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 /* Does any element of i follow or coincide with any element of j
1632 * at the current depth for equal values of the outer dimensions?
1634 static int domain_follows_at_depth(__isl_keep isl_basic_set
*i
,
1635 __isl_keep isl_basic_set
*j
, void *user
)
1637 int depth
= *(int *) user
;
1638 isl_basic_map
*test
;
1642 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
1643 isl_basic_set_copy(j
));
1644 for (l
= 0; l
< depth
; ++l
)
1645 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1647 test
= isl_basic_map_order_ge(test
, isl_dim_in
, depth
,
1648 isl_dim_out
, depth
);
1649 empty
= isl_basic_map_is_empty(test
);
1650 isl_basic_map_free(test
);
1652 return empty
< 0 ? -1 : !empty
;
1655 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1656 __isl_keep isl_basic_set_list
*domain_list
,
1657 __isl_keep isl_union_map
*executed
,
1658 __isl_keep isl_ast_build
*build
);
1660 /* Internal data structure for add_nodes.
1662 * "executed" and "build" are extra arguments to be passed to add_node.
1663 * "list" collects the results.
1665 struct isl_add_nodes_data
{
1666 isl_union_map
*executed
;
1667 isl_ast_build
*build
;
1669 isl_ast_graft_list
*list
;
1672 /* Generate code for the schedule domains in "scc"
1673 * and add the results to "list".
1675 * The domains in "scc" form a strongly connected component in the ordering.
1676 * If the number of domains in "scc" is larger than 1, then this means
1677 * that we cannot determine a valid ordering for the domains in the component.
1678 * This should be fairly rare because the individual domains
1679 * have been made disjoint first.
1680 * The problem is that the domains may be integrally disjoint but not
1681 * rationally disjoint. For example, we may have domains
1683 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1685 * These two domains have an empty intersection, but their rational
1686 * relaxations do intersect. It is impossible to order these domains
1687 * in the second dimension because the first should be ordered before
1688 * the second for outer dimension equal to 0, while it should be ordered
1689 * after for outer dimension equal to 1.
1691 * This may happen in particular in case of unrolling since the domain
1692 * of each slice is replaced by its simple hull.
1694 * We collect the basic sets in the component, call isl_set_make_disjoint
1695 * and try again. Note that we rely here on isl_set_make_disjoint also
1696 * making the basic sets rationally disjoint. If the basic sets
1697 * are rationally disjoint, then the ordering problem does not occur.
1698 * To see this, there can only be a problem if there are points
1699 * (i,a) and (j,b) in one set and (i,c) and (j,d) in the other with
1700 * a < c and b > d. This means that either the interval spanned
1701 * by a en b lies inside that spanned by c and or the other way around.
1702 * In either case, there is a point inside both intervals with the
1703 * convex combination in terms of a and b and in terms of c and d.
1704 * Taking the same combination of i and j gives a point in the intersection.
1706 static int add_nodes(__isl_take isl_basic_set_list
*scc
, void *user
)
1708 struct isl_add_nodes_data
*data
= user
;
1710 isl_basic_set
*bset
;
1713 n
= isl_basic_set_list_n_basic_set(scc
);
1714 bset
= isl_basic_set_list_get_basic_set(scc
, 0);
1716 isl_basic_set_list_free(scc
);
1717 data
->list
= add_node(data
->list
,
1718 isl_union_map_copy(data
->executed
), bset
,
1719 isl_ast_build_copy(data
->build
));
1720 return data
->list
? 0 : -1;
1723 set
= isl_set_from_basic_set(bset
);
1724 for (i
= 1; i
< n
; ++i
) {
1725 bset
= isl_basic_set_list_get_basic_set(scc
, i
);
1726 set
= isl_set_union(set
, isl_set_from_basic_set(bset
));
1729 set
= isl_set_make_disjoint(set
);
1730 if (isl_set_n_basic_set(set
) == n
)
1731 isl_die(isl_basic_set_list_get_ctx(scc
), isl_error_internal
,
1732 "unable to separate loop parts",
1733 set
= isl_set_free(set
));
1734 isl_basic_set_list_free(scc
);
1735 scc
= isl_basic_set_list_from_set(set
);
1736 data
->list
= isl_ast_graft_list_concat(data
->list
,
1737 generate_sorted_domains(scc
, data
->executed
, data
->build
));
1738 isl_basic_set_list_free(scc
);
1740 return data
->list
? 0 : -1;
1743 /* Sort the domains in "domain_list" according to the execution order
1744 * at the current depth (for equal values of the outer dimensions),
1745 * generate code for each of them, collecting the results in a list.
1746 * If no code is generated (because the intersection of the inverse schedule
1747 * with the domains turns out to be empty), then an empty list is returned.
1749 * The caller is responsible for ensuring that the basic sets in "domain_list"
1750 * are pair-wise disjoint. It can, however, in principle happen that
1751 * two basic sets should be ordered one way for one value of the outer
1752 * dimensions and the other way for some other value of the outer dimensions.
1753 * We therefore play safe and look for strongly connected components.
1754 * The function add_nodes takes care of handling non-trivial components.
1756 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1757 __isl_keep isl_basic_set_list
*domain_list
,
1758 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1761 struct isl_add_nodes_data data
;
1768 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1769 n
= isl_basic_set_list_n_basic_set(domain_list
);
1770 data
.list
= isl_ast_graft_list_alloc(ctx
, n
);
1774 return add_node(data
.list
, isl_union_map_copy(executed
),
1775 isl_basic_set_list_get_basic_set(domain_list
, 0),
1776 isl_ast_build_copy(build
));
1778 depth
= isl_ast_build_get_depth(build
);
1779 data
.executed
= executed
;
1781 if (isl_basic_set_list_foreach_scc(domain_list
,
1782 &domain_follows_at_depth
, &depth
,
1783 &add_nodes
, &data
) < 0)
1784 data
.list
= isl_ast_graft_list_free(data
.list
);
1789 /* Do i and j share any values for the outer dimensions?
1791 static int shared_outer(__isl_keep isl_basic_set
*i
,
1792 __isl_keep isl_basic_set
*j
, void *user
)
1794 int depth
= *(int *) user
;
1795 isl_basic_map
*test
;
1799 test
= isl_basic_map_from_domain_and_range(isl_basic_set_copy(i
),
1800 isl_basic_set_copy(j
));
1801 for (l
= 0; l
< depth
; ++l
)
1802 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1804 empty
= isl_basic_map_is_empty(test
);
1805 isl_basic_map_free(test
);
1807 return empty
< 0 ? -1 : !empty
;
1810 /* Internal data structure for generate_sorted_domains_wrap.
1812 * "n" is the total number of basic sets
1813 * "executed" and "build" are extra arguments to be passed
1814 * to generate_sorted_domains.
1816 * "single" is set to 1 by generate_sorted_domains_wrap if there
1817 * is only a single component.
1818 * "list" collects the results.
1820 struct isl_ast_generate_parallel_domains_data
{
1822 isl_union_map
*executed
;
1823 isl_ast_build
*build
;
1826 isl_ast_graft_list
*list
;
1829 /* Call generate_sorted_domains on "scc", fuse the result into a list
1830 * with either zero or one graft and collect the these single element
1831 * lists into data->list.
1833 * If there is only one component, i.e., if the number of basic sets
1834 * in the current component is equal to the total number of basic sets,
1835 * then data->single is set to 1 and the result of generate_sorted_domains
1838 static int generate_sorted_domains_wrap(__isl_take isl_basic_set_list
*scc
,
1841 struct isl_ast_generate_parallel_domains_data
*data
= user
;
1842 isl_ast_graft_list
*list
;
1844 list
= generate_sorted_domains(scc
, data
->executed
, data
->build
);
1845 data
->single
= isl_basic_set_list_n_basic_set(scc
) == data
->n
;
1847 list
= isl_ast_graft_list_fuse(list
, data
->build
);
1851 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
1853 isl_basic_set_list_free(scc
);
1860 /* Look for any (weakly connected) components in the "domain_list"
1861 * of domains that share some values of the outer dimensions.
1862 * That is, domains in different components do not share any values
1863 * of the outer dimensions. This means that these components
1864 * can be freely reordered.
