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
13 #include <isl/union_map.h>
15 #include <isl_tarjan.h>
16 #include <isl_ast_private.h>
17 #include <isl_ast_build_expr.h>
18 #include <isl_ast_build_private.h>
19 #include <isl_ast_graft_private.h>
20 #include <isl_list_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
);
112 list
= generate_code(isl_union_map_from_map(executed
), build
, 1);
114 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
119 /* Call the at_each_domain callback, if requested by the user,
120 * after recording the current inverse schedule in the build.
122 static __isl_give isl_ast_graft
*at_each_domain(__isl_take isl_ast_graft
*graft
,
123 __isl_keep isl_map
*executed
, __isl_keep isl_ast_build
*build
)
125 if (!graft
|| !build
)
126 return isl_ast_graft_free(graft
);
127 if (!build
->at_each_domain
)
130 build
= isl_ast_build_copy(build
);
131 build
= isl_ast_build_set_executed(build
,
132 isl_union_map_from_map(isl_map_copy(executed
)));
134 return isl_ast_graft_free(graft
);
136 graft
->node
= build
->at_each_domain(graft
->node
,
137 build
, build
->at_each_domain_user
);
138 isl_ast_build_free(build
);
141 graft
= isl_ast_graft_free(graft
);
146 /* Generate an AST for a single domain based on
147 * the inverse schedule "executed".
149 * If there is more than one domain element associated to the current
150 * schedule "time", then we need to continue the generation process
151 * in generate_non_single_valued.
152 * Note that the inverse schedule being single-valued may depend
153 * on constraints that are only available in the original context
154 * domain specified by the user. We therefore first introduce
155 * the constraints from data->build->domain.
156 * On the other hand, we only perform the test after having taken the gist
157 * of the domain as the resulting map is the one from which the call
158 * expression is constructed.
160 * Otherwise, we generate a call expression for the single executed
161 * domain element and put a guard around it based on the (simplified)
162 * domain of "executed".
164 * If the user has set an at_each_domain callback, it is called
165 * on the constructed call expression node.
167 static int generate_domain(__isl_take isl_map
*executed
, void *user
)
169 struct isl_generate_domain_data
*data
= user
;
170 isl_ast_graft
*graft
;
171 isl_ast_graft_list
*list
;
176 executed
= isl_map_intersect_domain(executed
,
177 isl_set_copy(data
->build
->domain
));
179 executed
= isl_map_coalesce(executed
);
180 map
= isl_map_copy(executed
);
181 map
= isl_ast_build_compute_gist_map_domain(data
->build
, map
);
182 sv
= isl_map_is_single_valued(map
);
187 return generate_non_single_valued(executed
, data
);
189 guard
= isl_map_domain(isl_map_copy(map
));
190 guard
= isl_set_coalesce(guard
);
191 guard
= isl_ast_build_compute_gist(data
->build
, guard
);
192 graft
= isl_ast_graft_alloc_domain(map
, data
->build
);
193 graft
= at_each_domain(graft
, executed
, data
->build
);
195 isl_map_free(executed
);
196 graft
= isl_ast_graft_add_guard(graft
, guard
, data
->build
);
198 list
= isl_ast_graft_list_from_ast_graft(graft
);
199 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
204 isl_map_free(executed
);
208 /* Call build->create_leaf to a create "leaf" node in the AST,
209 * encapsulate the result in an isl_ast_graft and return the result
210 * as a 1-element list.
212 * Note that the node returned by the user may be an entire tree.
214 * Before we pass control to the user, we first clear some information
215 * from the build that is (presumbably) only meaningful
216 * for the current code generation.
217 * This includes the create_leaf callback itself, so we make a copy
218 * of the build first.
220 static __isl_give isl_ast_graft_list
*call_create_leaf(
221 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
224 isl_ast_graft
*graft
;
225 isl_ast_build
*user_build
;
227 user_build
= isl_ast_build_copy(build
);
228 user_build
= isl_ast_build_set_executed(user_build
, executed
);
229 user_build
= isl_ast_build_clear_local_info(user_build
);
233 node
= build
->create_leaf(user_build
, build
->create_leaf_user
);
234 graft
= isl_ast_graft_alloc(node
, build
);
235 isl_ast_build_free(build
);
236 return isl_ast_graft_list_from_ast_graft(graft
);
239 /* Generate an AST after having handled the complete schedule
240 * of this call to the code generator.
242 * If the user has specified a create_leaf callback, control
243 * is passed to the user in call_create_leaf.
245 * Otherwise, we generate one or more calls for each individual
246 * domain in generate_domain.
248 static __isl_give isl_ast_graft_list
*generate_inner_level(
249 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
252 struct isl_generate_domain_data data
= { build
};
254 if (!build
|| !executed
)
257 if (build
->create_leaf
)
258 return call_create_leaf(executed
, build
);
260 ctx
= isl_union_map_get_ctx(executed
);
261 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
262 if (isl_union_map_foreach_map(executed
, &generate_domain
, &data
) < 0)
263 data
.list
= isl_ast_graft_list_free(data
.list
);
266 error
: data
.list
= NULL
;
267 isl_ast_build_free(build
);
268 isl_union_map_free(executed
);
272 /* Call the before_each_for callback, if requested by the user.
274 static __isl_give isl_ast_node
*before_each_for(__isl_take isl_ast_node
*node
,
275 __isl_keep isl_ast_build
*build
)
280 return isl_ast_node_free(node
);
281 if (!build
->before_each_for
)
283 id
= build
->before_each_for(build
, build
->before_each_for_user
);
284 node
= isl_ast_node_set_annotation(node
, id
);
288 /* Call the after_each_for callback, if requested by the user.
290 static __isl_give isl_ast_graft
*after_each_for(__isl_keep isl_ast_graft
*graft
,
291 __isl_keep isl_ast_build
*build
)
293 if (!graft
|| !build
)
294 isl_ast_graft_free(graft
);
295 if (!build
->after_each_for
)
297 graft
->node
= build
->after_each_for(graft
->node
, build
,
298 build
->after_each_for_user
);
300 return isl_ast_graft_free(graft
);
304 /* Eliminate the schedule dimension "pos" from "executed" and return
307 static __isl_give isl_union_map
*eliminate(__isl_take isl_union_map
*executed
,
308 int pos
, __isl_keep isl_ast_build
*build
)
313 space
= isl_ast_build_get_space(build
, 1);
314 space
= isl_space_map_from_set(space
);
315 elim
= isl_map_identity(space
);
316 elim
= isl_map_eliminate(elim
, isl_dim_in
, pos
, 1);
318 executed
= isl_union_map_apply_domain(executed
,
319 isl_union_map_from_map(elim
));
324 /* Check if the constraint "c" is a lower bound on dimension "pos",
325 * an upper bound, or independent of dimension "pos".
327 static int constraint_type(isl_constraint
*c
, int pos
)
329 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, pos
))
331 if (isl_constraint_is_upper_bound(c
, isl_dim_set
, pos
))
336 /* Compare the types of the constraints "a" and "b",
337 * resulting in constraints that are independent of "depth"
338 * to be sorted before the lower bounds on "depth", which in
339 * turn are sorted before the upper bounds on "depth".
341 static int cmp_constraint(const void *a
, const void *b
, void *user
)
344 isl_constraint
* const *c1
= a
;
345 isl_constraint
* const *c2
= b
;
346 int t1
= constraint_type(*c1
, *depth
);
347 int t2
= constraint_type(*c2
, *depth
);
352 /* Extract a lower bound on dimension "pos" from constraint "c".
354 * If the constraint is of the form
358 * then we essentially return
360 * l = ceil(-f(...)/a)
362 * However, if the current dimension is strided, then we need to make
363 * sure that the lower bound we construct is of the form
367 * with f the offset and s the stride.
368 * We therefore compute
370 * f + s * ceil((l - f)/s)
372 static __isl_give isl_aff
*lower_bound(__isl_keep isl_constraint
*c
,
373 int pos
, __isl_keep isl_ast_build
*build
)
377 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
378 aff
= isl_aff_ceil(aff
);
380 if (isl_ast_build_has_stride(build
, pos
)) {
384 isl_int_init(stride
);
386 offset
= isl_ast_build_get_offset(build
, pos
);
387 isl_ast_build_get_stride(build
, pos
, &stride
);
389 aff
= isl_aff_sub(aff
, isl_aff_copy(offset
));
390 aff
= isl_aff_scale_down(aff
, stride
);
391 aff
= isl_aff_ceil(aff
);
392 aff
= isl_aff_scale(aff
, stride
);
393 aff
= isl_aff_add(aff
, offset
);
395 isl_int_clear(stride
);
398 aff
= isl_ast_build_compute_gist_aff(build
, aff
);
403 /* Return the exact lower bound (or upper bound if "upper" is set)
404 * of "domain" as a piecewise affine expression.
406 * If we are computing a lower bound (of a strided dimension), then
407 * we need to make sure it is of the form
411 * where f is the offset and s is the stride.
412 * We therefore need to include the stride constraint before computing
415 static __isl_give isl_pw_aff
*exact_bound(__isl_keep isl_set
*domain
,
416 __isl_keep isl_ast_build
*build
, int upper
)
421 isl_pw_multi_aff
*pma
;
423 domain
= isl_set_copy(domain
);
425 stride
= isl_ast_build_get_stride_constraint(build
);
426 domain
= isl_set_intersect(domain
, stride
);
428 it_map
= isl_ast_build_map_to_iterator(build
, domain
);
430 pma
= isl_map_lexmax_pw_multi_aff(it_map
);
432 pma
= isl_map_lexmin_pw_multi_aff(it_map
);
433 pa
= isl_pw_multi_aff_get_pw_aff(pma
, 0);
434 isl_pw_multi_aff_free(pma
);
435 pa
= isl_ast_build_compute_gist_pw_aff(build
, pa
);
436 pa
= isl_pw_aff_coalesce(pa
);
441 /* Return a list of "n" lower bounds on dimension "pos"
442 * extracted from the "n" constraints starting at "constraint".
443 * If "n" is zero, then we extract a lower bound from "domain" instead.
445 static __isl_give isl_pw_aff_list
*lower_bounds(
446 __isl_keep isl_constraint
**constraint
, int n
, int pos
,
447 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
450 isl_pw_aff_list
*list
;
458 pa
= exact_bound(domain
, build
, 0);
459 return isl_pw_aff_list_from_pw_aff(pa
);
462 ctx
= isl_ast_build_get_ctx(build
);
463 list
= isl_pw_aff_list_alloc(ctx
,n
);
465 for (i
= 0; i
< n
; ++i
) {
468 aff
= lower_bound(constraint
[i
], pos
, build
);
469 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
475 /* Return a list of "n" upper bounds on dimension "pos"
476 * extracted from the "n" constraints starting at "constraint".
477 * If "n" is zero, then we extract an upper bound from "domain" instead.
479 static __isl_give isl_pw_aff_list
*upper_bounds(
480 __isl_keep isl_constraint
**constraint
, int n
, int pos
,
481 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
484 isl_pw_aff_list
*list
;
489 pa
= exact_bound(domain
, build
, 1);
490 return isl_pw_aff_list_from_pw_aff(pa
);
493 ctx
= isl_ast_build_get_ctx(build
);
494 list
= isl_pw_aff_list_alloc(ctx
,n
);
496 for (i
= 0; i
< n
; ++i
) {
499 aff
= isl_constraint_get_bound(constraint
[i
], isl_dim_set
, pos
);
500 aff
= isl_aff_floor(aff
);
501 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
507 /* Return an isl_ast_expr that performs the reduction of type "type"
508 * on AST expressions corresponding to the elements in "list".
510 * The list is assumed to contain at least one element.
511 * If the list contains exactly one element, then the returned isl_ast_expr
512 * simply computes that affine expression.
514 static __isl_give isl_ast_expr
*reduce_list(enum isl_ast_op_type type
,
515 __isl_keep isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
524 n
= isl_pw_aff_list_n_pw_aff(list
);
527 return isl_ast_build_expr_from_pw_aff_internal(build
,
528 isl_pw_aff_list_get_pw_aff(list
, 0));
530 ctx
= isl_pw_aff_list_get_ctx(list
);
531 expr
= isl_ast_expr_alloc_op(ctx
, type
, n
);
535 for (i
= 0; i
< n
; ++i
) {
536 isl_ast_expr
*expr_i
;
538 expr_i
= isl_ast_build_expr_from_pw_aff_internal(build
,
539 isl_pw_aff_list_get_pw_aff(list
, i
));
541 return isl_ast_expr_free(expr
);
542 expr
->u
.op
.args
[i
] = expr_i
;
548 /* Add a guard to "graft" based on "bound" in the case of a degenerate
549 * level (including the special case of an eliminated level).
551 * We eliminate the current dimension, simplify the result in the current
552 * build and add the result as guards to the graft.
554 * Note that we cannot simply drop the constraints on the current dimension
555 * even in the eliminated case, because the single affine expression may
556 * not be explicitly available in "bounds". Moreover, the single affine
557 * expression may only be defined on a subset of the build domain,
558 * so we do in some cases need to insert a guard even in the eliminated case.
560 static __isl_give isl_ast_graft
*add_degenerate_guard(
561 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
562 __isl_keep isl_ast_build
*build
)
567 depth
= isl_ast_build_get_depth(build
);
569 dom
= isl_set_from_basic_set(isl_basic_set_copy(bounds
));
570 if (isl_ast_build_has_stride(build
, depth
)) {
573 stride
= isl_ast_build_get_stride_constraint(build
);
574 dom
= isl_set_intersect(dom
, stride
);
576 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
577 dom
= isl_ast_build_compute_gist(build
, dom
);
579 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
584 /* Update "graft" based on "bounds" for the eliminated case.
586 * In the eliminated case, no for node is created, so we only need
587 * to check if "bounds" imply any guards that need to be inserted.
