2 * Copyright 2012 Ecole Normale Superieure
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege,
7 * Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
13 #include <isl/union_map.h>
15 #include <isl_tarjan.h>
16 #include <isl_ast_private.h>
17 #include <isl_ast_build_expr.h>
18 #include <isl_ast_build_private.h>
19 #include <isl_ast_graft_private.h>
20 #include <isl_list_private.h>
22 /* Add the constraint to the list that "user" points to, if it is not
25 static int collect_constraint(__isl_take isl_constraint
*constraint
,
28 isl_constraint_list
**list
= user
;
30 if (isl_constraint_is_div_constraint(constraint
))
31 isl_constraint_free(constraint
);
33 *list
= isl_constraint_list_add(*list
, constraint
);
38 /* Extract the constraints of "bset" (except the div constraints)
39 * and collect them in an isl_constraint_list.
41 static __isl_give isl_constraint_list
*isl_constraint_list_from_basic_set(
42 __isl_take isl_basic_set
*bset
)
46 isl_constraint_list
*list
;
51 ctx
= isl_basic_set_get_ctx(bset
);
53 n
= isl_basic_set_n_constraint(bset
);
54 list
= isl_constraint_list_alloc(ctx
, n
);
55 if (isl_basic_set_foreach_constraint(bset
,
56 &collect_constraint
, &list
) < 0)
57 list
= isl_constraint_list_free(list
);
59 isl_basic_set_free(bset
);
63 /* Data used in generate_domain.
65 * "build" is the input build.
66 * "list" collects the results.
68 struct isl_generate_domain_data
{
71 isl_ast_graft_list
*list
;
74 static __isl_give isl_ast_graft_list
*generate_next_level(
75 __isl_take isl_union_map
*executed
,
76 __isl_take isl_ast_build
*build
);
77 static __isl_give isl_ast_graft_list
*generate_code(
78 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
81 /* Generate an AST for a single domain based on
82 * the (non single valued) inverse schedule "executed".
84 * We extend the schedule with the iteration domain
85 * and continue generating through a call to generate_code.
87 * In particular, if executed has the form
91 * then we continue generating code on
95 * The extended inverse schedule is clearly single valued
96 * ensuring that the nested generate_code will not reach this function,
97 * but will instead create calls to all elements of D that need
98 * to be executed from the current schedule domain.
100 static int generate_non_single_valued(__isl_take isl_map
*executed
,
101 struct isl_generate_domain_data
*data
)
104 isl_ast_build
*build
;
105 isl_ast_graft_list
*list
;
107 build
= isl_ast_build_copy(data
->build
);
109 identity
= isl_set_identity(isl_map_range(isl_map_copy(executed
)));
110 executed
= isl_map_domain_product(executed
, identity
);
112 list
= generate_code(isl_union_map_from_map(executed
), build
, 1);
114 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
119 /* Call the at_each_domain callback, if requested by the user,
120 * after recording the current inverse schedule in the build.
122 static __isl_give isl_ast_graft
*at_each_domain(__isl_take isl_ast_graft
*graft
,
123 __isl_keep isl_map
*executed
, __isl_keep isl_ast_build
*build
)
125 if (!graft
|| !build
)
126 return isl_ast_graft_free(graft
);
127 if (!build
->at_each_domain
)
130 build
= isl_ast_build_copy(build
);
131 build
= isl_ast_build_set_executed(build
,
132 isl_union_map_from_map(isl_map_copy(executed
)));
134 return isl_ast_graft_free(graft
);
136 graft
->node
= build
->at_each_domain(graft
->node
,
137 build
, build
->at_each_domain_user
);
138 isl_ast_build_free(build
);
141 graft
= isl_ast_graft_free(graft
);
146 /* Generate an AST for a single domain based on
147 * the inverse schedule "executed".
149 * If there is more than one domain element associated to the current
150 * schedule "time", then we need to continue the generation process
151 * in generate_non_single_valued.
152 * Note that the inverse schedule being single-valued may depend
153 * on constraints that are only available in the original context
154 * domain specified by the user. If the bare inverse schedule
155 * is not single-valued, we double-check after introducing the constraints
156 * from data->build->domain.
158 * Otherwise, we generate a call expression for the single executed
159 * domain element and put a guard around it based on the (simplified)
160 * domain of "executed".
162 * If the user has set an at_each_domain callback, it is called
163 * on the constructed call expression node.
165 static int generate_domain(__isl_take isl_map
*executed
, void *user
)
167 struct isl_generate_domain_data
*data
= user
;
168 isl_ast_graft
*graft
;
169 isl_ast_graft_list
*list
;
174 sv
= isl_map_is_single_valued(executed
);
178 map
= isl_map_copy(executed
);
179 map
= isl_map_intersect_domain(map
,
180 isl_set_copy(data
->build
->domain
));
181 sv
= isl_map_is_single_valued(map
);
185 return generate_non_single_valued(executed
, data
);
187 executed
= isl_map_coalesce(executed
);
188 map
= isl_map_copy(executed
);
189 map
= isl_ast_build_compute_gist_map_domain(data
->build
, map
);
190 guard
= isl_map_domain(isl_map_copy(map
));
191 guard
= isl_set_coalesce(guard
);
192 guard
= isl_ast_build_compute_gist(data
->build
, guard
);
193 graft
= isl_ast_graft_alloc_domain(map
, data
->build
);
194 graft
= at_each_domain(graft
, executed
, data
->build
);
196 isl_map_free(executed
);
197 graft
= isl_ast_graft_add_guard(graft
, guard
, data
->build
);
199 list
= isl_ast_graft_list_from_ast_graft(graft
);
200 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
204 isl_map_free(executed
);
208 /* Call build->create_leaf to a create "leaf" node in the AST,
209 * encapsulate the result in an isl_ast_graft and return the result
210 * as a 1-element list.
212 * Note that the node returned by the user may be an entire tree.
214 * Before we pass control to the user, we first clear some information
215 * from the build that is (presumbably) only meaningful
216 * for the current code generation.
217 * This includes the create_leaf callback itself, so we make a copy
218 * of the build first.
220 static __isl_give isl_ast_graft_list
*call_create_leaf(
221 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
224 isl_ast_graft
*graft
;
225 isl_ast_build
*user_build
;
227 user_build
= isl_ast_build_copy(build
);
228 user_build
= isl_ast_build_set_executed(user_build
, executed
);
229 user_build
= isl_ast_build_clear_local_info(user_build
);
233 node
= build
->create_leaf(user_build
, build
->create_leaf_user
);
234 graft
= isl_ast_graft_alloc(node
, build
);
235 isl_ast_build_free(build
);
236 return isl_ast_graft_list_from_ast_graft(graft
);
239 /* Generate an AST after having handled the complete schedule
240 * of this call to the code generator.
242 * If the user has specified a create_leaf callback, control
243 * is passed to the user in call_create_leaf.
245 * Otherwise, we generate one or more calls for each individual
246 * domain in generate_domain.
248 static __isl_give isl_ast_graft_list
*generate_inner_level(
249 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
252 struct isl_generate_domain_data data
= { build
};
254 if (!build
|| !executed
)
257 if (build
->create_leaf
)
258 return call_create_leaf(executed
, build
);
260 ctx
= isl_union_map_get_ctx(executed
);
261 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
262 if (isl_union_map_foreach_map(executed
, &generate_domain
, &data
) < 0)
263 data
.list
= isl_ast_graft_list_free(data
.list
);
266 error
: data
.list
= NULL
;
267 isl_ast_build_free(build
);
268 isl_union_map_free(executed
);
272 /* Eliminate the schedule dimension "pos" from "executed" and return
275 static __isl_give isl_union_map
*eliminate(__isl_take isl_union_map
*executed
,
276 int pos
, __isl_keep isl_ast_build
*build
)
281 space
= isl_ast_build_get_space(build
, 1);
282 space
= isl_space_map_from_set(space
);
283 elim
= isl_map_identity(space
);
284 elim
= isl_map_eliminate(elim
, isl_dim_in
, pos
, 1);
286 executed
= isl_union_map_apply_domain(executed
,
287 isl_union_map_from_map(elim
));
292 /* Check if the constraint "c" is a lower bound on dimension "pos",
293 * an upper bound, or independent of dimension "pos".
295 static int constraint_type(isl_constraint
*c
, int pos
)
297 if (isl_constraint_is_lower_bound(c
, isl_dim_set
, pos
))
299 if (isl_constraint_is_upper_bound(c
, isl_dim_set
, pos
))
304 /* Compare the types of the constraints "a" and "b",
305 * resulting in constraints that are independent of "depth"
306 * to be sorted before the lower bounds on "depth", which in
307 * turn are sorted before the upper bounds on "depth".
309 static int cmp_constraint(const void *a
, const void *b
, void *user
)
312 isl_constraint
* const *c1
= a
;
313 isl_constraint
* const *c2
= b
;
314 int t1
= constraint_type(*c1
, *depth
);
315 int t2
= constraint_type(*c2
, *depth
);
320 /* Extract a lower bound on dimension "pos" from constraint "c".
322 * If the constraint is of the form
326 * then we essentially return
328 * l = ceil(-f(...)/a)
330 * However, if the current dimension is strided, then we need to make
331 * sure that the lower bound we construct is of the form
335 * with f the offset and s the stride.
336 * We therefore compute
338 * f + s * ceil((l - f)/s)
340 static __isl_give isl_aff
*lower_bound(__isl_keep isl_constraint
*c
,
341 int pos
, __isl_keep isl_ast_build
*build
)
345 aff
= isl_constraint_get_bound(c
, isl_dim_set
, pos
);
346 aff
= isl_aff_ceil(aff
);
348 if (isl_ast_build_has_stride(build
, pos
)) {
352 isl_int_init(stride
);
354 offset
= isl_ast_build_get_offset(build
, pos
);
355 isl_ast_build_get_stride(build
, pos
, &stride
);
357 aff
= isl_aff_sub(aff
, isl_aff_copy(offset
));
358 aff
= isl_aff_scale_down(aff
, stride
);
359 aff
= isl_aff_ceil(aff
);
360 aff
= isl_aff_scale(aff
, stride
);
361 aff
= isl_aff_add(aff
, offset
);
363 isl_int_clear(stride
);
366 aff
= isl_ast_build_compute_gist_aff(build
, aff
);
371 /* Return the exact lower bound (or upper bound if "upper" is set)
372 * of "domain" as a piecewise affine expression.
374 * If we are computing a lower bound (of a strided dimension), then
375 * we need to make sure it is of the form
379 * where f is the offset and s is the stride.
380 * We therefore need to include the stride constraint before computing
383 static __isl_give isl_pw_aff
*exact_bound(__isl_keep isl_set
*domain
,
384 __isl_keep isl_ast_build
*build
, int upper
)
389 isl_pw_multi_aff
*pma
;
391 domain
= isl_set_copy(domain
);
393 stride
= isl_ast_build_get_stride_constraint(build
);
394 domain
= isl_set_intersect(domain
, stride
);
396 it_map
= isl_ast_build_map_to_iterator(build
, domain
);
398 pma
= isl_map_lexmax_pw_multi_aff(it_map
);
400 pma
= isl_map_lexmin_pw_multi_aff(it_map
);
401 pa
= isl_pw_multi_aff_get_pw_aff(pma
, 0);
402 isl_pw_multi_aff_free(pma
);
403 pa
= isl_ast_build_compute_gist_pw_aff(build
, pa
);
404 pa
= isl_pw_aff_coalesce(pa
);
409 /* Return a list of "n" lower bounds on dimension "pos"
410 * extracted from the "n" constraints starting at "constraint".
411 * If "n" is zero, then we extract a lower bound from "domain" instead.
413 static __isl_give isl_pw_aff_list
*lower_bounds(
414 __isl_keep isl_constraint
**constraint
, int n
, int pos
,
415 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
418 isl_pw_aff_list
*list
;
426 pa
= exact_bound(domain
, build
, 0);
427 return isl_pw_aff_list_from_pw_aff(pa
);
430 ctx
= isl_ast_build_get_ctx(build
);
431 list
= isl_pw_aff_list_alloc(ctx
,n
);
433 for (i
= 0; i
< n
; ++i
) {
436 aff
= lower_bound(constraint
[i
], pos
, build
);
437 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
443 /* Return a list of "n" upper bounds on dimension "pos"
444 * extracted from the "n" constraints starting at "constraint".
445 * If "n" is zero, then we extract an upper bound from "domain" instead.
447 static __isl_give isl_pw_aff_list
*upper_bounds(
448 __isl_keep isl_constraint
**constraint
, int n
, int pos
,
449 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
452 isl_pw_aff_list
*list
;
457 pa
= exact_bound(domain
, build
, 1);
458 return isl_pw_aff_list_from_pw_aff(pa
);
461 ctx
= isl_ast_build_get_ctx(build
);
462 list
= isl_pw_aff_list_alloc(ctx
,n
);
464 for (i
= 0; i
< n
; ++i
) {
467 aff
= isl_constraint_get_bound(constraint
[i
], isl_dim_set
, pos
);
468 aff
= isl_aff_floor(aff
);
469 list
= isl_pw_aff_list_add(list
, isl_pw_aff_from_aff(aff
));
475 /* Return an isl_ast_expr that performs the reduction of type "type"
476 * on AST expressions corresponding to the elements in "list".
478 * The list is assumed to contain at least one element.
479 * If the list contains exactly one element, then the returned isl_ast_expr
480 * simply computes that affine expression.
482 static __isl_give isl_ast_expr
*reduce_list(enum isl_ast_op_type type
,
483 __isl_keep isl_pw_aff_list
*list
, __isl_keep isl_ast_build
*build
)
492 n
= isl_pw_aff_list_n_pw_aff(list
);
495 return isl_ast_build_expr_from_pw_aff_internal(build
,
496 isl_pw_aff_list_get_pw_aff(list
, 0));
498 ctx
= isl_pw_aff_list_get_ctx(list
);
499 expr
= isl_ast_expr_alloc_op(ctx
, type
, n
);
503 for (i
= 0; i
< n
; ++i
) {
504 isl_ast_expr
*expr_i
;
506 expr_i
= isl_ast_build_expr_from_pw_aff_internal(build
,
507 isl_pw_aff_list_get_pw_aff(list
, i
));
509 return isl_ast_expr_free(expr
);
510 expr
->u
.op
.args
[i
] = expr_i
;
516 /* Add a guard to "graft" based on "bound" in the case of a degenerate
517 * level (including the special case of an eliminated level).
