
*upper_set
, __isl_keep isl_ast_build
*build
)
953 build
= isl_ast_build_copy(build
);
954 build
= isl_ast_build_set_enforced(build
,
955 isl_ast_graft_get_enforced(graft
));
958 node
->u
.f
.init
= reduce_list(isl_ast_op_max
, lower
, build
);
959 node
->u
.f
.inc
= for_inc(build
);
962 graft
= set_for_cond_from_list(graft
, upper_list
, build
);
964 graft
= set_for_cond_from_set(graft
, upper_set
, build
);
966 isl_ast_build_free(build
);
968 if (!node
->u
.f
.iterator
|| !node
->u
.f
.init
||
969 !node
->u
.f
.cond
|| !node
->u
.f
.inc
)
970 return isl_ast_graft_free(graft
);
975 /* Update "graft" based on "bounds" and "domain" for the generic,
976 * non-degenerate, case.
978 * "c_lower" and "c_upper" contain the lower and upper bounds
979 * that the loop node should express.
980 * "domain" is the subset of the intersection of the constraints
981 * for which some code is executed.
983 * There may be zero lower bounds or zero upper bounds in "constraints"
984 * in case the list of constraints was created
985 * based on the atomic option or based on separation with explicit bounds.
986 * In that case, we use "domain" to derive lower and/or upper bounds.
988 * We first compute a list of one or more lower bounds.
990 * Then we decide if we want to express the condition as
992 * iterator <= min(list of upper bounds)
994 * or as a conjunction of constraints.
996 * The set of enforced constraints is then computed either based on
997 * a list of upper bounds or on a set of upper bound constraints.
998 * We do not compute any enforced constraints if we were forced
999 * to compute a lower or upper bound using exact_bound. The domains
1000 * of the resulting expressions may imply some bounds on outer dimensions
1001 * that we do not want to appear in the enforced constraints since
1002 * they are not actually enforced by the corresponding code.
1004 * Finally, we fill in the expressions of the for node.
1006 static __isl_give isl_ast_graft
*refine_generic_bounds(
1007 __isl_take isl_ast_graft
*graft
,
1008 __isl_take isl_constraint_list
*c_lower
,
1009 __isl_take isl_constraint_list
*c_upper
,
1010 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1014 isl_pw_aff_list
*lower
;
1016 isl_set
*upper_set
= NULL
;
1017 isl_pw_aff_list
*upper_list
= NULL
;
1018 int n_lower
, n_upper
;
1020 if (!graft
|| !c_lower
|| !c_upper
|| !build
)
1023 depth
= isl_ast_build_get_depth(build
);
1024 ctx
= isl_ast_graft_get_ctx(graft
);
1026 n_lower
= isl_constraint_list_n_constraint(c_lower
);
1027 n_upper
= isl_constraint_list_n_constraint(c_upper
);
1029 use_list
= use_upper_bound_list(ctx
, n_upper
, domain
, depth
);
1031 lower
= lower_bounds(c_lower
, depth
, domain
, build
);
1034 upper_list
= upper_bounds(c_upper
, depth
, domain
, build
);
1035 else if (n_upper
> 0)
1036 upper_set
= intersect_constraints(c_upper
);
1038 upper_set
= isl_set_universe(isl_set_get_space(domain
));
1040 if (n_lower
== 0 || n_upper
== 0)
1043 graft
= set_enforced_from_list(graft
, lower
, upper_list
);
1045 graft
= set_enforced_from_set(graft
, lower
, depth
, upper_set
);
1047 graft
= set_for_node_expressions(graft
, lower
, use_list
, upper_list
,
1050 isl_pw_aff_list_free(lower
);
1051 isl_pw_aff_list_free(upper_list
);
1052 isl_set_free(upper_set
);
1053 isl_constraint_list_free(c_lower
);
1054 isl_constraint_list_free(c_upper
);
1058 isl_constraint_list_free(c_lower
);
1059 isl_constraint_list_free(c_upper
);
1060 return isl_ast_graft_free(graft
);
1063 /* Internal data structure used inside count_constraints to keep
1064 * track of the number of constraints that are independent of dimension "pos",
1065 * the lower bounds in "pos" and the upper bounds in "pos".
1067 struct isl_ast_count_constraints_data
{
1075 /* Increment data->n_indep, data->lower or data->upper depending
1076 * on whether "c" is independenct of dimensions data->pos,
1077 * a lower bound or an upper bound.
1079 static int count_constraints(__isl_take isl_constraint
*c
, void *user
)
1081 struct isl_ast_count_constraints_data
*data
= user
;
1083 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->pos
))
1085 else if (isl_constraint_is_upper_bound(c
, isl_dim_set
, data
->pos
))
1090 isl_constraint_free(c
);
1095 /* Update "graft" based on "bounds" and "domain" for the generic,
1096 * non-degenerate, case.
1098 * "list" respresent the list of bounds that need to be encoded by
1099 * the for loop (or a guard around the for loop).
1100 * "domain" is the subset of the intersection of the constraints
1101 * for which some code is executed.
1102 * "build" is the build in which graft->node was created.
1104 * We separate lower bounds, upper bounds and constraints that
1105 * are independent of the loop iterator.
1107 * The actual for loop bounds are generated in refine_generic_bounds.
1108 * If there are any constraints that are independent of the loop iterator,
1109 * we need to put a guard around the for loop (which may get hoisted up
1110 * to higher levels) and we call refine_generic_bounds in a build
1111 * where this guard is enforced.
1113 static __isl_give isl_ast_graft
*refine_generic_split(
1114 __isl_take isl_ast_graft
*graft
, __isl_take isl_constraint_list
*list
,
1115 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1117 isl_ast_build
*for_build
;
1119 struct isl_ast_count_constraints_data data
;
1120 isl_constraint_list
*lower
;
1121 isl_constraint_list
*upper
;
1124 return isl_ast_graft_free(graft
);
1126 data
.pos
= isl_ast_build_get_depth(build
);
1128 list
= isl_constraint_list_sort(list
, &cmp_constraint
, &data
.pos
);
1130 return isl_ast_graft_free(graft
);
1132 data
.n_indep
= data
.n_lower
= data
.n_upper
= 0;
1133 if (isl_constraint_list_foreach(list
, &count_constraints
, &data
) < 0) {
1134 isl_constraint_list_free(list
);
1135 return isl_ast_graft_free(graft
);
1138 lower
= isl_constraint_list_copy(list
);
1139 lower
= isl_constraint_list_drop(lower
, 0, data
.n_indep
);
1140 upper
= isl_constraint_list_copy(lower
);
1141 lower
= isl_constraint_list_drop(lower
, data
.n_lower
, data
.n_upper
);
1142 upper
= isl_constraint_list_drop(upper
, 0, data
.n_lower
);
1144 if (data
.n_indep
== 0) {
1145 isl_constraint_list_free(list
);
1146 return refine_generic_bounds(graft
, lower
, upper
,
1150 list
= isl_constraint_list_drop(list
, data
.n_indep
,
1151 data
.n_lower
+ data
.n_upper
);
1152 guard
= intersect_constraints(list
);
1153 isl_constraint_list_free(list
);
1155 for_build
= isl_ast_build_copy(build
);
1156 for_build
= isl_ast_build_restrict_pending(for_build
,
1157 isl_set_copy(guard
));
1158 graft
= refine_generic_bounds(graft
, lower
, upper
, domain
, for_build
);
1159 isl_ast_build_free(for_build
);
1161 graft
= isl_ast_graft_add_guard(graft
, guard
, build
);
1166 /* Add the guard implied by the current stride constraint (if any),
1167 * but not (necessarily) enforced by the generated AST to "graft".
1169 static __isl_give isl_ast_graft
*add_stride_guard(
1170 __isl_take isl_ast_graft
*graft
, __isl_keep isl_ast_build
*build
)
1175 depth
= isl_ast_build_get_depth(build
);
1176 if (!isl_ast_build_has_stride(build
, depth
))
1179 dom
= isl_ast_build_get_stride_constraint(build
);
1180 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
1181 dom
= isl_ast_build_compute_gist(build
, dom
);
1183 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
1188 /* Update "graft" based on "bounds" and "domain" for the generic,
1189 * non-degenerate, case.
1191 * "bounds" respresent the bounds that need to be encoded by
1192 * the for loop (or a guard around the for loop).
1193 * "domain" is the subset of "bounds" for which some code is executed.
1194 * "build" is the build in which graft->node was created.
1196 * We break up "bounds" into a list of constraints and continue with
1197 * refine_generic_split.
1199 static __isl_give isl_ast_graft
*refine_generic(
1200 __isl_take isl_ast_graft
*graft
,
1201 __isl_keep isl_basic_set
*bounds
, __isl_keep isl_set
*domain
,
1202 __isl_keep isl_ast_build
*build
)
1204 isl_constraint_list
*list
;
1206 if (!build
|| !graft
)
1207 return isl_ast_graft_free(graft
);
1209 bounds
= isl_basic_set_copy(bounds
);
1210 bounds
= isl_ast_build_compute_gist_basic_set(build
, bounds
);
1211 list
= isl_basic_set_get_constraint_list(bounds
);
1212 isl_basic_set_free(bounds
);
1214 graft
= refine_generic_split(graft
, list
, domain
, build
);
1215 graft
= add_stride_guard(graft
, build
);
1220 /* Create a for node for the current level.
1222 * Mark the for node degenerate if "degenerate" is set.
1224 static __isl_give isl_ast_node
*create_for(__isl_keep isl_ast_build
*build
,
1234 depth
= isl_ast_build_get_depth(build
);
1235 id
= isl_ast_build_get_iterator_id(build
, depth
);
1236 node
= isl_ast_node_alloc_for(id
);
1238 node
= isl_ast_node_for_mark_degenerate(node
);
1243 /* Create an AST node for the current dimension based on
1244 * the schedule domain "bounds" and return the node encapsulated
1245 * in an isl_ast_graft.
1247 * "executed" is the current inverse schedule, taking into account
1248 * the bounds in "bounds"
1249 * "domain" is the domain of "executed", with inner dimensions projected out.
1250 * It may be a strict subset of "bounds" in case "bounds" was created
1251 * based on the atomic option or based on separation with explicit bounds.
1253 * "domain" may satisfy additional equalities that result
1254 * from intersecting "executed" with "bounds" in add_node.
1255 * It may also satisfy some global constraints that were dropped out because
1256 * we performed separation with explicit bounds.
1257 * The very first step is then to copy these constraints to "bounds".
1259 * Since we may be calling before_each_for and after_each_for
1260 * callbacks, we record the current inverse schedule in the build.
1262 * We consider three builds,
1263 * "build" is the one in which the current level is created,
1264 * "body_build" is the build in which the next level is created,
1265 * "sub_build" is essentially the same as "body_build", except that
1266 * the depth has not been increased yet.
1268 * "build" already contains information (in strides and offsets)
1269 * about the strides at the current level, but this information is not
1270 * reflected in the build->domain.
1271 * We first add this information and the "bounds" to the sub_build->domain.
1272 * isl_ast_build_set_loop_bounds checks whether the current dimension attains
1273 * only a single value and whether this single value can be represented using
1274 * a single affine expression.
1275 * In the first case, the current level is considered "degenerate".
1276 * In the second, sub-case, the current level is considered "eliminated".