589 static __isl_give isl_ast_graft
*refine_eliminated(
590 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
591 __isl_keep isl_ast_build
*build
)
593 return add_degenerate_guard(graft
, bounds
, build
);
596 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
598 * "build" is the build in which graft->node was created
599 * "sub_build" contains information about the current level itself,
600 * including the single value attained.
602 * We first set the initialization part of the for loop to the single
603 * value attained by the current dimension.
604 * The increment and condition are not strictly needed as the are known
605 * to be "1" and "iterator <= value" respectively.
606 * Then we set the size of the iterator and
607 * check if "bounds" imply any guards that need to be inserted.
609 static __isl_give isl_ast_graft
*refine_degenerate(
610 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
611 __isl_keep isl_ast_build
*build
,
612 __isl_keep isl_ast_build
*sub_build
)
616 if (!graft
|| !sub_build
)
617 return isl_ast_graft_free(graft
);
619 value
= isl_pw_aff_copy(sub_build
->value
);
621 graft
->node
->u
.f
.init
= isl_ast_build_expr_from_pw_aff_internal(build
,
623 if (!graft
->node
->u
.f
.init
)
624 return isl_ast_graft_free(graft
);
626 graft
= add_degenerate_guard(graft
, bounds
, build
);
631 /* Return the intersection of the "n" constraints starting at "constraint"
634 static __isl_give isl_set
*intersect_constraints(isl_ctx
*ctx
,
635 __isl_keep isl_constraint
**constraint
, int n
)
641 isl_die(ctx
, isl_error_internal
,
642 "expecting at least one constraint", return NULL
);
644 bset
= isl_basic_set_from_constraint(
645 isl_constraint_copy(constraint
[0]));
646 for (i
= 1; i
< n
; ++i
) {
647 isl_basic_set
*bset_i
;
649 bset_i
= isl_basic_set_from_constraint(
650 isl_constraint_copy(constraint
[i
]));
651 bset
= isl_basic_set_intersect(bset
, bset_i
);
654 return isl_set_from_basic_set(bset
);
657 /* Compute the constraints on the outer dimensions enforced by
658 * graft->node and add those constraints to graft->enforced,
659 * in case the upper bound is expressed as a set "upper".
661 * In particular, if l(...) is a lower bound in "lower", and
663 * -a i + f(...) >= 0 or a i <= f(...)
665 * is an upper bound ocnstraint on the current dimension i,
666 * then the for loop enforces the constraint
668 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
670 * We therefore simply take each lower bound in turn, plug it into
671 * the upper bounds and compute the intersection over all lower bounds.
673 * If a lower bound is a rational expression, then
674 * isl_basic_set_preimage_multi_aff will force this rational
675 * expression to have only integer values. However, the loop
676 * itself does not enforce this integrality constraint. We therefore
677 * use the ceil of the lower bounds instead of the lower bounds themselves.
678 * Other constraints will make sure that the for loop is only executed
679 * when each of the lower bounds attains an integral value.
680 * In particular, potentially rational values only occur in
681 * lower_bound if the offset is a (seemingly) rational expression,
682 * but then outer conditions will make sure that this rational expression
683 * only attains integer values.
685 static __isl_give isl_ast_graft
*set_enforced_from_set(
686 __isl_take isl_ast_graft
*graft
,
687 __isl_keep isl_pw_aff_list
*lower
, int pos
, __isl_keep isl_set
*upper
)
690 isl_basic_set
*enforced
;
691 isl_pw_multi_aff
*pma
;
694 if (!graft
|| !lower
)
695 return isl_ast_graft_free(graft
);
697 space
= isl_set_get_space(upper
);
698 enforced
= isl_basic_set_universe(isl_space_copy(space
));
700 space
= isl_space_map_from_set(space
);
701 pma
= isl_pw_multi_aff_identity(space
);
703 n
= isl_pw_aff_list_n_pw_aff(lower
);
704 for (i
= 0; i
< n
; ++i
) {
708 isl_pw_multi_aff
*pma_i
;
710 pa
= isl_pw_aff_list_get_pw_aff(lower
, i
);
711 pa
= isl_pw_aff_ceil(pa
);
712 pma_i
= isl_pw_multi_aff_copy(pma
);
713 pma_i
= isl_pw_multi_aff_set_pw_aff(pma_i
, pos
, pa
);
714 enforced_i
= isl_set_copy(upper
);
715 enforced_i
= isl_set_preimage_pw_multi_aff(enforced_i
, pma_i
);
716 hull
= isl_set_simple_hull(enforced_i
);
717 enforced
= isl_basic_set_intersect(enforced
, hull
);
720 isl_pw_multi_aff_free(pma
);
722 graft
= isl_ast_graft_enforce(graft
, enforced
);
727 /* Compute the constraints on the outer dimensions enforced by
728 * graft->node and add those constraints to graft->enforced,
729 * in case the upper bound is expressed as
730 * a list of affine expressions "upper".
732 * The enforced condition is that each lower bound expression is less
733 * than or equal to each upper bound expression.
735 static __isl_give isl_ast_graft
*set_enforced_from_list(
736 __isl_take isl_ast_graft
*graft
,
737 __isl_keep isl_pw_aff_list
*lower
, __isl_keep isl_pw_aff_list
*upper
)
740 isl_basic_set
*enforced
;
742 lower
= isl_pw_aff_list_copy(lower
);
743 upper
= isl_pw_aff_list_copy(upper
);
744 cond
= isl_pw_aff_list_le_set(lower
, upper
);
745 enforced
= isl_set_simple_hull(cond
);
746 graft
= isl_ast_graft_enforce(graft
, enforced
);
751 /* Does "aff" have a negative constant term?
753 static int aff_constant_is_negative(__isl_take isl_set
*set
,
754 __isl_take isl_aff
*aff
, void *user
)
760 isl_aff_get_constant(aff
, &v
);
761 *neg
= isl_int_is_neg(v
);
766 return *neg
? 0 : -1;
769 /* Does "pa" have a negative constant term over its entire domain?
771 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff
*pa
, void *user
)
776 r
= isl_pw_aff_foreach_piece(pa
, &aff_constant_is_negative
, user
);
779 return *neg
? 0 : -1;
782 /* Does each element in "list" have a negative constant term?
784 * The callback terminates the iteration as soon an element has been
785 * found that does not have a negative constant term.
787 static int list_constant_is_negative(__isl_keep isl_pw_aff_list
*list
)
791 if (isl_pw_aff_list_foreach(list
,
792 &pw_aff_constant_is_negative
, &neg
) < 0 && neg
)
798 /* Add 1 to each of the elements in "list", where each of these elements
799 * is defined over the internal schedule space of "build".
801 static __isl_give isl_pw_aff_list
*list_add_one(
802 __isl_take isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
809 space
= isl_ast_build_get_space(build
, 1);
810 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(space
));
811 aff
= isl_aff_add_constant_si(aff
, 1);
812 one
= isl_pw_aff_from_aff(aff
);
814 n
= isl_pw_aff_list_n_pw_aff(list
);
815 for (i
= 0; i
< n
; ++i
) {
817 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
818 pa
= isl_pw_aff_add(pa
, isl_pw_aff_copy(one
));
819 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
822 isl_pw_aff_free(one
);
827 /* Set the condition part of the for node graft->node in case
828 * the upper bound is represented as a list of piecewise affine expressions.
830 * In particular, set the condition to
832 * iterator <= min(list of upper bounds)
834 * If each of the upper bounds has a negative constant term, then
835 * set the condition to
837 * iterator < min(list of (upper bound + 1)s)
840 static __isl_give isl_ast_graft
*set_for_cond_from_list(
841 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*list
,
842 __isl_keep isl_ast_build
*build
)
845 isl_ast_expr
*bound
, *iterator
, *cond
;
846 enum isl_ast_op_type type
= isl_ast_op_le
;
849 return isl_ast_graft_free(graft
);
851 neg
= list_constant_is_negative(list
);
853 return isl_ast_graft_free(graft
);
854 list
= isl_pw_aff_list_copy(list
);
856 list
= list_add_one(list
, build
);
857 type
= isl_ast_op_lt
;
860 bound
= reduce_list(isl_ast_op_min
, list
, build
);
861 iterator
= isl_ast_expr_copy(graft
->node
->u
.f
.iterator
);
862 cond
= isl_ast_expr_alloc_binary(type
, iterator
, bound
);
863 graft
->node
->u
.f
.cond
= cond
;
865 isl_pw_aff_list_free(list
);
866 if (!graft
->node
->u
.f
.cond
)
867 return isl_ast_graft_free(graft
);
871 /* Set the condition part of the for node graft->node in case
872 * the upper bound is represented as a set.
874 static __isl_give isl_ast_graft
*set_for_cond_from_set(
875 __isl_take isl_ast_graft
*graft
, __isl_keep isl_set
*set
,
876 __isl_keep isl_ast_build
*build
)
883 cond
= isl_ast_build_expr_from_set(build
, isl_set_copy(set
));
884 graft
->node
->u
.f
.cond
= cond
;
885 if (!graft
->node
->u
.f
.cond
)
886 return isl_ast_graft_free(graft
);
890 /* Construct an isl_ast_expr for the increment (i.e., stride) of
891 * the current dimension.
893 static __isl_give isl_ast_expr
*for_inc(__isl_keep isl_ast_build
*build
)
900 ctx
= isl_ast_build_get_ctx(build
);
901 depth
= isl_ast_build_get_depth(build
);
903 if (!isl_ast_build_has_stride(build
, depth
))
904 return isl_ast_expr_alloc_int_si(ctx
, 1);
907 isl_ast_build_get_stride(build
, depth
, &v
);
908 inc
= isl_ast_expr_alloc_int(ctx
, v
);
914 /* Should we express the loop condition as
916 * iterator <= min(list of upper bounds)
918 * or as a conjunction of constraints?
920 * The first is constructed from a list of upper bounds.
921 * The second is constructed from a set.
923 * If there are no upper bounds in "constraints", then this could mean
924 * that "domain" simply doesn't have an upper bound or that we didn't
925 * pick any upper bound. In the first case, we want to generate the
926 * loop condition as a(n empty) conjunction of constraints
927 * In the second case, we will compute
928 * a single upper bound from "domain" and so we use the list form.
930 * If there are upper bounds in "constraints",
931 * then we use the list form iff the atomic_upper_bound option is set.
933 static int use_upper_bound_list(isl_ctx
*ctx
, int n_upper
,
934 __isl_keep isl_set
*domain
, int depth
)
937 return isl_options_get_ast_build_atomic_upper_bound(ctx
);
939 return isl_set_dim_has_upper_bound(domain
, isl_dim_set
, depth
);
942 /* Fill in the expressions of the for node in graft->node.
945 * - set the initialization part of the loop to the maximum of the lower bounds
946 * - set the size of the iterator based on the values attained by the iterator
947 * - extract the increment from the stride of the current dimension
948 * - construct the for condition either based on a list of upper bounds
949 * or on a set of upper bound constraints.
951 static __isl_give isl_ast_graft
*set_for_node_expressions(
952 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*lower
,
953 int use_list
, __isl_keep isl_pw_aff_list
*upper_list
,
954 __isl_keep isl_set
*upper_set
, __isl_keep isl_ast_build
*build
)
961 build
= isl_ast_build_copy(build
);
962 build
= isl_ast_build_set_enforced(build
,
963 isl_ast_graft_get_enforced(graft
));
966 node
->u
.f
.init
= reduce_list(isl_ast_op_max
, lower
, build
);
967 node
->u
.f
.inc
= for_inc(build
);
970 graft
= set_for_cond_from_list(graft
, upper_list
, build
);
972 graft
= set_for_cond_from_set(graft
, upper_set
, build
);
974 isl_ast_build_free(build
);
976 if (!node
->u
.f
.iterator
|| !node
->u
.f
.init
||
977 !node
->u
.f
.cond
|| !node
->u
.f
.inc
)
978 return isl_ast_graft_free(graft
);
983 /* Update "graft" based on "bounds" and "domain" for the generic,
984 * non-degenerate, case.
986 * "constraints" contains the "n_lower" lower and "n_upper" upper bounds
987 * that the loop node should express.
988 * "domain" is the subset of the intersection of the constraints
989 * for which some code is executed.
991 * There may be zero lower bounds or zero upper bounds in "constraints"
992 * in case the list of constraints was created
993 * based on the atomic option or based on separation with explicit bounds.
994 * In that case, we use "domain" to derive lower and/or upper bounds.
996 * We first compute a list of one or more lower bounds.
998 * Then we decide if we want to express the condition as
1000 * iterator <= min(list of upper bounds)
1002 * or as a conjunction of constraints.
1004 * The set of enforced constraints is then computed either based on
1005 * a list of upper bounds or on a set of upper bound constraints.
1006 * We do not compute any enforced constraints if we were forced
1007 * to compute a lower or upper bound using exact_bound. The domains
1008 * of the resulting expressions may imply some bounds on outer dimensions
1009 * that we do not want to appear in the enforced constraints since
1010 * they are not actually enforced by the corresponding code.
1012 * Finally, we fill in the expressions of the for node.
