2 * Copyright 2012 Ecole Normale Superieure
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege,
7 * Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 #include <isl/union_map.h>
16 #include <isl_tarjan.h>
17 #include <isl_ast_private.h>
18 #include <isl_ast_build_expr.h>
19 #include <isl_ast_build_private.h>
20 #include <isl_ast_graft_private.h>
21 #include <isl_list_private.h>
23 /* Add the constraint to the list that "user" points to, if it is not
26 static int collect_constraint(__isl_take isl_constraint
*constraint
,
29 isl_constraint_list
**list
= user
;
31 if (isl_constraint_is_div_constraint(constraint
))
32 isl_constraint_free(constraint
);
34 *list
= isl_constraint_list_add(*list
, constraint
);
39 /* Extract the constraints of "bset" (except the div constraints)
40 * and collect them in an isl_constraint_list.
42 static __isl_give isl_constraint_list
*isl_constraint_list_from_basic_set(
43 __isl_take isl_basic_set
*bset
)
47 isl_constraint_list
*list
;
52 ctx
= isl_basic_set_get_ctx(bset
);
54 n
= isl_basic_set_n_constraint(bset
);
55 list
= isl_constraint_list_alloc(ctx
, n
);
56 if (isl_basic_set_foreach_constraint(bset
,
57 &collect_constraint
, &list
) < 0)
58 list
= isl_constraint_list_free(list
);
60 isl_basic_set_free(bset
);
64 /* Data used in generate_domain.
66 * "build" is the input build.
67 * "list" collects the results.
69 struct isl_generate_domain_data
{
72 isl_ast_graft_list
*list
;
75 static __isl_give isl_ast_graft_list
*generate_next_level(
76 __isl_take isl_union_map
*executed
,
77 __isl_take isl_ast_build
*build
);
78 static __isl_give isl_ast_graft_list
*generate_code(
79 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
82 /* Generate an AST for a single domain based on
83 * the (non single valued) inverse schedule "executed".
85 * We extend the schedule with the iteration domain
86 * and continue generating through a call to generate_code.
88 * In particular, if executed has the form
92 * then we continue generating code on
96 * The extended inverse schedule is clearly single valued
97 * ensuring that the nested generate_code will not reach this function,
98 * but will instead create calls to all elements of D that need
99 * to be executed from the current schedule domain.
101 static int generate_non_single_valued(__isl_take isl_map
*executed
,
102 struct isl_generate_domain_data
*data
)
105 isl_ast_build
*build
;
106 isl_ast_graft_list
*list
;
108 build
= isl_ast_build_copy(data
->build
);
110 identity
= isl_set_identity(isl_map_range(isl_map_copy(executed
)));
111 executed
= isl_map_domain_product(executed
, identity
);
112 build
= isl_ast_build_set_single_valued(build
, 1);
114 list
= generate_code(isl_union_map_from_map(executed
), build
, 1);
116 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
121 /* Call the at_each_domain callback, if requested by the user,
122 * after recording the current inverse schedule in the build.
124 static __isl_give isl_ast_graft
*at_each_domain(__isl_take isl_ast_graft
*graft
,
125 __isl_keep isl_map
*executed
, __isl_keep isl_ast_build
*build
)
127 if (!graft
|| !build
)
128 return isl_ast_graft_free(graft
);
129 if (!build
->at_each_domain
)
132 build
= isl_ast_build_copy(build
);
133 build
= isl_ast_build_set_executed(build
,
134 isl_union_map_from_map(isl_map_copy(executed
)));
136 return isl_ast_graft_free(graft
);
138 graft
->node
= build
->at_each_domain(graft
->node
,
139 build
, build
->at_each_domain_user
);
140 isl_ast_build_free(build
);
143 graft
= isl_ast_graft_free(graft
);
148 /* Generate an AST for a single domain based on
149 * the inverse schedule "executed".
151 * If there is more than one domain element associated to the current
152 * schedule "time", then we need to continue the generation process
153 * in generate_non_single_valued.
154 * Note that the inverse schedule being single-valued may depend
155 * on constraints that are only available in the original context
156 * domain specified by the user. We therefore first introduce
157 * the constraints from data->build->domain.
158 * On the other hand, we only perform the test after having taken the gist
159 * of the domain as the resulting map is the one from which the call
160 * expression is constructed. Using this map to construct the call
161 * expression usually yields simpler results.
162 * Because we perform the single-valuedness test on the gisted map,
163 * we may in rare cases fail to recognize that the inverse schedule
164 * is single-valued. This becomes problematic if this happens
165 * from the recursive call through generate_non_single_valued
166 * as we would then end up in an infinite recursion.
167 * We therefore check if we are inside a call to generate_non_single_valued
168 * and revert to the ungisted map if the gisted map turns out not to be
171 * Otherwise, we generate a call expression for the single executed
172 * domain element and put a guard around it based on the (simplified)
173 * domain of "executed".
175 * If the user has set an at_each_domain callback, it is called
176 * on the constructed call expression node.
178 static int generate_domain(__isl_take isl_map
*executed
, void *user
)
180 struct isl_generate_domain_data
*data
= user
;
181 isl_ast_graft
*graft
;
182 isl_ast_graft_list
*list
;
187 executed
= isl_map_intersect_domain(executed
,
188 isl_set_copy(data
->build
->domain
));
190 executed
= isl_map_coalesce(executed
);
191 map
= isl_map_copy(executed
);
192 map
= isl_ast_build_compute_gist_map_domain(data
->build
, map
);
193 sv
= isl_map_is_single_valued(map
);
198 if (data
->build
->single_valued
)
199 map
= isl_map_copy(executed
);
201 return generate_non_single_valued(executed
, data
);
203 guard
= isl_map_domain(isl_map_copy(map
));
204 guard
= isl_set_coalesce(guard
);
205 guard
= isl_ast_build_compute_gist(data
->build
, guard
);
206 graft
= isl_ast_graft_alloc_domain(map
, data
->build
);
207 graft
= at_each_domain(graft
, executed
, data
->build
);
209 isl_map_free(executed
);
210 graft
= isl_ast_graft_add_guard(graft
, guard
, data
->build
);
212 list
= isl_ast_graft_list_from_ast_graft(graft
);
213 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
218 isl_map_free(executed
);
222 /* Call build->create_leaf to a create "leaf" node in the AST,
223 * encapsulate the result in an isl_ast_graft and return the result
224 * as a 1-element list.
226 * Note that the node returned by the user may be an entire tree.
228 * Before we pass control to the user, we first clear some information
229 * from the build that is (presumbably) only meaningful
230 * for the current code generation.
231 * This includes the create_leaf callback itself, so we make a copy
232 * of the build first.
234 static __isl_give isl_ast_graft_list
*call_create_leaf(
235 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
238 isl_ast_graft
*graft
;
239 isl_ast_build
*user_build
;
241 user_build
= isl_ast_build_copy(build
);
242 user_build
= isl_ast_build_set_executed(user_build
, executed
);
243 user_build
= isl_ast_build_clear_local_info(user_build
);
247 node
= build
->create_leaf(user_build
, build
->create_leaf_user
);
248 graft
= isl_ast_graft_alloc(node
, build
);
249 isl_ast_build_free(build
);
250 return isl_ast_graft_list_from_ast_graft(graft
);
253 /* Generate an AST after having handled the complete schedule
254 * of this call to the code generator.
256 * If the user has specified a create_leaf callback, control
257 * is passed to the user in call_create_leaf.
259 * Otherwise, we generate one or more calls for each individual
260 * domain in generate_domain.
262 static __isl_give isl_ast_graft_list
*generate_inner_level(
263 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
266 struct isl_generate_domain_data data
= { build
};
268 if (!build
|| !executed
)
271 if (build
->create_leaf
)
272 return call_create_leaf(executed
, build
);
274 ctx
= isl_union_map_get_ctx(executed
);
275 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
276 if (isl_union_map_foreach_map(executed
, &generate_domain
, &data
) < 0)
277 data
.list
= isl_ast_graft_list_free(data
.list
);
280 error
: data
.list
= NULL
;
281 isl_ast_build_free(build
);
282 isl_union_map_free(executed
);
286 /* Call the before_each_for callback, if requested by the user.
288 static __isl_give isl_ast_node
*before_each_for(__isl_take isl_ast_node
*node
,
289 __isl_keep isl_ast_build
*build
)
294 return isl_ast_node_free(node
);
295 if (!build
->before_each_for
)
297 id
= build
->before_each_for(build
, build
->before_each_for_user
);
298 node
= isl_ast_node_set_annotation(node
, id
);
302 /* Call the after_each_for callback, if requested by the user.
304 static __isl_give isl_ast_graft
*after_each_for(__isl_keep isl_ast_graft
*graft
,
305 __isl_keep isl_ast_build
*build
)
307 if (!graft
|| !build
)
308 return isl_ast_graft_free(graft
);
309 if (!build
->after_each_for
)
311 graft
->node
= build
->after_each_for(graft
->node
, build
,
312 build
->after_each_for_user
);
314 return isl_ast_graft_free(graft
);
318 /* Eliminate the schedule dimension "pos" from "executed" and return
321 static __isl_give isl_union_map
*eliminate(__isl_take isl_union_map
*executed
,
322 int pos
, __isl_keep isl_ast_build
*build
)
327 space
= isl_ast_build_get_space(build
, 1);
328 space
= isl_space_map_from_set(space
);
329 elim
= isl_map_identity(space
);
330 elim
= isl_map_eliminate(elim
, isl_dim_in
, pos
, 1);
332 executed
= isl_union_map_apply_domain(executed
,
333 isl_union_map_from_map(elim
));
338 /* Check if the constraint "c" is a lower bound on dimension "pos",
339 * an upper bound, or independent of dimension "pos".
341 static int constraint_type(isl_constraint
*c
, int pos
)
343 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, pos
))
345 if (isl_constraint_is_upper_bound(c
, isl_dim_set
, pos
))
350 /* Compare the types of the constraints "a" and "b",
351 * resulting in constraints that are independent of "depth"
352 * to be sorted before the lower bounds on "depth", which in
353 * turn are sorted before the upper bounds on "depth".
355 static int cmp_constraint(const void *a
, const void *b
, void *user
)
358 isl_constraint
* const *c1
= a
;
359 isl_constraint
* const *c2
= b
;
360 int t1
= constraint_type(*c1
, *depth
);
361 int t2
= constraint_type(*c2
, *depth
);
366 /* Extract a lower bound on dimension "pos" from constraint "c".
368 * If the constraint is of the form
372 * then we essentially return
374 * l = ceil(-f(...)/a)
376 * However, if the current dimension is strided, then we need to make
377 * sure that the lower bound we construct is of the form
381 * with f the offset and s the stride.
382 * We therefore compute
384 * f + s * ceil((l - f)/s)
386 static __isl_give isl_aff
*lower_bound(__isl_keep isl_constraint
*c
,
387 int pos
, __isl_keep isl_ast_build
*build
)
391 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
392 aff
= isl_aff_ceil(aff
);
394 if (isl_ast_build_has_stride(build
, pos
)) {
398 isl_int_init(stride
);
400 offset
= isl_ast_build_get_offset(build
, pos
);
401 isl_ast_build_get_stride(build
, pos
, &stride
);
403 aff
= isl_aff_sub(aff
, isl_aff_copy(offset
));
404 aff
= isl_aff_scale_down(aff
, stride
);
405 aff
= isl_aff_ceil(aff
);
406 aff
= isl_aff_scale(aff
, stride
);
407 aff
= isl_aff_add(aff
, offset
);
409 isl_int_clear(stride
);
412 aff
= isl_ast_build_compute_gist_aff(build
, aff
);
417 /* Return the exact lower bound (or upper bound if "upper" is set)
418 * of "domain" as a piecewise affine expression.
420 * If we are computing a lower bound (of a strided dimension), then
421 * we need to make sure it is of the form
425 * where f is the offset and s is the stride.
426 * We therefore need to include the stride constraint before computing
429 static __isl_give isl_pw_aff
*exact_bound(__isl_keep isl_set
*domain
,
430 __isl_keep isl_ast_build
*build
, int upper
)
435 isl_pw_multi_aff
*pma
;
437 domain
= isl_set_copy(domain
);
439 stride
= isl_ast_build_get_stride_constraint(build
);
440 domain
= isl_set_intersect(domain
, stride
);
442 it_map
= isl_ast_build_map_to_iterator(build
, domain
);
444 pma
= isl_map_lexmax_pw_multi_aff(it_map
);
446 pma
= isl_map_lexmin_pw_multi_aff(it_map
);
447 pa
= isl_pw_multi_aff_get_pw_aff(pma
, 0);
448 isl_pw_multi_aff_free(pma
);
449 pa
= isl_ast_build_compute_gist_pw_aff(build
, pa
);
450 pa
= isl_pw_aff_coalesce(pa
);
455 /* Return a list of "n" lower bounds on dimension "pos"
456 * extracted from the "n" constraints starting at "constraint".
457 * If "n" is zero, then we extract a lower bound from "domain" instead.
459 static __isl_give isl_pw_aff_list
*lower_bounds(
460 __isl_keep isl_constraint
**constraint
, int n
, int pos
,
461 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
464 isl_pw_aff_list
*list
;
472 pa
= exact_bound(domain
, build
, 0);
473 return isl_pw_aff_list_from_pw_aff(pa
);
476 ctx
= isl_ast_build_get_ctx(build
);
477 list
= isl_pw_aff_list_alloc(ctx
,n
);
479 for (i
= 0; i
< n
; ++i
) {
482 aff
= lower_bound(constraint
[i
], pos
, build
);
483 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
489 /* Return a list of "n" upper bounds on dimension "pos"
490 * extracted from the "n" constraints starting at "constraint".
491 * If "n" is zero, then we extract an upper bound from "domain" instead.
493 static __isl_give isl_pw_aff_list
*upper_bounds(
494 __isl_keep isl_constraint
**constraint
, int n
, int pos
,
495 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
498 isl_pw_aff_list
*list
;
503 pa
= exact_bound(domain
, build
, 1);
504 return isl_pw_aff_list_from_pw_aff(pa
);
507 ctx
= isl_ast_build_get_ctx(build
);
508 list
= isl_pw_aff_list_alloc(ctx
,n
);
510 for (i
= 0; i
< n
; ++i
) {
513 aff
= isl_constraint_get_bound(constraint
[i
], isl_dim_set
, pos
);
514 aff
= isl_aff_floor(aff
);
515 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
521 /* Return an isl_ast_expr that performs the reduction of type "type"
522 * on AST expressions corresponding to the elements in "list".