1277 * Eliminated levels don't need to be reflected in the AST since we can
1278 * simply plug in the affine expression. For degenerate, but non-eliminated,
1279 * levels, we do introduce a for node, but mark is as degenerate so that
1280 * it can be printed as an assignment of the single value to the loop
1283 * If the current level is eliminated, we explicitly plug in the value
1284 * for the current level found by isl_ast_build_set_loop_bounds in the
1285 * inverse schedule. This ensures that if we are working on a slice
1286 * of the domain based on information available in the inverse schedule
1287 * and the build domain, that then this information is also reflected
1288 * in the inverse schedule. This operation also eliminates the current
1289 * dimension from the inverse schedule making sure no inner dimensions depend
1290 * on the current dimension. Otherwise, we create a for node, marking
1291 * it degenerate if appropriate. The initial for node is still incomplete
1292 * and will be completed in either refine_degenerate or refine_generic.
1294 * We then generate a sequence of grafts for the next level,
1295 * create a surrounding graft for the current level and insert
1296 * the for node we created (if the current level is not eliminated).
1298 * Finally, we set the bounds of the for loop and insert guards
1299 * (either in the AST or in the graft) in one of
1300 * refine_eliminated, refine_degenerate or refine_generic.
1302 static __isl_give isl_ast_graft
*create_node_scaled(
1303 __isl_take isl_union_map
*executed
,
1304 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1305 __isl_take isl_ast_build
*build
)
1308 int degenerate
, eliminated
;
1309 isl_basic_set
*hull
;
1310 isl_ast_node
*node
= NULL
;
1311 isl_ast_graft
*graft
;
1312 isl_ast_graft_list
*children
;
1313 isl_ast_build
*sub_build
;
1314 isl_ast_build
*body_build
;
1316 domain
= isl_ast_build_eliminate_divs(build
, domain
);
1317 domain
= isl_set_detect_equalities(domain
);
1318 hull
= isl_set_unshifted_simple_hull(isl_set_copy(domain
));
1319 bounds
= isl_basic_set_intersect(bounds
, hull
);
1320 build
= isl_ast_build_set_executed(build
, isl_union_map_copy(executed
));
1322 depth
= isl_ast_build_get_depth(build
);
1323 sub_build
= isl_ast_build_copy(build
);
1324 sub_build
= isl_ast_build_include_stride(sub_build
);
1325 sub_build
= isl_ast_build_set_loop_bounds(sub_build
,
1326 isl_basic_set_copy(bounds
));
1327 degenerate
= isl_ast_build_has_value(sub_build
);
1328 eliminated
= isl_ast_build_has_affine_value(sub_build
, depth
);
1329 if (degenerate
< 0 || eliminated
< 0)
1330 executed
= isl_union_map_free(executed
);
1332 executed
= plug_in_values(executed
, sub_build
);
1334 node
= create_for(build
, degenerate
);
1336 body_build
= isl_ast_build_copy(sub_build
);
1337 body_build
= isl_ast_build_increase_depth(body_build
);
1339 node
= before_each_for(node
, body_build
);
1340 children
= generate_next_level(executed
,
1341 isl_ast_build_copy(body_build
));
1343 graft
= isl_ast_graft_alloc_level(children
, build
, sub_build
);
1345 graft
= isl_ast_graft_insert_for(graft
, node
);
1347 graft
= refine_eliminated(graft
, bounds
, build
);
1348 else if (degenerate
)
1349 graft
= refine_degenerate(graft
, bounds
, build
, sub_build
);
1351 graft
= refine_generic(graft
, bounds
, domain
, build
);
1353 graft
= after_each_for(graft
, body_build
);
1355 isl_ast_build_free(body_build
);
1356 isl_ast_build_free(sub_build
);
1357 isl_ast_build_free(build
);
1358 isl_basic_set_free(bounds
);
1359 isl_set_free(domain
);
1364 /* Internal data structure for checking if all constraints involving
1365 * the input dimension "depth" are such that the other coefficients
1366 * are multiples of "m", reducing "m" if they are not.
1367 * If "m" is reduced all the way down to "1", then the check has failed
1368 * and we break out of the iteration.
1370 struct isl_check_scaled_data
{
1375 /* If constraint "c" involves the input dimension data->depth,
1376 * then make sure that all the other coefficients are multiples of data->m,
1377 * reducing data->m if needed.
1378 * Break out of the iteration if data->m has become equal to "1".
1380 static int constraint_check_scaled(__isl_take isl_constraint
*c
, void *user
)
1382 struct isl_check_scaled_data
*data
= user
;
1384 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_out
,
1387 if (!isl_constraint_involves_dims(c
, isl_dim_in
, data
->depth
, 1)) {
1388 isl_constraint_free(c
);
1392 for (i
= 0; i
< 4; ++i
) {
1393 n
= isl_constraint_dim(c
, t
[i
]);
1394 for (j
= 0; j
< n
; ++j
) {
1397 if (t
[i
] == isl_dim_in
&& j
== data
->depth
)
1399 if (!isl_constraint_involves_dims(c
, t
[i
], j
, 1))
1401 d
= isl_constraint_get_coefficient_val(c
, t
[i
], j
);
1402 data
->m
= isl_val_gcd(data
->m
, d
);
1403 if (isl_val_is_one(data
->m
))
1410 isl_constraint_free(c
);
1412 return i
< 4 ? -1 : 0;
1415 /* For each constraint of "bmap" that involves the input dimension data->depth,
1416 * make sure that all the other coefficients are multiples of data->m,
1417 * reducing data->m if needed.
1418 * Break out of the iteration if data->m has become equal to "1".
1420 static int basic_map_check_scaled(__isl_take isl_basic_map
*bmap
, void *user
)
1424 r
= isl_basic_map_foreach_constraint(bmap
,
1425 &constraint_check_scaled
, user
);
1426 isl_basic_map_free(bmap
);
1431 /* For each constraint of "map" that involves the input dimension data->depth,
1432 * make sure that all the other coefficients are multiples of data->m,
1433 * reducing data->m if needed.
1434 * Break out of the iteration if data->m has become equal to "1".
1436 static int map_check_scaled(__isl_take isl_map
*map
, void *user
)
1440 r
= isl_map_foreach_basic_map(map
, &basic_map_check_scaled
, user
);
1446 /* Create an AST node for the current dimension based on
1447 * the schedule domain "bounds" and return the node encapsulated
1448 * in an isl_ast_graft.
1450 * "executed" is the current inverse schedule, taking into account
1451 * the bounds in "bounds"
1452 * "domain" is the domain of "executed", with inner dimensions projected out.
1455 * Before moving on to the actual AST node construction in create_node_scaled,
1456 * we first check if the current dimension is strided and if we can scale
1457 * down this stride. Note that we only do this if the ast_build_scale_strides
1460 * In particular, let the current dimension take on values
1464 * with a an integer. We check if we can find an integer m that (obviously)
1465 * divides both f and s.
1467 * If so, we check if the current dimension only appears in constraints
1468 * where the coefficients of the other variables are multiples of m.
1469 * We perform this extra check to avoid the risk of introducing
1470 * divisions by scaling down the current dimension.
1472 * If so, we scale the current dimension down by a factor of m.
1473 * That is, we plug in
1477 * Note that in principle we could always scale down strided loops
1482 * but this may result in i' taking on larger values than the original i,
1483 * due to the shift by "f".
1484 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1486 static __isl_give isl_ast_graft
*create_node(__isl_take isl_union_map
*executed
,
1487 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1488 __isl_take isl_ast_build
*build
)
1490 struct isl_check_scaled_data data
;
1495 ctx
= isl_ast_build_get_ctx(build
);
1496 if (!isl_options_get_ast_build_scale_strides(ctx
))
1497 return create_node_scaled(executed
, bounds
, domain
, build
);
1499 data
.depth
= isl_ast_build_get_depth(build
);
1500 if (!isl_ast_build_has_stride(build
, data
.depth
))
1501 return create_node_scaled(executed
, bounds
, domain
, build
);
1503 offset
= isl_ast_build_get_offset(build
, data
.depth
);
1504 data
.m
= isl_ast_build_get_stride(build
, data
.depth
);
1506 offset
= isl_aff_free(offset
);
1507 offset
= isl_aff_scale_down_val(offset
, isl_val_copy(data
.m
));
1508 d
= isl_aff_get_denominator_val(offset
);
1510 executed
= isl_union_map_free(executed
);
1512 if (executed
&& isl_val_is_divisible_by(data
.m
, d
))
1513 data
.m
= isl_val_div(data
.m
, d
);
1515 data
.m
= isl_val_set_si(data
.m
, 1);
1519 if (!isl_val_is_one(data
.m
)) {
1520 if (isl_union_map_foreach_map(executed
, &map_check_scaled
,
1522 !isl_val_is_one(data
.m
))
1523 executed
= isl_union_map_free(executed
);
1526 if (!isl_val_is_one(data
.m
)) {
1531 isl_union_map
*umap
;
1533 space
= isl_ast_build_get_space(build
, 1);
1534 space
= isl_space_map_from_set(space
);
1535 ma
= isl_multi_aff_identity(space
);
1536 aff
= isl_multi_aff_get_aff(ma
, data
.depth
);
1537 aff
= isl_aff_scale_val(aff
, isl_val_copy(data
.m
));
1538 ma
= isl_multi_aff_set_aff(ma
, data
.depth
, aff
);
1540 bounds
= isl_basic_set_preimage_multi_aff(bounds
,
1541 isl_multi_aff_copy(ma
));
1542 domain
= isl_set_preimage_multi_aff(domain
,
1543 isl_multi_aff_copy(ma
));
1544 map
= isl_map_reverse(isl_map_from_multi_aff(ma
));
1545 umap
= isl_union_map_from_map(map
);
1546 executed
= isl_union_map_apply_domain(executed
,
1547 isl_union_map_copy(umap
));
1548 build
= isl_ast_build_scale_down(build
, isl_val_copy(data
.m
),
1551 isl_aff_free(offset
);
1552 isl_val_free(data
.m
);
1554 return create_node_scaled(executed
, bounds
, domain
, build
);
1557 /* Add the basic set to the list that "user" points to.
1559 static int collect_basic_set(__isl_take isl_basic_set
*bset
, void *user
)
1561 isl_basic_set_list
**list
= user
;
1563 *list
= isl_basic_set_list_add(*list
, bset
);
1568 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1570 static __isl_give isl_basic_set_list
*isl_basic_set_list_from_set(
1571 __isl_take isl_set
*set
)
1575 isl_basic_set_list
*list
;
1580 ctx
= isl_set_get_ctx(set
);
1582 n
= isl_set_n_basic_set(set
);
1583 list
= isl_basic_set_list_alloc(ctx
, n
);
1584 if (isl_set_foreach_basic_set(set
, &collect_basic_set
, &list
) < 0)
1585 list
= isl_basic_set_list_free(list
);
1591 /* Generate code for the schedule domain "bounds"
1592 * and add the result to "list".
1594 * We mainly detect strides and additional equalities here
1595 * and then pass over control to create_node.
1597 * "bounds" reflects the bounds on the current dimension and possibly
1598 * some extra conditions on outer dimensions.
1599 * It does not, however, include any divs involving the current dimension,
1600 * so it does not capture any stride constraints.
1601 * We therefore need to compute that part of the schedule domain that
1602 * intersects with "bounds" and derive the strides from the result.