1014 static __isl_give isl_ast_graft
*refine_generic_bounds(
1015 __isl_take isl_ast_graft
*graft
,
1016 __isl_keep isl_constraint
**constraint
, int n_lower
, int n_upper
,
1017 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1021 isl_pw_aff_list
*lower
;
1023 isl_set
*upper_set
= NULL
;
1024 isl_pw_aff_list
*upper_list
= NULL
;
1026 if (!graft
|| !build
)
1027 return isl_ast_graft_free(graft
);
1029 depth
= isl_ast_build_get_depth(build
);
1030 ctx
= isl_ast_graft_get_ctx(graft
);
1032 use_list
= use_upper_bound_list(ctx
, n_upper
, domain
, depth
);
1034 lower
= lower_bounds(constraint
, n_lower
, depth
, domain
, build
);
1037 upper_list
= upper_bounds(constraint
+ n_lower
, n_upper
, depth
,
1039 else if (n_upper
> 0)
1040 upper_set
= intersect_constraints(ctx
, constraint
+ n_lower
,
1043 upper_set
= isl_set_universe(isl_set_get_space(domain
));
1045 if (n_lower
== 0 || n_upper
== 0)
1048 graft
= set_enforced_from_list(graft
, lower
, upper_list
);
1050 graft
= set_enforced_from_set(graft
, lower
, depth
, upper_set
);
1052 graft
= set_for_node_expressions(graft
, lower
, use_list
, upper_list
,
1055 isl_pw_aff_list_free(lower
);
1056 isl_pw_aff_list_free(upper_list
);
1057 isl_set_free(upper_set
);
1062 /* How many constraints in the "constraint" array, starting at position "first"
1063 * are of the give type? "n" represents the total number of elements
1066 static int count_constraints(isl_constraint
**constraint
, int n
, int first
,
1071 constraint
+= first
;
1073 for (i
= 0; first
+ i
< n
; i
++)
1074 if (constraint_type(constraint
[i
], pos
) != type
)
1080 /* Update "graft" based on "bounds" and "domain" for the generic,
1081 * non-degenerate, case.
1083 * "list" respresent the list of bounds that need to be encoded by
1084 * the for loop (or a guard around the for loop).
1085 * "domain" is the subset of the intersection of the constraints
1086 * for which some code is executed.
1087 * "build" is the build in which graft->node was created.
1089 * We separate lower bounds, upper bounds and constraints that
1090 * are independent of the loop iterator.
1092 * The actual for loop bounds are generated in refine_generic_bounds.
1093 * If there are any constraints that are independent of the loop iterator,
1094 * we need to put a guard around the for loop (which may get hoisted up
1095 * to higher levels) and we call refine_generic_bounds in a build
1096 * where this guard is enforced.
1098 static __isl_give isl_ast_graft
*refine_generic_split(
1099 __isl_take isl_ast_graft
*graft
, __isl_keep isl_constraint_list
*list
,
1100 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1103 isl_ast_build
*for_build
;
1105 int n_indep
, n_lower
, n_upper
;
1110 return isl_ast_graft_free(graft
);
1112 pos
= isl_ast_build_get_depth(build
);
1114 if (isl_sort(list
->p
, list
->n
, sizeof(isl_constraint
*),
1115 &cmp_constraint
, &pos
) < 0)
1116 return isl_ast_graft_free(graft
);
1119 n_indep
= count_constraints(list
->p
, n
, 0, pos
, 0);
1120 n_lower
= count_constraints(list
->p
, n
, n_indep
, pos
, 1);
1121 n_upper
= count_constraints(list
->p
, n
, n_indep
+ n_lower
, pos
, 2);
1124 return refine_generic_bounds(graft
,
1125 list
->p
+ n_indep
, n_lower
, n_upper
, domain
, build
);
1127 ctx
= isl_ast_graft_get_ctx(graft
);
1128 guard
= intersect_constraints(ctx
, list
->p
, n_indep
);
1130 for_build
= isl_ast_build_copy(build
);
1131 for_build
= isl_ast_build_restrict_pending(for_build
,
1132 isl_set_copy(guard
));
1133 graft
= refine_generic_bounds(graft
,
1134 list
->p
+ n_indep
, n_lower
, n_upper
, domain
, for_build
);
1135 isl_ast_build_free(for_build
);
1137 graft
= isl_ast_graft_add_guard(graft
, guard
, build
);
1142 /* Update "graft" based on "bounds" and "domain" for the generic,
1143 * non-degenerate, case.
1145 * "bounds" respresent the bounds that need to be encoded by
1146 * the for loop (or a guard around the for loop).
1147 * "domain" is the subset of "bounds" for which some code is executed.
1148 * "build" is the build in which graft->node was created.
1150 * We break up "bounds" into a list of constraints and continue with
1151 * refine_generic_split.
1153 static __isl_give isl_ast_graft
*refine_generic(
1154 __isl_take isl_ast_graft
*graft
,
1155 __isl_keep isl_basic_set
*bounds
, __isl_keep isl_set
*domain
,
1156 __isl_keep isl_ast_build
*build
)
1158 isl_constraint_list
*list
;
1160 if (!build
|| !graft
)
1161 return isl_ast_graft_free(graft
);
1163 bounds
= isl_basic_set_copy(bounds
);
1164 bounds
= isl_ast_build_compute_gist_basic_set(build
, bounds
);
1165 list
= isl_constraint_list_from_basic_set(bounds
);
1167 graft
= refine_generic_split(graft
, list
, domain
, build
);
1169 isl_constraint_list_free(list
);
1173 /* Create a for node for the current level.
1175 * Mark the for node degenerate if "degenerate" is set.
1177 static __isl_give isl_ast_node
*create_for(__isl_keep isl_ast_build
*build
,
1187 depth
= isl_ast_build_get_depth(build
);
1188 id
= isl_ast_build_get_iterator_id(build
, depth
);
1189 node
= isl_ast_node_alloc_for(id
);
1191 node
= isl_ast_node_for_mark_degenerate(node
);
1196 /* Create an AST node for the current dimension based on
1197 * the schedule domain "bounds" and return the node encapsulated
1198 * in an isl_ast_graft.
1200 * "executed" is the current inverse schedule, taking into account
1201 * the bounds in "bounds"
1202 * "domain" is the domain of "executed", with inner dimensions projected out.
1203 * It may be a strict subset of "bounds" in case "bounds" was created
1204 * based on the atomic option or based on separation with explicit bounds.
1206 * "domain" may satisfy additional equalities that result
1207 * from intersecting "executed" with "bounds" in add_node.
1208 * It may also satisfy some global constraints that were dropped out because
1209 * we performed separation with explicit bounds.
1210 * The very first step is then to copy these constraints to "bounds".
1212 * Since we may be calling before_each_for and after_each_for
1213 * callbacks, we record the current inverse schedule in the build.
1215 * We consider three builds,
1216 * "build" is the one in which the current level is created,
1217 * "body_build" is the build in which the next level is created,
1218 * "sub_build" is essentially the same as "body_build", except that
1219 * the depth has not been increased yet.
1221 * "build" already contains information (in strides and offsets)
1222 * about the strides at the current level, but this information is not
1223 * reflected in the build->domain.
1224 * We first add this information and the "bounds" to the sub_build->domain.
1225 * isl_ast_build_set_loop_bounds checks whether the current dimension attains
1226 * only a single value and whether this single value can be represented using
1227 * a single affine expression.
1228 * In the first case, the current level is considered "degenerate".
1229 * In the second, sub-case, the current level is considered "eliminated".
1230 * Eliminated level don't need to be reflected in the AST since we can
1231 * simply plug in the affine expression. For degenerate, but non-eliminated,
1232 * levels, we do introduce a for node, but mark is as degenerate so that
1233 * it can be printed as an assignment of the single value to the loop
1236 * If the current level is eliminated, we eliminate the current dimension
1237 * from the inverse schedule to make sure no inner dimensions depend
1238 * on the current dimension. Otherwise, we create a for node, marking
1239 * it degenerate if appropriate. The initial for node is still incomplete
1240 * and will be completed in either refine_degenerate or refine_generic.
1242 * We then generate a sequence of grafts for the next level,
1243 * create a surrounding graft for the current level and insert
1244 * the for node we created (if the current level is not eliminated).
1246 * Finally, we set the bounds of the for loop and insert guards
1247 * (either in the AST or in the graft) in one of
1248 * refine_eliminated, refine_degenerate or refine_generic.
1250 static __isl_give isl_ast_graft
*create_node_scaled(
1251 __isl_take isl_union_map
*executed
,
1252 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1253 __isl_take isl_ast_build
*build
)
1256 int degenerate
, eliminated
;
1257 isl_basic_set
*hull
;
1258 isl_ast_node
*node
= NULL
;
1259 isl_ast_graft
*graft
;
1260 isl_ast_graft_list
*children
;
1261 isl_ast_build
*sub_build
;
1262 isl_ast_build
*body_build
;
1264 domain
= isl_ast_build_eliminate_divs(build
, domain
);
1265 domain
= isl_set_detect_equalities(domain
);
1266 hull
= isl_set_unshifted_simple_hull(isl_set_copy(domain
));
1267 bounds
= isl_basic_set_intersect(bounds
, hull
);
1268 build
= isl_ast_build_set_executed(build
, isl_union_map_copy(executed
));
1270 depth
= isl_ast_build_get_depth(build
);
1271 sub_build
= isl_ast_build_copy(build
);
1272 sub_build
= isl_ast_build_include_stride(sub_build
);
1273 sub_build
= isl_ast_build_set_loop_bounds(sub_build
,
1274 isl_basic_set_copy(bounds
));
1275 degenerate
= isl_ast_build_has_value(sub_build
);
1276 eliminated
= isl_ast_build_has_affine_value(sub_build
, depth
);
1277 if (degenerate
< 0 || eliminated
< 0)
1278 executed
= isl_union_map_free(executed
);
1280 executed
= eliminate(executed
, depth
, build
);
1282 node
= create_for(build
, degenerate
);
1284 body_build
= isl_ast_build_copy(sub_build
);
1285 body_build
= isl_ast_build_increase_depth(body_build
);
1287 node
= before_each_for(node
, body_build
);
1288 children
= generate_next_level(executed
,
1289 isl_ast_build_copy(body_build
));
1291 graft
= isl_ast_graft_alloc_level(children
, sub_build
);
1293 graft
= isl_ast_graft_insert_for(graft
, node
);
1295 graft
= refine_eliminated(graft
, bounds
, build
);
1296 else if (degenerate
)
1297 graft
= refine_degenerate(graft
, bounds
, build
, sub_build
);
1299 graft
= refine_generic(graft
, bounds
, domain
, build
);
1301 graft
= after_each_for(graft
, body_build
);
1303 isl_ast_build_free(body_build
);
1304 isl_ast_build_free(sub_build
);
1305 isl_ast_build_free(build
);
1306 isl_basic_set_free(bounds
);
1307 isl_set_free(domain
);
1312 /* Internal data structure for checking if all constraints involving
1313 * the input dimension "depth" are such that the other coefficients
1314 * are multiples of "m", reducing "m" if they are not.
1315 * If "m" is reduced all the way down to "1", then the check has failed
1316 * and we break out of the iteration.
1317 * "d" is an initialized isl_int that can be used internally.
1319 struct isl_check_scaled_data
{
1324 /* If constraint "c" involves the input dimension data->depth,
1325 * then make sure that all the other coefficients are multiples of data->m,
1326 * reducing data->m if needed.
1327 * Break out of the iteration if data->m has become equal to "1".
1329 static int constraint_check_scaled(__isl_take isl_constraint
*c
, void *user
)
1331 struct isl_check_scaled_data
*data
= user
;
1333 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_out
,
1336 if (!isl_constraint_involves_dims(c
, isl_dim_in
, data
->depth
, 1)) {
1337 isl_constraint_free(c
);
1341 for (i
= 0; i
< 4; ++i
) {
1342 n
= isl_constraint_dim(c
, t
[i
]);
1343 for (j
= 0; j
< n
; ++j
) {
1344 if (t
[i
] == isl_dim_in
&& j
== data
->depth
)
1346 if (!isl_constraint_involves_dims(c
, t
[i
], j
, 1))
1348 isl_constraint_get_coefficient(c
, t
[i
], j
, &data
->d
);
1349 isl_int_gcd(data
->m
, data
->m
, data
->d
);
1350 if (isl_int_is_one(data
->m
))
1357 isl_constraint_free(c
);
1359 return i
< 4 ? -1 : 0;
1362 /* For each constraint of "bmap" that involves the input dimension data->depth,
1363 * make sure that all the other coefficients are multiples of data->m,
1364 * reducing data->m if needed.
1365 * Break out of the iteration if data->m has become equal to "1".
1367 static int basic_map_check_scaled(__isl_take isl_basic_map
*bmap
, void *user
)
1371 r
= isl_basic_map_foreach_constraint(bmap
,
1372 &constraint_check_scaled
, user
);
1373 isl_basic_map_free(bmap
);
1378 /* For each constraint of "map" that involves the input dimension data->depth,
1379 * make sure that all the other coefficients are multiples of data->m,
1380 * reducing data->m if needed.
1381 * Break out of the iteration if data->m has become equal to "1".
1383 static int map_check_scaled(__isl_take isl_map
*map
, void *user
)
1387 r
= isl_map_foreach_basic_map(map
, &basic_map_check_scaled
, user
);
1393 /* Create an AST node for the current dimension based on
1394 * the schedule domain "bounds" and return the node encapsulated
1395 * in an isl_ast_graft.
1397 * "executed" is the current inverse schedule, taking into account
1398 * the bounds in "bounds"
1399 * "domain" is the domain of "executed", with inner dimensions projected out.
1402 * Before moving on to the actual AST node construction in create_node_scaled,
1403 * we first check if the current dimension is strided and if we can scale
1404 * down this stride. Note that we only do this if the ast_build_scale_strides
1407 * In particular, let the current dimension take on values
1411 * with a an integer. We check if we can find an integer m that (obviouly)
1412 * divides both f and s.
1414 * If so, we check if the current dimension only appears in constraints
1415 * where the coefficients of the other variables are multiples of m.
1416 * We perform this extra check to avoid the risk of introducing
1417 * divisions by scaling down the current dimension.
1419 * If so, we scale the current dimension down by a factor of m.
1420 * That is, we plug in
1424 * Note that in principle we could always scale down strided loops
1429 * but this may result in i' taking on larger values than the original i,
1430 * due to the shift by "f".