524 * The list is assumed to contain at least one element.
525 * If the list contains exactly one element, then the returned isl_ast_expr
526 * simply computes that affine expression.
528 static __isl_give isl_ast_expr
*reduce_list(enum isl_ast_op_type type
,
529 __isl_keep isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
538 n
= isl_pw_aff_list_n_pw_aff(list
);
541 return isl_ast_build_expr_from_pw_aff_internal(build
,
542 isl_pw_aff_list_get_pw_aff(list
, 0));
544 ctx
= isl_pw_aff_list_get_ctx(list
);
545 expr
= isl_ast_expr_alloc_op(ctx
, type
, n
);
549 for (i
= 0; i
< n
; ++i
) {
550 isl_ast_expr
*expr_i
;
552 expr_i
= isl_ast_build_expr_from_pw_aff_internal(build
,
553 isl_pw_aff_list_get_pw_aff(list
, i
));
555 return isl_ast_expr_free(expr
);
556 expr
->u
.op
.args
[i
] = expr_i
;
562 /* Add a guard to "graft" based on "bound" in the case of a degenerate
563 * level (including the special case of an eliminated level).
565 * We eliminate the current dimension, simplify the result in the current
566 * build and add the result as guards to the graft.
568 * Note that we cannot simply drop the constraints on the current dimension
569 * even in the eliminated case, because the single affine expression may
570 * not be explicitly available in "bounds". Moreover, the single affine
571 * expression may only be defined on a subset of the build domain,
572 * so we do in some cases need to insert a guard even in the eliminated case.
574 static __isl_give isl_ast_graft
*add_degenerate_guard(
575 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
576 __isl_keep isl_ast_build
*build
)
581 depth
= isl_ast_build_get_depth(build
);
583 dom
= isl_set_from_basic_set(isl_basic_set_copy(bounds
));
584 if (isl_ast_build_has_stride(build
, depth
)) {
587 stride
= isl_ast_build_get_stride_constraint(build
);
588 dom
= isl_set_intersect(dom
, stride
);
590 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
591 dom
= isl_ast_build_compute_gist(build
, dom
);
593 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
598 /* Update "graft" based on "bounds" for the eliminated case.
600 * In the eliminated case, no for node is created, so we only need
601 * to check if "bounds" imply any guards that need to be inserted.
603 static __isl_give isl_ast_graft
*refine_eliminated(
604 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
605 __isl_keep isl_ast_build
*build
)
607 return add_degenerate_guard(graft
, bounds
, build
);
610 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
612 * "build" is the build in which graft->node was created
613 * "sub_build" contains information about the current level itself,
614 * including the single value attained.
616 * We first set the initialization part of the for loop to the single
617 * value attained by the current dimension.
618 * The increment and condition are not strictly needed as the are known
619 * to be "1" and "iterator <= value" respectively.
620 * Then we set the size of the iterator and
621 * check if "bounds" imply any guards that need to be inserted.
623 static __isl_give isl_ast_graft
*refine_degenerate(
624 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
625 __isl_keep isl_ast_build
*build
,
626 __isl_keep isl_ast_build
*sub_build
)
630 if (!graft
|| !sub_build
)
631 return isl_ast_graft_free(graft
);
633 value
= isl_pw_aff_copy(sub_build
->value
);
635 graft
->node
->u
.f
.init
= isl_ast_build_expr_from_pw_aff_internal(build
,
637 if (!graft
->node
->u
.f
.init
)
638 return isl_ast_graft_free(graft
);
640 graft
= add_degenerate_guard(graft
, bounds
, build
);
645 /* Return the intersection of the "n" constraints starting at "constraint"
648 static __isl_give isl_set
*intersect_constraints(isl_ctx
*ctx
,
649 __isl_keep isl_constraint
**constraint
, int n
)
655 isl_die(ctx
, isl_error_internal
,
656 "expecting at least one constraint", return NULL
);
658 bset
= isl_basic_set_from_constraint(
659 isl_constraint_copy(constraint
[0]));
660 for (i
= 1; i
< n
; ++i
) {
661 isl_basic_set
*bset_i
;
663 bset_i
= isl_basic_set_from_constraint(
664 isl_constraint_copy(constraint
[i
]));
665 bset
= isl_basic_set_intersect(bset
, bset_i
);
668 return isl_set_from_basic_set(bset
);
671 /* Compute the constraints on the outer dimensions enforced by
672 * graft->node and add those constraints to graft->enforced,
673 * in case the upper bound is expressed as a set "upper".
675 * In particular, if l(...) is a lower bound in "lower", and
677 * -a i + f(...) >= 0 or a i <= f(...)
679 * is an upper bound ocnstraint on the current dimension i,
680 * then the for loop enforces the constraint
682 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
684 * We therefore simply take each lower bound in turn, plug it into
685 * the upper bounds and compute the intersection over all lower bounds.
687 * If a lower bound is a rational expression, then
688 * isl_basic_set_preimage_multi_aff will force this rational
689 * expression to have only integer values. However, the loop
690 * itself does not enforce this integrality constraint. We therefore
691 * use the ceil of the lower bounds instead of the lower bounds themselves.
692 * Other constraints will make sure that the for loop is only executed
693 * when each of the lower bounds attains an integral value.
694 * In particular, potentially rational values only occur in
695 * lower_bound if the offset is a (seemingly) rational expression,
696 * but then outer conditions will make sure that this rational expression
697 * only attains integer values.
699 static __isl_give isl_ast_graft
*set_enforced_from_set(
700 __isl_take isl_ast_graft
*graft
,
701 __isl_keep isl_pw_aff_list
*lower
, int pos
, __isl_keep isl_set
*upper
)
704 isl_basic_set
*enforced
;
705 isl_pw_multi_aff
*pma
;
708 if (!graft
|| !lower
)
709 return isl_ast_graft_free(graft
);
711 space
= isl_set_get_space(upper
);
712 enforced
= isl_basic_set_universe(isl_space_copy(space
));
714 space
= isl_space_map_from_set(space
);
715 pma
= isl_pw_multi_aff_identity(space
);
717 n
= isl_pw_aff_list_n_pw_aff(lower
);
718 for (i
= 0; i
< n
; ++i
) {
722 isl_pw_multi_aff
*pma_i
;
724 pa
= isl_pw_aff_list_get_pw_aff(lower
, i
);
725 pa
= isl_pw_aff_ceil(pa
);
726 pma_i
= isl_pw_multi_aff_copy(pma
);
727 pma_i
= isl_pw_multi_aff_set_pw_aff(pma_i
, pos
, pa
);
728 enforced_i
= isl_set_copy(upper
);
729 enforced_i
= isl_set_preimage_pw_multi_aff(enforced_i
, pma_i
);
730 hull
= isl_set_simple_hull(enforced_i
);
731 enforced
= isl_basic_set_intersect(enforced
, hull
);
734 isl_pw_multi_aff_free(pma
);
736 graft
= isl_ast_graft_enforce(graft
, enforced
);
741 /* Compute the constraints on the outer dimensions enforced by
742 * graft->node and add those constraints to graft->enforced,
743 * in case the upper bound is expressed as
744 * a list of affine expressions "upper".
746 * The enforced condition is that each lower bound expression is less
747 * than or equal to each upper bound expression.
749 static __isl_give isl_ast_graft
*set_enforced_from_list(
750 __isl_take isl_ast_graft
*graft
,
751 __isl_keep isl_pw_aff_list
*lower
, __isl_keep isl_pw_aff_list
*upper
)
754 isl_basic_set
*enforced
;
756 lower
= isl_pw_aff_list_copy(lower
);
757 upper
= isl_pw_aff_list_copy(upper
);
758 cond
= isl_pw_aff_list_le_set(lower
, upper
);
759 enforced
= isl_set_simple_hull(cond
);
760 graft
= isl_ast_graft_enforce(graft
, enforced
);
765 /* Does "aff" have a negative constant term?
767 static int aff_constant_is_negative(__isl_take isl_set
*set
,
768 __isl_take isl_aff
*aff
, void *user
)
774 isl_aff_get_constant(aff
, &v
);
775 *neg
= isl_int_is_neg(v
);
780 return *neg
? 0 : -1;
783 /* Does "pa" have a negative constant term over its entire domain?
785 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff
*pa
, void *user
)
790 r
= isl_pw_aff_foreach_piece(pa
, &aff_constant_is_negative
, user
);
793 return *neg
? 0 : -1;
796 /* Does each element in "list" have a negative constant term?
798 * The callback terminates the iteration as soon an element has been
799 * found that does not have a negative constant term.
801 static int list_constant_is_negative(__isl_keep isl_pw_aff_list
*list
)
805 if (isl_pw_aff_list_foreach(list
,
806 &pw_aff_constant_is_negative
, &neg
) < 0 && neg
)
812 /* Add 1 to each of the elements in "list", where each of these elements
813 * is defined over the internal schedule space of "build".
815 static __isl_give isl_pw_aff_list
*list_add_one(
816 __isl_take isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
823 space
= isl_ast_build_get_space(build
, 1);
824 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(space
));
825 aff
= isl_aff_add_constant_si(aff
, 1);
826 one
= isl_pw_aff_from_aff(aff
);
828 n
= isl_pw_aff_list_n_pw_aff(list
);
829 for (i
= 0; i
< n
; ++i
) {
831 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
832 pa
= isl_pw_aff_add(pa
, isl_pw_aff_copy(one
));
833 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
836 isl_pw_aff_free(one
);
841 /* Set the condition part of the for node graft->node in case
842 * the upper bound is represented as a list of piecewise affine expressions.
844 * In particular, set the condition to
846 * iterator <= min(list of upper bounds)
848 * If each of the upper bounds has a negative constant term, then
849 * set the condition to
851 * iterator < min(list of (upper bound + 1)s)
854 static __isl_give isl_ast_graft
*set_for_cond_from_list(
855 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*list
,
856 __isl_keep isl_ast_build
*build
)
859 isl_ast_expr
*bound
, *iterator
, *cond
;
860 enum isl_ast_op_type type
= isl_ast_op_le
;
863 return isl_ast_graft_free(graft
);
865 neg
= list_constant_is_negative(list
);
867 return isl_ast_graft_free(graft
);
868 list
= isl_pw_aff_list_copy(list
);
870 list
= list_add_one(list
, build
);
871 type
= isl_ast_op_lt
;
874 bound
= reduce_list(isl_ast_op_min
, list
, build
);
875 iterator
= isl_ast_expr_copy(graft
->node
->u
.f
.iterator
);
876 cond
= isl_ast_expr_alloc_binary(type
, iterator
, bound
);
877 graft
->node
->u
.f
.cond
= cond
;
879 isl_pw_aff_list_free(list
);
880 if (!graft
->node
->u
.f
.cond
)
881 return isl_ast_graft_free(graft
);
885 /* Set the condition part of the for node graft->node in case
886 * the upper bound is represented as a set.
888 static __isl_give isl_ast_graft
*set_for_cond_from_set(
889 __isl_take isl_ast_graft
*graft
, __isl_keep isl_set
*set
,
890 __isl_keep isl_ast_build
*build
)
897 cond
= isl_ast_build_expr_from_set(build
, isl_set_copy(set
));
898 graft
->node
->u
.f
.cond
= cond
;
899 if (!graft
->node
->u
.f
.cond
)
900 return isl_ast_graft_free(graft
);
904 /* Construct an isl_ast_expr for the increment (i.e., stride) of
905 * the current dimension.
907 static __isl_give isl_ast_expr
*for_inc(__isl_keep isl_ast_build
*build
)
916 ctx
= isl_ast_build_get_ctx(build
);
917 depth
= isl_ast_build_get_depth(build
);
919 if (!isl_ast_build_has_stride(build
, depth
))
920 return isl_ast_expr_alloc_int_si(ctx
, 1);
923 isl_ast_build_get_stride(build
, depth
, &v
);
924 inc
= isl_ast_expr_alloc_int(ctx
, v
);
930 /* Should we express the loop condition as
932 * iterator <= min(list of upper bounds)
934 * or as a conjunction of constraints?
936 * The first is constructed from a list of upper bounds.
937 * The second is constructed from a set.
939 * If there are no upper bounds in "constraints", then this could mean
940 * that "domain" simply doesn't have an upper bound or that we didn't
941 * pick any upper bound. In the first case, we want to generate the
942 * loop condition as a(n empty) conjunction of constraints
943 * In the second case, we will compute
944 * a single upper bound from "domain" and so we use the list form.
946 * If there are upper bounds in "constraints",
947 * then we use the list form iff the atomic_upper_bound option is set.
949 static int use_upper_bound_list(isl_ctx
*ctx
, int n_upper
,
950 __isl_keep isl_set
*domain
, int depth
)
953 return isl_options_get_ast_build_atomic_upper_bound(ctx
);
955 return isl_set_dim_has_upper_bound(domain
, isl_dim_set
, depth
);
958 /* Fill in the expressions of the for node in graft->node.
961 * - set the initialization part of the loop to the maximum of the lower bounds
962 * - set the size of the iterator based on the values attained by the iterator
963 * - extract the increment from the stride of the current dimension
964 * - construct the for condition either based on a list of upper bounds
965 * or on a set of upper bound constraints.
967 static __isl_give isl_ast_graft
*set_for_node_expressions(
968 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*lower
,
969 int use_list
, __isl_keep isl_pw_aff_list
*upper_list
,
970 __isl_keep isl_set
*upper_set
, __isl_keep isl_ast_build
*build
)
977 build
= isl_ast_build_copy(build
);
978 build
= isl_ast_build_set_enforced(build
,
979 isl_ast_graft_get_enforced(graft
));
982 node
->u
.f
.init
= reduce_list(isl_ast_op_max
, lower
, build
);
983 node
->u
.f
.inc
= for_inc(build
);
986 graft
= set_for_cond_from_list(graft
, upper_list
, build
);
988 graft
= set_for_cond_from_set(graft
, upper_set
, build
);
990 isl_ast_build_free(build
);
992 if (!node
->u
.f
.iterator
|| !node
->u
.f
.init
||
993 !node
->u
.f
.cond
|| !node
->u
.f
.inc
)
994 return isl_ast_graft_free(graft
);
999 /* Update "graft" based on "bounds" and "domain" for the generic,
1000 * non-degenerate, case.