1865 * Within each of the components, we sort the domains according
1866 * to the execution order at the current depth.
1868 * If there is more than one component, then generate_sorted_domains_wrap
1869 * fuses the result of each call to generate_sorted_domains
1870 * into a list with either zero or one graft and collects these (at most)
1871 * single element lists into a bigger list. This means that the elements of the
1872 * final list can be freely reordered. In particular, we sort them
1873 * according to an arbitrary but fixed ordering to ease merging of
1874 * graft lists from different components.
1876 static __isl_give isl_ast_graft_list
*generate_parallel_domains(
1877 __isl_keep isl_basic_set_list
*domain_list
,
1878 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1881 struct isl_ast_generate_parallel_domains_data data
;
1886 data
.n
= isl_basic_set_list_n_basic_set(domain_list
);
1888 return generate_sorted_domains(domain_list
, executed
, build
);
1890 depth
= isl_ast_build_get_depth(build
);
1892 data
.executed
= executed
;
1895 if (isl_basic_set_list_foreach_scc(domain_list
, &shared_outer
, &depth
,
1896 &generate_sorted_domains_wrap
,
1898 data
.list
= isl_ast_graft_list_free(data
.list
);
1901 data
.list
= isl_ast_graft_list_sort_guard(data
.list
);
1906 /* Internal data for separate_domain.
1908 * "explicit" is set if we only want to use explicit bounds.
1910 * "domain" collects the separated domains.
1912 struct isl_separate_domain_data
{
1913 isl_ast_build
*build
;
1918 /* Extract implicit bounds on the current dimension for the executed "map".
1920 * The domain of "map" may involve inner dimensions, so we
1921 * need to eliminate them.
1923 static __isl_give isl_set
*implicit_bounds(__isl_take isl_map
*map
,
1924 __isl_keep isl_ast_build
*build
)
1928 domain
= isl_map_domain(map
);
1929 domain
= isl_ast_build_eliminate(build
, domain
);
1934 /* Extract explicit bounds on the current dimension for the executed "map".
1936 * Rather than eliminating the inner dimensions as in implicit_bounds,
1937 * we simply drop any constraints involving those inner dimensions.
1938 * The idea is that most bounds that are implied by constraints on the
1939 * inner dimensions will be enforced by for loops and not by explicit guards.
1940 * There is then no need to separate along those bounds.
1942 static __isl_give isl_set
*explicit_bounds(__isl_take isl_map
*map
,
1943 __isl_keep isl_ast_build
*build
)
1948 dim
= isl_map_dim(map
, isl_dim_out
);
1949 map
= isl_map_drop_constraints_involving_dims(map
, isl_dim_out
, 0, dim
);
1951 domain
= isl_map_domain(map
);
1952 depth
= isl_ast_build_get_depth(build
);
1953 dim
= isl_set_dim(domain
, isl_dim_set
);
1954 domain
= isl_set_detect_equalities(domain
);
1955 domain
= isl_set_drop_constraints_involving_dims(domain
,
1956 isl_dim_set
, depth
+ 1, dim
- (depth
+ 1));
1957 domain
= isl_set_remove_divs_involving_dims(domain
,
1958 isl_dim_set
, depth
, 1);
1959 domain
= isl_set_remove_unknown_divs(domain
);
1964 /* Split data->domain into pieces that intersect with the range of "map"
1965 * and pieces that do not intersect with the range of "map"
1966 * and then add that part of the range of "map" that does not intersect
1967 * with data->domain.
1969 static int separate_domain(__isl_take isl_map
*map
, void *user
)
1971 struct isl_separate_domain_data
*data
= user
;
1976 domain
= explicit_bounds(map
, data
->build
);
1978 domain
= implicit_bounds(map
, data
->build
);
1980 domain
= isl_set_coalesce(domain
);
1981 domain
= isl_set_make_disjoint(domain
);
1982 d1
= isl_set_subtract(isl_set_copy(domain
), isl_set_copy(data
->domain
));
1983 d2
= isl_set_subtract(isl_set_copy(data
->domain
), isl_set_copy(domain
));
1984 data
->domain
= isl_set_intersect(data
->domain
, domain
);
1985 data
->domain
= isl_set_union(data
->domain
, d1
);
1986 data
->domain
= isl_set_union(data
->domain
, d2
);
1991 /* Separate the schedule domains of "executed".
1993 * That is, break up the domain of "executed" into basic sets,
1994 * such that for each basic set S, every element in S is associated with
1995 * the same domain spaces.
1997 * "space" is the (single) domain space of "executed".
1999 static __isl_give isl_set
*separate_schedule_domains(
2000 __isl_take isl_space
*space
, __isl_take isl_union_map
*executed
,
2001 __isl_keep isl_ast_build
*build
)
2003 struct isl_separate_domain_data data
= { build
};
2006 ctx
= isl_ast_build_get_ctx(build
);
2007 data
.explicit = isl_options_get_ast_build_separation_bounds(ctx
) ==
2008 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
;
2009 data
.domain
= isl_set_empty(space
);
2010 if (isl_union_map_foreach_map(executed
, &separate_domain
, &data
) < 0)
2011 data
.domain
= isl_set_free(data
.domain
);
2013 isl_union_map_free(executed
);
2017 /* Temporary data used during the search for a lower bound for unrolling.
2019 * "domain" is the original set for which to find a lower bound
2020 * "depth" is the dimension for which to find a lower boudn
2022 * "lower" is the best lower bound found so far. It is NULL if we have not
2024 * "n" is the corresponding size. If lower is NULL, then the value of n
2027 * "tmp" is a temporary initialized isl_int.
2029 struct isl_find_unroll_data
{
2038 /* Check if we can use "c" as a lower bound and if it is better than
2039 * any previously found lower bound.
2041 * If "c" does not involve the dimension at the current depth,
2042 * then we cannot use it.
2043 * Otherwise, let "c" be of the form
2047 * We compute the maximal value of
2049 * -ceil(f(j)/a)) + i + 1
2051 * over the domain. If there is such a value "n", then we know
2053 * -ceil(f(j)/a)) + i + 1 <= n
2057 * i < ceil(f(j)/a)) + n
2059 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2060 * We just need to check if we have found any lower bound before and
2061 * if the new lower bound is better (smaller n) than the previously found
2064 static int update_unrolling_lower_bound(struct isl_find_unroll_data
*data
,
2065 __isl_keep isl_constraint
*c
)
2067 isl_aff
*aff
, *lower
;
2068 enum isl_lp_result res
;
2070 if (!isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->depth
))
2073 lower
= isl_constraint_get_bound(c
, isl_dim_set
, data
->depth
);
2074 lower
= isl_aff_ceil(lower
);
2075 aff
= isl_aff_copy(lower
);
2076 aff
= isl_aff_neg(aff
);
2077 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, data
->depth
, 1);
2078 aff
= isl_aff_add_constant_si(aff
, 1);
2079 res
= isl_set_max(data
->domain
, aff
, &data
->tmp
);
2082 if (res
== isl_lp_error
)
2084 if (res
== isl_lp_unbounded
) {
2085 isl_aff_free(lower
);
2089 if (isl_int_cmp_si(data
->tmp
, INT_MAX
) <= 0 &&
2090 (!data
->lower
|| isl_int_cmp_si(data
->tmp
, *data
->n
) < 0)) {
2091 isl_aff_free(data
->lower
);
2092 data
->lower
= lower
;
2093 *data
->n
= isl_int_get_si(data
->tmp
);
2095 isl_aff_free(lower
);
2099 isl_aff_free(lower
);
2103 /* Check if we can use "c" as a lower bound and if it is better than
2104 * any previously found lower bound.
2106 static int constraint_find_unroll(__isl_take isl_constraint
*c
, void *user
)
2108 struct isl_find_unroll_data
*data
;
2111 data
= (struct isl_find_unroll_data
*) user
;
2112 r
= update_unrolling_lower_bound(data
, c
);
2113 isl_constraint_free(c
);
2118 /* Look for a lower bound l(i) on the dimension at "depth"
2119 * and a size n such that "domain" is a subset of
2121 * { [i] : l(i) <= i_d < l(i) + n }
2123 * where d is "depth" and l(i) depends only on earlier dimensions.
