2 * Copyright 2012 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 /* Add the constraint to the list that "user" points to, if it is not
25 static int collect_constraint(__isl_take isl_constraint
*constraint
,
28 isl_constraint_list
**list
= user
;
30 if (isl_constraint_is_div_constraint(constraint
))
31 isl_constraint_free(constraint
);
33 *list
= isl_constraint_list_add(*list
, constraint
);
38 /* Extract the constraints of "bset" (except the div constraints)
39 * and collect them in an isl_constraint_list.
41 static __isl_give isl_constraint_list
*isl_constraint_list_from_basic_set(
42 __isl_take isl_basic_set
*bset
)
46 isl_constraint_list
*list
;
51 ctx
= isl_basic_set_get_ctx(bset
);
53 n
= isl_basic_set_n_constraint(bset
);
54 list
= isl_constraint_list_alloc(ctx
, n
);
55 if (isl_basic_set_foreach_constraint(bset
,
56 &collect_constraint
, &list
) < 0)
57 list
= isl_constraint_list_free(list
);
59 isl_basic_set_free(bset
);
63 /* Data used in generate_domain.
65 * "build" is the input build.
66 * "list" collects the results.
68 struct isl_generate_domain_data
{
71 isl_ast_graft_list
*list
;
74 static __isl_give isl_ast_graft_list
*generate_next_level(
75 __isl_take isl_union_map
*executed
,
76 __isl_take isl_ast_build
*build
);
77 static __isl_give isl_ast_graft_list
*generate_code(
78 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
81 /* Generate an AST for a single domain based on
82 * the (non single valued) inverse schedule "executed".
84 * We extend the schedule with the iteration domain
85 * and continue generating through a call to generate_code.
87 * In particular, if executed has the form
91 * then we continue generating code on
95 * The extended inverse schedule is clearly single valued
96 * ensuring that the nested generate_code will not reach this function,
97 * but will instead create calls to all elements of D that need
98 * to be executed from the current schedule domain.
100 static int generate_non_single_valued(__isl_take isl_map
*executed
,
101 struct isl_generate_domain_data
*data
)
104 isl_ast_build
*build
;
105 isl_ast_graft_list
*list
;
107 build
= isl_ast_build_copy(data
->build
);
109 identity
= isl_set_identity(isl_map_range(isl_map_copy(executed
)));
110 executed
= isl_map_domain_product(executed
, identity
);
111 build
= isl_ast_build_set_single_valued(build
, 1);
113 list
= generate_code(isl_union_map_from_map(executed
), build
, 1);
115 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
120 /* Call the at_each_domain callback, if requested by the user,
121 * after recording the current inverse schedule in the build.
123 static __isl_give isl_ast_graft
*at_each_domain(__isl_take isl_ast_graft
*graft
,
124 __isl_keep isl_map
*executed
, __isl_keep isl_ast_build
*build
)
126 if (!graft
|| !build
)
127 return isl_ast_graft_free(graft
);
128 if (!build
->at_each_domain
)
131 build
= isl_ast_build_copy(build
);
132 build
= isl_ast_build_set_executed(build
,
133 isl_union_map_from_map(isl_map_copy(executed
)));
135 return isl_ast_graft_free(graft
);
137 graft
->node
= build
->at_each_domain(graft
->node
,
138 build
, build
->at_each_domain_user
);
139 isl_ast_build_free(build
);
142 graft
= isl_ast_graft_free(graft
);
147 /* Generate an AST for a single domain based on
148 * the inverse schedule "executed".
150 * If there is more than one domain element associated to the current
151 * schedule "time", then we need to continue the generation process
152 * in generate_non_single_valued.
153 * Note that the inverse schedule being single-valued may depend
154 * on constraints that are only available in the original context
155 * domain specified by the user. We therefore first introduce
156 * the constraints from data->build->domain.
157 * On the other hand, we only perform the test after having taken the gist
158 * of the domain as the resulting map is the one from which the call
159 * expression is constructed. Using this map to construct the call
160 * expression usually yields simpler results.
161 * Because we perform the single-valuedness test on the gisted map,
162 * we may in rare cases fail to recognize that the inverse schedule
163 * is single-valued. This becomes problematic if this happens
164 * from the recursive call through generate_non_single_valued
165 * as we would then end up in an infinite recursion.
166 * We therefore check if we are inside a call to generate_non_single_valued
167 * and revert to the ungisted map if the gisted map turns out not to be
170 * Otherwise, we generate a call expression for the single executed
171 * domain element and put a guard around it based on the (simplified)
172 * domain of "executed".
174 * If the user has set an at_each_domain callback, it is called
175 * on the constructed call expression node.
177 static int generate_domain(__isl_take isl_map
*executed
, void *user
)
179 struct isl_generate_domain_data
*data
= user
;
180 isl_ast_graft
*graft
;
181 isl_ast_graft_list
*list
;
186 executed
= isl_map_intersect_domain(executed
,
187 isl_set_copy(data
->build
->domain
));
189 executed
= isl_map_coalesce(executed
);
190 map
= isl_map_copy(executed
);
191 map
= isl_ast_build_compute_gist_map_domain(data
->build
, map
);
192 sv
= isl_map_is_single_valued(map
);
197 if (data
->build
->single_valued
)
198 map
= isl_map_copy(executed
);
200 return generate_non_single_valued(executed
, data
);
202 guard
= isl_map_domain(isl_map_copy(map
));
203 guard
= isl_set_coalesce(guard
);
204 guard
= isl_ast_build_compute_gist(data
->build
, guard
);
205 graft
= isl_ast_graft_alloc_domain(map
, data
->build
);
206 graft
= at_each_domain(graft
, executed
, data
->build
);
208 isl_map_free(executed
);
209 graft
= isl_ast_graft_add_guard(graft
, guard
, data
->build
);
211 list
= isl_ast_graft_list_from_ast_graft(graft
);
212 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
217 isl_map_free(executed
);
221 /* Call build->create_leaf to a create "leaf" node in the AST,
222 * encapsulate the result in an isl_ast_graft and return the result
223 * as a 1-element list.
225 * Note that the node returned by the user may be an entire tree.
227 * Before we pass control to the user, we first clear some information
228 * from the build that is (presumbably) only meaningful
229 * for the current code generation.
230 * This includes the create_leaf callback itself, so we make a copy
231 * of the build first.
233 static __isl_give isl_ast_graft_list
*call_create_leaf(
234 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
237 isl_ast_graft
*graft
;
238 isl_ast_build
*user_build
;
240 user_build
= isl_ast_build_copy(build
);
241 user_build
= isl_ast_build_set_executed(user_build
, executed
);
242 user_build
= isl_ast_build_clear_local_info(user_build
);
246 node
= build
->create_leaf(user_build
, build
->create_leaf_user
);
247 graft
= isl_ast_graft_alloc(node
, build
);
248 isl_ast_build_free(build
);
249 return isl_ast_graft_list_from_ast_graft(graft
);
252 /* Generate an AST after having handled the complete schedule
253 * of this call to the code generator.
255 * If the user has specified a create_leaf callback, control
256 * is passed to the user in call_create_leaf.
258 * Otherwise, we generate one or more calls for each individual
259 * domain in generate_domain.
261 static __isl_give isl_ast_graft_list
*generate_inner_level(
262 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
265 struct isl_generate_domain_data data
= { build
};
267 if (!build
|| !executed
)
270 if (build
->create_leaf
)
271 return call_create_leaf(executed
, build
);
273 ctx
= isl_union_map_get_ctx(executed
);
274 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
275 if (isl_union_map_foreach_map(executed
, &generate_domain
, &data
) < 0)
276 data
.list
= isl_ast_graft_list_free(data
.list
);
279 error
: data
.list
= NULL
;
280 isl_ast_build_free(build
);
281 isl_union_map_free(executed
);
285 /* Call the before_each_for callback, if requested by the user.
287 static __isl_give isl_ast_node
*before_each_for(__isl_take isl_ast_node
*node
,
288 __isl_keep isl_ast_build
*build
)
293 return isl_ast_node_free(node
);
294 if (!build
->before_each_for
)
296 id
= build
->before_each_for(build
, build
->before_each_for_user
);
297 node
= isl_ast_node_set_annotation(node
, id
);
301 /* Call the after_each_for callback, if requested by the user.
303 static __isl_give isl_ast_graft
*after_each_for(__isl_keep isl_ast_graft
*graft
,
304 __isl_keep isl_ast_build
*build
)
306 if (!graft
|| !build
)
307 return isl_ast_graft_free(graft
);
308 if (!build
->after_each_for
)
310 graft
->node
= build
->after_each_for(graft
->node
, build
,
311 build
->after_each_for_user
);
313 return isl_ast_graft_free(graft
);
317 /* Plug in all the know values of the current and outer dimensions
318 * in the domain of "executed". In principle, we only need to plug
319 * in the known value of the current dimension since the values of
320 * outer dimensions have been plugged in already.
321 * However, it turns out to be easier to just plug in all known values.
323 static __isl_give isl_union_map
*plug_in_values(
324 __isl_take isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
326 return isl_ast_build_substitute_values_union_map_domain(build
,
330 /* Check if the constraint "c" is a lower bound on dimension "pos",
331 * an upper bound, or independent of dimension "pos".
333 static int constraint_type(isl_constraint
*c
, int pos
)
335 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, pos
))
337 if (isl_constraint_is_upper_bound(c
, isl_dim_set
, pos
))
342 /* Compare the types of the constraints "a" and "b",
343 * resulting in constraints that are independent of "depth"
344 * to be sorted before the lower bounds on "depth", which in
345 * turn are sorted before the upper bounds on "depth".
347 static int cmp_constraint(__isl_keep isl_constraint
*a
,
348 __isl_keep isl_constraint
*b
, void *user
)
351 int t1
= constraint_type(a
, *depth
);
352 int t2
= constraint_type(b
, *depth
);
357 /* Extract a lower bound on dimension "pos" from constraint "c".
359 * If the constraint is of the form
363 * then we essentially return
365 * l = ceil(-f(...)/a)
367 * However, if the current dimension is strided, then we need to make
368 * sure that the lower bound we construct is of the form
372 * with f the offset and s the stride.
373 * We therefore compute
375 * f + s * ceil((l - f)/s)
377 static __isl_give isl_aff
*lower_bound(__isl_keep isl_constraint
*c
,
378 int pos
, __isl_keep isl_ast_build
*build
)
382 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
383 aff
= isl_aff_ceil(aff
);
385 if (isl_ast_build_has_stride(build
, pos
)) {
389 isl_int_init(stride
);
391 offset
= isl_ast_build_get_offset(build
, pos
);
392 isl_ast_build_get_stride(build
, pos
, &stride
);
394 aff
= isl_aff_sub(aff
, isl_aff_copy(offset
));
395 aff
= isl_aff_scale_down(aff
, stride
);
396 aff
= isl_aff_ceil(aff
);
397 aff
= isl_aff_scale(aff
, stride
);
398 aff
= isl_aff_add(aff
, offset
);
400 isl_int_clear(stride
);
403 aff
= isl_ast_build_compute_gist_aff(build
, aff
);
408 /* Return the exact lower bound (or upper bound if "upper" is set)
409 * of "domain" as a piecewise affine expression.
411 * If we are computing a lower bound (of a strided dimension), then
412 * we need to make sure it is of the form
416 * where f is the offset and s is the stride.
417 * We therefore need to include the stride constraint before computing
420 static __isl_give isl_pw_aff
*exact_bound(__isl_keep isl_set
*domain
,
421 __isl_keep isl_ast_build
*build
, int upper
)
426 isl_pw_multi_aff
*pma
;
428 domain
= isl_set_copy(domain
);
430 stride
= isl_ast_build_get_stride_constraint(build
);
431 domain
= isl_set_intersect(domain
, stride
);
433 it_map
= isl_ast_build_map_to_iterator(build
, domain
);
435 pma
= isl_map_lexmax_pw_multi_aff(it_map
);
437 pma
= isl_map_lexmin_pw_multi_aff(it_map
);
438 pa
= isl_pw_multi_aff_get_pw_aff(pma
, 0);
439 isl_pw_multi_aff_free(pma
);
440 pa
= isl_ast_build_compute_gist_pw_aff(build
, pa
);
441 pa
= isl_pw_aff_coalesce(pa
);
446 /* Extract a lower bound on dimension "pos" from each constraint
447 * in "constraints" and return the list of lower bounds.
448 * If "constraints" has zero elements, then we extract a lower bound
449 * from "domain" instead.
451 static __isl_give isl_pw_aff_list
*lower_bounds(
452 __isl_keep isl_constraint_list
*constraints
, int pos
,
453 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
456 isl_pw_aff_list
*list
;
462 n
= isl_constraint_list_n_constraint(constraints
);
465 pa
= exact_bound(domain
, build
, 0);
466 return isl_pw_aff_list_from_pw_aff(pa
);
469 ctx
= isl_ast_build_get_ctx(build
);
470 list
= isl_pw_aff_list_alloc(ctx
,n
);
472 for (i
= 0; i
< n
; ++i
) {
476 c
= isl_constraint_list_get_constraint(constraints
, i
);
477 aff
= lower_bound(c
, pos
, build
);
478 isl_constraint_free(c
);
479 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
485 /* Extract an upper bound on dimension "pos" from each constraint
486 * in "constraints" and return the list of upper bounds.
487 * If "constraints" has zero elements, then we extract an upper bound
488 * from "domain" instead.
490 static __isl_give isl_pw_aff_list
*upper_bounds(
491 __isl_keep isl_constraint_list
*constraints
, int pos
,
492 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
495 isl_pw_aff_list
*list
;
498 n
= isl_constraint_list_n_constraint(constraints
);
501 pa
= exact_bound(domain
, build
, 1);
502 return isl_pw_aff_list_from_pw_aff(pa
);
505 ctx
= isl_ast_build_get_ctx(build
);
506 list
= isl_pw_aff_list_alloc(ctx
,n
);
508 for (i
= 0; i
< n
; ++i
) {
512 c
= isl_constraint_list_get_constraint(constraints
, i
);
513 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
514 isl_constraint_free(c
);
515 aff
= isl_aff_floor(aff
);
516 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
522 /* Return an isl_ast_expr that performs the reduction of type "type"
523 * on AST expressions corresponding to the elements in "list".
525 * The list is assumed to contain at least one element.
526 * If the list contains exactly one element, then the returned isl_ast_expr
527 * simply computes that affine expression.
