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 /* Plug in all the know values of the current and outer dimensions
319 * in the domain of "executed". In principle, we only need to plug
320 * in the known value of the current dimension since the values of
321 * outer dimensions have been plugged in already.
322 * However, it turns out to be easier to just plug in all known values.
324 static __isl_give isl_union_map
*plug_in_values(
325 __isl_take isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
327 return isl_ast_build_substitute_values_union_map_domain(build
,
331 /* Check if the constraint "c" is a lower bound on dimension "pos",
332 * an upper bound, or independent of dimension "pos".
334 static int constraint_type(isl_constraint
*c
, int pos
)
336 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, pos
))
338 if (isl_constraint_is_upper_bound(c
, isl_dim_set
, pos
))
343 /* Compare the types of the constraints "a" and "b",
344 * resulting in constraints that are independent of "depth"
345 * to be sorted before the lower bounds on "depth", which in
346 * turn are sorted before the upper bounds on "depth".
348 static int cmp_constraint(const void *a
, const void *b
, void *user
)
351 isl_constraint
* const *c1
= a
;
352 isl_constraint
* const *c2
= b
;
353 int t1
= constraint_type(*c1
, *depth
);
354 int t2
= constraint_type(*c2
, *depth
);
359 /* Extract a lower bound on dimension "pos" from constraint "c".
361 * If the constraint is of the form
365 * then we essentially return
367 * l = ceil(-f(...)/a)
369 * However, if the current dimension is strided, then we need to make
370 * sure that the lower bound we construct is of the form
374 * with f the offset and s the stride.
375 * We therefore compute
377 * f + s * ceil((l - f)/s)
379 static __isl_give isl_aff
*lower_bound(__isl_keep isl_constraint
*c
,
380 int pos
, __isl_keep isl_ast_build
*build
)
384 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
385 aff
= isl_aff_ceil(aff
);
387 if (isl_ast_build_has_stride(build
, pos
)) {
391 isl_int_init(stride
);
393 offset
= isl_ast_build_get_offset(build
, pos
);
394 isl_ast_build_get_stride(build
, pos
, &stride
);
396 aff
= isl_aff_sub(aff
, isl_aff_copy(offset
));
397 aff
= isl_aff_scale_down(aff
, stride
);
398 aff
= isl_aff_ceil(aff
);
399 aff
= isl_aff_scale(aff
, stride
);
400 aff
= isl_aff_add(aff
, offset
);
402 isl_int_clear(stride
);
405 aff
= isl_ast_build_compute_gist_aff(build
, aff
);
410 /* Return the exact lower bound (or upper bound if "upper" is set)
411 * of "domain" as a piecewise affine expression.
413 * If we are computing a lower bound (of a strided dimension), then
414 * we need to make sure it is of the form
418 * where f is the offset and s is the stride.
419 * We therefore need to include the stride constraint before computing
422 static __isl_give isl_pw_aff
*exact_bound(__isl_keep isl_set
*domain
,
423 __isl_keep isl_ast_build
*build
, int upper
)
428 isl_pw_multi_aff
*pma
;
430 domain
= isl_set_copy(domain
);
432 stride
= isl_ast_build_get_stride_constraint(build
);
433 domain
= isl_set_intersect(domain
, stride
);
435 it_map
= isl_ast_build_map_to_iterator(build
, domain
);
437 pma
= isl_map_lexmax_pw_multi_aff(it_map
);
439 pma
= isl_map_lexmin_pw_multi_aff(it_map
);
440 pa
= isl_pw_multi_aff_get_pw_aff(pma
, 0);
441 isl_pw_multi_aff_free(pma
);
442 pa
= isl_ast_build_compute_gist_pw_aff(build
, pa
);
443 pa
= isl_pw_aff_coalesce(pa
);
448 /* Return a list of "n" lower bounds on dimension "pos"
449 * extracted from the "n" constraints starting at "constraint".
450 * If "n" is zero, then we extract a lower bound from "domain" instead.
452 static __isl_give isl_pw_aff_list
*lower_bounds(
453 __isl_keep isl_constraint
**constraint
, int n
, int pos
,
454 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
457 isl_pw_aff_list
*list
;
465 pa
= exact_bound(domain
, build
, 0);
466 return isl_pw_aff_list_from_pw_aff(pa
);
469 ctx
= isl_ast_build_get_ctx(build
);
470 list
= isl_pw_aff_list_alloc(ctx
,n
);
472 for (i
= 0; i
< n
; ++i
) {
475 aff
= lower_bound(constraint
[i
], pos
, build
);
476 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
482 /* Return a list of "n" upper bounds on dimension "pos"
483 * extracted from the "n" constraints starting at "constraint".
484 * If "n" is zero, then we extract an upper bound from "domain" instead.
486 static __isl_give isl_pw_aff_list
*upper_bounds(
487 __isl_keep isl_constraint
**constraint
, int n
, int pos
,
488 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
491 isl_pw_aff_list
*list
;
496 pa
= exact_bound(domain
, build
, 1);
497 return isl_pw_aff_list_from_pw_aff(pa
);
500 ctx
= isl_ast_build_get_ctx(build
);
501 list
= isl_pw_aff_list_alloc(ctx
,n
);
503 for (i
= 0; i
< n
; ++i
) {
506 aff
= isl_constraint_get_bound(constraint
[i
], isl_dim_set
, pos
);
507 aff
= isl_aff_floor(aff
);
508 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
514 /* Return an isl_ast_expr that performs the reduction of type "type"
515 * on AST expressions corresponding to the elements in "list".
517 * The list is assumed to contain at least one element.
518 * If the list contains exactly one element, then the returned isl_ast_expr
519 * simply computes that affine expression.
521 static __isl_give isl_ast_expr
*reduce_list(enum isl_ast_op_type type
,
522 __isl_keep isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
531 n
= isl_pw_aff_list_n_pw_aff(list
);
534 return isl_ast_build_expr_from_pw_aff_internal(build
,
535 isl_pw_aff_list_get_pw_aff(list
, 0));
537 ctx
= isl_pw_aff_list_get_ctx(list
);
538 expr
= isl_ast_expr_alloc_op(ctx
, type
, n
);
542 for (i
= 0; i
< n
; ++i
) {
543 isl_ast_expr
*expr_i
;
545 expr_i
= isl_ast_build_expr_from_pw_aff_internal(build
,
546 isl_pw_aff_list_get_pw_aff(list
, i
));
548 return isl_ast_expr_free(expr
);
549 expr
->u
.op
.args
[i
] = expr_i
;
555 /* Add a guard to "graft" based on "bound" in the case of a degenerate
556 * level (including the special case of an eliminated level).
558 * We eliminate the current dimension, simplify the result in the current
559 * build and add the result as guards to the graft.
561 * Note that we cannot simply drop the constraints on the current dimension
562 * even in the eliminated case, because the single affine expression may
563 * not be explicitly available in "bounds". Moreover, the single affine
564 * expression may only be defined on a subset of the build domain,
565 * so we do in some cases need to insert a guard even in the eliminated case.
567 static __isl_give isl_ast_graft
*add_degenerate_guard(
568 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
569 __isl_keep isl_ast_build
*build
)
574 depth
= isl_ast_build_get_depth(build
);
576 dom
= isl_set_from_basic_set(isl_basic_set_copy(bounds
));
577 if (isl_ast_build_has_stride(build
, depth
)) {
580 stride
= isl_ast_build_get_stride_constraint(build
);
581 dom
= isl_set_intersect(dom
, stride
);
583 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
584 dom
= isl_ast_build_compute_gist(build
, dom
);
586 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
591 /* Update "graft" based on "bounds" for the eliminated case.
593 * In the eliminated case, no for node is created, so we only need
594 * to check if "bounds" imply any guards that need to be inserted.
596 static __isl_give isl_ast_graft
*refine_eliminated(
597 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
598 __isl_keep isl_ast_build
*build
)
600 return add_degenerate_guard(graft
, bounds
, build
);
603 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
605 * "build" is the build in which graft->node was created
606 * "sub_build" contains information about the current level itself,
607 * including the single value attained.
609 * We first set the initialization part of the for loop to the single
610 * value attained by the current dimension.
611 * The increment and condition are not strictly needed as the are known
612 * to be "1" and "iterator <= value" respectively.
613 * Then we set the size of the iterator and
614 * check if "bounds" imply any guards that need to be inserted.
616 static __isl_give isl_ast_graft
*refine_degenerate(
617 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
618 __isl_keep isl_ast_build
*build
,
619 __isl_keep isl_ast_build
*sub_build
)
623 if (!graft
|| !sub_build
)
624 return isl_ast_graft_free(graft
);
626 value
= isl_pw_aff_copy(sub_build
->value
);
628 graft
->node
->u
.f
.init
= isl_ast_build_expr_from_pw_aff_internal(build
,
630 if (!graft
->node
->u
.f
.init
)
631 return isl_ast_graft_free(graft
);
633 graft
= add_degenerate_guard(graft
, bounds
, build
);
638 /* Return the intersection of the "n" constraints starting at "constraint"
641 static __isl_give isl_set
*intersect_constraints(isl_ctx
*ctx
,
642 __isl_keep isl_constraint
**constraint
, int n
)
648 isl_die(ctx
, isl_error_internal
,
649 "expecting at least one constraint", return NULL
);
651 bset
= isl_basic_set_from_constraint(
652 isl_constraint_copy(constraint
[0]));
653 for (i
= 1; i
< n
; ++i
) {
654 isl_basic_set
*bset_i
;
656 bset_i
= isl_basic_set_from_constraint(
657 isl_constraint_copy(constraint
[i
]));
658 bset
= isl_basic_set_intersect(bset
, bset_i
);
661 return isl_set_from_basic_set(bset
);
664 /* Compute the constraints on the outer dimensions enforced by
665 * graft->node and add those constraints to graft->enforced,
666 * in case the upper bound is expressed as a set "upper".
668 * In particular, if l(...) is a lower bound in "lower", and
670 * -a i + f(...) >= 0 or a i <= f(...)
672 * is an upper bound ocnstraint on the current dimension i,
673 * then the for loop enforces the constraint
675 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
677 * We therefore simply take each lower bound in turn, plug it into
678 * the upper bounds and compute the intersection over all lower bounds.
680 * If a lower bound is a rational expression, then
681 * isl_basic_set_preimage_multi_aff will force this rational
682 * expression to have only integer values. However, the loop
683 * itself does not enforce this integrality constraint. We therefore
684 * use the ceil of the lower bounds instead of the lower bounds themselves.
685 * Other constraints will make sure that the for loop is only executed
686 * when each of the lower bounds attains an integral value.
687 * In particular, potentially rational values only occur in
688 * lower_bound if the offset is a (seemingly) rational expression,
689 * but then outer conditions will make sure that this rational expression
690 * only attains integer values.
692 static __isl_give isl_ast_graft
*set_enforced_from_set(
693 __isl_take isl_ast_graft
*graft
,
694 __isl_keep isl_pw_aff_list
*lower
, int pos
, __isl_keep isl_set
*upper
)
697 isl_basic_set
*enforced
;
698 isl_pw_multi_aff
*pma
;
701 if (!graft
|| !lower
)
702 return isl_ast_graft_free(graft
);
704 space
= isl_set_get_space(upper
);
705 enforced
= isl_basic_set_universe(isl_space_copy(space
));
707 space
= isl_space_map_from_set(space
);
708 pma
= isl_pw_multi_aff_identity(space
);
710 n
= isl_pw_aff_list_n_pw_aff(lower
);
711 for (i
= 0; i
< n
; ++i
) {
715 isl_pw_multi_aff
*pma_i
;
717 pa
= isl_pw_aff_list_get_pw_aff(lower
, i
);
718 pa
= isl_pw_aff_ceil(pa
);
719 pma_i
= isl_pw_multi_aff_copy(pma
);
720 pma_i
= isl_pw_multi_aff_set_pw_aff(pma_i
, pos
, pa
);
721 enforced_i
= isl_set_copy(upper
);
722 enforced_i
= isl_set_preimage_pw_multi_aff(enforced_i
, pma_i
);
723 hull
= isl_set_simple_hull(enforced_i
);
724 enforced
= isl_basic_set_intersect(enforced
, hull
);
727 isl_pw_multi_aff_free(pma
);
729 graft
= isl_ast_graft_enforce(graft
, enforced
);
734 /* Compute the constraints on the outer dimensions enforced by
735 * graft->node and add those constraints to graft->enforced,
736 * in case the upper bound is expressed as
737 * a list of affine expressions "upper".
739 * The enforced condition is that each lower bound expression is less
740 * than or equal to each upper bound expression.
742 static __isl_give isl_ast_graft
*set_enforced_from_list(
743 __isl_take isl_ast_graft
*graft
,
744 __isl_keep isl_pw_aff_list
*lower
, __isl_keep isl_pw_aff_list
*upper
)
747 isl_basic_set
*enforced
;
749 lower
= isl_pw_aff_list_copy(lower
);
750 upper
= isl_pw_aff_list_copy(upper
);
751 cond
= isl_pw_aff_list_le_set(lower
, upper
);
752 enforced
= isl_set_simple_hull(cond
);
753 graft
= isl_ast_graft_enforce(graft
, enforced
);
758 /* Does "aff" have a negative constant term?