519 * We eliminate the current dimension, simplify the result in the current
520 * build and add the result as guards to the graft.
522 * Note that we cannot simply drop the constraints on the current dimension
523 * even in the eliminated case, because the single affine expression may
524 * not be explicitly available in "bounds". Moreover, the single affine
525 * expression may only be defined on a subset of the build domain,
526 * so we do in some cases need to insert a guard even in the eliminated case.
528 static __isl_give isl_ast_graft
*add_degenerate_guard(
529 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
530 __isl_keep isl_ast_build
*build
)
535 depth
= isl_ast_build_get_depth(build
);
537 dom
= isl_set_from_basic_set(isl_basic_set_copy(bounds
));
538 if (isl_ast_build_has_stride(build
, depth
)) {
541 stride
= isl_ast_build_get_stride_constraint(build
);
542 dom
= isl_set_intersect(dom
, stride
);
544 dom
= isl_set_eliminate(dom
, isl_dim_set
, depth
, 1);
545 dom
= isl_ast_build_compute_gist(build
, dom
);
547 graft
= isl_ast_graft_add_guard(graft
, dom
, build
);
552 /* Update "graft" based on "bounds" for the eliminated case.
554 * In the eliminated case, no for node is created, so we only need
555 * to check if "bounds" imply any guards that need to be inserted.
557 static __isl_give isl_ast_graft
*refine_eliminated(
558 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
559 __isl_keep isl_ast_build
*build
)
561 return add_degenerate_guard(graft
, bounds
, build
);
564 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
566 * "build" is the build in which graft->node was created
567 * "sub_build" contains information about the current level itself,
568 * including the single value attained.
570 * We first set the initialization part of the for loop to the single
571 * value attained by the current dimension.
572 * The increment and condition are not strictly needed as the are known
573 * to be "1" and "iterator <= value" respectively.
574 * Then we set the size of the iterator and
575 * check if "bounds" imply any guards that need to be inserted.
577 static __isl_give isl_ast_graft
*refine_degenerate(
578 __isl_take isl_ast_graft
*graft
, __isl_keep isl_basic_set
*bounds
,
579 __isl_keep isl_ast_build
*build
,
580 __isl_keep isl_ast_build
*sub_build
)
584 if (!graft
|| !sub_build
)
585 return isl_ast_graft_free(graft
);
587 value
= isl_pw_aff_copy(sub_build
->value
);
589 graft
->node
->u
.f
.init
= isl_ast_build_expr_from_pw_aff_internal(build
,
591 if (!graft
->node
->u
.f
.init
)
592 return isl_ast_graft_free(graft
);
594 graft
= add_degenerate_guard(graft
, bounds
, build
);
599 /* Return the intersection of the "n" constraints starting at "constraint"
602 static __isl_give isl_set
*intersect_constraints(isl_ctx
*ctx
,
603 __isl_keep isl_constraint
**constraint
, int n
)
609 isl_die(ctx
, isl_error_internal
,
610 "expecting at least one constraint", return NULL
);
612 bset
= isl_basic_set_from_constraint(
613 isl_constraint_copy(constraint
[0]));
614 for (i
= 1; i
< n
; ++i
) {
615 isl_basic_set
*bset_i
;
617 bset_i
= isl_basic_set_from_constraint(
618 isl_constraint_copy(constraint
[i
]));
619 bset
= isl_basic_set_intersect(bset
, bset_i
);
622 return isl_set_from_basic_set(bset
);
625 /* Compute the constraints on the outer dimensions enforced by
626 * graft->node and add those constraints to graft->enforced,
627 * in case the upper bound is expressed as a set "upper".
629 * In particular, if l(...) is a lower bound in "lower", and
631 * -a i + f(...) >= 0 or a i <= f(...)
633 * is an upper bound ocnstraint on the current dimension i,
634 * then the for loop enforces the constraint
636 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
638 * We therefore simply take each lower bound in turn, plug it into
639 * the upper bounds and compute the intersection over all lower bounds.
641 * If a lower bound is a rational expression, then
642 * isl_basic_set_preimage_multi_aff will force this rational
643 * expression to have only integer values. However, the loop
644 * itself does not enforce this integrality constraint. We therefore
645 * use the ceil of the lower bounds instead of the lower bounds themselves.
646 * Other constraints will make sure that the for loop is only executed
647 * when each of the lower bounds attains an integral value.
648 * In particular, potentially rational values only occur in
649 * lower_bound if the offset is a (seemingly) rational expression,
650 * but then outer conditions will make sure that this rational expression
651 * only attains integer values.
653 static __isl_give isl_ast_graft
*set_enforced_from_set(
654 __isl_take isl_ast_graft
*graft
,
655 __isl_keep isl_pw_aff_list
*lower
, int pos
, __isl_keep isl_set
*upper
)
658 isl_basic_set
*enforced
;
659 isl_pw_multi_aff
*pma
;
662 if (!graft
|| !lower
)
663 return isl_ast_graft_free(graft
);
665 space
= isl_set_get_space(upper
);
666 enforced
= isl_basic_set_universe(isl_space_copy(space
));
668 space
= isl_space_map_from_set(space
);
669 pma
= isl_pw_multi_aff_identity(space
);
671 n
= isl_pw_aff_list_n_pw_aff(lower
);
672 for (i
= 0; i
< n
; ++i
) {
676 isl_pw_multi_aff
*pma_i
;
678 pa
= isl_pw_aff_list_get_pw_aff(lower
, i
);
679 pa
= isl_pw_aff_ceil(pa
);
680 pma_i
= isl_pw_multi_aff_copy(pma
);
681 pma_i
= isl_pw_multi_aff_set_pw_aff(pma_i
, pos
, pa
);
682 enforced_i
= isl_set_copy(upper
);
683 enforced_i
= isl_set_preimage_pw_multi_aff(enforced_i
, pma_i
);
684 hull
= isl_set_simple_hull(enforced_i
);
685 enforced
= isl_basic_set_intersect(enforced
, hull
);
688 isl_pw_multi_aff_free(pma
);
690 graft
= isl_ast_graft_enforce(graft
, enforced
);
695 /* Compute the constraints on the outer dimensions enforced by
696 * graft->node and add those constraints to graft->enforced,
697 * in case the upper bound is expressed as
698 * a list of affine expressions "upper".
700 * The enforced condition is that each lower bound expression is less
701 * than or equal to each upper bound expression.
703 static __isl_give isl_ast_graft
*set_enforced_from_list(
704 __isl_take isl_ast_graft
*graft
,
705 __isl_keep isl_pw_aff_list
*lower
, __isl_keep isl_pw_aff_list
*upper
)
708 isl_basic_set
*enforced
;
710 lower
= isl_pw_aff_list_copy(lower
);
711 upper
= isl_pw_aff_list_copy(upper
);
712 cond
= isl_pw_aff_list_le_set(lower
, upper
);
713 enforced
= isl_set_simple_hull(cond
);
714 graft
= isl_ast_graft_enforce(graft
, enforced
);
719 /* Set the condition part of the for node graft->node in case
720 * the upper bound is represented as a list of piecewise affine expressions.
722 * In particular, set the condition to
724 * iterator <= min(list of upper bounds)
726 static __isl_give isl_ast_graft
*set_for_cond_from_list(
727 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*list
,
728 __isl_keep isl_ast_build
*build
)
730 isl_ast_expr
*bound
, *iterator
, *cond
;
733 return isl_ast_graft_free(graft
);
735 bound
= reduce_list(isl_ast_op_min
, list
, build
);
736 iterator
= isl_ast_expr_copy(graft
->node
->u
.f
.iterator
);
737 cond
= isl_ast_expr_alloc_binary(isl_ast_op_le
, iterator
, bound
);
738 graft
->node
->u
.f
.cond
= cond
;
740 if (!graft
->node
->u
.f
.cond
)
741 return isl_ast_graft_free(graft
);
745 /* Set the condition part of the for node graft->node in case
746 * the upper bound is represented as a set.
748 static __isl_give isl_ast_graft
*set_for_cond_from_set(
749 __isl_take isl_ast_graft
*graft
, __isl_keep isl_set
*set
,
750 __isl_keep isl_ast_build
*build
)
757 cond
= isl_ast_build_expr_from_set(build
, isl_set_copy(set
));
758 graft
->node
->u
.f
.cond
= cond
;
759 if (!graft
->node
->u
.f
.cond
)
760 return isl_ast_graft_free(graft
);
764 /* Construct an isl_ast_expr for the increment (i.e., stride) of
765 * the current dimension.
767 static __isl_give isl_ast_expr
*for_inc(__isl_keep isl_ast_build
*build
)
774 ctx
= isl_ast_build_get_ctx(build
);
775 depth
= isl_ast_build_get_depth(build
);
777 if (!isl_ast_build_has_stride(build
, depth
))
778 return isl_ast_expr_alloc_int_si(ctx
, 1);
781 isl_ast_build_get_stride(build
, depth
, &v
);
782 inc
= isl_ast_expr_alloc_int(ctx
, v
);
788 /* Should we express the loop condition as
790 * iterator <= min(list of upper bounds)
792 * or as a conjunction of constraints?
794 * The first is constructed from a list of upper bounds.
795 * The second is constructed from a set.
797 * If there are no upper bounds in "constraints", then this could mean
798 * that "domain" simply doesn't have an upper bound or that we didn't
799 * pick any upper bound. In the first case, we want to generate the
800 * loop condition as a(n empty) conjunction of constraints
801 * In the second case, we will compute
802 * a single upper bound from "domain" and so we use the list form.
804 * If there are upper bounds in "constraints",
805 * then we use the list form iff the atomic_upper_bound option is set.
807 static int use_upper_bound_list(isl_ctx
*ctx
, int n_upper
,
808 __isl_keep isl_set
*domain
, int depth
)
811 return isl_options_get_ast_build_atomic_upper_bound(ctx
);
813 return isl_set_dim_has_upper_bound(domain
, isl_dim_set
, depth
);
816 /* Fill in the expressions of the for node in graft->node.
819 * - set the initialization part of the loop to the maximum of the lower bounds
820 * - set the size of the iterator based on the values attained by the iterator
821 * - extract the increment from the stride of the current dimension
822 * - construct the for condition either based on a list of upper bounds
823 * or on a set of upper bound constraints.
825 static __isl_give isl_ast_graft
*set_for_node_expressions(
826 __isl_take isl_ast_graft
*graft
, __isl_keep isl_pw_aff_list
*lower
,
827 int use_list
, __isl_keep isl_pw_aff_list
*upper_list
,
828 __isl_keep isl_set
*upper_set
, __isl_keep isl_ast_build
*build
)
835 build
= isl_ast_build_copy(build
);
836 build
= isl_ast_build_set_enforced(build
,
837 isl_ast_graft_get_enforced(graft
));
840 node
->u
.f
.init
= reduce_list(isl_ast_op_max
, lower
, build
);
841 node
->u
.f
.inc
= for_inc(build
);
844 graft
= set_for_cond_from_list(graft
, upper_list
, build
);
846 graft
= set_for_cond_from_set(graft
, upper_set
, build
);
848 isl_ast_build_free(build
);
850 if (!node
->u
.f
.iterator
|| !node
->u
.f
.init
||
851 !node
->u
.f
.cond
|| !node
->u
.f
.inc
)
852 return isl_ast_graft_free(graft
);
857 /* Update "graft" based on "bounds" and "domain" for the generic,
858 * non-degenerate, case.
860 * "constraints" contains the "n_lower" lower and "n_upper" upper bounds
861 * that the loop node should express.
862 * "domain" is the subset of the intersection of the constraints
863 * for which some code is executed.
865 * There may be zero lower bounds or zero upper bounds in "constraints"
866 * in case the list of constraints was created
867 * based on the atomic option or based on separation with explicit bounds.
868 * In that case, we use "domain" to derive lower and/or upper bounds.
870 * We first compute a list of one or more lower bounds.
872 * Then we decide if we want to express the condition as
874 * iterator <= min(list of upper bounds)
876 * or as a conjunction of constraints.
878 * The set of enforced constraints is then computed either based on
879 * a list of upper bounds or on a set of upper bound constraints.
880 * We do not compute any enforced constraints if we were forced
881 * to compute a lower or upper bound using exact_bound. The domains
882 * of the resulting expressions may imply some bounds on outer dimensions
883 * that we do not want to appear in the enforced constraints since
884 * they are not actually enforced by the corresponding code.
886 * Finally, we fill in the expressions of the for node.
888 static __isl_give isl_ast_graft
*refine_generic_bounds(
889 __isl_take isl_ast_graft
*graft
,
890 __isl_keep isl_constraint
**constraint
, int n_lower
, int n_upper
,
891 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
895 isl_pw_aff_list
*lower
;
897 isl_set
*upper_set
= NULL
;
898 isl_pw_aff_list
*upper_list
= NULL
;
900 if (!graft
|| !build
)
901 return isl_ast_graft_free(graft
);
903 depth
= isl_ast_build_get_depth(build
);
904 ctx
= isl_ast_graft_get_ctx(graft
);
906 use_list
= use_upper_bound_list(ctx
, n_upper
, domain
, depth
);
908 lower
= lower_bounds(constraint
, n_lower
, depth
, domain
, build
);
911 upper_list
= upper_bounds(constraint
+ n_lower
, n_upper
, depth
,
913 else if (n_upper
> 0)
914 upper_set
= intersect_constraints(ctx
, constraint
+ n_lower
,
917 upper_set
= isl_set_universe(isl_set_get_space(domain
));
919 if (n_lower
== 0 || n_upper
== 0)
922 graft
= set_enforced_from_list(graft
, lower
, upper_list
);
924 graft
= set_enforced_from_set(graft
, lower
, depth
, upper_set
);
926 graft
= set_for_node_expressions(graft
, lower
, use_list
, upper_list
,
929 isl_pw_aff_list_free(lower
);
930 isl_pw_aff_list_free(upper_list
);
931 isl_set_free(upper_set
);
936 /* How many constraints in the "constraint" array, starting at position "first"
937 * are of the give type? "n" represents the total number of elements
940 static int count_constraints(isl_constraint
**constraint
, int n
, int first
,
947 for (i
= 0; first
+ i
< n
; i
++)
948 if (constraint_type(constraint
[i
], pos
) != type
)
954 /* Update "graft" based on "bounds" and "domain" for the generic,
955 * non-degenerate, case.