529 static __isl_give isl_ast_expr
*reduce_list(enum isl_ast_op_type type
,
530 __isl_keep isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
539 n
= isl_pw_aff_list_n_pw_aff(list
);
542 return isl_ast_build_expr_from_pw_aff_internal(build
,
543 isl_pw_aff_list_get_pw_aff(list
, 0));
545 ctx
= isl_pw_aff_list_get_ctx(list
);
546 expr
= isl_ast_expr_alloc_op(ctx
, type
, n
);
550 for (i
= 0; i
< n
; ++i
) {
551 isl_ast_expr
*expr_i
;
553 expr_i
= isl_ast_build_expr_from_pw_aff_internal(build
,
554 isl_pw_aff_list_get_pw_aff(list
, i
));
556 return isl_ast_expr_free(expr
);
557 expr
->u
.op
.args
[i
] = expr_i
;
563 /* Add a guard to "graft" based on "bound" in the case of a degenerate
564 * level (including the special case of an eliminated level).
566 * We eliminate the current dimension, simplify the result in the current
567 * build and add the result as guards to the graft.
569 * Note that we cannot simply drop the constraints on the current dimension
570 * even in the eliminated case, because the single affine expression may
571 * not be explicitly available in "bounds". Moreover, the single affine
572 * expression may only be defined on a subset of the build domain,
573 * so we do in some cases need to insert a guard even in the eliminated case.
575 static __isl_give isl_ast_graft
*add_degenerate_guard(
576 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
577 __isl_keep isl_ast_build
*build
)
582 depth
= isl_ast_build_get_depth(build
);
584 dom
= isl_set_from_basic_set(isl_basic_set_copy(bounds
));
585 if (isl_ast_build_has_stride(build
, depth
)) {
588 stride
= isl_ast_build_get_stride_constraint(build
);
589 dom
= isl_set_intersect(dom
, stride
);
591 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
592 dom
= isl_ast_build_compute_gist(build
, dom
);
594 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
599 /* Update "graft" based on "bounds" for the eliminated case.
601 * In the eliminated case, no for node is created, so we only need
602 * to check if "bounds" imply any guards that need to be inserted.
604 static __isl_give isl_ast_graft
*refine_eliminated(
605 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
606 __isl_keep isl_ast_build
*build
)
608 return add_degenerate_guard(graft
, bounds
, build
);
611 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
613 * "build" is the build in which graft->node was created
614 * "sub_build" contains information about the current level itself,
615 * including the single value attained.
617 * We first set the initialization part of the for loop to the single
618 * value attained by the current dimension.
619 * The increment and condition are not strictly needed as the are known
620 * to be "1" and "iterator <= value" respectively.
621 * Then we set the size of the iterator and
622 * check if "bounds" imply any guards that need to be inserted.
624 static __isl_give isl_ast_graft
*refine_degenerate(
625 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
626 __isl_keep isl_ast_build
*build
,
627 __isl_keep isl_ast_build
*sub_build
)
631 if (!graft
|| !sub_build
)
632 return isl_ast_graft_free(graft
);
634 value
= isl_pw_aff_copy(sub_build
->value
);
636 graft
->node
->u
.f
.init
= isl_ast_build_expr_from_pw_aff_internal(build
,
638 if (!graft
->node
->u
.f
.init
)
639 return isl_ast_graft_free(graft
);
641 graft
= add_degenerate_guard(graft
, bounds
, build
);
646 /* Return the intersection of constraints in "list" as a set.
648 static __isl_give isl_set
*intersect_constraints(
649 __isl_keep isl_constraint_list
*list
)
654 n
= isl_constraint_list_n_constraint(list
);
656 isl_die(isl_constraint_list_get_ctx(list
), isl_error_internal
,
657 "expecting at least one constraint", return NULL
);
659 bset
= isl_basic_set_from_constraint(
660 isl_constraint_list_get_constraint(list
, 0));
661 for (i
= 1; i
< n
; ++i
) {
662 isl_basic_set
*bset_i
;
664 bset_i
= isl_basic_set_from_constraint(
665 isl_constraint_list_get_constraint(list
, i
));
666 bset
= isl_basic_set_intersect(bset
, bset_i
);
669 return isl_set_from_basic_set(bset
);
672 /* Compute the constraints on the outer dimensions enforced by
673 * graft->node and add those constraints to graft->enforced,
674 * in case the upper bound is expressed as a set "upper".
676 * In particular, if l(...) is a lower bound in "lower", and
678 * -a i + f(...) >= 0 or a i <= f(...)
680 * is an upper bound ocnstraint on the current dimension i,
681 * then the for loop enforces the constraint
683 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
685 * We therefore simply take each lower bound in turn, plug it into
686 * the upper bounds and compute the intersection over all lower bounds.
688 * If a lower bound is a rational expression, then
689 * isl_basic_set_preimage_multi_aff will force this rational
690 * expression to have only integer values. However, the loop
691 * itself does not enforce this integrality constraint. We therefore
692 * use the ceil of the lower bounds instead of the lower bounds themselves.
693 * Other constraints will make sure that the for loop is only executed
694 * when each of the lower bounds attains an integral value.
695 * In particular, potentially rational values only occur in
696 * lower_bound if the offset is a (seemingly) rational expression,
697 * but then outer conditions will make sure that this rational expression
698 * only attains integer values.
700 static __isl_give isl_ast_graft
*set_enforced_from_set(
701 __isl_take isl_ast_graft
*graft
,
702 __isl_keep isl_pw_aff_list
*lower
, int pos
, __isl_keep isl_set
*upper
)
705 isl_basic_set
*enforced
;
706 isl_pw_multi_aff
*pma
;
709 if (!graft
|| !lower
)
710 return isl_ast_graft_free(graft
);
712 space
= isl_set_get_space(upper
);
713 enforced
= isl_basic_set_universe(isl_space_copy(space
));
715 space
= isl_space_map_from_set(space
);
716 pma
= isl_pw_multi_aff_identity(space
);
718 n
= isl_pw_aff_list_n_pw_aff(lower
);
719 for (i
= 0; i
< n
; ++i
) {
723 isl_pw_multi_aff
*pma_i
;
725 pa
= isl_pw_aff_list_get_pw_aff(lower
, i
);
726 pa
= isl_pw_aff_ceil(pa
);
727 pma_i
= isl_pw_multi_aff_copy(pma
);
728 pma_i
= isl_pw_multi_aff_set_pw_aff(pma_i
, pos
, pa
);
729 enforced_i
= isl_set_copy(upper
);
730 enforced_i
= isl_set_preimage_pw_multi_aff(enforced_i
, pma_i
);
731 hull
= isl_set_simple_hull(enforced_i
);
732 enforced
= isl_basic_set_intersect(enforced
, hull
);
735 isl_pw_multi_aff_free(pma
);
737 graft
= isl_ast_graft_enforce(graft
, enforced
);
742 /* Compute the constraints on the outer dimensions enforced by
743 * graft->node and add those constraints to graft->enforced,
744 * in case the upper bound is expressed as
745 * a list of affine expressions "upper".
747 * The enforced condition is that each lower bound expression is less
748 * than or equal to each upper bound expression.
750 static __isl_give isl_ast_graft
*set_enforced_from_list(
751 __isl_take isl_ast_graft
*graft
,
752 __isl_keep isl_pw_aff_list
*lower
, __isl_keep isl_pw_aff_list
*upper
)
755 isl_basic_set
*enforced
;
757 lower
= isl_pw_aff_list_copy(lower
);
758 upper
= isl_pw_aff_list_copy(upper
);
759 cond
= isl_pw_aff_list_le_set(lower
, upper
);
760 enforced
= isl_set_simple_hull(cond
);
761 graft
= isl_ast_graft_enforce(graft
, enforced
);
766 /* Does "aff" have a negative constant term?
768 static int aff_constant_is_negative(__isl_take isl_set
*set
,
769 __isl_take isl_aff
*aff
, void *user
)
775 isl_aff_get_constant(aff
, &v
);
776 *neg
= isl_int_is_neg(v
);
781 return *neg
? 0 : -1;
784 /* Does "pa" have a negative constant term over its entire domain?
786 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff
*pa
, void *user
)
791 r
= isl_pw_aff_foreach_piece(pa
, &aff_constant_is_negative
, user
);
794 return *neg
? 0 : -1;
797 /* Does each element in "list" have a negative constant term?
799 * The callback terminates the iteration as soon an element has been
800 * found that does not have a negative constant term.
802 static int list_constant_is_negative(__isl_keep isl_pw_aff_list
*list
)
806 if (isl_pw_aff_list_foreach(list
,
807 &pw_aff_constant_is_negative
, &neg
) < 0 && neg
)
813 /* Add 1 to each of the elements in "list", where each of these elements
814 * is defined over the internal schedule space of "build".
816 static __isl_give isl_pw_aff_list
*list_add_one(
817 __isl_take isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
824 space
= isl_ast_build_get_space(build
, 1);
825 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(space
));
826 aff
= isl_aff_add_constant_si(aff
, 1);
827 one
= isl_pw_aff_from_aff(aff
);
829 n
= isl_pw_aff_list_n_pw_aff(list
);
830 for (i
= 0; i
< n
; ++i
) {
832 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
833 pa
= isl_pw_aff_add(pa
, isl_pw_aff_copy(one
));
834 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
837 isl_pw_aff_free(one
);
842 /* Set the condition part of the for node graft->node in case
843 * the upper bound is represented as a list of piecewise affine expressions.
845 * In particular, set the condition to
847 * iterator <= min(list of upper bounds)
849 * If each of the upper bounds has a negative constant term, then
850 * set the condition to
852 * iterator < min(list of (upper bound + 1)s)
855 static __isl_give isl_ast_graft
*set_for_cond_from_list(
856 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*list
,
857 __isl_keep isl_ast_build
*build
)
860 isl_ast_expr
*bound
, *iterator
, *cond
;
861 enum isl_ast_op_type type
= isl_ast_op_le
;
864 return isl_ast_graft_free(graft
);
866 neg
= list_constant_is_negative(list
);
868 return isl_ast_graft_free(graft
);
869 list
= isl_pw_aff_list_copy(list
);
871 list
= list_add_one(list
, build
);
872 type
= isl_ast_op_lt
;
875 bound
= reduce_list(isl_ast_op_min
, list
, build
);
876 iterator
= isl_ast_expr_copy(graft
->node
->u
.f
.iterator
);
877 cond
= isl_ast_expr_alloc_binary(type
, iterator
, bound
);
878 graft
->node
->u
.f
.cond
= cond
;
880 isl_pw_aff_list_free(list
);
881 if (!graft
->node
->u
.f
.cond
)
882 return isl_ast_graft_free(graft
);
886 /* Set the condition part of the for node graft->node in case
887 * the upper bound is represented as a set.
889 static __isl_give isl_ast_graft
*set_for_cond_from_set(
890 __isl_take isl_ast_graft
*graft
, __isl_keep isl_set
*set
,
891 __isl_keep isl_ast_build
*build
)
898 cond
= isl_ast_build_expr_from_set(build
, isl_set_copy(set
));
899 graft
->node
->u
.f
.cond
= cond
;
900 if (!graft
->node
->u
.f
.cond
)
901 return isl_ast_graft_free(graft
);
905 /* Construct an isl_ast_expr for the increment (i.e., stride) of
906 * the current dimension.
908 static __isl_give isl_ast_expr
*for_inc(__isl_keep isl_ast_build
*build
)
917 ctx
= isl_ast_build_get_ctx(build
);
918 depth
= isl_ast_build_get_depth(build
);
920 if (!isl_ast_build_has_stride(build
, depth
))
921 return isl_ast_expr_alloc_int_si(ctx
, 1);
924 isl_ast_build_get_stride(build
, depth
, &v
);
925 inc
= isl_ast_expr_alloc_int(ctx
, v
);
931 /* Should we express the loop condition as
933 * iterator <= min(list of upper bounds)
935 * or as a conjunction of constraints?
937 * The first is constructed from a list of upper bounds.
938 * The second is constructed from a set.
940 * If there are no upper bounds in "constraints", then this could mean
941 * that "domain" simply doesn't have an upper bound or that we didn't
942 * pick any upper bound. In the first case, we want to generate the
943 * loop condition as a(n empty) conjunction of constraints
944 * In the second case, we will compute
945 * a single upper bound from "domain" and so we use the list form.
947 * If there are upper bounds in "constraints",
948 * then we use the list form iff the atomic_upper_bound option is set.
950 static int use_upper_bound_list(isl_ctx
*ctx
, int n_upper
,
951 __isl_keep isl_set
*domain
, int depth
)
954 return isl_options_get_ast_build_atomic_upper_bound(ctx
);
956 return isl_set_dim_has_upper_bound(domain
, isl_dim_set
, depth
);
959 /* Fill in the expressions of the for node in graft->node.
962 * - set the initialization part of the loop to the maximum of the lower bounds
963 * - set the size of the iterator based on the values attained by the iterator
964 * - extract the increment from the stride of the current dimension
965 * - construct the for condition either based on a list of upper bounds
966 * or on a set of upper bound constraints.
968 static __isl_give isl_ast_graft
*set_for_node_expressions(
969 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*lower
,
970 int use_list
, __isl_keep isl_pw_aff_list
*upper_list
,
971 __isl_keep isl_set
*upper_set
, __isl_keep isl_ast_build
*build
)
978 build
= isl_ast_build_copy(build
);
979 build
= isl_ast_build_set_enforced(build
,
980 isl_ast_graft_get_enforced(graft
));
983 node
->u
.f
.init
= reduce_list(isl_ast_op_max
, lower
, build
);
984 node
->u
.f
.inc
= for_inc(build
);
987 graft
= set_for_cond_from_list(graft
, upper_list
, build
);
989 graft
= set_for_cond_from_set(graft
, upper_set
, build
);
991 isl_ast_build_free(build
);
993 if (!node
->u
.f
.iterator
|| !node
->u
.f
.init
||
994 !node
->u
.f
.cond
|| !node
->u
.f
.inc
)
995 return isl_ast_graft_free(graft
);
1000 /* Update "graft" based on "bounds" and "domain" for the generic,
1001 * non-degenerate, case.
1003 * "c_lower" and "c_upper" contain the lower and upper bounds
1004 * that the loop node should express.
1005 * "domain" is the subset of the intersection of the constraints
1006 * for which some code is executed.
1008 * There may be zero lower bounds or zero upper bounds in "constraints"
1009 * in case the list of constraints was created
1010 * based on the atomic option or based on separation with explicit bounds.
1011 * In that case, we use "domain" to derive lower and/or upper bounds.