1431 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1433 static __isl_give isl_ast_graft
*create_node(__isl_take isl_union_map
*executed
,
1434 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1435 __isl_take isl_ast_build
*build
)
1437 struct isl_check_scaled_data data
;
1441 ctx
= isl_ast_build_get_ctx(build
);
1442 if (!isl_options_get_ast_build_scale_strides(ctx
))
1443 return create_node_scaled(executed
, bounds
, domain
, build
);
1445 data
.depth
= isl_ast_build_get_depth(build
);
1446 if (!isl_ast_build_has_stride(build
, data
.depth
))
1447 return create_node_scaled(executed
, bounds
, domain
, build
);
1449 isl_int_init(data
.m
);
1450 isl_int_init(data
.d
);
1452 offset
= isl_ast_build_get_offset(build
, data
.depth
);
1453 if (isl_ast_build_get_stride(build
, data
.depth
, &data
.m
) < 0)
1454 offset
= isl_aff_free(offset
);
1455 offset
= isl_aff_scale_down(offset
, data
.m
);
1456 if (isl_aff_get_denominator(offset
, &data
.d
) < 0)
1457 executed
= isl_union_map_free(executed
);
1459 if (isl_int_is_divisible_by(data
.m
, data
.d
))
1460 isl_int_divexact(data
.m
, data
.m
, data
.d
);
1462 isl_int_set_si(data
.m
, 1);
1464 if (!isl_int_is_one(data
.m
)) {
1465 if (isl_union_map_foreach_map(executed
, &map_check_scaled
,
1467 !isl_int_is_one(data
.m
))
1468 executed
= isl_union_map_free(executed
);
1471 if (!isl_int_is_one(data
.m
)) {
1476 isl_union_map
*umap
;
1478 space
= isl_ast_build_get_space(build
, 1);
1479 space
= isl_space_map_from_set(space
);
1480 ma
= isl_multi_aff_identity(space
);
1481 aff
= isl_multi_aff_get_aff(ma
, data
.depth
);
1482 aff
= isl_aff_scale(aff
, data
.m
);
1483 ma
= isl_multi_aff_set_aff(ma
, data
.depth
, aff
);
1485 bounds
= isl_basic_set_preimage_multi_aff(bounds
,
1486 isl_multi_aff_copy(ma
));
1487 domain
= isl_set_preimage_multi_aff(domain
,
1488 isl_multi_aff_copy(ma
));
1489 map
= isl_map_reverse(isl_map_from_multi_aff(ma
));
1490 umap
= isl_union_map_from_map(map
);
1491 executed
= isl_union_map_apply_domain(executed
,
1492 isl_union_map_copy(umap
));
1493 build
= isl_ast_build_scale_down(build
, data
.m
, umap
);
1495 isl_aff_free(offset
);
1497 isl_int_clear(data
.d
);
1498 isl_int_clear(data
.m
);
1500 return create_node_scaled(executed
, bounds
, domain
, build
);
1503 /* Add the basic set to the list that "user" points to.
1505 static int collect_basic_set(__isl_take isl_basic_set
*bset
, void *user
)
1507 isl_basic_set_list
**list
= user
;
1509 *list
= isl_basic_set_list_add(*list
, bset
);
1514 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1516 static __isl_give isl_basic_set_list
*isl_basic_set_list_from_set(
1517 __isl_take isl_set
*set
)
1521 isl_basic_set_list
*list
;
1526 ctx
= isl_set_get_ctx(set
);
1528 n
= isl_set_n_basic_set(set
);
1529 list
= isl_basic_set_list_alloc(ctx
, n
);
1530 if (isl_set_foreach_basic_set(set
, &collect_basic_set
, &list
) < 0)
1531 list
= isl_basic_set_list_free(list
);
1537 /* Generate code for the schedule domain "bounds"
1538 * and add the result to "list".
1540 * We mainly detect strides and additional equalities here
1541 * and then pass over control to create_node.
1543 * "bounds" reflects the bounds on the current dimension and possibly
1544 * some extra conditions on outer dimensions.
1545 * It does not, however, include any divs involving the current dimension,
1546 * so it does not capture any stride constraints.
1547 * We therefore need to compute that part of the schedule domain that
1548 * intersects with "bounds" and derive the strides from the result.
1550 static __isl_give isl_ast_graft_list
*add_node(
1551 __isl_take isl_ast_graft_list
*list
, __isl_take isl_union_map
*executed
,
1552 __isl_take isl_basic_set
*bounds
, __isl_take isl_ast_build
*build
)
1554 isl_ast_graft
*graft
;
1555 isl_set
*domain
= NULL
;
1556 isl_union_set
*uset
;
1559 uset
= isl_union_set_from_basic_set(isl_basic_set_copy(bounds
));
1560 executed
= isl_union_map_intersect_domain(executed
, uset
);
1561 empty
= isl_union_map_is_empty(executed
);
1567 uset
= isl_union_map_domain(isl_union_map_copy(executed
));
1568 domain
= isl_set_from_union_set(uset
);
1569 domain
= isl_ast_build_compute_gist(build
, domain
);
1570 empty
= isl_set_is_empty(domain
);
1576 domain
= isl_ast_build_eliminate_inner(build
, domain
);
1577 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
1579 graft
= create_node(executed
, bounds
, domain
,
1580 isl_ast_build_copy(build
));
1581 list
= isl_ast_graft_list_add(list
, graft
);
1582 isl_ast_build_free(build
);
1585 list
= isl_ast_graft_list_free(list
);
1587 isl_set_free(domain
);
1588 isl_basic_set_free(bounds
);
1589 isl_union_map_free(executed
);
1590 isl_ast_build_free(build
);
1594 struct isl_domain_follows_at_depth_data
{
1596 isl_basic_set
**piece
;
1599 /* Does any element of i follow or coincide with any element of j
1600 * at the current depth (data->depth) for equal values of the outer
1603 static int domain_follows_at_depth(int i
, int j
, void *user
)
1605 struct isl_domain_follows_at_depth_data
*data
= user
;
1606 isl_basic_map
*test
;
1610 test
= isl_basic_map_from_domain_and_range(
1611 isl_basic_set_copy(data
->piece
[i
]),
1612 isl_basic_set_copy(data
->piece
[j
]));
1613 for (l
= 0; l
< data
->depth
; ++l
)
1614 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1616 test
= isl_basic_map_order_ge(test
, isl_dim_in
, data
->depth
,
1617 isl_dim_out
, data
->depth
);
1618 empty
= isl_basic_map_is_empty(test
);
1619 isl_basic_map_free(test
);
1621 return empty
< 0 ? -1 : !empty
;
1624 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1625 __isl_keep isl_basic_set_list
*domain_list
,
1626 __isl_keep isl_union_map
*executed
,
1627 __isl_keep isl_ast_build
*build
);
1629 /* Generate code for the "n" schedule domains in "domain_list"
1630 * with positions specified by the entries of the "pos" array
1631 * and add the results to "list".
1633 * The "n" domains form a strongly connected component in the ordering.
1634 * If n is larger than 1, then this means that we cannot determine a valid
1635 * ordering for the n domains in the component. This should be fairly
1636 * rare because the individual domains have been made disjoint first.
1637 * The problem is that the domains may be integrally disjoint but not
1638 * rationally disjoint. For example, we may have domains
1640 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1642 * These two domains have an empty intersection, but their rational
1643 * relaxations do intersect. It is impossible to order these domains
1644 * in the second dimension because the first should be ordered before
1645 * the second for outer dimension equal to 0, while it should be ordered
1646 * after for outer dimension equal to 1.
1648 * This may happen in particular in case of unrolling since the domain
1649 * of each slice is replaced by its simple hull.
1651 * We collect the basic sets in the component, call isl_set_make_disjoint
1652 * and try again. Note that we rely here on isl_set_make_disjoint also
1653 * making the basic sets rationally disjoint. If the basic sets
1654 * are rationally disjoint, then the ordering problem does not occur.
1655 * To see this, there can only be a problem if there are points
1656 * (i,a) and (j,b) in one set and (i,c) and (j,d) in the other with
1657 * a < c and b > d. This means that either the interval spanned
1658 * by a en b lies inside that spanned by c and or the other way around.
1659 * In either case, there is a point inside both intervals with the
1660 * convex combination in terms of a and b and in terms of c and d.
1661 * Taking the same combination of i and j gives a point in the intersection.
1663 static __isl_give isl_ast_graft_list
*add_nodes(
1664 __isl_take isl_ast_graft_list
*list
, int *pos
, int n
,
1665 __isl_keep isl_basic_set_list
*domain_list
,
1666 __isl_keep isl_union_map
*executed
,
1667 __isl_keep isl_ast_build
*build
)
1670 isl_basic_set
*bset
;
1673 bset
= isl_basic_set_list_get_basic_set(domain_list
, pos
[0]);
1675 return add_node(list
, isl_union_map_copy(executed
), bset
,
1676 isl_ast_build_copy(build
));
1678 set
= isl_set_from_basic_set(bset
);
1679 for (i
= 1; i
< n
; ++i
) {
1680 bset
= isl_basic_set_list_get_basic_set(domain_list
, pos
[i
]);
1681 set
= isl_set_union(set
, isl_set_from_basic_set(bset
));
1684 set
= isl_set_make_disjoint(set
);
1685 if (isl_set_n_basic_set(set
) == n
)
1686 isl_die(isl_ast_graft_list_get_ctx(list
), isl_error_internal
,
1687 "unable to separate loop parts", goto error
);
1688 domain_list
= isl_basic_set_list_from_set(set
);
1689 list
= isl_ast_graft_list_concat(list
,
1690 generate_sorted_domains(domain_list
, executed
, build
));
1691 isl_basic_set_list_free(domain_list
);
1696 return isl_ast_graft_list_free(list
);
1699 /* Sort the domains in "domain_list" according to the execution order
1700 * at the current depth (for equal values of the outer dimensions),
1701 * generate code for each of them, collecting the results in a list.
1702 * If no code is generated (because the intersection of the inverse schedule
1703 * with the domains turns out to be empty), then an empty list is returned.
1705 * The caller is responsible for ensuring that the basic sets in "domain_list"
1706 * are pair-wise disjoint. It can, however, in principle happen that
1707 * two basic sets should be ordered one way for one value of the outer
1708 * dimensions and the other way for some other value of the outer dimensions.
1709 * We therefore play safe and look for strongly connected components.
1710 * The function add_nodes takes care of handling non-trivial components.
1712 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1713 __isl_keep isl_basic_set_list
*domain_list
,
1714 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1717 isl_ast_graft_list
*list
;
1718 struct isl_domain_follows_at_depth_data data
;
1719 struct isl_tarjan_graph
*g
;
1725 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1726 n
= isl_basic_set_list_n_basic_set(domain_list
);
1727 list
= isl_ast_graft_list_alloc(ctx
, n
);
1731 return add_node(list
, isl_union_map_copy(executed
),
1732 isl_basic_set_list_get_basic_set(domain_list
, 0),
1733 isl_ast_build_copy(build
));
1735 data
.depth
= isl_ast_build_get_depth(build
);
1736 data
.piece
= domain_list
->p
;
1737 g
= isl_tarjan_graph_init(ctx
, n
, &domain_follows_at_depth
, &data
);
1743 if (g
->order
[i
] == -1)
1744 isl_die(ctx
, isl_error_internal
, "cannot happen",
1747 while (g
->order
[i
] != -1) {
1750 list
= add_nodes(list
, g
->order
+ first
, i
- first
,
1751 domain_list
, executed
, build
);
1756 error
: list
= isl_ast_graft_list_free(list
);
1757 isl_tarjan_graph_free(g
);
1762 struct isl_shared_outer_data
{
1764 isl_basic_set
**piece
;
1767 /* Do elements i and j share any values for the outer dimensions?
1769 static int shared_outer(int i
, int j
, void *user
)
1771 struct isl_shared_outer_data
*data
= user
;
1772 isl_basic_map
*test
;
1776 test
= isl_basic_map_from_domain_and_range(
1777 isl_basic_set_copy(data
->piece
[i
]),
1778 isl_basic_set_copy(data
->piece
[j
]));
1779 for (l
= 0; l
< data
->depth
; ++l
)
1780 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1782 empty
= isl_basic_map_is_empty(test
);
1783 isl_basic_map_free(test
);
1785 return empty
< 0 ? -1 : !empty
;
1788 /* Call generate_sorted_domains on a list containing the elements
1789 * of "domain_list indexed by the first "n" elements of "pos".
1791 static __isl_give isl_ast_graft_list
*generate_sorted_domains_part(
1792 __isl_keep isl_basic_set_list
*domain_list
, int *pos
, int n
,
1793 __isl_keep isl_union_map
*executed
,
1794 __isl_keep isl_ast_build
*build
)
1798 isl_basic_set_list
*slice
;
1799 isl_ast_graft_list
*list
;
1801 ctx
= isl_ast_build_get_ctx(build
);
1802 slice
= isl_basic_set_list_alloc(ctx
, n
);
1803 for (i
= 0; i
< n
; ++i
) {
1804 isl_basic_set
*bset
;
1806 bset
= isl_basic_set_copy(domain_list
->p
[pos
[i
]]);
1807 slice
= isl_basic_set_list_add(slice
, bset
);
1810 list
= generate_sorted_domains(slice
, executed
, build
);
1811 isl_basic_set_list_free(slice
);
1816 /* Look for any (weakly connected) components in the "domain_list"
1817 * of domains that share some values of the outer dimensions.
1818 * That is, domains in different components do not share any values
1819 * of the outer dimensions. This means that these components
1820 * can be freely reorderd.
1821 * Within each of the components, we sort the domains according
1822 * to the execution order at the current depth.