1002 * "constraints" contains the "n_lower" lower and "n_upper" upper bounds
1003 * that the loop node should express.
1004 * "domain" is the subset of the intersection of the constraints
1005 * for which some code is executed.
1007 * There may be zero lower bounds or zero upper bounds in "constraints"
1008 * in case the list of constraints was created
1009 * based on the atomic option or based on separation with explicit bounds.
1010 * In that case, we use "domain" to derive lower and/or upper bounds.
1012 * We first compute a list of one or more lower bounds.
1014 * Then we decide if we want to express the condition as
1016 * iterator <= min(list of upper bounds)
1018 * or as a conjunction of constraints.
1020 * The set of enforced constraints is then computed either based on
1021 * a list of upper bounds or on a set of upper bound constraints.
1022 * We do not compute any enforced constraints if we were forced
1023 * to compute a lower or upper bound using exact_bound. The domains
1024 * of the resulting expressions may imply some bounds on outer dimensions
1025 * that we do not want to appear in the enforced constraints since
1026 * they are not actually enforced by the corresponding code.
1028 * Finally, we fill in the expressions of the for node.
1030 static __isl_give isl_ast_graft
*refine_generic_bounds(
1031 __isl_take isl_ast_graft
*graft
,
1032 __isl_keep isl_constraint
**constraint
, int n_lower
, int n_upper
,
1033 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1037 isl_pw_aff_list
*lower
;
1039 isl_set
*upper_set
= NULL
;
1040 isl_pw_aff_list
*upper_list
= NULL
;
1042 if (!graft
|| !build
)
1043 return isl_ast_graft_free(graft
);
1045 depth
= isl_ast_build_get_depth(build
);
1046 ctx
= isl_ast_graft_get_ctx(graft
);
1048 use_list
= use_upper_bound_list(ctx
, n_upper
, domain
, depth
);
1050 lower
= lower_bounds(constraint
, n_lower
, depth
, domain
, build
);
1053 upper_list
= upper_bounds(constraint
+ n_lower
, n_upper
, depth
,
1055 else if (n_upper
> 0)
1056 upper_set
= intersect_constraints(ctx
, constraint
+ n_lower
,
1059 upper_set
= isl_set_universe(isl_set_get_space(domain
));
1061 if (n_lower
== 0 || n_upper
== 0)
1064 graft
= set_enforced_from_list(graft
, lower
, upper_list
);
1066 graft
= set_enforced_from_set(graft
, lower
, depth
, upper_set
);
1068 graft
= set_for_node_expressions(graft
, lower
, use_list
, upper_list
,
1071 isl_pw_aff_list_free(lower
);
1072 isl_pw_aff_list_free(upper_list
);
1073 isl_set_free(upper_set
);
1078 /* How many constraints in the "constraint" array, starting at position "first"
1079 * are of the give type? "n" represents the total number of elements
1082 static int count_constraints(isl_constraint
**constraint
, int n
, int first
,
1087 constraint
+= first
;
1089 for (i
= 0; first
+ i
< n
; i
++)
1090 if (constraint_type(constraint
[i
], pos
) != type
)
1096 /* Update "graft" based on "bounds" and "domain" for the generic,
1097 * non-degenerate, case.
1099 * "list" respresent the list of bounds that need to be encoded by
1100 * the for loop (or a guard around the for loop).
1101 * "domain" is the subset of the intersection of the constraints
1102 * for which some code is executed.
1103 * "build" is the build in which graft->node was created.
1105 * We separate lower bounds, upper bounds and constraints that
1106 * are independent of the loop iterator.
1108 * The actual for loop bounds are generated in refine_generic_bounds.
1109 * If there are any constraints that are independent of the loop iterator,
1110 * we need to put a guard around the for loop (which may get hoisted up
1111 * to higher levels) and we call refine_generic_bounds in a build
1112 * where this guard is enforced.
1114 static __isl_give isl_ast_graft
*refine_generic_split(
1115 __isl_take isl_ast_graft
*graft
, __isl_keep isl_constraint_list
*list
,
1116 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1119 isl_ast_build
*for_build
;
1121 int n_indep
, n_lower
, n_upper
;
1126 return isl_ast_graft_free(graft
);
1128 pos
= isl_ast_build_get_depth(build
);
1130 if (isl_sort(list
->p
, list
->n
, sizeof(isl_constraint
*),
1131 &cmp_constraint
, &pos
) < 0)
1132 return isl_ast_graft_free(graft
);
1135 n_indep
= count_constraints(list
->p
, n
, 0, pos
, 0);
1136 n_lower
= count_constraints(list
->p
, n
, n_indep
, pos
, 1);
1137 n_upper
= count_constraints(list
->p
, n
, n_indep
+ n_lower
, pos
, 2);
1140 return refine_generic_bounds(graft
,
1141 list
->p
+ n_indep
, n_lower
, n_upper
, domain
, build
);
1143 ctx
= isl_ast_graft_get_ctx(graft
);
1144 guard
= intersect_constraints(ctx
, list
->p
, n_indep
);
1146 for_build
= isl_ast_build_copy(build
);
1147 for_build
= isl_ast_build_restrict_pending(for_build
,
1148 isl_set_copy(guard
));
1149 graft
= refine_generic_bounds(graft
,
1150 list
->p
+ n_indep
, n_lower
, n_upper
, domain
, for_build
);
1151 isl_ast_build_free(for_build
);
1153 graft
= isl_ast_graft_add_guard(graft
, guard
, build
);
1158 /* Update "graft" based on "bounds" and "domain" for the generic,
1159 * non-degenerate, case.
1161 * "bounds" respresent the bounds that need to be encoded by
1162 * the for loop (or a guard around the for loop).
1163 * "domain" is the subset of "bounds" for which some code is executed.
1164 * "build" is the build in which graft->node was created.
1166 * We break up "bounds" into a list of constraints and continue with
1167 * refine_generic_split.
1169 static __isl_give isl_ast_graft
*refine_generic(
1170 __isl_take isl_ast_graft
*graft
,
1171 __isl_keep isl_basic_set
*bounds
, __isl_keep isl_set
*domain
,
1172 __isl_keep isl_ast_build
*build
)
1174 isl_constraint_list
*list
;
1176 if (!build
|| !graft
)
1177 return isl_ast_graft_free(graft
);
1179 bounds
= isl_basic_set_copy(bounds
);
1180 bounds
= isl_ast_build_compute_gist_basic_set(build
, bounds
);
1181 list
= isl_constraint_list_from_basic_set(bounds
);
1183 graft
= refine_generic_split(graft
, list
, domain
, build
);
1185 isl_constraint_list_free(list
);
1189 /* Create a for node for the current level.
1191 * Mark the for node degenerate if "degenerate" is set.
1193 static __isl_give isl_ast_node
*create_for(__isl_keep isl_ast_build
*build
,
1203 depth
= isl_ast_build_get_depth(build
);
1204 id
= isl_ast_build_get_iterator_id(build
, depth
);
1205 node
= isl_ast_node_alloc_for(id
);
1207 node
= isl_ast_node_for_mark_degenerate(node
);
1212 /* Create an AST node for the current dimension based on
1213 * the schedule domain "bounds" and return the node encapsulated
1214 * in an isl_ast_graft.
1216 * "executed" is the current inverse schedule, taking into account
1217 * the bounds in "bounds"
1218 * "domain" is the domain of "executed", with inner dimensions projected out.
1219 * It may be a strict subset of "bounds" in case "bounds" was created
1220 * based on the atomic option or based on separation with explicit bounds.
1222 * "domain" may satisfy additional equalities that result
1223 * from intersecting "executed" with "bounds" in add_node.
1224 * It may also satisfy some global constraints that were dropped out because
1225 * we performed separation with explicit bounds.
1226 * The very first step is then to copy these constraints to "bounds".
1228 * Since we may be calling before_each_for and after_each_for
1229 * callbacks, we record the current inverse schedule in the build.
1231 * We consider three builds,
1232 * "build" is the one in which the current level is created,
1233 * "body_build" is the build in which the next level is created,
1234 * "sub_build" is essentially the same as "body_build", except that
1235 * the depth has not been increased yet.
1237 * "build" already contains information (in strides and offsets)
1238 * about the strides at the current level, but this information is not
1239 * reflected in the build->domain.
1240 * We first add this information and the "bounds" to the sub_build->domain.
1241 * isl_ast_build_set_loop_bounds checks whether the current dimension attains
1242 * only a single value and whether this single value can be represented using
1243 * a single affine expression.
1244 * In the first case, the current level is considered "degenerate".
1245 * In the second, sub-case, the current level is considered "eliminated".
1246 * Eliminated level don't need to be reflected in the AST since we can
1247 * simply plug in the affine expression. For degenerate, but non-eliminated,
1248 * levels, we do introduce a for node, but mark is as degenerate so that
1249 * it can be printed as an assignment of the single value to the loop
1252 * If the current level is eliminated, we eliminate the current dimension
1253 * from the inverse schedule to make sure no inner dimensions depend
1254 * on the current dimension. Otherwise, we create a for node, marking
1255 * it degenerate if appropriate. The initial for node is still incomplete
1256 * and will be completed in either refine_degenerate or refine_generic.
1258 * We then generate a sequence of grafts for the next level,
1259 * create a surrounding graft for the current level and insert
1260 * the for node we created (if the current level is not eliminated).
1262 * Finally, we set the bounds of the for loop and insert guards
1263 * (either in the AST or in the graft) in one of
1264 * refine_eliminated, refine_degenerate or refine_generic.
1266 static __isl_give isl_ast_graft
*create_node_scaled(
1267 __isl_take isl_union_map
*executed
,
1268 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1269 __isl_take isl_ast_build
*build
)
1272 int degenerate
, eliminated
;
1273 isl_basic_set
*hull
;
1274 isl_ast_node
*node
= NULL
;
1275 isl_ast_graft
*graft
;
1276 isl_ast_graft_list
*children
;
1277 isl_ast_build
*sub_build
;
1278 isl_ast_build
*body_build
;
1280 domain
= isl_ast_build_eliminate_divs(build
, domain
);
1281 domain
= isl_set_detect_equalities(domain
);
1282 hull
= isl_set_unshifted_simple_hull(isl_set_copy(domain
));
1283 bounds
= isl_basic_set_intersect(bounds
, hull
);
1284 build
= isl_ast_build_set_executed(build
, isl_union_map_copy(executed
));
1286 depth
= isl_ast_build_get_depth(build
);
1287 sub_build
= isl_ast_build_copy(build
);
1288 sub_build
= isl_ast_build_include_stride(sub_build
);
1289 sub_build
= isl_ast_build_set_loop_bounds(sub_build
,
1290 isl_basic_set_copy(bounds
));
1291 degenerate
= isl_ast_build_has_value(sub_build
);
1292 eliminated
= isl_ast_build_has_affine_value(sub_build
, depth
);
1293 if (degenerate
< 0 || eliminated
< 0)
1294 executed
= isl_union_map_free(executed
);
1296 executed
= eliminate(executed
, depth
, build
);
1298 node
= create_for(build
, degenerate
);
1300 body_build
= isl_ast_build_copy(sub_build
);
1301 body_build
= isl_ast_build_increase_depth(body_build
);
1303 node
= before_each_for(node
, body_build
);
1304 children
= generate_next_level(executed
,
1305 isl_ast_build_copy(body_build
));
1307 graft
= isl_ast_graft_alloc_level(children
, build
, sub_build
);
1309 graft
= isl_ast_graft_insert_for(graft
, node
);
1311 graft
= refine_eliminated(graft
, bounds
, build
);
1312 else if (degenerate
)
1313 graft
= refine_degenerate(graft
, bounds
, build
, sub_build
);
1315 graft
= refine_generic(graft
, bounds
, domain
, build
);
1317 graft
= after_each_for(graft
, body_build
);
1319 isl_ast_build_free(body_build
);
1320 isl_ast_build_free(sub_build
);
1321 isl_ast_build_free(build
);
1322 isl_basic_set_free(bounds
);
1323 isl_set_free(domain
);
1328 /* Internal data structure for checking if all constraints involving
1329 * the input dimension "depth" are such that the other coefficients
1330 * are multiples of "m", reducing "m" if they are not.
1331 * If "m" is reduced all the way down to "1", then the check has failed
1332 * and we break out of the iteration.
1333 * "d" is an initialized isl_int that can be used internally.
1335 struct isl_check_scaled_data
{
1340 /* If constraint "c" involves the input dimension data->depth,
1341 * then make sure that all the other coefficients are multiples of data->m,
1342 * reducing data->m if needed.
1343 * Break out of the iteration if data->m has become equal to "1".
1345 static int constraint_check_scaled(__isl_take isl_constraint
*c
, void *user
)
1347 struct isl_check_scaled_data
*data
= user
;
1349 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_out
,
1352 if (!isl_constraint_involves_dims(c
, isl_dim_in
, data
->depth
, 1)) {
1353 isl_constraint_free(c
);
1357 for (i
= 0; i
< 4; ++i
) {
1358 n
= isl_constraint_dim(c
, t
[i
]);
1359 for (j
= 0; j
< n
; ++j
) {
1360 if (t
[i
] == isl_dim_in
&& j
== data
->depth
)
1362 if (!isl_constraint_involves_dims(c
, t
[i
], j
, 1))
1364 isl_constraint_get_coefficient(c
, t
[i
], j
, &data
->d
);
1365 isl_int_gcd(data
->m
, data
->m
, data
->d
);
1366 if (isl_int_is_one(data
->m
))
1373 isl_constraint_free(c
);
1375 return i
< 4 ? -1 : 0;
1378 /* For each constraint of "bmap" 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 basic_map_check_scaled(__isl_take isl_basic_map
*bmap
, void *user
)
1387 r
= isl_basic_map_foreach_constraint(bmap
,
1388 &constraint_check_scaled
, user
);
1389 isl_basic_map_free(bmap
);
1394 /* For each constraint of "map" that involves the input dimension data->depth,
1395 * make sure that all the other coefficients are multiples of data->m,
1396 * reducing data->m if needed.
