2 * Copyright 2012 Ecole Normale Superieure
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege,
7 * Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 #include <isl/union_map.h>
16 #include <isl_tarjan.h>
17 #include <isl_ast_private.h>
18 #include <isl_ast_build_expr.h>
19 #include <isl_ast_build_private.h>
20 #include <isl_ast_graft_private.h>
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);
111 build = isl_ast_build_set_single_valued(build, 1);
113 list = generate_code(isl_union_map_from_map(executed), build, 1);
115 data->list = isl_ast_graft_list_concat(data->list, list);
120 /* Call the at_each_domain callback, if requested by the user,
121 * after recording the current inverse schedule in the build.
123 static __isl_give isl_ast_graft *at_each_domain(__isl_take isl_ast_graft *graft,
124 __isl_keep isl_map *executed, __isl_keep isl_ast_build *build)
126 if (!graft || !build)
127 return isl_ast_graft_free(graft);
128 if (!build->at_each_domain)
131 build = isl_ast_build_copy(build);
132 build = isl_ast_build_set_executed(build,
133 isl_union_map_from_map(isl_map_copy(executed)));
135 return isl_ast_graft_free(graft);
137 graft->node = build->at_each_domain(graft->node,
138 build, build->at_each_domain_user);
139 isl_ast_build_free(build);
142 graft = isl_ast_graft_free(graft);
147 /* Generate an AST for a single domain based on
148 * the inverse schedule "executed".
150 * If there is more than one domain element associated to the current
151 * schedule "time", then we need to continue the generation process
152 * in generate_non_single_valued.
153 * Note that the inverse schedule being single-valued may depend
154 * on constraints that are only available in the original context
155 * domain specified by the user. We therefore first introduce
156 * the constraints from data->build->domain.
157 * On the other hand, we only perform the test after having taken the gist
158 * of the domain as the resulting map is the one from which the call
159 * expression is constructed. Using this map to construct the call
160 * expression usually yields simpler results.
161 * Because we perform the single-valuedness test on the gisted map,
162 * we may in rare cases fail to recognize that the inverse schedule
163 * is single-valued. This becomes problematic if this happens
164 * from the recursive call through generate_non_single_valued
165 * as we would then end up in an infinite recursion.
166 * We therefore check if we are inside a call to generate_non_single_valued
167 * and revert to the ungisted map if the gisted map turns out not to be
170 * Otherwise, we generate a call expression for the single executed
171 * domain element and put a guard around it based on the (simplified)
172 * domain of "executed".
174 * If the user has set an at_each_domain callback, it is called
175 * on the constructed call expression node.
177 static int generate_domain(__isl_take isl_map *executed, void *user)
179 struct isl_generate_domain_data *data = user;
180 isl_ast_graft *graft;
181 isl_ast_graft_list *list;
186 executed = isl_map_intersect_domain(executed,
187 isl_set_copy(data->build->domain));
189 executed = isl_map_coalesce(executed);
190 map = isl_map_copy(executed);
191 map = isl_ast_build_compute_gist_map_domain(data->build, map);
192 sv = isl_map_is_single_valued(map);
197 if (data->build->single_valued)
198 map = isl_map_copy(executed);
200 return generate_non_single_valued(executed, data);
202 guard = isl_map_domain(isl_map_copy(map));
203 guard = isl_set_coalesce(guard);
204 guard = isl_ast_build_compute_gist(data->build, guard);
205 graft = isl_ast_graft_alloc_domain(map, data->build);
206 graft = at_each_domain(graft, executed, data->build);
208 isl_map_free(executed);
209 graft = isl_ast_graft_add_guard(graft, guard, data->build);
211 list = isl_ast_graft_list_from_ast_graft(graft);
212 data->list = isl_ast_graft_list_concat(data->list, list);
217 isl_map_free(executed);
221 /* Call build->create_leaf to a create "leaf" node in the AST,
222 * encapsulate the result in an isl_ast_graft and return the result
223 * as a 1-element list.
225 * Note that the node returned by the user may be an entire tree.