760 static int aff_constant_is_negative(__isl_take isl_set
*set
,
761 __isl_take isl_aff
*aff
, void *user
)
767 isl_aff_get_constant(aff
, &v
);
768 *neg
= isl_int_is_neg(v
);
773 return *neg
? 0 : -1;
776 /* Does "pa" have a negative constant term over its entire domain?
778 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff
*pa
, void *user
)
783 r
= isl_pw_aff_foreach_piece(pa
, &aff_constant_is_negative
, user
);
786 return *neg
? 0 : -1;
789 /* Does each element in "list" have a negative constant term?
791 * The callback terminates the iteration as soon an element has been
792 * found that does not have a negative constant term.
794 static int list_constant_is_negative(__isl_keep isl_pw_aff_list
*list
)
798 if (isl_pw_aff_list_foreach(list
,
799 &pw_aff_constant_is_negative
, &neg
) < 0 && neg
)
805 /* Add 1 to each of the elements in "list", where each of these elements
806 * is defined over the internal schedule space of "build".
808 static __isl_give isl_pw_aff_list
*list_add_one(
809 __isl_take isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
816 space
= isl_ast_build_get_space(build
, 1);
817 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(space
));
818 aff
= isl_aff_add_constant_si(aff
, 1);
819 one
= isl_pw_aff_from_aff(aff
);
821 n
= isl_pw_aff_list_n_pw_aff(list
);
822 for (i
= 0; i
< n
; ++i
) {
824 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
825 pa
= isl_pw_aff_add(pa
, isl_pw_aff_copy(one
));
826 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
829 isl_pw_aff_free(one
);
834 /* Set the condition part of the for node graft->node in case
835 * the upper bound is represented as a list of piecewise affine expressions.
837 * In particular, set the condition to
839 * iterator <= min(list of upper bounds)
841 * If each of the upper bounds has a negative constant term, then
842 * set the condition to
844 * iterator < min(list of (upper bound + 1)s)
847 static __isl_give isl_ast_graft
*set_for_cond_from_list(
848 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*list
,
849 __isl_keep isl_ast_build
*build
)
852 isl_ast_expr
*bound
, *iterator
, *cond
;
853 enum isl_ast_op_type type
= isl_ast_op_le
;
856 return isl_ast_graft_free(graft
);
858 neg
= list_constant_is_negative(list
);
860 return isl_ast_graft_free(graft
);
861 list
= isl_pw_aff_list_copy(list
);
863 list
= list_add_one(list
, build
);
864 type
= isl_ast_op_lt
;
867 bound
= reduce_list(isl_ast_op_min
, list
, build
);
868 iterator
= isl_ast_expr_copy(graft
->node
->u
.f
.iterator
);
869 cond
= isl_ast_expr_alloc_binary(type
, iterator
, bound
);
870 graft
->node
->u
.f
.cond
= cond
;
872 isl_pw_aff_list_free(list
);
873 if (!graft
->node
->u
.f
.cond
)
874 return isl_ast_graft_free(graft
);
878 /* Set the condition part of the for node graft->node in case
879 * the upper bound is represented as a set.
881 static __isl_give isl_ast_graft
*set_for_cond_from_set(
882 __isl_take isl_ast_graft
*graft
, __isl_keep isl_set
*set
,
883 __isl_keep isl_ast_build
*build
)
890 cond
= isl_ast_build_expr_from_set(build
, isl_set_copy(set
));
891 graft
->node
->u
.f
.cond
= cond
;
892 if (!graft
->node
->u
.f
.cond
)
893 return isl_ast_graft_free(graft
);
897 /* Construct an isl_ast_expr for the increment (i.e., stride) of
898 * the current dimension.
900 static __isl_give isl_ast_expr
*for_inc(__isl_keep isl_ast_build
*build
)
909 ctx
= isl_ast_build_get_ctx(build
);
910 depth
= isl_ast_build_get_depth(build
);
912 if (!isl_ast_build_has_stride(build
, depth
))
913 return isl_ast_expr_alloc_int_si(ctx
, 1);
916 isl_ast_build_get_stride(build
, depth
, &v
);
917 inc
= isl_ast_expr_alloc_int(ctx
, v
);
923 /* Should we express the loop condition as
925 * iterator <= min(list of upper bounds)
927 * or as a conjunction of constraints?
929 * The first is constructed from a list of upper bounds.
930 * The second is constructed from a set.
932 * If there are no upper bounds in "constraints", then this could mean
933 * that "domain" simply doesn't have an upper bound or that we didn't
934 * pick any upper bound. In the first case, we want to generate the
935 * loop condition as a(n empty) conjunction of constraints
936 * In the second case, we will compute
937 * a single upper bound from "domain" and so we use the list form.
939 * If there are upper bounds in "constraints",
940 * then we use the list form iff the atomic_upper_bound option is set.
942 static int use_upper_bound_list(isl_ctx
*ctx
, int n_upper
,
943 __isl_keep isl_set
*domain
, int depth
)
946 return isl_options_get_ast_build_atomic_upper_bound(ctx
);
948 return isl_set_dim_has_upper_bound(domain
, isl_dim_set
, depth
);
951 /* Fill in the expressions of the for node in graft->node.
954 * - set the initialization part of the loop to the maximum of the lower bounds
955 * - set the size of the iterator based on the values attained by the iterator
956 * - extract the increment from the stride of the current dimension
957 * - construct the for condition either based on a list of upper bounds
958 * or on a set of upper bound constraints.
960 static __isl_give isl_ast_graft
*set_for_node_expressions(
961 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*lower
,
962 int use_list
, __isl_keep isl_pw_aff_list
*upper_list
,
963 __isl_keep isl_set
*upper_set
, __isl_keep isl_ast_build
*build
)
970 build
= isl_ast_build_copy(build
);
971 build
= isl_ast_build_set_enforced(build
,
972 isl_ast_graft_get_enforced(graft
));
975 node
->u
.f
.init
= reduce_list(isl_ast_op_max
, lower
, build
);
976 node
->u
.f
.inc
= for_inc(build
);
979 graft
= set_for_cond_from_list(graft
, upper_list
, build
);
981 graft
= set_for_cond_from_set(graft
, upper_set
, build
);
983 isl_ast_build_free(build
);
985 if (!node
->u
.f
.iterator
|| !node
->u
.f
.init
||
986 !node
->u
.f
.cond
|| !node
->u
.f
.inc
)
987 return isl_ast_graft_free(graft
);
992 /* Update "graft" based on "bounds" and "domain" for the generic,
993 * non-degenerate, case.
995 * "constraints" contains the "n_lower" lower and "n_upper" upper bounds
996 * that the loop node should express.
997 * "domain" is the subset of the intersection of the constraints
998 * for which some code is executed.
1000 * There may be zero lower bounds or zero upper bounds in "constraints"
1001 * in case the list of constraints was created
1002 * based on the atomic option or based on separation with explicit bounds.
1003 * In that case, we use "domain" to derive lower and/or upper bounds.
1005 * We first compute a list of one or more lower bounds.
1007 * Then we decide if we want to express the condition as
1009 * iterator <= min(list of upper bounds)
1011 * or as a conjunction of constraints.
1013 * The set of enforced constraints is then computed either based on
1014 * a list of upper bounds or on a set of upper bound constraints.
1015 * We do not compute any enforced constraints if we were forced
1016 * to compute a lower or upper bound using exact_bound. The domains
1017 * of the resulting expressions may imply some bounds on outer dimensions
1018 * that we do not want to appear in the enforced constraints since
1019 * they are not actually enforced by the corresponding code.
1021 * Finally, we fill in the expressions of the for node.
1023 static __isl_give isl_ast_graft
*refine_generic_bounds(
1024 __isl_take isl_ast_graft
*graft
,
1025 __isl_keep isl_constraint
**constraint
, int n_lower
, int n_upper
,
1026 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1030 isl_pw_aff_list
*lower
;
1032 isl_set
*upper_set
= NULL
;
1033 isl_pw_aff_list
*upper_list
= NULL
;
1035 if (!graft
|| !build
)
1036 return isl_ast_graft_free(graft
);
1038 depth
= isl_ast_build_get_depth(build
);
1039 ctx
= isl_ast_graft_get_ctx(graft
);
1041 use_list
= use_upper_bound_list(ctx
, n_upper
, domain
, depth
);
1043 lower
= lower_bounds(constraint
, n_lower
, depth
, domain
, build
);
1046 upper_list
= upper_bounds(constraint
+ n_lower
, n_upper
, depth
,
1048 else if (n_upper
> 0)
1049 upper_set
= intersect_constraints(ctx
, constraint
+ n_lower
,
1052 upper_set
= isl_set_universe(isl_set_get_space(domain
));
1054 if (n_lower
== 0 || n_upper
== 0)
1057 graft
= set_enforced_from_list(graft
, lower
, upper_list
);
1059 graft
= set_enforced_from_set(graft
, lower
, depth
, upper_set
);
1061 graft
= set_for_node_expressions(graft
, lower
, use_list
, upper_list
,
1064 isl_pw_aff_list_free(lower
);
1065 isl_pw_aff_list_free(upper_list
);
1066 isl_set_free(upper_set
);
1071 /* How many constraints in the "constraint" array, starting at position "first"
1072 * are of the give type? "n" represents the total number of elements
1075 static int count_constraints(isl_constraint
**constraint
, int n
, int first
,
1080 constraint
+= first
;
1082 for (i
= 0; first
+ i
< n
; i
++)
1083 if (constraint_type(constraint
[i
], pos
) != type
)
1089 /* Update "graft" based on "bounds" and "domain" for the generic,
1090 * non-degenerate, case.
1092 * "list" respresent the list of bounds that need to be encoded by
1093 * the for loop (or a guard around the for loop).
1094 * "domain" is the subset of the intersection of the constraints
1095 * for which some code is executed.
1096 * "build" is the build in which graft->node was created.
1098 * We separate lower bounds, upper bounds and constraints that
1099 * are independent of the loop iterator.
1101 * The actual for loop bounds are generated in refine_generic_bounds.
1102 * If there are any constraints that are independent of the loop iterator,
1103 * we need to put a guard around the for loop (which may get hoisted up
1104 * to higher levels) and we call refine_generic_bounds in a build
1105 * where this guard is enforced.
1107 static __isl_give isl_ast_graft
*refine_generic_split(
1108 __isl_take isl_ast_graft
*graft
, __isl_keep isl_constraint_list
*list
,
1109 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
1112 isl_ast_build
*for_build
;
1114 int n_indep
, n_lower
, n_upper
;
1119 return isl_ast_graft_free(graft
);
1121 pos
= isl_ast_build_get_depth(build
);
1123 if (isl_sort(list
->p
, list
->n
, sizeof(isl_constraint
*),
1124 &cmp_constraint
, &pos
) < 0)
1125 return isl_ast_graft_free(graft
);
1128 n_indep
= count_constraints(list
->p
, n
, 0, pos
, 0);
1129 n_lower
= count_constraints(list
->p
, n
, n_indep
, pos
, 1);
1130 n_upper
= count_constraints(list
->p
, n
, n_indep
+ n_lower
, pos
, 2);
1133 return refine_generic_bounds(graft
,
1134 list
->p
+ n_indep
, n_lower
, n_upper
, domain
, build
);
1136 ctx
= isl_ast_graft_get_ctx(graft
);
1137 guard
= intersect_constraints(ctx
, list
->p
, n_indep
);
1139 for_build
= isl_ast_build_copy(build
);
1140 for_build
= isl_ast_build_restrict_pending(for_build
,
1141 isl_set_copy(guard
));
1142 graft
= refine_generic_bounds(graft
,
1143 list
->p
+ n_indep
, n_lower
, n_upper
, domain
, for_build
);
1144 isl_ast_build_free(for_build
);
1146 graft
= isl_ast_graft_add_guard(graft
, guard
, build
);
1151 /* Add the guard implied by the current stride constraint (if any),
1152 * but not (necessarily) enforced by the generated AST to "graft".
1154 static __isl_give isl_ast_graft
*add_stride_guard(
1155 __isl_take isl_ast_graft
*graft
, __isl_keep isl_ast_build
*build
)
1160 depth
= isl_ast_build_get_depth(build
);
1161 if (!isl_ast_build_has_stride(build
, depth
))
1164 dom
= isl_ast_build_get_stride_constraint(build
);
1165 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
1166 dom
= isl_ast_build_compute_gist(build
, dom
);
1168 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
1173 /* Update "graft" based on "bounds" and "domain" for the generic,
1174 * non-degenerate, case.
1176 * "bounds" respresent the bounds that need to be encoded by
1177 * the for loop (or a guard around the for loop).
1178 * "domain" is the subset of "bounds" for which some code is executed.
1179 * "build" is the build in which graft->node was created.
1181 * We break up "bounds" into a list of constraints and continue with
1182 * refine_generic_split.
1184 static __isl_give isl_ast_graft
*refine_generic(
1185 __isl_take isl_ast_graft
*graft
,
1186 __isl_keep isl_basic_set
*bounds
, __isl_keep isl_set
*domain
,
1187 __isl_keep isl_ast_build
*build
)
1189 isl_constraint_list
*list
;
1191 if (!build
|| !graft
)
1192 return isl_ast_graft_free(graft
);
1194 bounds
= isl_basic_set_copy(bounds
);
1195 bounds
= isl_ast_build_compute_gist_basic_set(build
, bounds
);
1196 list
= isl_constraint_list_from_basic_set(bounds
);
1198 graft
= refine_generic_split(graft
, list
, domain
, build
);
1199 graft
= add_stride_guard(graft
, build
);
1201 isl_constraint_list_free(list
);
1205 /* Create a for node for the current level.