1397 * Break out of the iteration if data->m has become equal to "1".
1399 static int map_check_scaled(__isl_take isl_map
*map
, void *user
)
1403 r
= isl_map_foreach_basic_map(map
, &basic_map_check_scaled
, user
);
1409 /* Create an AST node for the current dimension based on
1410 * the schedule domain "bounds" and return the node encapsulated
1411 * in an isl_ast_graft.
1413 * "executed" is the current inverse schedule, taking into account
1414 * the bounds in "bounds"
1415 * "domain" is the domain of "executed", with inner dimensions projected out.
1418 * Before moving on to the actual AST node construction in create_node_scaled,
1419 * we first check if the current dimension is strided and if we can scale
1420 * down this stride. Note that we only do this if the ast_build_scale_strides
1423 * In particular, let the current dimension take on values
1427 * with a an integer. We check if we can find an integer m that (obviouly)
1428 * divides both f and s.
1430 * If so, we check if the current dimension only appears in constraints
1431 * where the coefficients of the other variables are multiples of m.
1432 * We perform this extra check to avoid the risk of introducing
1433 * divisions by scaling down the current dimension.
1435 * If so, we scale the current dimension down by a factor of m.
1436 * That is, we plug in
1440 * Note that in principle we could always scale down strided loops
1445 * but this may result in i' taking on larger values than the original i,
1446 * due to the shift by "f".
1447 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1449 static __isl_give isl_ast_graft
*create_node(__isl_take isl_union_map
*executed
,
1450 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1451 __isl_take isl_ast_build
*build
)
1453 struct isl_check_scaled_data data
;
1457 ctx
= isl_ast_build_get_ctx(build
);
1458 if (!isl_options_get_ast_build_scale_strides(ctx
))
1459 return create_node_scaled(executed
, bounds
, domain
, build
);
1461 data
.depth
= isl_ast_build_get_depth(build
);
1462 if (!isl_ast_build_has_stride(build
, data
.depth
))
1463 return create_node_scaled(executed
, bounds
, domain
, build
);
1465 isl_int_init(data
.m
);
1466 isl_int_init(data
.d
);
1468 offset
= isl_ast_build_get_offset(build
, data
.depth
);
1469 if (isl_ast_build_get_stride(build
, data
.depth
, &data
.m
) < 0)
1470 offset
= isl_aff_free(offset
);
1471 offset
= isl_aff_scale_down(offset
, data
.m
);
1472 if (isl_aff_get_denominator(offset
, &data
.d
) < 0)
1473 executed
= isl_union_map_free(executed
);
1475 if (executed
&& isl_int_is_divisible_by(data
.m
, data
.d
))
1476 isl_int_divexact(data
.m
, data
.m
, data
.d
);
1478 isl_int_set_si(data
.m
, 1);
1480 if (!isl_int_is_one(data
.m
)) {
1481 if (isl_union_map_foreach_map(executed
, &map_check_scaled
,
1483 !isl_int_is_one(data
.m
))
1484 executed
= isl_union_map_free(executed
);
1487 if (!isl_int_is_one(data
.m
)) {
1492 isl_union_map
*umap
;
1494 space
= isl_ast_build_get_space(build
, 1);
1495 space
= isl_space_map_from_set(space
);
1496 ma
= isl_multi_aff_identity(space
);
1497 aff
= isl_multi_aff_get_aff(ma
, data
.depth
);
1498 aff
= isl_aff_scale(aff
, data
.m
);
1499 ma
= isl_multi_aff_set_aff(ma
, data
.depth
, aff
);
1501 bounds
= isl_basic_set_preimage_multi_aff(bounds
,
1502 isl_multi_aff_copy(ma
));
1503 domain
= isl_set_preimage_multi_aff(domain
,
1504 isl_multi_aff_copy(ma
));
1505 map
= isl_map_reverse(isl_map_from_multi_aff(ma
));
1506 umap
= isl_union_map_from_map(map
);
1507 executed
= isl_union_map_apply_domain(executed
,
1508 isl_union_map_copy(umap
));
1509 build
= isl_ast_build_scale_down(build
, data
.m
, umap
);
1511 isl_aff_free(offset
);
1513 isl_int_clear(data
.d
);
1514 isl_int_clear(data
.m
);
1516 return create_node_scaled(executed
, bounds
, domain
, build
);
1519 /* Add the basic set to the list that "user" points to.
1521 static int collect_basic_set(__isl_take isl_basic_set
*bset
, void *user
)
1523 isl_basic_set_list
**list
= user
;
1525 *list
= isl_basic_set_list_add(*list
, bset
);
1530 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1532 static __isl_give isl_basic_set_list
*isl_basic_set_list_from_set(
1533 __isl_take isl_set
*set
)
1537 isl_basic_set_list
*list
;
1542 ctx
= isl_set_get_ctx(set
);
1544 n
= isl_set_n_basic_set(set
);
1545 list
= isl_basic_set_list_alloc(ctx
, n
);
1546 if (isl_set_foreach_basic_set(set
, &collect_basic_set
, &list
) < 0)
1547 list
= isl_basic_set_list_free(list
);
1553 /* Generate code for the schedule domain "bounds"
1554 * and add the result to "list".
1556 * We mainly detect strides and additional equalities here
1557 * and then pass over control to create_node.
1559 * "bounds" reflects the bounds on the current dimension and possibly
1560 * some extra conditions on outer dimensions.
1561 * It does not, however, include any divs involving the current dimension,
1562 * so it does not capture any stride constraints.
1563 * We therefore need to compute that part of the schedule domain that
1564 * intersects with "bounds" and derive the strides from the result.
1566 static __isl_give isl_ast_graft_list
*add_node(
1567 __isl_take isl_ast_graft_list
*list
, __isl_take isl_union_map
*executed
,
1568 __isl_take isl_basic_set
*bounds
, __isl_take isl_ast_build
*build
)
1570 isl_ast_graft
*graft
;
1571 isl_set
*domain
= NULL
;
1572 isl_union_set
*uset
;
1575 uset
= isl_union_set_from_basic_set(isl_basic_set_copy(bounds
));
1576 executed
= isl_union_map_intersect_domain(executed
, uset
);
1577 empty
= isl_union_map_is_empty(executed
);
1583 uset
= isl_union_map_domain(isl_union_map_copy(executed
));
1584 domain
= isl_set_from_union_set(uset
);
1585 domain
= isl_ast_build_compute_gist(build
, domain
);
1586 empty
= isl_set_is_empty(domain
);
1592 domain
= isl_ast_build_eliminate_inner(build
, domain
);
1593 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
1595 graft
= create_node(executed
, bounds
, domain
,
1596 isl_ast_build_copy(build
));
1597 list
= isl_ast_graft_list_add(list
, graft
);
1598 isl_ast_build_free(build
);
1601 list
= isl_ast_graft_list_free(list
);
1603 isl_set_free(domain
);
1604 isl_basic_set_free(bounds
);
1605 isl_union_map_free(executed
);
1606 isl_ast_build_free(build
);
1610 struct isl_domain_follows_at_depth_data
{
1612 isl_basic_set
**piece
;
1615 /* Does any element of i follow or coincide with any element of j
1616 * at the current depth (data->depth) for equal values of the outer
1619 static int domain_follows_at_depth(int i
, int j
, void *user
)
1621 struct isl_domain_follows_at_depth_data
*data
= user
;
1622 isl_basic_map
*test
;
1626 test
= isl_basic_map_from_domain_and_range(
1627 isl_basic_set_copy(data
->piece
[i
]),
1628 isl_basic_set_copy(data
->piece
[j
]));
1629 for (l
= 0; l
< data
->depth
; ++l
)
1630 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1632 test
= isl_basic_map_order_ge(test
, isl_dim_in
, data
->depth
,
1633 isl_dim_out
, data
->depth
);
1634 empty
= isl_basic_map_is_empty(test
);
1635 isl_basic_map_free(test
);
1637 return empty
< 0 ? -1 : !empty
;
1640 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1641 __isl_keep isl_basic_set_list
*domain_list
,
1642 __isl_keep isl_union_map
*executed
,
1643 __isl_keep isl_ast_build
*build
);
1645 /* Generate code for the "n" schedule domains in "domain_list"
1646 * with positions specified by the entries of the "pos" array
1647 * and add the results to "list".
1649 * The "n" domains form a strongly connected component in the ordering.
1650 * If n is larger than 1, then this means that we cannot determine a valid
1651 * ordering for the n domains in the component. This should be fairly
1652 * rare because the individual domains have been made disjoint first.
1653 * The problem is that the domains may be integrally disjoint but not
1654 * rationally disjoint. For example, we may have domains
1656 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1658 * These two domains have an empty intersection, but their rational
1659 * relaxations do intersect. It is impossible to order these domains
1660 * in the second dimension because the first should be ordered before
1661 * the second for outer dimension equal to 0, while it should be ordered
1662 * after for outer dimension equal to 1.
1664 * This may happen in particular in case of unrolling since the domain
1665 * of each slice is replaced by its simple hull.
1667 * We collect the basic sets in the component, call isl_set_make_disjoint
1668 * and try again. Note that we rely here on isl_set_make_disjoint also
1669 * making the basic sets rationally disjoint. If the basic sets
1670 * are rationally disjoint, then the ordering problem does not occur.
1671 * To see this, there can only be a problem if there are points
1672 * (i,a) and (j,b) in one set and (i,c) and (j,d) in the other with
1673 * a < c and b > d. This means that either the interval spanned
1674 * by a en b lies inside that spanned by c and or the other way around.
1675 * In either case, there is a point inside both intervals with the
1676 * convex combination in terms of a and b and in terms of c and d.
1677 * Taking the same combination of i and j gives a point in the intersection.
1679 static __isl_give isl_ast_graft_list
*add_nodes(
1680 __isl_take isl_ast_graft_list
*list
, int *pos
, int n
,
1681 __isl_keep isl_basic_set_list
*domain_list
,
1682 __isl_keep isl_union_map
*executed
,
1683 __isl_keep isl_ast_build
*build
)
1686 isl_basic_set
*bset
;
1689 bset
= isl_basic_set_list_get_basic_set(domain_list
, pos
[0]);
1691 return add_node(list
, isl_union_map_copy(executed
), bset
,
1692 isl_ast_build_copy(build
));
1694 set
= isl_set_from_basic_set(bset
);
1695 for (i
= 1; i
< n
; ++i
) {
1696 bset
= isl_basic_set_list_get_basic_set(domain_list
, pos
[i
]);
1697 set
= isl_set_union(set
, isl_set_from_basic_set(bset
));
1700 set
= isl_set_make_disjoint(set
);
1701 if (isl_set_n_basic_set(set
) == n
)
1702 isl_die(isl_ast_graft_list_get_ctx(list
), isl_error_internal
,
1703 "unable to separate loop parts", goto error
);
1704 domain_list
= isl_basic_set_list_from_set(set
);
1705 list
= isl_ast_graft_list_concat(list
,
1706 generate_sorted_domains(domain_list
, executed
, build
));
1707 isl_basic_set_list_free(domain_list
);
1712 return isl_ast_graft_list_free(list
);
1715 /* Sort the domains in "domain_list" according to the execution order
1716 * at the current depth (for equal values of the outer dimensions),
1717 * generate code for each of them, collecting the results in a list.
1718 * If no code is generated (because the intersection of the inverse schedule
1719 * with the domains turns out to be empty), then an empty list is returned.
1721 * The caller is responsible for ensuring that the basic sets in "domain_list"
1722 * are pair-wise disjoint. It can, however, in principle happen that
1723 * two basic sets should be ordered one way for one value of the outer
1724 * dimensions and the other way for some other value of the outer dimensions.
1725 * We therefore play safe and look for strongly connected components.
1726 * The function add_nodes takes care of handling non-trivial components.
1728 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1729 __isl_keep isl_basic_set_list
*domain_list
,
1730 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1733 isl_ast_graft_list
*list
;
1734 struct isl_domain_follows_at_depth_data data
;
1735 struct isl_tarjan_graph
*g
;
1741 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1742 n
= isl_basic_set_list_n_basic_set(domain_list
);
1743 list
= isl_ast_graft_list_alloc(ctx
, n
);
1747 return add_node(list
, isl_union_map_copy(executed
),
1748 isl_basic_set_list_get_basic_set(domain_list
, 0),
1749 isl_ast_build_copy(build
));
1751 data
.depth
= isl_ast_build_get_depth(build
);
1752 data
.piece
= domain_list
->p
;
1753 g
= isl_tarjan_graph_init(ctx
, n
, &domain_follows_at_depth
, &data
);
1761 if (g
->order
[i
] == -1)
1762 isl_die(ctx
, isl_error_internal
, "cannot happen",
1765 while (g
->order
[i
] != -1) {
1768 list
= add_nodes(list
, g
->order
+ first
, i
- first
,
1769 domain_list
, executed
, build
);
1774 error
: list
= isl_ast_graft_list_free(list
);
1775 isl_tarjan_graph_free(g
);
1780 struct isl_shared_outer_data
{
1782 isl_basic_set
**piece
;
1785 /* Do elements i and j share any values for the outer dimensions?
1787 static int shared_outer(int i
, int j
, void *user
)
1789 struct isl_shared_outer_data
*data
= user
;
1790 isl_basic_map
*test
;
1794 test
= isl_basic_map_from_domain_and_range(
1795 isl_basic_set_copy(data
->piece
[i
]),
1796 isl_basic_set_copy(data
->piece
[j
]));
1797 for (l
= 0; l
< data
->depth
; ++l
)
1798 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1800 empty
= isl_basic_map_is_empty(test
);
1801 isl_basic_map_free(test
);
1803 return empty
< 0 ? -1 : !empty
;
1806 /* Call generate_sorted_domains on a list containing the elements
1807 * of "domain_list indexed by the first "n" elements of "pos".