1824 * We fuse the result of each call to generate_sorted_domains_part
1825 * into a list with either zero or one graft and collect these (at most)
1826 * single element lists into a bigger list. This means that the elements of the
1827 * final list can be freely reordered. In particular, we sort them
1828 * according to an arbitrary but fixed ordering to ease merging of
1829 * graft lists from different components.
1831 static __isl_give isl_ast_graft_list
*generate_parallel_domains(
1832 __isl_keep isl_basic_set_list
*domain_list
,
1833 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1837 isl_ast_graft_list
*list
;
1838 struct isl_shared_outer_data data
;
1839 struct isl_tarjan_graph
*g
;
1844 n
= isl_basic_set_list_n_basic_set(domain_list
);
1846 return generate_sorted_domains(domain_list
, executed
, build
);
1848 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1850 data
.depth
= isl_ast_build_get_depth(build
);
1851 data
.piece
= domain_list
->p
;
1852 g
= isl_tarjan_graph_init(ctx
, n
, &shared_outer
, &data
);
1859 isl_ast_graft_list
*list_c
;
1861 if (g
->order
[i
] == -1)
1862 isl_die(ctx
, isl_error_internal
, "cannot happen",
1865 while (g
->order
[i
] != -1) {
1868 if (first
== 0 && n
== 0) {
1869 isl_tarjan_graph_free(g
);
1870 return generate_sorted_domains(domain_list
,
1873 list_c
= generate_sorted_domains_part(domain_list
,
1874 g
->order
+ first
, i
- first
, executed
, build
);
1875 list_c
= isl_ast_graft_list_fuse(list_c
, build
);
1879 list
= isl_ast_graft_list_concat(list
, list_c
);
1881 } while (list
&& n
);
1884 list
= isl_ast_graft_list_free(list
);
1886 list
= isl_ast_graft_list_sort(list
);
1888 isl_tarjan_graph_free(g
);
1893 /* Internal data for separate_domain.
1895 * "explicit" is set if we only want to use explicit bounds.
1897 * "domain" collects the separated domains.
1899 struct isl_separate_domain_data
{
1900 isl_ast_build
*build
;
1905 /* Extract implicit bounds on the current dimension for the executed "map".
1907 * The domain of "map" may involve inner dimensions, so we
1908 * need to eliminate them.
1910 static __isl_give isl_set
*implicit_bounds(__isl_take isl_map
*map
,
1911 __isl_keep isl_ast_build
*build
)
1915 domain
= isl_map_domain(map
);
1916 domain
= isl_ast_build_eliminate(build
, domain
);
1921 /* Extract explicit bounds on the current dimension for the executed "map".
1923 * Rather than eliminating the inner dimensions as in implicit_bounds,
1924 * we simply drop any constraints involving those inner dimensions.
1925 * The idea is that most bounds that are implied by constraints on the
1926 * inner dimensions will be enforced by for loops and not by explicit guards.
1927 * There is then no need to separate along those bounds.
1929 static __isl_give isl_set
*explicit_bounds(__isl_take isl_map
*map
,
1930 __isl_keep isl_ast_build
*build
)
1935 dim
= isl_map_dim(map
, isl_dim_out
);
1936 map
= isl_map_drop_constraints_involving_dims(map
, isl_dim_out
, 0, dim
);
1938 domain
= isl_map_domain(map
);
1939 depth
= isl_ast_build_get_depth(build
);
1940 dim
= isl_set_dim(domain
, isl_dim_set
);
1941 domain
= isl_set_detect_equalities(domain
);
1942 domain
= isl_set_drop_constraints_involving_dims(domain
,
1943 isl_dim_set
, depth
+ 1, dim
- (depth
+ 1));
1944 domain
= isl_set_remove_divs_involving_dims(domain
,
1945 isl_dim_set
, depth
, 1);
1946 domain
= isl_set_remove_unknown_divs(domain
);
1951 /* Split data->domain into pieces that intersect with the range of "map"
1952 * and pieces that do not intersect with the range of "map"
1953 * and then add that part of the range of "map" that does not intersect
1954 * with data->domain.
1956 static int separate_domain(__isl_take isl_map
*map
, void *user
)
1958 struct isl_separate_domain_data
*data
= user
;
1963 domain
= explicit_bounds(map
, data
->build
);
1965 domain
= implicit_bounds(map
, data
->build
);
1967 domain
= isl_set_coalesce(domain
);
1968 domain
= isl_set_make_disjoint(domain
);
1969 d1
= isl_set_subtract(isl_set_copy(domain
), isl_set_copy(data
->domain
));
1970 d2
= isl_set_subtract(isl_set_copy(data
->domain
), isl_set_copy(domain
));
1971 data
->domain
= isl_set_intersect(data
->domain
, domain
);
1972 data
->domain
= isl_set_union(data
->domain
, d1
);
1973 data
->domain
= isl_set_union(data
->domain
, d2
);
1978 /* Separate the schedule domains of "executed".
1980 * That is, break up the domain of "executed" into basic sets,
1981 * such that for each basic set S, every element in S is associated with
1982 * the same domain spaces.
1984 * "space" is the (single) domain space of "executed".
1986 static __isl_give isl_set
*separate_schedule_domains(
1987 __isl_take isl_space
*space
, __isl_take isl_union_map
*executed
,
1988 __isl_keep isl_ast_build
*build
)
1990 struct isl_separate_domain_data data
= { build
};
1993 ctx
= isl_ast_build_get_ctx(build
);
1994 data
.explicit = isl_options_get_ast_build_separation_bounds(ctx
) ==
1995 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
;
1996 data
.domain
= isl_set_empty(space
);
1997 if (isl_union_map_foreach_map(executed
, &separate_domain
, &data
) < 0)
1998 data
.domain
= isl_set_free(data
.domain
);
2000 isl_union_map_free(executed
);
2004 /* Temporary data used during the search for a lower bound for unrolling.
2006 * "domain" is the original set for which to find a lower bound
2007 * "depth" is the dimension for which to find a lower boudn
2009 * "lower" is the best lower bound found so far. It is NULL if we have not
2011 * "n" is the corresponding size. If lower is NULL, then the value of n
2014 * "tmp" is a temporary initialized isl_int.
2016 struct isl_find_unroll_data
{
2025 /* Check if we can use "c" as a lower bound and if it is better than
2026 * any previously found lower bound.
2028 * If "c" does not involve the dimension at the current depth,
2029 * then we cannot use it.
2030 * Otherwise, let "c" be of the form
2034 * We compute the maximal value of
2036 * -ceil(f(j)/a)) + i + 1
2038 * over the domain. If there is such a value "n", then we know
2040 * -ceil(f(j)/a)) + i + 1 <= n
2044 * i < ceil(f(j)/a)) + n
2046 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2047 * We just need to check if we have found any lower bound before and
2048 * if the new lower bound is better (smaller n) than the previously found
2051 static int update_unrolling_lower_bound(struct isl_find_unroll_data
*data
,
2052 __isl_keep isl_constraint
*c
)
2054 isl_aff
*aff
, *lower
;
2055 enum isl_lp_result res
;
2057 if (!isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->depth
))
2060 lower
= isl_constraint_get_bound(c
, isl_dim_set
, data
->depth
);
2061 lower
= isl_aff_ceil(lower
);
2062 aff
= isl_aff_copy(lower
);
2063 aff
= isl_aff_neg(aff
);
2064 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, data
->depth
, 1);
2065 aff
= isl_aff_add_constant_si(aff
, 1);
2066 res
= isl_set_max(data
->domain
, aff
, &data
->tmp
);
2069 if (res
== isl_lp_error
)
2071 if (res
== isl_lp_unbounded
) {
2072 isl_aff_free(lower
);
2076 if (!data
->lower
|| isl_int_cmp_si(data
->tmp
, *data
->n
) < 0) {
2077 isl_aff_free(data
->lower
);
2078 data
->lower
= lower
;
2079 *data
->n
= isl_int_get_si(data
->tmp
);
2081 isl_aff_free(lower
);
2085 isl_aff_free(lower
);
2089 /* Check if we can use "c" as a lower bound and if it is better than
2090 * any previously found lower bound.
2092 static int constraint_find_unroll(__isl_take isl_constraint
*c
, void *user
)
2094 struct isl_find_unroll_data
*data
;
2097 data
= (struct isl_find_unroll_data
*) user
;
2098 r
= update_unrolling_lower_bound(data
, c
);
2099 isl_constraint_free(c
);
2104 /* Look for a lower bound l(i) on the dimension at "depth"
2105 * and a size n such that "domain" is a subset of
2107 * { [i] : l(i) <= i_d < l(i) + n }
2109 * where d is "depth" and l(i) depends only on earlier dimensions.
2110 * Furthermore, try and find a lower bound such that n is as small as possible.
2111 * In particular, "n" needs to be finite.
2113 * Inner dimensions have been eliminated from "domain" by the caller.
2115 * We first construct a collection of lower bounds on the input set
2116 * by computing its simple hull. We then iterate through them,
2117 * discarding those that we cannot use (either because they do not
2118 * involve the dimension at "depth" or because they have no corresponding
2119 * upper bound, meaning that "n" would be unbounded) and pick out the
2120 * best from the remaining ones.
2122 * If we cannot find a suitable lower bound, then we consider that
2125 static __isl_give isl_aff
*find_unroll_lower_bound(__isl_keep isl_set
*domain
,
2128 struct isl_find_unroll_data data
= { domain
, depth
, NULL
, n
};
2129 isl_basic_set
*hull
;
2131 isl_int_init(data
.tmp
);
2132 hull
= isl_set_simple_hull(isl_set_copy(domain
));
2134 if (isl_basic_set_foreach_constraint(hull
,
2135 &constraint_find_unroll
, &data
) < 0)
2138 isl_basic_set_free(hull
);
2139 isl_int_clear(data
.tmp
);
2142 isl_die(isl_set_get_ctx(domain
), isl_error_invalid
,
2143 "cannot find lower bound for unrolling", return NULL
);
2147 isl_basic_set_free(hull
);
2148 isl_int_clear(data
.tmp
);
2149 return isl_aff_free(data
.lower
);
2152 /* Intersect "set" with the constraint
2154 * i_"depth" = aff + offset
2156 static __isl_give isl_set
*at_offset(__isl_take isl_set
*set
, int depth
,
2157 __isl_keep isl_aff
*aff
, int offset
)
2161 aff
= isl_aff_copy(aff
);
2162 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, depth
, -1);
2163 aff
= isl_aff_add_constant_si(aff
, offset
);
2164 eq
= isl_equality_from_aff(aff
);
2165 set
= isl_set_add_constraint(set
, eq
);
2170 /* Return a list of basic sets, one for each value of the current dimension
2172 * The divs that involve the current dimension have not been projected out
2175 * Since we are going to be iterating over the individual values,
2176 * we first check if there are any strides on the current dimension.
2177 * If there is, we rewrite the current dimension i as
2179 * i = stride i' + offset
2181 * and then iterate over individual values of i' instead.
2183 * We then look for a lower bound on i' and a size such that the domain
2186 * { [j,i'] : l(j) <= i' < l(j) + n }
2188 * and then take slices of the domain at values of i'
2189 * between l(j) and l(j) + n - 1.
2191 * We compute the unshifted simple hull of each slice to ensure that
2192 * we have a single basic set per offset. The slicing constraint
2193 * is preserved by taking the unshifted simple hull, so these basic sets
2194 * remain disjoint. The constraints that are dropped by taking the hull
2195 * will be taken into account at the next level, as in the case of the
2198 * Finally, we map i' back to i and add each basic set to the list.
2200 static __isl_give isl_basic_set_list
*do_unroll(__isl_take isl_set
*domain
,
2201 __isl_keep isl_ast_build
*build
)
2207 isl_basic_set_list
*list
;
2208 isl_multi_aff
*expansion
;
2209 isl_basic_map
*bmap
;
2214 ctx
= isl_set_get_ctx(domain
);
2215 depth
= isl_ast_build_get_depth(build
);
2216 build
= isl_ast_build_copy(build
);
2217 domain
= isl_ast_build_eliminate_inner(build
, domain
);
2218 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
2219 expansion
= isl_ast_build_get_stride_expansion(build
);
2221 domain
= isl_set_preimage_multi_aff(domain
,
2222 isl_multi_aff_copy(expansion
));
2223 domain
= isl_ast_build_eliminate_divs(build
, domain
);
2225 isl_ast_build_free(build
);
2227 list
= isl_basic_set_list_alloc(ctx
, 0);
2229 lower
= find_unroll_lower_bound(domain
, depth
, &n
);
2231 list
= isl_basic_set_list_free(list
);
2233 bmap
= isl_basic_map_from_multi_aff(expansion
);
2235 for (i
= 0; list
&& i
< n
; ++i
) {
2237 isl_basic_set
*bset
;
2239 set
= at_offset(isl_set_copy(domain
), depth
, lower
, i
);
2240 bset
= isl_set_unshifted_simple_hull(set
);
2241 bset
= isl_basic_set_apply(bset
, isl_basic_map_copy(bmap
));
2242 list
= isl_basic_set_list_add(list
, bset
);
2245 isl_aff_free(lower
);
2246 isl_set_free(domain
);
2247 isl_basic_map_free(bmap
);
2252 /* Data structure for storing the results and the intermediate objects
2253 * of compute_domains.
2255 * "list" is the main result of the function and contains a list
2256 * of disjoint basic sets for which code should be generated.
2258 * "executed" and "build" are inputs to compute_domains.
2259 * "schedule_domain" is the domain of "executed".
2261 * "option" constains the domains at the current depth that should by
2262 * atomic, separated or unrolled. These domains are as specified by
2263 * the user, except that inner dimensions have been eliminated and
2264 * that they have been made pair-wise disjoint.
2266 * "sep_class" contains the user-specified split into separation classes
2267 * specialized to the current depth.