1207 * Mark the for node degenerate if "degenerate" is set.
1209 static __isl_give isl_ast_node
*create_for(__isl_keep isl_ast_build
*build
,
1219 depth
= isl_ast_build_get_depth(build
);
1220 id
= isl_ast_build_get_iterator_id(build
, depth
);
1221 node
= isl_ast_node_alloc_for(id
);
1223 node
= isl_ast_node_for_mark_degenerate(node
);
1228 /* Create an AST node for the current dimension based on
1229 * the schedule domain "bounds" and return the node encapsulated
1230 * in an isl_ast_graft.
1232 * "executed" is the current inverse schedule, taking into account
1233 * the bounds in "bounds"
1234 * "domain" is the domain of "executed", with inner dimensions projected out.
1235 * It may be a strict subset of "bounds" in case "bounds" was created
1236 * based on the atomic option or based on separation with explicit bounds.
1238 * "domain" may satisfy additional equalities that result
1239 * from intersecting "executed" with "bounds" in add_node.
1240 * It may also satisfy some global constraints that were dropped out because
1241 * we performed separation with explicit bounds.
1242 * The very first step is then to copy these constraints to "bounds".
1244 * Since we may be calling before_each_for and after_each_for
1245 * callbacks, we record the current inverse schedule in the build.
1247 * We consider three builds,
1248 * "build" is the one in which the current level is created,
1249 * "body_build" is the build in which the next level is created,
1250 * "sub_build" is essentially the same as "body_build", except that
1251 * the depth has not been increased yet.
1253 * "build" already contains information (in strides and offsets)
1254 * about the strides at the current level, but this information is not
1255 * reflected in the build->domain.
1256 * We first add this information and the "bounds" to the sub_build->domain.
1257 * isl_ast_build_set_loop_bounds checks whether the current dimension attains
1258 * only a single value and whether this single value can be represented using
1259 * a single affine expression.
1260 * In the first case, the current level is considered "degenerate".
1261 * In the second, sub-case, the current level is considered "eliminated".
1262 * Eliminated level don't need to be reflected in the AST since we can
1263 * simply plug in the affine expression. For degenerate, but non-eliminated,
1264 * levels, we do introduce a for node, but mark is as degenerate so that
1265 * it can be printed as an assignment of the single value to the loop
1268 * If the current level is eliminated, we explicitly plug in the value
1269 * for the current level found by isl_ast_build_set_loop_bounds in the
1270 * inverse schedule. This ensures that if we are working on a slice
1271 * of the domain based on information available in the inverse schedule
1272 * and the build domain, that then this information is also reflected
1273 * in the inverse schedule. This operation also eliminates the current
1274 * dimension from the inverse schedule making sure no inner dimensions depend
1275 * on the current dimension. Otherwise, we create a for node, marking
1276 * it degenerate if appropriate. The initial for node is still incomplete
1277 * and will be completed in either refine_degenerate or refine_generic.
1279 * We then generate a sequence of grafts for the next level,
1280 * create a surrounding graft for the current level and insert
1281 * the for node we created (if the current level is not eliminated).
1283 * Finally, we set the bounds of the for loop and insert guards
1284 * (either in the AST or in the graft) in one of
1285 * refine_eliminated, refine_degenerate or refine_generic.
1287 static __isl_give isl_ast_graft
*create_node_scaled(
1288 __isl_take isl_union_map
*executed
,
1289 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1290 __isl_take isl_ast_build
*build
)
1293 int degenerate
, eliminated
;
1294 isl_basic_set
*hull
;
1295 isl_ast_node
*node
= NULL
;
1296 isl_ast_graft
*graft
;
1297 isl_ast_graft_list
*children
;
1298 isl_ast_build
*sub_build
;
1299 isl_ast_build
*body_build
;
1301 domain
= isl_ast_build_eliminate_divs(build
, domain
);
1302 domain
= isl_set_detect_equalities(domain
);
1303 hull
= isl_set_unshifted_simple_hull(isl_set_copy(domain
));
1304 bounds
= isl_basic_set_intersect(bounds
, hull
);
1305 build
= isl_ast_build_set_executed(build
, isl_union_map_copy(executed
));
1307 depth
= isl_ast_build_get_depth(build
);
1308 sub_build
= isl_ast_build_copy(build
);
1309 sub_build
= isl_ast_build_include_stride(sub_build
);
1310 sub_build
= isl_ast_build_set_loop_bounds(sub_build
,
1311 isl_basic_set_copy(bounds
));
1312 degenerate
= isl_ast_build_has_value(sub_build
);
1313 eliminated
= isl_ast_build_has_affine_value(sub_build
, depth
);
1314 if (degenerate
< 0 || eliminated
< 0)
1315 executed
= isl_union_map_free(executed
);
1317 executed
= plug_in_values(executed
, sub_build
);
1319 node
= create_for(build
, degenerate
);
1321 body_build
= isl_ast_build_copy(sub_build
);
1322 body_build
= isl_ast_build_increase_depth(body_build
);
1324 node
= before_each_for(node
, body_build
);
1325 children
= generate_next_level(executed
,
1326 isl_ast_build_copy(body_build
));
1328 graft
= isl_ast_graft_alloc_level(children
, build
, sub_build
);
1330 graft
= isl_ast_graft_insert_for(graft
, node
);
1332 graft
= refine_eliminated(graft
, bounds
, build
);
1333 else if (degenerate
)
1334 graft
= refine_degenerate(graft
, bounds
, build
, sub_build
);
1336 graft
= refine_generic(graft
, bounds
, domain
, build
);
1338 graft
= after_each_for(graft
, body_build
);
1340 isl_ast_build_free(body_build
);
1341 isl_ast_build_free(sub_build
);
1342 isl_ast_build_free(build
);
1343 isl_basic_set_free(bounds
);
1344 isl_set_free(domain
);
1349 /* Internal data structure for checking if all constraints involving
1350 * the input dimension "depth" are such that the other coefficients
1351 * are multiples of "m", reducing "m" if they are not.
1352 * If "m" is reduced all the way down to "1", then the check has failed
1353 * and we break out of the iteration.
1354 * "d" is an initialized isl_int that can be used internally.
1356 struct isl_check_scaled_data
{
1361 /* If constraint "c" involves the input dimension data->depth,
1362 * then make sure that all the other coefficients are multiples of data->m,
1363 * reducing data->m if needed.
1364 * Break out of the iteration if data->m has become equal to "1".
1366 static int constraint_check_scaled(__isl_take isl_constraint
*c
, void *user
)
1368 struct isl_check_scaled_data
*data
= user
;
1370 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_out
,
1373 if (!isl_constraint_involves_dims(c
, isl_dim_in
, data
->depth
, 1)) {
1374 isl_constraint_free(c
);
1378 for (i
= 0; i
< 4; ++i
) {
1379 n
= isl_constraint_dim(c
, t
[i
]);
1380 for (j
= 0; j
< n
; ++j
) {
1381 if (t
[i
] == isl_dim_in
&& j
== data
->depth
)
1383 if (!isl_constraint_involves_dims(c
, t
[i
], j
, 1))
1385 isl_constraint_get_coefficient(c
, t
[i
], j
, &data
->d
);
1386 isl_int_gcd(data
->m
, data
->m
, data
->d
);
1387 if (isl_int_is_one(data
->m
))
1394 isl_constraint_free(c
);
1396 return i
< 4 ? -1 : 0;
1399 /* For each constraint of "bmap" that involves the input dimension data->depth,
1400 * make sure that all the other coefficients are multiples of data->m,
1401 * reducing data->m if needed.
1402 * Break out of the iteration if data->m has become equal to "1".
1404 static int basic_map_check_scaled(__isl_take isl_basic_map
*bmap
, void *user
)
1408 r
= isl_basic_map_foreach_constraint(bmap
,
1409 &constraint_check_scaled
, user
);
1410 isl_basic_map_free(bmap
);
1415 /* For each constraint of "map" that involves the input dimension data->depth,
1416 * make sure that all the other coefficients are multiples of data->m,
1417 * reducing data->m if needed.
1418 * Break out of the iteration if data->m has become equal to "1".
1420 static int map_check_scaled(__isl_take isl_map
*map
, void *user
)
1424 r
= isl_map_foreach_basic_map(map
, &basic_map_check_scaled
, user
);
1430 /* Create an AST node for the current dimension based on
1431 * the schedule domain "bounds" and return the node encapsulated
1432 * in an isl_ast_graft.
1434 * "executed" is the current inverse schedule, taking into account
1435 * the bounds in "bounds"
1436 * "domain" is the domain of "executed", with inner dimensions projected out.
1439 * Before moving on to the actual AST node construction in create_node_scaled,
1440 * we first check if the current dimension is strided and if we can scale
1441 * down this stride. Note that we only do this if the ast_build_scale_strides
1444 * In particular, let the current dimension take on values
1448 * with a an integer. We check if we can find an integer m that (obviouly)
1449 * divides both f and s.
1451 * If so, we check if the current dimension only appears in constraints
1452 * where the coefficients of the other variables are multiples of m.
1453 * We perform this extra check to avoid the risk of introducing
1454 * divisions by scaling down the current dimension.
1456 * If so, we scale the current dimension down by a factor of m.
1457 * That is, we plug in
1461 * Note that in principle we could always scale down strided loops
1466 * but this may result in i' taking on larger values than the original i,
1467 * due to the shift by "f".
1468 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1470 static __isl_give isl_ast_graft
*create_node(__isl_take isl_union_map
*executed
,
1471 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1472 __isl_take isl_ast_build
*build
)
1474 struct isl_check_scaled_data data
;
1478 ctx
= isl_ast_build_get_ctx(build
);
1479 if (!isl_options_get_ast_build_scale_strides(ctx
))
1480 return create_node_scaled(executed
, bounds
, domain
, build
);
1482 data
.depth
= isl_ast_build_get_depth(build
);
1483 if (!isl_ast_build_has_stride(build
, data
.depth
))
1484 return create_node_scaled(executed
, bounds
, domain
, build
);
1486 isl_int_init(data
.m
);
1487 isl_int_init(data
.d
);
1489 offset
= isl_ast_build_get_offset(build
, data
.depth
);
1490 if (isl_ast_build_get_stride(build
, data
.depth
, &data
.m
) < 0)
1491 offset
= isl_aff_free(offset
);
1492 offset
= isl_aff_scale_down(offset
, data
.m
);
1493 if (isl_aff_get_denominator(offset
, &data
.d
) < 0)
1494 executed
= isl_union_map_free(executed
);
1496 if (executed
&& isl_int_is_divisible_by(data
.m
, data
.d
))
1497 isl_int_divexact(data
.m
, data
.m
, data
.d
);
1499 isl_int_set_si(data
.m
, 1);
1501 if (!isl_int_is_one(data
.m
)) {
1502 if (isl_union_map_foreach_map(executed
, &map_check_scaled
,
1504 !isl_int_is_one(data
.m
))
1505 executed
= isl_union_map_free(executed
);
1508 if (!isl_int_is_one(data
.m
)) {
1513 isl_union_map
*umap
;
1515 space
= isl_ast_build_get_space(build
, 1);
1516 space
= isl_space_map_from_set(space
);
1517 ma
= isl_multi_aff_identity(space
);
1518 aff
= isl_multi_aff_get_aff(ma
, data
.depth
);
1519 aff
= isl_aff_scale(aff
, data
.m
);
1520 ma
= isl_multi_aff_set_aff(ma
, data
.depth
, aff
);
1522 bounds
= isl_basic_set_preimage_multi_aff(bounds
,
1523 isl_multi_aff_copy(ma
));
1524 domain
= isl_set_preimage_multi_aff(domain
,
1525 isl_multi_aff_copy(ma
));
1526 map
= isl_map_reverse(isl_map_from_multi_aff(ma
));
1527 umap
= isl_union_map_from_map(map
);
1528 executed
= isl_union_map_apply_domain(executed
,
1529 isl_union_map_copy(umap
));
1530 build
= isl_ast_build_scale_down(build
, data
.m
, umap
);
1532 isl_aff_free(offset
);
1534 isl_int_clear(data
.d
);
1535 isl_int_clear(data
.m
);
1537 return create_node_scaled(executed
, bounds
, domain
, build
);
1540 /* Add the basic set to the list that "user" points to.
1542 static int collect_basic_set(__isl_take isl_basic_set
*bset
, void *user
)
1544 isl_basic_set_list
**list
= user
;
1546 *list
= isl_basic_set_list_add(*list
, bset
);
1551 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1553 static __isl_give isl_basic_set_list
*isl_basic_set_list_from_set(
1554 __isl_take isl_set
*set
)
1558 isl_basic_set_list
*list
;
1563 ctx
= isl_set_get_ctx(set
);
1565 n
= isl_set_n_basic_set(set
);
1566 list
= isl_basic_set_list_alloc(ctx
, n
);
1567 if (isl_set_foreach_basic_set(set
, &collect_basic_set
, &list
) < 0)
1568 list
= isl_basic_set_list_free(list
);
1574 /* Generate code for the schedule domain "bounds"
1575 * and add the result to "list".
1577 * We mainly detect strides and additional equalities here
1578 * and then pass over control to create_node.