957 * "list" respresent the list of bounds that need to be encoded by
958 * the for loop (or a guard around the for loop).
959 * "domain" is the subset of the intersection of the constraints
960 * for which some code is executed.
961 * "build" is the build in which graft->node was created.
963 * We separate lower bounds, upper bounds and constraints that
964 * are independent of the loop iterator.
966 * The actual for loop bounds are generated in refine_generic_bounds.
967 * If there are any constraints that are independent of the loop iterator,
968 * we need to put a guard around the for loop (which may get hoisted up
969 * to higher levels) and we call refine_generic_bounds in a build
970 * where this guard is enforced.
972 static __isl_give isl_ast_graft
*refine_generic_split(
973 __isl_take isl_ast_graft
*graft
, __isl_keep isl_constraint_list
*list
,
974 __isl_keep isl_set
*domain
, __isl_keep isl_ast_build
*build
)
977 isl_ast_build
*for_build
;
979 int n_indep
, n_lower
, n_upper
;
984 return isl_ast_graft_free(graft
);
986 pos
= isl_ast_build_get_depth(build
);
988 if (isl_sort(list
->p
, list
->n
, sizeof(isl_constraint
*),
989 &cmp_constraint
, &pos
) < 0)
990 return isl_ast_graft_free(graft
);
993 n_indep
= count_constraints(list
->p
, n
, 0, pos
, 0);
994 n_lower
= count_constraints(list
->p
, n
, n_indep
, pos
, 1);
995 n_upper
= count_constraints(list
->p
, n
, n_indep
+ n_lower
, pos
, 2);
998 return refine_generic_bounds(graft
,
999 list
->p
+ n_indep
, n_lower
, n_upper
, domain
, build
);
1001 ctx
= isl_ast_graft_get_ctx(graft
);
1002 guard
= intersect_constraints(ctx
, list
->p
, n_indep
);
1004 for_build
= isl_ast_build_copy(build
);
1005 for_build
= isl_ast_build_restrict_pending(for_build
,
1006 isl_set_copy(guard
));
1007 graft
= refine_generic_bounds(graft
,
1008 list
->p
+ n_indep
, n_lower
, n_upper
, domain
, for_build
);
1009 isl_ast_build_free(for_build
);
1011 graft
= isl_ast_graft_add_guard(graft
, guard
, build
);
1016 /* Update "graft" based on "bounds" and "domain" for the generic,
1017 * non-degenerate, case.
1019 * "bounds" respresent the bounds that need to be encoded by
1020 * the for loop (or a guard around the for loop).
1021 * "domain" is the subset of "bounds" for which some code is executed.
1022 * "build" is the build in which graft->node was created.
1024 * We break up "bounds" into a list of constraints and continue with
1025 * refine_generic_split.
1027 static __isl_give isl_ast_graft
*refine_generic(
1028 __isl_take isl_ast_graft
*graft
,
1029 __isl_keep isl_basic_set
*bounds
, __isl_keep isl_set
*domain
,
1030 __isl_keep isl_ast_build
*build
)
1032 isl_constraint_list
*list
;
1034 if (!build
|| !graft
)
1035 return isl_ast_graft_free(graft
);
1037 bounds
= isl_basic_set_copy(bounds
);
1038 bounds
= isl_ast_build_compute_gist_basic_set(build
, bounds
);
1039 list
= isl_constraint_list_from_basic_set(bounds
);
1041 graft
= refine_generic_split(graft
, list
, domain
, build
);
1043 isl_constraint_list_free(list
);
1047 /* Create a for node for the current level.
1049 * Mark the for node degenerate if "degenerate" is set.
1051 static __isl_give isl_ast_node
*create_for(__isl_keep isl_ast_build
*build
,
1061 depth
= isl_ast_build_get_depth(build
);
1062 id
= isl_ast_build_get_iterator_id(build
, depth
);
1063 node
= isl_ast_node_alloc_for(id
);
1065 node
= isl_ast_node_for_mark_degenerate(node
);
1070 /* Create an AST node for the current dimension based on
1071 * the schedule domain "bounds" and return the node encapsulated
1072 * in an isl_ast_graft.
1074 * "executed" is the current inverse schedule, taking into account
1075 * the bounds in "bounds"
1076 * "domain" is the domain of "executed", with inner dimensions projected out.
1077 * It may be a strict subset of "bounds" in case "bounds" was created
1078 * based on the atomic option or based on separation with explicit bounds.
1080 * "domain" may satisfy additional equalities that result
1081 * from intersecting "executed" with "bounds" in add_node.
1082 * It may also satisfy some global constraints that were dropped out because
1083 * we performed separation with explicit bounds.
1084 * The very first step is then to copy these constraints to "bounds".
1086 * We consider three builds,
1087 * "build" is the one in which the current level is created,
1088 * "body_build" is the build in which the next level is created,
1089 * "sub_build" is essentially the same as "body_build", except that
1090 * the depth has not been increased yet.
1092 * "build" already contains information (in strides and offsets)
1093 * about the strides at the current level, but this information is not
1094 * reflected in the build->domain.
1095 * We first add this information and the "bounds" to the sub_build->domain.
1096 * isl_ast_build_set_loop_bounds checks whether the current dimension attains
1097 * only a single value and whether this single value can be represented using
1098 * a single affine expression.
1099 * In the first case, the current level is considered "degenerate".
1100 * In the second, sub-case, the current level is considered "eliminated".
1101 * Eliminated level don't need to be reflected in the AST since we can
1102 * simply plug in the affine expression. For degenerate, but non-eliminated,
1103 * levels, we do introduce a for node, but mark is as degenerate so that
1104 * it can be printed as an assignment of the single value to the loop
1107 * If the current level is eliminated, we eliminate the current dimension
1108 * from the inverse schedule to make sure no inner dimensions depend
1109 * on the current dimension. Otherwise, we create a for node, marking
1110 * it degenerate if appropriate. The initial for node is still incomplete
1111 * and will be completed in either refine_degenerate or refine_generic.
1113 * We then generate a sequence of grafts for the next level,
1114 * create a surrounding graft for the current level and insert
1115 * the for node we created (if the current level is not eliminated).
1117 * Finally, we set the bounds of the for loop and insert guards
1118 * (either in the AST or in the graft) in one of
1119 * refine_eliminated, refine_degenerate or refine_generic.
1121 static __isl_give isl_ast_graft
*create_node_scaled(
1122 __isl_take isl_union_map
*executed
,
1123 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1124 __isl_take isl_ast_build
*build
)
1127 int degenerate
, eliminated
;
1128 isl_basic_set
*hull
;
1129 isl_ast_node
*node
= NULL
;
1130 isl_ast_graft
*graft
;
1131 isl_ast_graft_list
*children
;
1132 isl_ast_build
*sub_build
;
1133 isl_ast_build
*body_build
;
1135 domain
= isl_ast_build_eliminate_divs(build
, domain
);
1136 domain
= isl_set_detect_equalities(domain
);
1137 hull
= isl_set_unshifted_simple_hull(isl_set_copy(domain
));
1138 bounds
= isl_basic_set_intersect(bounds
, hull
);
1140 depth
= isl_ast_build_get_depth(build
);
1141 sub_build
= isl_ast_build_copy(build
);
1142 sub_build
= isl_ast_build_include_stride(sub_build
);
1143 sub_build
= isl_ast_build_set_loop_bounds(sub_build
,
1144 isl_basic_set_copy(bounds
));
1145 degenerate
= isl_ast_build_has_value(sub_build
);
1146 eliminated
= isl_ast_build_has_affine_value(sub_build
, depth
);
1147 if (degenerate
< 0 || eliminated
< 0)
1148 executed
= isl_union_map_free(executed
);
1150 executed
= eliminate(executed
, depth
, build
);
1152 node
= create_for(build
, degenerate
);
1154 body_build
= isl_ast_build_copy(sub_build
);
1155 body_build
= isl_ast_build_increase_depth(body_build
);
1156 children
= generate_next_level(executed
,
1157 isl_ast_build_copy(body_build
));
1159 graft
= isl_ast_graft_alloc_level(children
, sub_build
);
1161 graft
= isl_ast_graft_insert_for(graft
, node
);
1163 graft
= refine_eliminated(graft
, bounds
, build
);
1164 else if (degenerate
)
1165 graft
= refine_degenerate(graft
, bounds
, build
, sub_build
);
1167 graft
= refine_generic(graft
, bounds
, domain
, build
);
1169 isl_ast_build_free(body_build
);
1170 isl_ast_build_free(sub_build
);
1171 isl_ast_build_free(build
);
1172 isl_basic_set_free(bounds
);
1173 isl_set_free(domain
);
1178 /* Internal data structure for checking if all constraints involving
1179 * the input dimension "depth" are such that the other coefficients
1180 * are multiples of "m", reducing "m" if they are not.
1181 * If "m" is reduced all the way down to "1", then the check has failed
1182 * and we break out of the iteration.
1183 * "d" is an initialized isl_int that can be used internally.
1185 struct isl_check_scaled_data
{
1190 /* If constraint "c" involves the input dimension data->depth,
1191 * then make sure that all the other coefficients are multiples of data->m,
1192 * reducing data->m if needed.
1193 * Break out of the iteration if data->m has become equal to "1".
1195 static int constraint_check_scaled(__isl_take isl_constraint
*c
, void *user
)
1197 struct isl_check_scaled_data
*data
= user
;
1199 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_out
,
1202 if (!isl_constraint_involves_dims(c
, isl_dim_in
, data
->depth
, 1)) {
1203 isl_constraint_free(c
);
1207 for (i
= 0; i
< 4; ++i
) {
1208 n
= isl_constraint_dim(c
, t
[i
]);
1209 for (j
= 0; j
< n
; ++j
) {
1210 if (t
[i
] == isl_dim_in
&& j
== data
->depth
)
1212 if (!isl_constraint_involves_dims(c
, t
[i
], j
, 1))
1214 isl_constraint_get_coefficient(c
, t
[i
], j
, &data
->d
);
1215 isl_int_gcd(data
->m
, data
->m
, data
->d
);
1216 if (isl_int_is_one(data
->m
))
1223 isl_constraint_free(c
);
1225 return i
< 4 ? -1 : 0;
1228 /* For each constraint of "bmap" that involves the input dimension data->depth,
1229 * make sure that all the other coefficients are multiples of data->m,
1230 * reducing data->m if needed.
1231 * Break out of the iteration if data->m has become equal to "1".
1233 static int basic_map_check_scaled(__isl_take isl_basic_map
*bmap
, void *user
)
1237 r
= isl_basic_map_foreach_constraint(bmap
,
1238 &constraint_check_scaled
, user
);
1239 isl_basic_map_free(bmap
);
1244 /* For each constraint of "map" that involves the input dimension data->depth,
1245 * make sure that all the other coefficients are multiples of data->m,
1246 * reducing data->m if needed.
1247 * Break out of the iteration if data->m has become equal to "1".
1249 static int map_check_scaled(__isl_take isl_map
*map
, void *user
)
1253 r
= isl_map_foreach_basic_map(map
, &basic_map_check_scaled
, user
);
1259 /* Create an AST node for the current dimension based on
1260 * the schedule domain "bounds" and return the node encapsulated
1261 * in an isl_ast_graft.
1263 * "executed" is the current inverse schedule, taking into account
1264 * the bounds in "bounds"
1265 * "domain" is the domain of "executed", with inner dimensions projected out.
1268 * Before moving on to the actual AST node construction in create_node_scaled,
1269 * we first check if the current dimension is strided and if we can scale
1270 * down this stride. Note that we only do this if the ast_build_scale_strides
1273 * In particular, let the current dimension take on values
1277 * with a an integer. We check if we can find an integer m that (obviouly)
1278 * divides both f and s.
1280 * If so, we check if the current dimension only appears in constraints
1281 * where the coefficients of the other variables are multiples of m.
1282 * We perform this extra check to avoid the risk of introducing
1283 * divisions by scaling down the current dimension.
1285 * If so, we scale the current dimension down by a factor of m.
1286 * That is, we plug in
1290 * Note that in principle we could always scale down strided loops
1295 * but this may result in i' taking on larger values than the original i,
1296 * due to the shift by "f".