1604 static __isl_give isl_ast_graft_list
*add_node(
1605 __isl_take isl_ast_graft_list
*list
, __isl_take isl_union_map
*executed
,
1606 __isl_take isl_basic_set
*bounds
, __isl_take isl_ast_build
*build
)
1608 isl_ast_graft
*graft
;
1609 isl_set
*domain
= NULL
;
1610 isl_union_set
*uset
;
1613 uset
= isl_union_set_from_basic_set(isl_basic_set_copy(bounds
));
1614 executed
= isl_union_map_intersect_domain(executed
, uset
);
1615 empty
= isl_union_map_is_empty(executed
);
1621 uset
= isl_union_map_domain(isl_union_map_copy(executed
));
1622 domain
= isl_set_from_union_set(uset
);
1623 domain
= isl_ast_build_compute_gist(build
, domain
);
1624 empty
= isl_set_is_empty(domain
);
1630 domain
= isl_ast_build_eliminate_inner(build
, domain
);
1631 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
1633 graft
= create_node(executed
, bounds
, domain
,
1634 isl_ast_build_copy(build
));
1635 list
= isl_ast_graft_list_add(list
, graft
);
1636 isl_ast_build_free(build
);
1639 list
= isl_ast_graft_list_free(list
);
1641 isl_set_free(domain
);
1642 isl_basic_set_free(bounds
);
1643 isl_union_map_free(executed
);
1644 isl_ast_build_free(build
);
1648 /* Does any element of i follow or coincide with any element of j
1649 * at the current depth for equal values of the outer dimensions?
1651 static int domain_follows_at_depth(__isl_keep isl_basic_set
*i
,
1652 __isl_keep isl_basic_set
*j
, void *user
)
1654 int depth
= *(int *) user
;
1655 isl_basic_map
*test
;
1659 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
1660 isl_basic_set_copy(j
));
1661 for (l
= 0; l
< depth
; ++l
)
1662 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1664 test
= isl_basic_map_order_ge(test
, isl_dim_in
, depth
,
1665 isl_dim_out
, depth
);
1666 empty
= isl_basic_map_is_empty(test
);
1667 isl_basic_map_free(test
);
1669 return empty
< 0 ? -1 : !empty
;
1672 /* Split up each element of "list" into a part that is related to "bset"
1673 * according to "gt" and a part that is not.
1674 * Return a list that consist of "bset" and all the pieces.
1676 static __isl_give isl_basic_set_list
*add_split_on(
1677 __isl_take isl_basic_set_list
*list
, __isl_take isl_basic_set
*bset
,
1678 __isl_keep isl_basic_map
*gt
)
1681 isl_basic_set_list
*res
;
1684 bset
= isl_basic_set_free(bset
);
1686 gt
= isl_basic_map_copy(gt
);
1687 gt
= isl_basic_map_intersect_domain(gt
, isl_basic_set_copy(bset
));
1688 n
= isl_basic_set_list_n_basic_set(list
);
1689 res
= isl_basic_set_list_from_basic_set(bset
);
1690 for (i
= 0; res
&& i
< n
; ++i
) {
1691 isl_basic_set
*bset
;
1692 isl_set
*set1
, *set2
;
1693 isl_basic_map
*bmap
;
1696 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1697 bmap
= isl_basic_map_copy(gt
);
1698 bmap
= isl_basic_map_intersect_range(bmap
, bset
);
1699 bset
= isl_basic_map_range(bmap
);
1700 empty
= isl_basic_set_is_empty(bset
);
1702 res
= isl_basic_set_list_free(res
);
1704 isl_basic_set_free(bset
);
1705 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1706 res
= isl_basic_set_list_add(res
, bset
);
1710 res
= isl_basic_set_list_add(res
, isl_basic_set_copy(bset
));
1711 set1
= isl_set_from_basic_set(bset
);
1712 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1713 set2
= isl_set_from_basic_set(bset
);
1714 set1
= isl_set_subtract(set2
, set1
);
1715 set1
= isl_set_make_disjoint(set1
);
1717 res
= isl_basic_set_list_concat(res
,
1718 isl_basic_set_list_from_set(set1
));
1720 isl_basic_map_free(gt
);
1721 isl_basic_set_list_free(list
);
1725 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1726 __isl_keep isl_basic_set_list
*domain_list
,
1727 __isl_keep isl_union_map
*executed
,
1728 __isl_keep isl_ast_build
*build
);
1730 /* Internal data structure for add_nodes.
1732 * "executed" and "build" are extra arguments to be passed to add_node.
1733 * "list" collects the results.
1735 struct isl_add_nodes_data
{
1736 isl_union_map
*executed
;
1737 isl_ast_build
*build
;
1739 isl_ast_graft_list
*list
;
1742 /* Generate code for the schedule domains in "scc"
1743 * and add the results to "list".
1745 * The domains in "scc" form a strongly connected component in the ordering.
1746 * If the number of domains in "scc" is larger than 1, then this means
1747 * that we cannot determine a valid ordering for the domains in the component.
1748 * This should be fairly rare because the individual domains
1749 * have been made disjoint first.
1750 * The problem is that the domains may be integrally disjoint but not
1751 * rationally disjoint. For example, we may have domains
1753 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1755 * These two domains have an empty intersection, but their rational
1756 * relaxations do intersect. It is impossible to order these domains
1757 * in the second dimension because the first should be ordered before
1758 * the second for outer dimension equal to 0, while it should be ordered
1759 * after for outer dimension equal to 1.
1761 * This may happen in particular in case of unrolling since the domain
1762 * of each slice is replaced by its simple hull.
1764 * For each basic set i in "scc" and for each of the following basic sets j,
1765 * we split off that part of the basic set i that shares the outer dimensions
1766 * with j and lies before j in the current dimension.
1767 * We collect all the pieces in a new list that replaces "scc".
1769 * While the elements in "scc" should be disjoint, we double-check
1770 * this property to avoid running into an infinite recursion in case
1771 * they intersect due to some internal error.
1773 static int add_nodes(__isl_take isl_basic_set_list
*scc
, void *user
)
1775 struct isl_add_nodes_data
*data
= user
;
1777 isl_basic_set
*bset
, *first
;
1778 isl_basic_set_list
*list
;
1782 n
= isl_basic_set_list_n_basic_set(scc
);
1783 bset
= isl_basic_set_list_get_basic_set(scc
, 0);
1785 isl_basic_set_list_free(scc
);
1786 data
->list
= add_node(data
->list
,
1787 isl_union_map_copy(data
->executed
), bset
,
1788 isl_ast_build_copy(data
->build
));
1789 return data
->list
? 0 : -1;
1792 depth
= isl_ast_build_get_depth(data
->build
);
1793 space
= isl_basic_set_get_space(bset
);
1794 space
= isl_space_map_from_set(space
);
1795 gt
= isl_basic_map_universe(space
);
1796 for (i
= 0; i
< depth
; ++i
)
1797 gt
= isl_basic_map_equate(gt
, isl_dim_in
, i
, isl_dim_out
, i
);
1798 gt
= isl_basic_map_order_gt(gt
, isl_dim_in
, depth
, isl_dim_out
, depth
);
1800 first
= isl_basic_set_copy(bset
);
1801 list
= isl_basic_set_list_from_basic_set(bset
);
1802 for (i
= 1; i
< n
; ++i
) {
1805 bset
= isl_basic_set_list_get_basic_set(scc
, i
);
1807 disjoint
= isl_basic_set_is_disjoint(bset
, first
);
1809 list
= isl_basic_set_list_free(list
);
1811 isl_die(isl_basic_set_list_get_ctx(scc
),
1813 "basic sets in scc are assumed to be disjoint",
1814 list
= isl_basic_set_list_free(list
));
1816 list
= add_split_on(list
, bset
, gt
);
1818 isl_basic_set_free(first
);
1819 isl_basic_map_free(gt
);
1820 isl_basic_set_list_free(scc
);
1822 data
->list
= isl_ast_graft_list_concat(data
->list
,
1823 generate_sorted_domains(scc
, data
->executed
, data
->build
));
1824 isl_basic_set_list_free(scc
);
1826 return data
->list
? 0 : -1;
1829 /* Sort the domains in "domain_list" according to the execution order
1830 * at the current depth (for equal values of the outer dimensions),
1831 * generate code for each of them, collecting the results in a list.
1832 * If no code is generated (because the intersection of the inverse schedule
1833 * with the domains turns out to be empty), then an empty list is returned.
1835 * The caller is responsible for ensuring that the basic sets in "domain_list"
1836 * are pair-wise disjoint. It can, however, in principle happen that
1837 * two basic sets should be ordered one way for one value of the outer
1838 * dimensions and the other way for some other value of the outer dimensions.
1839 * We therefore play safe and look for strongly connected components.
1840 * The function add_nodes takes care of handling non-trivial components.
1842 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1843 __isl_keep isl_basic_set_list
*domain_list
,
1844 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1847 struct isl_add_nodes_data data
;
1854 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1855 n
= isl_basic_set_list_n_basic_set(domain_list
);
1856 data
.list
= isl_ast_graft_list_alloc(ctx
, n
);
1860 return add_node(data
.list
, isl_union_map_copy(executed
),
1861 isl_basic_set_list_get_basic_set(domain_list
, 0),
1862 isl_ast_build_copy(build
));
1864 depth
= isl_ast_build_get_depth(build
);
1865 data
.executed
= executed
;
1867 if (isl_basic_set_list_foreach_scc(domain_list
,
1868 &domain_follows_at_depth
, &depth
,
1869 &add_nodes
, &data
) < 0)
1870 data
.list
= isl_ast_graft_list_free(data
.list
);
1875 /* Do i and j share any values for the outer dimensions?
1877 static int shared_outer(__isl_keep isl_basic_set
*i
,
1878 __isl_keep isl_basic_set
*j
, void *user
)
1880 int depth
= *(int *) user
;
1881 isl_basic_map
*test
;
1885 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
1886 isl_basic_set_copy(j
));
1887 for (l
= 0; l
< depth
; ++l
)
1888 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1890 empty
= isl_basic_map_is_empty(test
);
1891 isl_basic_map_free(test
);
1893 return empty
< 0 ? -1 : !empty
;
1896 /* Internal data structure for generate_sorted_domains_wrap.
1898 * "n" is the total number of basic sets
1899 * "executed" and "build" are extra arguments to be passed
1900 * to generate_sorted_domains.
1902 * "single" is set to 1 by generate_sorted_domains_wrap if there
1903 * is only a single component.
1904 * "list" collects the results.
1906 struct isl_ast_generate_parallel_domains_data
{
1908 isl_union_map
*executed
;
1909 isl_ast_build
*build
;
1912 isl_ast_graft_list
*list
;
1915 /* Call generate_sorted_domains on "scc", fuse the result into a list
1916 * with either zero or one graft and collect the these single element
1917 * lists into data->list.
1919 * If there is only one component, i.e., if the number of basic sets
1920 * in the current component is equal to the total number of basic sets,
1921 * then data->single is set to 1 and the result of generate_sorted_domains
1924 static int generate_sorted_domains_wrap(__isl_take isl_basic_set_list
*scc
,
1927 struct isl_ast_generate_parallel_domains_data
*data
= user
;
1928 isl_ast_graft_list
*list
;
1930 list
= generate_sorted_domains(scc
, data
->executed
, data
->build
);
1931 data
->single
= isl_basic_set_list_n_basic_set(scc
) == data
->n
;
1933 list
= isl_ast_graft_list_fuse(list
, data
->build
);
1937 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
1939 isl_basic_set_list_free(scc
);
1946 /* Look for any (weakly connected) components in the "domain_list"
1947 * of domains that share some values of the outer dimensions.
1948 * That is, domains in different components do not share any values
1949 * of the outer dimensions. This means that these components
1950 * can be freely reordered.
1951 * Within each of the components, we sort the domains according
1952 * to the execution order at the current depth.