2124 * Furthermore, try and find a lower bound such that n is as small as possible.
2125 * In particular, "n" needs to be finite.
2127 * Inner dimensions have been eliminated from "domain" by the caller.
2129 * We first construct a collection of lower bounds on the input set
2130 * by computing its simple hull. We then iterate through them,
2131 * discarding those that we cannot use (either because they do not
2132 * involve the dimension at "depth" or because they have no corresponding
2133 * upper bound, meaning that "n" would be unbounded) and pick out the
2134 * best from the remaining ones.
2136 * If we cannot find a suitable lower bound, then we consider that
2139 static __isl_give isl_aff
*find_unroll_lower_bound(__isl_keep isl_set
*domain
,
2142 struct isl_find_unroll_data data
= { domain
, depth
, NULL
, n
};
2143 isl_basic_set
*hull
;
2145 isl_int_init(data
.tmp
);
2146 hull
= isl_set_simple_hull(isl_set_copy(domain
));
2148 if (isl_basic_set_foreach_constraint(hull
,
2149 &constraint_find_unroll
, &data
) < 0)
2152 isl_basic_set_free(hull
);
2153 isl_int_clear(data
.tmp
);
2156 isl_die(isl_set_get_ctx(domain
), isl_error_invalid
,
2157 "cannot find lower bound for unrolling", return NULL
);
2161 isl_basic_set_free(hull
);
2162 isl_int_clear(data
.tmp
);
2163 return isl_aff_free(data
.lower
);
2166 /* Return the constraint
2168 * i_"depth" = aff + offset
2170 static __isl_give isl_constraint
*at_offset(int depth
, __isl_keep isl_aff
*aff
,
2173 aff
= isl_aff_copy(aff
);
2174 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, depth
, -1);
2175 aff
= isl_aff_add_constant_si(aff
, offset
);
2176 return isl_equality_from_aff(aff
);
2179 /* Return a list of basic sets, one for each value of the current dimension
2181 * The divs that involve the current dimension have not been projected out
2184 * Since we are going to be iterating over the individual values,
2185 * we first check if there are any strides on the current dimension.
2186 * If there is, we rewrite the current dimension i as
2188 * i = stride i' + offset
2190 * and then iterate over individual values of i' instead.
2192 * We then look for a lower bound on i' and a size such that the domain
2195 * { [j,i'] : l(j) <= i' < l(j) + n }
2197 * and then take slices of the domain at values of i'
2198 * between l(j) and l(j) + n - 1.
2200 * We compute the unshifted simple hull of each slice to ensure that
2201 * we have a single basic set per offset. The slicing constraint
2202 * may get simplified away before the unshifted simple hull is taken
2203 * and may therefore in some rare cases disappear from the result.
2204 * We therefore explicitly add the constraint back after computing
2205 * the unshifted simple hull to ensure that the basic sets
2206 * remain disjoint. The constraints that are dropped by taking the hull
2207 * will be taken into account at the next level, as in the case of the
2210 * Finally, we map i' back to i and add each basic set to the list.
2212 static __isl_give isl_basic_set_list
*do_unroll(__isl_take isl_set
*domain
,
2213 __isl_keep isl_ast_build
*build
)
2219 isl_basic_set_list
*list
;
2220 isl_multi_aff
*expansion
;
2221 isl_basic_map
*bmap
;
2226 ctx
= isl_set_get_ctx(domain
);
2227 depth
= isl_ast_build_get_depth(build
);
2228 build
= isl_ast_build_copy(build
);
2229 domain
= isl_ast_build_eliminate_inner(build
, domain
);
2230 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
2231 expansion
= isl_ast_build_get_stride_expansion(build
);
2233 domain
= isl_set_preimage_multi_aff(domain
,
2234 isl_multi_aff_copy(expansion
));
2235 domain
= isl_ast_build_eliminate_divs(build
, domain
);
2237 isl_ast_build_free(build
);
2239 list
= isl_basic_set_list_alloc(ctx
, 0);
2241 lower
= find_unroll_lower_bound(domain
, depth
, &n
);
2243 list
= isl_basic_set_list_free(list
);
2245 bmap
= isl_basic_map_from_multi_aff(expansion
);
2247 for (i
= 0; list
&& i
< n
; ++i
) {
2249 isl_basic_set
*bset
;
2250 isl_constraint
*slice
;
2252 slice
= at_offset(depth
, lower
, i
);
2253 set
= isl_set_copy(domain
);
2254 set
= isl_set_add_constraint(set
, isl_constraint_copy(slice
));
2255 bset
= isl_set_unshifted_simple_hull(set
);
2256 bset
= isl_basic_set_add_constraint(bset
, slice
);
2257 bset
= isl_basic_set_apply(bset
, isl_basic_map_copy(bmap
));
2258 list
= isl_basic_set_list_add(list
, bset
);
2261 isl_aff_free(lower
);
2262 isl_set_free(domain
);
2263 isl_basic_map_free(bmap
);
2268 /* Data structure for storing the results and the intermediate objects
2269 * of compute_domains.
2271 * "list" is the main result of the function and contains a list
2272 * of disjoint basic sets for which code should be generated.
2274 * "executed" and "build" are inputs to compute_domains.
2275 * "schedule_domain" is the domain of "executed".
2277 * "option" constains the domains at the current depth that should by
2278 * atomic, separated or unrolled. These domains are as specified by
2279 * the user, except that inner dimensions have been eliminated and
2280 * that they have been made pair-wise disjoint.
2282 * "sep_class" contains the user-specified split into separation classes
2283 * specialized to the current depth.
2284 * "done" contains the union of the separation domains that have already
2286 * "atomic" contains the domain that has effectively been made atomic.
2287 * This domain may be larger than the intersection of option[atomic]
2288 * and the schedule domain.
2290 struct isl_codegen_domains
{
2291 isl_basic_set_list
*list
;
2293 isl_union_map
*executed
;
2294 isl_ast_build
*build
;
2295 isl_set
*schedule_domain
;
2304 /* Add domains to domains->list for each individual value of the current
2305 * dimension, for that part of the schedule domain that lies in the
2306 * intersection of the option domain and the class domain.
2308 * "domain" is the intersection of the class domain and the schedule domain.
2309 * The divs that involve the current dimension have not been projected out
2312 * We first break up the unroll option domain into individual pieces
2313 * and then handle each of them separately. The unroll option domain
2314 * has been made disjoint in compute_domains_init_options,
2316 * Note that we actively want to combine different pieces of the
2317 * schedule domain that have the same value at the current dimension.
2318 * We therefore need to break up the unroll option domain before
2319 * intersecting with class and schedule domain, hoping that the
2320 * unroll option domain specified by the user is relatively simple.
2322 static int compute_unroll_domains(struct isl_codegen_domains
*domains
,
2323 __isl_keep isl_set
*domain
)
2325 isl_set
*unroll_domain
;
2326 isl_basic_set_list
*unroll_list
;
2330 empty
= isl_set_is_empty(domains
->option
[unroll
]);
2336 unroll_domain
= isl_set_copy(domains
->option
[unroll
]);
2337 unroll_list
= isl_basic_set_list_from_set(unroll_domain
);
2339 n
= isl_basic_set_list_n_basic_set(unroll_list
);
2340 for (i
= 0; i
< n
; ++i
) {
2341 isl_basic_set
*bset
;
2342 isl_basic_set_list
*list
;
2344 bset
= isl_basic_set_list_get_basic_set(unroll_list
, i
);
2345 unroll_domain
= isl_set_from_basic_set(bset
);
2346 unroll_domain
= isl_set_intersect(unroll_domain
,
2347 isl_set_copy(domain
));
2349 empty
= isl_set_is_empty(unroll_domain
);
2350 if (empty
>= 0 && empty
) {
2351 isl_set_free(unroll_domain
);
2355 list
= do_unroll(unroll_domain
, domains
->build
);
2356 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2359 isl_basic_set_list_free(unroll_list
);
2364 /* Construct a single basic set that includes the intersection of
2365 * the schedule domain, the atomic option domain and the class domain.