1580 * "bounds" reflects the bounds on the current dimension and possibly
1581 * some extra conditions on outer dimensions.
1582 * It does not, however, include any divs involving the current dimension,
1583 * so it does not capture any stride constraints.
1584 * We therefore need to compute that part of the schedule domain that
1585 * intersects with "bounds" and derive the strides from the result.
1587 static __isl_give isl_ast_graft_list
*add_node(
1588 __isl_take isl_ast_graft_list
*list
, __isl_take isl_union_map
*executed
,
1589 __isl_take isl_basic_set
*bounds
, __isl_take isl_ast_build
*build
)
1591 isl_ast_graft
*graft
;
1592 isl_set
*domain
= NULL
;
1593 isl_union_set
*uset
;
1596 uset
= isl_union_set_from_basic_set(isl_basic_set_copy(bounds
));
1597 executed
= isl_union_map_intersect_domain(executed
, uset
);
1598 empty
= isl_union_map_is_empty(executed
);
1604 uset
= isl_union_map_domain(isl_union_map_copy(executed
));
1605 domain
= isl_set_from_union_set(uset
);
1606 domain
= isl_ast_build_compute_gist(build
, domain
);
1607 empty
= isl_set_is_empty(domain
);
1613 domain
= isl_ast_build_eliminate_inner(build
, domain
);
1614 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
1616 graft
= create_node(executed
, bounds
, domain
,
1617 isl_ast_build_copy(build
));
1618 list
= isl_ast_graft_list_add(list
, graft
);
1619 isl_ast_build_free(build
);
1622 list
= isl_ast_graft_list_free(list
);
1624 isl_set_free(domain
);
1625 isl_basic_set_free(bounds
);
1626 isl_union_map_free(executed
);
1627 isl_ast_build_free(build
);
1631 struct isl_domain_follows_at_depth_data
{
1633 isl_basic_set
**piece
;
1636 /* Does any element of i follow or coincide with any element of j
1637 * at the current depth (data->depth) for equal values of the outer
1640 static int domain_follows_at_depth(int i
, int j
, void *user
)
1642 struct isl_domain_follows_at_depth_data
*data
= user
;
1643 isl_basic_map
*test
;
1647 test
= isl_basic_map_from_domain_and_range(
1648 isl_basic_set_copy(data
->piece
[i
]),
1649 isl_basic_set_copy(data
->piece
[j
]));
1650 for (l
= 0; l
< data
->depth
; ++l
)
1651 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1653 test
= isl_basic_map_order_ge(test
, isl_dim_in
, data
->depth
,
1654 isl_dim_out
, data
->depth
);
1655 empty
= isl_basic_map_is_empty(test
);
1656 isl_basic_map_free(test
);
1658 return empty
< 0 ? -1 : !empty
;
1661 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1662 __isl_keep isl_basic_set_list
*domain_list
,
1663 __isl_keep isl_union_map
*executed
,
1664 __isl_keep isl_ast_build
*build
);
1666 /* Generate code for the "n" schedule domains in "domain_list"
1667 * with positions specified by the entries of the "pos" array
1668 * and add the results to "list".
1670 * The "n" domains form a strongly connected component in the ordering.
1671 * If n is larger than 1, then this means that we cannot determine a valid
1672 * ordering for the n domains in the component. This should be fairly
1673 * rare because the individual domains have been made disjoint first.
1674 * The problem is that the domains may be integrally disjoint but not
1675 * rationally disjoint. For example, we may have domains
1677 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1679 * These two domains have an empty intersection, but their rational
1680 * relaxations do intersect. It is impossible to order these domains
1681 * in the second dimension because the first should be ordered before
1682 * the second for outer dimension equal to 0, while it should be ordered
1683 * after for outer dimension equal to 1.
1685 * This may happen in particular in case of unrolling since the domain
1686 * of each slice is replaced by its simple hull.
1688 * We collect the basic sets in the component, call isl_set_make_disjoint
1689 * and try again. Note that we rely here on isl_set_make_disjoint also
1690 * making the basic sets rationally disjoint. If the basic sets
1691 * are rationally disjoint, then the ordering problem does not occur.
1692 * To see this, there can only be a problem if there are points
1693 * (i,a) and (j,b) in one set and (i,c) and (j,d) in the other with
1694 * a < c and b > d. This means that either the interval spanned
1695 * by a en b lies inside that spanned by c and or the other way around.
1696 * In either case, there is a point inside both intervals with the
1697 * convex combination in terms of a and b and in terms of c and d.
1698 * Taking the same combination of i and j gives a point in the intersection.
1700 static __isl_give isl_ast_graft_list
*add_nodes(
1701 __isl_take isl_ast_graft_list
*list
, int *pos
, int n
,
1702 __isl_keep isl_basic_set_list
*domain_list
,
1703 __isl_keep isl_union_map
*executed
,
1704 __isl_keep isl_ast_build
*build
)
1707 isl_basic_set
*bset
;
1710 bset
= isl_basic_set_list_get_basic_set(domain_list
, pos
[0]);
1712 return add_node(list
, isl_union_map_copy(executed
), bset
,
1713 isl_ast_build_copy(build
));
1715 set
= isl_set_from_basic_set(bset
);
1716 for (i
= 1; i
< n
; ++i
) {
1717 bset
= isl_basic_set_list_get_basic_set(domain_list
, pos
[i
]);
1718 set
= isl_set_union(set
, isl_set_from_basic_set(bset
));
1721 set
= isl_set_make_disjoint(set
);
1722 if (isl_set_n_basic_set(set
) == n
)
1723 isl_die(isl_ast_graft_list_get_ctx(list
), isl_error_internal
,
1724 "unable to separate loop parts", goto error
);
1725 domain_list
= isl_basic_set_list_from_set(set
);
1726 list
= isl_ast_graft_list_concat(list
,
1727 generate_sorted_domains(domain_list
, executed
, build
));
1728 isl_basic_set_list_free(domain_list
);
1733 return isl_ast_graft_list_free(list
);
1736 /* Sort the domains in "domain_list" according to the execution order
1737 * at the current depth (for equal values of the outer dimensions),
1738 * generate code for each of them, collecting the results in a list.
1739 * If no code is generated (because the intersection of the inverse schedule
1740 * with the domains turns out to be empty), then an empty list is returned.
1742 * The caller is responsible for ensuring that the basic sets in "domain_list"
1743 * are pair-wise disjoint. It can, however, in principle happen that
1744 * two basic sets should be ordered one way for one value of the outer
1745 * dimensions and the other way for some other value of the outer dimensions.
1746 * We therefore play safe and look for strongly connected components.
1747 * The function add_nodes takes care of handling non-trivial components.
1749 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1750 __isl_keep isl_basic_set_list
*domain_list
,
1751 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1754 isl_ast_graft_list
*list
;
1755 struct isl_domain_follows_at_depth_data data
;
1756 struct isl_tarjan_graph
*g
;
1762 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1763 n
= isl_basic_set_list_n_basic_set(domain_list
);
1764 list
= isl_ast_graft_list_alloc(ctx
, n
);
1768 return add_node(list
, isl_union_map_copy(executed
),
1769 isl_basic_set_list_get_basic_set(domain_list
, 0),
1770 isl_ast_build_copy(build
));
1772 data
.depth
= isl_ast_build_get_depth(build
);
1773 data
.piece
= domain_list
->p
;
1774 g
= isl_tarjan_graph_init(ctx
, n
, &domain_follows_at_depth
, &data
);
1782 if (g
->order
[i
] == -1)
1783 isl_die(ctx
, isl_error_internal
, "cannot happen",
1786 while (g
->order
[i
] != -1) {
1789 list
= add_nodes(list
, g
->order
+ first
, i
- first
,
1790 domain_list
, executed
, build
);
1795 error
: list
= isl_ast_graft_list_free(list
);
1796 isl_tarjan_graph_free(g
);
1801 struct isl_shared_outer_data
{
1803 isl_basic_set
**piece
;
1806 /* Do elements i and j share any values for the outer dimensions?
1808 static int shared_outer(int i
, int j
, void *user
)
1810 struct isl_shared_outer_data
*data
= user
;
1811 isl_basic_map
*test
;
1815 test
= isl_basic_map_from_domain_and_range(
1816 isl_basic_set_copy(data
->piece
[i
]),
1817 isl_basic_set_copy(data
->piece
[j
]));
1818 for (l
= 0; l
< data
->depth
; ++l
)
1819 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1821 empty
= isl_basic_map_is_empty(test
);
1822 isl_basic_map_free(test
);
1824 return empty
< 0 ? -1 : !empty
;
1827 /* Call generate_sorted_domains on a list containing the elements
1828 * of "domain_list indexed by the first "n" elements of "pos".
1830 static __isl_give isl_ast_graft_list
*generate_sorted_domains_part(
1831 __isl_keep isl_basic_set_list
*domain_list
, int *pos
, int n
,
1832 __isl_keep isl_union_map
*executed
,
1833 __isl_keep isl_ast_build
*build
)
1837 isl_basic_set_list
*slice
;
1838 isl_ast_graft_list
*list
;
1840 ctx
= isl_ast_build_get_ctx(build
);
1841 slice
= isl_basic_set_list_alloc(ctx
, n
);
1842 for (i
= 0; i
< n
; ++i
) {
1843 isl_basic_set
*bset
;
1845 bset
= isl_basic_set_copy(domain_list
->p
[pos
[i
]]);
1846 slice
= isl_basic_set_list_add(slice
, bset
);
1849 list
= generate_sorted_domains(slice
, executed
, build
);
1850 isl_basic_set_list_free(slice
);
1855 /* Look for any (weakly connected) components in the "domain_list"
1856 * of domains that share some values of the outer dimensions.
1857 * That is, domains in different components do not share any values
1858 * of the outer dimensions. This means that these components
1859 * can be freely reordered.
1860 * Within each of the components, we sort the domains according
1861 * to the execution order at the current depth.
1863 * We fuse the result of each call to generate_sorted_domains_part
1864 * into a list with either zero or one graft and collect these (at most)
1865 * single element lists into a bigger list. This means that the elements of the
1866 * final list can be freely reordered. In particular, we sort them
1867 * according to an arbitrary but fixed ordering to ease merging of
1868 * graft lists from different components.
1870 static __isl_give isl_ast_graft_list
*generate_parallel_domains(
1871 __isl_keep isl_basic_set_list
*domain_list
,
1872 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1876 isl_ast_graft_list
*list
;
1877 struct isl_shared_outer_data data
;
1878 struct isl_tarjan_graph
*g
;
1883 n
= isl_basic_set_list_n_basic_set(domain_list
);
1885 return generate_sorted_domains(domain_list
, executed
, build
);
1887 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1889 data
.depth
= isl_ast_build_get_depth(build
);
1890 data
.piece
= domain_list
->p
;
1891 g
= isl_tarjan_graph_init(ctx
, n
, &shared_outer
, &data
);
1898 isl_ast_graft_list
*list_c
;
1900 if (g
->order
[i
] == -1)
1901 isl_die(ctx
, isl_error_internal
, "cannot happen",
1904 while (g
->order
[i
] != -1) {
1907 if (first
== 0 && n
== 0) {
1908 isl_tarjan_graph_free(g
);
1909 return generate_sorted_domains(domain_list
,
1912 list_c
= generate_sorted_domains_part(domain_list
,
1913 g
->order
+ first
, i
- first
, executed
, build
);
1914 list_c
= isl_ast_graft_list_fuse(list_c
, build
);
1918 list
= isl_ast_graft_list_concat(list
, list_c
);
1920 } while (list
&& n
);
1923 list
= isl_ast_graft_list_free(list
);
1925 list
= isl_ast_graft_list_sort_guard(list
);
1927 isl_tarjan_graph_free(g
);
1932 /* Internal data for separate_domain.
1934 * "explicit" is set if we only want to use explicit bounds.
1936 * "domain" collects the separated domains.
1938 struct isl_separate_domain_data
{
1939 isl_ast_build
*build
;
1944 /* Extract implicit bounds on the current dimension for the executed "map".
1946 * The domain of "map" may involve inner dimensions, so we
1947 * need to eliminate them.
1949 static __isl_give isl_set
*implicit_bounds(__isl_take isl_map
*map
,
1950 __isl_keep isl_ast_build
*build
)
1954 domain
= isl_map_domain(map
);
1955 domain
= isl_ast_build_eliminate(build
, domain
);
1960 /* Extract explicit bounds on the current dimension for the executed "map".
1962 * Rather than eliminating the inner dimensions as in implicit_bounds,
1963 * we simply drop any constraints involving those inner dimensions.
1964 * The idea is that most bounds that are implied by constraints on the
1965 * inner dimensions will be enforced by for loops and not by explicit guards.
1966 * There is then no need to separate along those bounds.
1968 static __isl_give isl_set
*explicit_bounds(__isl_take isl_map
*map
,
1969 __isl_keep isl_ast_build
*build
)
1974 dim
= isl_map_dim(map
, isl_dim_out
);
1975 map
= isl_map_drop_constraints_involving_dims(map
, isl_dim_out
, 0, dim
);
1977 domain
= isl_map_domain(map
);
1978 depth
= isl_ast_build_get_depth(build
);
1979 dim
= isl_set_dim(domain
, isl_dim_set
);
1980 domain
= isl_set_detect_equalities(domain
);
1981 domain
= isl_set_drop_constraints_involving_dims(domain
,
1982 isl_dim_set
, depth
+ 1, dim
- (depth
+ 1));
1983 domain
= isl_set_remove_divs_involving_dims(domain
,
1984 isl_dim_set
, depth
, 1);
1985 domain
= isl_set_remove_unknown_divs(domain
);
1990 /* Split data->domain into pieces that intersect with the range of "map"
1991 * and pieces that do not intersect with the range of "map"
1992 * and then add that part of the range of "map" that does not intersect
1993 * with data->domain.