1954 * If there is more than one component, then generate_sorted_domains_wrap
1955 * fuses the result of each call to generate_sorted_domains
1956 * into a list with either zero or one graft and collects these (at most)
1957 * single element lists into a bigger list. This means that the elements of the
1958 * final list can be freely reordered. In particular, we sort them
1959 * according to an arbitrary but fixed ordering to ease merging of
1960 * graft lists from different components.
1962 static __isl_give isl_ast_graft_list
*generate_parallel_domains(
1963 __isl_keep isl_basic_set_list
*domain_list
,
1964 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1967 struct isl_ast_generate_parallel_domains_data data
;
1972 data
.n
= isl_basic_set_list_n_basic_set(domain_list
);
1974 return generate_sorted_domains(domain_list
, executed
, build
);
1976 depth
= isl_ast_build_get_depth(build
);
1978 data
.executed
= executed
;
1981 if (isl_basic_set_list_foreach_scc(domain_list
, &shared_outer
, &depth
,
1982 &generate_sorted_domains_wrap
,
1984 data
.list
= isl_ast_graft_list_free(data
.list
);
1987 data
.list
= isl_ast_graft_list_sort_guard(data
.list
);
1992 /* Internal data for separate_domain.
1994 * "explicit" is set if we only want to use explicit bounds.
1996 * "domain" collects the separated domains.
1998 struct isl_separate_domain_data
{
1999 isl_ast_build
*build
;
2004 /* Extract implicit bounds on the current dimension for the executed "map".
2006 * The domain of "map" may involve inner dimensions, so we
2007 * need to eliminate them.
2009 static __isl_give isl_set
*implicit_bounds(__isl_take isl_map
*map
,
2010 __isl_keep isl_ast_build
*build
)
2014 domain
= isl_map_domain(map
);
2015 domain
= isl_ast_build_eliminate(build
, domain
);
2020 /* Extract explicit bounds on the current dimension for the executed "map".
2022 * Rather than eliminating the inner dimensions as in implicit_bounds,
2023 * we simply drop any constraints involving those inner dimensions.
2024 * The idea is that most bounds that are implied by constraints on the
2025 * inner dimensions will be enforced by for loops and not by explicit guards.
2026 * There is then no need to separate along those bounds.
2028 static __isl_give isl_set
*explicit_bounds(__isl_take isl_map
*map
,
2029 __isl_keep isl_ast_build
*build
)
2034 dim
= isl_map_dim(map
, isl_dim_out
);
2035 map
= isl_map_drop_constraints_involving_dims(map
, isl_dim_out
, 0, dim
);
2037 domain
= isl_map_domain(map
);
2038 depth
= isl_ast_build_get_depth(build
);
2039 dim
= isl_set_dim(domain
, isl_dim_set
);
2040 domain
= isl_set_detect_equalities(domain
);
2041 domain
= isl_set_drop_constraints_involving_dims(domain
,
2042 isl_dim_set
, depth
+ 1, dim
- (depth
+ 1));
2043 domain
= isl_set_remove_divs_involving_dims(domain
,
2044 isl_dim_set
, depth
, 1);
2045 domain
= isl_set_remove_unknown_divs(domain
);
2050 /* Split data->domain into pieces that intersect with the range of "map"
2051 * and pieces that do not intersect with the range of "map"
2052 * and then add that part of the range of "map" that does not intersect
2053 * with data->domain.
2055 static int separate_domain(__isl_take isl_map
*map
, void *user
)
2057 struct isl_separate_domain_data
*data
= user
;
2062 domain
= explicit_bounds(map
, data
->build
);
2064 domain
= implicit_bounds(map
, data
->build
);
2066 domain
= isl_set_coalesce(domain
);
2067 domain
= isl_set_make_disjoint(domain
);
2068 d1
= isl_set_subtract(isl_set_copy(domain
), isl_set_copy(data
->domain
));
2069 d2
= isl_set_subtract(isl_set_copy(data
->domain
), isl_set_copy(domain
));
2070 data
->domain
= isl_set_intersect(data
->domain
, domain
);
2071 data
->domain
= isl_set_union(data
->domain
, d1
);
2072 data
->domain
= isl_set_union(data
->domain
, d2
);
2077 /* Separate the schedule domains of "executed".
2079 * That is, break up the domain of "executed" into basic sets,
2080 * such that for each basic set S, every element in S is associated with
2081 * the same domain spaces.
2083 * "space" is the (single) domain space of "executed".
2085 static __isl_give isl_set
*separate_schedule_domains(
2086 __isl_take isl_space
*space
, __isl_take isl_union_map
*executed
,
2087 __isl_keep isl_ast_build
*build
)
2089 struct isl_separate_domain_data data
= { build
};
2092 ctx
= isl_ast_build_get_ctx(build
);
2093 data
.explicit = isl_options_get_ast_build_separation_bounds(ctx
) ==
2094 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
;
2095 data
.domain
= isl_set_empty(space
);
2096 if (isl_union_map_foreach_map(executed
, &separate_domain
, &data
) < 0)
2097 data
.domain
= isl_set_free(data
.domain
);
2099 isl_union_map_free(executed
);
2103 /* Temporary data used during the search for a lower bound for unrolling.
2105 * "domain" is the original set for which to find a lower bound
2106 * "depth" is the dimension for which to find a lower boudn
2108 * "lower" is the best lower bound found so far. It is NULL if we have not
2110 * "n" is the corresponding size. If lower is NULL, then the value of n
2113 struct isl_find_unroll_data
{
2121 /* Check if we can use "c" as a lower bound and if it is better than
2122 * any previously found lower bound.
2124 * If "c" does not involve the dimension at the current depth,
2125 * then we cannot use it.
2126 * Otherwise, let "c" be of the form
2130 * We compute the maximal value of
2132 * -ceil(f(j)/a)) + i + 1
2134 * over the domain. If there is such a value "n", then we know
2136 * -ceil(f(j)/a)) + i + 1 <= n
2140 * i < ceil(f(j)/a)) + n
2142 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2143 * We just need to check if we have found any lower bound before and
2144 * if the new lower bound is better (smaller n) than the previously found
2147 static int update_unrolling_lower_bound(struct isl_find_unroll_data
*data
,
2148 __isl_keep isl_constraint
*c
)
2150 isl_aff
*aff
, *lower
;
2153 if (!isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->depth
))
2156 lower
= isl_constraint_get_bound(c
, isl_dim_set
, data
->depth
);
2157 lower
= isl_aff_ceil(lower
);
2158 aff
= isl_aff_copy(lower
);
2159 aff
= isl_aff_neg(aff
);
2160 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, data
->depth
, 1);
2161 aff
= isl_aff_add_constant_si(aff
, 1);
2162 max
= isl_set_max_val(data
->domain
, aff
);
2167 if (isl_val_is_infty(max
)) {
2169 isl_aff_free(lower
);
2173 if (isl_val_cmp_si(max
, INT_MAX
) <= 0 &&
2174 (!data
->lower
|| isl_val_cmp_si(max
, *data
->n
) < 0)) {
2175 isl_aff_free(data
->lower
);
2176 data
->lower
= lower
;
2177 *data
->n
= isl_val_get_num_si(max
);
2179 isl_aff_free(lower
);
2184 isl_aff_free(lower
);
2188 /* Check if we can use "c" as a lower bound and if it is better than
2189 * any previously found lower bound.
2191 static int constraint_find_unroll(__isl_take isl_constraint
*c
, void *user
)
2193 struct isl_find_unroll_data
*data
;
2196 data
= (struct isl_find_unroll_data
*) user
;
2197 r
= update_unrolling_lower_bound(data
, c
);
2198 isl_constraint_free(c
);
2203 /* Look for a lower bound l(i) on the dimension at "depth"
2204 * and a size n such that "domain" is a subset of
2206 * { [i] : l(i) <= i_d < l(i) + n }
2208 * where d is "depth" and l(i) depends only on earlier dimensions.
2209 * Furthermore, try and find a lower bound such that n is as small as possible.
2210 * In particular, "n" needs to be finite.
2212 * Inner dimensions have been eliminated from "domain" by the caller.
2214 * We first construct a collection of lower bounds on the input set
2215 * by computing its simple hull. We then iterate through them,
2216 * discarding those that we cannot use (either because they do not
2217 * involve the dimension at "depth" or because they have no corresponding
2218 * upper bound, meaning that "n" would be unbounded) and pick out the
2219 * best from the remaining ones.
2221 * If we cannot find a suitable lower bound, then we consider that
2224 static __isl_give isl_aff
*find_unroll_lower_bound(__isl_keep isl_set
*domain
,
2227 struct isl_find_unroll_data data
= { domain
, depth
, NULL
, n
};
2228 isl_basic_set
*hull
;
2230 hull
= isl_set_simple_hull(isl_set_copy(domain
));
2232 if (isl_basic_set_foreach_constraint(hull
,
2233 &constraint_find_unroll
, &data
) < 0)
2236 isl_basic_set_free(hull
);
2239 isl_die(isl_set_get_ctx(domain
), isl_error_invalid
,
2240 "cannot find lower bound for unrolling", return NULL
);
2244 isl_basic_set_free(hull
);
2245 return isl_aff_free(data
.lower
);
2248 /* Return the constraint
2250 * i_"depth" = aff + offset
2252 static __isl_give isl_constraint
*at_offset(int depth
, __isl_keep isl_aff
*aff
,
2255 aff
= isl_aff_copy(aff
);
2256 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, depth
, -1);
2257 aff
= isl_aff_add_constant_si(aff
, offset
);
2258 return isl_equality_from_aff(aff
);
2261 /* Data structure for storing the results and the intermediate objects
2262 * of compute_domains.
2264 * "list" is the main result of the function and contains a list
2265 * of disjoint basic sets for which code should be generated.
2267 * "executed" and "build" are inputs to compute_domains.
2268 * "schedule_domain" is the domain of "executed".
2270 * "option" constains the domains at the current depth that should by
2271 * atomic, separated or unrolled. These domains are as specified by
2272 * the user, except that inner dimensions have been eliminated and
2273 * that they have been made pair-wise disjoint.
2275 * "sep_class" contains the user-specified split into separation classes
2276 * specialized to the current depth.
2277 * "done" contains the union of the separation domains that have already
2280 struct isl_codegen_domains
{
2281 isl_basic_set_list
*list
;
2283 isl_union_map
*executed
;
2284 isl_ast_build
*build
;
2285 isl_set
*schedule_domain
;
2293 /* Extend domains->list with a list of basic sets, one for each value
2294 * of the current dimension in "domain" and remove the corresponding
2295 * sets from the class domain. Return the updated class domain.
2296 * The divs that involve the current dimension have not been projected out
2299 * Since we are going to be iterating over the individual values,
2300 * we first check if there are any strides on the current dimension.
2301 * If there is, we rewrite the current dimension i as
2303 * i = stride i' + offset
2305 * and then iterate over individual values of i' instead.
2307 * We then look for a lower bound on i' and a size such that the domain
2310 * { [j,i'] : l(j) <= i' < l(j) + n }
2312 * and then take slices of the domain at values of i'
2313 * between l(j) and l(j) + n - 1.
2315 * We compute the unshifted simple hull of each slice to ensure that
2316 * we have a single basic set per offset. The slicing constraint
2317 * may get simplified away before the unshifted simple hull is taken
2318 * and may therefore in some rare cases disappear from the result.
2319 * We therefore explicitly add the constraint back after computing
2320 * the unshifted simple hull to ensure that the basic sets
2321 * remain disjoint. The constraints that are dropped by taking the hull
2322 * will be taken into account at the next level, as in the case of the
2325 * Finally, we map i' back to i and add each basic set to the list.