1013 * We first compute a list of one or more lower bounds.
1015 * Then we decide if we want to express the condition as
1017 * iterator <= min(list of upper bounds)
1019 * or as a conjunction of constraints.
1021 * The set of enforced constraints is then computed either based on
1022 * a list of upper bounds or on a set of upper bound constraints.
1023 * We do not compute any enforced constraints if we were forced
1024 * to compute a lower or upper bound using exact_bound. The domains
1025 * of the resulting expressions may imply some bounds on outer dimensions
1026 * that we do not want to appear in the enforced constraints since
1027 * they are not actually enforced by the corresponding code.
1029 * Finally, we fill in the expressions of the for node.
1031 static __isl_give isl_ast_graft
*refine_generic_bounds(
1032 __isl_take isl_ast_graft
*graft
,
1033 __isl_take isl_constraint_list
*c_lower
,
1034 __isl_take isl_constraint_list
*c_upper
,
1035 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1039 isl_pw_aff_list
*lower
;
1041 isl_set
*upper_set
= NULL
;
1042 isl_pw_aff_list
*upper_list
= NULL
;
1043 int n_lower
, n_upper
;
1045 if (!graft
|| !c_lower
|| !c_upper
|| !build
)
1048 depth
= isl_ast_build_get_depth(build
);
1049 ctx
= isl_ast_graft_get_ctx(graft
);
1051 n_lower
= isl_constraint_list_n_constraint(c_lower
);
1052 n_upper
= isl_constraint_list_n_constraint(c_upper
);
1054 use_list
= use_upper_bound_list(ctx
, n_upper
, domain
, depth
);
1056 lower
= lower_bounds(c_lower
, depth
, domain
, build
);
1059 upper_list
= upper_bounds(c_upper
, depth
, domain
, build
);
1060 else if (n_upper
> 0)
1061 upper_set
= intersect_constraints(c_upper
);
1063 upper_set
= isl_set_universe(isl_set_get_space(domain
));
1065 if (n_lower
== 0 || n_upper
== 0)
1068 graft
= set_enforced_from_list(graft
, lower
, upper_list
);
1070 graft
= set_enforced_from_set(graft
, lower
, depth
, upper_set
);
1072 graft
= set_for_node_expressions(graft
, lower
, use_list
, upper_list
,
1075 isl_pw_aff_list_free(lower
);
1076 isl_pw_aff_list_free(upper_list
);
1077 isl_set_free(upper_set
);
1078 isl_constraint_list_free(c_lower
);
1079 isl_constraint_list_free(c_upper
);
1083 isl_constraint_list_free(c_lower
);
1084 isl_constraint_list_free(c_upper
);
1085 return isl_ast_graft_free(graft
);
1088 /* Internal data structure used inside count_constraints to keep
1089 * track of the number of constraints that are independent of dimension "pos",
1090 * the lower bounds in "pos" and the upper bounds in "pos".
1092 struct isl_ast_count_constraints_data
{
1100 /* Increment data->n_indep, data->lower or data->upper depending
1101 * on whether "c" is independenct of dimensions data->pos,
1102 * a lower bound or an upper bound.
1104 static int count_constraints(__isl_take isl_constraint
*c
, void *user
)
1106 struct isl_ast_count_constraints_data
*data
= user
;
1108 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->pos
))
1110 else if (isl_constraint_is_upper_bound(c
, isl_dim_set
, data
->pos
))
1115 isl_constraint_free(c
);
1120 /* Update "graft" based on "bounds" and "domain" for the generic,
1121 * non-degenerate, case.
1123 * "list" respresent the list of bounds that need to be encoded by
1124 * the for loop (or a guard around the for loop).
1125 * "domain" is the subset of the intersection of the constraints
1126 * for which some code is executed.
1127 * "build" is the build in which graft->node was created.
1129 * We separate lower bounds, upper bounds and constraints that
1130 * are independent of the loop iterator.
1132 * The actual for loop bounds are generated in refine_generic_bounds.
1133 * If there are any constraints that are independent of the loop iterator,
1134 * we need to put a guard around the for loop (which may get hoisted up
1135 * to higher levels) and we call refine_generic_bounds in a build
1136 * where this guard is enforced.
1138 static __isl_give isl_ast_graft
*refine_generic_split(
1139 __isl_take isl_ast_graft
*graft
, __isl_take isl_constraint_list
*list
,
1140 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1142 isl_ast_build
*for_build
;
1144 struct isl_ast_count_constraints_data data
;
1145 isl_constraint_list
*lower
;
1146 isl_constraint_list
*upper
;
1149 return isl_ast_graft_free(graft
);
1151 data
.pos
= isl_ast_build_get_depth(build
);
1153 list
= isl_constraint_list_sort(list
, &cmp_constraint
, &data
.pos
);
1155 return isl_ast_graft_free(graft
);
1157 data
.n_indep
= data
.n_lower
= data
.n_upper
= 0;
1158 if (isl_constraint_list_foreach(list
, &count_constraints
, &data
) < 0) {
1159 isl_constraint_list_free(list
);
1160 return isl_ast_graft_free(graft
);
1163 lower
= isl_constraint_list_copy(list
);
1164 lower
= isl_constraint_list_drop(lower
, 0, data
.n_indep
);
1165 upper
= isl_constraint_list_copy(lower
);
1166 lower
= isl_constraint_list_drop(lower
, data
.n_lower
, data
.n_upper
);
1167 upper
= isl_constraint_list_drop(upper
, 0, data
.n_lower
);
1169 if (data
.n_indep
== 0) {
1170 isl_constraint_list_free(list
);
1171 return refine_generic_bounds(graft
, lower
, upper
,
1175 list
= isl_constraint_list_drop(list
, data
.n_indep
,
1176 data
.n_lower
+ data
.n_upper
);
1177 guard
= intersect_constraints(list
);
1178 isl_constraint_list_free(list
);
1180 for_build
= isl_ast_build_copy(build
);
1181 for_build
= isl_ast_build_restrict_pending(for_build
,
1182 isl_set_copy(guard
));
1183 graft
= refine_generic_bounds(graft
, lower
, upper
, domain
, for_build
);
1184 isl_ast_build_free(for_build
);
1186 graft
= isl_ast_graft_add_guard(graft
, guard
, build
);
1191 /* Add the guard implied by the current stride constraint (if any),
1192 * but not (necessarily) enforced by the generated AST to "graft".
1194 static __isl_give isl_ast_graft
*add_stride_guard(
1195 __isl_take isl_ast_graft
*graft
, __isl_keep isl_ast_build
*build
)
1200 depth
= isl_ast_build_get_depth(build
);
1201 if (!isl_ast_build_has_stride(build
, depth
))
1204 dom
= isl_ast_build_get_stride_constraint(build
);
1205 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
1206 dom
= isl_ast_build_compute_gist(build
, dom
);
1208 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
1213 /* Update "graft" based on "bounds" and "domain" for the generic,
1214 * non-degenerate, case.
1216 * "bounds" respresent the bounds that need to be encoded by
1217 * the for loop (or a guard around the for loop).
1218 * "domain" is the subset of "bounds" for which some code is executed.
1219 * "build" is the build in which graft->node was created.
1221 * We break up "bounds" into a list of constraints and continue with
1222 * refine_generic_split.
1224 static __isl_give isl_ast_graft
*refine_generic(
1225 __isl_take isl_ast_graft
*graft
,
1226 __isl_keep isl_basic_set
*bounds
, __isl_keep isl_set
*domain
,
1227 __isl_keep isl_ast_build
*build
)
1229 isl_constraint_list
*list
;
1231 if (!build
|| !graft
)
1232 return isl_ast_graft_free(graft
);
1234 bounds
= isl_basic_set_copy(bounds
);
1235 bounds
= isl_ast_build_compute_gist_basic_set(build
, bounds
);
1236 list
= isl_constraint_list_from_basic_set(bounds
);
1238 graft
= refine_generic_split(graft
, list
, domain
, build
);
1239 graft
= add_stride_guard(graft
, build
);
1244 /* Create a for node for the current level.
1246 * Mark the for node degenerate if "degenerate" is set.
1248 static __isl_give isl_ast_node
*create_for(__isl_keep isl_ast_build
*build
,
1258 depth
= isl_ast_build_get_depth(build
);
1259 id
= isl_ast_build_get_iterator_id(build
, depth
);
1260 node
= isl_ast_node_alloc_for(id
);
1262 node
= isl_ast_node_for_mark_degenerate(node
);
1267 /* Create an AST node for the current dimension based on
1268 * the schedule domain "bounds" and return the node encapsulated
1269 * in an isl_ast_graft.
1271 * "executed" is the current inverse schedule, taking into account
1272 * the bounds in "bounds"
1273 * "domain" is the domain of "executed", with inner dimensions projected out.
1274 * It may be a strict subset of "bounds" in case "bounds" was created
1275 * based on the atomic option or based on separation with explicit bounds.
1277 * "domain" may satisfy additional equalities that result
1278 * from intersecting "executed" with "bounds" in add_node.
1279 * It may also satisfy some global constraints that were dropped out because
1280 * we performed separation with explicit bounds.
1281 * The very first step is then to copy these constraints to "bounds".
1283 * Since we may be calling before_each_for and after_each_for
1284 * callbacks, we record the current inverse schedule in the build.
1286 * We consider three builds,
1287 * "build" is the one in which the current level is created,
1288 * "body_build" is the build in which the next level is created,
1289 * "sub_build" is essentially the same as "body_build", except that
1290 * the depth has not been increased yet.
1292 * "build" already contains information (in strides and offsets)
1293 * about the strides at the current level, but this information is not
1294 * reflected in the build->domain.
1295 * We first add this information and the "bounds" to the sub_build->domain.
1296 * isl_ast_build_set_loop_bounds checks whether the current dimension attains
1297 * only a single value and whether this single value can be represented using
1298 * a single affine expression.
1299 * In the first case, the current level is considered "degenerate".
1300 * In the second, sub-case, the current level is considered "eliminated".
1301 * Eliminated level don't need to be reflected in the AST since we can
1302 * simply plug in the affine expression. For degenerate, but non-eliminated,
1303 * levels, we do introduce a for node, but mark is as degenerate so that
1304 * it can be printed as an assignment of the single value to the loop
1307 * If the current level is eliminated, we explicitly plug in the value
1308 * for the current level found by isl_ast_build_set_loop_bounds in the
1309 * inverse schedule. This ensures that if we are working on a slice
1310 * of the domain based on information available in the inverse schedule
1311 * and the build domain, that then this information is also reflected
1312 * in the inverse schedule. This operation also eliminates the current
1313 * dimension from the inverse schedule making sure no inner dimensions depend
1314 * on the current dimension. Otherwise, we create a for node, marking
1315 * it degenerate if appropriate. The initial for node is still incomplete
1316 * and will be completed in either refine_degenerate or refine_generic.
1318 * We then generate a sequence of grafts for the next level,
1319 * create a surrounding graft for the current level and insert
1320 * the for node we created (if the current level is not eliminated).
1322 * Finally, we set the bounds of the for loop and insert guards
1323 * (either in the AST or in the graft) in one of
1324 * refine_eliminated, refine_degenerate or refine_generic.
1326 static __isl_give isl_ast_graft
*create_node_scaled(
1327 __isl_take isl_union_map
*executed
,
1328 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1329 __isl_take isl_ast_build
*build
)
1332 int degenerate
, eliminated
;
1333 isl_basic_set
*hull
;
1334 isl_ast_node
*node
= NULL
;
1335 isl_ast_graft
*graft
;
1336 isl_ast_graft_list
*children
;
1337 isl_ast_build
*sub_build
;
1338 isl_ast_build
*body_build
;
1340 domain
= isl_ast_build_eliminate_divs(build
, domain
);
1341 domain
= isl_set_detect_equalities(domain
);
1342 hull
= isl_set_unshifted_simple_hull(isl_set_copy(domain
));
1343 bounds
= isl_basic_set_intersect(bounds
, hull
);
1344 build
= isl_ast_build_set_executed(build
, isl_union_map_copy(executed
));
1346 depth
= isl_ast_build_get_depth(build
);
1347 sub_build
= isl_ast_build_copy(build
);
1348 sub_build
= isl_ast_build_include_stride(sub_build
);
1349 sub_build
= isl_ast_build_set_loop_bounds(sub_build
,
1350 isl_basic_set_copy(bounds
));
1351 degenerate
= isl_ast_build_has_value(sub_build
);
1352 eliminated
= isl_ast_build_has_affine_value(sub_build
, depth
);
1353 if (degenerate
< 0 || eliminated
< 0)
1354 executed
= isl_union_map_free(executed
);
1356 executed
= plug_in_values(executed
, sub_build
);
1358 node
= create_for(build
, degenerate
);
1360 body_build
= isl_ast_build_copy(sub_build
);
1361 body_build
= isl_ast_build_increase_depth(body_build
);
1363 node
= before_each_for(node
, body_build
);
1364 children
= generate_next_level(executed
,
1365 isl_ast_build_copy(body_build
));
1367 graft
= isl_ast_graft_alloc_level(children
, build
, sub_build
);
1369 graft
= isl_ast_graft_insert_for(graft
, node
);
1371 graft
= refine_eliminated(graft
, bounds
, build
);
1372 else if (degenerate
)
1373 graft
= refine_degenerate(graft
, bounds
, build
, sub_build
);
1375 graft
= refine_generic(graft
, bounds
, domain
, build
);
1377 graft
= after_each_for(graft
, body_build
);
1379 isl_ast_build_free(body_build
);
1380 isl_ast_build_free(sub_build
);
1381 isl_ast_build_free(build
);
1382 isl_basic_set_free(bounds
);
1383 isl_set_free(domain
);
1388 /* Internal data structure for checking if all constraints involving
1389 * the input dimension "depth" are such that the other coefficients
1390 * are multiples of "m", reducing "m" if they are not.
1391 * If "m" is reduced all the way down to "1", then the check has failed
1392 * and we break out of the iteration.
1393 * "d" is an initialized isl_int that can be used internally.
1395 struct isl_check_scaled_data
{
1400 /* If constraint "c" involves the input dimension data->depth,
1401 * then make sure that all the other coefficients are multiples of data->m,
1402 * reducing data->m if needed.
1403 * Break out of the iteration if data->m has become equal to "1".