2268 * "done" contains the union of th separation domains that have already
2271 struct isl_codegen_domains
{
2272 isl_basic_set_list
*list
;
2274 isl_union_map
*executed
;
2275 isl_ast_build
*build
;
2276 isl_set
*schedule_domain
;
2284 /* Add domains to domains->list for each individual value of the current
2285 * dimension, for that part of the schedule domain that lies in the
2286 * intersection of the option domain and the class domain.
2288 * "domain" is the intersection of the class domain and the schedule domain.
2289 * The divs that involve the current dimension have not been projected out
2292 * We first break up the unroll option domain into individual pieces
2293 * and then handle each of them separately. The unroll option domain
2294 * has been made disjoint in compute_domains_init_options,
2296 * Note that we actively want to combine different pieces of the
2297 * schedule domain that have the same value at the current dimension.
2298 * We therefore need to break up the unroll option domain before
2299 * intersecting with class and schedule domain, hoping that the
2300 * unroll option domain specified by the user is relatively simple.
2302 static int compute_unroll_domains(struct isl_codegen_domains
*domains
,
2303 __isl_keep isl_set
*domain
)
2305 isl_set
*unroll_domain
;
2306 isl_basic_set_list
*unroll_list
;
2310 empty
= isl_set_is_empty(domains
->option
[unroll
]);
2316 unroll_domain
= isl_set_copy(domains
->option
[unroll
]);
2317 unroll_list
= isl_basic_set_list_from_set(unroll_domain
);
2319 n
= isl_basic_set_list_n_basic_set(unroll_list
);
2320 for (i
= 0; i
< n
; ++i
) {
2321 isl_basic_set
*bset
;
2322 isl_basic_set_list
*list
;
2324 bset
= isl_basic_set_list_get_basic_set(unroll_list
, i
);
2325 unroll_domain
= isl_set_from_basic_set(bset
);
2326 unroll_domain
= isl_set_intersect(unroll_domain
,
2327 isl_set_copy(domain
));
2329 empty
= isl_set_is_empty(unroll_domain
);
2330 if (empty
>= 0 && empty
) {
2331 isl_set_free(unroll_domain
);
2335 list
= do_unroll(unroll_domain
, domains
->build
);
2336 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2339 isl_basic_set_list_free(unroll_list
);
2344 /* Construct a single basic set that includes the intersection of
2345 * the schedule domain, the atomic option domain and the class domain.
2346 * Add the resulting basic set to domains->list.
2348 * We construct a single domain rather than trying to combine
2349 * the schedule domains of individual domains because we are working
2350 * within a single component so that non-overlapping schedule domains
2351 * should already have been separated.
2352 * Note, though, that this does not take into account the class domain.
2353 * So, it is possible for a class domain to carve out a piece of the
2354 * schedule domain with independent pieces and then we would only
2355 * generate a single domain for them. If this proves to be problematic
2356 * for some users, then this function will have to be adjusted.
2358 * "domain" is the intersection of the schedule domain and the class domain,
2359 * with inner dimensions projected out.
2361 static int compute_atomic_domain(struct isl_codegen_domains
*domains
,
2362 __isl_keep isl_set
*domain
)
2364 isl_basic_set
*bset
;
2365 isl_set
*atomic_domain
;
2368 atomic_domain
= isl_set_copy(domains
->option
[atomic
]);
2369 atomic_domain
= isl_set_intersect(atomic_domain
, isl_set_copy(domain
));
2370 empty
= isl_set_is_empty(atomic_domain
);
2371 if (empty
< 0 || empty
) {
2372 isl_set_free(atomic_domain
);
2373 return empty
< 0 ? -1 : 0;
2376 atomic_domain
= isl_set_coalesce(atomic_domain
);
2377 bset
= isl_set_unshifted_simple_hull(atomic_domain
);
2378 domains
->list
= isl_basic_set_list_add(domains
->list
, bset
);
2383 /* Split up the schedule domain into uniform basic sets,
2384 * in the sense that each element in a basic set is associated to
2385 * elements of the same domains, and add the result to domains->list.
2386 * Do this for that part of the schedule domain that lies in the
2387 * intersection of "class_domain" and the separate option domain.
2389 * "class_domain" may or may not include the constraints
2390 * of the schedule domain, but this does not make a difference
2391 * since we are going to intersect it with the domain of the inverse schedule.
2392 * If it includes schedule domain constraints, then they may involve
2393 * inner dimensions, but we will eliminate them in separation_domain.
2395 static int compute_separate_domain(struct isl_codegen_domains
*domains
,
2396 __isl_keep isl_set
*class_domain
)
2400 isl_union_map
*executed
;
2401 isl_basic_set_list
*list
;
2404 domain
= isl_set_copy(domains
->option
[separate
]);
2405 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2406 executed
= isl_union_map_copy(domains
->executed
);
2407 executed
= isl_union_map_intersect_domain(executed
,
2408 isl_union_set_from_set(domain
));
2409 empty
= isl_union_map_is_empty(executed
);
2410 if (empty
< 0 || empty
) {
2411 isl_union_map_free(executed
);
2412 return empty
< 0 ? -1 : 0;
2415 space
= isl_set_get_space(class_domain
);
2416 domain
= separate_schedule_domains(space
, executed
, domains
->build
);
2418 list
= isl_basic_set_list_from_set(domain
);
2419 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2424 /* Split up the domain at the current depth into disjoint
2425 * basic sets for which code should be generated separately
2426 * for the given separation class domain.
2428 * If any separation classes have been defined, then "class_domain"
2429 * is the domain of the current class and does not refer to inner dimensions.
2430 * Otherwise, "class_domain" is the universe domain.
2432 * We first make sure that the class domain is disjoint from
2433 * previously considered class domains.
2435 * The separate domains can be computed directly from the "class_domain".
2437 * The unroll, atomic and remainder domains need the constraints
2438 * from the schedule domain.
2440 * For unrolling, the actual schedule domain is needed (with divs that
2441 * may refer to the current dimension) so that stride detection can be
2444 * For atomic and remainder domains, inner dimensions and divs involving
2445 * the current dimensions should be eliminated.
2446 * In case we are working within a separation class, we need to intersect
2447 * the result with the current "class_domain" to ensure that the domains
2448 * are disjoint from those generated from other class domains.
2450 * If anything is left after handling separate, unroll and atomic,
2451 * we split it up into basic sets and append the basic sets to domains->list.
2453 static int compute_partial_domains(struct isl_codegen_domains
*domains
,
2454 __isl_take isl_set
*class_domain
)
2456 isl_basic_set_list
*list
;
2459 class_domain
= isl_set_subtract(class_domain
,
2460 isl_set_copy(domains
->done
));
2461 domains
->done
= isl_set_union(domains
->done
,
2462 isl_set_copy(class_domain
));
2464 domain
= isl_set_copy(class_domain
);
2466 if (compute_separate_domain(domains
, domain
) < 0)
2468 domain
= isl_set_subtract(domain
,
2469 isl_set_copy(domains
->option
[separate
]));
2471 domain
= isl_set_intersect(domain
,
2472 isl_set_copy(domains
->schedule_domain
));
2474 if (compute_unroll_domains(domains
, domain
) < 0)
2476 domain
= isl_set_subtract(domain
,
2477 isl_set_copy(domains
->option
[unroll
]));
2479 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2480 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2482 if (compute_atomic_domain(domains
, domain
) < 0)
2484 domain
= isl_set_subtract(domain
,
2485 isl_set_copy(domains
->option
[atomic
]));
2487 domain
= isl_set_coalesce(domain
);
2488 domain
= isl_set_make_disjoint(domain
);
2490 list
= isl_basic_set_list_from_set(domain
);
2491 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2493 isl_set_free(class_domain
);
2497 isl_set_free(domain
);
2498 isl_set_free(class_domain
);
2502 /* Split up the domain at the current depth into disjoint
2503 * basic sets for which code should be generated separately
2504 * for the separation class identified by "pnt".
2506 * We extract the corresponding class domain from domains->sep_class,
2507 * eliminate inner dimensions and pass control to compute_partial_domains.
2509 static int compute_class_domains(__isl_take isl_point
*pnt
, void *user
)
2511 struct isl_codegen_domains
*domains
= user
;
2516 class_set
= isl_set_from_point(pnt
);
2517 domain
= isl_map_domain(isl_map_intersect_range(
2518 isl_map_copy(domains
->sep_class
), class_set
));
2519 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2521 disjoint
= isl_set_plain_is_disjoint(domain
, domains
->schedule_domain
);
2525 isl_set_free(domain
);
2529 return compute_partial_domains(domains
, domain
);
2532 /* Extract the domains at the current depth that should be atomic,
2533 * separated or unrolled and store them in option.
2535 * The domains specified by the user might overlap, so we make
2536 * them disjoint by subtracting earlier domains from later domains.
2538 static void compute_domains_init_options(isl_set
*option
[3],
2539 __isl_keep isl_ast_build
*build
)
2541 enum isl_ast_build_domain_type type
, type2
;
2543 for (type
= atomic
; type
<= separate
; ++type
) {
2544 option
[type
] = isl_ast_build_get_option_domain(build
, type
);
2545 for (type2
= atomic
; type2
< type
; ++type2
)
2546 option
[type
] = isl_set_subtract(option
[type
],
2547 isl_set_copy(option
[type2
]));
2550 option
[unroll
] = isl_set_coalesce(option
[unroll
]);
2551 option
[unroll
] = isl_set_make_disjoint(option
[unroll
]);
2554 /* Split up the domain at the current depth into disjoint
2555 * basic sets for which code should be generated separately,
2556 * based on the user-specified options.
2557 * Return the list of disjoint basic sets.
2559 * There are three kinds of domains that we need to keep track of.
2560 * - the "schedule domain" is the domain of "executed"
2561 * - the "class domain" is the domain corresponding to the currrent
2563 * - the "option domain" is the domain corresponding to one of the options
2564 * atomic, unroll or separate
2566 * We first consider the individial values of the separation classes
2567 * and split up the domain for each of them separately.
2568 * Finally, we consider the remainder. If no separation classes were
2569 * specified, then we call compute_partial_domains with the universe
2570 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2571 * with inner dimensions removed. We do this because we want to
2572 * avoid computing the complement of the class domains (i.e., the difference
2573 * between the universe and domains->done).
2575 static __isl_give isl_basic_set_list
*compute_domains(
2576 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
2578 struct isl_codegen_domains domains
;
2581 isl_union_set
*schedule_domain
;
2585 enum isl_ast_build_domain_type type
;
2588 ctx
= isl_union_map_get_ctx(executed
);
2589 domains
.list
= isl_basic_set_list_alloc(ctx
, 0);
2591 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
2592 domain
= isl_set_from_union_set(schedule_domain
);
2594 compute_domains_init_options(domains
.option
, build
);
2596 domains
.sep_class
= isl_ast_build_get_separation_class(build
);
2597 classes
= isl_map_range(isl_map_copy(domains
.sep_class
));
2598 n_param
= isl_set_dim(classes
, isl_dim_param
);
2599 classes
= isl_set_project_out(classes
, isl_dim_param
, 0, n_param
);
2601 space
= isl_set_get_space(domain
);
2602 domains
.build
= build
;
2603 domains
.schedule_domain
= isl_set_copy(domain
);
2604 domains
.executed
= executed
;
2605 domains
.done
= isl_set_empty(space
);
2607 if (isl_set_foreach_point(classes
, &compute_class_domains
, &domains
) < 0)
2608 domains
.list
= isl_basic_set_list_free(domains
.list
);
2609 isl_set_free(classes
);
2611 empty
= isl_set_is_empty(domains
.done
);
2613 domains
.list
= isl_basic_set_list_free(domains
.list
);
2614 domain
= isl_set_free(domain
);
2616 isl_set_free(domain
);
2617 domain
= isl_set_universe(isl_set_get_space(domains
.done
));
2619 domain
= isl_ast_build_eliminate(build
, domain
);
2621 if (compute_partial_domains(&domains
, domain
) < 0)
2622 domains
.list
= isl_basic_set_list_free(domains
.list
);
2624 isl_set_free(domains
.schedule_domain
);
2625 isl_set_free(domains
.done
);
2626 isl_map_free(domains
.sep_class
);
2627 for (type
= atomic
; type
<= separate
; ++type
)
2628 isl_set_free(domains
.option
[type
]);
2630 return domains
.list
;
2633 /* Generate code for a single component, after shifting (if any)
2636 * We first split up the domain at the current depth into disjoint
2637 * basic sets based on the user-specified options.
2638 * Then we generated code for each of them and concatenate the results.
2640 static __isl_give isl_ast_graft_list
*generate_shifted_component(
2641 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
2643 isl_basic_set_list
*domain_list
;
2644 isl_ast_graft_list
*list
= NULL
;
2646 domain_list
= compute_domains(executed
, build
);
2647 list
= generate_parallel_domains(domain_list
, executed
, build
);
2649 isl_basic_set_list_free(domain_list
);
2650 isl_union_map_free(executed
);
2651 isl_ast_build_free(build
);
2656 struct isl_set_map_pair
{
2661 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2662 * of indices into the "domain" array,
2663 * return the union of the "map" fields of the elements
2664 * indexed by the first "n" elements of "order".
2666 static __isl_give isl_union_map
*construct_component_executed(
2667 struct isl_set_map_pair
*domain
, int *order
, int n
)
2671 isl_union_map
*executed
;
2673 map
= isl_map_copy(domain
[order
[0]].map
);
2674 executed
= isl_union_map_from_map(map
);
2675 for (i
= 1; i
< n
; ++i
) {
2676 map
= isl_map_copy(domain
[order
[i
]].map
);
2677 executed
= isl_union_map_add_map(executed
, map
);
2683 /* Generate code for a single component, after shifting (if any)
2686 * The component inverse schedule is specified as the "map" fields
2687 * of the elements of "domain" indexed by the first "n" elements of "order".