2326 * Since we may have dropped some constraints, we intersect with
2327 * the class domain again to ensure that each element in the list
2328 * is disjoint from the other class domains.
2330 static __isl_give isl_set
*do_unroll(struct isl_codegen_domains
*domains
,
2331 __isl_take isl_set
*domain
, __isl_take isl_set
*class_domain
)
2337 isl_multi_aff
*expansion
;
2338 isl_basic_map
*bmap
;
2339 isl_set
*unroll_domain
;
2340 isl_ast_build
*build
;
2343 return isl_set_free(class_domain
);
2345 ctx
= isl_set_get_ctx(domain
);
2346 depth
= isl_ast_build_get_depth(domains
->build
);
2347 build
= isl_ast_build_copy(domains
->build
);
2348 domain
= isl_ast_build_eliminate_inner(build
, domain
);
2349 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
2350 expansion
= isl_ast_build_get_stride_expansion(build
);
2352 domain
= isl_set_preimage_multi_aff(domain
,
2353 isl_multi_aff_copy(expansion
));
2354 domain
= isl_ast_build_eliminate_divs(build
, domain
);
2356 isl_ast_build_free(build
);
2358 lower
= find_unroll_lower_bound(domain
, depth
, &n
);
2360 class_domain
= isl_set_free(class_domain
);
2362 bmap
= isl_basic_map_from_multi_aff(expansion
);
2364 unroll_domain
= isl_set_empty(isl_set_get_space(domain
));
2366 for (i
= 0; class_domain
&& i
< n
; ++i
) {
2368 isl_basic_set
*bset
;
2369 isl_constraint
*slice
;
2370 isl_basic_set_list
*list
;
2372 slice
= at_offset(depth
, lower
, i
);
2373 set
= isl_set_copy(domain
);
2374 set
= isl_set_add_constraint(set
, isl_constraint_copy(slice
));
2375 bset
= isl_set_unshifted_simple_hull(set
);
2376 bset
= isl_basic_set_add_constraint(bset
, slice
);
2377 bset
= isl_basic_set_apply(bset
, isl_basic_map_copy(bmap
));
2378 set
= isl_set_from_basic_set(bset
);
2379 unroll_domain
= isl_set_union(unroll_domain
, isl_set_copy(set
));
2380 set
= isl_set_intersect(set
, isl_set_copy(class_domain
));
2381 set
= isl_set_make_disjoint(set
);
2382 list
= isl_basic_set_list_from_set(set
);
2383 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2386 class_domain
= isl_set_subtract(class_domain
, unroll_domain
);
2388 isl_aff_free(lower
);
2389 isl_set_free(domain
);
2390 isl_basic_map_free(bmap
);
2392 return class_domain
;
2395 /* Add domains to domains->list for each individual value of the current
2396 * dimension, for that part of the schedule domain that lies in the
2397 * intersection of the option domain and the class domain.
2398 * Remove the corresponding sets from the class domain and
2399 * return the updated class domain.
2401 * We first break up the unroll option domain into individual pieces
2402 * and then handle each of them separately. The unroll option domain
2403 * has been made disjoint in compute_domains_init_options,
2405 * Note that we actively want to combine different pieces of the
2406 * schedule domain that have the same value at the current dimension.
2407 * We therefore need to break up the unroll option domain before
2408 * intersecting with class and schedule domain, hoping that the
2409 * unroll option domain specified by the user is relatively simple.
2411 static __isl_give isl_set
*compute_unroll_domains(
2412 struct isl_codegen_domains
*domains
, __isl_take isl_set
*class_domain
)
2414 isl_set
*unroll_domain
;
2415 isl_basic_set_list
*unroll_list
;
2419 empty
= isl_set_is_empty(domains
->option
[unroll
]);
2421 return isl_set_free(class_domain
);
2423 return class_domain
;
2425 unroll_domain
= isl_set_copy(domains
->option
[unroll
]);
2426 unroll_list
= isl_basic_set_list_from_set(unroll_domain
);
2428 n
= isl_basic_set_list_n_basic_set(unroll_list
);
2429 for (i
= 0; i
< n
; ++i
) {
2430 isl_basic_set
*bset
;
2432 bset
= isl_basic_set_list_get_basic_set(unroll_list
, i
);
2433 unroll_domain
= isl_set_from_basic_set(bset
);
2434 unroll_domain
= isl_set_intersect(unroll_domain
,
2435 isl_set_copy(class_domain
));
2436 unroll_domain
= isl_set_intersect(unroll_domain
,
2437 isl_set_copy(domains
->schedule_domain
));
2439 empty
= isl_set_is_empty(unroll_domain
);
2440 if (empty
>= 0 && empty
) {
2441 isl_set_free(unroll_domain
);
2445 class_domain
= do_unroll(domains
, unroll_domain
, class_domain
);
2448 isl_basic_set_list_free(unroll_list
);
2450 return class_domain
;
2453 /* Try and construct a single basic set that includes the intersection of
2454 * the schedule domain, the atomic option domain and the class domain.
2455 * Add the resulting basic set(s) to domains->list and remove them
2456 * from class_domain. Return the updated class domain.
2458 * We construct a single domain rather than trying to combine
2459 * the schedule domains of individual domains because we are working
2460 * within a single component so that non-overlapping schedule domains
2461 * should already have been separated.
2462 * We do however need to make sure that this single domains is a subset
2463 * of the class domain so that it would not intersect with any other
2464 * class domains. This means that we may end up splitting up the atomic
2465 * domain in case separation classes are being used.
2467 * "domain" is the intersection of the schedule domain and the class domain,
2468 * with inner dimensions projected out.
2470 static __isl_give isl_set
*compute_atomic_domain(
2471 struct isl_codegen_domains
*domains
, __isl_take isl_set
*class_domain
)
2473 isl_basic_set
*bset
;
2474 isl_basic_set_list
*list
;
2475 isl_set
*domain
, *atomic_domain
;
2478 domain
= isl_set_copy(domains
->option
[atomic
]);
2479 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2480 domain
= isl_set_intersect(domain
,
2481 isl_set_copy(domains
->schedule_domain
));
2482 empty
= isl_set_is_empty(domain
);
2484 class_domain
= isl_set_free(class_domain
);
2486 isl_set_free(domain
);
2487 return class_domain
;
2490 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2491 domain
= isl_set_coalesce(domain
);
2492 bset
= isl_set_unshifted_simple_hull(domain
);
2493 domain
= isl_set_from_basic_set(bset
);
2494 atomic_domain
= isl_set_copy(domain
);
2495 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2496 class_domain
= isl_set_subtract(class_domain
, atomic_domain
);
2497 domain
= isl_set_make_disjoint(domain
);
2498 list
= isl_basic_set_list_from_set(domain
);
2499 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2501 return class_domain
;
2504 /* Split up the schedule domain into uniform basic sets,
2505 * in the sense that each element in a basic set is associated to
2506 * elements of the same domains, and add the result to domains->list.
2507 * Do this for that part of the schedule domain that lies in the
2508 * intersection of "class_domain" and the separate option domain.
2510 * "class_domain" may or may not include the constraints
2511 * of the schedule domain, but this does not make a difference
2512 * since we are going to intersect it with the domain of the inverse schedule.
2513 * If it includes schedule domain constraints, then they may involve
2514 * inner dimensions, but we will eliminate them in separation_domain.
2516 static int compute_separate_domain(struct isl_codegen_domains
*domains
,
2517 __isl_keep isl_set
*class_domain
)
2521 isl_union_map
*executed
;
2522 isl_basic_set_list
*list
;
2525 domain
= isl_set_copy(domains
->option
[separate
]);
2526 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2527 executed
= isl_union_map_copy(domains
->executed
);
2528 executed
= isl_union_map_intersect_domain(executed
,
2529 isl_union_set_from_set(domain
));
2530 empty
= isl_union_map_is_empty(executed
);
2531 if (empty
< 0 || empty
) {
2532 isl_union_map_free(executed
);
2533 return empty
< 0 ? -1 : 0;
2536 space
= isl_set_get_space(class_domain
);
2537 domain
= separate_schedule_domains(space
, executed
, domains
->build
);
2539 list
= isl_basic_set_list_from_set(domain
);
2540 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2545 /* Split up the domain at the current depth into disjoint
2546 * basic sets for which code should be generated separately
2547 * for the given separation class domain.
2549 * If any separation classes have been defined, then "class_domain"
2550 * is the domain of the current class and does not refer to inner dimensions.
2551 * Otherwise, "class_domain" is the universe domain.
2553 * We first make sure that the class domain is disjoint from
2554 * previously considered class domains.
2556 * The separate domains can be computed directly from the "class_domain".
2558 * The unroll, atomic and remainder domains need the constraints
2559 * from the schedule domain.
2561 * For unrolling, the actual schedule domain is needed (with divs that
2562 * may refer to the current dimension) so that stride detection can be
2565 * For atomic and remainder domains, inner dimensions and divs involving
2566 * the current dimensions should be eliminated.
2567 * In case we are working within a separation class, we need to intersect
2568 * the result with the current "class_domain" to ensure that the domains
2569 * are disjoint from those generated from other class domains.
2571 * The domain that has been made atomic may be larger than specified
2572 * by the user since it needs to be representable as a single basic set.
2573 * This possibly larger domain is removed from class_domain by
2574 * compute_atomic_domain. It is computed first so that the extended domain
2575 * would not overlap with any domains computed before.
2576 * Similary, the unrolled domains may have some constraints removed and
2577 * may therefore also be larger than specified by the user.
2579 * If anything is left after handling separate, unroll and atomic,
2580 * we split it up into basic sets and append the basic sets to domains->list.
2582 static int compute_partial_domains(struct isl_codegen_domains
*domains
,
2583 __isl_take isl_set
*class_domain
)
2585 isl_basic_set_list
*list
;
2588 class_domain
= isl_set_subtract(class_domain
,
2589 isl_set_copy(domains
->done
));
2590 domains
->done
= isl_set_union(domains
->done
,
2591 isl_set_copy(class_domain
));
2593 class_domain
= compute_atomic_domain(domains
, class_domain
);
2594 class_domain
= compute_unroll_domains(domains
, class_domain
);
2596 domain
= isl_set_copy(class_domain
);
2598 if (compute_separate_domain(domains
, domain
) < 0)
2600 domain
= isl_set_subtract(domain
,
2601 isl_set_copy(domains
->option
[separate
]));
2603 domain
= isl_set_intersect(domain
,
2604 isl_set_copy(domains
->schedule_domain
));
2606 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2607 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2609 domain
= isl_set_coalesce(domain
);
2610 domain
= isl_set_make_disjoint(domain
);
2612 list
= isl_basic_set_list_from_set(domain
);
2613 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2615 isl_set_free(class_domain
);
2619 isl_set_free(domain
);
2620 isl_set_free(class_domain
);
2624 /* Split up the domain at the current depth into disjoint
2625 * basic sets for which code should be generated separately
2626 * for the separation class identified by "pnt".
2628 * We extract the corresponding class domain from domains->sep_class,
2629 * eliminate inner dimensions and pass control to compute_partial_domains.
2631 static int compute_class_domains(__isl_take isl_point
*pnt
, void *user
)
2633 struct isl_codegen_domains
*domains
= user
;
2638 class_set
= isl_set_from_point(pnt
);
2639 domain
= isl_map_domain(isl_map_intersect_range(
2640 isl_map_copy(domains
->sep_class
), class_set
));
2641 domain
= isl_ast_build_compute_gist(domains
->build
, domain
);
2642 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2644 disjoint
= isl_set_plain_is_disjoint(domain
, domains
->schedule_domain
);
2648 isl_set_free(domain
);
2652 return compute_partial_domains(domains
, domain
);
2655 /* Extract the domains at the current depth that should be atomic,
2656 * separated or unrolled and store them in option.