1405 static int constraint_check_scaled(__isl_take isl_constraint
*c
, void *user
)
1407 struct isl_check_scaled_data
*data
= user
;
1409 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_out
,
1412 if (!isl_constraint_involves_dims(c
, isl_dim_in
, data
->depth
, 1)) {
1413 isl_constraint_free(c
);
1417 for (i
= 0; i
< 4; ++i
) {
1418 n
= isl_constraint_dim(c
, t
[i
]);
1419 for (j
= 0; j
< n
; ++j
) {
1420 if (t
[i
] == isl_dim_in
&& j
== data
->depth
)
1422 if (!isl_constraint_involves_dims(c
, t
[i
], j
, 1))
1424 isl_constraint_get_coefficient(c
, t
[i
], j
, &data
->d
);
1425 isl_int_gcd(data
->m
, data
->m
, data
->d
);
1426 if (isl_int_is_one(data
->m
))
1433 isl_constraint_free(c
);
1435 return i
< 4 ? -1 : 0;
1438 /* For each constraint of "bmap" that involves the input dimension data->depth,
1439 * make sure that all the other coefficients are multiples of data->m,
1440 * reducing data->m if needed.
1441 * Break out of the iteration if data->m has become equal to "1".
1443 static int basic_map_check_scaled(__isl_take isl_basic_map
*bmap
, void *user
)
1447 r
= isl_basic_map_foreach_constraint(bmap
,
1448 &constraint_check_scaled
, user
);
1449 isl_basic_map_free(bmap
);
1454 /* For each constraint of "map" that involves the input dimension data->depth,
1455 * make sure that all the other coefficients are multiples of data->m,
1456 * reducing data->m if needed.
1457 * Break out of the iteration if data->m has become equal to "1".
1459 static int map_check_scaled(__isl_take isl_map
*map
, void *user
)
1463 r
= isl_map_foreach_basic_map(map
, &basic_map_check_scaled
, user
);
1469 /* Create an AST node for the current dimension based on
1470 * the schedule domain "bounds" and return the node encapsulated
1471 * in an isl_ast_graft.
1473 * "executed" is the current inverse schedule, taking into account
1474 * the bounds in "bounds"
1475 * "domain" is the domain of "executed", with inner dimensions projected out.
1478 * Before moving on to the actual AST node construction in create_node_scaled,
1479 * we first check if the current dimension is strided and if we can scale
1480 * down this stride. Note that we only do this if the ast_build_scale_strides
1483 * In particular, let the current dimension take on values
1487 * with a an integer. We check if we can find an integer m that (obviouly)
1488 * divides both f and s.
1490 * If so, we check if the current dimension only appears in constraints
1491 * where the coefficients of the other variables are multiples of m.
1492 * We perform this extra check to avoid the risk of introducing
1493 * divisions by scaling down the current dimension.
1495 * If so, we scale the current dimension down by a factor of m.
1496 * That is, we plug in
1500 * Note that in principle we could always scale down strided loops
1505 * but this may result in i' taking on larger values than the original i,
1506 * due to the shift by "f".
1507 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1509 static __isl_give isl_ast_graft
*create_node(__isl_take isl_union_map
*executed
,
1510 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1511 __isl_take isl_ast_build
*build
)
1513 struct isl_check_scaled_data data
;
1517 ctx
= isl_ast_build_get_ctx(build
);
1518 if (!isl_options_get_ast_build_scale_strides(ctx
))
1519 return create_node_scaled(executed
, bounds
, domain
, build
);
1521 data
.depth
= isl_ast_build_get_depth(build
);
1522 if (!isl_ast_build_has_stride(build
, data
.depth
))
1523 return create_node_scaled(executed
, bounds
, domain
, build
);
1525 isl_int_init(data
.m
);
1526 isl_int_init(data
.d
);
1528 offset
= isl_ast_build_get_offset(build
, data
.depth
);
1529 if (isl_ast_build_get_stride(build
, data
.depth
, &data
.m
) < 0)
1530 offset
= isl_aff_free(offset
);
1531 offset
= isl_aff_scale_down(offset
, data
.m
);
1532 if (isl_aff_get_denominator(offset
, &data
.d
) < 0)
1533 executed
= isl_union_map_free(executed
);
1535 if (executed
&& isl_int_is_divisible_by(data
.m
, data
.d
))
1536 isl_int_divexact(data
.m
, data
.m
, data
.d
);
1538 isl_int_set_si(data
.m
, 1);
1540 if (!isl_int_is_one(data
.m
)) {
1541 if (isl_union_map_foreach_map(executed
, &map_check_scaled
,
1543 !isl_int_is_one(data
.m
))
1544 executed
= isl_union_map_free(executed
);
1547 if (!isl_int_is_one(data
.m
)) {
1552 isl_union_map
*umap
;
1554 space
= isl_ast_build_get_space(build
, 1);
1555 space
= isl_space_map_from_set(space
);
1556 ma
= isl_multi_aff_identity(space
);
1557 aff
= isl_multi_aff_get_aff(ma
, data
.depth
);
1558 aff
= isl_aff_scale(aff
, data
.m
);
1559 ma
= isl_multi_aff_set_aff(ma
, data
.depth
, aff
);
1561 bounds
= isl_basic_set_preimage_multi_aff(bounds
,
1562 isl_multi_aff_copy(ma
));
1563 domain
= isl_set_preimage_multi_aff(domain
,
1564 isl_multi_aff_copy(ma
));
1565 map
= isl_map_reverse(isl_map_from_multi_aff(ma
));
1566 umap
= isl_union_map_from_map(map
);
1567 executed
= isl_union_map_apply_domain(executed
,
1568 isl_union_map_copy(umap
));
1569 build
= isl_ast_build_scale_down(build
, data
.m
, umap
);
1571 isl_aff_free(offset
);
1573 isl_int_clear(data
.d
);
1574 isl_int_clear(data
.m
);
1576 return create_node_scaled(executed
, bounds
, domain
, build
);
1579 /* Add the basic set to the list that "user" points to.
1581 static int collect_basic_set(__isl_take isl_basic_set
*bset
, void *user
)
1583 isl_basic_set_list
**list
= user
;
1585 *list
= isl_basic_set_list_add(*list
, bset
);
1590 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1592 static __isl_give isl_basic_set_list
*isl_basic_set_list_from_set(
1593 __isl_take isl_set
*set
)
1597 isl_basic_set_list
*list
;
1602 ctx
= isl_set_get_ctx(set
);
1604 n
= isl_set_n_basic_set(set
);
1605 list
= isl_basic_set_list_alloc(ctx
, n
);
1606 if (isl_set_foreach_basic_set(set
, &collect_basic_set
, &list
) < 0)
1607 list
= isl_basic_set_list_free(list
);
1613 /* Generate code for the schedule domain "bounds"
1614 * and add the result to "list".
1616 * We mainly detect strides and additional equalities here
1617 * and then pass over control to create_node.
1619 * "bounds" reflects the bounds on the current dimension and possibly
1620 * some extra conditions on outer dimensions.
1621 * It does not, however, include any divs involving the current dimension,
1622 * so it does not capture any stride constraints.
1623 * We therefore need to compute that part of the schedule domain that
1624 * intersects with "bounds" and derive the strides from the result.
1626 static __isl_give isl_ast_graft_list
*add_node(
1627 __isl_take isl_ast_graft_list
*list
, __isl_take isl_union_map
*executed
,
1628 __isl_take isl_basic_set
*bounds
, __isl_take isl_ast_build
*build
)
1630 isl_ast_graft
*graft
;
1631 isl_set
*domain
= NULL
;
1632 isl_union_set
*uset
;
1635 uset
= isl_union_set_from_basic_set(isl_basic_set_copy(bounds
));
1636 executed
= isl_union_map_intersect_domain(executed
, uset
);
1637 empty
= isl_union_map_is_empty(executed
);
1643 uset
= isl_union_map_domain(isl_union_map_copy(executed
));
1644 domain
= isl_set_from_union_set(uset
);
1645 domain
= isl_ast_build_compute_gist(build
, domain
);
1646 empty
= isl_set_is_empty(domain
);
1652 domain
= isl_ast_build_eliminate_inner(build
, domain
);
1653 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
1655 graft
= create_node(executed
, bounds
, domain
,
1656 isl_ast_build_copy(build
));
1657 list
= isl_ast_graft_list_add(list
, graft
);
1658 isl_ast_build_free(build
);
1661 list
= isl_ast_graft_list_free(list
);
1663 isl_set_free(domain
);
1664 isl_basic_set_free(bounds
);
1665 isl_union_map_free(executed
);
1666 isl_ast_build_free(build
);
1670 /* Does any element of i follow or coincide with any element of j
1671 * at the current depth for equal values of the outer dimensions?
1673 static int domain_follows_at_depth(__isl_keep isl_basic_set
*i
,
1674 __isl_keep isl_basic_set
*j
, void *user
)
1676 int depth
= *(int *) user
;
1677 isl_basic_map
*test
;
1681 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
1682 isl_basic_set_copy(j
));
1683 for (l
= 0; l
< depth
; ++l
)
1684 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1686 test
= isl_basic_map_order_ge(test
, isl_dim_in
, depth
,
1687 isl_dim_out
, depth
);
1688 empty
= isl_basic_map_is_empty(test
);
1689 isl_basic_map_free(test
);
1691 return empty
< 0 ? -1 : !empty
;
1694 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1695 __isl_keep isl_basic_set_list
*domain_list
,
1696 __isl_keep isl_union_map
*executed
,
1697 __isl_keep isl_ast_build
*build
);
1699 /* Internal data structure for add_nodes.
1701 * "executed" and "build" are extra arguments to be passed to add_node.
1702 * "list" collects the results.
1704 struct isl_add_nodes_data
{
1705 isl_union_map
*executed
;
1706 isl_ast_build
*build
;
1708 isl_ast_graft_list
*list
;
1711 /* Generate code for the schedule domains in "scc"
1712 * and add the results to "list".
1714 * The domains in "scc" form a strongly connected component in the ordering.
1715 * If the number of domains in "scc" is larger than 1, then this means
1716 * that we cannot determine a valid ordering for the domains in the component.
1717 * This should be fairly rare because the individual domains
1718 * have been made disjoint first.
1719 * The problem is that the domains may be integrally disjoint but not
1720 * rationally disjoint. For example, we may have domains
1722 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1724 * These two domains have an empty intersection, but their rational
1725 * relaxations do intersect. It is impossible to order these domains
1726 * in the second dimension because the first should be ordered before
1727 * the second for outer dimension equal to 0, while it should be ordered
1728 * after for outer dimension equal to 1.
1730 * This may happen in particular in case of unrolling since the domain
1731 * of each slice is replaced by its simple hull.
1733 * We collect the basic sets in the component, call isl_set_make_disjoint
1734 * and try again. Note that we rely here on isl_set_make_disjoint also
1735 * making the basic sets rationally disjoint. If the basic sets
1736 * are rationally disjoint, then the ordering problem does not occur.
1737 * To see this, there can only be a problem if there are points
1738 * (i,a) and (j,b) in one set and (i,c) and (j,d) in the other with
1739 * a < c and b > d. This means that either the interval spanned
1740 * by a en b lies inside that spanned by c and or the other way around.
1741 * In either case, there is a point inside both intervals with the
1742 * convex combination in terms of a and b and in terms of c and d.
1743 * Taking the same combination of i and j gives a point in the intersection.
1745 static int add_nodes(__isl_take isl_basic_set_list
*scc
, void *user
)
1747 struct isl_add_nodes_data
*data
= user
;
1749 isl_basic_set
*bset
;
1752 n
= isl_basic_set_list_n_basic_set(scc
);
1753 bset
= isl_basic_set_list_get_basic_set(scc
, 0);
1755 isl_basic_set_list_free(scc
);
1756 data
->list
= add_node(data
->list
,
1757 isl_union_map_copy(data
->executed
), bset
,
1758 isl_ast_build_copy(data
->build
));
1759 return data
->list
? 0 : -1;
1762 set
= isl_set_from_basic_set(bset
);
1763 for (i
= 1; i
< n
; ++i
) {
1764 bset
= isl_basic_set_list_get_basic_set(scc
, i
);
1765 set
= isl_set_union(set
, isl_set_from_basic_set(bset
));
1768 set
= isl_set_make_disjoint(set
);
1769 if (isl_set_n_basic_set(set
) == n
)
1770 isl_die(isl_basic_set_list_get_ctx(scc
), isl_error_internal
,
1771 "unable to separate loop parts",
1772 set
= isl_set_free(set
));
1773 isl_basic_set_list_free(scc
);
1774 scc
= isl_basic_set_list_from_set(set
);
1775 data
->list
= isl_ast_graft_list_concat(data
->list
,
1776 generate_sorted_domains(scc
, data
->executed
, data
->build
));
1777 isl_basic_set_list_free(scc
);
1779 return data
->list
? 0 : -1;
1782 /* Sort the domains in "domain_list" according to the execution order
1783 * at the current depth (for equal values of the outer dimensions),
1784 * generate code for each of them, collecting the results in a list.
1785 * If no code is generated (because the intersection of the inverse schedule
1786 * with the domains turns out to be empty), then an empty list is returned.
1788 * The caller is responsible for ensuring that the basic sets in "domain_list"
1789 * are pair-wise disjoint. It can, however, in principle happen that
1790 * two basic sets should be ordered one way for one value of the outer
1791 * dimensions and the other way for some other value of the outer dimensions.
1792 * We therefore play safe and look for strongly connected components.
1793 * The function add_nodes takes care of handling non-trivial components.
1795 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1796 __isl_keep isl_basic_set_list
*domain_list
,
1797 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1800 struct isl_add_nodes_data data
;
1807 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1808 n
= isl_basic_set_list_n_basic_set(domain_list
);
1809 data
.list
= isl_ast_graft_list_alloc(ctx
, n
);
1813 return add_node(data
.list
, isl_union_map_copy(executed
),
1814 isl_basic_set_list_get_basic_set(domain_list
, 0),
1815 isl_ast_build_copy(build
));
1817 depth
= isl_ast_build_get_depth(build
);
1818 data
.executed
= executed
;
1820 if (isl_basic_set_list_foreach_scc(domain_list
,
1821 &domain_follows_at_depth
, &depth
,
1822 &add_nodes
, &data
) < 0)
1823 data
.list
= isl_ast_graft_list_free(data
.list
);
1828 /* Do i and j share any values for the outer dimensions?
1830 static int shared_outer(__isl_keep isl_basic_set
*i
,
1831 __isl_keep isl_basic_set
*j
, void *user
)
1833 int depth
= *(int *) user
;
1834 isl_basic_map
*test
;
1838 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
1839 isl_basic_set_copy(j
));
1840 for (l
= 0; l
< depth
; ++l
)
1841 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1843 empty
= isl_basic_map_is_empty(test
);
1844 isl_basic_map_free(test
);
1846 return empty
< 0 ? -1 : !empty
;
1849 /* Internal data structure for generate_sorted_domains_wrap.