1297 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1299 static __isl_give isl_ast_graft
*create_node(__isl_take isl_union_map
*executed
,
1300 __isl_take isl_basic_set
*bounds
, __isl_take isl_set
*domain
,
1301 __isl_take isl_ast_build
*build
)
1303 struct isl_check_scaled_data data
;
1307 ctx
= isl_ast_build_get_ctx(build
);
1308 if (!isl_options_get_ast_build_scale_strides(ctx
))
1309 return create_node_scaled(executed
, bounds
, domain
, build
);
1311 data
.depth
= isl_ast_build_get_depth(build
);
1312 if (!isl_ast_build_has_stride(build
, data
.depth
))
1313 return create_node_scaled(executed
, bounds
, domain
, build
);
1315 isl_int_init(data
.m
);
1316 isl_int_init(data
.d
);
1318 offset
= isl_ast_build_get_offset(build
, data
.depth
);
1319 if (isl_ast_build_get_stride(build
, data
.depth
, &data
.m
) < 0)
1320 offset
= isl_aff_free(offset
);
1321 offset
= isl_aff_scale_down(offset
, data
.m
);
1322 if (isl_aff_get_denominator(offset
, &data
.d
) < 0)
1323 executed
= isl_union_map_free(executed
);
1325 if (isl_int_is_divisible_by(data
.m
, data
.d
))
1326 isl_int_divexact(data
.m
, data
.m
, data
.d
);
1328 isl_int_set_si(data
.m
, 1);
1330 if (!isl_int_is_one(data
.m
)) {
1331 if (isl_union_map_foreach_map(executed
, &map_check_scaled
,
1333 !isl_int_is_one(data
.m
))
1334 executed
= isl_union_map_free(executed
);
1337 if (!isl_int_is_one(data
.m
)) {
1342 isl_union_map
*umap
;
1344 space
= isl_ast_build_get_space(build
, 1);
1345 space
= isl_space_map_from_set(space
);
1346 ma
= isl_multi_aff_identity(space
);
1347 aff
= isl_multi_aff_get_aff(ma
, data
.depth
);
1348 aff
= isl_aff_scale(aff
, data
.m
);
1349 ma
= isl_multi_aff_set_aff(ma
, data
.depth
, aff
);
1351 bounds
= isl_basic_set_preimage_multi_aff(bounds
,
1352 isl_multi_aff_copy(ma
));
1353 domain
= isl_set_preimage_multi_aff(domain
,
1354 isl_multi_aff_copy(ma
));
1355 map
= isl_map_reverse(isl_map_from_multi_aff(ma
));
1356 umap
= isl_union_map_from_map(map
);
1357 executed
= isl_union_map_apply_domain(executed
,
1358 isl_union_map_copy(umap
));
1359 build
= isl_ast_build_scale_down(build
, data
.m
, umap
);
1361 isl_aff_free(offset
);
1363 isl_int_clear(data
.d
);
1364 isl_int_clear(data
.m
);
1366 return create_node_scaled(executed
, bounds
, domain
, build
);
1369 /* Add the basic set to the list that "user" points to.
1371 static int collect_basic_set(__isl_take isl_basic_set
*bset
, void *user
)
1373 isl_basic_set_list
**list
= user
;
1375 *list
= isl_basic_set_list_add(*list
, bset
);
1380 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1382 static __isl_give isl_basic_set_list
*isl_basic_set_list_from_set(
1383 __isl_take isl_set
*set
)
1387 isl_basic_set_list
*list
;
1392 ctx
= isl_set_get_ctx(set
);
1394 n
= isl_set_n_basic_set(set
);
1395 list
= isl_basic_set_list_alloc(ctx
, n
);
1396 if (isl_set_foreach_basic_set(set
, &collect_basic_set
, &list
) < 0)
1397 list
= isl_basic_set_list_free(list
);
1403 /* Generate code for the schedule domain "bounds"
1404 * and add the result to "list".
1406 * We mainly detect strides and additional equalities here
1407 * and then pass over control to create_node.
1409 * "bounds" reflects the bounds on the current dimension and possibly
1410 * some extra conditions on outer dimensions.
1411 * It does not, however, include any divs involving the current dimension,
1412 * so it does not capture any stride constraints.
1413 * We therefore need to compute that part of the schedule domain that
1414 * intersects with "bounds" and derive the strides from the result.
1416 static __isl_give isl_ast_graft_list
*add_node(
1417 __isl_take isl_ast_graft_list
*list
, __isl_take isl_union_map
*executed
,
1418 __isl_take isl_basic_set
*bounds
, __isl_take isl_ast_build
*build
)
1420 isl_ast_graft
*graft
;
1421 isl_set
*domain
= NULL
;
1422 isl_union_set
*uset
;
1425 uset
= isl_union_set_from_basic_set(isl_basic_set_copy(bounds
));
1426 executed
= isl_union_map_intersect_domain(executed
, uset
);
1427 empty
= isl_union_map_is_empty(executed
);
1433 uset
= isl_union_map_domain(isl_union_map_copy(executed
));
1434 domain
= isl_set_from_union_set(uset
);
1435 domain
= isl_ast_build_compute_gist(build
, domain
);
1436 empty
= isl_set_is_empty(domain
);
1442 domain
= isl_ast_build_eliminate_inner(build
, domain
);
1443 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
1445 graft
= create_node(executed
, bounds
, domain
,
1446 isl_ast_build_copy(build
));
1447 list
= isl_ast_graft_list_add(list
, graft
);
1448 isl_ast_build_free(build
);
1451 list
= isl_ast_graft_list_free(list
);
1453 isl_set_free(domain
);
1454 isl_basic_set_free(bounds
);
1455 isl_union_map_free(executed
);
1456 isl_ast_build_free(build
);
1460 struct isl_domain_follows_at_depth_data
{
1462 isl_basic_set
**piece
;
1465 /* Does any element of i follow or coincide with any element of j
1466 * at the current depth (data->depth) for equal values of the outer
1469 static int domain_follows_at_depth(int i
, int j
, void *user
)
1471 struct isl_domain_follows_at_depth_data
*data
= user
;
1472 isl_basic_map
*test
;
1476 test
= isl_basic_map_from_domain_and_range(
1477 isl_basic_set_copy(data
->piece
[i
]),
1478 isl_basic_set_copy(data
->piece
[j
]));
1479 for (l
= 0; l
< data
->depth
; ++l
)
1480 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1482 test
= isl_basic_map_order_ge(test
, isl_dim_in
, data
->depth
,
1483 isl_dim_out
, data
->depth
);
1484 empty
= isl_basic_map_is_empty(test
);
1485 isl_basic_map_free(test
);
1487 return empty
< 0 ? -1 : !empty
;
1490 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1491 __isl_keep isl_basic_set_list
*domain_list
,
1492 __isl_keep isl_union_map
*executed
,
1493 __isl_keep isl_ast_build
*build
);
1495 /* Generate code for the "n" schedule domains in "domain_list"
1496 * with positions specified by the entries of the "pos" array
1497 * and add the results to "list".
1499 * The "n" domains form a strongly connected component in the ordering.
1500 * If n is larger than 1, then this means that we cannot determine a valid
1501 * ordering for the n domains in the component. This should be fairly
1502 * rare because the individual domains have been made disjoint first.
1503 * The problem is that the domains may be integrally disjoint but not
1504 * rationally disjoint. For example, we may have domains
1506 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1508 * These two domains have an empty intersection, but their rational
1509 * relaxations do intersect. It is impossible to order these domains
1510 * in the second dimension because the first should be ordered before
1511 * the second for outer dimension equal to 0, while it should be ordered
1512 * after for outer dimension equal to 1.
1514 * This may happen in particular in case of unrolling since the domain
1515 * of each slice is replaced by its simple hull.
1517 * We collect the basic sets in the component, call isl_set_make_disjoint
1518 * and try again. Note that we rely here on isl_set_make_disjoint also
1519 * making the basic sets rationally disjoint. If the basic sets
1520 * are rationally disjoint, then the ordering problem does not occur.
1521 * To see this, there can only be a problem if there are points
1522 * (i,a) and (j,b) in one set and (i,c) and (j,d) in the other with
1523 * a < c and b > d. This means that either the interval spanned
1524 * by a en b lies inside that spanned by c and or the other way around.
1525 * In either case, there is a point inside both intervals with the
1526 * convex combination in terms of a and b and in terms of c and d.
1527 * Taking the same combination of i and j gives a point in the intersection.
1529 static __isl_give isl_ast_graft_list
*add_nodes(
1530 __isl_take isl_ast_graft_list
*list
, int *pos
, int n
,
1531 __isl_keep isl_basic_set_list
*domain_list
,
1532 __isl_keep isl_union_map
*executed
,
1533 __isl_keep isl_ast_build
*build
)
1536 isl_basic_set
*bset
;
1539 bset
= isl_basic_set_list_get_basic_set(domain_list
, pos
[0]);
1541 return add_node(list
, isl_union_map_copy(executed
), bset
,
1542 isl_ast_build_copy(build
));
1544 set
= isl_set_from_basic_set(bset
);
1545 for (i
= 1; i
< n
; ++i
) {
1546 bset
= isl_basic_set_list_get_basic_set(domain_list
, pos
[i
]);
1547 set
= isl_set_union(set
, isl_set_from_basic_set(bset
));
1550 set
= isl_set_make_disjoint(set
);
1551 if (isl_set_n_basic_set(set
) == n
)
1552 isl_die(isl_ast_graft_list_get_ctx(list
), isl_error_internal
,
1553 "unable to separate loop parts", goto error
);
1554 domain_list
= isl_basic_set_list_from_set(set
);
1555 list
= isl_ast_graft_list_concat(list
,
1556 generate_sorted_domains(domain_list
, executed
, build
));
1557 isl_basic_set_list_free(domain_list
);
1562 return isl_ast_graft_list_free(list
);
1565 /* Sort the domains in "domain_list" according to the execution order
1566 * at the current depth (for equal values of the outer dimensions),
1567 * generate code for each of them, collecting the results in a list.
1568 * If no code is generated (because the intersection of the inverse schedule
1569 * with the domains turns out to be empty), then an empty list is returned.
1571 * The caller is responsible for ensuring that the basic sets in "domain_list"
1572 * are pair-wise disjoint. It can, however, in principle happen that
1573 * two basic sets should be ordered one way for one value of the outer
1574 * dimensions and the other way for some other value of the outer dimensions.
1575 * We therefore play safe and look for strongly connected components.
1576 * The function add_nodes takes care of handling non-trivial components.
1578 static __isl_give isl_ast_graft_list
*generate_sorted_domains(
1579 __isl_keep isl_basic_set_list
*domain_list
,
1580 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1583 isl_ast_graft_list
*list
;
1584 struct isl_domain_follows_at_depth_data data
;
1585 struct isl_tarjan_graph
*g
;
1591 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1592 n
= isl_basic_set_list_n_basic_set(domain_list
);
1593 list
= isl_ast_graft_list_alloc(ctx
, n
);
1597 return add_node(list
, isl_union_map_copy(executed
),
1598 isl_basic_set_list_get_basic_set(domain_list
, 0),
1599 isl_ast_build_copy(build
));
1601 data
.depth
= isl_ast_build_get_depth(build
);
1602 data
.piece
= domain_list
->p
;
1603 g
= isl_tarjan_graph_init(ctx
, n
, &domain_follows_at_depth
, &data
);
1609 if (g
->order
[i
] == -1)
1610 isl_die(ctx
, isl_error_internal
, "cannot happen",
1613 while (g
->order
[i
] != -1) {
1616 list
= add_nodes(list
, g
->order
+ first
, i
- first
,
1617 domain_list
, executed
, build
);
1622 error
: list
= isl_ast_graft_list_free(list
);
1623 isl_tarjan_graph_free(g
);
1628 struct isl_shared_outer_data
{
1630 isl_basic_set
**piece
;
1633 /* Do elements i and j share any values for the outer dimensions?
1635 static int shared_outer(int i
, int j
, void *user
)
1637 struct isl_shared_outer_data
*data
= user
;
1638 isl_basic_map
*test
;
1642 test
= isl_basic_map_from_domain_and_range(
1643 isl_basic_set_copy(data
->piece
[i
]),
1644 isl_basic_set_copy(data
->piece
[j
]));
1645 for (l
= 0; l
< data
->depth
; ++l
)
1646 test
= isl_basic_map_equate(test
, isl_dim_in
, l
,
1648 empty
= isl_basic_map_is_empty(test
);
1649 isl_basic_map_free(test
);
1651 return empty
< 0 ? -1 : !empty
;
1654 /* Call generate_sorted_domains on a list containing the elements
1655 * of "domain_list indexed by the first "n" elements of "pos".
1657 static __isl_give isl_ast_graft_list
*generate_sorted_domains_part(
1658 __isl_keep isl_basic_set_list
*domain_list
, int *pos
, int n
,
1659 __isl_keep isl_union_map
*executed
,
1660 __isl_keep isl_ast_build
*build
)
1664 isl_basic_set_list
*slice
;
1665 isl_ast_graft_list
*list
;
1667 ctx
= isl_ast_build_get_ctx(build
);
1668 slice
= isl_basic_set_list_alloc(ctx
, n
);
1669 for (i
= 0; i
< n
; ++i
) {
1670 isl_basic_set
*bset
;
1672 bset
= isl_basic_set_copy(domain_list
->p
[pos
[i
]]);
1673 slice
= isl_basic_set_list_add(slice
, bset
);
1676 list
= generate_sorted_domains(slice
, executed
, build
);
1677 isl_basic_set_list_free(slice
);
1682 /* Look for any (weakly connected) components in the "domain_list"
1683 * of domains that share some values of the outer dimensions.
1684 * That is, domains in different components do not share any values
1685 * of the outer dimensions. This means that these components
1686 * can be freely reorderd.
1687 * Within each of the components, we sort the domains according
1688 * to the execution order at the current depth.
1690 * We fuse the result of each call to generate_sorted_domains_part
1691 * into a list with either zero or one graft and collect these (at most)
1692 * single element lists into a bigger list. This means that the elements of the
1693 * final list can be freely reordered. In particular, we sort them
1694 * according to an arbitrary but fixed ordering to ease merging of
1695 * graft lists from different components.