2658 * The domains specified by the user might overlap, so we make
2659 * them disjoint by subtracting earlier domains from later domains.
2661 static void compute_domains_init_options(isl_set
*option
[3],
2662 __isl_keep isl_ast_build
*build
)
2664 enum isl_ast_build_domain_type type
, type2
;
2666 for (type
= atomic
; type
<= separate
; ++type
) {
2667 option
[type
] = isl_ast_build_get_option_domain(build
, type
);
2668 for (type2
= atomic
; type2
< type
; ++type2
)
2669 option
[type
] = isl_set_subtract(option
[type
],
2670 isl_set_copy(option
[type2
]));
2673 option
[unroll
] = isl_set_coalesce(option
[unroll
]);
2674 option
[unroll
] = isl_set_make_disjoint(option
[unroll
]);
2677 /* Split up the domain at the current depth into disjoint
2678 * basic sets for which code should be generated separately,
2679 * based on the user-specified options.
2680 * Return the list of disjoint basic sets.
2682 * There are three kinds of domains that we need to keep track of.
2683 * - the "schedule domain" is the domain of "executed"
2684 * - the "class domain" is the domain corresponding to the currrent
2686 * - the "option domain" is the domain corresponding to one of the options
2687 * atomic, unroll or separate
2689 * We first consider the individial values of the separation classes
2690 * and split up the domain for each of them separately.
2691 * Finally, we consider the remainder. If no separation classes were
2692 * specified, then we call compute_partial_domains with the universe
2693 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2694 * with inner dimensions removed. We do this because we want to
2695 * avoid computing the complement of the class domains (i.e., the difference
2696 * between the universe and domains->done).
2698 static __isl_give isl_basic_set_list
*compute_domains(
2699 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
2701 struct isl_codegen_domains domains
;
2704 isl_union_set
*schedule_domain
;
2708 enum isl_ast_build_domain_type type
;
2714 ctx
= isl_union_map_get_ctx(executed
);
2715 domains
.list
= isl_basic_set_list_alloc(ctx
, 0);
2717 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
2718 domain
= isl_set_from_union_set(schedule_domain
);
2720 compute_domains_init_options(domains
.option
, build
);
2722 domains
.sep_class
= isl_ast_build_get_separation_class(build
);
2723 classes
= isl_map_range(isl_map_copy(domains
.sep_class
));
2724 n_param
= isl_set_dim(classes
, isl_dim_param
);
2725 classes
= isl_set_project_out(classes
, isl_dim_param
, 0, n_param
);
2727 space
= isl_set_get_space(domain
);
2728 domains
.build
= build
;
2729 domains
.schedule_domain
= isl_set_copy(domain
);
2730 domains
.executed
= executed
;
2731 domains
.done
= isl_set_empty(space
);
2733 if (isl_set_foreach_point(classes
, &compute_class_domains
, &domains
) < 0)
2734 domains
.list
= isl_basic_set_list_free(domains
.list
);
2735 isl_set_free(classes
);
2737 empty
= isl_set_is_empty(domains
.done
);
2739 domains
.list
= isl_basic_set_list_free(domains
.list
);
2740 domain
= isl_set_free(domain
);
2742 isl_set_free(domain
);
2743 domain
= isl_set_universe(isl_set_get_space(domains
.done
));
2745 domain
= isl_ast_build_eliminate(build
, domain
);
2747 if (compute_partial_domains(&domains
, domain
) < 0)
2748 domains
.list
= isl_basic_set_list_free(domains
.list
);
2750 isl_set_free(domains
.schedule_domain
);
2751 isl_set_free(domains
.done
);
2752 isl_map_free(domains
.sep_class
);
2753 for (type
= atomic
; type
<= separate
; ++type
)
2754 isl_set_free(domains
.option
[type
]);
2756 return domains
.list
;
2759 /* Generate code for a single component, after shifting (if any)
2762 * We first split up the domain at the current depth into disjoint
2763 * basic sets based on the user-specified options.
2764 * Then we generated code for each of them and concatenate the results.
2766 static __isl_give isl_ast_graft_list
*generate_shifted_component(
2767 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
2769 isl_basic_set_list
*domain_list
;
2770 isl_ast_graft_list
*list
= NULL
;
2772 domain_list
= compute_domains(executed
, build
);
2773 list
= generate_parallel_domains(domain_list
, executed
, build
);
2775 isl_basic_set_list_free(domain_list
);
2776 isl_union_map_free(executed
);
2777 isl_ast_build_free(build
);
2782 struct isl_set_map_pair
{
2787 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2788 * of indices into the "domain" array,
2789 * return the union of the "map" fields of the elements
2790 * indexed by the first "n" elements of "order".
2792 static __isl_give isl_union_map
*construct_component_executed(
2793 struct isl_set_map_pair
*domain
, int *order
, int n
)
2797 isl_union_map
*executed
;
2799 map
= isl_map_copy(domain
[order
[0]].map
);
2800 executed
= isl_union_map_from_map(map
);
2801 for (i
= 1; i
< n
; ++i
) {
2802 map
= isl_map_copy(domain
[order
[i
]].map
);
2803 executed
= isl_union_map_add_map(executed
, map
);
2809 /* Generate code for a single component, after shifting (if any)
2812 * The component inverse schedule is specified as the "map" fields
2813 * of the elements of "domain" indexed by the first "n" elements of "order".
2815 static __isl_give isl_ast_graft_list
*generate_shifted_component_from_list(
2816 struct isl_set_map_pair
*domain
, int *order
, int n
,
2817 __isl_take isl_ast_build
*build
)
2819 isl_union_map
*executed
;
2821 executed
= construct_component_executed(domain
, order
, n
);
2822 return generate_shifted_component(executed
, build
);
2825 /* Does set dimension "pos" of "set" have an obviously fixed value?
2827 static int dim_is_fixed(__isl_keep isl_set
*set
, int pos
)
2832 v
= isl_set_plain_get_val_if_fixed(set
, isl_dim_set
, pos
);
2835 fixed
= !isl_val_is_nan(v
);
2841 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2842 * of indices into the "domain" array,
2843 * do all (except for at most one) of the "set" field of the elements
2844 * indexed by the first "n" elements of "order" have a fixed value
2845 * at position "depth"?
2847 static int at_most_one_non_fixed(struct isl_set_map_pair
*domain
,
2848 int *order
, int n
, int depth
)
2853 for (i
= 0; i
< n
; ++i
) {
2856 f
= dim_is_fixed(domain
[order
[i
]].set
, depth
);
2869 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2870 * of indices into the "domain" array,
2871 * eliminate the inner dimensions from the "set" field of the elements
2872 * indexed by the first "n" elements of "order", provided the current
2873 * dimension does not have a fixed value.
2875 * Return the index of the first element in "order" with a corresponding
2876 * "set" field that does not have an (obviously) fixed value.
2878 static int eliminate_non_fixed(struct isl_set_map_pair
*domain
,
2879 int *order
, int n
, int depth
, __isl_keep isl_ast_build
*build
)
2884 for (i
= n
- 1; i
>= 0; --i
) {
2886 f
= dim_is_fixed(domain
[order
[i
]].set
, depth
);
2891 domain
[order
[i
]].set
= isl_ast_build_eliminate_inner(build
,
2892 domain
[order
[i
]].set
);
2899 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2900 * of indices into the "domain" array,
2901 * find the element of "domain" (amongst those indexed by the first "n"
2902 * elements of "order") with the "set" field that has the smallest
2903 * value for the current iterator.
2905 * Note that the domain with the smallest value may depend on the parameters
2906 * and/or outer loop dimension. Since the result of this function is only
2907 * used as heuristic, we only make a reasonable attempt at finding the best
2908 * domain, one that should work in case a single domain provides the smallest
2909 * value for the current dimension over all values of the parameters
2910 * and outer dimensions.
2912 * In particular, we compute the smallest value of the first domain
2913 * and replace it by that of any later domain if that later domain
2914 * has a smallest value that is smaller for at least some value
2915 * of the parameters and outer dimensions.
2917 static int first_offset(struct isl_set_map_pair
*domain
, int *order
, int n
,
2918 __isl_keep isl_ast_build
*build
)
2924 min_first
= isl_ast_build_map_to_iterator(build
,
2925 isl_set_copy(domain
[order
[0]].set
));
2926 min_first
= isl_map_lexmin(min_first
);
2928 for (i
= 1; i
< n
; ++i
) {
2929 isl_map
*min
, *test
;
2932 min
= isl_ast_build_map_to_iterator(build
,
2933 isl_set_copy(domain
[order
[i
]].set
));
2934 min
= isl_map_lexmin(min
);
2935 test
= isl_map_copy(min
);
2936 test
= isl_map_apply_domain(isl_map_copy(min_first
), test
);
2937 test
= isl_map_order_lt(test
, isl_dim_in
, 0, isl_dim_out
, 0);
2938 empty
= isl_map_is_empty(test
);
2940 if (empty
>= 0 && !empty
) {
2941 isl_map_free(min_first
);
2951 isl_map_free(min_first
);
2953 return i
< n
? -1 : first
;
2956 /* Construct a shifted inverse schedule based on the original inverse schedule,
2957 * the stride and the offset.
2959 * The original inverse schedule is specified as the "map" fields
2960 * of the elements of "domain" indexed by the first "n" elements of "order".
2962 * "stride" and "offset" are such that the difference
2963 * between the values of the current dimension of domain "i"
2964 * and the values of the current dimension for some reference domain are
2967 * stride * integer + offset[i]
2969 * Moreover, 0 <= offset[i] < stride.
2971 * For each domain, we create a map
2973 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2975 * where j refers to the current dimension and the other dimensions are
2976 * unchanged, and apply this map to the original schedule domain.
2978 * For example, for the original schedule
2980 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2982 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2983 * we apply the mapping
2987 * to the schedule of the "A" domain and the mapping
2989 * { [j - 1] -> [j, 1] }
2991 * to the schedule of the "B" domain.
2994 * Note that after the transformation, the differences between pairs
2995 * of values of the current dimension over all domains are multiples
2996 * of stride and that we have therefore exposed the stride.
2999 * To see that the mapping preserves the lexicographic order,
3000 * first note that each of the individual maps above preserves the order.
3001 * If the value of the current iterator is j1 in one domain and j2 in another,
3002 * then if j1 = j2, we know that the same map is applied to both domains
3003 * and the order is preserved.
3004 * Otherwise, let us assume, without loss of generality, that j1 < j2.
3005 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
3009 * and the order is preserved.
3010 * If c1 < c2, then we know
3016 * j2 - j1 = n * s + r
3018 * with n >= 0 and 0 <= r < s.
3019 * In other words, r = c2 - c1.