2366 * Add the resulting basic set to domains->list and save a copy
2367 * in domains->atomic for use in compute_partial_domains.
2369 * We construct a single domain rather than trying to combine
2370 * the schedule domains of individual domains because we are working
2371 * within a single component so that non-overlapping schedule domains
2372 * should already have been separated.
2373 * Note, though, that this does not take into account the class domain.
2374 * So, it is possible for a class domain to carve out a piece of the
2375 * schedule domain with independent pieces and then we would only
2376 * generate a single domain for them. If this proves to be problematic
2377 * for some users, then this function will have to be adjusted.
2379 * "domain" is the intersection of the schedule domain and the class domain,
2380 * with inner dimensions projected out.
2382 static int compute_atomic_domain(struct isl_codegen_domains
*domains
,
2383 __isl_keep isl_set
*domain
)
2385 isl_basic_set
*bset
;
2386 isl_set
*atomic_domain
;
2389 atomic_domain
= isl_set_copy(domains
->option
[atomic
]);
2390 atomic_domain
= isl_set_intersect(atomic_domain
, isl_set_copy(domain
));
2391 empty
= isl_set_is_empty(atomic_domain
);
2392 if (empty
< 0 || empty
) {
2393 domains
->atomic
= atomic_domain
;
2394 return empty
< 0 ? -1 : 0;
2397 atomic_domain
= isl_set_coalesce(atomic_domain
);
2398 bset
= isl_set_unshifted_simple_hull(atomic_domain
);
2399 domains
->atomic
= isl_set_from_basic_set(isl_basic_set_copy(bset
));
2400 domains
->list
= isl_basic_set_list_add(domains
->list
, bset
);
2405 /* Split up the schedule domain into uniform basic sets,
2406 * in the sense that each element in a basic set is associated to
2407 * elements of the same domains, and add the result to domains->list.
2408 * Do this for that part of the schedule domain that lies in the
2409 * intersection of "class_domain" and the separate option domain.
2411 * "class_domain" may or may not include the constraints
2412 * of the schedule domain, but this does not make a difference
2413 * since we are going to intersect it with the domain of the inverse schedule.
2414 * If it includes schedule domain constraints, then they may involve
2415 * inner dimensions, but we will eliminate them in separation_domain.
2417 static int compute_separate_domain(struct isl_codegen_domains
*domains
,
2418 __isl_keep isl_set
*class_domain
)
2422 isl_union_map
*executed
;
2423 isl_basic_set_list
*list
;
2426 domain
= isl_set_copy(domains
->option
[separate
]);
2427 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2428 executed
= isl_union_map_copy(domains
->executed
);
2429 executed
= isl_union_map_intersect_domain(executed
,
2430 isl_union_set_from_set(domain
));
2431 empty
= isl_union_map_is_empty(executed
);
2432 if (empty
< 0 || empty
) {
2433 isl_union_map_free(executed
);
2434 return empty
< 0 ? -1 : 0;
2437 space
= isl_set_get_space(class_domain
);
2438 domain
= separate_schedule_domains(space
, executed
, domains
->build
);
2440 list
= isl_basic_set_list_from_set(domain
);
2441 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2446 /* Split up the domain at the current depth into disjoint
2447 * basic sets for which code should be generated separately
2448 * for the given separation class domain.
2450 * If any separation classes have been defined, then "class_domain"
2451 * is the domain of the current class and does not refer to inner dimensions.
2452 * Otherwise, "class_domain" is the universe domain.
2454 * We first make sure that the class domain is disjoint from
2455 * previously considered class domains.
2457 * The separate domains can be computed directly from the "class_domain".
2459 * The unroll, atomic and remainder domains need the constraints
2460 * from the schedule domain.
2462 * For unrolling, the actual schedule domain is needed (with divs that
2463 * may refer to the current dimension) so that stride detection can be
2466 * For atomic and remainder domains, inner dimensions and divs involving
2467 * the current dimensions should be eliminated.
2468 * In case we are working within a separation class, we need to intersect
2469 * the result with the current "class_domain" to ensure that the domains
2470 * are disjoint from those generated from other class domains.
2472 * The domain that has been made atomic may be larger than specified
2473 * by the user since it needs to be representable as a single basic set.
2474 * This possibly larger domain is stored in domains->atomic by
2475 * compute_atomic_domain.
2477 * If anything is left after handling separate, unroll and atomic,
2478 * we split it up into basic sets and append the basic sets to domains->list.
2480 static int compute_partial_domains(struct isl_codegen_domains
*domains
,
2481 __isl_take isl_set
*class_domain
)
2483 isl_basic_set_list
*list
;
2486 class_domain
= isl_set_subtract(class_domain
,
2487 isl_set_copy(domains
->done
));
2488 domains
->done
= isl_set_union(domains
->done
,
2489 isl_set_copy(class_domain
));
2491 domain
= isl_set_copy(class_domain
);
2493 if (compute_separate_domain(domains
, domain
) < 0)
2495 domain
= isl_set_subtract(domain
,
2496 isl_set_copy(domains
->option
[separate
]));
2498 domain
= isl_set_intersect(domain
,
2499 isl_set_copy(domains
->schedule_domain
));
2501 if (compute_unroll_domains(domains
, domain
) < 0)
2503 domain
= isl_set_subtract(domain
,
2504 isl_set_copy(domains
->option
[unroll
]));
2506 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2507 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2509 if (compute_atomic_domain(domains
, domain
) < 0)
2510 domain
= isl_set_free(domain
);
2511 domain
= isl_set_subtract(domain
, domains
->atomic
);
2513 domain
= isl_set_coalesce(domain
);
2514 domain
= isl_set_make_disjoint(domain
);
2516 list
= isl_basic_set_list_from_set(domain
);
2517 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2519 isl_set_free(class_domain
);
2523 isl_set_free(domain
);
2524 isl_set_free(class_domain
);
2528 /* Split up the domain at the current depth into disjoint
2529 * basic sets for which code should be generated separately
2530 * for the separation class identified by "pnt".
2532 * We extract the corresponding class domain from domains->sep_class,
2533 * eliminate inner dimensions and pass control to compute_partial_domains.
2535 static int compute_class_domains(__isl_take isl_point
*pnt
, void *user
)
2537 struct isl_codegen_domains
*domains
= user
;
2542 class_set
= isl_set_from_point(pnt
);
2543 domain
= isl_map_domain(isl_map_intersect_range(
2544 isl_map_copy(domains
->sep_class
), class_set
));
2545 domain
= isl_ast_build_compute_gist(domains
->build
, domain
);
2546 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2548 disjoint
= isl_set_plain_is_disjoint(domain
, domains
->schedule_domain
);
2552 isl_set_free(domain
);
2556 return compute_partial_domains(domains
, domain
);
2559 /* Extract the domains at the current depth that should be atomic,
2560 * separated or unrolled and store them in option.
2562 * The domains specified by the user might overlap, so we make
2563 * them disjoint by subtracting earlier domains from later domains.
2565 static void compute_domains_init_options(isl_set
*option
[3],
2566 __isl_keep isl_ast_build
*build
)
2568 enum isl_ast_build_domain_type type
, type2
;
2570 for (type
= atomic
; type
<= separate
; ++type
) {
2571 option
[type
] = isl_ast_build_get_option_domain(build
, type
);
2572 for (type2
= atomic
; type2
< type
; ++type2
)
2573 option
[type
] = isl_set_subtract(option
[type
],
2574 isl_set_copy(option
[type2
]));
2577 option
[unroll
] = isl_set_coalesce(option
[unroll
]);
2578 option
[unroll
] = isl_set_make_disjoint(option
[unroll
]);
2581 /* Split up the domain at the current depth into disjoint
2582 * basic sets for which code should be generated separately,
2583 * based on the user-specified options.
2584 * Return the list of disjoint basic sets.
2586 * There are three kinds of domains that we need to keep track of.
2587 * - the "schedule domain" is the domain of "executed"
2588 * - the "class domain" is the domain corresponding to the currrent
2590 * - the "option domain" is the domain corresponding to one of the options
2591 * atomic, unroll or separate
2593 * We first consider the individial values of the separation classes
2594 * and split up the domain for each of them separately.