227 * Before we pass control to the user, we first clear some information
228 * from the build that is (presumbably) only meaningful
229 * for the current code generation.
230 * This includes the create_leaf callback itself, so we make a copy
231 * of the build first.
233 static __isl_give isl_ast_graft_list *call_create_leaf(
234 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
237 isl_ast_graft *graft;
238 isl_ast_build *user_build;
240 user_build = isl_ast_build_copy(build);
241 user_build = isl_ast_build_set_executed(user_build, executed);
242 user_build = isl_ast_build_clear_local_info(user_build);
246 node = build->create_leaf(user_build, build->create_leaf_user);
247 graft = isl_ast_graft_alloc(node, build);
248 isl_ast_build_free(build);
249 return isl_ast_graft_list_from_ast_graft(graft);
252 /* Generate an AST after having handled the complete schedule
253 * of this call to the code generator.
255 * If the user has specified a create_leaf callback, control
256 * is passed to the user in call_create_leaf.
258 * Otherwise, we generate one or more calls for each individual
259 * domain in generate_domain.
261 static __isl_give isl_ast_graft_list *generate_inner_level(
262 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
265 struct isl_generate_domain_data data = { build };
267 if (!build || !executed)
270 if (build->create_leaf)
271 return call_create_leaf(executed, build);
273 ctx = isl_union_map_get_ctx(executed);
274 data.list = isl_ast_graft_list_alloc(ctx, 0);
275 if (isl_union_map_foreach_map(executed, &generate_domain, &data) < 0)
276 data.list = isl_ast_graft_list_free(data.list);
279 error: data.list = NULL;
280 isl_ast_build_free(build);
281 isl_union_map_free(executed);
285 /* Call the before_each_for callback, if requested by the user.
287 static __isl_give isl_ast_node *before_each_for(__isl_take isl_ast_node *node,
288 __isl_keep isl_ast_build *build)
293 return isl_ast_node_free(node);
294 if (!build->before_each_for)
296 id = build->before_each_for(build, build->before_each_for_user);
297 node = isl_ast_node_set_annotation(node, id);
301 /* Call the after_each_for callback, if requested by the user.
303 static __isl_give isl_ast_graft *after_each_for(__isl_keep isl_ast_graft *graft,
304 __isl_keep isl_ast_build *build)
306 if (!graft || !build)
307 return isl_ast_graft_free(graft);
308 if (!build->after_each_for)
310 graft->node = build->after_each_for(graft->node, build,
311 build->after_each_for_user);
313 return isl_ast_graft_free(graft);
317 /* Plug in all the know values of the current and outer dimensions
318 * in the domain of "executed". In principle, we only need to plug
319 * in the known value of the current dimension since the values of
320 * outer dimensions have been plugged in already.
321 * However, it turns out to be easier to just plug in all known values.
323 static __isl_give isl_union_map *plug_in_values(
324 __isl_take isl_union_map *executed, __isl_keep isl_ast_build *build)
326 return isl_ast_build_substitute_values_union_map_domain(build,
330 /* Check if the constraint "c" is a lower bound on dimension "pos",
331 * an upper bound, or independent of dimension "pos".
333 static int constraint_type(isl_constraint *c, int pos)
335 if (isl_constraint_is_lower_bound(c, isl_dim_set, pos))
337 if (isl_constraint_is_upper_bound(c, isl_dim_set, pos))
342 /* Compare the types of the constraints "a" and "b",
343 * resulting in constraints that are independent of "depth"
344 * to be sorted before the lower bounds on "depth", which in
345 * turn are sorted before the upper bounds on "depth".
347 static int cmp_constraint(__isl_keep isl_constraint *a,
348 __isl_keep isl_constraint *b, void *user)
351 int t1 = constraint_type(a, *depth);
352 int t2 = constraint_type(b, *depth);
357 /* Extract a lower bound on dimension "pos" from constraint "c".
359 * If the constraint is of the form
363 * then we essentially return
365 * l = ceil(-f(...)/a)
367 * However, if the current dimension is strided, then we need to make
368 * sure that the lower bound we construct is of the form
372 * with f the offset and s the stride.