1851 * "n" is the total number of basic sets
1852 * "executed" and "build" are extra arguments to be passed
1853 * to generate_sorted_domains.
1855 * "single" is set to 1 by generate_sorted_domains_wrap if there
1856 * is only a single component.
1857 * "list" collects the results.
1859 struct isl_ast_generate_parallel_domains_data
{
1861 isl_union_map
*executed
;
1862 isl_ast_build
*build
;
1865 isl_ast_graft_list
*list
;
1868 /* Call generate_sorted_domains on "scc", fuse the result into a list
1869 * with either zero or one graft and collect the these single element
1870 * lists into data->list.
1872 * If there is only one component, i.e., if the number of basic sets
1873 * in the current component is equal to the total number of basic sets,
1874 * then data->single is set to 1 and the result of generate_sorted_domains
1877 static int generate_sorted_domains_wrap(__isl_take isl_basic_set_list
*scc
,
1880 struct isl_ast_generate_parallel_domains_data
*data
= user
;
1881 isl_ast_graft_list
*list
;
1883 list
= generate_sorted_domains(scc
, data
->executed
, data
->build
);
1884 data
->single
= isl_basic_set_list_n_basic_set(scc
) == data
->n
;
1886 list
= isl_ast_graft_list_fuse(list
, data
->build
);
1890 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
1892 isl_basic_set_list_free(scc
);
1899 /* Look for any (weakly connected) components in the "domain_list"
1900 * of domains that share some values of the outer dimensions.
1901 * That is, domains in different components do not share any values
1902 * of the outer dimensions. This means that these components
1903 * can be freely reordered.
1904 * Within each of the components, we sort the domains according
1905 * to the execution order at the current depth.
1907 * If there is more than one component, then generate_sorted_domains_wrap
1908 * fuses the result of each call to generate_sorted_domains
1909 * into a list with either zero or one graft and collects these (at most)
1910 * single element lists into a bigger list. This means that the elements of the
1911 * final list can be freely reordered. In particular, we sort them
1912 * according to an arbitrary but fixed ordering to ease merging of
1913 * graft lists from different components.
1915 static __isl_give isl_ast_graft_list
*generate_parallel_domains(
1916 __isl_keep isl_basic_set_list
*domain_list
,
1917 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1920 struct isl_ast_generate_parallel_domains_data data
;
1925 data
.n
= isl_basic_set_list_n_basic_set(domain_list
);
1927 return generate_sorted_domains(domain_list
, executed
, build
);
1929 depth
= isl_ast_build_get_depth(build
);
1931 data
.executed
= executed
;
1934 if (isl_basic_set_list_foreach_scc(domain_list
, &shared_outer
, &depth
,
1935 &generate_sorted_domains_wrap
,
1937 data
.list
= isl_ast_graft_list_free(data
.list
);
1940 data
.list
= isl_ast_graft_list_sort_guard(data
.list
);
1945 /* Internal data for separate_domain.
1947 * "explicit" is set if we only want to use explicit bounds.
1949 * "domain" collects the separated domains.
1951 struct isl_separate_domain_data
{
1952 isl_ast_build
*build
;
1957 /* Extract implicit bounds on the current dimension for the executed "map".
1959 * The domain of "map" may involve inner dimensions, so we
1960 * need to eliminate them.
1962 static __isl_give isl_set
*implicit_bounds(__isl_take isl_map
*map
,
1963 __isl_keep isl_ast_build
*build
)
1967 domain
= isl_map_domain(map
);
1968 domain
= isl_ast_build_eliminate(build
, domain
);
1973 /* Extract explicit bounds on the current dimension for the executed "map".
1975 * Rather than eliminating the inner dimensions as in implicit_bounds,
1976 * we simply drop any constraints involving those inner dimensions.
1977 * The idea is that most bounds that are implied by constraints on the
1978 * inner dimensions will be enforced by for loops and not by explicit guards.
1979 * There is then no need to separate along those bounds.
1981 static __isl_give isl_set
*explicit_bounds(__isl_take isl_map
*map
,
1982 __isl_keep isl_ast_build
*build
)
1987 dim
= isl_map_dim(map
, isl_dim_out
);
1988 map
= isl_map_drop_constraints_involving_dims(map
, isl_dim_out
, 0, dim
);
1990 domain
= isl_map_domain(map
);
1991 depth
= isl_ast_build_get_depth(build
);
1992 dim
= isl_set_dim(domain
, isl_dim_set
);
1993 domain
= isl_set_detect_equalities(domain
);
1994 domain
= isl_set_drop_constraints_involving_dims(domain
,
1995 isl_dim_set
, depth
+ 1, dim
- (depth
+ 1));
1996 domain
= isl_set_remove_divs_involving_dims(domain
,
1997 isl_dim_set
, depth
, 1);
1998 domain
= isl_set_remove_unknown_divs(domain
);
2003 /* Split data->domain into pieces that intersect with the range of "map"
2004 * and pieces that do not intersect with the range of "map"
2005 * and then add that part of the range of "map" that does not intersect
2006 * with data->domain.
2008 static int separate_domain(__isl_take isl_map
*map
, void *user
)
2010 struct isl_separate_domain_data
*data
= user
;
2015 domain
= explicit_bounds(map
, data
->build
);
2017 domain
= implicit_bounds(map
, data
->build
);
2019 domain
= isl_set_coalesce(domain
);
2020 domain
= isl_set_make_disjoint(domain
);
2021 d1
= isl_set_subtract(isl_set_copy(domain
), isl_set_copy(data
->domain
));
2022 d2
= isl_set_subtract(isl_set_copy(data
->domain
), isl_set_copy(domain
));
2023 data
->domain
= isl_set_intersect(data
->domain
, domain
);
2024 data
->domain
= isl_set_union(data
->domain
, d1
);
2025 data
->domain
= isl_set_union(data
->domain
, d2
);
2030 /* Separate the schedule domains of "executed".
2032 * That is, break up the domain of "executed" into basic sets,
2033 * such that for each basic set S, every element in S is associated with
2034 * the same domain spaces.
2036 * "space" is the (single) domain space of "executed".
2038 static __isl_give isl_set
*separate_schedule_domains(
2039 __isl_take isl_space
*space
, __isl_take isl_union_map
*executed
,
2040 __isl_keep isl_ast_build
*build
)
2042 struct isl_separate_domain_data data
= { build
};
2045 ctx
= isl_ast_build_get_ctx(build
);
2046 data
.explicit = isl_options_get_ast_build_separation_bounds(ctx
) ==
2047 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
;
2048 data
.domain
= isl_set_empty(space
);
2049 if (isl_union_map_foreach_map(executed
, &separate_domain
, &data
) < 0)
2050 data
.domain
= isl_set_free(data
.domain
);
2052 isl_union_map_free(executed
);
2056 /* Temporary data used during the search for a lower bound for unrolling.
2058 * "domain" is the original set for which to find a lower bound
2059 * "depth" is the dimension for which to find a lower boudn
2061 * "lower" is the best lower bound found so far. It is NULL if we have not
2063 * "n" is the corresponding size. If lower is NULL, then the value of n
2066 * "tmp" is a temporary initialized isl_int.
2068 struct isl_find_unroll_data
{
2077 /* Check if we can use "c" as a lower bound and if it is better than
2078 * any previously found lower bound.
2080 * If "c" does not involve the dimension at the current depth,
2081 * then we cannot use it.
2082 * Otherwise, let "c" be of the form
2086 * We compute the maximal value of
2088 * -ceil(f(j)/a)) + i + 1
2090 * over the domain. If there is such a value "n", then we know
2092 * -ceil(f(j)/a)) + i + 1 <= n
2096 * i < ceil(f(j)/a)) + n
2098 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2099 * We just need to check if we have found any lower bound before and
2100 * if the new lower bound is better (smaller n) than the previously found
2103 static int update_unrolling_lower_bound(struct isl_find_unroll_data
*data
,
2104 __isl_keep isl_constraint
*c
)
2106 isl_aff
*aff
, *lower
;
2107 enum isl_lp_result res
;
2109 if (!isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->depth
))
2112 lower
= isl_constraint_get_bound(c
, isl_dim_set
, data
->depth
);
2113 lower
= isl_aff_ceil(lower
);
2114 aff
= isl_aff_copy(lower
);
2115 aff
= isl_aff_neg(aff
);
2116 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, data
->depth
, 1);
2117 aff
= isl_aff_add_constant_si(aff
, 1);
2118 res
= isl_set_max(data
->domain
, aff
, &data
->tmp
);
2121 if (res
== isl_lp_error
)
2123 if (res
== isl_lp_unbounded
) {
2124 isl_aff_free(lower
);
2128 if (isl_int_cmp_si(data
->tmp
, INT_MAX
) <= 0 &&
2129 (!data
->lower
|| isl_int_cmp_si(data
->tmp
, *data
->n
) < 0)) {
2130 isl_aff_free(data
->lower
);
2131 data
->lower
= lower
;
2132 *data
->n
= isl_int_get_si(data
->tmp
);
2134 isl_aff_free(lower
);
2138 isl_aff_free(lower
);
2142 /* Check if we can use "c" as a lower bound and if it is better than
2143 * any previously found lower bound.
2145 static int constraint_find_unroll(__isl_take isl_constraint
*c
, void *user
)
2147 struct isl_find_unroll_data
*data
;
2150 data
= (struct isl_find_unroll_data
*) user
;
2151 r
= update_unrolling_lower_bound(data
, c
);
2152 isl_constraint_free(c
);
2157 /* Look for a lower bound l(i) on the dimension at "depth"
2158 * and a size n such that "domain" is a subset of
2160 * { [i] : l(i) <= i_d < l(i) + n }
2162 * where d is "depth" and l(i) depends only on earlier dimensions.
2163 * Furthermore, try and find a lower bound such that n is as small as possible.
2164 * In particular, "n" needs to be finite.
2166 * Inner dimensions have been eliminated from "domain" by the caller.
2168 * We first construct a collection of lower bounds on the input set
2169 * by computing its simple hull. We then iterate through them,
2170 * discarding those that we cannot use (either because they do not
2171 * involve the dimension at "depth" or because they have no corresponding
2172 * upper bound, meaning that "n" would be unbounded) and pick out the
2173 * best from the remaining ones.
2175 * If we cannot find a suitable lower bound, then we consider that
2178 static __isl_give isl_aff
*find_unroll_lower_bound(__isl_keep isl_set
*domain
,
2181 struct isl_find_unroll_data data
= { domain
, depth
, NULL
, n
};
2182 isl_basic_set
*hull
;
2184 isl_int_init(data
.tmp
);
2185 hull
= isl_set_simple_hull(isl_set_copy(domain
));
2187 if (isl_basic_set_foreach_constraint(hull
,
2188 &constraint_find_unroll
, &data
) < 0)
2191 isl_basic_set_free(hull
);
2192 isl_int_clear(data
.tmp
);
2195 isl_die(isl_set_get_ctx(domain
), isl_error_invalid
,
2196 "cannot find lower bound for unrolling", return NULL
);
2200 isl_basic_set_free(hull
);
2201 isl_int_clear(data
.tmp
);
2202 return isl_aff_free(data
.lower
);
2205 /* Return the constraint
2207 * i_"depth" = aff + offset
2209 static __isl_give isl_constraint
*at_offset(int depth
, __isl_keep isl_aff
*aff
,
2212 aff
= isl_aff_copy(aff
);
2213 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, depth
, -1);
2214 aff
= isl_aff_add_constant_si(aff
, offset
);
2215 return isl_equality_from_aff(aff
);
2218 /* Return a list of basic sets, one for each value of the current dimension
2220 * The divs that involve the current dimension have not been projected out
2223 * Since we are going to be iterating over the individual values,
2224 * we first check if there are any strides on the current dimension.
2225 * If there is, we rewrite the current dimension i as
2227 * i = stride i' + offset
2229 * and then iterate over individual values of i' instead.
2231 * We then look for a lower bound on i' and a size such that the domain
2234 * { [j,i'] : l(j) <= i' < l(j) + n }
2236 * and then take slices of the domain at values of i'
2237 * between l(j) and l(j) + n - 1.
2239 * We compute the unshifted simple hull of each slice to ensure that
2240 * we have a single basic set per offset. The slicing constraint
2241 * may get simplified away before the unshifted simple hull is taken
2242 * and may therefore in some rare cases disappear from the result.
2243 * We therefore explicitly add the constraint back after computing
2244 * the unshifted simple hull to ensure that the basic sets
2245 * remain disjoint. The constraints that are dropped by taking the hull
2246 * will be taken into account at the next level, as in the case of the
2249 * Finally, we map i' back to i and add each basic set to the list.
2251 static __isl_give isl_basic_set_list
*do_unroll(__isl_take isl_set
*domain
,
2252 __isl_keep isl_ast_build
*build
)
2258 isl_basic_set_list
*list
;
2259 isl_multi_aff
*expansion
;
2260 isl_basic_map
*bmap
;
2265 ctx
= isl_set_get_ctx(domain
);
2266 depth
= isl_ast_build_get_depth(build
);
2267 build
= isl_ast_build_copy(build
);
2268 domain
= isl_ast_build_eliminate_inner(build
, domain
);
2269 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
2270 expansion
= isl_ast_build_get_stride_expansion(build
);
2272 domain
= isl_set_preimage_multi_aff(domain
,
2273 isl_multi_aff_copy(expansion
));
2274 domain
= isl_ast_build_eliminate_divs(build
, domain
);
2276 isl_ast_build_free(build
);
2278 list
= isl_basic_set_list_alloc(ctx
, 0);
2280 lower
= find_unroll_lower_bound(domain
, depth
, &n
);
2282 list
= isl_basic_set_list_free(list
);
2284 bmap
= isl_basic_map_from_multi_aff(expansion
);
2286 for (i
= 0; list
&& i
< n
; ++i
) {
2288 isl_basic_set
*bset
;
2289 isl_constraint
*slice
;
2291 slice
= at_offset(depth
, lower
, i
);
2292 set
= isl_set_copy(domain
);
2293 set
= isl_set_add_constraint(set
, isl_constraint_copy(slice
));
2294 bset
= isl_set_unshifted_simple_hull(set
);
2295 bset
= isl_basic_set_add_constraint(bset
, slice
);
2296 bset
= isl_basic_set_apply(bset
, isl_basic_map_copy(bmap
));
2297 list
= isl_basic_set_list_add(list
, bset
);
2300 isl_aff_free(lower
);
2301 isl_set_free(domain
);
2302 isl_basic_map_free(bmap
);
2307 /* Data structure for storing the results and the intermediate objects
2308 * of compute_domains.