2689 static __isl_give isl_ast_graft_list
*generate_shifted_component_from_list(
2690 struct isl_set_map_pair
*domain
, int *order
, int n
,
2691 __isl_take isl_ast_build
*build
)
2693 isl_union_map
*executed
;
2695 executed
= construct_component_executed(domain
, order
, n
);
2696 return generate_shifted_component(executed
, build
);
2699 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2700 * of indices into the "domain" array,
2701 * do all (except for at most one) of the "set" field of the elements
2702 * indexed by the first "n" elements of "order" have a fixed value
2703 * at position "depth"?
2705 static int at_most_one_non_fixed(struct isl_set_map_pair
*domain
,
2706 int *order
, int n
, int depth
)
2711 for (i
= 0; i
< n
; ++i
) {
2714 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2715 isl_dim_set
, depth
, NULL
);
2728 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2729 * of indices into the "domain" array,
2730 * eliminate the inner dimensions from the "set" field of the elements
2731 * indexed by the first "n" elements of "order", provided the current
2732 * dimension does not have a fixed value.
2734 * Return the index of the first element in "order" with a corresponding
2735 * "set" field that does not have an (obviously) fixed value.
2737 static int eliminate_non_fixed(struct isl_set_map_pair
*domain
,
2738 int *order
, int n
, int depth
, __isl_keep isl_ast_build
*build
)
2743 for (i
= n
- 1; i
>= 0; --i
) {
2745 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2746 isl_dim_set
, depth
, NULL
);
2751 domain
[order
[i
]].set
= isl_ast_build_eliminate_inner(build
,
2752 domain
[order
[i
]].set
);
2759 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2760 * of indices into the "domain" array,
2761 * find the element of "domain" (amongst those indexed by the first "n"
2762 * elements of "order") with the "set" field that has the smallest
2763 * value for the current iterator.
2765 * Note that the domain with the smallest value may depend on the parameters
2766 * and/or outer loop dimension. Since the result of this function is only
2767 * used as heuristic, we only make a reasonable attempt at finding the best
2768 * domain, one that should work in case a single domain provides the smallest
2769 * value for the current dimension over all values of the parameters
2770 * and outer dimensions.
2772 * In particular, we compute the smallest value of the first domain
2773 * and replace it by that of any later domain if that later domain
2774 * has a smallest value that is smaller for at least some value
2775 * of the parameters and outer dimensions.
2777 static int first_offset(struct isl_set_map_pair
*domain
, int *order
, int n
,
2778 __isl_keep isl_ast_build
*build
)
2784 min_first
= isl_ast_build_map_to_iterator(build
,
2785 isl_set_copy(domain
[order
[0]].set
));
2786 min_first
= isl_map_lexmin(min_first
);
2788 for (i
= 1; i
< n
; ++i
) {
2789 isl_map
*min
, *test
;
2792 min
= isl_ast_build_map_to_iterator(build
,
2793 isl_set_copy(domain
[order
[i
]].set
));
2794 min
= isl_map_lexmin(min
);
2795 test
= isl_map_copy(min
);
2796 test
= isl_map_apply_domain(isl_map_copy(min_first
), test
);
2797 test
= isl_map_order_lt(test
, isl_dim_in
, 0, isl_dim_out
, 0);
2798 empty
= isl_map_is_empty(test
);
2800 if (empty
>= 0 && !empty
) {
2801 isl_map_free(min_first
);
2811 isl_map_free(min_first
);
2813 return i
< n
? -1 : first
;
2816 /* Construct a shifted inverse schedule based on the original inverse schedule,
2817 * the stride and the offset.
2819 * The original inverse schedule is specified as the "map" fields
2820 * of the elements of "domain" indexed by the first "n" elements of "order".
2822 * "stride" and "offset" are such that the difference
2823 * between the values of the current dimension of domain "i"
2824 * and the values of the current dimension for some reference domain are
2827 * stride * integer + offset[i]
2829 * Moreover, 0 <= offset[i] < stride.
2831 * For each domain, we create a map
2833 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2835 * where j refers to the current dimension and the other dimensions are
2836 * unchanged, and apply this map to the original schedule domain.
2838 * For example, for the original schedule
2840 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2842 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2843 * we apply the mapping
2847 * to the schedule of the "A" domain and the mapping
2849 * { [j - 1] -> [j, 1] }
2851 * to the schedule of the "B" domain.
2854 * Note that after the transformation, the differences between pairs
2855 * of values of the current dimension over all domains are multiples
2856 * of stride and that we have therefore exposed the stride.
2859 * To see that the mapping preserves the lexicographic order,
2860 * first note that each of the individual maps above preserves the order.
2861 * If the value of the current iterator is j1 in one domain and j2 in another,
2862 * then if j1 = j2, we know that the same map is applied to both domains
2863 * and the order is preserved.
2864 * Otherwise, let us assume, without loss of generality, that j1 < j2.
2865 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
2869 * and the order is preserved.
2870 * If c1 < c2, then we know
2876 * j2 - j1 = n * s + r
2878 * with n >= 0 and 0 <= r < s.
2879 * In other words, r = c2 - c1.
2890 * (j1 - c1, c1) << (j2 - c2, c2)
2892 * with "<<" the lexicographic order, proving that the order is preserved
2895 static __isl_give isl_union_map
*contruct_shifted_executed(
2896 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
2897 __isl_keep isl_vec
*offset
, __isl_keep isl_ast_build
*build
)
2901 isl_union_map
*executed
;
2907 depth
= isl_ast_build_get_depth(build
);
2908 space
= isl_ast_build_get_space(build
, 1);
2909 executed
= isl_union_map_empty(isl_space_copy(space
));
2910 space
= isl_space_map_from_set(space
);
2911 map
= isl_map_identity(isl_space_copy(space
));
2912 map
= isl_map_eliminate(map
, isl_dim_out
, depth
, 1);
2913 map
= isl_map_insert_dims(map
, isl_dim_out
, depth
+ 1, 1);
2914 space
= isl_space_insert_dims(space
, isl_dim_out
, depth
+ 1, 1);
2916 c
= isl_equality_alloc(isl_local_space_from_space(space
));
2917 c
= isl_constraint_set_coefficient_si(c
, isl_dim_in
, depth
, 1);
2918 c
= isl_constraint_set_coefficient_si(c
, isl_dim_out
, depth
, -1);
2922 for (i
= 0; i
< n
; ++i
) {
2925 if (isl_vec_get_element(offset
, i
, &v
) < 0)
2927 map_i
= isl_map_copy(map
);
2928 map_i
= isl_map_fix(map_i
, isl_dim_out
, depth
+ 1, v
);
2930 c
= isl_constraint_set_constant(c
, v
);
2931 map_i
= isl_map_add_constraint(map_i
, isl_constraint_copy(c
));
2933 map_i
= isl_map_apply_domain(isl_map_copy(domain
[order
[i
]].map
),
2935 executed
= isl_union_map_add_map(executed
, map_i
);
2938 isl_constraint_free(c
);
2944 executed
= isl_union_map_free(executed
);
2949 /* Generate code for a single component, after exposing the stride,
2950 * given that the schedule domain is "shifted strided".
2952 * The component inverse schedule is specified as the "map" fields
2953 * of the elements of "domain" indexed by the first "n" elements of "order".
2955 * The schedule domain being "shifted strided" means that the differences
2956 * between the values of the current dimension of domain "i"
2957 * and the values of the current dimension for some reference domain are
2960 * stride * integer + offset[i]
2962 * We first look for the domain with the "smallest" value for the current
2963 * dimension and adjust the offsets such that the offset of the "smallest"
2964 * domain is equal to zero. The other offsets are reduced modulo stride.
2966 * Based on this information, we construct a new inverse schedule in
2967 * contruct_shifted_executed that exposes the stride.
2968 * Since this involves the introduction of a new schedule dimension,
2969 * the build needs to be changed accodingly.
2970 * After computing the AST, the newly introduced dimension needs
2971 * to be removed again from the list of grafts. We do this by plugging
2972 * in a mapping that represents the new schedule domain in terms of the
2973 * old schedule domain.
2975 static __isl_give isl_ast_graft_list
*generate_shift_component(
2976 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
2977 __isl_keep isl_vec
*offset
, __isl_take isl_ast_build
*build
)
2979 isl_ast_graft_list
*list
;
2986 isl_multi_aff
*ma
, *zero
;
2987 isl_union_map
*executed
;
2989 ctx
= isl_ast_build_get_ctx(build
);
2990 depth
= isl_ast_build_get_depth(build
);
2992 first
= first_offset(domain
, order
, n
, build
);
2994 return isl_ast_build_free(build
);
2997 v
= isl_vec_alloc(ctx
, n
);
2998 if (isl_vec_get_element(offset
, first
, &val
) < 0)
2999 v
= isl_vec_free(v
);
3000 isl_int_neg(val
, val
);
3001 v
= isl_vec_set(v
, val
);
3002 v
= isl_vec_add(v
, isl_vec_copy(offset
));
3003 v
= isl_vec_fdiv_r(v
, stride
);
3005 executed
= contruct_shifted_executed(domain
, order
, n
, stride
, v
,
3007 space
= isl_ast_build_get_space(build
, 1);
3008 space
= isl_space_map_from_set(space
);
3009 ma
= isl_multi_aff_identity(isl_space_copy(space
));
3010 space
= isl_space_from_domain(isl_space_domain(space
));
3011 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
3012 zero
= isl_multi_aff_zero(space
);
3013 ma
= isl_multi_aff_range_splice(ma
, depth
+ 1, zero
);
3014 build
= isl_ast_build_insert_dim(build
, depth
+ 1);
3015 list
= generate_shifted_component(executed
, build
);
3017 list
= isl_ast_graft_list_preimage_multi_aff(list
, ma
);
3025 /* Generate code for a single component.
3027 * The component inverse schedule is specified as the "map" fields
3028 * of the elements of "domain" indexed by the first "n" elements of "order".
3030 * This function may modify the "set" fields of "domain".
3032 * Before proceeding with the actual code generation for the component,
3033 * we first check if there are any "shifted" strides, meaning that
3034 * the schedule domains of the individual domains are all strided,
3035 * but that they have different offsets, resulting in the union
3036 * of schedule domains not being strided anymore.
3038 * The simplest example is the schedule
3040 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3042 * Both schedule domains are strided, but their union is not.
3043 * This function detects such cases and then rewrites the schedule to
3045 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3047 * In the new schedule, the schedule domains have the same offset (modulo
3048 * the stride), ensuring that the union of schedule domains is also strided.
3051 * If there is only a single domain in the component, then there is
3052 * nothing to do. Similarly, if the current schedule dimension has
3053 * a fixed value for almost all domains then there is nothing to be done.
3054 * In particular, we need at least two domains where the current schedule
3055 * dimension does not have a fixed value.
3056 * Finally, if any of the options refer to the current schedule dimension,
3057 * then we bail out as well. It would be possible to reformulate the options
3058 * in terms of the new schedule domain, but that would introduce constraints
3059 * that separate the domains in the options and that is something we would
3063 * To see if there is any shifted stride, we look at the differences
3064 * between the values of the current dimension in pairs of domains
3065 * for equal values of outer dimensions. These differences should be
3070 * with "m" the stride and "r" a constant. Note that we cannot perform
3071 * this analysis on individual domains as the lower bound in each domain
3072 * may depend on parameters or outer dimensions and so the current dimension
3073 * itself may not have a fixed remainder on division by the stride.
3075 * In particular, we compare the first domain that does not have an
3076 * obviously fixed value for the current dimension to itself and all
3077 * other domains and collect the offsets and the gcd of the strides.
3078 * If the gcd becomes one, then we failed to find shifted strides.
3079 * If all the offsets are the same (for those domains that do not have
3080 * an obviously fixed value for the current dimension), then we do not
3081 * apply the transformation.
3082 * If none of the domains were skipped, then there is nothing to do.
3083 * If some of them were skipped, then if we apply separation, the schedule
3084 * domain should get split in pieces with a (non-shifted) stride.
3086 * Otherwise, we apply a shift to expose the stride in
3087 * generate_shift_component.
3089 static __isl_give isl_ast_graft_list
*generate_component(
3090 struct isl_set_map_pair
*domain
, int *order
, int n
,
3091 __isl_take isl_ast_build
*build
)
3102 isl_ast_graft_list
*list
;
3105 depth
= isl_ast_build_get_depth(build
);
3108 if (skip
>= 0 && !skip
)
3109 skip
= at_most_one_non_fixed(domain
, order
, n
, depth
);
3110 if (skip
>= 0 && !skip
)
3111 skip
= isl_ast_build_options_involve_depth(build
);
3113 return isl_ast_build_free(build
);
3115 return generate_shifted_component_from_list(domain
,
3118 base
= eliminate_non_fixed(domain
, order
, n
, depth
, build
);
3120 return isl_ast_build_free(build
);
3122 ctx
= isl_ast_build_get_ctx(build
);
3127 v
= isl_vec_alloc(ctx
, n
);
3130 for (i
= 0; i
< n
; ++i
) {
3131 map
= isl_map_from_domain_and_range(
3132 isl_set_copy(domain
[order
[base
]].set
),
3133 isl_set_copy(domain
[order
[i
]].set
));
3134 for (d
= 0; d
< depth
; ++d
)
3135 map
= isl_map_equate(map
, isl_dim_in
, d
,
3137 deltas
= isl_map_deltas(map
);
3138 res
= isl_set_dim_residue_class(deltas
, depth
, &m
, &r
);
3139 isl_set_free(deltas
);
3144 isl_int_set(gcd
, m
);
3146 isl_int_gcd(gcd
, gcd
, m
);
3147 if (isl_int_is_one(gcd
))
3149 v
= isl_vec_set_element(v
, i
, r
);
3151 res
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
3152 isl_dim_set
, depth
, NULL
);
3158 if (fixed
&& i
> base
) {
3159 isl_vec_get_element(v
, base
, &m
);
3160 if (isl_int_ne(m
, r
))
3166 isl_ast_build_free(build
);
3168 } else if (i
< n
|| fixed
) {
3169 list
= generate_shifted_component_from_list(domain
,
3172 list
= generate_shift_component(domain
, order
, n
, gcd
, v
,
3184 /* Store both "map" itself and its domain in the
3185 * structure pointed to by *next and advance to the next array element.