1995 static int separate_domain(__isl_take isl_map
*map
, void *user
)
1997 struct isl_separate_domain_data
*data
= user
;
2002 domain
= explicit_bounds(map
, data
->build
);
2004 domain
= implicit_bounds(map
, data
->build
);
2006 domain
= isl_set_coalesce(domain
);
2007 domain
= isl_set_make_disjoint(domain
);
2008 d1
= isl_set_subtract(isl_set_copy(domain
), isl_set_copy(data
->domain
));
2009 d2
= isl_set_subtract(isl_set_copy(data
->domain
), isl_set_copy(domain
));
2010 data
->domain
= isl_set_intersect(data
->domain
, domain
);
2011 data
->domain
= isl_set_union(data
->domain
, d1
);
2012 data
->domain
= isl_set_union(data
->domain
, d2
);
2017 /* Separate the schedule domains of "executed".
2019 * That is, break up the domain of "executed" into basic sets,
2020 * such that for each basic set S, every element in S is associated with
2021 * the same domain spaces.
2023 * "space" is the (single) domain space of "executed".
2025 static __isl_give isl_set
*separate_schedule_domains(
2026 __isl_take isl_space
*space
, __isl_take isl_union_map
*executed
,
2027 __isl_keep isl_ast_build
*build
)
2029 struct isl_separate_domain_data data
= { build
};
2032 ctx
= isl_ast_build_get_ctx(build
);
2033 data
.explicit = isl_options_get_ast_build_separation_bounds(ctx
) ==
2034 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
;
2035 data
.domain
= isl_set_empty(space
);
2036 if (isl_union_map_foreach_map(executed
, &separate_domain
, &data
) < 0)
2037 data
.domain
= isl_set_free(data
.domain
);
2039 isl_union_map_free(executed
);
2043 /* Temporary data used during the search for a lower bound for unrolling.
2045 * "domain" is the original set for which to find a lower bound
2046 * "depth" is the dimension for which to find a lower boudn
2048 * "lower" is the best lower bound found so far. It is NULL if we have not
2050 * "n" is the corresponding size. If lower is NULL, then the value of n
2053 * "tmp" is a temporary initialized isl_int.
2055 struct isl_find_unroll_data
{
2064 /* Check if we can use "c" as a lower bound and if it is better than
2065 * any previously found lower bound.
2067 * If "c" does not involve the dimension at the current depth,
2068 * then we cannot use it.
2069 * Otherwise, let "c" be of the form
2073 * We compute the maximal value of
2075 * -ceil(f(j)/a)) + i + 1
2077 * over the domain. If there is such a value "n", then we know
2079 * -ceil(f(j)/a)) + i + 1 <= n
2083 * i < ceil(f(j)/a)) + n
2085 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2086 * We just need to check if we have found any lower bound before and
2087 * if the new lower bound is better (smaller n) than the previously found
2090 static int update_unrolling_lower_bound(struct isl_find_unroll_data
*data
,
2091 __isl_keep isl_constraint
*c
)
2093 isl_aff
*aff
, *lower
;
2094 enum isl_lp_result res
;
2096 if (!isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->depth
))
2099 lower
= isl_constraint_get_bound(c
, isl_dim_set
, data
->depth
);
2100 lower
= isl_aff_ceil(lower
);
2101 aff
= isl_aff_copy(lower
);
2102 aff
= isl_aff_neg(aff
);
2103 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, data
->depth
, 1);
2104 aff
= isl_aff_add_constant_si(aff
, 1);
2105 res
= isl_set_max(data
->domain
, aff
, &data
->tmp
);
2108 if (res
== isl_lp_error
)
2110 if (res
== isl_lp_unbounded
) {
2111 isl_aff_free(lower
);
2115 if (isl_int_cmp_si(data
->tmp
, INT_MAX
) <= 0 &&
2116 (!data
->lower
|| isl_int_cmp_si(data
->tmp
, *data
->n
) < 0)) {
2117 isl_aff_free(data
->lower
);
2118 data
->lower
= lower
;
2119 *data
->n
= isl_int_get_si(data
->tmp
);
2121 isl_aff_free(lower
);
2125 isl_aff_free(lower
);
2129 /* Check if we can use "c" as a lower bound and if it is better than
2130 * any previously found lower bound.
2132 static int constraint_find_unroll(__isl_take isl_constraint
*c
, void *user
)
2134 struct isl_find_unroll_data
*data
;
2137 data
= (struct isl_find_unroll_data
*) user
;
2138 r
= update_unrolling_lower_bound(data
, c
);
2139 isl_constraint_free(c
);
2144 /* Look for a lower bound l(i) on the dimension at "depth"
2145 * and a size n such that "domain" is a subset of
2147 * { [i] : l(i) <= i_d < l(i) + n }
2149 * where d is "depth" and l(i) depends only on earlier dimensions.
2150 * Furthermore, try and find a lower bound such that n is as small as possible.
2151 * In particular, "n" needs to be finite.
2153 * Inner dimensions have been eliminated from "domain" by the caller.
2155 * We first construct a collection of lower bounds on the input set
2156 * by computing its simple hull. We then iterate through them,
2157 * discarding those that we cannot use (either because they do not
2158 * involve the dimension at "depth" or because they have no corresponding
2159 * upper bound, meaning that "n" would be unbounded) and pick out the
2160 * best from the remaining ones.
2162 * If we cannot find a suitable lower bound, then we consider that
2165 static __isl_give isl_aff
*find_unroll_lower_bound(__isl_keep isl_set
*domain
,
2168 struct isl_find_unroll_data data
= { domain
, depth
, NULL
, n
};
2169 isl_basic_set
*hull
;
2171 isl_int_init(data
.tmp
);
2172 hull
= isl_set_simple_hull(isl_set_copy(domain
));
2174 if (isl_basic_set_foreach_constraint(hull
,
2175 &constraint_find_unroll
, &data
) < 0)
2178 isl_basic_set_free(hull
);
2179 isl_int_clear(data
.tmp
);
2182 isl_die(isl_set_get_ctx(domain
), isl_error_invalid
,
2183 "cannot find lower bound for unrolling", return NULL
);
2187 isl_basic_set_free(hull
);
2188 isl_int_clear(data
.tmp
);
2189 return isl_aff_free(data
.lower
);
2192 /* Return the constraint
2194 * i_"depth" = aff + offset
2196 static __isl_give isl_constraint
*at_offset(int depth
, __isl_keep isl_aff
*aff
,
2199 aff
= isl_aff_copy(aff
);
2200 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, depth
, -1);
2201 aff
= isl_aff_add_constant_si(aff
, offset
);
2202 return isl_equality_from_aff(aff
);
2205 /* Return a list of basic sets, one for each value of the current dimension
2207 * The divs that involve the current dimension have not been projected out
2210 * Since we are going to be iterating over the individual values,
2211 * we first check if there are any strides on the current dimension.
2212 * If there is, we rewrite the current dimension i as
2214 * i = stride i' + offset
2216 * and then iterate over individual values of i' instead.
2218 * We then look for a lower bound on i' and a size such that the domain
2221 * { [j,i'] : l(j) <= i' < l(j) + n }
2223 * and then take slices of the domain at values of i'
2224 * between l(j) and l(j) + n - 1.
2226 * We compute the unshifted simple hull of each slice to ensure that
2227 * we have a single basic set per offset. The slicing constraint
2228 * may get simplified away before the unshifted simple hull is taken
2229 * and may therefore in some rare cases disappear from the result.
2230 * We therefore explicitly add the constraint back after computing
2231 * the unshifted simple hull to ensure that the basic sets
2232 * remain disjoint. The constraints that are dropped by taking the hull
2233 * will be taken into account at the next level, as in the case of the
2236 * Finally, we map i' back to i and add each basic set to the list.
2238 static __isl_give isl_basic_set_list
*do_unroll(__isl_take isl_set
*domain
,
2239 __isl_keep isl_ast_build
*build
)
2245 isl_basic_set_list
*list
;
2246 isl_multi_aff
*expansion
;
2247 isl_basic_map
*bmap
;
2252 ctx
= isl_set_get_ctx(domain
);
2253 depth
= isl_ast_build_get_depth(build
);
2254 build
= isl_ast_build_copy(build
);
2255 domain
= isl_ast_build_eliminate_inner(build
, domain
);
2256 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
2257 expansion
= isl_ast_build_get_stride_expansion(build
);
2259 domain
= isl_set_preimage_multi_aff(domain
,
2260 isl_multi_aff_copy(expansion
));
2261 domain
= isl_ast_build_eliminate_divs(build
, domain
);
2263 isl_ast_build_free(build
);
2265 list
= isl_basic_set_list_alloc(ctx
, 0);
2267 lower
= find_unroll_lower_bound(domain
, depth
, &n
);
2269 list
= isl_basic_set_list_free(list
);
2271 bmap
= isl_basic_map_from_multi_aff(expansion
);
2273 for (i
= 0; list
&& i
< n
; ++i
) {
2275 isl_basic_set
*bset
;
2276 isl_constraint
*slice
;
2278 slice
= at_offset(depth
, lower
, i
);
2279 set
= isl_set_copy(domain
);
2280 set
= isl_set_add_constraint(set
, isl_constraint_copy(slice
));
2281 bset
= isl_set_unshifted_simple_hull(set
);
2282 bset
= isl_basic_set_add_constraint(bset
, slice
);
2283 bset
= isl_basic_set_apply(bset
, isl_basic_map_copy(bmap
));
2284 list
= isl_basic_set_list_add(list
, bset
);
2287 isl_aff_free(lower
);
2288 isl_set_free(domain
);
2289 isl_basic_map_free(bmap
);
2294 /* Data structure for storing the results and the intermediate objects
2295 * of compute_domains.
2297 * "list" is the main result of the function and contains a list
2298 * of disjoint basic sets for which code should be generated.
2300 * "executed" and "build" are inputs to compute_domains.
2301 * "schedule_domain" is the domain of "executed".
2303 * "option" constains the domains at the current depth that should by
2304 * atomic, separated or unrolled. These domains are as specified by
2305 * the user, except that inner dimensions have been eliminated and
2306 * that they have been made pair-wise disjoint.
2308 * "sep_class" contains the user-specified split into separation classes
2309 * specialized to the current depth.
2310 * "done" contains the union of the separation domains that have already
2312 * "atomic" contains the domain that has effectively been made atomic.
2313 * This domain may be larger than the intersection of option[atomic]
2314 * and the schedule domain.
2316 struct isl_codegen_domains
{
2317 isl_basic_set_list
*list
;
2319 isl_union_map
*executed
;
2320 isl_ast_build
*build
;
2321 isl_set
*schedule_domain
;
2330 /* Add domains to domains->list for each individual value of the current
2331 * dimension, for that part of the schedule domain that lies in the
2332 * intersection of the option domain and the class domain.
2334 * "domain" is the intersection of the class domain and the schedule domain.
2335 * The divs that involve the current dimension have not been projected out
2338 * We first break up the unroll option domain into individual pieces
2339 * and then handle each of them separately. The unroll option domain
2340 * has been made disjoint in compute_domains_init_options,
2342 * Note that we actively want to combine different pieces of the
2343 * schedule domain that have the same value at the current dimension.
2344 * We therefore need to break up the unroll option domain before
2345 * intersecting with class and schedule domain, hoping that the
2346 * unroll option domain specified by the user is relatively simple.
2348 static int compute_unroll_domains(struct isl_codegen_domains
*domains
,
2349 __isl_keep isl_set
*domain
)
2351 isl_set
*unroll_domain
;
2352 isl_basic_set_list
*unroll_list
;
2356 empty
= isl_set_is_empty(domains
->option
[unroll
]);
2362 unroll_domain
= isl_set_copy(domains
->option
[unroll
]);
2363 unroll_list
= isl_basic_set_list_from_set(unroll_domain
);
2365 n
= isl_basic_set_list_n_basic_set(unroll_list
);
2366 for (i
= 0; i
< n
; ++i
) {
2367 isl_basic_set
*bset
;
2368 isl_basic_set_list
*list
;
2370 bset
= isl_basic_set_list_get_basic_set(unroll_list
, i
);
2371 unroll_domain
= isl_set_from_basic_set(bset
);
2372 unroll_domain
= isl_set_intersect(unroll_domain
,
2373 isl_set_copy(domain
));
2375 empty
= isl_set_is_empty(unroll_domain
);
2376 if (empty
>= 0 && empty
) {
2377 isl_set_free(unroll_domain
);
2381 list
= do_unroll(unroll_domain
, domains
->build
);
2382 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2385 isl_basic_set_list_free(unroll_list
);
2390 /* Construct a single basic set that includes the intersection of
2391 * the schedule domain, the atomic option domain and the class domain.
2392 * Add the resulting basic set to domains->list and save a copy
2393 * in domains->atomic for use in compute_partial_domains.