1697 static __isl_give isl_ast_graft_list
*generate_parallel_domains(
1698 __isl_keep isl_basic_set_list
*domain_list
,
1699 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
1703 isl_ast_graft_list
*list
;
1704 struct isl_shared_outer_data data
;
1705 struct isl_tarjan_graph
*g
;
1710 n
= isl_basic_set_list_n_basic_set(domain_list
);
1712 return generate_sorted_domains(domain_list
, executed
, build
);
1714 ctx
= isl_basic_set_list_get_ctx(domain_list
);
1716 data
.depth
= isl_ast_build_get_depth(build
);
1717 data
.piece
= domain_list
->p
;
1718 g
= isl_tarjan_graph_init(ctx
, n
, &shared_outer
, &data
);
1725 isl_ast_graft_list
*list_c
;
1727 if (g
->order
[i
] == -1)
1728 isl_die(ctx
, isl_error_internal
, "cannot happen",
1731 while (g
->order
[i
] != -1) {
1734 if (first
== 0 && n
== 0) {
1735 isl_tarjan_graph_free(g
);
1736 return generate_sorted_domains(domain_list
,
1739 list_c
= generate_sorted_domains_part(domain_list
,
1740 g
->order
+ first
, i
- first
, executed
, build
);
1741 list_c
= isl_ast_graft_list_fuse(list_c
, build
);
1745 list
= isl_ast_graft_list_concat(list
, list_c
);
1747 } while (list
&& n
);
1750 list
= isl_ast_graft_list_free(list
);
1752 list
= isl_ast_graft_list_sort(list
);
1754 isl_tarjan_graph_free(g
);
1759 /* Internal data for separate_domain.
1761 * "explicit" is set if we only want to use explicit bounds.
1763 * "domain" collects the separated domains.
1765 struct isl_separate_domain_data
{
1766 isl_ast_build
*build
;
1771 /* Extract implicit bounds on the current dimension for the executed "map".
1773 * The domain of "map" may involve inner dimensions, so we
1774 * need to eliminate them.
1776 static __isl_give isl_set
*implicit_bounds(__isl_take isl_map
*map
,
1777 __isl_keep isl_ast_build
*build
)
1781 domain
= isl_map_domain(map
);
1782 domain
= isl_ast_build_eliminate(build
, domain
);
1787 /* Extract explicit bounds on the current dimension for the executed "map".
1789 * Rather than eliminating the inner dimensions as in implicit_bounds,
1790 * we simply drop any constraints involving those inner dimensions.
1791 * The idea is that most bounds that are implied by constraints on the
1792 * inner dimensions will be enforced by for loops and not by explicit guards.
1793 * There is then no need to separate along those bounds.
1795 static __isl_give isl_set
*explicit_bounds(__isl_take isl_map
*map
,
1796 __isl_keep isl_ast_build
*build
)
1801 dim
= isl_map_dim(map
, isl_dim_out
);
1802 map
= isl_map_drop_constraints_involving_dims(map
, isl_dim_out
, 0, dim
);
1804 domain
= isl_map_domain(map
);
1805 depth
= isl_ast_build_get_depth(build
);
1806 dim
= isl_set_dim(domain
, isl_dim_set
);
1807 domain
= isl_set_detect_equalities(domain
);
1808 domain
= isl_set_drop_constraints_involving_dims(domain
,
1809 isl_dim_set
, depth
+ 1, dim
- (depth
+ 1));
1810 domain
= isl_set_remove_divs_involving_dims(domain
,
1811 isl_dim_set
, depth
, 1);
1812 domain
= isl_set_remove_unknown_divs(domain
);
1817 /* Split data->domain into pieces that intersect with the range of "map"
1818 * and pieces that do not intersect with the range of "map"
1819 * and then add that part of the range of "map" that does not intersect
1820 * with data->domain.
1822 static int separate_domain(__isl_take isl_map
*map
, void *user
)
1824 struct isl_separate_domain_data
*data
= user
;
1829 domain
= explicit_bounds(map
, data
->build
);
1831 domain
= implicit_bounds(map
, data
->build
);
1833 domain
= isl_set_coalesce(domain
);
1834 domain
= isl_set_make_disjoint(domain
);
1835 d1
= isl_set_subtract(isl_set_copy(domain
), isl_set_copy(data
->domain
));
1836 d2
= isl_set_subtract(isl_set_copy(data
->domain
), isl_set_copy(domain
));
1837 data
->domain
= isl_set_intersect(data
->domain
, domain
);
1838 data
->domain
= isl_set_union(data
->domain
, d1
);
1839 data
->domain
= isl_set_union(data
->domain
, d2
);
1844 /* Separate the schedule domains of "executed".
1846 * That is, break up the domain of "executed" into basic sets,
1847 * such that for each basic set S, every element in S is associated with
1848 * the same domain spaces.
1850 * "space" is the (single) domain space of "executed".
1852 static __isl_give isl_set
*separate_schedule_domains(
1853 __isl_take isl_space
*space
, __isl_take isl_union_map
*executed
,
1854 __isl_keep isl_ast_build
*build
)
1856 struct isl_separate_domain_data data
= { build
};
1859 ctx
= isl_ast_build_get_ctx(build
);
1860 data
.explicit = isl_options_get_ast_build_separation_bounds(ctx
) ==
1861 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
;
1862 data
.domain
= isl_set_empty(space
);
1863 if (isl_union_map_foreach_map(executed
, &separate_domain
, &data
) < 0)
1864 data
.domain
= isl_set_free(data
.domain
);
1866 isl_union_map_free(executed
);
1870 /* Temporary data used during the search for a lower bound for unrolling.
1872 * "domain" is the original set for which to find a lower bound
1873 * "depth" is the dimension for which to find a lower boudn
1875 * "lower" is the best lower bound found so far. It is NULL if we have not
1877 * "n" is the corresponding size. If lower is NULL, then the value of n
1880 * "tmp" is a temporary initialized isl_int.
1882 struct isl_find_unroll_data
{
1891 /* Check if we can use "c" as a lower bound and if it is better than
1892 * any previously found lower bound.
1894 * If "c" does not involve the dimension at the current depth,
1895 * then we cannot use it.
1896 * Otherwise, let "c" be of the form
1900 * We compute the maximal value of
1902 * -ceil(f(j)/a)) + i + 1
1904 * over the domain. If there is such a value "n", then we know
1906 * -ceil(f(j)/a)) + i + 1 <= n
1910 * i < ceil(f(j)/a)) + n
1912 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
1913 * We just need to check if we have found any lower bound before and
1914 * if the new lower bound is better (smaller n) than the previously found
1917 static int update_unrolling_lower_bound(struct isl_find_unroll_data
*data
,
1918 __isl_keep isl_constraint
*c
)
1920 isl_aff
*aff
, *lower
;
1921 enum isl_lp_result res
;
1923 if (!isl_constraint_is_lower_bound(c
, isl_dim_set
, data
->depth
))
1926 lower
= isl_constraint_get_bound(c
, isl_dim_set
, data
->depth
);
1927 lower
= isl_aff_ceil(lower
);
1928 aff
= isl_aff_copy(lower
);
1929 aff
= isl_aff_neg(aff
);
1930 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, data
->depth
, 1);
1931 aff
= isl_aff_add_constant_si(aff
, 1);
1932 res
= isl_set_max(data
->domain
, aff
, &data
->tmp
);
1935 if (res
== isl_lp_error
)
1937 if (res
== isl_lp_unbounded
) {
1938 isl_aff_free(lower
);
1942 if (!data
->lower
|| isl_int_cmp_si(data
->tmp
, *data
->n
) < 0) {
1943 isl_aff_free(data
->lower
);
1944 data
->lower
= lower
;
1945 *data
->n
= isl_int_get_si(data
->tmp
);
1947 isl_aff_free(lower
);
1951 isl_aff_free(lower
);
1955 /* Check if we can use "c" as a lower bound and if it is better than
1956 * any previously found lower bound.
1958 static int constraint_find_unroll(__isl_take isl_constraint
*c
, void *user
)
1960 struct isl_find_unroll_data
*data
;
1963 data
= (struct isl_find_unroll_data
*) user
;
1964 r
= update_unrolling_lower_bound(data
, c
);
1965 isl_constraint_free(c
);
1970 /* Look for a lower bound l(i) on the dimension at "depth"
1971 * and a size n such that "domain" is a subset of
1973 * { [i] : l(i) <= i_d < l(i) + n }
1975 * where d is "depth" and l(i) depends only on earlier dimensions.
1976 * Furthermore, try and find a lower bound such that n is as small as possible.
1977 * In particular, "n" needs to be finite.
1979 * Inner dimensions have been eliminated from "domain" by the caller.
1981 * We first construct a collection of lower bounds on the input set
1982 * by computing its simple hull. We then iterate through them,
1983 * discarding those that we cannot use (either because they do not
1984 * involve the dimension at "depth" or because they have no corresponding
1985 * upper bound, meaning that "n" would be unbounded) and pick out the
1986 * best from the remaining ones.
1988 * If we cannot find a suitable lower bound, then we consider that
1991 static __isl_give isl_aff
*find_unroll_lower_bound(__isl_keep isl_set
*domain
,
1994 struct isl_find_unroll_data data
= { domain
, depth
, NULL
, n
};
1995 isl_basic_set
*hull
;
1997 isl_int_init(data
.tmp
);
1998 hull
= isl_set_simple_hull(isl_set_copy(domain
));
2000 if (isl_basic_set_foreach_constraint(hull
,
2001 &constraint_find_unroll
, &data
) < 0)
2004 isl_basic_set_free(hull
);
2005 isl_int_clear(data
.tmp
);
2008 isl_die(isl_set_get_ctx(domain
), isl_error_invalid
,
2009 "cannot find lower bound for unrolling", return NULL
);
2013 isl_basic_set_free(hull
);
2014 isl_int_clear(data
.tmp
);
2015 return isl_aff_free(data
.lower
);
2018 /* Intersect "set" with the constraint
2020 * i_"depth" = aff + offset
2022 static __isl_give isl_set
*at_offset(__isl_take isl_set
*set
, int depth
,
2023 __isl_keep isl_aff
*aff
, int offset
)
2027 aff
= isl_aff_copy(aff
);
2028 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, depth
, -1);
2029 aff
= isl_aff_add_constant_si(aff
, offset
);
2030 eq
= isl_equality_from_aff(aff
);
2031 set
= isl_set_add_constraint(set
, eq
);
2036 /* Return a list of basic sets, one for each value of the current dimension
2038 * The divs that involve the current dimension have not been projected out
2041 * Since we are going to be iterating over the individual values,
2042 * we first check if there are any strides on the current dimension.
2043 * If there is, we rewrite the current dimension i as
2045 * i = stride i' + offset
2047 * and then iterate over individual values of i' instead.
2049 * We then look for a lower bound on i' and a size such that the domain
2052 * { [j,i'] : l(j) <= i' < l(j) + n }
2054 * and then take slices of the domain at values of i'
2055 * between l(j) and l(j) + n - 1.
2057 * We compute the unshifted simple hull of each slice to ensure that
2058 * we have a single basic set per offset. The slicing constraint
2059 * is preserved by taking the unshifted simple hull, so these basic sets
2060 * remain disjoint. The constraints that are dropped by taking the hull
2061 * will be taken into account at the next level, as in the case of the
2064 * Finally, we map i' back to i and add each basic set to the list.
2066 static __isl_give isl_basic_set_list
*do_unroll(__isl_take isl_set
*domain
,
2067 __isl_keep isl_ast_build
*build
)
2073 isl_basic_set_list
*list
;
2074 isl_multi_aff
*expansion
;
2075 isl_basic_map
*bmap
;
2080 ctx
= isl_set_get_ctx(domain
);
2081 depth
= isl_ast_build_get_depth(build
);
2082 build
= isl_ast_build_copy(build
);
2083 domain
= isl_ast_build_eliminate_inner(build
, domain
);
2084 build
= isl_ast_build_detect_strides(build
, isl_set_copy(domain
));
2085 expansion
= isl_ast_build_get_stride_expansion(build
);
2087 domain
= isl_set_preimage_multi_aff(domain
,
2088 isl_multi_aff_copy(expansion
));
2089 domain
= isl_ast_build_eliminate_divs(build
, domain
);
2091 isl_ast_build_free(build
);
2093 list
= isl_basic_set_list_alloc(ctx
, 0);
2095 lower
= find_unroll_lower_bound(domain
, depth
, &n
);
2097 list
= isl_basic_set_list_free(list
);
2099 bmap
= isl_basic_map_from_multi_aff(expansion
);
2101 for (i
= 0; list
&& i
< n
; ++i
) {
2103 isl_basic_set
*bset
;
2105 set
= at_offset(isl_set_copy(domain
), depth
, lower
, i
);
2106 bset
= isl_set_unshifted_simple_hull(set
);
2107 bset
= isl_basic_set_apply(bset
, isl_basic_map_copy(bmap
));
2108 list
= isl_basic_set_list_add(list
, bset
);
2111 isl_aff_free(lower
);
2112 isl_set_free(domain
);
2113 isl_basic_map_free(bmap
);
2118 /* Data structure for storing the results and the intermediate objects
2119 * of compute_domains.
2121 * "list" is the main result of the function and contains a list
2122 * of disjoint basic sets for which code should be generated.
2124 * "executed" and "build" are inputs to compute_domains.
2125 * "schedule_domain" is the domain of "executed".
2127 * "option" constains the domains at the current depth that should by
2128 * atomic, separated or unrolled. These domains are as specified by
2129 * the user, except that inner dimensions have been eliminated and
2130 * that they have been made pair-wise disjoint.
2132 * "includes_schedule_domain" is set if the "class_domain" (not stored
2133 * in this structure, but passed to the various functions) has been
2134 * intersected with "schedule_domain".
2136 * "sep_class" contains the user-specified split into separation classes
2137 * specialized to the current depth.
2138 * "done" contains the union of th separation domains that have already
2141 struct isl_codegen_domains
{
2142 isl_basic_set_list
*list
;
2144 isl_union_map
*executed
;
2145 isl_ast_build
*build
;
2146 isl_set
*schedule_domain
;
2150 int includes_schedule_domain
;
2156 /* Add domains to domains->list for each individual value of the current
2157 * dimension, for that part of the schedule domain that lies in the
2158 * intersection of the option domain and the class domain.
2160 * "domain" is the intersection of the class domain and the schedule domain.
2161 * The divs that involve the current dimension have not been projected out
2164 * We first break up the unroll option domain into individual pieces
2165 * and then handle each of them separately. The unroll option domain
2166 * has been made disjoint in compute_domains_init_options,
2168 * Note that we actively want to combine different pieces of the
2169 * schedule domain that have the same value at the current dimension.