1809 static __isl_give isl_ast_graft_list
*generate_sorted_domains_part(
1810 __isl_keep isl_basic_set_list
*domain_list
, int *pos
, int n
,
1811 __isl_keep isl_union_map
*executed
,
1812 __isl_keep isl_ast_build
*build
)
1816 isl_basic_set_list
*slice
;
1817 isl_ast_graft_list
*list
;
1819 ctx
= isl_ast_build_get_ctx(build
);
1820 slice
= isl_basic_set_list_alloc(ctx
, n
);
1821 for (i
= 0; i
< n
; ++i
) {
1822 isl_basic_set
*bset
;
1824 bset
= isl_basic_set_copy(domain_list
->p
[pos
[i
]]);
1825 slice
= isl_basic_set_list_add(slice
, bset
);
1828 list
= generate_sorted_domains(slice
, executed
, build
);
1829 isl_basic_set_list_free(slice
);
1834 /* Look for any (weakly connected) components in the "domain_list"
1835 * of domains that share some values of the outer dimensions.
1836 * That is, domains in different components do not share any values
1837 * of the outer dimensions. This means that these components
1838 * can be freely reorderd.
1839 * Within each of the components, we sort the domains according
1840 * to the execution order at the current depth.
1842 * We fuse the result of each call to generate_sorted_domains_part
1843 * into a list with either zero or one graft and collect these (at most)
1844 * single element lists into a bigger list. This means that the elements of the
1845 * final list can be freely reordered. In particular, we sort them
1846 * according to an arbitrary but fixed ordering to ease merging of
1847 * graft lists from different components.
1849 static __isl_give isl_ast_graft_list
*generate_parallel_domains(
1850 __isl_keep isl_basic_set_list
*domain_list
,
1851 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1855 isl_ast_graft_list
*list
;
1856 struct isl_shared_outer_data data
;
1857 struct isl_tarjan_graph
*g
;
1862 n
= isl_basic_set_list_n_basic_set(domain_list
);
1864 return generate_sorted_domains(domain_list
, executed
, build
);
1866 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1868 data
.depth
= isl_ast_build_get_depth(build
);
1869 data
.piece
= domain_list
->p
;
1870 g
= isl_tarjan_graph_init(ctx
, n
, &shared_outer
, &data
);
1877 isl_ast_graft_list
*list_c
;
1879 if (g
->order
[i
] == -1)
1880 isl_die(ctx
, isl_error_internal
, "cannot happen",
1883 while (g
->order
[i
] != -1) {
1886 if (first
== 0 && n
== 0) {
1887 isl_tarjan_graph_free(g
);
1888 return generate_sorted_domains(domain_list
,
1891 list_c
= generate_sorted_domains_part(domain_list
,
1892 g
->order
+ first
, i
- first
, executed
, build
);
1893 list_c
= isl_ast_graft_list_fuse(list_c
, build
);
1897 list
= isl_ast_graft_list_concat(list
, list_c
);
1899 } while (list
&& n
);
1902 list
= isl_ast_graft_list_free(list
);
1904 list
= isl_ast_graft_list_sort(list
);
1906 isl_tarjan_graph_free(g
);
1911 /* Internal data for separate_domain.
1913 * "explicit" is set if we only want to use explicit bounds.
1915 * "domain" collects the separated domains.
1917 struct isl_separate_domain_data
{
1918 isl_ast_build
*build
;
1923 /* Extract implicit bounds on the current dimension for the executed "map".
1925 * The domain of "map" may involve inner dimensions, so we
1926 * need to eliminate them.
1928 static __isl_give isl_set
*implicit_bounds(__isl_take isl_map
*map
,
1929 __isl_keep isl_ast_build
*build
)
1933 domain
= isl_map_domain(map
);
1934 domain
= isl_ast_build_eliminate(build
, domain
);
1939 /* Extract explicit bounds on the current dimension for the executed "map".
1941 * Rather than eliminating the inner dimensions as in implicit_bounds,
1942 * we simply drop any constraints involving those inner dimensions.
1943 * The idea is that most bounds that are implied by constraints on the
1944 * inner dimensions will be enforced by for loops and not by explicit guards.
1945 * There is then no need to separate along those bounds.
1947 static __isl_give isl_set
*explicit_bounds(__isl_take isl_map
*map
,
1948 __isl_keep isl_ast_build
*build
)
1953 dim
= isl_map_dim(map
, isl_dim_out
);
1954 map
= isl_map_drop_constraints_involving_dims(map
, isl_dim_out
, 0, dim
);
1956 domain
= isl_map_domain(map
);
1957 depth
= isl_ast_build_get_depth(build
);
1958 dim
= isl_set_dim(domain
, isl_dim_set
);
1959 domain
= isl_set_detect_equalities(domain
);
1960 domain
= isl_set_drop_constraints_involving_dims(domain
,
1961 isl_dim_set
, depth
+ 1, dim
- (depth
+ 1));
1962 domain
= isl_set_remove_divs_involving_dims(domain
,
1963 isl_dim_set
, depth
, 1);
1964 domain
= isl_set_remove_unknown_divs(domain
);
1969 /* Split data->domain into pieces that intersect with the range of "map"
1970 * and pieces that do not intersect with the range of "map"
1971 * and then add that part of the range of "map" that does not intersect
1972 * with data->domain.
1974 static int separate_domain(__isl_take isl_map
*map
, void *user
)
1976 struct isl_separate_domain_data
*data
= user
;
1981 domain
= explicit_bounds(map
, data
->build
);
1983 domain
= implicit_bounds(map
, data
->build
);
1985 domain
= isl_set_coalesce(domain
);
1986 domain
= isl_set_make_disjoint(domain
);
1987 d1
= isl_set_subtract(isl_set_copy(domain
), isl_set_copy(data
->domain
));
1988 d2
= isl_set_subtract(isl_set_copy(data
->domain
), isl_set_copy(domain
));
1989 data
->domain
= isl_set_intersect(data
->domain
, domain
);
1990 data
->domain
= isl_set_union(data
->domain
, d1
);
1991 data
->domain
= isl_set_union(data
->domain
, d2
);
1996 /* Separate the schedule domains of "executed".
1998 * That is, break up the domain of "executed" into basic sets,
1999 * such that for each basic set S, every element in S is associated with
2000 * the same domain spaces.
2002 * "space" is the (single) domain space of "executed".
2004 static __isl_give isl_set
*separate_schedule_domains(
2005 __isl_take isl_space
*space
, __isl_take isl_union_map
*executed
,
2006 __isl_keep isl_ast_build
*build
)
2008 struct isl_separate_domain_data data
= { build
};
2011 ctx
= isl_ast_build_get_ctx(build
);
2012 data
.explicit = isl_options_get_ast_build_separation_bounds(ctx
) ==
2013 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
;
2014 data
.domain
= isl_set_empty(space
);
2015 if (isl_union_map_foreach_map(executed
, &separate_domain
, &data
) < 0)
2016 data
.domain
= isl_set_free(data
.domain
);
2018 isl_union_map_free(executed
);
2022 /* Temporary data used during the search for a lower bound for unrolling.
2024 * "domain" is the original set for which to find a lower bound
2025 * "depth" is the dimension for which to find a lower boudn
2027 * "lower" is the best lower bound found so far. It is NULL if we have not
2029 * "n" is the corresponding size. If lower is NULL, then the value of n
2032 * "tmp" is a temporary initialized isl_int.
2034 struct isl_find_unroll_data
{
2043 /* Check if we can use "c" as a lower bound and if it is better than
2044 * any previously found lower bound.
2046 * If "c" does not involve the dimension at the current depth,
2047 * then we cannot use it.
2048 * Otherwise, let "c" be of the form
2052 * We compute the maximal value of
2054 * -ceil(f(j)/a)) + i + 1
2056 * over the domain. If there is such a value "n", then we know
2058 * -ceil(f(j)/a)) + i + 1 <= n
2062 * i < ceil(f(j)/a)) + n
2064 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2065 * We just need to check if we have found any lower bound before and
2066 * if the new lower bound is better (smaller n) than the previously found
2069 static int update_unrolling_lower_bound(struct isl_find_unroll_data
*data
,
2070 __isl_keep isl_constraint
*c
)
2072 isl_aff
*aff
, *lower
;
2073 enum isl_lp_result res
;
2075 if (!isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->depth
))
2078 lower
= isl_constraint_get_bound(c
, isl_dim_set
, data
->depth
);
2079 lower
= isl_aff_ceil(lower
);
2080 aff
= isl_aff_copy(lower
);
2081 aff
= isl_aff_neg(aff
);
2082 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, data
->depth
, 1);
2083 aff
= isl_aff_add_constant_si(aff
, 1);
2084 res
= isl_set_max(data
->domain
, aff
, &data
->tmp
);
2087 if (res
== isl_lp_error
)
2089 if (res
== isl_lp_unbounded
) {
2090 isl_aff_free(lower
);
2094 if (isl_int_cmp_si(data
->tmp
, INT_MAX
) <= 0 &&
2095 (!data
->lower
|| isl_int_cmp_si(data
->tmp
, *data
->n
) < 0)) {
2096 isl_aff_free(data
->lower
);
2097 data
->lower
= lower
;
2098 *data
->n
= isl_int_get_si(data
->tmp
);
2100 isl_aff_free(lower
);
2104 isl_aff_free(lower
);
2108 /* Check if we can use "c" as a lower bound and if it is better than
2109 * any previously found lower bound.
2111 static int constraint_find_unroll(__isl_take isl_constraint
*c
, void *user
)
2113 struct isl_find_unroll_data
*data
;
2116 data
= (struct isl_find_unroll_data
*) user
;
2117 r
= update_unrolling_lower_bound(data
, c
);
2118 isl_constraint_free(c
);
2123 /* Look for a lower bound l(i) on the dimension at "depth"
2124 * and a size n such that "domain" is a subset of
2126 * { [i] : l(i) <= i_d < l(i) + n }
2128 * where d is "depth" and l(i) depends only on earlier dimensions.
2129 * Furthermore, try and find a lower bound such that n is as small as possible.
2130 * In particular, "n" needs to be finite.
2132 * Inner dimensions have been eliminated from "domain" by the caller.
2134 * We first construct a collection of lower bounds on the input set
2135 * by computing its simple hull. We then iterate through them,
2136 * discarding those that we cannot use (either because they do not
2137 * involve the dimension at "depth" or because they have no corresponding
2138 * upper bound, meaning that "n" would be unbounded) and pick out the
2139 * best from the remaining ones.
2141 * If we cannot find a suitable lower bound, then we consider that
2144 static __isl_give isl_aff
*find_unroll_lower_bound(__isl_keep isl_set
*domain
,
2147 struct isl_find_unroll_data data
= { domain
, depth
, NULL
, n
};
2148 isl_basic_set
*hull
;
2150 isl_int_init(data
.tmp
);
2151 hull
= isl_set_simple_hull(isl_set_copy(domain
));
2153 if (isl_basic_set_foreach_constraint(hull
,
2154 &constraint_find_unroll
, &data
) < 0)
2157 isl_basic_set_free(hull
);
2158 isl_int_clear(data
.tmp
);
2161 isl_die(isl_set_get_ctx(domain
), isl_error_invalid
,
2162 "cannot find lower bound for unrolling", return NULL
);
2166 isl_basic_set_free(hull
);
2167 isl_int_clear(data
.tmp
);
2168 return isl_aff_free(data
.lower
);
2171 /* Return the constraint
2173 * i_"depth" = aff + offset
2175 static __isl_give isl_constraint
*at_offset(int depth
, __isl_keep isl_aff
*aff
,
2178 aff
= isl_aff_copy(aff
);
2179 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, depth
, -1);
2180 aff
= isl_aff_add_constant_si(aff
, offset
);
2181 return isl_equality_from_aff(aff
);
2184 /* Return a list of basic sets, one for each value of the current dimension
2186 * The divs that involve the current dimension have not been projected out
2189 * Since we are going to be iterating over the individual values,
2190 * we first check if there are any strides on the current dimension.
2191 * If there is, we rewrite the current dimension i as
2193 * i = stride i' + offset
2195 * and then iterate over individual values of i' instead.
2197 * We then look for a lower bound on i' and a size such that the domain
2200 * { [j,i'] : l(j) <= i' < l(j) + n }
2202 * and then take slices of the domain at values of i'
2203 * between l(j) and l(j) + n - 1.
2205 * We compute the unshifted simple hull of each slice to ensure that
2206 * we have a single basic set per offset. The slicing constraint
2207 * may get simplified away before the unshifted simple hull is taken
2208 * and may therefore in some rare cases disappear from the result.
2209 * We therefore explicitly add the constraint back after computing
2210 * the unshifted simple hull to ensure that the basic sets
2211 * remain disjoint. The constraints that are dropped by taking the hull
2212 * will be taken into account at the next level, as in the case of the
2215 * Finally, we map i' back to i and add each basic set to the list.
2217 static __isl_give isl_basic_set_list
*do_unroll(__isl_take isl_set
*domain
,
2218 __isl_keep isl_ast_build
*build
)
2224 isl_basic_set_list
*list
;
2225 isl_multi_aff
*expansion
;
2226 isl_basic_map
*bmap
;
2231 ctx
= isl_set_get_ctx(domain
);
2232 depth
= isl_ast_build_get_depth(build
);
2233 build
= isl_ast_build_copy(build
);
2234 domain
= isl_ast_build_eliminate_inner(build
, domain
);
2235 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
2236 expansion
= isl_ast_build_get_stride_expansion(build
);
2238 domain
= isl_set_preimage_multi_aff(domain
,
2239 isl_multi_aff_copy(expansion
));
2240 domain
= isl_ast_build_eliminate_divs(build
, domain
);
2242 isl_ast_build_free(build
);
2244 list
= isl_basic_set_list_alloc(ctx
, 0);
2246 lower
= find_unroll_lower_bound(domain
, depth
, &n
);
2248 list
= isl_basic_set_list_free(list
);
2250 bmap
= isl_basic_map_from_multi_aff(expansion
);
2252 for (i
= 0; list
&& i
< n
; ++i
) {
2254 isl_basic_set
*bset
;
2255 isl_constraint
*slice
;
2257 slice
= at_offset(depth
, lower
, i
);
2258 set
= isl_set_copy(domain
);
2259 set
= isl_set_add_constraint(set
, isl_constraint_copy(slice
));
2260 bset
= isl_set_unshifted_simple_hull(set
);
2261 bset
= isl_basic_set_add_constraint(bset
, slice
);
2262 bset
= isl_basic_set_apply(bset
, isl_basic_map_copy(bmap
));
2263 list
= isl_basic_set_list_add(list
, bset
);
2266 isl_aff_free(lower
);
2267 isl_set_free(domain
);
2268 isl_basic_map_free(bmap
);
2273 /* Data structure for storing the results and the intermediate objects
2274 * of compute_domains.