373 * We therefore compute
375 * f + s * ceil((l - f)/s)
377 static __isl_give isl_aff *lower_bound(__isl_keep isl_constraint *c,
378 int pos, __isl_keep isl_ast_build *build)
382 aff = isl_constraint_get_bound(c, isl_dim_set, pos);
383 aff = isl_aff_ceil(aff);
385 if (isl_ast_build_has_stride(build, pos)) {
389 offset = isl_ast_build_get_offset(build, pos);
390 stride = isl_ast_build_get_stride(build, pos);
392 aff = isl_aff_sub(aff, isl_aff_copy(offset));
393 aff = isl_aff_scale_down_val(aff, isl_val_copy(stride));
394 aff = isl_aff_ceil(aff);
395 aff = isl_aff_scale_val(aff, stride);
396 aff = isl_aff_add(aff, offset);
399 aff = isl_ast_build_compute_gist_aff(build, aff);
404 /* Return the exact lower bound (or upper bound if "upper" is set)
405 * of "domain" as a piecewise affine expression.
407 * If we are computing a lower bound (of a strided dimension), then
408 * we need to make sure it is of the form
412 * where f is the offset and s is the stride.
413 * We therefore need to include the stride constraint before computing
416 static __isl_give isl_pw_aff *exact_bound(__isl_keep isl_set *domain,
417 __isl_keep isl_ast_build *build, int upper)
422 isl_pw_multi_aff *pma;
424 domain = isl_set_copy(domain);
426 stride = isl_ast_build_get_stride_constraint(build);
427 domain = isl_set_intersect(domain, stride);
429 it_map = isl_ast_build_map_to_iterator(build, domain);
431 pma = isl_map_lexmax_pw_multi_aff(it_map);
433 pma = isl_map_lexmin_pw_multi_aff(it_map);
434 pa = isl_pw_multi_aff_get_pw_aff(pma, 0);
435 isl_pw_multi_aff_free(pma);
436 pa = isl_ast_build_compute_gist_pw_aff(build, pa);
437 pa = isl_pw_aff_coalesce(pa);
442 /* Extract a lower bound on dimension "pos" from each constraint
443 * in "constraints" and return the list of lower bounds.
444 * If "constraints" has zero elements, then we extract a lower bound
445 * from "domain" instead.
447 static __isl_give isl_pw_aff_list *lower_bounds(
448 __isl_keep isl_constraint_list *constraints, int pos,
449 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
452 isl_pw_aff_list *list;
458 n = isl_constraint_list_n_constraint(constraints);
461 pa = exact_bound(domain, build, 0);
462 return isl_pw_aff_list_from_pw_aff(pa);
465 ctx = isl_ast_build_get_ctx(build);
466 list = isl_pw_aff_list_alloc(ctx,n);
468 for (i = 0; i < n; ++i) {
472 c = isl_constraint_list_get_constraint(constraints, i);
473 aff = lower_bound(c, pos, build);
474 isl_constraint_free(c);
475 list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
481 /* Extract an upper bound on dimension "pos" from each constraint
482 * in "constraints" and return the list of upper bounds.
483 * If "constraints" has zero elements, then we extract an upper bound
484 * from "domain" instead.
486 static __isl_give isl_pw_aff_list *upper_bounds(
487 __isl_keep isl_constraint_list *constraints, int pos,
488 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
491 isl_pw_aff_list *list;
494 n = isl_constraint_list_n_constraint(constraints);
497 pa = exact_bound(domain, build, 1);
498 return isl_pw_aff_list_from_pw_aff(pa);
501 ctx = isl_ast_build_get_ctx(build);
502 list = isl_pw_aff_list_alloc(ctx,n);
504 for (i = 0; i < n; ++i) {
508 c = isl_constraint_list_get_constraint(constraints, i);
509 aff = isl_constraint_get_bound(c, isl_dim_set, pos);
510 isl_constraint_free(c);
511 aff = isl_aff_floor(aff);
512 list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
518 /* Return an isl_ast_expr that performs the reduction of type "type"
519 * on AST expressions corresponding to the elements in "list".