2170 * We therefore need to break up the unroll option domain before
2171 * intersecting with class and schedule domain, hoping that the
2172 * unroll option domain specified by the user is relatively simple.
2174 static int compute_unroll_domains(struct isl_codegen_domains
*domains
,
2175 __isl_keep isl_set
*domain
)
2177 isl_set
*unroll_domain
;
2178 isl_basic_set_list
*unroll_list
;
2182 empty
= isl_set_is_empty(domains
->option
[unroll
]);
2188 unroll_domain
= isl_set_copy(domains
->option
[unroll
]);
2189 unroll_list
= isl_basic_set_list_from_set(unroll_domain
);
2191 n
= isl_basic_set_list_n_basic_set(unroll_list
);
2192 for (i
= 0; i
< n
; ++i
) {
2193 isl_basic_set
*bset
;
2194 isl_basic_set_list
*list
;
2196 bset
= isl_basic_set_list_get_basic_set(unroll_list
, i
);
2197 unroll_domain
= isl_set_from_basic_set(bset
);
2198 unroll_domain
= isl_set_intersect(unroll_domain
,
2199 isl_set_copy(domain
));
2201 empty
= isl_set_is_empty(unroll_domain
);
2202 if (empty
>= 0 && empty
) {
2203 isl_set_free(unroll_domain
);
2207 list
= do_unroll(unroll_domain
, domains
->build
);
2208 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2211 isl_basic_set_list_free(unroll_list
);
2216 /* Construct a single basic set that includes the intersection of
2217 * the schedule domain, the atomic option domain and the class domain.
2218 * Add the resulting basic set to domains->list.
2220 * We construct a single domain rather than trying to combine
2221 * the schedule domains of individual domains because we are working
2222 * within a single component so that non-overlapping schedule domains
2223 * should already have been separated.
2224 * Note, though, that this does not take into account the class domain.
2225 * So, it is possible for a class domain to carve out a piece of the
2226 * schedule domain with independent pieces and then we would only
2227 * generate a single domain for them. If this proves to be problematic
2228 * for some users, then this function will have to be adjusted.
2230 * "domain" is the intersection of the schedule domain and the class domain,
2231 * with inner dimensions projected out.
2233 static int compute_atomic_domain(struct isl_codegen_domains
*domains
,
2234 __isl_keep isl_set
*domain
)
2236 isl_basic_set
*bset
;
2237 isl_set
*atomic_domain
;
2240 atomic_domain
= isl_set_copy(domains
->option
[atomic
]);
2241 atomic_domain
= isl_set_intersect(atomic_domain
, isl_set_copy(domain
));
2242 empty
= isl_set_is_empty(atomic_domain
);
2243 if (empty
< 0 || empty
) {
2244 isl_set_free(atomic_domain
);
2245 return empty
< 0 ? -1 : 0;
2248 atomic_domain
= isl_set_coalesce(atomic_domain
);
2249 bset
= isl_set_unshifted_simple_hull(atomic_domain
);
2250 domains
->list
= isl_basic_set_list_add(domains
->list
, bset
);
2255 /* Split up the schedule domain into uniform basic sets,
2256 * in the sense that each element in a basic set is associated to
2257 * elements of the same domains, and add the result to domains->list.
2258 * Do this for that part of the schedule domain that lies in the
2259 * intersection of "class_domain" and the separate option domain.
2261 * "class_domain" may or may not include the constraints
2262 * of the schedule domain, but this does not make a difference
2263 * since we are going to intersect it with the domain of the inverse schedule.
2264 * If it includes schedule domain constraints, then they may involve
2265 * inner dimensions, but we will eliminate them in separation_domain.
2267 static int compute_separate_domain(struct isl_codegen_domains
*domains
,
2268 __isl_keep isl_set
*class_domain
)
2272 isl_union_map
*executed
;
2273 isl_basic_set_list
*list
;
2276 domain
= isl_set_copy(domains
->option
[separate
]);
2277 domain
= isl_set_intersect(domain
, isl_set_copy(class_domain
));
2278 executed
= isl_union_map_copy(domains
->executed
);
2279 executed
= isl_union_map_intersect_domain(executed
,
2280 isl_union_set_from_set(domain
));
2281 empty
= isl_union_map_is_empty(executed
);
2282 if (empty
< 0 || empty
) {
2283 isl_union_map_free(executed
);
2284 return empty
< 0 ? -1 : 0;
2287 space
= isl_set_get_space(class_domain
);
2288 domain
= separate_schedule_domains(space
, executed
, domains
->build
);
2290 list
= isl_basic_set_list_from_set(domain
);
2291 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2296 /* Split up the domain at the current depth into disjoint
2297 * basic sets for which code should be generated separately
2298 * for the given separation class domain.
2300 * We first make sure that the class domain is disjoint from
2301 * previously considered class domains.
2303 * The separate domains can be computed directly from the "class_domain".
2305 * The unroll, atomic and remainder domains need the constraints
2306 * from the schedule domain.
2308 * For unrolling, the actual schedule domain is needed (with divs that
2309 * may refer to the current dimension) so that stride detection can be
2312 * For atomic and remainder domains, inner dimensions and divs involving
2313 * the current dimensions should be eliminated.
2315 * If anything is left after handling separate, unroll and atomic,
2316 * we split it up into basic sets and append the basic sets to domains->list.
2318 static int compute_partial_domains(struct isl_codegen_domains
*domains
,
2319 __isl_take isl_set
*class_domain
)
2321 isl_basic_set_list
*list
;
2323 class_domain
= isl_set_subtract(class_domain
,
2324 isl_set_copy(domains
->done
));
2325 domains
->done
= isl_set_union(domains
->done
,
2326 isl_set_copy(class_domain
));
2328 if (compute_separate_domain(domains
, class_domain
) < 0)
2330 class_domain
= isl_set_subtract(class_domain
,
2331 isl_set_copy(domains
->option
[separate
]));
2333 if (!domains
->includes_schedule_domain
)
2334 class_domain
= isl_set_intersect(class_domain
,
2335 isl_set_copy(domains
->schedule_domain
));
2337 if (compute_unroll_domains(domains
, class_domain
) < 0)
2339 class_domain
= isl_set_subtract(class_domain
,
2340 isl_set_copy(domains
->option
[unroll
]));
2342 class_domain
= isl_ast_build_eliminate(domains
->build
,
2345 if (compute_atomic_domain(domains
, class_domain
) < 0)
2347 class_domain
= isl_set_subtract(class_domain
,
2348 isl_set_copy(domains
->option
[atomic
]));
2350 class_domain
= isl_set_coalesce(class_domain
);
2351 class_domain
= isl_set_make_disjoint(class_domain
);
2353 list
= isl_basic_set_list_from_set(class_domain
);
2354 domains
->list
= isl_basic_set_list_concat(domains
->list
, list
);
2358 isl_set_free(class_domain
);
2362 /* Split up the domain at the current depth into disjoint
2363 * basic sets for which code should be generated separately
2364 * for the separation class identified by "pnt".
2366 * We extract the corresponding class domain from domains->sep_class,
2367 * eliminate inner dimensions and pass control to compute_partial_domains.
2369 static int compute_class_domains(__isl_take isl_point
*pnt
, void *user
)
2371 struct isl_codegen_domains
*domains
= user
;
2376 class_set
= isl_set_from_point(pnt
);
2377 domain
= isl_map_domain(isl_map_intersect_range(
2378 isl_map_copy(domains
->sep_class
), class_set
));
2379 domain
= isl_ast_build_eliminate(domains
->build
, domain
);
2381 disjoint
= isl_set_plain_is_disjoint(domain
, domains
->schedule_domain
);
2385 isl_set_free(domain
);
2389 domains
->includes_schedule_domain
= 0;
2390 return compute_partial_domains(domains
, domain
);
2393 /* Extract the domains at the current depth that should be atomic,
2394 * separated or unrolled and store them in option.
2396 * The domains specified by the user might overlap, so we make
2397 * them disjoint by subtracting earlier domains from later domains.
2399 static void compute_domains_init_options(isl_set
*option
[3],
2400 __isl_keep isl_ast_build
*build
)
2402 enum isl_ast_build_domain_type type
, type2
;
2404 for (type
= atomic
; type
<= separate
; ++type
) {
2405 option
[type
] = isl_ast_build_get_option_domain(build
, type
);
2406 for (type2
= atomic
; type2
< type
; ++type2
)
2407 option
[type
] = isl_set_subtract(option
[type
],
2408 isl_set_copy(option
[type2
]));
2411 option
[unroll
] = isl_set_coalesce(option
[unroll
]);
2412 option
[unroll
] = isl_set_make_disjoint(option
[unroll
]);
2415 /* Split up the domain at the current depth into disjoint
2416 * basic sets for which code should be generated separately,
2417 * based on the user-specified options.
2418 * Return the list of disjoint basic sets.
2420 * There are three kinds of domains that we need to keep track of.
2421 * - the "schedule domain" is the domain of "executed"
2422 * - the "class domain" is the domain corresponding to the currrent
2424 * - the "option domain" is the domain corresponding to one of the options
2425 * atomic, unroll or separate
2427 * We first consider the individial values of the separation classes
2428 * and split up the domain for each of them separately.
2429 * Finally, we consider the remainder. If no separation classes were
2430 * specified, then we call compute_partial_domains with the universe
2431 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain"
2432 * and set includes_schedule_domain to reflect that the schedule domain
2433 * has already been taken into account. We do this because we want to
2434 * avoid computing the complement of the class domains (i.e., the difference
2435 * between the universe and domains->done).
2437 static __isl_give isl_basic_set_list
*compute_domains(
2438 __isl_keep isl_union_map
*executed
, __isl_keep isl_ast_build
*build
)
2440 struct isl_codegen_domains domains
;
2443 isl_union_set
*schedule_domain
;
2447 enum isl_ast_build_domain_type type
;
2449 ctx
= isl_union_map_get_ctx(executed
);
2450 domains
.list
= isl_basic_set_list_alloc(ctx
, 0);
2452 schedule_domain
= isl_union_map_domain(isl_union_map_copy(executed
));
2453 domain
= isl_set_from_union_set(schedule_domain
);
2455 compute_domains_init_options(domains
.option
, build
);
2457 domains
.sep_class
= isl_ast_build_get_separation_class(build
);
2458 classes
= isl_map_range(isl_map_copy(domains
.sep_class
));
2459 n_param
= isl_set_dim(classes
, isl_dim_param
);
2460 classes
= isl_set_project_out(classes
, isl_dim_param
, 0, n_param
);
2462 space
= isl_set_get_space(domain
);
2463 domains
.build
= build
;
2464 domains
.schedule_domain
= isl_set_copy(domain
);
2465 domains
.executed
= executed
;
2466 domains
.done
= isl_set_empty(space
);
2468 if (isl_set_foreach_point(classes
, &compute_class_domains
, &domains
) < 0)
2469 domains
.list
= isl_basic_set_list_free(domains
.list
);
2470 isl_set_free(classes
);
2473 domains
.list
= isl_basic_set_list_free(domains
.list
);
2474 domains
.includes_schedule_domain
= !isl_set_is_empty(domains
.done
);
2475 if (!domains
.includes_schedule_domain
) {
2476 isl_set_free(domain
);
2477 domain
= isl_set_universe(isl_set_get_space(domains
.done
));
2479 if (compute_partial_domains(&domains
, domain
) < 0)
2480 domains
.list
= isl_basic_set_list_free(domains
.list
);
2482 isl_set_free(domains
.schedule_domain
);
2483 isl_set_free(domains
.done
);
2484 isl_map_free(domains
.sep_class
);
2485 for (type
= atomic
; type
<= separate
; ++type
)
2486 isl_set_free(domains
.option
[type
]);
2488 return domains
.list
;
2491 /* Generate code for a single component, after shifting (if any)
2494 * We first split up the domain at the current depth into disjoint
2495 * basic sets based on the user-specified options.
2496 * Then we generated code for each of them and concatenate the results.
2498 static __isl_give isl_ast_graft_list
*generate_shifted_component(
2499 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
2501 isl_basic_set_list
*domain_list
;
2502 isl_ast_graft_list
*list
= NULL
;
2504 domain_list
= compute_domains(executed
, build
);
2505 list
= generate_parallel_domains(domain_list
, executed
, build
);
2507 isl_basic_set_list_free(domain_list
);
2508 isl_union_map_free(executed
);
2509 isl_ast_build_free(build
);
2514 struct isl_set_map_pair
{
2519 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2520 * of indices into the "domain" array,
2521 * return the union of the "map" fields of the elements
2522 * indexed by the first "n" elements of "order".
2524 static __isl_give isl_union_map
*construct_component_executed(
2525 struct isl_set_map_pair
*domain
, int *order
, int n
)
2529 isl_union_map
*executed
;
2531 map
= isl_map_copy(domain
[order
[0]].map
);
2532 executed
= isl_union_map_from_map(map
);
2533 for (i
= 1; i
< n
; ++i
) {
2534 map
= isl_map_copy(domain
[order
[i
]].map
);
2535 executed
= isl_union_map_add_map(executed
, map
);
2541 /* Generate code for a single component, after shifting (if any)
2544 * The component inverse schedule is specified as the "map" fields
2545 * of the elements of "domain" indexed by the first "n" elements of "order".
2547 static __isl_give isl_ast_graft_list
*generate_shifted_component_from_list(
2548 struct isl_set_map_pair
*domain
, int *order
, int n
,
2549 __isl_take isl_ast_build
*build
)
2551 isl_union_map
*executed
;
2553 executed
= construct_component_executed(domain
, order
, n
);
2554 return generate_shifted_component(executed
, build
);
2557 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2558 * of indices into the "domain" array,
2559 * do all (except for at most one) of the "set" field of the elements
2560 * indexed by the first "n" elements of "order" have a fixed value
2561 * at position "depth"?