2310 * "list" is the main result of the function and contains a list
2311 * of disjoint basic sets for which code should be generated.
2313 * "executed" and "build" are inputs to compute_domains.
2314 * "schedule_domain" is the domain of "executed".
2316 * "option" constains the domains at the current depth that should by
2317 * atomic, separated or unrolled. These domains are as specified by
2318 * the user, except that inner dimensions have been eliminated and
2319 * that they have been made pair-wise disjoint.
2321 * "sep_class" contains the user-specified split into separation classes
2322 * specialized to the current depth.
2323 * "done" contains the union of the separation domains that have already
2325 * "atomic" contains the domain that has effectively been made atomic.
2326 * This domain may be larger than the intersection of option[atomic]
2327 * and the schedule domain.
2329 struct isl_codegen_domains
{
2330 isl_basic_set_list
*list
;
2332 isl_union_map
*executed
;
2333 isl_ast_build
*build
;
2334 isl_set
*schedule_domain
;
2343 /* Add domains to domains->list for each individual value of the current
2344 * dimension, for that part of the schedule domain that lies in the
2345 * intersection of the option domain and the class domain.
2347 * "domain" is the intersection of the class domain and the schedule domain.
2348 * The divs that involve the current dimension have not been projected out
2351 * We first break up the unroll option domain into individual pieces
2352 * and then handle each of them separately. The unroll option domain
2353 * has been made disjoint in compute_domains_init_options,
2355 * Note that we actively want to combine different pieces of the
2356 * schedule domain that have the same value at the current dimension.
2357 * We therefore need to break up the unroll option domain before
2358 * intersecting with class and schedule domain, hoping that the
2359 * unroll option domain specified by the user is relatively simple.
2361 static int compute_unroll_domains(struct isl_codegen_domains
*domains
,
2362 __isl_keep isl_set
*domain
)
2364 isl_set
*unroll_domain
;
2365 isl_basic_set_list
*unroll_list
;
2369 empty
= isl_set_is_empty(domains
->option
[unroll
]);
2375 unroll_domain
= isl_set_copy(domains
->option
[unroll
]);
2376 unroll_list
= isl_basic_set_list_from_set(unroll_domain
);
2378 n
= isl_basic_set_list_n_basic_set(unroll_list
);
2379 for (i
= 0; i
< n
; ++i
) {
2380 isl_basic_set
*bset
;
2381 isl_basic_set_list
*list
;
2383 bset
= isl_basic_set_list_get_basic_set(unroll_list
, i
);
2384 unroll_domain
= isl_set_from_basic_set(bset
);
2385 unroll_domain
= isl_set_intersect(unroll_domain
,
2386 isl_set_copy(domain
));
2388 empty
= isl_set_is_empty(unroll_domain
);
2389 if (empty
>= 0 && empty
) {
2390 isl_set_free(unroll_domain
);
2394 list
= do_unroll(unroll_domain
, domains
->build
);
2395 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2398 isl_basic_set_list_free(unroll_list
);
2403 /* Construct a single basic set that includes the intersection of
2404 * the schedule domain, the atomic option domain and the class domain.
2405 * Add the resulting basic set to domains->list and save a copy
2406 * in domains->atomic for use in compute_partial_domains.
2408 * We construct a single domain rather than trying to combine
2409 * the schedule domains of individual domains because we are working
2410 * within a single component so that non-overlapping schedule domains
2411 * should already have been separated.
2412 * Note, though, that this does not take into account the class domain.
2413 * So, it is possible for a class domain to carve out a piece of the
2414 * schedule domain with independent pieces and then we would only
2415 * generate a single domain for them. If this proves to be problematic
2416 * for some users, then this function will have to be adjusted.
2418 * "domain" is the intersection of the schedule domain and the class domain,
2419 * with inner dimensions projected out.
2421 static int compute_atomic_domain(struct isl_codegen_domains
*domains
,
2422 __isl_keep isl_set
*domain
)
2424 isl_basic_set
*bset
;
2425 isl_set
*atomic_domain
;
2428 atomic_domain
= isl_set_copy(domains
->option
[atomic
]);
2429 atomic_domain
= isl_set_intersect(atomic_domain
, isl_set_copy(domain
));
2430 empty
= isl_set_is_empty(atomic_domain
);
2431 if (empty
< 0 || empty
) {
2432 domains
->atomic
= atomic_domain
;
2433 return empty
< 0 ? -1 : 0;
2436 atomic_domain
= isl_set_coalesce(atomic_domain
);
2437 bset
= isl_set_unshifted_simple_hull(atomic_domain
);
2438 domains
->atomic
= isl_set_from_basic_set(isl_basic_set_copy(bset
));
2439 domains
->list
= isl_basic_set_list_add(domains
->list
, bset
);
2444 /* Split up the schedule domain into uniform basic sets,
2445 * in the sense that each element in a basic set is associated to
2446 * elements of the same domains, and add the result to domains->list.
2447 * Do this for that part of the schedule domain that lies in the
2448 * intersection of "class_domain" and the separate option domain.
2450 * "class_domain" may or may not include the constraints
2451 * of the schedule domain, but this does not make a difference
2452 * since we are going to intersect it with the domain of the inverse schedule.
2453 * If it includes schedule domain constraints, then they may involve
2454 * inner dimensions, but we will eliminate them in separation_domain.
2456 static int compute_separate_domain(struct isl_codegen_domains
*domains
,
2457 __isl_keep isl_set
*class_domain
)
2461 isl_union_map
*executed
;
2462 isl_basic_set_list
*list
;
2465 domain
= isl_set_copy(domains
->option
[separate
]);
2466 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2467 executed
= isl_union_map_copy(domains
->executed
);
2468 executed
= isl_union_map_intersect_domain(executed
,
2469 isl_union_set_from_set(domain
));
2470 empty
= isl_union_map_is_empty(executed
);
2471 if (empty
< 0 || empty
) {
2472 isl_union_map_free(executed
);
2473 return empty
< 0 ? -1 : 0;
2476 space
= isl_set_get_space(class_domain
);
2477 domain
= separate_schedule_domains(space
, executed
, domains
->build
);
2479 list
= isl_basic_set_list_from_set(domain
);
2480 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2485 /* Split up the domain at the current depth into disjoint
2486 * basic sets for which code should be generated separately
2487 * for the given separation class domain.
2489 * If any separation classes have been defined, then "class_domain"
2490 * is the domain of the current class and does not refer to inner dimensions.
2491 * Otherwise, "class_domain" is the universe domain.
2493 * We first make sure that the class domain is disjoint from
2494 * previously considered class domains.
2496 * The separate domains can be computed directly from the "class_domain".
2498 * The unroll, atomic and remainder domains need the constraints
2499 * from the schedule domain.
2501 * For unrolling, the actual schedule domain is needed (with divs that
2502 * may refer to the current dimension) so that stride detection can be
2505 * For atomic and remainder domains, inner dimensions and divs involving
2506 * the current dimensions should be eliminated.
2507 * In case we are working within a separation class, we need to intersect
2508 * the result with the current "class_domain" to ensure that the domains
2509 * are disjoint from those generated from other class domains.
2511 * The domain that has been made atomic may be larger than specified
2512 * by the user since it needs to be representable as a single basic set.
2513 * This possibly larger domain is stored in domains->atomic by
2514 * compute_atomic_domain.
2516 * If anything is left after handling separate, unroll and atomic,
2517 * we split it up into basic sets and append the basic sets to domains->list.
2519 static int compute_partial_domains(struct isl_codegen_domains
*domains
,
2520 __isl_take isl_set
*class_domain
)
2522 isl_basic_set_list
*list
;
2525 class_domain
= isl_set_subtract(class_domain
,
2526 isl_set_copy(domains
->done
));
2527 domains
->done
= isl_set_union(domains
->done
,
2528 isl_set_copy(class_domain
));
2530 domain
= isl_set_copy(class_domain
);
2532 if (compute_separate_domain(domains
, domain
) < 0)
2534 domain
= isl_set_subtract(domain
,
2535 isl_set_copy(domains
->option
[separate
]));
2537 domain
= isl_set_intersect(domain
,
2538 isl_set_copy(domains
->schedule_domain
));
2540 if (compute_unroll_domains(domains
, domain
) < 0)
2542 domain
= isl_set_subtract(domain
,
2543 isl_set_copy(domains
->option
[unroll
]));
2545 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2546 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2548 if (compute_atomic_domain(domains
, domain
) < 0)
2549 domain
= isl_set_free(domain
);
2550 domain
= isl_set_subtract(domain
, domains
->atomic
);
2552 domain
= isl_set_coalesce(domain
);
2553 domain
= isl_set_make_disjoint(domain
);
2555 list
= isl_basic_set_list_from_set(domain
);
2556 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2558 isl_set_free(class_domain
);
2562 isl_set_free(domain
);
2563 isl_set_free(class_domain
);
2567 /* Split up the domain at the current depth into disjoint
2568 * basic sets for which code should be generated separately
2569 * for the separation class identified by "pnt".
2571 * We extract the corresponding class domain from domains->sep_class,
2572 * eliminate inner dimensions and pass control to compute_partial_domains.
2574 static int compute_class_domains(__isl_take isl_point
*pnt
, void *user
)
2576 struct isl_codegen_domains
*domains
= user
;
2581 class_set
= isl_set_from_point(pnt
);
2582 domain
= isl_map_domain(isl_map_intersect_range(
2583 isl_map_copy(domains
->sep_class
), class_set
));
2584 domain
= isl_ast_build_compute_gist(domains
->build
, domain
);
2585 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2587 disjoint
= isl_set_plain_is_disjoint(domain
, domains
->schedule_domain
);
2591 isl_set_free(domain
);
2595 return compute_partial_domains(domains
, domain
);
2598 /* Extract the domains at the current depth that should be atomic,
2599 * separated or unrolled and store them in option.
2601 * The domains specified by the user might overlap, so we make
2602 * them disjoint by subtracting earlier domains from later domains.
2604 static void compute_domains_init_options(isl_set
*option
[3],
2605 __isl_keep isl_ast_build
*build
)
2607 enum isl_ast_build_domain_type type
, type2
;
2609 for (type
= atomic
; type
<= separate
; ++type
) {
2610 option
[type
] = isl_ast_build_get_option_domain(build
, type
);
2611 for (type2
= atomic
; type2
< type
; ++type2
)
2612 option
[type
] = isl_set_subtract(option
[type
],
2613 isl_set_copy(option
[type2
]));
2616 option
[unroll
] = isl_set_coalesce(option
[unroll
]);
2617 option
[unroll
] = isl_set_make_disjoint(option
[unroll
]);
2620 /* Split up the domain at the current depth into disjoint
2621 * basic sets for which code should be generated separately,
2622 * based on the user-specified options.
2623 * Return the list of disjoint basic sets.
2625 * There are three kinds of domains that we need to keep track of.
2626 * - the "schedule domain" is the domain of "executed"
2627 * - the "class domain" is the domain corresponding to the currrent
2629 * - the "option domain" is the domain corresponding to one of the options
2630 * atomic, unroll or separate
2632 * We first consider the individial values of the separation classes
2633 * and split up the domain for each of them separately.
2634 * Finally, we consider the remainder. If no separation classes were
2635 * specified, then we call compute_partial_domains with the universe
2636 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2637 * with inner dimensions removed. We do this because we want to
2638 * avoid computing the complement of the class domains (i.e., the difference
2639 * between the universe and domains->done).
2641 static __isl_give isl_basic_set_list
*compute_domains(
2642 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
2644 struct isl_codegen_domains domains
;
2647 isl_union_set
*schedule_domain
;
2651 enum isl_ast_build_domain_type type
;
2657 ctx
= isl_union_map_get_ctx(executed
);
2658 domains
.list
= isl_basic_set_list_alloc(ctx
, 0);
2660 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
2661 domain
= isl_set_from_union_set(schedule_domain
);
2663 compute_domains_init_options(domains
.option
, build
);
2665 domains
.sep_class
= isl_ast_build_get_separation_class(build
);
2666 classes
= isl_map_range(isl_map_copy(domains
.sep_class
));
2667 n_param
= isl_set_dim(classes
, isl_dim_param
);
2668 classes
= isl_set_project_out(classes
, isl_dim_param
, 0, n_param
);
2670 space
= isl_set_get_space(domain
);
2671 domains
.build
= build
;
2672 domains
.schedule_domain
= isl_set_copy(domain
);
2673 domains
.executed
= executed
;
2674 domains
.done
= isl_set_empty(space
);
2676 if (isl_set_foreach_point(classes
, &compute_class_domains
, &domains
) < 0)
2677 domains
.list
= isl_basic_set_list_free(domains
.list
);
2678 isl_set_free(classes
);
2680 empty
= isl_set_is_empty(domains
.done
);
2682 domains
.list
= isl_basic_set_list_free(domains
.list
);
2683 domain
= isl_set_free(domain
);
2685 isl_set_free(domain
);
2686 domain
= isl_set_universe(isl_set_get_space(domains
.done
));
2688 domain
= isl_ast_build_eliminate(build
, domain
);
2690 if (compute_partial_domains(&domains
, domain
) < 0)
2691 domains
.list
= isl_basic_set_list_free(domains
.list
);
2693 isl_set_free(domains
.schedule_domain
);
2694 isl_set_free(domains
.done
);
2695 isl_map_free(domains
.sep_class
);
2696 for (type
= atomic
; type
<= separate
; ++type
)
2697 isl_set_free(domains
.option
[type
]);
2699 return domains
.list
;
2702 /* Generate code for a single component, after shifting (if any)
2705 * We first split up the domain at the current depth into disjoint
2706 * basic sets based on the user-specified options.
2707 * Then we generated code for each of them and concatenate the results.
2709 static __isl_give isl_ast_graft_list
*generate_shifted_component(
2710 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
2712 isl_basic_set_list
*domain_list
;
2713 isl_ast_graft_list
*list
= NULL
;
2715 domain_list
= compute_domains(executed
, build
);
2716 list
= generate_parallel_domains(domain_list
, executed
, build
);
2718 isl_basic_set_list_free(domain_list
);
2719 isl_union_map_free(executed
);
2720 isl_ast_build_free(build
);
2725 struct isl_set_map_pair
{
2730 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2731 * of indices into the "domain" array,
2732 * return the union of the "map" fields of the elements
2733 * indexed by the first "n" elements of "order".