2276 * "list" is the main result of the function and contains a list
2277 * of disjoint basic sets for which code should be generated.
2279 * "executed" and "build" are inputs to compute_domains.
2280 * "schedule_domain" is the domain of "executed".
2282 * "option" constains the domains at the current depth that should by
2283 * atomic, separated or unrolled. These domains are as specified by
2284 * the user, except that inner dimensions have been eliminated and
2285 * that they have been made pair-wise disjoint.
2287 * "sep_class" contains the user-specified split into separation classes
2288 * specialized to the current depth.
2289 * "done" contains the union of th separation domains that have already
2292 struct isl_codegen_domains
{
2293 isl_basic_set_list
*list
;
2295 isl_union_map
*executed
;
2296 isl_ast_build
*build
;
2297 isl_set
*schedule_domain
;
2305 /* Add domains to domains->list for each individual value of the current
2306 * dimension, for that part of the schedule domain that lies in the
2307 * intersection of the option domain and the class domain.
2309 * "domain" is the intersection of the class domain and the schedule domain.
2310 * The divs that involve the current dimension have not been projected out
2313 * We first break up the unroll option domain into individual pieces
2314 * and then handle each of them separately. The unroll option domain
2315 * has been made disjoint in compute_domains_init_options,
2317 * Note that we actively want to combine different pieces of the
2318 * schedule domain that have the same value at the current dimension.
2319 * We therefore need to break up the unroll option domain before
2320 * intersecting with class and schedule domain, hoping that the
2321 * unroll option domain specified by the user is relatively simple.
2323 static int compute_unroll_domains(struct isl_codegen_domains
*domains
,
2324 __isl_keep isl_set
*domain
)
2326 isl_set
*unroll_domain
;
2327 isl_basic_set_list
*unroll_list
;
2331 empty
= isl_set_is_empty(domains
->option
[unroll
]);
2337 unroll_domain
= isl_set_copy(domains
->option
[unroll
]);
2338 unroll_list
= isl_basic_set_list_from_set(unroll_domain
);
2340 n
= isl_basic_set_list_n_basic_set(unroll_list
);
2341 for (i
= 0; i
< n
; ++i
) {
2342 isl_basic_set
*bset
;
2343 isl_basic_set_list
*list
;
2345 bset
= isl_basic_set_list_get_basic_set(unroll_list
, i
);
2346 unroll_domain
= isl_set_from_basic_set(bset
);
2347 unroll_domain
= isl_set_intersect(unroll_domain
,
2348 isl_set_copy(domain
));
2350 empty
= isl_set_is_empty(unroll_domain
);
2351 if (empty
>= 0 && empty
) {
2352 isl_set_free(unroll_domain
);
2356 list
= do_unroll(unroll_domain
, domains
->build
);
2357 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2360 isl_basic_set_list_free(unroll_list
);
2365 /* Construct a single basic set that includes the intersection of
2366 * the schedule domain, the atomic option domain and the class domain.
2367 * Add the resulting basic set to domains->list.
2369 * We construct a single domain rather than trying to combine
2370 * the schedule domains of individual domains because we are working
2371 * within a single component so that non-overlapping schedule domains
2372 * should already have been separated.
2373 * Note, though, that this does not take into account the class domain.
2374 * So, it is possible for a class domain to carve out a piece of the
2375 * schedule domain with independent pieces and then we would only
2376 * generate a single domain for them. If this proves to be problematic
2377 * for some users, then this function will have to be adjusted.
2379 * "domain" is the intersection of the schedule domain and the class domain,
2380 * with inner dimensions projected out.
2382 static int compute_atomic_domain(struct isl_codegen_domains
*domains
,
2383 __isl_keep isl_set
*domain
)
2385 isl_basic_set
*bset
;
2386 isl_set
*atomic_domain
;
2389 atomic_domain
= isl_set_copy(domains
->option
[atomic
]);
2390 atomic_domain
= isl_set_intersect(atomic_domain
, isl_set_copy(domain
));
2391 empty
= isl_set_is_empty(atomic_domain
);
2392 if (empty
< 0 || empty
) {
2393 isl_set_free(atomic_domain
);
2394 return empty
< 0 ? -1 : 0;
2397 atomic_domain
= isl_set_coalesce(atomic_domain
);
2398 bset
= isl_set_unshifted_simple_hull(atomic_domain
);
2399 domains
->list
= isl_basic_set_list_add(domains
->list
, bset
);
2404 /* Split up the schedule domain into uniform basic sets,
2405 * in the sense that each element in a basic set is associated to
2406 * elements of the same domains, and add the result to domains->list.
2407 * Do this for that part of the schedule domain that lies in the
2408 * intersection of "class_domain" and the separate option domain.
2410 * "class_domain" may or may not include the constraints
2411 * of the schedule domain, but this does not make a difference
2412 * since we are going to intersect it with the domain of the inverse schedule.
2413 * If it includes schedule domain constraints, then they may involve
2414 * inner dimensions, but we will eliminate them in separation_domain.
2416 static int compute_separate_domain(struct isl_codegen_domains
*domains
,
2417 __isl_keep isl_set
*class_domain
)
2421 isl_union_map
*executed
;
2422 isl_basic_set_list
*list
;
2425 domain
= isl_set_copy(domains
->option
[separate
]);
2426 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2427 executed
= isl_union_map_copy(domains
->executed
);
2428 executed
= isl_union_map_intersect_domain(executed
,
2429 isl_union_set_from_set(domain
));
2430 empty
= isl_union_map_is_empty(executed
);
2431 if (empty
< 0 || empty
) {
2432 isl_union_map_free(executed
);
2433 return empty
< 0 ? -1 : 0;
2436 space
= isl_set_get_space(class_domain
);
2437 domain
= separate_schedule_domains(space
, executed
, domains
->build
);
2439 list
= isl_basic_set_list_from_set(domain
);
2440 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2445 /* Split up the domain at the current depth into disjoint
2446 * basic sets for which code should be generated separately
2447 * for the given separation class domain.
2449 * If any separation classes have been defined, then "class_domain"
2450 * is the domain of the current class and does not refer to inner dimensions.
2451 * Otherwise, "class_domain" is the universe domain.
2453 * We first make sure that the class domain is disjoint from
2454 * previously considered class domains.
2456 * The separate domains can be computed directly from the "class_domain".
2458 * The unroll, atomic and remainder domains need the constraints
2459 * from the schedule domain.
2461 * For unrolling, the actual schedule domain is needed (with divs that
2462 * may refer to the current dimension) so that stride detection can be
2465 * For atomic and remainder domains, inner dimensions and divs involving
2466 * the current dimensions should be eliminated.
2467 * In case we are working within a separation class, we need to intersect
2468 * the result with the current "class_domain" to ensure that the domains
2469 * are disjoint from those generated from other class domains.
2471 * If anything is left after handling separate, unroll and atomic,
2472 * we split it up into basic sets and append the basic sets to domains->list.
2474 static int compute_partial_domains(struct isl_codegen_domains
*domains
,
2475 __isl_take isl_set
*class_domain
)
2477 isl_basic_set_list
*list
;
2480 class_domain
= isl_set_subtract(class_domain
,
2481 isl_set_copy(domains
->done
));
2482 domains
->done
= isl_set_union(domains
->done
,
2483 isl_set_copy(class_domain
));
2485 domain
= isl_set_copy(class_domain
);
2487 if (compute_separate_domain(domains
, domain
) < 0)
2489 domain
= isl_set_subtract(domain
,
2490 isl_set_copy(domains
->option
[separate
]));
2492 domain
= isl_set_intersect(domain
,
2493 isl_set_copy(domains
->schedule_domain
));
2495 if (compute_unroll_domains(domains
, domain
) < 0)
2497 domain
= isl_set_subtract(domain
,
2498 isl_set_copy(domains
->option
[unroll
]));
2500 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2501 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2503 if (compute_atomic_domain(domains
, domain
) < 0)
2505 domain
= isl_set_subtract(domain
,
2506 isl_set_copy(domains
->option
[atomic
]));
2508 domain
= isl_set_coalesce(domain
);
2509 domain
= isl_set_make_disjoint(domain
);
2511 list
= isl_basic_set_list_from_set(domain
);
2512 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2514 isl_set_free(class_domain
);
2518 isl_set_free(domain
);
2519 isl_set_free(class_domain
);
2523 /* Split up the domain at the current depth into disjoint
2524 * basic sets for which code should be generated separately
2525 * for the separation class identified by "pnt".
2527 * We extract the corresponding class domain from domains->sep_class,
2528 * eliminate inner dimensions and pass control to compute_partial_domains.
2530 static int compute_class_domains(__isl_take isl_point
*pnt
, void *user
)
2532 struct isl_codegen_domains
*domains
= user
;
2537 class_set
= isl_set_from_point(pnt
);
2538 domain
= isl_map_domain(isl_map_intersect_range(
2539 isl_map_copy(domains
->sep_class
), class_set
));
2540 domain
= isl_ast_build_compute_gist(domains
->build
, domain
);
2541 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2543 disjoint
= isl_set_plain_is_disjoint(domain
, domains
->schedule_domain
);
2547 isl_set_free(domain
);
2551 return compute_partial_domains(domains
, domain
);
2554 /* Extract the domains at the current depth that should be atomic,
2555 * separated or unrolled and store them in option.
2557 * The domains specified by the user might overlap, so we make
2558 * them disjoint by subtracting earlier domains from later domains.
2560 static void compute_domains_init_options(isl_set
*option
[3],
2561 __isl_keep isl_ast_build
*build
)
2563 enum isl_ast_build_domain_type type
, type2
;
2565 for (type
= atomic
; type
<= separate
; ++type
) {
2566 option
[type
] = isl_ast_build_get_option_domain(build
, type
);
2567 for (type2
= atomic
; type2
< type
; ++type2
)
2568 option
[type
] = isl_set_subtract(option
[type
],
2569 isl_set_copy(option
[type2
]));
2572 option
[unroll
] = isl_set_coalesce(option
[unroll
]);
2573 option
[unroll
] = isl_set_make_disjoint(option
[unroll
]);
2576 /* Split up the domain at the current depth into disjoint
2577 * basic sets for which code should be generated separately,
2578 * based on the user-specified options.
2579 * Return the list of disjoint basic sets.
2581 * There are three kinds of domains that we need to keep track of.
2582 * - the "schedule domain" is the domain of "executed"
2583 * - the "class domain" is the domain corresponding to the currrent
2585 * - the "option domain" is the domain corresponding to one of the options
2586 * atomic, unroll or separate
2588 * We first consider the individial values of the separation classes
2589 * and split up the domain for each of them separately.
2590 * Finally, we consider the remainder. If no separation classes were
2591 * specified, then we call compute_partial_domains with the universe
2592 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2593 * with inner dimensions removed. We do this because we want to
2594 * avoid computing the complement of the class domains (i.e., the difference
2595 * between the universe and domains->done).
2597 static __isl_give isl_basic_set_list
*compute_domains(
2598 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
2600 struct isl_codegen_domains domains
;
2603 isl_union_set
*schedule_domain
;
2607 enum isl_ast_build_domain_type type
;
2613 ctx
= isl_union_map_get_ctx(executed
);
2614 domains
.list
= isl_basic_set_list_alloc(ctx
, 0);
2616 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
2617 domain
= isl_set_from_union_set(schedule_domain
);
2619 compute_domains_init_options(domains
.option
, build
);
2621 domains
.sep_class
= isl_ast_build_get_separation_class(build
);
2622 classes
= isl_map_range(isl_map_copy(domains
.sep_class
));
2623 n_param
= isl_set_dim(classes
, isl_dim_param
);
2624 classes
= isl_set_project_out(classes
, isl_dim_param
, 0, n_param
);
2626 space
= isl_set_get_space(domain
);
2627 domains
.build
= build
;
2628 domains
.schedule_domain
= isl_set_copy(domain
);
2629 domains
.executed
= executed
;
2630 domains
.done
= isl_set_empty(space
);
2632 if (isl_set_foreach_point(classes
, &compute_class_domains
, &domains
) < 0)
2633 domains
.list
= isl_basic_set_list_free(domains
.list
);
2634 isl_set_free(classes
);
2636 empty
= isl_set_is_empty(domains
.done
);
2638 domains
.list
= isl_basic_set_list_free(domains
.list
);
2639 domain
= isl_set_free(domain
);
2641 isl_set_free(domain
);
2642 domain
= isl_set_universe(isl_set_get_space(domains
.done
));
2644 domain
= isl_ast_build_eliminate(build
, domain
);
2646 if (compute_partial_domains(&domains
, domain
) < 0)
2647 domains
.list
= isl_basic_set_list_free(domains
.list
);
2649 isl_set_free(domains
.schedule_domain
);
2650 isl_set_free(domains
.done
);
2651 isl_map_free(domains
.sep_class
);
2652 for (type
= atomic
; type
<= separate
; ++type
)
2653 isl_set_free(domains
.option
[type
]);
2655 return domains
.list
;
2658 /* Generate code for a single component, after shifting (if any)
2661 * We first split up the domain at the current depth into disjoint
2662 * basic sets based on the user-specified options.
2663 * Then we generated code for each of them and concatenate the results.
2665 static __isl_give isl_ast_graft_list
*generate_shifted_component(
2666 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
2668 isl_basic_set_list
*domain_list
;
2669 isl_ast_graft_list
*list
= NULL
;
2671 domain_list
= compute_domains(executed
, build
);
2672 list
= generate_parallel_domains(domain_list
, executed
, build
);
2674 isl_basic_set_list_free(domain_list
);
2675 isl_union_map_free(executed
);
2676 isl_ast_build_free(build
);
2681 struct isl_set_map_pair
{
2686 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2687 * of indices into the "domain" array,
2688 * return the union of the "map" fields of the elements
2689 * indexed by the first "n" elements of "order".