2395 * We construct a single domain rather than trying to combine
2396 * the schedule domains of individual domains because we are working
2397 * within a single component so that non-overlapping schedule domains
2398 * should already have been separated.
2399 * Note, though, that this does not take into account the class domain.
2400 * So, it is possible for a class domain to carve out a piece of the
2401 * schedule domain with independent pieces and then we would only
2402 * generate a single domain for them. If this proves to be problematic
2403 * for some users, then this function will have to be adjusted.
2405 * "domain" is the intersection of the schedule domain and the class domain,
2406 * with inner dimensions projected out.
2408 static int compute_atomic_domain(struct isl_codegen_domains
*domains
,
2409 __isl_keep isl_set
*domain
)
2411 isl_basic_set
*bset
;
2412 isl_set
*atomic_domain
;
2415 atomic_domain
= isl_set_copy(domains
->option
[atomic
]);
2416 atomic_domain
= isl_set_intersect(atomic_domain
, isl_set_copy(domain
));
2417 empty
= isl_set_is_empty(atomic_domain
);
2418 if (empty
< 0 || empty
) {
2419 domains
->atomic
= atomic_domain
;
2420 return empty
< 0 ? -1 : 0;
2423 atomic_domain
= isl_set_coalesce(atomic_domain
);
2424 bset
= isl_set_unshifted_simple_hull(atomic_domain
);
2425 domains
->atomic
= isl_set_from_basic_set(isl_basic_set_copy(bset
));
2426 domains
->list
= isl_basic_set_list_add(domains
->list
, bset
);
2431 /* Split up the schedule domain into uniform basic sets,
2432 * in the sense that each element in a basic set is associated to
2433 * elements of the same domains, and add the result to domains->list.
2434 * Do this for that part of the schedule domain that lies in the
2435 * intersection of "class_domain" and the separate option domain.
2437 * "class_domain" may or may not include the constraints
2438 * of the schedule domain, but this does not make a difference
2439 * since we are going to intersect it with the domain of the inverse schedule.
2440 * If it includes schedule domain constraints, then they may involve
2441 * inner dimensions, but we will eliminate them in separation_domain.
2443 static int compute_separate_domain(struct isl_codegen_domains
*domains
,
2444 __isl_keep isl_set
*class_domain
)
2448 isl_union_map
*executed
;
2449 isl_basic_set_list
*list
;
2452 domain
= isl_set_copy(domains
->option
[separate
]);
2453 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2454 executed
= isl_union_map_copy(domains
->executed
);
2455 executed
= isl_union_map_intersect_domain(executed
,
2456 isl_union_set_from_set(domain
));
2457 empty
= isl_union_map_is_empty(executed
);
2458 if (empty
< 0 || empty
) {
2459 isl_union_map_free(executed
);
2460 return empty
< 0 ? -1 : 0;
2463 space
= isl_set_get_space(class_domain
);
2464 domain
= separate_schedule_domains(space
, executed
, domains
->build
);
2466 list
= isl_basic_set_list_from_set(domain
);
2467 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2472 /* Split up the domain at the current depth into disjoint
2473 * basic sets for which code should be generated separately
2474 * for the given separation class domain.
2476 * If any separation classes have been defined, then "class_domain"
2477 * is the domain of the current class and does not refer to inner dimensions.
2478 * Otherwise, "class_domain" is the universe domain.
2480 * We first make sure that the class domain is disjoint from
2481 * previously considered class domains.
2483 * The separate domains can be computed directly from the "class_domain".
2485 * The unroll, atomic and remainder domains need the constraints
2486 * from the schedule domain.
2488 * For unrolling, the actual schedule domain is needed (with divs that
2489 * may refer to the current dimension) so that stride detection can be
2492 * For atomic and remainder domains, inner dimensions and divs involving
2493 * the current dimensions should be eliminated.
2494 * In case we are working within a separation class, we need to intersect
2495 * the result with the current "class_domain" to ensure that the domains
2496 * are disjoint from those generated from other class domains.
2498 * The domain that has been made atomic may be larger than specified
2499 * by the user since it needs to be representable as a single basic set.
2500 * This possibly larger domain is stored in domains->atomic by
2501 * compute_atomic_domain.
2503 * If anything is left after handling separate, unroll and atomic,
2504 * we split it up into basic sets and append the basic sets to domains->list.
2506 static int compute_partial_domains(struct isl_codegen_domains
*domains
,
2507 __isl_take isl_set
*class_domain
)
2509 isl_basic_set_list
*list
;
2512 class_domain
= isl_set_subtract(class_domain
,
2513 isl_set_copy(domains
->done
));
2514 domains
->done
= isl_set_union(domains
->done
,
2515 isl_set_copy(class_domain
));
2517 domain
= isl_set_copy(class_domain
);
2519 if (compute_separate_domain(domains
, domain
) < 0)
2521 domain
= isl_set_subtract(domain
,
2522 isl_set_copy(domains
->option
[separate
]));
2524 domain
= isl_set_intersect(domain
,
2525 isl_set_copy(domains
->schedule_domain
));
2527 if (compute_unroll_domains(domains
, domain
) < 0)
2529 domain
= isl_set_subtract(domain
,
2530 isl_set_copy(domains
->option
[unroll
]));
2532 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2533 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2535 if (compute_atomic_domain(domains
, domain
) < 0)
2536 domain
= isl_set_free(domain
);
2537 domain
= isl_set_subtract(domain
, domains
->atomic
);
2539 domain
= isl_set_coalesce(domain
);
2540 domain
= isl_set_make_disjoint(domain
);
2542 list
= isl_basic_set_list_from_set(domain
);
2543 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2545 isl_set_free(class_domain
);
2549 isl_set_free(domain
);
2550 isl_set_free(class_domain
);
2554 /* Split up the domain at the current depth into disjoint
2555 * basic sets for which code should be generated separately
2556 * for the separation class identified by "pnt".
2558 * We extract the corresponding class domain from domains->sep_class,
2559 * eliminate inner dimensions and pass control to compute_partial_domains.
2561 static int compute_class_domains(__isl_take isl_point
*pnt
, void *user
)
2563 struct isl_codegen_domains
*domains
= user
;
2568 class_set
= isl_set_from_point(pnt
);
2569 domain
= isl_map_domain(isl_map_intersect_range(
2570 isl_map_copy(domains
->sep_class
), class_set
));
2571 domain
= isl_ast_build_compute_gist(domains
->build
, domain
);
2572 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2574 disjoint
= isl_set_plain_is_disjoint(domain
, domains
->schedule_domain
);
2578 isl_set_free(domain
);
2582 return compute_partial_domains(domains
, domain
);
2585 /* Extract the domains at the current depth that should be atomic,
2586 * separated or unrolled and store them in option.
2588 * The domains specified by the user might overlap, so we make
2589 * them disjoint by subtracting earlier domains from later domains.
2591 static void compute_domains_init_options(isl_set
*option
[3],
2592 __isl_keep isl_ast_build
*build
)
2594 enum isl_ast_build_domain_type type
, type2
;
2596 for (type
= atomic
; type
<= separate
; ++type
) {
2597 option
[type
] = isl_ast_build_get_option_domain(build
, type
);
2598 for (type2
= atomic
; type2
< type
; ++type2
)
2599 option
[type
] = isl_set_subtract(option
[type
],
2600 isl_set_copy(option
[type2
]));
2603 option
[unroll
] = isl_set_coalesce(option
[unroll
]);
2604 option
[unroll
] = isl_set_make_disjoint(option
[unroll
]);
2607 /* Split up the domain at the current depth into disjoint
2608 * basic sets for which code should be generated separately,
2609 * based on the user-specified options.
2610 * Return the list of disjoint basic sets.
2612 * There are three kinds of domains that we need to keep track of.
2613 * - the "schedule domain" is the domain of "executed"
2614 * - the "class domain" is the domain corresponding to the currrent
2616 * - the "option domain" is the domain corresponding to one of the options
2617 * atomic, unroll or separate
2619 * We first consider the individial values of the separation classes
2620 * and split up the domain for each of them separately.
2621 * Finally, we consider the remainder. If no separation classes were
2622 * specified, then we call compute_partial_domains with the universe
2623 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2624 * with inner dimensions removed. We do this because we want to
2625 * avoid computing the complement of the class domains (i.e., the difference
2626 * between the universe and domains->done).
2628 static __isl_give isl_basic_set_list
*compute_domains(
2629 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
2631 struct isl_codegen_domains domains
;
2634 isl_union_set
*schedule_domain
;
2638 enum isl_ast_build_domain_type type
;
2644 ctx
= isl_union_map_get_ctx(executed
);
2645 domains
.list
= isl_basic_set_list_alloc(ctx
, 0);
2647 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
2648 domain
= isl_set_from_union_set(schedule_domain
);
2650 compute_domains_init_options(domains
.option
, build
);
2652 domains
.sep_class
= isl_ast_build_get_separation_class(build
);
2653 classes
= isl_map_range(isl_map_copy(domains
.sep_class
));
2654 n_param
= isl_set_dim(classes
, isl_dim_param
);
2655 classes
= isl_set_project_out(classes
, isl_dim_param
, 0, n_param
);
2657 space
= isl_set_get_space(domain
);
2658 domains
.build
= build
;
2659 domains
.schedule_domain
= isl_set_copy(domain
);
2660 domains
.executed
= executed
;
2661 domains
.done
= isl_set_empty(space
);
2663 if (isl_set_foreach_point(classes
, &compute_class_domains
, &domains
) < 0)
2664 domains
.list
= isl_basic_set_list_free(domains
.list
);
2665 isl_set_free(classes
);
2667 empty
= isl_set_is_empty(domains
.done
);
2669 domains
.list
= isl_basic_set_list_free(domains
.list
);
2670 domain
= isl_set_free(domain
);
2672 isl_set_free(domain
);
2673 domain
= isl_set_universe(isl_set_get_space(domains
.done
));
2675 domain
= isl_ast_build_eliminate(build
, domain
);
2677 if (compute_partial_domains(&domains
, domain
) < 0)
2678 domains
.list
= isl_basic_set_list_free(domains
.list
);
2680 isl_set_free(domains
.schedule_domain
);
2681 isl_set_free(domains
.done
);
2682 isl_map_free(domains
.sep_class
);
2683 for (type
= atomic
; type
<= separate
; ++type
)
2684 isl_set_free(domains
.option
[type
]);
2686 return domains
.list
;
2689 /* Generate code for a single component, after shifting (if any)
2692 * We first split up the domain at the current depth into disjoint
2693 * basic sets based on the user-specified options.
2694 * Then we generated code for each of them and concatenate the results.
2696 static __isl_give isl_ast_graft_list
*generate_shifted_component(
2697 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
2699 isl_basic_set_list
*domain_list
;
2700 isl_ast_graft_list
*list
= NULL
;
2702 domain_list
= compute_domains(executed
, build
);
2703 list
= generate_parallel_domains(domain_list
, executed
, build
);
2705 isl_basic_set_list_free(domain_list
);
2706 isl_union_map_free(executed
);
2707 isl_ast_build_free(build
);
2712 struct isl_set_map_pair
{
2717 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2718 * of indices into the "domain" array,
2719 * return the union of the "map" fields of the elements
2720 * indexed by the first "n" elements of "order".
2722 static __isl_give isl_union_map
*construct_component_executed(
2723 struct isl_set_map_pair
*domain
, int *order
, int n
)
2727 isl_union_map
*executed
;
2729 map
= isl_map_copy(domain
[order
[0]].map
);
2730 executed
= isl_union_map_from_map(map
);
2731 for (i
= 1; i
< n
; ++i
) {
2732 map
= isl_map_copy(domain
[order
[i
]].map
);
2733 executed
= isl_union_map_add_map(executed
, map
);
2739 /* Generate code for a single component, after shifting (if any)
2742 * The component inverse schedule is specified as the "map" fields
2743 * of the elements of "domain" indexed by the first "n" elements of "order".
2745 static __isl_give isl_ast_graft_list
*generate_shifted_component_from_list(
2746 struct isl_set_map_pair
*domain
, int *order
, int n
,
2747 __isl_take isl_ast_build
*build
)
2749 isl_union_map
*executed
;
2751 executed
= construct_component_executed(domain
, order
, n
);
2752 return generate_shifted_component(executed
, build
);
2755 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2756 * of indices into the "domain" array,
2757 * do all (except for at most one) of the "set" field of the elements
2758 * indexed by the first "n" elements of "order" have a fixed value
2759 * at position "depth"?
2761 static int at_most_one_non_fixed(struct isl_set_map_pair
*domain
,
2762 int *order
, int n
, int depth
)
2767 for (i
= 0; i
< n
; ++i
) {
2770 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2771 isl_dim_set
, depth
, NULL
);
2784 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2785 * of indices into the "domain" array,
2786 * eliminate the inner dimensions from the "set" field of the elements
2787 * indexed by the first "n" elements of "order", provided the current
2788 * dimension does not have a fixed value.
2790 * Return the index of the first element in "order" with a corresponding
2791 * "set" field that does not have an (obviously) fixed value.
2793 static int eliminate_non_fixed(struct isl_set_map_pair
*domain
,
2794 int *order
, int n
, int depth
, __isl_keep isl_ast_build
*build
)
2799 for (i
= n
- 1; i
>= 0; --i
) {
2801 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2802 isl_dim_set
, depth
, NULL
);
2807 domain
[order
[i
]].set
= isl_ast_build_eliminate_inner(build
,
2808 domain
[order
[i
]].set
);
2815 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2816 * of indices into the "domain" array,
2817 * find the element of "domain" (amongst those indexed by the first "n"
2818 * elements of "order") with the "set" field that has the smallest
2819 * value for the current iterator.