2735 static __isl_give isl_union_map
*construct_component_executed(
2736 struct isl_set_map_pair
*domain
, int *order
, int n
)
2740 isl_union_map
*executed
;
2742 map
= isl_map_copy(domain
[order
[0]].map
);
2743 executed
= isl_union_map_from_map(map
);
2744 for (i
= 1; i
< n
; ++i
) {
2745 map
= isl_map_copy(domain
[order
[i
]].map
);
2746 executed
= isl_union_map_add_map(executed
, map
);
2752 /* Generate code for a single component, after shifting (if any)
2755 * The component inverse schedule is specified as the "map" fields
2756 * of the elements of "domain" indexed by the first "n" elements of "order".
2758 static __isl_give isl_ast_graft_list
*generate_shifted_component_from_list(
2759 struct isl_set_map_pair
*domain
, int *order
, int n
,
2760 __isl_take isl_ast_build
*build
)
2762 isl_union_map
*executed
;
2764 executed
= construct_component_executed(domain
, order
, n
);
2765 return generate_shifted_component(executed
, build
);
2768 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2769 * of indices into the "domain" array,
2770 * do all (except for at most one) of the "set" field of the elements
2771 * indexed by the first "n" elements of "order" have a fixed value
2772 * at position "depth"?
2774 static int at_most_one_non_fixed(struct isl_set_map_pair
*domain
,
2775 int *order
, int n
, int depth
)
2780 for (i
= 0; i
< n
; ++i
) {
2783 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2784 isl_dim_set
, depth
, NULL
);
2797 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2798 * of indices into the "domain" array,
2799 * eliminate the inner dimensions from the "set" field of the elements
2800 * indexed by the first "n" elements of "order", provided the current
2801 * dimension does not have a fixed value.
2803 * Return the index of the first element in "order" with a corresponding
2804 * "set" field that does not have an (obviously) fixed value.
2806 static int eliminate_non_fixed(struct isl_set_map_pair
*domain
,
2807 int *order
, int n
, int depth
, __isl_keep isl_ast_build
*build
)
2812 for (i
= n
- 1; i
>= 0; --i
) {
2814 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2815 isl_dim_set
, depth
, NULL
);
2820 domain
[order
[i
]].set
= isl_ast_build_eliminate_inner(build
,
2821 domain
[order
[i
]].set
);
2828 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2829 * of indices into the "domain" array,
2830 * find the element of "domain" (amongst those indexed by the first "n"
2831 * elements of "order") with the "set" field that has the smallest
2832 * value for the current iterator.
2834 * Note that the domain with the smallest value may depend on the parameters
2835 * and/or outer loop dimension. Since the result of this function is only
2836 * used as heuristic, we only make a reasonable attempt at finding the best
2837 * domain, one that should work in case a single domain provides the smallest
2838 * value for the current dimension over all values of the parameters
2839 * and outer dimensions.
2841 * In particular, we compute the smallest value of the first domain
2842 * and replace it by that of any later domain if that later domain
2843 * has a smallest value that is smaller for at least some value
2844 * of the parameters and outer dimensions.
2846 static int first_offset(struct isl_set_map_pair
*domain
, int *order
, int n
,
2847 __isl_keep isl_ast_build
*build
)
2853 min_first
= isl_ast_build_map_to_iterator(build
,
2854 isl_set_copy(domain
[order
[0]].set
));
2855 min_first
= isl_map_lexmin(min_first
);
2857 for (i
= 1; i
< n
; ++i
) {
2858 isl_map
*min
, *test
;
2861 min
= isl_ast_build_map_to_iterator(build
,
2862 isl_set_copy(domain
[order
[i
]].set
));
2863 min
= isl_map_lexmin(min
);
2864 test
= isl_map_copy(min
);
2865 test
= isl_map_apply_domain(isl_map_copy(min_first
), test
);
2866 test
= isl_map_order_lt(test
, isl_dim_in
, 0, isl_dim_out
, 0);
2867 empty
= isl_map_is_empty(test
);
2869 if (empty
>= 0 && !empty
) {
2870 isl_map_free(min_first
);
2880 isl_map_free(min_first
);
2882 return i
< n
? -1 : first
;
2885 /* Construct a shifted inverse schedule based on the original inverse schedule,
2886 * the stride and the offset.
2888 * The original inverse schedule is specified as the "map" fields
2889 * of the elements of "domain" indexed by the first "n" elements of "order".
2891 * "stride" and "offset" are such that the difference
2892 * between the values of the current dimension of domain "i"
2893 * and the values of the current dimension for some reference domain are
2896 * stride * integer + offset[i]
2898 * Moreover, 0 <= offset[i] < stride.
2900 * For each domain, we create a map
2902 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2904 * where j refers to the current dimension and the other dimensions are
2905 * unchanged, and apply this map to the original schedule domain.
2907 * For example, for the original schedule
2909 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2911 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2912 * we apply the mapping
2916 * to the schedule of the "A" domain and the mapping
2918 * { [j - 1] -> [j, 1] }
2920 * to the schedule of the "B" domain.
2923 * Note that after the transformation, the differences between pairs
2924 * of values of the current dimension over all domains are multiples
2925 * of stride and that we have therefore exposed the stride.
2928 * To see that the mapping preserves the lexicographic order,
2929 * first note that each of the individual maps above preserves the order.
2930 * If the value of the current iterator is j1 in one domain and j2 in another,
2931 * then if j1 = j2, we know that the same map is applied to both domains
2932 * and the order is preserved.
2933 * Otherwise, let us assume, without loss of generality, that j1 < j2.
2934 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
2938 * and the order is preserved.
2939 * If c1 < c2, then we know
2945 * j2 - j1 = n * s + r
2947 * with n >= 0 and 0 <= r < s.
2948 * In other words, r = c2 - c1.
2959 * (j1 - c1, c1) << (j2 - c2, c2)
2961 * with "<<" the lexicographic order, proving that the order is preserved
2964 static __isl_give isl_union_map
*contruct_shifted_executed(
2965 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
2966 __isl_keep isl_vec
*offset
, __isl_keep isl_ast_build
*build
)
2970 isl_union_map
*executed
;
2976 depth
= isl_ast_build_get_depth(build
);
2977 space
= isl_ast_build_get_space(build
, 1);
2978 executed
= isl_union_map_empty(isl_space_copy(space
));
2979 space
= isl_space_map_from_set(space
);
2980 map
= isl_map_identity(isl_space_copy(space
));
2981 map
= isl_map_eliminate(map
, isl_dim_out
, depth
, 1);
2982 map
= isl_map_insert_dims(map
, isl_dim_out
, depth
+ 1, 1);
2983 space
= isl_space_insert_dims(space
, isl_dim_out
, depth
+ 1, 1);
2985 c
= isl_equality_alloc(isl_local_space_from_space(space
));
2986 c
= isl_constraint_set_coefficient_si(c
, isl_dim_in
, depth
, 1);
2987 c
= isl_constraint_set_coefficient_si(c
, isl_dim_out
, depth
, -1);
2991 for (i
= 0; i
< n
; ++i
) {
2994 if (isl_vec_get_element(offset
, i
, &v
) < 0)
2996 map_i
= isl_map_copy(map
);
2997 map_i
= isl_map_fix(map_i
, isl_dim_out
, depth
+ 1, v
);
2999 c
= isl_constraint_set_constant(c
, v
);
3000 map_i
= isl_map_add_constraint(map_i
, isl_constraint_copy(c
));
3002 map_i
= isl_map_apply_domain(isl_map_copy(domain
[order
[i
]].map
),
3004 executed
= isl_union_map_add_map(executed
, map_i
);
3007 isl_constraint_free(c
);
3013 executed
= isl_union_map_free(executed
);
3018 /* Generate code for a single component, after exposing the stride,
3019 * given that the schedule domain is "shifted strided".
3021 * The component inverse schedule is specified as the "map" fields
3022 * of the elements of "domain" indexed by the first "n" elements of "order".
3024 * The schedule domain being "shifted strided" means that the differences
3025 * between the values of the current dimension of domain "i"
3026 * and the values of the current dimension for some reference domain are
3029 * stride * integer + offset[i]
3031 * We first look for the domain with the "smallest" value for the current
3032 * dimension and adjust the offsets such that the offset of the "smallest"
3033 * domain is equal to zero. The other offsets are reduced modulo stride.
3035 * Based on this information, we construct a new inverse schedule in
3036 * contruct_shifted_executed that exposes the stride.
3037 * Since this involves the introduction of a new schedule dimension,
3038 * the build needs to be changed accodingly.
3039 * After computing the AST, the newly introduced dimension needs
3040 * to be removed again from the list of grafts. We do this by plugging
3041 * in a mapping that represents the new schedule domain in terms of the
3042 * old schedule domain.
3044 static __isl_give isl_ast_graft_list
*generate_shift_component(
3045 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
3046 __isl_keep isl_vec
*offset
, __isl_take isl_ast_build
*build
)
3048 isl_ast_graft_list
*list
;
3055 isl_multi_aff
*ma
, *zero
;
3056 isl_union_map
*executed
;
3058 ctx
= isl_ast_build_get_ctx(build
);
3059 depth
= isl_ast_build_get_depth(build
);
3061 first
= first_offset(domain
, order
, n
, build
);
3063 return isl_ast_build_free(build
);
3066 v
= isl_vec_alloc(ctx
, n
);
3067 if (isl_vec_get_element(offset
, first
, &val
) < 0)
3068 v
= isl_vec_free(v
);
3069 isl_int_neg(val
, val
);
3070 v
= isl_vec_set(v
, val
);
3071 v
= isl_vec_add(v
, isl_vec_copy(offset
));
3072 v
= isl_vec_fdiv_r(v
, stride
);
3074 executed
= contruct_shifted_executed(domain
, order
, n
, stride
, v
,
3076 space
= isl_ast_build_get_space(build
, 1);
3077 space
= isl_space_map_from_set(space
);
3078 ma
= isl_multi_aff_identity(isl_space_copy(space
));
3079 space
= isl_space_from_domain(isl_space_domain(space
));
3080 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
3081 zero
= isl_multi_aff_zero(space
);
3082 ma
= isl_multi_aff_range_splice(ma
, depth
+ 1, zero
);
3083 build
= isl_ast_build_insert_dim(build
, depth
+ 1);
3084 list
= generate_shifted_component(executed
, build
);
3086 list
= isl_ast_graft_list_preimage_multi_aff(list
, ma
);
3094 /* Generate code for a single component.
3096 * The component inverse schedule is specified as the "map" fields
3097 * of the elements of "domain" indexed by the first "n" elements of "order".
3099 * This function may modify the "set" fields of "domain".
3101 * Before proceeding with the actual code generation for the component,
3102 * we first check if there are any "shifted" strides, meaning that
3103 * the schedule domains of the individual domains are all strided,
3104 * but that they have different offsets, resulting in the union
3105 * of schedule domains not being strided anymore.
3107 * The simplest example is the schedule
3109 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3111 * Both schedule domains are strided, but their union is not.
3112 * This function detects such cases and then rewrites the schedule to
3114 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3116 * In the new schedule, the schedule domains have the same offset (modulo
3117 * the stride), ensuring that the union of schedule domains is also strided.
3120 * If there is only a single domain in the component, then there is
3121 * nothing to do. Similarly, if the current schedule dimension has
3122 * a fixed value for almost all domains then there is nothing to be done.
3123 * In particular, we need at least two domains where the current schedule
3124 * dimension does not have a fixed value.
3125 * Finally, if any of the options refer to the current schedule dimension,
3126 * then we bail out as well. It would be possible to reformulate the options
3127 * in terms of the new schedule domain, but that would introduce constraints
3128 * that separate the domains in the options and that is something we would
3132 * To see if there is any shifted stride, we look at the differences
3133 * between the values of the current dimension in pairs of domains
3134 * for equal values of outer dimensions. These differences should be
3139 * with "m" the stride and "r" a constant. Note that we cannot perform
3140 * this analysis on individual domains as the lower bound in each domain
3141 * may depend on parameters or outer dimensions and so the current dimension
3142 * itself may not have a fixed remainder on division by the stride.
3144 * In particular, we compare the first domain that does not have an
3145 * obviously fixed value for the current dimension to itself and all
3146 * other domains and collect the offsets and the gcd of the strides.
3147 * If the gcd becomes one, then we failed to find shifted strides.
3148 * If all the offsets are the same (for those domains that do not have
3149 * an obviously fixed value for the current dimension), then we do not
3150 * apply the transformation.
3151 * If none of the domains were skipped, then there is nothing to do.
3152 * If some of them were skipped, then if we apply separation, the schedule
3153 * domain should get split in pieces with a (non-shifted) stride.
3155 * Otherwise, we apply a shift to expose the stride in
3156 * generate_shift_component.
3158 static __isl_give isl_ast_graft_list
*generate_component(
3159 struct isl_set_map_pair
*domain
, int *order
, int n
,
3160 __isl_take isl_ast_build
*build
)
3171 isl_ast_graft_list
*list
;
3174 depth
= isl_ast_build_get_depth(build
);
3177 if (skip
>= 0 && !skip
)
3178 skip
= at_most_one_non_fixed(domain
, order
, n
, depth
);
3179 if (skip
>= 0 && !skip
)
3180 skip
= isl_ast_build_options_involve_depth(build
);
3182 return isl_ast_build_free(build
);
3184 return generate_shifted_component_from_list(domain
,
3187 base
= eliminate_non_fixed(domain
, order
, n
, depth
, build
);
3189 return isl_ast_build_free(build
);
3191 ctx
= isl_ast_build_get_ctx(build
);
3196 v
= isl_vec_alloc(ctx
, n
);
3199 for (i
= 0; i
< n
; ++i
) {
3200 map
= isl_map_from_domain_and_range(
3201 isl_set_copy(domain
[order
[base
]].set
),
3202 isl_set_copy(domain
[order
[i
]].set
));
3203 for (d
= 0; d
< depth
; ++d
)
3204 map
= isl_map_equate(map
, isl_dim_in
, d
,
3206 deltas
= isl_map_deltas(map
);
3207 res
= isl_set_dim_residue_class(deltas
, depth
, &m
, &r
);
3208 isl_set_free(deltas
);
3213 isl_int_set(gcd
, m
);
3215 isl_int_gcd(gcd
, gcd
, m
);
3216 if (isl_int_is_one(gcd
))
3218 v
= isl_vec_set_element(v
, i
, r
);
3220 res
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
3221 isl_dim_set
, depth
, NULL
);
3227 if (fixed
&& i
> base
) {
3228 isl_vec_get_element(v
, base
, &m
);
3229 if (isl_int_ne(m
, r
))
3235 isl_ast_build_free(build
);
3237 } else if (i
< n
|| fixed
) {
3238 list
= generate_shifted_component_from_list(domain
,
3241 list
= generate_shift_component(domain
, order
, n
, gcd
, v
,
3253 /* Store both "map" itself and its domain in the
3254 * structure pointed to by *next and advance to the next array element.