2691 static __isl_give isl_union_map
*construct_component_executed(
2692 struct isl_set_map_pair
*domain
, int *order
, int n
)
2696 isl_union_map
*executed
;
2698 map
= isl_map_copy(domain
[order
[0]].map
);
2699 executed
= isl_union_map_from_map(map
);
2700 for (i
= 1; i
< n
; ++i
) {
2701 map
= isl_map_copy(domain
[order
[i
]].map
);
2702 executed
= isl_union_map_add_map(executed
, map
);
2708 /* Generate code for a single component, after shifting (if any)
2711 * The component inverse schedule is specified as the "map" fields
2712 * of the elements of "domain" indexed by the first "n" elements of "order".
2714 static __isl_give isl_ast_graft_list
*generate_shifted_component_from_list(
2715 struct isl_set_map_pair
*domain
, int *order
, int n
,
2716 __isl_take isl_ast_build
*build
)
2718 isl_union_map
*executed
;
2720 executed
= construct_component_executed(domain
, order
, n
);
2721 return generate_shifted_component(executed
, build
);
2724 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2725 * of indices into the "domain" array,
2726 * do all (except for at most one) of the "set" field of the elements
2727 * indexed by the first "n" elements of "order" have a fixed value
2728 * at position "depth"?
2730 static int at_most_one_non_fixed(struct isl_set_map_pair
*domain
,
2731 int *order
, int n
, int depth
)
2736 for (i
= 0; i
< n
; ++i
) {
2739 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2740 isl_dim_set
, depth
, NULL
);
2753 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2754 * of indices into the "domain" array,
2755 * eliminate the inner dimensions from the "set" field of the elements
2756 * indexed by the first "n" elements of "order", provided the current
2757 * dimension does not have a fixed value.
2759 * Return the index of the first element in "order" with a corresponding
2760 * "set" field that does not have an (obviously) fixed value.
2762 static int eliminate_non_fixed(struct isl_set_map_pair
*domain
,
2763 int *order
, int n
, int depth
, __isl_keep isl_ast_build
*build
)
2768 for (i
= n
- 1; i
>= 0; --i
) {
2770 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2771 isl_dim_set
, depth
, NULL
);
2776 domain
[order
[i
]].set
= isl_ast_build_eliminate_inner(build
,
2777 domain
[order
[i
]].set
);
2784 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2785 * of indices into the "domain" array,
2786 * find the element of "domain" (amongst those indexed by the first "n"
2787 * elements of "order") with the "set" field that has the smallest
2788 * value for the current iterator.
2790 * Note that the domain with the smallest value may depend on the parameters
2791 * and/or outer loop dimension. Since the result of this function is only
2792 * used as heuristic, we only make a reasonable attempt at finding the best
2793 * domain, one that should work in case a single domain provides the smallest
2794 * value for the current dimension over all values of the parameters
2795 * and outer dimensions.
2797 * In particular, we compute the smallest value of the first domain
2798 * and replace it by that of any later domain if that later domain
2799 * has a smallest value that is smaller for at least some value
2800 * of the parameters and outer dimensions.
2802 static int first_offset(struct isl_set_map_pair
*domain
, int *order
, int n
,
2803 __isl_keep isl_ast_build
*build
)
2809 min_first
= isl_ast_build_map_to_iterator(build
,
2810 isl_set_copy(domain
[order
[0]].set
));
2811 min_first
= isl_map_lexmin(min_first
);
2813 for (i
= 1; i
< n
; ++i
) {
2814 isl_map
*min
, *test
;
2817 min
= isl_ast_build_map_to_iterator(build
,
2818 isl_set_copy(domain
[order
[i
]].set
));
2819 min
= isl_map_lexmin(min
);
2820 test
= isl_map_copy(min
);
2821 test
= isl_map_apply_domain(isl_map_copy(min_first
), test
);
2822 test
= isl_map_order_lt(test
, isl_dim_in
, 0, isl_dim_out
, 0);
2823 empty
= isl_map_is_empty(test
);
2825 if (empty
>= 0 && !empty
) {
2826 isl_map_free(min_first
);
2836 isl_map_free(min_first
);
2838 return i
< n
? -1 : first
;
2841 /* Construct a shifted inverse schedule based on the original inverse schedule,
2842 * the stride and the offset.
2844 * The original inverse schedule is specified as the "map" fields
2845 * of the elements of "domain" indexed by the first "n" elements of "order".
2847 * "stride" and "offset" are such that the difference
2848 * between the values of the current dimension of domain "i"
2849 * and the values of the current dimension for some reference domain are
2852 * stride * integer + offset[i]
2854 * Moreover, 0 <= offset[i] < stride.
2856 * For each domain, we create a map
2858 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2860 * where j refers to the current dimension and the other dimensions are
2861 * unchanged, and apply this map to the original schedule domain.
2863 * For example, for the original schedule
2865 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2867 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2868 * we apply the mapping
2872 * to the schedule of the "A" domain and the mapping
2874 * { [j - 1] -> [j, 1] }
2876 * to the schedule of the "B" domain.
2879 * Note that after the transformation, the differences between pairs
2880 * of values of the current dimension over all domains are multiples
2881 * of stride and that we have therefore exposed the stride.
2884 * To see that the mapping preserves the lexicographic order,
2885 * first note that each of the individual maps above preserves the order.
2886 * If the value of the current iterator is j1 in one domain and j2 in another,
2887 * then if j1 = j2, we know that the same map is applied to both domains
2888 * and the order is preserved.
2889 * Otherwise, let us assume, without loss of generality, that j1 < j2.
2890 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
2894 * and the order is preserved.
2895 * If c1 < c2, then we know
2901 * j2 - j1 = n * s + r
2903 * with n >= 0 and 0 <= r < s.
2904 * In other words, r = c2 - c1.
2915 * (j1 - c1, c1) << (j2 - c2, c2)
2917 * with "<<" the lexicographic order, proving that the order is preserved
2920 static __isl_give isl_union_map
*contruct_shifted_executed(
2921 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
2922 __isl_keep isl_vec
*offset
, __isl_keep isl_ast_build
*build
)
2926 isl_union_map
*executed
;
2932 depth
= isl_ast_build_get_depth(build
);
2933 space
= isl_ast_build_get_space(build
, 1);
2934 executed
= isl_union_map_empty(isl_space_copy(space
));
2935 space
= isl_space_map_from_set(space
);
2936 map
= isl_map_identity(isl_space_copy(space
));
2937 map
= isl_map_eliminate(map
, isl_dim_out
, depth
, 1);
2938 map
= isl_map_insert_dims(map
, isl_dim_out
, depth
+ 1, 1);
2939 space
= isl_space_insert_dims(space
, isl_dim_out
, depth
+ 1, 1);
2941 c
= isl_equality_alloc(isl_local_space_from_space(space
));
2942 c
= isl_constraint_set_coefficient_si(c
, isl_dim_in
, depth
, 1);
2943 c
= isl_constraint_set_coefficient_si(c
, isl_dim_out
, depth
, -1);
2947 for (i
= 0; i
< n
; ++i
) {
2950 if (isl_vec_get_element(offset
, i
, &v
) < 0)
2952 map_i
= isl_map_copy(map
);
2953 map_i
= isl_map_fix(map_i
, isl_dim_out
, depth
+ 1, v
);
2955 c
= isl_constraint_set_constant(c
, v
);
2956 map_i
= isl_map_add_constraint(map_i
, isl_constraint_copy(c
));
2958 map_i
= isl_map_apply_domain(isl_map_copy(domain
[order
[i
]].map
),
2960 executed
= isl_union_map_add_map(executed
, map_i
);
2963 isl_constraint_free(c
);
2969 executed
= isl_union_map_free(executed
);
2974 /* Generate code for a single component, after exposing the stride,
2975 * given that the schedule domain is "shifted strided".
2977 * The component inverse schedule is specified as the "map" fields
2978 * of the elements of "domain" indexed by the first "n" elements of "order".
2980 * The schedule domain being "shifted strided" means that the differences
2981 * between the values of the current dimension of domain "i"
2982 * and the values of the current dimension for some reference domain are
2985 * stride * integer + offset[i]
2987 * We first look for the domain with the "smallest" value for the current
2988 * dimension and adjust the offsets such that the offset of the "smallest"
2989 * domain is equal to zero. The other offsets are reduced modulo stride.
2991 * Based on this information, we construct a new inverse schedule in
2992 * contruct_shifted_executed that exposes the stride.
2993 * Since this involves the introduction of a new schedule dimension,
2994 * the build needs to be changed accodingly.
2995 * After computing the AST, the newly introduced dimension needs
2996 * to be removed again from the list of grafts. We do this by plugging
2997 * in a mapping that represents the new schedule domain in terms of the
2998 * old schedule domain.
3000 static __isl_give isl_ast_graft_list
*generate_shift_component(
3001 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
3002 __isl_keep isl_vec
*offset
, __isl_take isl_ast_build
*build
)
3004 isl_ast_graft_list
*list
;
3011 isl_multi_aff
*ma
, *zero
;
3012 isl_union_map
*executed
;
3014 ctx
= isl_ast_build_get_ctx(build
);
3015 depth
= isl_ast_build_get_depth(build
);
3017 first
= first_offset(domain
, order
, n
, build
);
3019 return isl_ast_build_free(build
);
3022 v
= isl_vec_alloc(ctx
, n
);
3023 if (isl_vec_get_element(offset
, first
, &val
) < 0)
3024 v
= isl_vec_free(v
);
3025 isl_int_neg(val
, val
);
3026 v
= isl_vec_set(v
, val
);
3027 v
= isl_vec_add(v
, isl_vec_copy(offset
));
3028 v
= isl_vec_fdiv_r(v
, stride
);
3030 executed
= contruct_shifted_executed(domain
, order
, n
, stride
, v
,
3032 space
= isl_ast_build_get_space(build
, 1);
3033 space
= isl_space_map_from_set(space
);
3034 ma
= isl_multi_aff_identity(isl_space_copy(space
));
3035 space
= isl_space_from_domain(isl_space_domain(space
));
3036 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
3037 zero
= isl_multi_aff_zero(space
);
3038 ma
= isl_multi_aff_range_splice(ma
, depth
+ 1, zero
);
3039 build
= isl_ast_build_insert_dim(build
, depth
+ 1);
3040 list
= generate_shifted_component(executed
, build
);
3042 list
= isl_ast_graft_list_preimage_multi_aff(list
, ma
);
3050 /* Generate code for a single component.
3052 * The component inverse schedule is specified as the "map" fields
3053 * of the elements of "domain" indexed by the first "n" elements of "order".
3055 * This function may modify the "set" fields of "domain".
3057 * Before proceeding with the actual code generation for the component,
3058 * we first check if there are any "shifted" strides, meaning that
3059 * the schedule domains of the individual domains are all strided,
3060 * but that they have different offsets, resulting in the union
3061 * of schedule domains not being strided anymore.
3063 * The simplest example is the schedule
3065 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3067 * Both schedule domains are strided, but their union is not.
3068 * This function detects such cases and then rewrites the schedule to
3070 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3072 * In the new schedule, the schedule domains have the same offset (modulo
3073 * the stride), ensuring that the union of schedule domains is also strided.
3076 * If there is only a single domain in the component, then there is
3077 * nothing to do. Similarly, if the current schedule dimension has
3078 * a fixed value for almost all domains then there is nothing to be done.
3079 * In particular, we need at least two domains where the current schedule
3080 * dimension does not have a fixed value.
3081 * Finally, if any of the options refer to the current schedule dimension,
3082 * then we bail out as well. It would be possible to reformulate the options
3083 * in terms of the new schedule domain, but that would introduce constraints
3084 * that separate the domains in the options and that is something we would
3088 * To see if there is any shifted stride, we look at the differences
3089 * between the values of the current dimension in pairs of domains
3090 * for equal values of outer dimensions. These differences should be
3095 * with "m" the stride and "r" a constant. Note that we cannot perform
3096 * this analysis on individual domains as the lower bound in each domain
3097 * may depend on parameters or outer dimensions and so the current dimension
3098 * itself may not have a fixed remainder on division by the stride.
3100 * In particular, we compare the first domain that does not have an
3101 * obviously fixed value for the current dimension to itself and all
3102 * other domains and collect the offsets and the gcd of the strides.
3103 * If the gcd becomes one, then we failed to find shifted strides.
3104 * If all the offsets are the same (for those domains that do not have
3105 * an obviously fixed value for the current dimension), then we do not
3106 * apply the transformation.
3107 * If none of the domains were skipped, then there is nothing to do.
3108 * If some of them were skipped, then if we apply separation, the schedule
3109 * domain should get split in pieces with a (non-shifted) stride.
3111 * Otherwise, we apply a shift to expose the stride in
3112 * generate_shift_component.
3114 static __isl_give isl_ast_graft_list
*generate_component(
3115 struct isl_set_map_pair
*domain
, int *order
, int n
,
3116 __isl_take isl_ast_build
*build
)
3127 isl_ast_graft_list
*list
;
3130 depth
= isl_ast_build_get_depth(build
);
3133 if (skip
>= 0 && !skip
)
3134 skip
= at_most_one_non_fixed(domain
, order
, n
, depth
);
3135 if (skip
>= 0 && !skip
)
3136 skip
= isl_ast_build_options_involve_depth(build
);
3138 return isl_ast_build_free(build
);
3140 return generate_shifted_component_from_list(domain
,
3143 base
= eliminate_non_fixed(domain
, order
, n
, depth
, build
);
3145 return isl_ast_build_free(build
);
3147 ctx
= isl_ast_build_get_ctx(build
);
3152 v
= isl_vec_alloc(ctx
, n
);
3155 for (i
= 0; i
< n
; ++i
) {
3156 map
= isl_map_from_domain_and_range(
3157 isl_set_copy(domain
[order
[base
]].set
),
3158 isl_set_copy(domain
[order
[i
]].set
));
3159 for (d
= 0; d
< depth
; ++d
)
3160 map
= isl_map_equate(map
, isl_dim_in
, d
,
3162 deltas
= isl_map_deltas(map
);
3163 res
= isl_set_dim_residue_class(deltas
, depth
, &m
, &r
);
3164 isl_set_free(deltas
);
3169 isl_int_set(gcd
, m
);
3171 isl_int_gcd(gcd
, gcd
, m
);
3172 if (isl_int_is_one(gcd
))
3174 v
= isl_vec_set_element(v
, i
, r
);
3176 res
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
3177 isl_dim_set
, depth
, NULL
);
3183 if (fixed
&& i
> base
) {
3184 isl_vec_get_element(v
, base
, &m
);
3185 if (isl_int_ne(m
, r
))
3191 isl_ast_build_free(build
);
3193 } else if (i
< n
|| fixed
) {
3194 list
= generate_shifted_component_from_list(domain
,
3197 list
= generate_shift_component(domain
, order
, n
, gcd
, v
,
3209 /* Store both "map" itself and its domain in the
3210 * structure pointed to by *next and advance to the next array element.