3030 * (j1 - c1, c1) << (j2 - c2, c2)
3032 * with "<<" the lexicographic order, proving that the order is preserved
3035 static __isl_give isl_union_map
*contruct_shifted_executed(
3036 struct isl_set_map_pair
*domain
, int *order
, int n
,
3037 __isl_keep isl_val
*stride
, __isl_keep isl_multi_val
*offset
,
3038 __isl_take isl_ast_build
*build
)
3041 isl_union_map
*executed
;
3047 depth
= isl_ast_build_get_depth(build
);
3048 space
= isl_ast_build_get_space(build
, 1);
3049 executed
= isl_union_map_empty(isl_space_copy(space
));
3050 space
= isl_space_map_from_set(space
);
3051 map
= isl_map_identity(isl_space_copy(space
));
3052 map
= isl_map_eliminate(map
, isl_dim_out
, depth
, 1);
3053 map
= isl_map_insert_dims(map
, isl_dim_out
, depth
+ 1, 1);
3054 space
= isl_space_insert_dims(space
, isl_dim_out
, depth
+ 1, 1);
3056 c
= isl_equality_alloc(isl_local_space_from_space(space
));
3057 c
= isl_constraint_set_coefficient_si(c
, isl_dim_in
, depth
, 1);
3058 c
= isl_constraint_set_coefficient_si(c
, isl_dim_out
, depth
, -1);
3060 for (i
= 0; i
< n
; ++i
) {
3064 v
= isl_multi_val_get_val(offset
, i
);
3067 map_i
= isl_map_copy(map
);
3068 map_i
= isl_map_fix_val(map_i
, isl_dim_out
, depth
+ 1,
3071 c
= isl_constraint_set_constant_val(c
, v
);
3072 map_i
= isl_map_add_constraint(map_i
, isl_constraint_copy(c
));
3074 map_i
= isl_map_apply_domain(isl_map_copy(domain
[order
[i
]].map
),
3076 executed
= isl_union_map_add_map(executed
, map_i
);
3079 isl_constraint_free(c
);
3083 executed
= isl_union_map_free(executed
);
3088 /* Generate code for a single component, after exposing the stride,
3089 * given that the schedule domain is "shifted strided".
3091 * The component inverse schedule is specified as the "map" fields
3092 * of the elements of "domain" indexed by the first "n" elements of "order".
3094 * The schedule domain being "shifted strided" means that the differences
3095 * between the values of the current dimension of domain "i"
3096 * and the values of the current dimension for some reference domain are
3099 * stride * integer + offset[i]
3101 * We first look for the domain with the "smallest" value for the current
3102 * dimension and adjust the offsets such that the offset of the "smallest"
3103 * domain is equal to zero. The other offsets are reduced modulo stride.
3105 * Based on this information, we construct a new inverse schedule in
3106 * contruct_shifted_executed that exposes the stride.
3107 * Since this involves the introduction of a new schedule dimension,
3108 * the build needs to be changed accodingly.
3109 * After computing the AST, the newly introduced dimension needs
3110 * to be removed again from the list of grafts. We do this by plugging
3111 * in a mapping that represents the new schedule domain in terms of the
3112 * old schedule domain.
3114 static __isl_give isl_ast_graft_list
*generate_shift_component(
3115 struct isl_set_map_pair
*domain
, int *order
, int n
,
3116 __isl_keep isl_val
*stride
, __isl_keep isl_multi_val
*offset
,
3117 __isl_take isl_ast_build
*build
)
3119 isl_ast_graft_list
*list
;
3126 isl_multi_aff
*ma
, *zero
;
3127 isl_union_map
*executed
;
3129 ctx
= isl_ast_build_get_ctx(build
);
3130 depth
= isl_ast_build_get_depth(build
);
3132 first
= first_offset(domain
, order
, n
, build
);
3136 mv
= isl_multi_val_copy(offset
);
3137 val
= isl_multi_val_get_val(offset
, first
);
3138 val
= isl_val_neg(val
);
3139 mv
= isl_multi_val_add_val(mv
, val
);
3140 mv
= isl_multi_val_mod_val(mv
, isl_val_copy(stride
));
3142 executed
= contruct_shifted_executed(domain
, order
, n
, stride
, mv
,
3144 space
= isl_ast_build_get_space(build
, 1);
3145 space
= isl_space_map_from_set(space
);
3146 ma
= isl_multi_aff_identity(isl_space_copy(space
));
3147 space
= isl_space_from_domain(isl_space_domain(space
));
3148 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
3149 zero
= isl_multi_aff_zero(space
);
3150 ma
= isl_multi_aff_range_splice(ma
, depth
+ 1, zero
);
3151 build
= isl_ast_build_insert_dim(build
, depth
+ 1);
3152 list
= generate_shifted_component(executed
, build
);
3154 list
= isl_ast_graft_list_preimage_multi_aff(list
, ma
);
3156 isl_multi_val_free(mv
);
3160 isl_ast_build_free(build
);
3164 /* Generate code for a single component.
3166 * The component inverse schedule is specified as the "map" fields
3167 * of the elements of "domain" indexed by the first "n" elements of "order".
3169 * This function may modify the "set" fields of "domain".
3171 * Before proceeding with the actual code generation for the component,
3172 * we first check if there are any "shifted" strides, meaning that
3173 * the schedule domains of the individual domains are all strided,
3174 * but that they have different offsets, resulting in the union
3175 * of schedule domains not being strided anymore.
3177 * The simplest example is the schedule
3179 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3181 * Both schedule domains are strided, but their union is not.
3182 * This function detects such cases and then rewrites the schedule to
3184 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3186 * In the new schedule, the schedule domains have the same offset (modulo
3187 * the stride), ensuring that the union of schedule domains is also strided.
3190 * If there is only a single domain in the component, then there is
3191 * nothing to do. Similarly, if the current schedule dimension has
3192 * a fixed value for almost all domains then there is nothing to be done.
3193 * In particular, we need at least two domains where the current schedule
3194 * dimension does not have a fixed value.
3195 * Finally, if any of the options refer to the current schedule dimension,
3196 * then we bail out as well. It would be possible to reformulate the options
3197 * in terms of the new schedule domain, but that would introduce constraints
3198 * that separate the domains in the options and that is something we would
3202 * To see if there is any shifted stride, we look at the differences
3203 * between the values of the current dimension in pairs of domains
3204 * for equal values of outer dimensions. These differences should be
3209 * with "m" the stride and "r" a constant. Note that we cannot perform
3210 * this analysis on individual domains as the lower bound in each domain
3211 * may depend on parameters or outer dimensions and so the current dimension
3212 * itself may not have a fixed remainder on division by the stride.
3214 * In particular, we compare the first domain that does not have an
3215 * obviously fixed value for the current dimension to itself and all
3216 * other domains and collect the offsets and the gcd of the strides.
3217 * If the gcd becomes one, then we failed to find shifted strides.
3218 * If the gcd is zero, then the differences were all fixed, meaning
3219 * that some domains had non-obviously fixed values for the current dimension.
3220 * If all the offsets are the same (for those domains that do not have
3221 * an obviously fixed value for the current dimension), then we do not
3222 * apply the transformation.
3223 * If none of the domains were skipped, then there is nothing to do.
3224 * If some of them were skipped, then if we apply separation, the schedule
3225 * domain should get split in pieces with a (non-shifted) stride.
3227 * Otherwise, we apply a shift to expose the stride in
3228 * generate_shift_component.
3230 static __isl_give isl_ast_graft_list
*generate_component(
3231 struct isl_set_map_pair
*domain
, int *order
, int n
,
3232 __isl_take isl_ast_build
*build
)
3239 isl_val
*gcd
= NULL
;
3243 isl_ast_graft_list
*list
;
3246 depth
= isl_ast_build_get_depth(build
);
3249 if (skip
>= 0 && !skip
)
3250 skip
= at_most_one_non_fixed(domain
, order
, n
, depth
);
3251 if (skip
>= 0 && !skip
)
3252 skip
= isl_ast_build_options_involve_depth(build
);
3256 return generate_shifted_component_from_list(domain
,
3259 base
= eliminate_non_fixed(domain
, order
, n
, depth
, build
);
3263 ctx
= isl_ast_build_get_ctx(build
);
3265 mv
= isl_multi_val_zero(isl_space_set_alloc(ctx
, 0, n
));
3268 for (i
= 0; i
< n
; ++i
) {
3271 map
= isl_map_from_domain_and_range(
3272 isl_set_copy(domain
[order
[base
]].set
),
3273 isl_set_copy(domain
[order
[i
]].set
));
3274 for (d
= 0; d
< depth
; ++d
)
3275 map
= isl_map_equate(map
, isl_dim_in
, d
,
3277 deltas
= isl_map_deltas(map
);
3278 res
= isl_set_dim_residue_class_val(deltas
, depth
, &m
, &r
);
3279 isl_set_free(deltas
);
3286 gcd
= isl_val_gcd(gcd
, m
);
3287 if (isl_val_is_one(gcd
)) {
3291 mv
= isl_multi_val_set_val(mv
, i
, r
);
3293 res
= dim_is_fixed(domain
[order
[i
]].set
, depth
);
3299 if (fixed
&& i
> base
) {
3301 a
= isl_multi_val_get_val(mv
, i
);
3302 b
= isl_multi_val_get_val(mv
, base
);
3303 if (isl_val_ne(a
, b
))
3310 if (res
< 0 || !gcd
) {
3311 isl_ast_build_free(build
);
3313 } else if (i
< n
|| fixed
|| isl_val_is_zero(gcd
)) {
3314 list
= generate_shifted_component_from_list(domain
,
3317 list
= generate_shift_component(domain
, order
, n
, gcd
, mv
,
3322 isl_multi_val_free(mv
);
3326 isl_ast_build_free(build
);
3330 /* Store both "map" itself and its domain in the
3331 * structure pointed to by *next and advance to the next array element.
3333 static int extract_domain(__isl_take isl_map
*map
, void *user
)
3335 struct isl_set_map_pair
**next
= user
;
3337 (*next
)->map
= isl_map_copy(map
);
3338 (*next
)->set
= isl_map_domain(map
);
3344 /* Internal data for any_scheduled_after.
3346 * "depth" is the number of loops that have already been generated
3347 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3348 * "domain" is an array of set-map pairs corresponding to the different
3349 * iteration domains. The set is the schedule domain, i.e., the domain
3350 * of the inverse schedule, while the map is the inverse schedule itself.
3352 struct isl_any_scheduled_after_data
{
3354 int group_coscheduled
;
3355 struct isl_set_map_pair
*domain
;
3358 /* Is any element of domain "i" scheduled after any element of domain "j"
3359 * (for a common iteration of the first data->depth loops)?
3361 * data->domain[i].set contains the domain of the inverse schedule
3362 * for domain "i", i.e., elements in the schedule domain.
3364 * If data->group_coscheduled is set, then we also return 1 if there
3365 * is any pair of elements in the two domains that are scheduled together.
3367 static int any_scheduled_after(int i
, int j
, void *user
)
3369 struct isl_any_scheduled_after_data
*data
= user
;
3370 int dim
= isl_set_dim(data
->domain
[i
].set
, isl_dim_set
);
3373 for (pos
= data
->depth
; pos
< dim
; ++pos
) {
3376 follows
= isl_set_follows_at(data
->domain
[i
].set
,
3377 data
->domain
[j
].set
, pos
);
3387 return data
->group_coscheduled
;
3390 /* Look for independent components at the current depth and generate code
3391 * for each component separately. The resulting lists of grafts are
3392 * merged in an attempt to combine grafts with identical guards.
3394 * Code for two domains can be generated separately if all the elements
3395 * of one domain are scheduled before (or together with) all the elements
3396 * of the other domain. We therefore consider the graph with as nodes
3397 * the domains and an edge between two nodes if any element of the first
3398 * node is scheduled after any element of the second node.
3399 * If the ast_build_group_coscheduled is set, then we also add an edge if
3400 * there is any pair of elements in the two domains that are scheduled
3402 * Code is then generated (by generate_component)
3403 * for each of the strongly connected components in this graph
3404 * in their topological order.
3406 * Since the test is performed on the domain of the inverse schedules of
3407 * the different domains, we precompute these domains and store
3408 * them in data.domain.