2563 static int at_most_one_non_fixed(struct isl_set_map_pair
*domain
,
2564 int *order
, int n
, int depth
)
2569 for (i
= 0; i
< n
; ++i
) {
2572 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2573 isl_dim_set
, depth
, NULL
);
2586 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2587 * of indices into the "domain" array,
2588 * eliminate the inner dimensions from the "set" field of the elements
2589 * indexed by the first "n" elements of "order", provided the current
2590 * dimension does not have a fixed value.
2592 * Return the index of the first element in "order" with a corresponding
2593 * "set" field that does not have an (obviously) fixed value.
2595 static int eliminate_non_fixed(struct isl_set_map_pair
*domain
,
2596 int *order
, int n
, int depth
, __isl_keep isl_ast_build
*build
)
2601 for (i
= n
- 1; i
>= 0; --i
) {
2603 f
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
2604 isl_dim_set
, depth
, NULL
);
2609 domain
[order
[i
]].set
= isl_ast_build_eliminate_inner(build
,
2610 domain
[order
[i
]].set
);
2617 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2618 * of indices into the "domain" array,
2619 * find the element of "domain" (amongst those indexed by the first "n"
2620 * elements of "order") with the "set" field that has the smallest
2621 * value for the current iterator.
2623 * Note that the domain with the smallest value may depend on the parameters
2624 * and/or outer loop dimension. Since the result of this function is only
2625 * used as heuristic, we only make a reasonable attempt at finding the best
2626 * domain, one that should work in case a single domain provides the smallest
2627 * value for the current dimension over all values of the parameters
2628 * and outer dimensions.
2630 * In particular, we compute the smallest value of the first domain
2631 * and replace it by that of any later domain if that later domain
2632 * has a smallest value that is smaller for at least some value
2633 * of the parameters and outer dimensions.
2635 static int first_offset(struct isl_set_map_pair
*domain
, int *order
, int n
,
2636 __isl_keep isl_ast_build
*build
)
2642 min_first
= isl_ast_build_map_to_iterator(build
,
2643 isl_set_copy(domain
[order
[0]].set
));
2644 min_first
= isl_map_lexmin(min_first
);
2646 for (i
= 1; i
< n
; ++i
) {
2647 isl_map
*min
, *test
;
2650 min
= isl_ast_build_map_to_iterator(build
,
2651 isl_set_copy(domain
[order
[i
]].set
));
2652 min
= isl_map_lexmin(min
);
2653 test
= isl_map_copy(min
);
2654 test
= isl_map_apply_domain(isl_map_copy(min_first
), test
);
2655 test
= isl_map_order_lt(test
, isl_dim_in
, 0, isl_dim_out
, 0);
2656 empty
= isl_map_is_empty(test
);
2658 if (empty
>= 0 && !empty
) {
2659 isl_map_free(min_first
);
2669 isl_map_free(min_first
);
2671 return i
< n
? -1 : first
;
2674 /* Construct a shifted inverse schedule based on the original inverse schedule,
2675 * the stride and the offset.
2677 * The original inverse schedule is specified as the "map" fields
2678 * of the elements of "domain" indexed by the first "n" elements of "order".
2680 * "stride" and "offset" are such that the difference
2681 * between the values of the current dimension of domain "i"
2682 * and the values of the current dimension for some reference domain are
2685 * stride * integer + offset[i]
2687 * Moreover, 0 <= offset[i] < stride.
2689 * For each domain, we create a map
2691 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2693 * where j refers to the current dimension and the other dimensions are
2694 * unchanged, and apply this map to the original schedule domain.
2696 * For example, for the original schedule
2698 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2700 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2701 * we apply the mapping
2705 * to the schedule of the "A" domain and the mapping
2707 * { [j - 1] -> [j, 1] }
2709 * to the schedule of the "B" domain.
2712 * Note that after the transformation, the differences between pairs
2713 * of values of the current dimension over all domains are multiples
2714 * of stride and that we have therefore exposed the stride.
2717 * To see that the mapping preserves the lexicographic order,
2718 * first note that each of the individual maps above preserves the order.
2719 * If the value of the current iterator is j1 in one domain and j2 in another,
2720 * then if j1 = j2, we know that the same map is applied to both domains
2721 * and the order is preserved.
2722 * Otherwise, let us assume, without loss of generality, that j1 < j2.
2723 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
2727 * and the order is preserved.
2728 * If c1 < c2, then we know
2734 * j2 - j1 = n * s + r
2736 * with n >= 0 and 0 <= r < s.
2737 * In other words, r = c2 - c1.
2748 * (j1 - c1, c1) << (j2 - c2, c2)
2750 * with "<<" the lexicographic order, proving that the order is preserved
2753 static __isl_give isl_union_map
*contruct_shifted_executed(
2754 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
2755 __isl_keep isl_vec
*offset
, __isl_keep isl_ast_build
*build
)
2759 isl_union_map
*executed
;
2765 depth
= isl_ast_build_get_depth(build
);
2766 space
= isl_ast_build_get_space(build
, 1);
2767 executed
= isl_union_map_empty(isl_space_copy(space
));
2768 space
= isl_space_map_from_set(space
);
2769 map
= isl_map_identity(isl_space_copy(space
));
2770 map
= isl_map_eliminate(map
, isl_dim_out
, depth
, 1);
2771 map
= isl_map_insert_dims(map
, isl_dim_out
, depth
+ 1, 1);
2772 space
= isl_space_insert_dims(space
, isl_dim_out
, depth
+ 1, 1);
2774 c
= isl_equality_alloc(isl_local_space_from_space(space
));
2775 c
= isl_constraint_set_coefficient_si(c
, isl_dim_in
, depth
, 1);
2776 c
= isl_constraint_set_coefficient_si(c
, isl_dim_out
, depth
, -1);
2780 for (i
= 0; i
< n
; ++i
) {
2783 if (isl_vec_get_element(offset
, i
, &v
) < 0)
2785 map_i
= isl_map_copy(map
);
2786 map_i
= isl_map_fix(map_i
, isl_dim_out
, depth
+ 1, v
);
2788 c
= isl_constraint_set_constant(c
, v
);
2789 map_i
= isl_map_add_constraint(map_i
, isl_constraint_copy(c
));
2791 map_i
= isl_map_apply_domain(isl_map_copy(domain
[order
[i
]].map
),
2793 executed
= isl_union_map_add_map(executed
, map_i
);
2796 isl_constraint_free(c
);
2802 executed
= isl_union_map_free(executed
);
2807 /* Generate code for a single component, after exposing the stride,
2808 * given that the schedule domain is "shifted strided".
2810 * The component inverse schedule is specified as the "map" fields
2811 * of the elements of "domain" indexed by the first "n" elements of "order".
2813 * The schedule domain being "shifted strided" means that the differences
2814 * between the values of the current dimension of domain "i"
2815 * and the values of the current dimension for some reference domain are
2818 * stride * integer + offset[i]
2820 * We first look for the domain with the "smallest" value for the current
2821 * dimension and adjust the offsets such that the offset of the "smallest"
2822 * domain is equal to zero. The other offsets are reduced modulo stride.
2824 * Based on this information, we construct a new inverse schedule in
2825 * contruct_shifted_executed that exposes the stride.
2826 * Since this involves the introduction of a new schedule dimension,
2827 * the build needs to be changed accodingly.
2828 * After computing the AST, the newly introduced dimension needs
2829 * to be removed again from the list of grafts. We do this by plugging
2830 * in a mapping that represents the new schedule domain in terms of the
2831 * old schedule domain.
2833 static __isl_give isl_ast_graft_list
*generate_shift_component(
2834 struct isl_set_map_pair
*domain
, int *order
, int n
, isl_int stride
,
2835 __isl_keep isl_vec
*offset
, __isl_take isl_ast_build
*build
)
2837 isl_ast_graft_list
*list
;
2844 isl_multi_aff
*ma
, *zero
;
2845 isl_union_map
*executed
;
2847 ctx
= isl_ast_build_get_ctx(build
);
2848 depth
= isl_ast_build_get_depth(build
);
2850 first
= first_offset(domain
, order
, n
, build
);
2852 return isl_ast_build_free(build
);
2855 v
= isl_vec_alloc(ctx
, n
);
2856 if (isl_vec_get_element(offset
, first
, &val
) < 0)
2857 v
= isl_vec_free(v
);
2858 isl_int_neg(val
, val
);
2859 v
= isl_vec_set(v
, val
);
2860 v
= isl_vec_add(v
, isl_vec_copy(offset
));
2861 v
= isl_vec_fdiv_r(v
, stride
);
2863 executed
= contruct_shifted_executed(domain
, order
, n
, stride
, v
,
2865 space
= isl_ast_build_get_space(build
, 1);
2866 space
= isl_space_map_from_set(space
);
2867 ma
= isl_multi_aff_identity(isl_space_copy(space
));
2868 space
= isl_space_from_domain(isl_space_domain(space
));
2869 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
2870 zero
= isl_multi_aff_zero(space
);
2871 ma
= isl_multi_aff_range_splice(ma
, depth
+ 1, zero
);
2872 build
= isl_ast_build_insert_dim(build
, depth
+ 1);
2873 list
= generate_shifted_component(executed
, build
);
2875 list
= isl_ast_graft_list_preimage_multi_aff(list
, ma
);
2883 /* Generate code for a single component.
2885 * The component inverse schedule is specified as the "map" fields
2886 * of the elements of "domain" indexed by the first "n" elements of "order".
2888 * This function may modify the "set" fields of "domain".
2890 * Before proceeding with the actual code generation for the component,
2891 * we first check if there are any "shifted" strides, meaning that
2892 * the schedule domains of the individual domains are all strided,
2893 * but that they have different offsets, resulting in the union
2894 * of schedule domains not being strided anymore.
2896 * The simplest example is the schedule
2898 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2900 * Both schedule domains are strided, but their union is not.
2901 * This function detects such cases and then rewrites the schedule to
2903 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
2905 * In the new schedule, the schedule domains have the same offset (modulo
2906 * the stride), ensuring that the union of schedule domains is also strided.
2909 * If there is only a single domain in the component, then there is
2910 * nothing to do. Similarly, if the current schedule dimension has
2911 * a fixed value for almost all domains then there is nothing to be done.
2912 * In particular, we need at least two domains where the current schedule
2913 * dimension does not have a fixed value.
2914 * Finally, if any of the options refer to the current schedule dimension,
2915 * then we bail out as well. It would be possible to reformulate the options
2916 * in terms of the new schedule domain, but that would introduce constraints
2917 * that separate the domains in the options and that is something we would
2921 * To see if there is any shifted stride, we look at the differences
2922 * between the values of the current dimension in pairs of domains
2923 * for equal values of outer dimensions. These differences should be
2928 * with "m" the stride and "r" a constant. Note that we cannot perform
2929 * this analysis on individual domains as the lower bound in each domain
2930 * may depend on parameters or outer dimensions and so the current dimension
2931 * itself may not have a fixed remainder on division by the stride.
2933 * In particular, we compare the first domain that does not have an
2934 * obviously fixed value for the current dimension to itself and all
2935 * other domains and collect the offsets and the gcd of the strides.
2936 * If the gcd becomes one, then we failed to find shifted strides.
2937 * If all the offsets are the same (for those domains that do not have
2938 * an obviously fixed value for the current dimension), then we do not
2939 * apply the transformation.
2940 * If none of the domains were skipped, then there is nothing to do.
2941 * If some of them were skipped, then if we apply separation, the schedule
2942 * domain should get split in pieces with a (non-shifted) stride.
2944 * Otherwise, we apply a shift to expose the stride in
2945 * generate_shift_component.
2947 static __isl_give isl_ast_graft_list
*generate_component(
2948 struct isl_set_map_pair
*domain
, int *order
, int n
,
2949 __isl_take isl_ast_build
*build
)
2960 isl_ast_graft_list
*list
;
2963 depth
= isl_ast_build_get_depth(build
);
2966 if (skip
>= 0 && !skip
)
2967 skip
= at_most_one_non_fixed(domain
, order
, n
, depth
);
2968 if (skip
>= 0 && !skip
)
2969 skip
= isl_ast_build_options_involve_depth(build
);
2971 return isl_ast_build_free(build
);
2973 return generate_shifted_component_from_list(domain
,
2976 base
= eliminate_non_fixed(domain
, order
, n
, depth
, build
);
2978 return isl_ast_build_free(build
);
2980 ctx
= isl_ast_build_get_ctx(build
);
2985 v
= isl_vec_alloc(ctx
, n
);
2988 for (i
= 0; i
< n
; ++i
) {
2989 map
= isl_map_from_domain_and_range(
2990 isl_set_copy(domain
[order
[base
]].set
),
2991 isl_set_copy(domain
[order
[i
]].set
));
2992 for (d
= 0; d
< depth
; ++d
)
2993 map
= isl_map_equate(map
, isl_dim_in
, d
,
2995 deltas
= isl_map_deltas(map
);
2996 res
= isl_set_dim_residue_class(deltas
, depth
, &m
, &r
);
2997 isl_set_free(deltas
);
3002 isl_int_set(gcd
, m
);
3004 isl_int_gcd(gcd
, gcd
, m
);
3005 if (isl_int_is_one(gcd
))
3007 v
= isl_vec_set_element(v
, i
, r
);
3009 res
= isl_set_plain_is_fixed(domain
[order
[i
]].set
,
3010 isl_dim_set
, depth
, NULL
);
3016 if (fixed
&& i
> base
) {
3017 isl_vec_get_element(v
, base
, &m
);
3018 if (isl_int_ne(m
, r
))
3024 isl_ast_build_free(build
);
3026 } else if (i
< n
|| fixed
) {
3027 list
= generate_shifted_component_from_list(domain
,
3030 list
= generate_shift_component(domain
, order
, n
, gcd
, v
,
3042 /* Store both "map" itself and its domain in the
3043 * structure pointed to by *next and advance to the next array element.