2821 * Note that the domain with the smallest value may depend on the parameters
2822 * and/or outer loop dimension. Since the result of this function is only
2823 * used as heuristic, we only make a reasonable attempt at finding the best
2824 * domain, one that should work in case a single domain provides the smallest
2825 * value for the current dimension over all values of the parameters
2826 * and outer dimensions.
2828 * In particular, we compute the smallest value of the first domain
2829 * and replace it by that of any later domain if that later domain
2830 * has a smallest value that is smaller for at least some value
2831 * of the parameters and outer dimensions.
2833 static int first_offset(struct isl_set_map_pair
*domain
, int *order
, int n
,
2834 __isl_keep isl_ast_build
*build
)
2840 min_first
= isl_ast_build_map_to_iterator(build
,
2841 isl_set_copy(domain
[order
[0]].set
));
2842 min_first
= isl_map_lexmin(min_first
);
2844 for (i
= 1; i
< n
; ++i
) {
2845 isl_map
*min
, *test
;
2848 min
= isl_ast_build_map_to_iterator(build
,
2849 isl_set_copy(domain
[order
[i
]].set
));
2850 min
= isl_map_lexmin(min
);
2851 test
= isl_map_copy(min
);
2852 test
= isl_map_apply_domain(isl_map_copy(min_first
), test
);
2853 test
= isl_map_order_lt(test
, isl_dim_in
, 0, isl_dim_out
, 0);
2854 empty
= isl_map_is_empty(test
);
2856 if (empty
>= 0 && !empty
) {
2857 isl_map_free(min_first
);
2867 isl_map_free(min_first
);
2869 return i
< n
? -1 : first
;
2872 /* Construct a shifted inverse schedule based on the original inverse schedule,
2873 * the stride and the offset.
2875 * The original inverse schedule is specified as the "map" fields
2876 * of the elements of "domain" indexed by the first "n" elements of "order".
2878 * "stride" and "offset" are such that the difference
2879 * between the values of the current dimension of domain "i"
2880 * and the values of the current dimension for some reference domain are
2883 * stride * integer + offset[i]
2885 * Moreover, 0 <= offset[i] < stride.
2887 * For each domain, we create a map
2889 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2891 * where j refers to the current dimension and the other dimensions are
2892 * unchanged, and apply this map to the original schedule domain.
2894 * For example, for the original schedule
2896 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2898 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2899 * we apply the mapping
2903 * to the schedule of the "A" domain and the mapping
2905 * { [j - 1] -> [j, 1] }
2907 * to the schedule of the "B" domain.
2910 * Note that after the transformation, the differences between pairs
2911 * of values of the current dimension over all domains are multiples
2912 * of stride and that we have therefore exposed the stride.
2915 * To see that the mapping preserves the lexicographic order,
2916 * first note that each of the individual maps above preserves the order.
2917 * If the value of the current iterator is j1 in one domain and j2 in another,
2918 * then if j1 = j2, we know that the same map is applied to both domains
2919 * and the order is preserved.
2920 * Otherwise, let us assume, without loss of generality, that j1 < j2.
2921 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
2925 * and the order is preserved.
2926 * If c1 < c2, then we know
2932 * j2 - j1 = n * s + r
2934 * with n >= 0 and 0 <= r < s.
2935 * In other words, r = c2 - c1.
2946 * (j1 - c1, c1) << (j2 - c2, c2)
2948 * with "<<" the lexicographic order, proving that the order is preserved
2951 static __isl_give isl_union_map
*contruct_shifted_executed(
2952 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
2953 __isl_keep isl_vec
*offset
, __isl_keep isl_ast_build
*build
)
2957 isl_union_map
*executed
;
2963 depth
= isl_ast_build_get_depth(build
);
2964 space
= isl_ast_build_get_space(build
, 1);
2965 executed
= isl_union_map_empty(isl_space_copy(space
));
2966 space
= isl_space_map_from_set(space
);
2967 map
= isl_map_identity(isl_space_copy(space
));
2968 map
= isl_map_eliminate(map
, isl_dim_out
, depth
, 1);
2969 map
= isl_map_insert_dims(map
, isl_dim_out
, depth
+ 1, 1);
2970 space
= isl_space_insert_dims(space
, isl_dim_out
, depth
+ 1, 1);
2972 c
= isl_equality_alloc(isl_local_space_from_space(space
));
2973 c
= isl_constraint_set_coefficient_si(c
, isl_dim_in
, depth
, 1);
2974 c
= isl_constraint_set_coefficient_si(c
, isl_dim_out
, depth
, -1);
2978 for (i
= 0; i
< n
; ++i
) {
2981 if (isl_vec_get_element(offset
, i
, &v
) < 0)
2983 map_i
= isl_map_copy(map
);
2984 map_i
= isl_map_fix(map_i
, isl_dim_out
, depth
+ 1, v
);
2986 c
= isl_constraint_set_constant(c
, v
);
2987 map_i
= isl_map_add_constraint(map_i
, isl_constraint_copy(c
));
2989 map_i
= isl_map_apply_domain(isl_map_copy(domain
[order
[i
]].map
),
2991 executed
= isl_union_map_add_map(executed
, map_i
);
2994 isl_constraint_free(c
);
3000 executed
= isl_union_map_free(executed
);
3005 /* Generate code for a single component, after exposing the stride,
3006 * given that the schedule domain is "shifted strided".
3008 * The component inverse schedule is specified as the "map" fields
3009 * of the elements of "domain" indexed by the first "n" elements of "order".
3011 * The schedule domain being "shifted strided" means that the differences
3012 * between the values of the current dimension of domain "i"
3013 * and the values of the current dimension for some reference domain are
3016 * stride * integer + offset[i]
3018 * We first look for the domain with the "smallest" value for the current
3019 * dimension and adjust the offsets such that the offset of the "smallest"
3020 * domain is equal to zero. The other offsets are reduced modulo stride.
3022 * Based on this information, we construct a new inverse schedule in
3023 * contruct_shifted_executed that exposes the stride.
3024 * Since this involves the introduction of a new schedule dimension,
3025 * the build needs to be changed accodingly.
3026 * After computing the AST, the newly introduced dimension needs
3027 * to be removed again from the list of grafts. We do this by plugging
3028 * in a mapping that represents the new schedule domain in terms of the
3029 * old schedule domain.
3031 static __isl_give isl_ast_graft_list
*generate_shift_component(
3032 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
3033 __isl_keep isl_vec
*offset
, __isl_take isl_ast_build
*build
)
3035 isl_ast_graft_list
*list
;
3042 isl_multi_aff
*ma
, *zero
;
3043 isl_union_map
*executed
;
3045 ctx
= isl_ast_build_get_ctx(build
);
3046 depth
= isl_ast_build_get_depth(build
);
3048 first
= first_offset(domain
, order
, n
, build
);
3050 return isl_ast_build_free(build
);
3053 v
= isl_vec_alloc(ctx
, n
);
3054 if (isl_vec_get_element(offset
, first
, &val
) < 0)
3055 v
= isl_vec_free(v
);
3056 isl_int_neg(val
, val
);
3057 v
= isl_vec_set(v
, val
);
3058 v
= isl_vec_add(v
, isl_vec_copy(offset
));
3059 v
= isl_vec_fdiv_r(v
, stride
);
3061 executed
= contruct_shifted_executed(domain
, order
, n
, stride
, v
,
3063 space
= isl_ast_build_get_space(build
, 1);
3064 space
= isl_space_map_from_set(space
);
3065 ma
= isl_multi_aff_identity(isl_space_copy(space
));
3066 space
= isl_space_from_domain(isl_space_domain(space
));
3067 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
3068 zero
= isl_multi_aff_zero(space
);
3069 ma
= isl_multi_aff_range_splice(ma
, depth
+ 1, zero
);
3070 build
= isl_ast_build_insert_dim(build
, depth
+ 1);
3071 list
= generate_shifted_component(executed
, build
);
3073 list
= isl_ast_graft_list_preimage_multi_aff(list
, ma
);
3081 /* Generate code for a single component.
3083 * The component inverse schedule is specified as the "map" fields
3084 * of the elements of "domain" indexed by the first "n" elements of "order".
3086 * This function may modify the "set" fields of "domain".
3088 * Before proceeding with the actual code generation for the component,
3089 * we first check if there are any "shifted" strides, meaning that
3090 * the schedule domains of the individual domains are all strided,
3091 * but that they have different offsets, resulting in the union
3092 * of schedule domains not being strided anymore.
3094 * The simplest example is the schedule
3096 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3098 * Both schedule domains are strided, but their union is not.
3099 * This function detects such cases and then rewrites the schedule to
3101 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3103 * In the new schedule, the schedule domains have the same offset (modulo
3104 * the stride), ensuring that the union of schedule domains is also strided.
3107 * If there is only a single domain in the component, then there is
3108 * nothing to do. Similarly, if the current schedule dimension has
3109 * a fixed value for almost all domains then there is nothing to be done.
3110 * In particular, we need at least two domains where the current schedule
3111 * dimension does not have a fixed value.
3112 * Finally, if any of the options refer to the current schedule dimension,
3113 * then we bail out as well. It would be possible to reformulate the options
3114 * in terms of the new schedule domain, but that would introduce constraints
3115 * that separate the domains in the options and that is something we would
3119 * To see if there is any shifted stride, we look at the differences
3120 * between the values of the current dimension in pairs of domains
3121 * for equal values of outer dimensions. These differences should be
3126 * with "m" the stride and "r" a constant. Note that we cannot perform
3127 * this analysis on individual domains as the lower bound in each domain
3128 * may depend on parameters or outer dimensions and so the current dimension
3129 * itself may not have a fixed remainder on division by the stride.
3131 * In particular, we compare the first domain that does not have an
3132 * obviously fixed value for the current dimension to itself and all
3133 * other domains and collect the offsets and the gcd of the strides.
3134 * If the gcd becomes one, then we failed to find shifted strides.
3135 * If all the offsets are the same (for those domains that do not have
3136 * an obviously fixed value for the current dimension), then we do not
3137 * apply the transformation.
3138 * If none of the domains were skipped, then there is nothing to do.
3139 * If some of them were skipped, then if we apply separation, the schedule
3140 * domain should get split in pieces with a (non-shifted) stride.
3142 * Otherwise, we apply a shift to expose the stride in
3143 * generate_shift_component.
3145 static __isl_give isl_ast_graft_list
*generate_component(
3146 struct isl_set_map_pair
*domain
, int *order
, int n
,
3147 __isl_take isl_ast_build
*build
)
3158 isl_ast_graft_list
*list
;
3161 depth
= isl_ast_build_get_depth(build
);
3164 if (skip
>= 0 && !skip
)
3165 skip
= at_most_one_non_fixed(domain
, order
, n
, depth
);
3166 if (skip
>= 0 && !skip
)
3167 skip
= isl_ast_build_options_involve_depth(build
);
3169 return isl_ast_build_free(build
);
3171 return generate_shifted_component_from_list(domain
,
3174 base
= eliminate_non_fixed(domain
, order
, n
, depth
, build
);
3176 return isl_ast_build_free(build
);
3178 ctx
= isl_ast_build_get_ctx(build
);
3183 v
= isl_vec_alloc(ctx
, n
);
3186 for (i
= 0; i
< n
; ++i
) {
3187 map
= isl_map_from_domain_and_range(
3188 isl_set_copy(domain
[order
[base
]].set
),
3189 isl_set_copy(domain
[order
[i
]].set
));
3190 for (d
= 0; d
< depth
; ++d
)
3191 map
= isl_map_equate(map
, isl_dim_in
, d
,
3193 deltas
= isl_map_deltas(map
);
3194 res
= isl_set_dim_residue_class(deltas
, depth
, &m
, &r
);
3195 isl_set_free(deltas
);
3200 isl_int_set(gcd
, m
);
3202 isl_int_gcd(gcd
, gcd
, m
);
3203 if (isl_int_is_one(gcd
))
3205 v
= isl_vec_set_element(v
, i
, r
);
3207 res
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
3208 isl_dim_set
, depth
, NULL
);
3214 if (fixed
&& i
> base
) {
3215 isl_vec_get_element(v
, base
, &m
);
3216 if (isl_int_ne(m
, r
))
3222 isl_ast_build_free(build
);
3224 } else if (i
< n
|| fixed
) {
3225 list
= generate_shifted_component_from_list(domain
,
3228 list
= generate_shift_component(domain
, order
, n
, gcd
, v
,
3240 /* Store both "map" itself and its domain in the
3241 * structure pointed to by *next and advance to the next array element.
3243 static int extract_domain(__isl_take isl_map
*map
, void *user
)
3245 struct isl_set_map_pair
**next
= user
;
3247 (*next
)->map
= isl_map_copy(map
);
3248 (*next
)->set
= isl_map_domain(map
);
3254 /* Internal data for any_scheduled_after.
3256 * "depth" is the number of loops that have already been generated
3257 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3258 * "domain" is an array of set-map pairs corresponding to the different
3259 * iteration domains. The set is the schedule domain, i.e., the domain
3260 * of the inverse schedule, while the map is the inverse schedule itself.