3187 static int extract_domain(__isl_take isl_map
*map
, void *user
)
3189 struct isl_set_map_pair
**next
= user
;
3191 (*next
)->map
= isl_map_copy(map
);
3192 (*next
)->set
= isl_map_domain(map
);
3198 /* Internal data for any_scheduled_after.
3200 * "depth" is the number of loops that have already been generated
3201 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3202 * "domain" is an array of set-map pairs corresponding to the different
3203 * iteration domains. The set is the schedule domain, i.e., the domain
3204 * of the inverse schedule, while the map is the inverse schedule itself.
3206 struct isl_any_scheduled_after_data
{
3208 int group_coscheduled
;
3209 struct isl_set_map_pair
*domain
;
3212 /* Is any element of domain "i" scheduled after any element of domain "j"
3213 * (for a common iteration of the first data->depth loops)?
3215 * data->domain[i].set contains the domain of the inverse schedule
3216 * for domain "i", i.e., elements in the schedule domain.
3218 * If data->group_coscheduled is set, then we also return 1 if there
3219 * is any pair of elements in the two domains that are scheduled together.
3221 static int any_scheduled_after(int i
, int j
, void *user
)
3223 struct isl_any_scheduled_after_data
*data
= user
;
3224 int dim
= isl_set_dim(data
->domain
[i
].set
, isl_dim_set
);
3227 for (pos
= data
->depth
; pos
< dim
; ++pos
) {
3230 follows
= isl_set_follows_at(data
->domain
[i
].set
,
3231 data
->domain
[j
].set
, pos
);
3241 return data
->group_coscheduled
;
3244 /* Look for independent components at the current depth and generate code
3245 * for each component separately. The resulting lists of grafts are
3246 * merged in an attempt to combine grafts with identical guards.
3248 * Code for two domains can be generated separately if all the elements
3249 * of one domain are scheduled before (or together with) all the elements
3250 * of the other domain. We therefore consider the graph with as nodes
3251 * the domains and an edge between two nodes if any element of the first
3252 * node is scheduled after any element of the second node.
3253 * If the ast_build_group_coscheduled is set, then we also add an edge if
3254 * there is any pair of elements in the two domains that are scheduled
3256 * Code is then generated (by generate_component)
3257 * for each of the strongly connected components in this graph
3258 * in their topological order.
3260 * Since the test is performed on the domain of the inverse schedules of
3261 * the different domains, we precompute these domains and store
3262 * them in data.domain.
3264 static __isl_give isl_ast_graft_list
*generate_components(
3265 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3268 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3269 int n
= isl_union_map_n_map(executed
);
3270 struct isl_any_scheduled_after_data data
;
3271 struct isl_set_map_pair
*next
;
3272 struct isl_tarjan_graph
*g
= NULL
;
3273 isl_ast_graft_list
*list
= NULL
;
3276 data
.domain
= isl_calloc_array(ctx
, struct isl_set_map_pair
, n
);
3282 if (isl_union_map_foreach_map(executed
, &extract_domain
, &next
) < 0)
3287 data
.depth
= isl_ast_build_get_depth(build
);
3288 data
.group_coscheduled
= isl_options_get_ast_build_group_coscheduled(ctx
);
3289 g
= isl_tarjan_graph_init(ctx
, n
, &any_scheduled_after
, &data
);
3291 list
= isl_ast_graft_list_alloc(ctx
, 0);
3295 isl_ast_graft_list
*list_c
;
3298 if (g
->order
[i
] == -1)
3299 isl_die(ctx
, isl_error_internal
, "cannot happen",
3302 while (g
->order
[i
] != -1) {
3306 list_c
= generate_component(data
.domain
,
3307 g
->order
+ first
, i
- first
,
3308 isl_ast_build_copy(build
));
3309 list
= isl_ast_graft_list_merge(list
, list_c
, build
);
3315 error
: list
= isl_ast_graft_list_free(list
);
3316 isl_tarjan_graph_free(g
);
3317 for (i
= 0; i
< n_domain
; ++i
) {
3318 isl_map_free(data
.domain
[i
].map
);
3319 isl_set_free(data
.domain
[i
].set
);
3322 isl_union_map_free(executed
);
3323 isl_ast_build_free(build
);
3328 /* Generate code for the next level (and all inner levels).
3330 * If "executed" is empty, i.e., no code needs to be generated,
3331 * then we return an empty list.
3333 * If we have already generated code for all loop levels, then we pass
3334 * control to generate_inner_level.
3336 * If "executed" lives in a single space, i.e., if code needs to be
3337 * generated for a single domain, then there can only be a single
3338 * component and we go directly to generate_shifted_component.
3339 * Otherwise, we call generate_components to detect the components
3340 * and to call generate_component on each of them separately.
3342 static __isl_give isl_ast_graft_list
*generate_next_level(
3343 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3347 if (!build
|| !executed
)
3350 if (isl_union_map_is_empty(executed
)) {
3351 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3352 isl_union_map_free(executed
);
3353 isl_ast_build_free(build
);
3354 return isl_ast_graft_list_alloc(ctx
, 0);
3357 depth
= isl_ast_build_get_depth(build
);
3358 if (depth
>= isl_set_dim(build
->domain
, isl_dim_set
))
3359 return generate_inner_level(executed
, build
);
3361 if (isl_union_map_n_map(executed
) == 1)
3362 return generate_shifted_component(executed
, build
);
3364 return generate_components(executed
, build
);
3366 isl_union_map_free(executed
);
3367 isl_ast_build_free(build
);
3371 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3372 * internal, executed and build are the inputs to generate_code.
3373 * list collects the output.
3375 struct isl_generate_code_data
{
3377 isl_union_map
*executed
;
3378 isl_ast_build
*build
;
3380 isl_ast_graft_list
*list
;
3383 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3387 * with E the external build schedule and S the additional schedule "space",
3388 * reformulate the inverse schedule in terms of the internal schedule domain,
3393 * We first obtain a mapping
3397 * take the inverse and the product with S -> S, resulting in
3399 * [I -> S] -> [E -> S]
3401 * Applying the map to the input produces the desired result.
3403 static __isl_give isl_union_map
*internal_executed(
3404 __isl_take isl_union_map
*executed
, __isl_keep isl_space
*space
,
3405 __isl_keep isl_ast_build
*build
)
3409 proj
= isl_ast_build_get_schedule_map(build
);
3410 proj
= isl_map_reverse(proj
);
3411 space
= isl_space_map_from_set(isl_space_copy(space
));
3412 id
= isl_map_identity(space
);
3413 proj
= isl_map_product(proj
, id
);
3414 executed
= isl_union_map_apply_domain(executed
,
3415 isl_union_map_from_map(proj
));
3419 /* Generate an AST that visits the elements in the range of data->executed
3420 * in the relative order specified by the corresponding image element(s)
3421 * for those image elements that belong to "set".
3422 * Add the result to data->list.
3424 * The caller ensures that "set" is a universe domain.
3425 * "space" is the space of the additional part of the schedule.
3426 * It is equal to the space of "set" if build->domain is parametric.
3427 * Otherwise, it is equal to the range of the wrapped space of "set".
3429 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3430 * was called from an outside user (data->internal not set), then
3431 * the (inverse) schedule refers to the external build domain and needs to
3432 * be transformed to refer to the internal build domain.
3434 * The build is extended to include the additional part of the schedule.
3435 * If the original build space was not parametric, then the options
3436 * in data->build refer only to the additional part of the schedule
3437 * and they need to be adjusted to refer to the complete AST build
3440 * After having adjusted inverse schedule and build, we start generating
3441 * code with the outer loop of the current code generation
3442 * in generate_next_level.
3444 * If the original build space was not parametric, we undo the embedding
3445 * on the resulting isl_ast_node_list so that it can be used within
3446 * the outer AST build.
3448 static int generate_code_in_space(struct isl_generate_code_data
*data
,
3449 __isl_take isl_set
*set
, __isl_take isl_space
*space
)
3451 isl_union_map
*executed
;
3452 isl_ast_build
*build
;
3453 isl_ast_graft_list
*list
;
3456 executed
= isl_union_map_copy(data
->executed
);
3457 executed
= isl_union_map_intersect_domain(executed
,
3458 isl_union_set_from_set(set
));
3460 embed
= !isl_set_is_params(data
->build
->domain
);
3461 if (embed
&& !data
->internal
)
3462 executed
= internal_executed(executed
, space
, data
->build
);
3464 build
= isl_ast_build_copy(data
->build
);
3465 build
= isl_ast_build_product(build
, space
);
3467 list
= generate_next_level(executed
, build
);
3469 list
= isl_ast_graft_list_unembed(list
, embed
);
3471 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
3476 /* Generate an AST that visits the elements in the range of data->executed
3477 * in the relative order specified by the corresponding domain element(s)
3478 * for those domain elements that belong to "set".
3479 * Add the result to data->list.
3481 * The caller ensures that "set" is a universe domain.
3483 * If the build space S is not parametric, then the space of "set"
3484 * need to be a wrapped relation with S as domain. That is, it needs
3489 * Check this property and pass control to generate_code_in_space
3491 * If the build space is not parametric, then T is the space of "set".
3493 static int generate_code_set(__isl_take isl_set
*set
, void *user
)
3495 struct isl_generate_code_data
*data
= user
;
3496 isl_space
*space
, *build_space
;
3499 space
= isl_set_get_space(set
);
3501 if (isl_set_is_params(data
->build
->domain
))
3502 return generate_code_in_space(data
, set
, space
);
3504 build_space
= isl_ast_build_get_space(data
->build
, data
->internal
);
3505 space
= isl_space_unwrap(space
);
3506 is_domain
= isl_space_is_domain(build_space
, space
);
3507 isl_space_free(build_space
);
3508 space
= isl_space_range(space
);
3513 isl_die(isl_set_get_ctx(set
), isl_error_invalid
,
3514 "invalid nested schedule space", goto error
);
3516 return generate_code_in_space(data
, set
, space
);
3519 isl_space_free(space
);
3523 /* Generate an AST that visits the elements in the range of "executed"
3524 * in the relative order specified by the corresponding domain element(s).
3526 * "build" is an isl_ast_build that has either been constructed by
3527 * isl_ast_build_from_context or passed to a callback set by
3528 * isl_ast_build_set_create_leaf.
3529 * In the first case, the space of the isl_ast_build is typically
3530 * a parametric space, although this is currently not enforced.
3531 * In the second case, the space is never a parametric space.
3532 * If the space S is not parametric, then the domain space(s) of "executed"
3533 * need to be wrapped relations with S as domain.
3535 * If the domain of "executed" consists of several spaces, then an AST
3536 * is generated for each of them (in arbitrary order) and the results
3539 * If "internal" is set, then the domain "S" above refers to the internal
3540 * schedule domain representation. Otherwise, it refers to the external
3541 * representation, as returned by isl_ast_build_get_schedule_space.
3543 * We essentially run over all the spaces in the domain of "executed"
3544 * and call generate_code_set on each of them.
3546 static __isl_give isl_ast_graft_list
*generate_code(
3547 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
3551 struct isl_generate_code_data data
= { 0 };
3553 isl_union_set
*schedule_domain
;
3554 isl_union_map
*universe
;
3558 space
= isl_ast_build_get_space(build
, 1);
3559 space
= isl_space_align_params(space
,
3560 isl_union_map_get_space(executed
));
3561 space
= isl_space_align_params(space
,
3562 isl_union_map_get_space(build
->options
));
3563 build
= isl_ast_build_align_params(build
, isl_space_copy(space
));
3564 executed
= isl_union_map_align_params(executed
, space
);
3565 if (!executed
|| !build
)
3568 ctx
= isl_ast_build_get_ctx(build
);
3570 data
.internal
= internal
;
3571 data
.executed
= executed
;
3573 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
3575 universe
= isl_union_map_universe(isl_union_map_copy(executed
));
3576 schedule_domain
= isl_union_map_domain(universe
);
3577 if (isl_union_set_foreach_set(schedule_domain
, &generate_code_set
,
3579 data
.list
= isl_ast_graft_list_free(data
.list
);
3581 isl_union_set_free(schedule_domain
);
3582 isl_union_map_free(executed
);
3584 isl_ast_build_free(build
);
3587 isl_union_map_free(executed
);
3588 isl_ast_build_free(build
);
3592 /* Generate an AST that visits the elements in the domain of "schedule"
3593 * in the relative order specified by the corresponding image 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 range space(s) of "schedule"
3602 * need to be wrapped relations with S as domain.
3604 * If the range of "schedule" consists of several spaces, then an AST
3605 * is generated for each of them (in arbitrary order) and the results
3608 * We first initialize the local copies of the relevant options.
3609 * We do this here rather than when the isl_ast_build is created
3610 * because the options may have changed between the construction
3611 * of the isl_ast_build and the call to isl_generate_code.
3613 * The main computation is performed on an inverse schedule (with
3614 * the schedule domain in the domain and the elements to be executed
3615 * in the range) called "executed".
3617 __isl_give isl_ast_node
*isl_ast_build_ast_from_schedule(
3618 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
3620 isl_ast_graft_list
*list
;
3622 isl_union_map
*executed
;
3624 executed
= isl_union_map_reverse(schedule
);
3625 list
= generate_code(executed
, isl_ast_build_copy(build
), 0);
3626 node
= isl_ast_node_from_graft_list(list
, build
);