2595 * Finally, we consider the remainder. If no separation classes were
2596 * specified, then we call compute_partial_domains with the universe
2597 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2598 * with inner dimensions removed. We do this because we want to
2599 * avoid computing the complement of the class domains (i.e., the difference
2600 * between the universe and domains->done).
2602 static __isl_give isl_basic_set_list
*compute_domains(
2603 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
2605 struct isl_codegen_domains domains
;
2608 isl_union_set
*schedule_domain
;
2612 enum isl_ast_build_domain_type type
;
2618 ctx
= isl_union_map_get_ctx(executed
);
2619 domains
.list
= isl_basic_set_list_alloc(ctx
, 0);
2621 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
2622 domain
= isl_set_from_union_set(schedule_domain
);
2624 compute_domains_init_options(domains
.option
, build
);
2626 domains
.sep_class
= isl_ast_build_get_separation_class(build
);
2627 classes
= isl_map_range(isl_map_copy(domains
.sep_class
));
2628 n_param
= isl_set_dim(classes
, isl_dim_param
);
2629 classes
= isl_set_project_out(classes
, isl_dim_param
, 0, n_param
);
2631 space
= isl_set_get_space(domain
);
2632 domains
.build
= build
;
2633 domains
.schedule_domain
= isl_set_copy(domain
);
2634 domains
.executed
= executed
;
2635 domains
.done
= isl_set_empty(space
);
2637 if (isl_set_foreach_point(classes
, &compute_class_domains
, &domains
) < 0)
2638 domains
.list
= isl_basic_set_list_free(domains
.list
);
2639 isl_set_free(classes
);
2641 empty
= isl_set_is_empty(domains
.done
);
2643 domains
.list
= isl_basic_set_list_free(domains
.list
);
2644 domain
= isl_set_free(domain
);
2646 isl_set_free(domain
);
2647 domain
= isl_set_universe(isl_set_get_space(domains
.done
));
2649 domain
= isl_ast_build_eliminate(build
, domain
);
2651 if (compute_partial_domains(&domains
, domain
) < 0)
2652 domains
.list
= isl_basic_set_list_free(domains
.list
);
2654 isl_set_free(domains
.schedule_domain
);
2655 isl_set_free(domains
.done
);
2656 isl_map_free(domains
.sep_class
);
2657 for (type
= atomic
; type
<= separate
; ++type
)
2658 isl_set_free(domains
.option
[type
]);
2660 return domains
.list
;
2663 /* Generate code for a single component, after shifting (if any)
2666 * We first split up the domain at the current depth into disjoint
2667 * basic sets based on the user-specified options.
2668 * Then we generated code for each of them and concatenate the results.
2670 static __isl_give isl_ast_graft_list
*generate_shifted_component(
2671 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
2673 isl_basic_set_list
*domain_list
;
2674 isl_ast_graft_list
*list
= NULL
;
2676 domain_list
= compute_domains(executed
, build
);
2677 list
= generate_parallel_domains(domain_list
, executed
, build
);
2679 isl_basic_set_list_free(domain_list
);
2680 isl_union_map_free(executed
);
2681 isl_ast_build_free(build
);
2686 struct isl_set_map_pair
{
2691 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2692 * of indices into the "domain" array,
2693 * return the union of the "map" fields of the elements
2694 * indexed by the first "n" elements of "order".
2696 static __isl_give isl_union_map
*construct_component_executed(
2697 struct isl_set_map_pair
*domain
, int *order
, int n
)
2701 isl_union_map
*executed
;
2703 map
= isl_map_copy(domain
[order
[0]].map
);
2704 executed
= isl_union_map_from_map(map
);
2705 for (i
= 1; i
< n
; ++i
) {
2706 map
= isl_map_copy(domain
[order
[i
]].map
);
2707 executed
= isl_union_map_add_map(executed
, map
);
2713 /* Generate code for a single component, after shifting (if any)
2716 * The component inverse schedule is specified as the "map" fields
2717 * of the elements of "domain" indexed by the first "n" elements of "order".
2719 static __isl_give isl_ast_graft_list
*generate_shifted_component_from_list(
2720 struct isl_set_map_pair
*domain
, int *order
, int n
,
2721 __isl_take isl_ast_build
*build
)
2723 isl_union_map
*executed
;
2725 executed
= construct_component_executed(domain
, order
, n
);
2726 return generate_shifted_component(executed
, build
);
2729 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2730 * of indices into the "domain" array,
2731 * do all (except for at most one) of the "set" field of the elements
2732 * indexed by the first "n" elements of "order" have a fixed value
2733 * at position "depth"?
2735 static int at_most_one_non_fixed(struct isl_set_map_pair
*domain
,
2736 int *order
, int n
, int depth
)
2741 for (i
= 0; i
< n
; ++i
) {
2744 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2745 isl_dim_set
, depth
, NULL
);
2758 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2759 * of indices into the "domain" array,
2760 * eliminate the inner dimensions from the "set" field of the elements
2761 * indexed by the first "n" elements of "order", provided the current
2762 * dimension does not have a fixed value.
2764 * Return the index of the first element in "order" with a corresponding
2765 * "set" field that does not have an (obviously) fixed value.
2767 static int eliminate_non_fixed(struct isl_set_map_pair
*domain
,
2768 int *order
, int n
, int depth
, __isl_keep isl_ast_build
*build
)
2773 for (i
= n
- 1; i
>= 0; --i
) {
2775 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2776 isl_dim_set
, depth
, NULL
);
2781 domain
[order
[i
]].set
= isl_ast_build_eliminate_inner(build
,
2782 domain
[order
[i
]].set
);
2789 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2790 * of indices into the "domain" array,
2791 * find the element of "domain" (amongst those indexed by the first "n"
2792 * elements of "order") with the "set" field that has the smallest
2793 * value for the current iterator.
2795 * Note that the domain with the smallest value may depend on the parameters
2796 * and/or outer loop dimension. Since the result of this function is only
2797 * used as heuristic, we only make a reasonable attempt at finding the best
2798 * domain, one that should work in case a single domain provides the smallest
2799 * value for the current dimension over all values of the parameters
2800 * and outer dimensions.
2802 * In particular, we compute the smallest value of the first domain
2803 * and replace it by that of any later domain if that later domain
2804 * has a smallest value that is smaller for at least some value
2805 * of the parameters and outer dimensions.
2807 static int first_offset(struct isl_set_map_pair
*domain
, int *order
, int n
,
2808 __isl_keep isl_ast_build
*build
)
2814 min_first
= isl_ast_build_map_to_iterator(build
,
2815 isl_set_copy(domain
[order
[0]].set
));
2816 min_first
= isl_map_lexmin(min_first
);
2818 for (i
= 1; i
< n
; ++i
) {
2819 isl_map
*min
, *test
;
2822 min
= isl_ast_build_map_to_iterator(build
,
2823 isl_set_copy(domain
[order
[i
]].set
));
2824 min
= isl_map_lexmin(min
);
2825 test
= isl_map_copy(min
);
2826 test
= isl_map_apply_domain(isl_map_copy(min_first
), test
);
2827 test
= isl_map_order_lt(test
, isl_dim_in
, 0, isl_dim_out
, 0);
2828 empty
= isl_map_is_empty(test
);
2830 if (empty
>= 0 && !empty
) {
2831 isl_map_free(min_first
);
2841 isl_map_free(min_first
);
2843 return i
< n
? -1 : first
;
2846 /* Construct a shifted inverse schedule based on the original inverse schedule,
2847 * the stride and the offset.
2849 * The original inverse schedule is specified as the "map" fields
2850 * of the elements of "domain" indexed by the first "n" elements of "order".
2852 * "stride" and "offset" are such that the difference
2853 * between the values of the current dimension of domain "i"
2854 * and the values of the current dimension for some reference domain are
2857 * stride * integer + offset[i]
2859 * Moreover, 0 <= offset[i] < stride.
2861 * For each domain, we create a map
2863 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2865 * where j refers to the current dimension and the other dimensions are
2866 * unchanged, and apply this map to the original schedule domain.