3212 static int extract_domain(__isl_take isl_map
*map
, void *user
)
3214 struct isl_set_map_pair
**next
= user
;
3216 (*next
)->map
= isl_map_copy(map
);
3217 (*next
)->set
= isl_map_domain(map
);
3223 /* Internal data for any_scheduled_after.
3225 * "depth" is the number of loops that have already been generated
3226 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3227 * "domain" is an array of set-map pairs corresponding to the different
3228 * iteration domains. The set is the schedule domain, i.e., the domain
3229 * of the inverse schedule, while the map is the inverse schedule itself.
3231 struct isl_any_scheduled_after_data
{
3233 int group_coscheduled
;
3234 struct isl_set_map_pair
*domain
;
3237 /* Is any element of domain "i" scheduled after any element of domain "j"
3238 * (for a common iteration of the first data->depth loops)?
3240 * data->domain[i].set contains the domain of the inverse schedule
3241 * for domain "i", i.e., elements in the schedule domain.
3243 * If data->group_coscheduled is set, then we also return 1 if there
3244 * is any pair of elements in the two domains that are scheduled together.
3246 static int any_scheduled_after(int i
, int j
, void *user
)
3248 struct isl_any_scheduled_after_data
*data
= user
;
3249 int dim
= isl_set_dim(data
->domain
[i
].set
, isl_dim_set
);
3252 for (pos
= data
->depth
; pos
< dim
; ++pos
) {
3255 follows
= isl_set_follows_at(data
->domain
[i
].set
,
3256 data
->domain
[j
].set
, pos
);
3266 return data
->group_coscheduled
;
3269 /* Look for independent components at the current depth and generate code
3270 * for each component separately. The resulting lists of grafts are
3271 * merged in an attempt to combine grafts with identical guards.
3273 * Code for two domains can be generated separately if all the elements
3274 * of one domain are scheduled before (or together with) all the elements
3275 * of the other domain. We therefore consider the graph with as nodes
3276 * the domains and an edge between two nodes if any element of the first
3277 * node is scheduled after any element of the second node.
3278 * If the ast_build_group_coscheduled is set, then we also add an edge if
3279 * there is any pair of elements in the two domains that are scheduled
3281 * Code is then generated (by generate_component)
3282 * for each of the strongly connected components in this graph
3283 * in their topological order.
3285 * Since the test is performed on the domain of the inverse schedules of
3286 * the different domains, we precompute these domains and store
3287 * them in data.domain.
3289 static __isl_give isl_ast_graft_list
*generate_components(
3290 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3293 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3294 int n
= isl_union_map_n_map(executed
);
3295 struct isl_any_scheduled_after_data data
;
3296 struct isl_set_map_pair
*next
;
3297 struct isl_tarjan_graph
*g
= NULL
;
3298 isl_ast_graft_list
*list
= NULL
;
3301 data
.domain
= isl_calloc_array(ctx
, struct isl_set_map_pair
, n
);
3307 if (isl_union_map_foreach_map(executed
, &extract_domain
, &next
) < 0)
3312 data
.depth
= isl_ast_build_get_depth(build
);
3313 data
.group_coscheduled
= isl_options_get_ast_build_group_coscheduled(ctx
);
3314 g
= isl_tarjan_graph_init(ctx
, n
, &any_scheduled_after
, &data
);
3316 list
= isl_ast_graft_list_alloc(ctx
, 0);
3320 isl_ast_graft_list
*list_c
;
3323 if (g
->order
[i
] == -1)
3324 isl_die(ctx
, isl_error_internal
, "cannot happen",
3327 while (g
->order
[i
] != -1) {
3331 list_c
= generate_component(data
.domain
,
3332 g
->order
+ first
, i
- first
,
3333 isl_ast_build_copy(build
));
3334 list
= isl_ast_graft_list_merge(list
, list_c
, build
);
3340 error
: list
= isl_ast_graft_list_free(list
);
3341 isl_tarjan_graph_free(g
);
3342 for (i
= 0; i
< n_domain
; ++i
) {
3343 isl_map_free(data
.domain
[i
].map
);
3344 isl_set_free(data
.domain
[i
].set
);
3347 isl_union_map_free(executed
);
3348 isl_ast_build_free(build
);
3353 /* Generate code for the next level (and all inner levels).
3355 * If "executed" is empty, i.e., no code needs to be generated,
3356 * then we return an empty list.
3358 * If we have already generated code for all loop levels, then we pass
3359 * control to generate_inner_level.
3361 * If "executed" lives in a single space, i.e., if code needs to be
3362 * generated for a single domain, then there can only be a single
3363 * component and we go directly to generate_shifted_component.
3364 * Otherwise, we call generate_components to detect the components
3365 * and to call generate_component on each of them separately.
3367 static __isl_give isl_ast_graft_list
*generate_next_level(
3368 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3372 if (!build
|| !executed
)
3375 if (isl_union_map_is_empty(executed
)) {
3376 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3377 isl_union_map_free(executed
);
3378 isl_ast_build_free(build
);
3379 return isl_ast_graft_list_alloc(ctx
, 0);
3382 depth
= isl_ast_build_get_depth(build
);
3383 if (depth
>= isl_set_dim(build
->domain
, isl_dim_set
))
3384 return generate_inner_level(executed
, build
);
3386 if (isl_union_map_n_map(executed
) == 1)
3387 return generate_shifted_component(executed
, build
);
3389 return generate_components(executed
, build
);
3391 isl_union_map_free(executed
);
3392 isl_ast_build_free(build
);
3396 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3397 * internal, executed and build are the inputs to generate_code.
3398 * list collects the output.
3400 struct isl_generate_code_data
{
3402 isl_union_map
*executed
;
3403 isl_ast_build
*build
;
3405 isl_ast_graft_list
*list
;
3408 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3412 * with E the external build schedule and S the additional schedule "space",
3413 * reformulate the inverse schedule in terms of the internal schedule domain,
3418 * We first obtain a mapping
3422 * take the inverse and the product with S -> S, resulting in
3424 * [I -> S] -> [E -> S]
3426 * Applying the map to the input produces the desired result.
3428 static __isl_give isl_union_map
*internal_executed(
3429 __isl_take isl_union_map
*executed
, __isl_keep isl_space
*space
,
3430 __isl_keep isl_ast_build
*build
)
3434 proj
= isl_ast_build_get_schedule_map(build
);
3435 proj
= isl_map_reverse(proj
);
3436 space
= isl_space_map_from_set(isl_space_copy(space
));
3437 id
= isl_map_identity(space
);
3438 proj
= isl_map_product(proj
, id
);
3439 executed
= isl_union_map_apply_domain(executed
,
3440 isl_union_map_from_map(proj
));
3444 /* Generate an AST that visits the elements in the range of data->executed
3445 * in the relative order specified by the corresponding image element(s)
3446 * for those image elements that belong to "set".
3447 * Add the result to data->list.
3449 * The caller ensures that "set" is a universe domain.
3450 * "space" is the space of the additional part of the schedule.
3451 * It is equal to the space of "set" if build->domain is parametric.
3452 * Otherwise, it is equal to the range of the wrapped space of "set".
3454 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3455 * was called from an outside user (data->internal not set), then
3456 * the (inverse) schedule refers to the external build domain and needs to
3457 * be transformed to refer to the internal build domain.
3459 * The build is extended to include the additional part of the schedule.
3460 * If the original build space was not parametric, then the options
3461 * in data->build refer only to the additional part of the schedule
3462 * and they need to be adjusted to refer to the complete AST build
3465 * After having adjusted inverse schedule and build, we start generating
3466 * code with the outer loop of the current code generation
3467 * in generate_next_level.
3469 * If the original build space was not parametric, we undo the embedding
3470 * on the resulting isl_ast_node_list so that it can be used within
3471 * the outer AST build.
3473 static int generate_code_in_space(struct isl_generate_code_data
*data
,
3474 __isl_take isl_set
*set
, __isl_take isl_space
*space
)
3476 isl_union_map
*executed
;
3477 isl_ast_build
*build
;
3478 isl_ast_graft_list
*list
;
3481 executed
= isl_union_map_copy(data
->executed
);
3482 executed
= isl_union_map_intersect_domain(executed
,
3483 isl_union_set_from_set(set
));
3485 embed
= !isl_set_is_params(data
->build
->domain
);
3486 if (embed
&& !data
->internal
)
3487 executed
= internal_executed(executed
, space
, data
->build
);
3489 build
= isl_ast_build_copy(data
->build
);
3490 build
= isl_ast_build_product(build
, space
);
3492 list
= generate_next_level(executed
, build
);
3494 list
= isl_ast_graft_list_unembed(list
, embed
);
3496 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
3501 /* Generate an AST that visits the elements in the range of data->executed
3502 * in the relative order specified by the corresponding domain element(s)
3503 * for those domain elements that belong to "set".
3504 * Add the result to data->list.
3506 * The caller ensures that "set" is a universe domain.
3508 * If the build space S is not parametric, then the space of "set"
3509 * need to be a wrapped relation with S as domain. That is, it needs
3514 * Check this property and pass control to generate_code_in_space
3516 * If the build space is not parametric, then T is the space of "set".
3518 static int generate_code_set(__isl_take isl_set
*set
, void *user
)
3520 struct isl_generate_code_data
*data
= user
;
3521 isl_space
*space
, *build_space
;
3524 space
= isl_set_get_space(set
);
3526 if (isl_set_is_params(data
->build
->domain
))
3527 return generate_code_in_space(data
, set
, space
);
3529 build_space
= isl_ast_build_get_space(data
->build
, data
->internal
);
3530 space
= isl_space_unwrap(space
);
3531 is_domain
= isl_space_is_domain(build_space
, space
);
3532 isl_space_free(build_space
);
3533 space
= isl_space_range(space
);
3538 isl_die(isl_set_get_ctx(set
), isl_error_invalid
,
3539 "invalid nested schedule space", goto error
);
3541 return generate_code_in_space(data
, set
, space
);
3544 isl_space_free(space
);
3548 /* Generate an AST that visits the elements in the range of "executed"
3549 * in the relative order specified by the corresponding domain element(s).
3551 * "build" is an isl_ast_build that has either been constructed by
3552 * isl_ast_build_from_context or passed to a callback set by
3553 * isl_ast_build_set_create_leaf.
3554 * In the first case, the space of the isl_ast_build is typically
3555 * a parametric space, although this is currently not enforced.
3556 * In the second case, the space is never a parametric space.
3557 * If the space S is not parametric, then the domain space(s) of "executed"
3558 * need to be wrapped relations with S as domain.
3560 * If the domain of "executed" consists of several spaces, then an AST
3561 * is generated for each of them (in arbitrary order) and the results
3564 * If "internal" is set, then the domain "S" above refers to the internal
3565 * schedule domain representation. Otherwise, it refers to the external
3566 * representation, as returned by isl_ast_build_get_schedule_space.
3568 * We essentially run over all the spaces in the domain of "executed"
3569 * and call generate_code_set on each of them.
3571 static __isl_give isl_ast_graft_list
*generate_code(
3572 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
3576 struct isl_generate_code_data data
= { 0 };
3578 isl_union_set
*schedule_domain
;
3579 isl_union_map
*universe
;
3583 space
= isl_ast_build_get_space(build
, 1);
3584 space
= isl_space_align_params(space
,
3585 isl_union_map_get_space(executed
));
3586 space
= isl_space_align_params(space
,
3587 isl_union_map_get_space(build
->options
));
3588 build
= isl_ast_build_align_params(build
, isl_space_copy(space
));
3589 executed
= isl_union_map_align_params(executed
, space
);
3590 if (!executed
|| !build
)
3593 ctx
= isl_ast_build_get_ctx(build
);
3595 data
.internal
= internal
;
3596 data
.executed
= executed
;
3598 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
3600 universe
= isl_union_map_universe(isl_union_map_copy(executed
));
3601 schedule_domain
= isl_union_map_domain(universe
);
3602 if (isl_union_set_foreach_set(schedule_domain
, &generate_code_set
,
3604 data
.list
= isl_ast_graft_list_free(data
.list
);
3606 isl_union_set_free(schedule_domain
);
3607 isl_union_map_free(executed
);
3609 isl_ast_build_free(build
);
3612 isl_union_map_free(executed
);
3613 isl_ast_build_free(build
);
3617 /* Generate an AST that visits the elements in the domain of "schedule"
3618 * in the relative order specified by the corresponding image element(s).
3620 * "build" is an isl_ast_build that has either been constructed by
3621 * isl_ast_build_from_context or passed to a callback set by
3622 * isl_ast_build_set_create_leaf.
3623 * In the first case, the space of the isl_ast_build is typically
3624 * a parametric space, although this is currently not enforced.
3625 * In the second case, the space is never a parametric space.
3626 * If the space S is not parametric, then the range space(s) of "schedule"
3627 * need to be wrapped relations with S as domain.
3629 * If the range of "schedule" consists of several spaces, then an AST
3630 * is generated for each of them (in arbitrary order) and the results
3633 * We first initialize the local copies of the relevant options.
3634 * We do this here rather than when the isl_ast_build is created
3635 * because the options may have changed between the construction
3636 * of the isl_ast_build and the call to isl_generate_code.
3638 * The main computation is performed on an inverse schedule (with
3639 * the schedule domain in the domain and the elements to be executed
3640 * in the range) called "executed".
3642 __isl_give isl_ast_node
*isl_ast_build_ast_from_schedule(
3643 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
3645 isl_ast_graft_list
*list
;
3647 isl_union_map
*executed
;
3649 build
= isl_ast_build_copy(build
);
3650 build
= isl_ast_build_set_single_valued(build
, 0);
3651 executed
= isl_union_map_reverse(schedule
);
3652 list
= generate_code(executed
, isl_ast_build_copy(build
), 0);
3653 node
= isl_ast_node_from_graft_list(list
, build
);
3654 isl_ast_build_free(build
);