3256 static int extract_domain(__isl_take isl_map
*map
, void *user
)
3258 struct isl_set_map_pair
**next
= user
;
3260 (*next
)->map
= isl_map_copy(map
);
3261 (*next
)->set
= isl_map_domain(map
);
3267 /* Internal data for any_scheduled_after.
3269 * "depth" is the number of loops that have already been generated
3270 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3271 * "domain" is an array of set-map pairs corresponding to the different
3272 * iteration domains. The set is the schedule domain, i.e., the domain
3273 * of the inverse schedule, while the map is the inverse schedule itself.
3275 struct isl_any_scheduled_after_data
{
3277 int group_coscheduled
;
3278 struct isl_set_map_pair
*domain
;
3281 /* Is any element of domain "i" scheduled after any element of domain "j"
3282 * (for a common iteration of the first data->depth loops)?
3284 * data->domain[i].set contains the domain of the inverse schedule
3285 * for domain "i", i.e., elements in the schedule domain.
3287 * If data->group_coscheduled is set, then we also return 1 if there
3288 * is any pair of elements in the two domains that are scheduled together.
3290 static int any_scheduled_after(int i
, int j
, void *user
)
3292 struct isl_any_scheduled_after_data
*data
= user
;
3293 int dim
= isl_set_dim(data
->domain
[i
].set
, isl_dim_set
);
3296 for (pos
= data
->depth
; pos
< dim
; ++pos
) {
3299 follows
= isl_set_follows_at(data
->domain
[i
].set
,
3300 data
->domain
[j
].set
, pos
);
3310 return data
->group_coscheduled
;
3313 /* Look for independent components at the current depth and generate code
3314 * for each component separately. The resulting lists of grafts are
3315 * merged in an attempt to combine grafts with identical guards.
3317 * Code for two domains can be generated separately if all the elements
3318 * of one domain are scheduled before (or together with) all the elements
3319 * of the other domain. We therefore consider the graph with as nodes
3320 * the domains and an edge between two nodes if any element of the first
3321 * node is scheduled after any element of the second node.
3322 * If the ast_build_group_coscheduled is set, then we also add an edge if
3323 * there is any pair of elements in the two domains that are scheduled
3325 * Code is then generated (by generate_component)
3326 * for each of the strongly connected components in this graph
3327 * in their topological order.
3329 * Since the test is performed on the domain of the inverse schedules of
3330 * the different domains, we precompute these domains and store
3331 * them in data.domain.
3333 static __isl_give isl_ast_graft_list
*generate_components(
3334 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3337 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3338 int n
= isl_union_map_n_map(executed
);
3339 struct isl_any_scheduled_after_data data
;
3340 struct isl_set_map_pair
*next
;
3341 struct isl_tarjan_graph
*g
= NULL
;
3342 isl_ast_graft_list
*list
= NULL
;
3345 data
.domain
= isl_calloc_array(ctx
, struct isl_set_map_pair
, n
);
3351 if (isl_union_map_foreach_map(executed
, &extract_domain
, &next
) < 0)
3356 data
.depth
= isl_ast_build_get_depth(build
);
3357 data
.group_coscheduled
= isl_options_get_ast_build_group_coscheduled(ctx
);
3358 g
= isl_tarjan_graph_init(ctx
, n
, &any_scheduled_after
, &data
);
3360 list
= isl_ast_graft_list_alloc(ctx
, 0);
3364 isl_ast_graft_list
*list_c
;
3367 if (g
->order
[i
] == -1)
3368 isl_die(ctx
, isl_error_internal
, "cannot happen",
3371 while (g
->order
[i
] != -1) {
3375 list_c
= generate_component(data
.domain
,
3376 g
->order
+ first
, i
- first
,
3377 isl_ast_build_copy(build
));
3378 list
= isl_ast_graft_list_merge(list
, list_c
, build
);
3384 error
: list
= isl_ast_graft_list_free(list
);
3385 isl_tarjan_graph_free(g
);
3386 for (i
= 0; i
< n_domain
; ++i
) {
3387 isl_map_free(data
.domain
[i
].map
);
3388 isl_set_free(data
.domain
[i
].set
);
3391 isl_union_map_free(executed
);
3392 isl_ast_build_free(build
);
3397 /* Generate code for the next level (and all inner levels).
3399 * If "executed" is empty, i.e., no code needs to be generated,
3400 * then we return an empty list.
3402 * If we have already generated code for all loop levels, then we pass
3403 * control to generate_inner_level.
3405 * If "executed" lives in a single space, i.e., if code needs to be
3406 * generated for a single domain, then there can only be a single
3407 * component and we go directly to generate_shifted_component.
3408 * Otherwise, we call generate_components to detect the components
3409 * and to call generate_component on each of them separately.
3411 static __isl_give isl_ast_graft_list
*generate_next_level(
3412 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3416 if (!build
|| !executed
)
3419 if (isl_union_map_is_empty(executed
)) {
3420 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3421 isl_union_map_free(executed
);
3422 isl_ast_build_free(build
);
3423 return isl_ast_graft_list_alloc(ctx
, 0);
3426 depth
= isl_ast_build_get_depth(build
);
3427 if (depth
>= isl_set_dim(build
->domain
, isl_dim_set
))
3428 return generate_inner_level(executed
, build
);
3430 if (isl_union_map_n_map(executed
) == 1)
3431 return generate_shifted_component(executed
, build
);
3433 return generate_components(executed
, build
);
3435 isl_union_map_free(executed
);
3436 isl_ast_build_free(build
);
3440 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3441 * internal, executed and build are the inputs to generate_code.
3442 * list collects the output.
3444 struct isl_generate_code_data
{
3446 isl_union_map
*executed
;
3447 isl_ast_build
*build
;
3449 isl_ast_graft_list
*list
;
3452 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3456 * with E the external build schedule and S the additional schedule "space",
3457 * reformulate the inverse schedule in terms of the internal schedule domain,
3462 * We first obtain a mapping
3466 * take the inverse and the product with S -> S, resulting in
3468 * [I -> S] -> [E -> S]
3470 * Applying the map to the input produces the desired result.
3472 static __isl_give isl_union_map
*internal_executed(
3473 __isl_take isl_union_map
*executed
, __isl_keep isl_space
*space
,
3474 __isl_keep isl_ast_build
*build
)
3478 proj
= isl_ast_build_get_schedule_map(build
);
3479 proj
= isl_map_reverse(proj
);
3480 space
= isl_space_map_from_set(isl_space_copy(space
));
3481 id
= isl_map_identity(space
);
3482 proj
= isl_map_product(proj
, id
);
3483 executed
= isl_union_map_apply_domain(executed
,
3484 isl_union_map_from_map(proj
));
3488 /* Generate an AST that visits the elements in the range of data->executed
3489 * in the relative order specified by the corresponding image element(s)
3490 * for those image elements that belong to "set".
3491 * Add the result to data->list.
3493 * The caller ensures that "set" is a universe domain.
3494 * "space" is the space of the additional part of the schedule.
3495 * It is equal to the space of "set" if build->domain is parametric.
3496 * Otherwise, it is equal to the range of the wrapped space of "set".
3498 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3499 * was called from an outside user (data->internal not set), then
3500 * the (inverse) schedule refers to the external build domain and needs to
3501 * be transformed to refer to the internal build domain.
3503 * The build is extended to include the additional part of the schedule.
3504 * If the original build space was not parametric, then the options
3505 * in data->build refer only to the additional part of the schedule
3506 * and they need to be adjusted to refer to the complete AST build
3509 * After having adjusted inverse schedule and build, we start generating
3510 * code with the outer loop of the current code generation
3511 * in generate_next_level.
3513 * If the original build space was not parametric, we undo the embedding
3514 * on the resulting isl_ast_node_list so that it can be used within
3515 * the outer AST build.
3517 static int generate_code_in_space(struct isl_generate_code_data
*data
,
3518 __isl_take isl_set
*set
, __isl_take isl_space
*space
)
3520 isl_union_map
*executed
;
3521 isl_ast_build
*build
;
3522 isl_ast_graft_list
*list
;
3525 executed
= isl_union_map_copy(data
->executed
);
3526 executed
= isl_union_map_intersect_domain(executed
,
3527 isl_union_set_from_set(set
));
3529 embed
= !isl_set_is_params(data
->build
->domain
);
3530 if (embed
&& !data
->internal
)
3531 executed
= internal_executed(executed
, space
, data
->build
);
3533 build
= isl_ast_build_copy(data
->build
);
3534 build
= isl_ast_build_product(build
, space
);
3536 list
= generate_next_level(executed
, build
);
3538 list
= isl_ast_graft_list_unembed(list
, embed
);
3540 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
3545 /* Generate an AST that visits the elements in the range of data->executed
3546 * in the relative order specified by the corresponding domain element(s)
3547 * for those domain elements that belong to "set".
3548 * Add the result to data->list.
3550 * The caller ensures that "set" is a universe domain.
3552 * If the build space S is not parametric, then the space of "set"
3553 * need to be a wrapped relation with S as domain. That is, it needs
3558 * Check this property and pass control to generate_code_in_space
3560 * If the build space is not parametric, then T is the space of "set".
3562 static int generate_code_set(__isl_take isl_set
*set
, void *user
)
3564 struct isl_generate_code_data
*data
= user
;
3565 isl_space
*space
, *build_space
;
3568 space
= isl_set_get_space(set
);
3570 if (isl_set_is_params(data
->build
->domain
))
3571 return generate_code_in_space(data
, set
, space
);
3573 build_space
= isl_ast_build_get_space(data
->build
, data
->internal
);
3574 space
= isl_space_unwrap(space
);
3575 is_domain
= isl_space_is_domain(build_space
, space
);
3576 isl_space_free(build_space
);
3577 space
= isl_space_range(space
);
3582 isl_die(isl_set_get_ctx(set
), isl_error_invalid
,
3583 "invalid nested schedule space", goto error
);
3585 return generate_code_in_space(data
, set
, space
);
3588 isl_space_free(space
);
3592 /* Generate an AST that visits the elements in the range of "executed"
3593 * in the relative order specified by the corresponding domain element(s).
3595 * "build" is an isl_ast_build that has either been constructed by
3596 * isl_ast_build_from_context or passed to a callback set by
3597 * isl_ast_build_set_create_leaf.
3598 * In the first case, the space of the isl_ast_build is typically
3599 * a parametric space, although this is currently not enforced.
3600 * In the second case, the space is never a parametric space.
3601 * If the space S is not parametric, then the domain space(s) of "executed"
3602 * need to be wrapped relations with S as domain.
3604 * If the domain of "executed" consists of several spaces, then an AST
3605 * is generated for each of them (in arbitrary order) and the results
3608 * If "internal" is set, then the domain "S" above refers to the internal
3609 * schedule domain representation. Otherwise, it refers to the external
3610 * representation, as returned by isl_ast_build_get_schedule_space.
3612 * We essentially run over all the spaces in the domain of "executed"
3613 * and call generate_code_set on each of them.
3615 static __isl_give isl_ast_graft_list
*generate_code(
3616 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
3620 struct isl_generate_code_data data
= { 0 };
3622 isl_union_set
*schedule_domain
;
3623 isl_union_map
*universe
;
3627 space
= isl_ast_build_get_space(build
, 1);
3628 space
= isl_space_align_params(space
,
3629 isl_union_map_get_space(executed
));
3630 space
= isl_space_align_params(space
,
3631 isl_union_map_get_space(build
->options
));
3632 build
= isl_ast_build_align_params(build
, isl_space_copy(space
));
3633 executed
= isl_union_map_align_params(executed
, space
);
3634 if (!executed
|| !build
)
3637 ctx
= isl_ast_build_get_ctx(build
);
3639 data
.internal
= internal
;
3640 data
.executed
= executed
;
3642 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
3644 universe
= isl_union_map_universe(isl_union_map_copy(executed
));
3645 schedule_domain
= isl_union_map_domain(universe
);
3646 if (isl_union_set_foreach_set(schedule_domain
, &generate_code_set
,
3648 data
.list
= isl_ast_graft_list_free(data
.list
);
3650 isl_union_set_free(schedule_domain
);
3651 isl_union_map_free(executed
);
3653 isl_ast_build_free(build
);
3656 isl_union_map_free(executed
);
3657 isl_ast_build_free(build
);
3661 /* Generate an AST that visits the elements in the domain of "schedule"
3662 * in the relative order specified by the corresponding image element(s).
3664 * "build" is an isl_ast_build that has either been constructed by
3665 * isl_ast_build_from_context or passed to a callback set by
3666 * isl_ast_build_set_create_leaf.
3667 * In the first case, the space of the isl_ast_build is typically
3668 * a parametric space, although this is currently not enforced.
3669 * In the second case, the space is never a parametric space.
3670 * If the space S is not parametric, then the range space(s) of "schedule"
3671 * need to be wrapped relations with S as domain.
3673 * If the range of "schedule" consists of several spaces, then an AST
3674 * is generated for each of them (in arbitrary order) and the results
3677 * We first initialize the local copies of the relevant options.
3678 * We do this here rather than when the isl_ast_build is created
3679 * because the options may have changed between the construction
3680 * of the isl_ast_build and the call to isl_generate_code.
3682 * The main computation is performed on an inverse schedule (with
3683 * the schedule domain in the domain and the elements to be executed
3684 * in the range) called "executed".
3686 __isl_give isl_ast_node
*isl_ast_build_ast_from_schedule(
3687 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
3689 isl_ast_graft_list
*list
;
3691 isl_union_map
*executed
;
3693 build
= isl_ast_build_copy(build
);
3694 build
= isl_ast_build_set_single_valued(build
, 0);
3695 executed
= isl_union_map_reverse(schedule
);
3696 list
= generate_code(executed
, isl_ast_build_copy(build
), 0);
3697 node
= isl_ast_node_from_graft_list(list
, build
);
3698 isl_ast_build_free(build
);