2868 * For example, for the original schedule
2870 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2872 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2873 * we apply the mapping
2877 * to the schedule of the "A" domain and the mapping
2879 * { [j - 1] -> [j, 1] }
2881 * to the schedule of the "B" domain.
2884 * Note that after the transformation, the differences between pairs
2885 * of values of the current dimension over all domains are multiples
2886 * of stride and that we have therefore exposed the stride.
2889 * To see that the mapping preserves the lexicographic order,
2890 * first note that each of the individual maps above preserves the order.
2891 * If the value of the current iterator is j1 in one domain and j2 in another,
2892 * then if j1 = j2, we know that the same map is applied to both domains
2893 * and the order is preserved.
2894 * Otherwise, let us assume, without loss of generality, that j1 < j2.
2895 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
2899 * and the order is preserved.
2900 * If c1 < c2, then we know
2906 * j2 - j1 = n * s + r
2908 * with n >= 0 and 0 <= r < s.
2909 * In other words, r = c2 - c1.
2920 * (j1 - c1, c1) << (j2 - c2, c2)
2922 * with "<<" the lexicographic order, proving that the order is preserved
2925 static __isl_give isl_union_map
*contruct_shifted_executed(
2926 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
2927 __isl_keep isl_vec
*offset
, __isl_keep isl_ast_build
*build
)
2931 isl_union_map
*executed
;
2937 depth
= isl_ast_build_get_depth(build
);
2938 space
= isl_ast_build_get_space(build
, 1);
2939 executed
= isl_union_map_empty(isl_space_copy(space
));
2940 space
= isl_space_map_from_set(space
);
2941 map
= isl_map_identity(isl_space_copy(space
));
2942 map
= isl_map_eliminate(map
, isl_dim_out
, depth
, 1);
2943 map
= isl_map_insert_dims(map
, isl_dim_out
, depth
+ 1, 1);
2944 space
= isl_space_insert_dims(space
, isl_dim_out
, depth
+ 1, 1);
2946 c
= isl_equality_alloc(isl_local_space_from_space(space
));
2947 c
= isl_constraint_set_coefficient_si(c
, isl_dim_in
, depth
, 1);
2948 c
= isl_constraint_set_coefficient_si(c
, isl_dim_out
, depth
, -1);
2952 for (i
= 0; i
< n
; ++i
) {
2955 if (isl_vec_get_element(offset
, i
, &v
) < 0)
2957 map_i
= isl_map_copy(map
);
2958 map_i
= isl_map_fix(map_i
, isl_dim_out
, depth
+ 1, v
);
2960 c
= isl_constraint_set_constant(c
, v
);
2961 map_i
= isl_map_add_constraint(map_i
, isl_constraint_copy(c
));
2963 map_i
= isl_map_apply_domain(isl_map_copy(domain
[order
[i
]].map
),
2965 executed
= isl_union_map_add_map(executed
, map_i
);
2968 isl_constraint_free(c
);
2974 executed
= isl_union_map_free(executed
);
2979 /* Generate code for a single component, after exposing the stride,
2980 * given that the schedule domain is "shifted strided".
2982 * The component inverse schedule is specified as the "map" fields
2983 * of the elements of "domain" indexed by the first "n" elements of "order".
2985 * The schedule domain being "shifted strided" means that the differences
2986 * between the values of the current dimension of domain "i"
2987 * and the values of the current dimension for some reference domain are
2990 * stride * integer + offset[i]
2992 * We first look for the domain with the "smallest" value for the current
2993 * dimension and adjust the offsets such that the offset of the "smallest"
2994 * domain is equal to zero. The other offsets are reduced modulo stride.
2996 * Based on this information, we construct a new inverse schedule in
2997 * contruct_shifted_executed that exposes the stride.
2998 * Since this involves the introduction of a new schedule dimension,
2999 * the build needs to be changed accodingly.
3000 * After computing the AST, the newly introduced dimension needs
3001 * to be removed again from the list of grafts. We do this by plugging
3002 * in a mapping that represents the new schedule domain in terms of the
3003 * old schedule domain.
3005 static __isl_give isl_ast_graft_list
*generate_shift_component(
3006 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
3007 __isl_keep isl_vec
*offset
, __isl_take isl_ast_build
*build
)
3009 isl_ast_graft_list
*list
;
3016 isl_multi_aff
*ma
, *zero
;
3017 isl_union_map
*executed
;
3019 ctx
= isl_ast_build_get_ctx(build
);
3020 depth
= isl_ast_build_get_depth(build
);
3022 first
= first_offset(domain
, order
, n
, build
);
3024 return isl_ast_build_free(build
);
3027 v
= isl_vec_alloc(ctx
, n
);
3028 if (isl_vec_get_element(offset
, first
, &val
) < 0)
3029 v
= isl_vec_free(v
);
3030 isl_int_neg(val
, val
);
3031 v
= isl_vec_set(v
, val
);
3032 v
= isl_vec_add(v
, isl_vec_copy(offset
));
3033 v
= isl_vec_fdiv_r(v
, stride
);
3035 executed
= contruct_shifted_executed(domain
, order
, n
, stride
, v
,
3037 space
= isl_ast_build_get_space(build
, 1);
3038 space
= isl_space_map_from_set(space
);
3039 ma
= isl_multi_aff_identity(isl_space_copy(space
));
3040 space
= isl_space_from_domain(isl_space_domain(space
));
3041 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
3042 zero
= isl_multi_aff_zero(space
);
3043 ma
= isl_multi_aff_range_splice(ma
, depth
+ 1, zero
);
3044 build
= isl_ast_build_insert_dim(build
, depth
+ 1);
3045 list
= generate_shifted_component(executed
, build
);
3047 list
= isl_ast_graft_list_preimage_multi_aff(list
, ma
);
3055 /* Generate code for a single component.
3057 * The component inverse schedule is specified as the "map" fields
3058 * of the elements of "domain" indexed by the first "n" elements of "order".
3060 * This function may modify the "set" fields of "domain".
3062 * Before proceeding with the actual code generation for the component,
3063 * we first check if there are any "shifted" strides, meaning that
3064 * the schedule domains of the individual domains are all strided,
3065 * but that they have different offsets, resulting in the union
3066 * of schedule domains not being strided anymore.
3068 * The simplest example is the schedule
3070 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3072 * Both schedule domains are strided, but their union is not.
3073 * This function detects such cases and then rewrites the schedule to
3075 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3077 * In the new schedule, the schedule domains have the same offset (modulo
3078 * the stride), ensuring that the union of schedule domains is also strided.
3081 * If there is only a single domain in the component, then there is
3082 * nothing to do. Similarly, if the current schedule dimension has
3083 * a fixed value for almost all domains then there is nothing to be done.
3084 * In particular, we need at least two domains where the current schedule
3085 * dimension does not have a fixed value.
3086 * Finally, if any of the options refer to the current schedule dimension,
3087 * then we bail out as well. It would be possible to reformulate the options
3088 * in terms of the new schedule domain, but that would introduce constraints
3089 * that separate the domains in the options and that is something we would
3093 * To see if there is any shifted stride, we look at the differences
3094 * between the values of the current dimension in pairs of domains
3095 * for equal values of outer dimensions. These differences should be
3100 * with "m" the stride and "r" a constant. Note that we cannot perform
3101 * this analysis on individual domains as the lower bound in each domain
3102 * may depend on parameters or outer dimensions and so the current dimension
3103 * itself may not have a fixed remainder on division by the stride.
3105 * In particular, we compare the first domain that does not have an
3106 * obviously fixed value for the current dimension to itself and all
3107 * other domains and collect the offsets and the gcd of the strides.
3108 * If the gcd becomes one, then we failed to find shifted strides.
3109 * If all the offsets are the same (for those domains that do not have
3110 * an obviously fixed value for the current dimension), then we do not
3111 * apply the transformation.
3112 * If none of the domains were skipped, then there is nothing to do.
3113 * If some of them were skipped, then if we apply separation, the schedule
3114 * domain should get split in pieces with a (non-shifted) stride.
3116 * Otherwise, we apply a shift to expose the stride in
3117 * generate_shift_component.