3262 struct isl_any_scheduled_after_data
{
3264 int group_coscheduled
;
3265 struct isl_set_map_pair
*domain
;
3268 /* Is any element of domain "i" scheduled after any element of domain "j"
3269 * (for a common iteration of the first data->depth loops)?
3271 * data->domain[i].set contains the domain of the inverse schedule
3272 * for domain "i", i.e., elements in the schedule domain.
3274 * If data->group_coscheduled is set, then we also return 1 if there
3275 * is any pair of elements in the two domains that are scheduled together.
3277 static int any_scheduled_after(int i
, int j
, void *user
)
3279 struct isl_any_scheduled_after_data
*data
= user
;
3280 int dim
= isl_set_dim(data
->domain
[i
].set
, isl_dim_set
);
3283 for (pos
= data
->depth
; pos
< dim
; ++pos
) {
3286 follows
= isl_set_follows_at(data
->domain
[i
].set
,
3287 data
->domain
[j
].set
, pos
);
3297 return data
->group_coscheduled
;
3300 /* Look for independent components at the current depth and generate code
3301 * for each component separately. The resulting lists of grafts are
3302 * merged in an attempt to combine grafts with identical guards.
3304 * Code for two domains can be generated separately if all the elements
3305 * of one domain are scheduled before (or together with) all the elements
3306 * of the other domain. We therefore consider the graph with as nodes
3307 * the domains and an edge between two nodes if any element of the first
3308 * node is scheduled after any element of the second node.
3309 * If the ast_build_group_coscheduled is set, then we also add an edge if
3310 * there is any pair of elements in the two domains that are scheduled
3312 * Code is then generated (by generate_component)
3313 * for each of the strongly connected components in this graph
3314 * in their topological order.
3316 * Since the test is performed on the domain of the inverse schedules of
3317 * the different domains, we precompute these domains and store
3318 * them in data.domain.
3320 static __isl_give isl_ast_graft_list
*generate_components(
3321 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3324 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3325 int n
= isl_union_map_n_map(executed
);
3326 struct isl_any_scheduled_after_data data
;
3327 struct isl_set_map_pair
*next
;
3328 struct isl_tarjan_graph
*g
= NULL
;
3329 isl_ast_graft_list
*list
= NULL
;
3332 data
.domain
= isl_calloc_array(ctx
, struct isl_set_map_pair
, n
);
3338 if (isl_union_map_foreach_map(executed
, &extract_domain
, &next
) < 0)
3343 data
.depth
= isl_ast_build_get_depth(build
);
3344 data
.group_coscheduled
= isl_options_get_ast_build_group_coscheduled(ctx
);
3345 g
= isl_tarjan_graph_init(ctx
, n
, &any_scheduled_after
, &data
);
3347 list
= isl_ast_graft_list_alloc(ctx
, 0);
3351 isl_ast_graft_list
*list_c
;
3354 if (g
->order
[i
] == -1)
3355 isl_die(ctx
, isl_error_internal
, "cannot happen",
3358 while (g
->order
[i
] != -1) {
3362 list_c
= generate_component(data
.domain
,
3363 g
->order
+ first
, i
- first
,
3364 isl_ast_build_copy(build
));
3365 list
= isl_ast_graft_list_merge(list
, list_c
, build
);
3371 error
: list
= isl_ast_graft_list_free(list
);
3372 isl_tarjan_graph_free(g
);
3373 for (i
= 0; i
< n_domain
; ++i
) {
3374 isl_map_free(data
.domain
[i
].map
);
3375 isl_set_free(data
.domain
[i
].set
);
3378 isl_union_map_free(executed
);
3379 isl_ast_build_free(build
);
3384 /* Generate code for the next level (and all inner levels).
3386 * If "executed" is empty, i.e., no code needs to be generated,
3387 * then we return an empty list.
3389 * If we have already generated code for all loop levels, then we pass
3390 * control to generate_inner_level.
3392 * If "executed" lives in a single space, i.e., if code needs to be
3393 * generated for a single domain, then there can only be a single
3394 * component and we go directly to generate_shifted_component.
3395 * Otherwise, we call generate_components to detect the components
3396 * and to call generate_component on each of them separately.
3398 static __isl_give isl_ast_graft_list
*generate_next_level(
3399 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3403 if (!build
|| !executed
)
3406 if (isl_union_map_is_empty(executed
)) {
3407 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3408 isl_union_map_free(executed
);
3409 isl_ast_build_free(build
);
3410 return isl_ast_graft_list_alloc(ctx
, 0);
3413 depth
= isl_ast_build_get_depth(build
);
3414 if (depth
>= isl_set_dim(build
->domain
, isl_dim_set
))
3415 return generate_inner_level(executed
, build
);
3417 if (isl_union_map_n_map(executed
) == 1)
3418 return generate_shifted_component(executed
, build
);
3420 return generate_components(executed
, build
);
3422 isl_union_map_free(executed
);
3423 isl_ast_build_free(build
);
3427 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3428 * internal, executed and build are the inputs to generate_code.
3429 * list collects the output.
3431 struct isl_generate_code_data
{
3433 isl_union_map
*executed
;
3434 isl_ast_build
*build
;
3436 isl_ast_graft_list
*list
;
3439 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3443 * with E the external build schedule and S the additional schedule "space",
3444 * reformulate the inverse schedule in terms of the internal schedule domain,
3449 * We first obtain a mapping
3453 * take the inverse and the product with S -> S, resulting in
3455 * [I -> S] -> [E -> S]
3457 * Applying the map to the input produces the desired result.
3459 static __isl_give isl_union_map
*internal_executed(
3460 __isl_take isl_union_map
*executed
, __isl_keep isl_space
*space
,
3461 __isl_keep isl_ast_build
*build
)
3465 proj
= isl_ast_build_get_schedule_map(build
);
3466 proj
= isl_map_reverse(proj
);
3467 space
= isl_space_map_from_set(isl_space_copy(space
));
3468 id
= isl_map_identity(space
);
3469 proj
= isl_map_product(proj
, id
);
3470 executed
= isl_union_map_apply_domain(executed
,
3471 isl_union_map_from_map(proj
));
3475 /* Generate an AST that visits the elements in the range of data->executed
3476 * in the relative order specified by the corresponding image element(s)
3477 * for those image elements that belong to "set".
3478 * Add the result to data->list.
3480 * The caller ensures that "set" is a universe domain.
3481 * "space" is the space of the additional part of the schedule.
3482 * It is equal to the space of "set" if build->domain is parametric.
3483 * Otherwise, it is equal to the range of the wrapped space of "set".
3485 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3486 * was called from an outside user (data->internal not set), then
3487 * the (inverse) schedule refers to the external build domain and needs to
3488 * be transformed to refer to the internal build domain.
3490 * The build is extended to include the additional part of the schedule.
3491 * If the original build space was not parametric, then the options
3492 * in data->build refer only to the additional part of the schedule
3493 * and they need to be adjusted to refer to the complete AST build
3496 * After having adjusted inverse schedule and build, we start generating
3497 * code with the outer loop of the current code generation
3498 * in generate_next_level.
3500 * If the original build space was not parametric, we undo the embedding
3501 * on the resulting isl_ast_node_list so that it can be used within
3502 * the outer AST build.
3504 static int generate_code_in_space(struct isl_generate_code_data
*data
,
3505 __isl_take isl_set
*set
, __isl_take isl_space
*space
)
3507 isl_union_map
*executed
;
3508 isl_ast_build
*build
;
3509 isl_ast_graft_list
*list
;
3512 executed
= isl_union_map_copy(data
->executed
);
3513 executed
= isl_union_map_intersect_domain(executed
,
3514 isl_union_set_from_set(set
));
3516 embed
= !isl_set_is_params(data
->build
->domain
);
3517 if (embed
&& !data
->internal
)
3518 executed
= internal_executed(executed
, space
, data
->build
);
3520 build
= isl_ast_build_copy(data
->build
);
3521 build
= isl_ast_build_product(build
, space
);
3523 list
= generate_next_level(executed
, build
);
3525 list
= isl_ast_graft_list_unembed(list
, embed
);
3527 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
3532 /* Generate an AST that visits the elements in the range of data->executed
3533 * in the relative order specified by the corresponding domain element(s)
3534 * for those domain elements that belong to "set".
3535 * Add the result to data->list.
3537 * The caller ensures that "set" is a universe domain.
3539 * If the build space S is not parametric, then the space of "set"
3540 * need to be a wrapped relation with S as domain. That is, it needs
3545 * Check this property and pass control to generate_code_in_space
3547 * If the build space is not parametric, then T is the space of "set".
3549 static int generate_code_set(__isl_take isl_set
*set
, void *user
)
3551 struct isl_generate_code_data
*data
= user
;
3552 isl_space
*space
, *build_space
;
3555 space
= isl_set_get_space(set
);
3557 if (isl_set_is_params(data
->build
->domain
))
3558 return generate_code_in_space(data
, set
, space
);
3560 build_space
= isl_ast_build_get_space(data
->build
, data
->internal
);
3561 space
= isl_space_unwrap(space
);
3562 is_domain
= isl_space_is_domain(build_space
, space
);
3563 isl_space_free(build_space
);
3564 space
= isl_space_range(space
);
3569 isl_die(isl_set_get_ctx(set
), isl_error_invalid
,
3570 "invalid nested schedule space", goto error
);
3572 return generate_code_in_space(data
, set
, space
);
3575 isl_space_free(space
);
3579 /* Generate an AST that visits the elements in the range of "executed"
3580 * in the relative order specified by the corresponding domain element(s).
3582 * "build" is an isl_ast_build that has either been constructed by
3583 * isl_ast_build_from_context or passed to a callback set by
3584 * isl_ast_build_set_create_leaf.
3585 * In the first case, the space of the isl_ast_build is typically
3586 * a parametric space, although this is currently not enforced.
3587 * In the second case, the space is never a parametric space.
3588 * If the space S is not parametric, then the domain space(s) of "executed"
3589 * need to be wrapped relations with S as domain.
3591 * If the domain of "executed" consists of several spaces, then an AST
3592 * is generated for each of them (in arbitrary order) and the results
3595 * If "internal" is set, then the domain "S" above refers to the internal
3596 * schedule domain representation. Otherwise, it refers to the external
3597 * representation, as returned by isl_ast_build_get_schedule_space.
3599 * We essentially run over all the spaces in the domain of "executed"
3600 * and call generate_code_set on each of them.
3602 static __isl_give isl_ast_graft_list
*generate_code(
3603 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
3607 struct isl_generate_code_data data
= { 0 };
3609 isl_union_set
*schedule_domain
;
3610 isl_union_map
*universe
;
3614 space
= isl_ast_build_get_space(build
, 1);
3615 space
= isl_space_align_params(space
,
3616 isl_union_map_get_space(executed
));
3617 space
= isl_space_align_params(space
,
3618 isl_union_map_get_space(build
->options
));
3619 build
= isl_ast_build_align_params(build
, isl_space_copy(space
));
3620 executed
= isl_union_map_align_params(executed
, space
);
3621 if (!executed
|| !build
)
3624 ctx
= isl_ast_build_get_ctx(build
);
3626 data
.internal
= internal
;
3627 data
.executed
= executed
;
3629 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
3631 universe
= isl_union_map_universe(isl_union_map_copy(executed
));
3632 schedule_domain
= isl_union_map_domain(universe
);
3633 if (isl_union_set_foreach_set(schedule_domain
, &generate_code_set
,
3635 data
.list
= isl_ast_graft_list_free(data
.list
);
3637 isl_union_set_free(schedule_domain
);
3638 isl_union_map_free(executed
);
3640 isl_ast_build_free(build
);
3643 isl_union_map_free(executed
);
3644 isl_ast_build_free(build
);
3648 /* Generate an AST that visits the elements in the domain of "schedule"
3649 * in the relative order specified by the corresponding image element(s).
3651 * "build" is an isl_ast_build that has either been constructed by
3652 * isl_ast_build_from_context or passed to a callback set by
3653 * isl_ast_build_set_create_leaf.
3654 * In the first case, the space of the isl_ast_build is typically
3655 * a parametric space, although this is currently not enforced.
3656 * In the second case, the space is never a parametric space.
3657 * If the space S is not parametric, then the range space(s) of "schedule"
3658 * need to be wrapped relations with S as domain.
3660 * If the range of "schedule" consists of several spaces, then an AST
3661 * is generated for each of them (in arbitrary order) and the results
3664 * We first initialize the local copies of the relevant options.
3665 * We do this here rather than when the isl_ast_build is created
3666 * because the options may have changed between the construction
3667 * of the isl_ast_build and the call to isl_generate_code.
3669 * The main computation is performed on an inverse schedule (with
3670 * the schedule domain in the domain and the elements to be executed
3671 * in the range) called "executed".
3673 __isl_give isl_ast_node
*isl_ast_build_ast_from_schedule(
3674 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
3676 isl_ast_graft_list
*list
;
3678 isl_union_map
*executed
;
3680 build
= isl_ast_build_copy(build
);
3681 build
= isl_ast_build_set_single_valued(build
, 0);
3682 executed
= isl_union_map_reverse(schedule
);
3683 list
= generate_code(executed
, isl_ast_build_copy(build
), 0);
3684 node
= isl_ast_node_from_graft_list(list
, build
);
3685 isl_ast_build_free(build
);