3045 static int extract_domain(__isl_take isl_map
*map
, void *user
)
3047 struct isl_set_map_pair
**next
= user
;
3049 (*next
)->map
= isl_map_copy(map
);
3050 (*next
)->set
= isl_map_domain(map
);
3056 /* Internal data for any_scheduled_after.
3058 * "depth" is the number of loops that have already been generated
3059 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3060 * "domain" is an array of set-map pairs corresponding to the different
3061 * iteration domains. The set is the schedule domain, i.e., the domain
3062 * of the inverse schedule, while the map is the inverse schedule itself.
3064 struct isl_any_scheduled_after_data
{
3066 int group_coscheduled
;
3067 struct isl_set_map_pair
*domain
;
3070 /* Is any element of domain "i" scheduled after any element of domain "j"
3071 * (for a common iteration of the first data->depth loops)?
3073 * data->domain[i].set contains the domain of the inverse schedule
3074 * for domain "i", i.e., elements in the schedule domain.
3076 * If data->group_coscheduled is set, then we also return 1 if there
3077 * is any pair of elements in the two domains that are scheduled together.
3079 static int any_scheduled_after(int i
, int j
, void *user
)
3081 struct isl_any_scheduled_after_data
*data
= user
;
3082 int dim
= isl_set_dim(data
->domain
[i
].set
, isl_dim_set
);
3085 for (pos
= data
->depth
; pos
< dim
; ++pos
) {
3088 follows
= isl_set_follows_at(data
->domain
[i
].set
,
3089 data
->domain
[j
].set
, pos
);
3099 return data
->group_coscheduled
;
3102 /* Look for independent components at the current depth and generate code
3103 * for each component separately. The resulting lists of grafts are
3104 * merged in an attempt to combine grafts with identical guards.
3106 * Code for two domains can be generated separately if all the elements
3107 * of one domain are scheduled before (or together with) all the elements
3108 * of the other domain. We therefore consider the graph with as nodes
3109 * the domains and an edge between two nodes if any element of the first
3110 * node is scheduled after any element of the second node.
3111 * If the ast_build_group_coscheduled is set, then we also add an edge if
3112 * there is any pair of elements in the two domains that are scheduled
3114 * Code is then generated (by generate_component)
3115 * for each of the strongly connected components in this graph
3116 * in their topological order.
3118 * Since the test is performed on the domain of the inverse schedules of
3119 * the different domains, we precompute these domains and store
3120 * them in data.domain.
3122 static __isl_give isl_ast_graft_list
*generate_components(
3123 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3126 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3127 int n
= isl_union_map_n_map(executed
);
3128 struct isl_any_scheduled_after_data data
;
3129 struct isl_set_map_pair
*next
;
3130 struct isl_tarjan_graph
*g
= NULL
;
3131 isl_ast_graft_list
*list
= NULL
;
3134 data
.domain
= isl_calloc_array(ctx
, struct isl_set_map_pair
, n
);
3140 if (isl_union_map_foreach_map(executed
, &extract_domain
, &next
) < 0)
3145 data
.depth
= isl_ast_build_get_depth(build
);
3146 data
.group_coscheduled
= isl_options_get_ast_build_group_coscheduled(ctx
);
3147 g
= isl_tarjan_graph_init(ctx
, n
, &any_scheduled_after
, &data
);
3149 list
= isl_ast_graft_list_alloc(ctx
, 0);
3153 isl_ast_graft_list
*list_c
;
3156 if (g
->order
[i
] == -1)
3157 isl_die(ctx
, isl_error_internal
, "cannot happen",
3160 while (g
->order
[i
] != -1) {
3164 list_c
= generate_component(data
.domain
,
3165 g
->order
+ first
, i
- first
,
3166 isl_ast_build_copy(build
));
3167 list
= isl_ast_graft_list_merge(list
, list_c
, build
);
3173 error
: list
= isl_ast_graft_list_free(list
);
3174 isl_tarjan_graph_free(g
);
3175 for (i
= 0; i
< n_domain
; ++i
) {
3176 isl_map_free(data
.domain
[i
].map
);
3177 isl_set_free(data
.domain
[i
].set
);
3180 isl_union_map_free(executed
);
3181 isl_ast_build_free(build
);
3186 /* Generate code for the next level (and all inner levels).
3188 * If "executed" is empty, i.e., no code needs to be generated,
3189 * then we return an empty list.
3191 * If we have already generated code for all loop levels, then we pass
3192 * control to generate_inner_level.
3194 * If "executed" lives in a single space, i.e., if code needs to be
3195 * generated for a single domain, then there can only be a single
3196 * component and we go directly to generate_shifted_component.
3197 * Otherwise, we call generate_components to detect the components
3198 * and to call generate_component on each of them separately.
3200 static __isl_give isl_ast_graft_list
*generate_next_level(
3201 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
)
3205 if (!build
|| !executed
)
3208 if (isl_union_map_is_empty(executed
)) {
3209 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
3210 isl_union_map_free(executed
);
3211 isl_ast_build_free(build
);
3212 return isl_ast_graft_list_alloc(ctx
, 0);
3215 depth
= isl_ast_build_get_depth(build
);
3216 if (depth
>= isl_set_dim(build
->domain
, isl_dim_set
))
3217 return generate_inner_level(executed
, build
);
3219 if (isl_union_map_n_map(executed
) == 1)
3220 return generate_shifted_component(executed
, build
);
3222 return generate_components(executed
, build
);
3224 isl_union_map_free(executed
);
3225 isl_ast_build_free(build
);
3229 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3230 * internal, executed and build are the inputs to generate_code.
3231 * list collects the output.
3233 struct isl_generate_code_data
{
3235 isl_union_map
*executed
;
3236 isl_ast_build
*build
;
3238 isl_ast_graft_list
*list
;
3241 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3245 * with E the external build schedule and S the additional schedule "space",
3246 * reformulate the inverse schedule in terms of the internal schedule domain,
3251 * We first obtain a mapping
3255 * take the inverse and the product with S -> S, resulting in
3257 * [I -> S] -> [E -> S]
3259 * Applying the map to the input produces the desired result.
3261 static __isl_give isl_union_map
*internal_executed(
3262 __isl_take isl_union_map
*executed
, __isl_keep isl_space
*space
,
3263 __isl_keep isl_ast_build
*build
)
3267 proj
= isl_ast_build_get_schedule_map(build
);
3268 proj
= isl_map_reverse(proj
);
3269 space
= isl_space_map_from_set(isl_space_copy(space
));
3270 id
= isl_map_identity(space
);
3271 proj
= isl_map_product(proj
, id
);
3272 executed
= isl_union_map_apply_domain(executed
,
3273 isl_union_map_from_map(proj
));
3277 /* Generate an AST that visits the elements in the range of data->executed
3278 * in the relative order specified by the corresponding image element(s)
3279 * for those image elements that belong to "set".
3280 * Add the result to data->list.
3282 * The caller ensures that "set" is a universe domain.
3283 * "space" is the space of the additional part of the schedule.
3284 * It is equal to the space of "set" if build->domain is parametric.
3285 * Otherwise, it is equal to the range of the wrapped space of "set".
3287 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3288 * was called from an outside user (data->internal not set), then
3289 * the (inverse) schedule refers to the external build domain and needs to
3290 * be transformed to refer to the internal build domain.
3292 * The build is extended to include the additional part of the schedule.
3293 * If the original build space was not parametric, then the options
3294 * in data->build refer only to the additional part of the schedule
3295 * and they need to be adjusted to refer to the complete AST build
3298 * After having adjusted inverse schedule and build, we start generating
3299 * code with the outer loop of the current code generation
3300 * in generate_next_level.
3302 * If the original build space was not parametric, we undo the embedding
3303 * on the resulting isl_ast_node_list so that it can be used within
3304 * the outer AST build.
3306 static int generate_code_in_space(struct isl_generate_code_data
*data
,
3307 __isl_take isl_set
*set
, __isl_take isl_space
*space
)
3309 isl_union_map
*executed
;
3310 isl_ast_build
*build
;
3311 isl_ast_graft_list
*list
;
3314 executed
= isl_union_map_copy(data
->executed
);
3315 executed
= isl_union_map_intersect_domain(executed
,
3316 isl_union_set_from_set(set
));
3318 embed
= !isl_set_is_params(data
->build
->domain
);
3319 if (embed
&& !data
->internal
)
3320 executed
= internal_executed(executed
, space
, data
->build
);
3322 build
= isl_ast_build_copy(data
->build
);
3323 build
= isl_ast_build_product(build
, space
);
3325 list
= generate_next_level(executed
, build
);
3327 list
= isl_ast_graft_list_unembed(list
, embed
);
3329 data
->list
= isl_ast_graft_list_concat(data
->list
, list
);
3334 /* Generate an AST that visits the elements in the range of data->executed
3335 * in the relative order specified by the corresponding domain element(s)
3336 * for those domain elements that belong to "set".
3337 * Add the result to data->list.
3339 * The caller ensures that "set" is a universe domain.
3341 * If the build space S is not parametric, then the space of "set"
3342 * need to be a wrapped relation with S as domain. That is, it needs
3347 * Check this property and pass control to generate_code_in_space
3349 * If the build space is not parametric, then T is the space of "set".
3351 static int generate_code_set(__isl_take isl_set
*set
, void *user
)
3353 struct isl_generate_code_data
*data
= user
;
3354 isl_space
*space
, *build_space
;
3357 space
= isl_set_get_space(set
);
3359 if (isl_set_is_params(data
->build
->domain
))
3360 return generate_code_in_space(data
, set
, space
);
3362 build_space
= isl_ast_build_get_space(data
->build
, data
->internal
);
3363 space
= isl_space_unwrap(space
);
3364 is_domain
= isl_space_is_domain(build_space
, space
);
3365 isl_space_free(build_space
);
3366 space
= isl_space_range(space
);
3371 isl_die(isl_set_get_ctx(set
), isl_error_invalid
,
3372 "invalid nested schedule space", goto error
);
3374 return generate_code_in_space(data
, set
, space
);
3377 isl_space_free(space
);
3381 /* Generate an AST that visits the elements in the range of "executed"
3382 * in the relative order specified by the corresponding domain element(s).
3384 * "build" is an isl_ast_build that has either been constructed by
3385 * isl_ast_build_from_context or passed to a callback set by
3386 * isl_ast_build_set_create_leaf.
3387 * In the first case, the space of the isl_ast_build is typically
3388 * a parametric space, although this is currently not enforced.
3389 * In the second case, the space is never a parametric space.
3390 * If the space S is not parametric, then the domain space(s) of "executed"
3391 * need to be wrapped relations with S as domain.
3393 * If the domain of "executed" consists of several spaces, then an AST
3394 * is generated for each of them (in arbitrary order) and the results
3397 * If "internal" is set, then the domain "S" above refers to the internal
3398 * schedule domain representation. Otherwise, it refers to the external
3399 * representation, as returned by isl_ast_build_get_schedule_space.
3401 * We essentially run over all the spaces in the domain of "executed"
3402 * and call generate_code_set on each of them.
3404 static __isl_give isl_ast_graft_list
*generate_code(
3405 __isl_take isl_union_map
*executed
, __isl_take isl_ast_build
*build
,
3409 struct isl_generate_code_data data
= { 0 };
3411 isl_union_set
*schedule_domain
;
3412 isl_union_map
*universe
;
3416 space
= isl_ast_build_get_space(build
, 1);
3417 space
= isl_space_align_params(space
,
3418 isl_union_map_get_space(executed
));
3419 space
= isl_space_align_params(space
,
3420 isl_union_map_get_space(build
->options
));
3421 build
= isl_ast_build_align_params(build
, isl_space_copy(space
));
3422 executed
= isl_union_map_align_params(executed
, space
);
3423 if (!executed
|| !build
)
3426 ctx
= isl_ast_build_get_ctx(build
);
3428 data
.internal
= internal
;
3429 data
.executed
= executed
;
3431 data
.list
= isl_ast_graft_list_alloc(ctx
, 0);
3433 universe
= isl_union_map_universe(isl_union_map_copy(executed
));
3434 schedule_domain
= isl_union_map_domain(universe
);
3435 if (isl_union_set_foreach_set(schedule_domain
, &generate_code_set
,
3437 data
.list
= isl_ast_graft_list_free(data
.list
);
3439 isl_union_set_free(schedule_domain
);
3440 isl_union_map_free(executed
);
3442 isl_ast_build_free(build
);
3445 isl_union_map_free(executed
);
3446 isl_ast_build_free(build
);
3450 /* Generate an AST that visits the elements in the domain of "schedule"
3451 * in the relative order specified by the corresponding image element(s).
3453 * "build" is an isl_ast_build that has either been constructed by
3454 * isl_ast_build_from_context or passed to a callback set by
3455 * isl_ast_build_set_create_leaf.
3456 * In the first case, the space of the isl_ast_build is typically
3457 * a parametric space, although this is currently not enforced.
3458 * In the second case, the space is never a parametric space.
3459 * If the space S is not parametric, then the range space(s) of "schedule"
3460 * need to be wrapped relations with S as domain.
3462 * If the range of "schedule" consists of several spaces, then an AST
3463 * is generated for each of them (in arbitrary order) and the results
3466 * We first initialize the local copies of the relevant options.
3467 * We do this here rather than when the isl_ast_build is created
3468 * because the options may have changed between the construction
3469 * of the isl_ast_build and the call to isl_generate_code.
3471 * The main computation is performed on an inverse schedule (with
3472 * the schedule domain in the domain and the elements to be executed
3473 * in the range) called "executed".
3475 __isl_give isl_ast_node
*isl_ast_build_ast_from_schedule(
3476 __isl_keep isl_ast_build
*build
, __isl_take isl_union_map
*schedule
)
3478 isl_ast_graft_list
*list
;
3480 isl_union_map
*executed
;
3482 executed
= isl_union_map_reverse(schedule
);
3483 list
= generate_code(executed
, isl_ast_build_copy(build
), 0);
3484 node
= isl_ast_node_from_graft_list(list
, build
);