3119 static __isl_give isl_ast_graft_list
*generate_component(
3120 struct isl_set_map_pair
*domain
, int *order
, int n
,
3121 __isl_take isl_ast_build
*build
)
3132 isl_ast_graft_list
*list
;
3135 depth
= isl_ast_build_get_depth(build
);
3138 if (skip
>= 0 && !skip
)
3139 skip
= at_most_one_non_fixed(domain
, order
, n
, depth
);
3140 if (skip
>= 0 && !skip
)
3141 skip
= isl_ast_build_options_involve_depth(build
);
3143 return isl_ast_build_free(build
);
3145 return generate_shifted_component_from_list(domain
,
3148 base
= eliminate_non_fixed(domain
, order
, n
, depth
, build
);
3150 return isl_ast_build_free(build
);
3152 ctx
= isl_ast_build_get_ctx(build
);
3157 v
= isl_vec_alloc(ctx
, n
);
3160 for (i
= 0; i
< n
; ++i
) {
3161 map
= isl_map_from_domain_and_range(
3162 isl_set_copy(domain
[order
[base
]].set
),
3163 isl_set_copy(domain
[order
[i
]].set
));
3164 for (d
= 0; d
< depth
; ++d
)
3165 map
= isl_map_equate(map
, isl_dim_in
, d
,
3167 deltas
= isl_map_deltas(map
);
3168 res
= isl_set_dim_residue_class(deltas
, depth
, &m
, &r
);
3169 isl_set_free(deltas
);
3174 isl_int_set(gcd
, m
);
3176 isl_int_gcd(gcd
, gcd
, m
);
3177 if (isl_int_is_one(gcd
))
3179 v
= isl_vec_set_element(v
, i
, r
);
3181 res
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
3182 isl_dim_set
, depth
, NULL
);
3188 if (fixed
&& i
> base
) {
3189 isl_vec_get_element(v
, base
, &m
);
3190 if (isl_int_ne(m
, r
))
3196 isl_ast_build_free(build
);
3198 } else if (i
< n
|| fixed
) {
3199 list
= generate_shifted_component_from_list(domain
,
3202 list
= generate_shift_component(domain
, order
, n
, gcd
, v
,
3214 /* Store both "map" itself and its domain in the
3215 * structure pointed to by *next and advance to the next array element.
3217 static int extract_domain(__isl_take isl_map
*map
, void *user
)
3219 struct isl_set_map_pair
**next
= user
;
3221 (*next
)->map
= isl_map_copy(map
);
3222 (*next
)->set
= isl_map_domain(map
);
3228 /* Internal data for any_scheduled_after.
3230 * "depth" is the number of loops that have already been generated
3231 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3232 * "domain" is an array of set-map pairs corresponding to the different
3233 * iteration domains. The set is the schedule domain, i.e., the domain
3234 * of the inverse schedule, while the map is the inverse schedule itself.
3236 struct isl_any_scheduled_after_data
{
3238 int group_coscheduled
;
3239 struct isl_set_map_pair
*domain
;
3242 /* Is any element of domain "i" scheduled after any element of domain "j"
3243 * (for a common iteration of the first data->depth loops)?
3245 * data->domain[i].set contains the domain of the inverse schedule
3246 * for domain "i", i.e., elements in the schedule domain.
3248 * If data->group_coscheduled is set, then we also return 1 if there
3249 * is any pair of elements in the two domains that are scheduled together.
3251 static int any_scheduled_after(int i
, int j
, void *user
)
3253 struct isl_any_scheduled_after_data
*data
= user
;
3254 int dim
= isl_set_dim(data
->domain
[i
].set
, isl_dim_set
);
3257 for (pos
= data
->depth
; pos
< dim
; ++pos
) {
3260 follows
= isl_set_follows_at(data
->domain
[i
].set
,
3261 data
->domain
[j
].set
, pos
);
3271 return data
->group_coscheduled
;
3274 /* Look for independent components at the current depth and generate code
3275 * for each component separately. The resulting lists of grafts are
3276 * merged in an attempt to combine grafts with identical guards.
3278 * Code for two domains can be generated separately if all the elements
3279 * of one domain are scheduled before (or together with) all the elements
3280 * of the other domain. We therefore consider the graph with as nodes
3281 * the domains and an edge between two nodes if any element of the first
3282 * node is scheduled after any element of the second node.
3283 * If the ast_build_group_coscheduled is set, then we also add an edge if
3284 * there is any pair of elements in the two domains that are scheduled
3286 * Code is then generated (by generate_component)
3287 * for each of the strongly connected components in this graph
3288 * in their topological order.
3290 * Since the test is performed on the domain of the inverse schedules of
3291 * the different domains, we precompute these domains and store
3292 * them in data.domain.
3294 static __isl_give isl_ast_graft_list
*generate_components(
3295 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3298 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3299 int n
= isl_union_map_n_map(executed
);
3300 struct isl_any_scheduled_after_data data
;
3301 struct isl_set_map_pair
*next
;
3302 struct isl_tarjan_graph
*g
= NULL
;
3303 isl_ast_graft_list
*list
= NULL
;
3306 data
.domain
= isl_calloc_array(ctx
, struct isl_set_map_pair
, n
);
3312 if (isl_union_map_foreach_map(executed
, &extract_domain
, &next
) < 0)
3317 data
.depth
= isl_ast_build_get_depth(build
);
3318 data
.group_coscheduled
= isl_options_get_ast_build_group_coscheduled(ctx
);
3319 g
= isl_tarjan_graph_init(ctx
, n
, &any_scheduled_after
, &data
);
3321 list
= isl_ast_graft_list_alloc(ctx
, 0);
3325 isl_ast_graft_list
*list_c
;
3328 if (g
->order
[i
] == -1)
3329 isl_die(ctx
, isl_error_internal
, "cannot happen",
3332 while (g
->order
[i
] != -1) {
3336 list_c
= generate_component(data
.domain
,
3337 g
->order
+ first
, i
- first
,
3338 isl_ast_build_copy(build
));
3339 list
= isl_ast_graft_list_merge(list
, list_c
, build
);
3345 error
: list
= isl_ast_graft_list_free(list
);
3346 isl_tarjan_graph_free(g
);
3347 for (i
= 0; i
< n_domain
; ++i
) {
3348 isl_map_free(data
.domain
[i
].map
);
3349 isl_set_free(data
.domain
[i
].set
);
3352 isl_union_map_free(executed
);
3353 isl_ast_build_free(build
);
3358 /* Generate code for the next level (and all inner levels).
3360 * If "executed" is empty, i.e., no code needs to be generated,
3361 * then we return an empty list.
3363 * If we have already generated code for all loop levels, then we pass
3364 * control to generate_inner_level.
3366 * If "executed" lives in a single space, i.e., if code needs to be
3367 * generated for a single domain, then there can only be a single
3368 * component and we go directly to generate_shifted_component.
3369 * Otherwise, we call generate_components to detect the components
3370 * and to call generate_component on each of them separately.
3372 static __isl_give isl_ast_graft_list
*generate_next_level(
3373 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3377 if (!build
|| !executed
)
3380 if (isl_union_map_is_empty(executed
)) {
3381 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3382 isl_union_map_free(executed
);
3383 isl_ast_build_free(build
);
3384 return isl_ast_graft_list_alloc(ctx
, 0);
3387 depth
= isl_ast_build_get_depth(build
);
3388 if (depth
>= isl_set_dim(build
->domain
, isl_dim_set
))
3389 return generate_inner_level(executed
, build
);
3391 if (isl_union_map_n_map(executed
) == 1)
3392 return generate_shifted_component(executed
, build
);
3394 return generate_components(executed
, build
);
3396 isl_union_map_free(executed
);
3397 isl_ast_build_free(build
);
3401 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3402 * internal, executed and build are the inputs to generate_code.
3403 * list collects the output.
3405 struct isl_generate_code_data
{
3407 isl_union_map
*executed
;
3408 isl_ast_build
*build
;
3410 isl_ast_graft_list
*list
;
3413 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3417 * with E the external build schedule and S the additional schedule "space",
3418 * reformulate the inverse schedule in terms of the internal schedule domain,
3423 * We first obtain a mapping
3427 * take the inverse and the product with S -> S, resulting in
3429 * [I -> S] -> [E -> S]
3431 * Applying the map to the input produces the desired result.