3410 static __isl_give isl_ast_graft_list
*generate_components(
3411 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3414 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3415 int n
= isl_union_map_n_map(executed
);
3416 struct isl_any_scheduled_after_data data
;
3417 struct isl_set_map_pair
*next
;
3418 struct isl_tarjan_graph
*g
= NULL
;
3419 isl_ast_graft_list
*list
= NULL
;
3422 data
.domain
= isl_calloc_array(ctx
, struct isl_set_map_pair
, n
);
3428 if (isl_union_map_foreach_map(executed
, &extract_domain
, &next
) < 0)
3433 data
.depth
= isl_ast_build_get_depth(build
);
3434 data
.group_coscheduled
= isl_options_get_ast_build_group_coscheduled(ctx
);
3435 g
= isl_tarjan_graph_init(ctx
, n
, &any_scheduled_after
, &data
);
3439 list
= isl_ast_graft_list_alloc(ctx
, 0);
3443 isl_ast_graft_list
*list_c
;
3446 if (g
->order
[i
] == -1)
3447 isl_die(ctx
, isl_error_internal
, "cannot happen",
3450 while (g
->order
[i
] != -1) {
3454 list_c
= generate_component(data
.domain
,
3455 g
->order
+ first
, i
- first
,
3456 isl_ast_build_copy(build
));
3457 list
= isl_ast_graft_list_merge(list
, list_c
, build
);
3463 error
: list
= isl_ast_graft_list_free(list
);
3464 isl_tarjan_graph_free(g
);
3465 for (i
= 0; i
< n_domain
; ++i
) {
3466 isl_map_free(data
.domain
[i
].map
);
3467 isl_set_free(data
.domain
[i
].set
);
3470 isl_union_map_free(executed
);
3471 isl_ast_build_free(build
);
3476 /* Generate code for the next level (and all inner levels).
3478 * If "executed" is empty, i.e., no code needs to be generated,
3479 * then we return an empty list.
3481 * If we have already generated code for all loop levels, then we pass
3482 * control to generate_inner_level.
3484 * If "executed" lives in a single space, i.e., if code needs to be
3485 * generated for a single domain, then there can only be a single
3486 * component and we go directly to generate_shifted_component.
3487 * Otherwise, we call generate_components to detect the components
3488 * and to call generate_component on each of them separately.
3490 static __isl_give isl_ast_graft_list
*generate_next_level(
3491 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3495 if (!build
|| !executed
)
3498 if (isl_union_map_is_empty(executed
)) {
3499 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3500 isl_union_map_free(executed
);
3501 isl_ast_build_free(build
);
3502 return isl_ast_graft_list_alloc(ctx
, 0);
3505 depth
= isl_ast_build_get_depth(build
);
3506 if (depth
>= isl_set_dim(build
->domain
, isl_dim_set
))
3507 return generate_inner_level(executed
, build
);
3509 if (isl_union_map_n_map(executed
) == 1)
3510 return generate_shifted_component(executed
, build
);
3512 return generate_components(executed
, build
);
3514 isl_union_map_free(executed
);
3515 isl_ast_build_free(build
);
3519 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3520 * internal, executed and build are the inputs to generate_code.
3521 * list collects the output.
3523 struct isl_generate_code_data
{
3525 isl_union_map
*executed
;
3526 isl_ast_build
*build
;
3528 isl_ast_graft_list
*list
;
3531 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3535 * with E the external build schedule and S the additional schedule "space",
3536 * reformulate the inverse schedule in terms of the internal schedule domain,
3541 * We first obtain a mapping
3545 * take the inverse and the product with S -> S, resulting in
3547 * [I -> S] -> [E -> S]
3549 * Applying the map to the input produces the desired result.
3551 static __isl_give isl_union_map
*internal_executed(
3552 __isl_take isl_union_map
*executed
, __isl_keep isl_space
*space
,
3553 __isl_keep isl_ast_build
*build
)
3557 proj
= isl_ast_build_get_schedule_map(build
);
3558 proj
= isl_map_reverse(proj
);
3559 space
= isl_space_map_from_set(isl_space_copy(space
));
3560 id
= isl_map_identity(space
);
3561 proj
= isl_map_product(proj
, id
);
3562 executed
= isl_union_map_apply_domain(executed
,
3563 isl_union_map_from_map(proj
));
3567 /* Generate an AST that visits the elements in the range of data->executed
3568 * in the relative order specified by the corresponding domain element(s)
3569 * for those domain elements that belong to "set".
3570 * Add the result to data->list.
3572 * The caller ensures that "set" is a universe domain.
3573 * "space" is the space of the additional part of the schedule.
3574 * It is equal to the space of "set" if build->domain is parametric.
3575 * Otherwise, it is equal to the range of the wrapped space of "set".
3577 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3578 * was called from an outside user (data->internal not set), then
3579 * the (inverse) schedule refers to the external build domain and needs to
3580 * be transformed to refer to the internal build domain.
3582 * The build is extended to include the additional part of the schedule.
3583 * If the original build space was not parametric, then the options
3584 * in data->build refer only to the additional part of the schedule
3585 * and they need to be adjusted to refer to the complete AST build
3588 * After having adjusted inverse schedule and build, we start generating
3589 * code with the outer loop of the current code generation
3590 * in generate_next_level.
3592 * If the original build space was not parametric, we undo the embedding
3593 * on the resulting isl_ast_node_list so that it can be used within
3594 * the outer AST build.
3596 static int generate_code_in_space(struct isl_generate_code_data
*data
,
3597 __isl_take isl_set
*set
, __isl_take isl_space
*space
)
3599 isl_union_map
*executed
;
3600 isl_ast_build
*build
;
3601 isl_ast_graft_list
*list
;
3604 executed
= isl_union_map_copy(data
->executed
);
3605 executed
= isl_union_map_intersect_domain(executed
,
3606 isl_union_set_from_set(set
));
3608 embed
= !isl_set_is_params(data
->build
->domain
);
3609 if (embed
&& !data
->internal
)
3610 executed
= internal_executed(executed
, space
, data
->build
);
3612 build
= isl_ast_build_copy(data
->build
);
3613 build
= isl_ast_build_product(build
, space
);
3615 list
= generate_next_level(executed
, build
);
3617 list
= isl_ast_graft_list_unembed(list
, embed
);
3619 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
3624 /* Generate an AST that visits the elements in the range of data->executed
3625 * in the relative order specified by the corresponding domain element(s)
3626 * for those domain elements that belong to "set".
3627 * Add the result to data->list.
3629 * The caller ensures that "set" is a universe domain.
3631 * If the build space S is not parametric, then the space of "set"
3632 * need to be a wrapped relation with S as domain. That is, it needs
3637 * Check this property and pass control to generate_code_in_space
3639 * If the build space is not parametric, then T is the space of "set".
3641 static int generate_code_set(__isl_take isl_set
*set
, void *user
)
3643 struct isl_generate_code_data
*data
= user
;
3644 isl_space
*space
, *build_space
;
3647 space
= isl_set_get_space(set
);
3649 if (isl_set_is_params(data
->build
->domain
))
3650 return generate_code_in_space(data
, set
, space
);
3652 build_space
= isl_ast_build_get_space(data
->build
, data
->internal
);
3653 space
= isl_space_unwrap(space
);
3654 is_domain
= isl_space_is_domain(build_space
, space
);
3655 isl_space_free(build_space
);
3656 space
= isl_space_range(space
);
3661 isl_die(isl_set_get_ctx(set
), isl_error_invalid
,
3662 "invalid nested schedule space", goto error
);
3664 return generate_code_in_space(data
, set
, space
);
3667 isl_space_free(space
);
3671 /* Generate an AST that visits the elements in the range of "executed"
3672 * in the relative order specified by the corresponding domain element(s).
3674 * "build" is an isl_ast_build that has either been constructed by
3675 * isl_ast_build_from_context or passed to a callback set by
3676 * isl_ast_build_set_create_leaf.
3677 * In the first case, the space of the isl_ast_build is typically
3678 * a parametric space, although this is currently not enforced.
3679 * In the second case, the space is never a parametric space.
3680 * If the space S is not parametric, then the domain space(s) of "executed"
3681 * need to be wrapped relations with S as domain.
3683 * If the domain of "executed" consists of several spaces, then an AST
3684 * is generated for each of them (in arbitrary order) and the results
3687 * If "internal" is set, then the domain "S" above refers to the internal
3688 * schedule domain representation. Otherwise, it refers to the external
3689 * representation, as returned by isl_ast_build_get_schedule_space.
3691 * We essentially run over all the spaces in the domain of "executed"
3692 * and call generate_code_set on each of them.
3694 static __isl_give isl_ast_graft_list
*generate_code(
3695 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
3699 struct isl_generate_code_data data
= { 0 };
3701 isl_union_set
*schedule_domain
;
3702 isl_union_map
*universe
;
3706 space
= isl_ast_build_get_space(build
, 1);
3707 space
= isl_space_align_params(space
,
3708 isl_union_map_get_space(executed
));
3709 space
= isl_space_align_params(space
,
3710 isl_union_map_get_space(build
->options
));
3711 build
= isl_ast_build_align_params(build
, isl_space_copy(space
));
3712 executed
= isl_union_map_align_params(executed
, space
);
3713 if (!executed
|| !build
)
3716 ctx
= isl_ast_build_get_ctx(build
);
3718 data
.internal
= internal
;
3719 data
.executed
= executed
;
3721 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
3723 universe
= isl_union_map_universe(isl_union_map_copy(executed
));
3724 schedule_domain
= isl_union_map_domain(universe
);
3725 if (isl_union_set_foreach_set(schedule_domain
, &generate_code_set
,
3727 data
.list
= isl_ast_graft_list_free(data
.list
);
3729 isl_union_set_free(schedule_domain
);
3730 isl_union_map_free(executed
);
3732 isl_ast_build_free(build
);
3735 isl_union_map_free(executed
);
3736 isl_ast_build_free(build
);
3740 /* Generate an AST that visits the elements in the domain of "schedule"
3741 * in the relative order specified by the corresponding image element(s).
3743 * "build" is an isl_ast_build that has either been constructed by
3744 * isl_ast_build_from_context or passed to a callback set by
3745 * isl_ast_build_set_create_leaf.
3746 * In the first case, the space of the isl_ast_build is typically
3747 * a parametric space, although this is currently not enforced.
3748 * In the second case, the space is never a parametric space.
3749 * If the space S is not parametric, then the range space(s) of "schedule"
3750 * need to be wrapped relations with S as domain.
3752 * If the range of "schedule" consists of several spaces, then an AST
3753 * is generated for each of them (in arbitrary order) and the results
3756 * We first initialize the local copies of the relevant options.
3757 * We do this here rather than when the isl_ast_build is created
3758 * because the options may have changed between the construction
3759 * of the isl_ast_build and the call to isl_generate_code.
3761 * The main computation is performed on an inverse schedule (with
3762 * the schedule domain in the domain and the elements to be executed
3763 * in the range) called "executed".
3765 __isl_give isl_ast_node
*isl_ast_build_ast_from_schedule(
3766 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
3768 isl_ast_graft_list
*list
;
3770 isl_union_map
*executed
;
3772 build
= isl_ast_build_copy(build
);
3773 build
= isl_ast_build_set_single_valued(build
, 0);
3774 schedule
= isl_union_map_coalesce(schedule
);
3775 executed
= isl_union_map_reverse(schedule
);
3776 list
= generate_code(executed
, isl_ast_build_copy(build
), 0);
3777 node
= isl_ast_node_from_graft_list(list
, build
);
3778 isl_ast_build_free(build
);