3433 static __isl_give isl_union_map
*internal_executed(
3434 __isl_take isl_union_map
*executed
, __isl_keep isl_space
*space
,
3435 __isl_keep isl_ast_build
*build
)
3439 proj
= isl_ast_build_get_schedule_map(build
);
3440 proj
= isl_map_reverse(proj
);
3441 space
= isl_space_map_from_set(isl_space_copy(space
));
3442 id
= isl_map_identity(space
);
3443 proj
= isl_map_product(proj
, id
);
3444 executed
= isl_union_map_apply_domain(executed
,
3445 isl_union_map_from_map(proj
));
3449 /* Generate an AST that visits the elements in the range of data->executed
3450 * in the relative order specified by the corresponding image element(s)
3451 * for those image elements that belong to "set".
3452 * Add the result to data->list.
3454 * The caller ensures that "set" is a universe domain.
3455 * "space" is the space of the additional part of the schedule.
3456 * It is equal to the space of "set" if build->domain is parametric.
3457 * Otherwise, it is equal to the range of the wrapped space of "set".
3459 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3460 * was called from an outside user (data->internal not set), then
3461 * the (inverse) schedule refers to the external build domain and needs to
3462 * be transformed to refer to the internal build domain.
3464 * The build is extended to include the additional part of the schedule.
3465 * If the original build space was not parametric, then the options
3466 * in data->build refer only to the additional part of the schedule
3467 * and they need to be adjusted to refer to the complete AST build
3470 * After having adjusted inverse schedule and build, we start generating
3471 * code with the outer loop of the current code generation
3472 * in generate_next_level.
3474 * If the original build space was not parametric, we undo the embedding
3475 * on the resulting isl_ast_node_list so that it can be used within
3476 * the outer AST build.
3478 static int generate_code_in_space(struct isl_generate_code_data
*data
,
3479 __isl_take isl_set
*set
, __isl_take isl_space
*space
)
3481 isl_union_map
*executed
;
3482 isl_ast_build
*build
;
3483 isl_ast_graft_list
*list
;
3486 executed
= isl_union_map_copy(data
->executed
);
3487 executed
= isl_union_map_intersect_domain(executed
,
3488 isl_union_set_from_set(set
));
3490 embed
= !isl_set_is_params(data
->build
->domain
);
3491 if (embed
&& !data
->internal
)
3492 executed
= internal_executed(executed
, space
, data
->build
);
3494 build
= isl_ast_build_copy(data
->build
);
3495 build
= isl_ast_build_product(build
, space
);
3497 list
= generate_next_level(executed
, build
);
3499 list
= isl_ast_graft_list_unembed(list
, embed
);
3501 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
3506 /* Generate an AST that visits the elements in the range of data->executed
3507 * in the relative order specified by the corresponding domain element(s)
3508 * for those domain elements that belong to "set".
3509 * Add the result to data->list.
3511 * The caller ensures that "set" is a universe domain.
3513 * If the build space S is not parametric, then the space of "set"
3514 * need to be a wrapped relation with S as domain. That is, it needs
3519 * Check this property and pass control to generate_code_in_space
3521 * If the build space is not parametric, then T is the space of "set".
3523 static int generate_code_set(__isl_take isl_set
*set
, void *user
)
3525 struct isl_generate_code_data
*data
= user
;
3526 isl_space
*space
, *build_space
;
3529 space
= isl_set_get_space(set
);
3531 if (isl_set_is_params(data
->build
->domain
))
3532 return generate_code_in_space(data
, set
, space
);
3534 build_space
= isl_ast_build_get_space(data
->build
, data
->internal
);
3535 space
= isl_space_unwrap(space
);
3536 is_domain
= isl_space_is_domain(build_space
, space
);
3537 isl_space_free(build_space
);
3538 space
= isl_space_range(space
);
3543 isl_die(isl_set_get_ctx(set
), isl_error_invalid
,
3544 "invalid nested schedule space", goto error
);
3546 return generate_code_in_space(data
, set
, space
);
3549 isl_space_free(space
);
3553 /* Generate an AST that visits the elements in the range of "executed"
3554 * in the relative order specified by the corresponding domain element(s).
3556 * "build" is an isl_ast_build that has either been constructed by
3557 * isl_ast_build_from_context or passed to a callback set by
3558 * isl_ast_build_set_create_leaf.
3559 * In the first case, the space of the isl_ast_build is typically
3560 * a parametric space, although this is currently not enforced.
3561 * In the second case, the space is never a parametric space.
3562 * If the space S is not parametric, then the domain space(s) of "executed"
3563 * need to be wrapped relations with S as domain.
3565 * If the domain of "executed" consists of several spaces, then an AST
3566 * is generated for each of them (in arbitrary order) and the results
3569 * If "internal" is set, then the domain "S" above refers to the internal
3570 * schedule domain representation. Otherwise, it refers to the external
3571 * representation, as returned by isl_ast_build_get_schedule_space.
3573 * We essentially run over all the spaces in the domain of "executed"
3574 * and call generate_code_set on each of them.
3576 static __isl_give isl_ast_graft_list
*generate_code(
3577 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
3581 struct isl_generate_code_data data
= { 0 };
3583 isl_union_set
*schedule_domain
;
3584 isl_union_map
*universe
;
3588 space
= isl_ast_build_get_space(build
, 1);
3589 space
= isl_space_align_params(space
,
3590 isl_union_map_get_space(executed
));
3591 space
= isl_space_align_params(space
,
3592 isl_union_map_get_space(build
->options
));
3593 build
= isl_ast_build_align_params(build
, isl_space_copy(space
));
3594 executed
= isl_union_map_align_params(executed
, space
);
3595 if (!executed
|| !build
)
3598 ctx
= isl_ast_build_get_ctx(build
);
3600 data
.internal
= internal
;
3601 data
.executed
= executed
;
3603 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
3605 universe
= isl_union_map_universe(isl_union_map_copy(executed
));
3606 schedule_domain
= isl_union_map_domain(universe
);
3607 if (isl_union_set_foreach_set(schedule_domain
, &generate_code_set
,
3609 data
.list
= isl_ast_graft_list_free(data
.list
);
3611 isl_union_set_free(schedule_domain
);
3612 isl_union_map_free(executed
);
3614 isl_ast_build_free(build
);
3617 isl_union_map_free(executed
);
3618 isl_ast_build_free(build
);
3622 /* Generate an AST that visits the elements in the domain of "schedule"
3623 * in the relative order specified by the corresponding image element(s).
3625 * "build" is an isl_ast_build that has either been constructed by
3626 * isl_ast_build_from_context or passed to a callback set by
3627 * isl_ast_build_set_create_leaf.
3628 * In the first case, the space of the isl_ast_build is typically
3629 * a parametric space, although this is currently not enforced.
3630 * In the second case, the space is never a parametric space.
3631 * If the space S is not parametric, then the range space(s) of "schedule"
3632 * need to be wrapped relations with S as domain.
3634 * If the range of "schedule" consists of several spaces, then an AST
3635 * is generated for each of them (in arbitrary order) and the results
3638 * We first initialize the local copies of the relevant options.
3639 * We do this here rather than when the isl_ast_build is created
3640 * because the options may have changed between the construction
3641 * of the isl_ast_build and the call to isl_generate_code.
3643 * The main computation is performed on an inverse schedule (with
3644 * the schedule domain in the domain and the elements to be executed
3645 * in the range) called "executed".
3647 __isl_give isl_ast_node
*isl_ast_build_ast_from_schedule(
3648 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
3650 isl_ast_graft_list
*list
;
3652 isl_union_map
*executed
;
3654 build
= isl_ast_build_copy(build
);
3655 build
= isl_ast_build_set_single_valued(build
, 0);
3656 executed
= isl_union_map_reverse(schedule
);
3657 list
= generate_code(executed
, isl_ast_build_copy(build
), 0);
3658 node
= isl_ast_node_from_graft_list(list
, build
);
3659 isl_ast_build_free(build
);