521 * The list is assumed to contain at least one element.
522 * If the list contains exactly one element, then the returned isl_ast_expr
523 * simply computes that affine expression.
525 static __isl_give isl_ast_expr *reduce_list(enum isl_ast_op_type type,
526 __isl_keep isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
535 n = isl_pw_aff_list_n_pw_aff(list);
538 return isl_ast_build_expr_from_pw_aff_internal(build,
539 isl_pw_aff_list_get_pw_aff(list, 0));
541 ctx = isl_pw_aff_list_get_ctx(list);
542 expr = isl_ast_expr_alloc_op(ctx, type, n);
546 for (i = 0; i < n; ++i) {
547 isl_ast_expr *expr_i;
549 expr_i = isl_ast_build_expr_from_pw_aff_internal(build,
550 isl_pw_aff_list_get_pw_aff(list, i));
552 return isl_ast_expr_free(expr);
553 expr->u.op.args[i] = expr_i;
559 /* Add a guard to "graft" based on "bound" in the case of a degenerate
560 * level (including the special case of an eliminated level).
562 * We eliminate the current dimension, simplify the result in the current
563 * build and add the result as guards to the graft.
565 * Note that we cannot simply drop the constraints on the current dimension
566 * even in the eliminated case, because the single affine expression may
567 * not be explicitly available in "bounds". Moreover, the single affine
568 * expression may only be defined on a subset of the build domain,
569 * so we do in some cases need to insert a guard even in the eliminated case.
571 static __isl_give isl_ast_graft *add_degenerate_guard(
572 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
573 __isl_keep isl_ast_build *build)
578 depth = isl_ast_build_get_depth(build);
580 dom = isl_set_from_basic_set(isl_basic_set_copy(bounds));
581 if (isl_ast_build_has_stride(build, depth)) {
584 stride = isl_ast_build_get_stride_constraint(build);
585 dom = isl_set_intersect(dom, stride);
587 dom = isl_set_eliminate(dom, isl_dim_set, depth, 1);
588 dom = isl_ast_build_compute_gist(build, dom);
590 graft = isl_ast_graft_add_guard(graft, dom, build);
595 /* Update "graft" based on "bounds" for the eliminated case.
597 * In the eliminated case, no for node is created, so we only need
598 * to check if "bounds" imply any guards that need to be inserted.
600 static __isl_give isl_ast_graft *refine_eliminated(
601 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
602 __isl_keep isl_ast_build *build)
604 return add_degenerate_guard(graft, bounds, build);
607 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
609 * "build" is the build in which graft->node was created
610 * "sub_build" contains information about the current level itself,
611 * including the single value attained.
613 * We first set the initialization part of the for loop to the single
614 * value attained by the current dimension.
615 * The increment and condition are not strictly needed as the are known
616 * to be "1" and "iterator <= value" respectively.
617 * Then we set the size of the iterator and
618 * check if "bounds" imply any guards that need to be inserted.
620 static __isl_give isl_ast_graft *refine_degenerate(
621 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
622 __isl_keep isl_ast_build *build,
623 __isl_keep isl_ast_build *sub_build)
627 if (!graft || !sub_build)
628 return isl_ast_graft_free(graft);
630 value = isl_pw_aff_copy(sub_build->value);
632 graft->node->u.f.init = isl_ast_build_expr_from_pw_aff_internal(build,
634 if (!graft->node->u.f.init)
635 return isl_ast_graft_free(graft);
637 graft = add_degenerate_guard(graft, bounds, build);
642 /* Return the intersection of constraints in "list" as a set.
644 static __isl_give isl_set *intersect_constraints(
645 __isl_keep isl_constraint_list *list)
650 n = isl_constraint_list_n_constraint(list);
652 isl_die(isl_constraint_list_get_ctx(list), isl_error_internal,
653 "expecting at least one constraint", return NULL);
655 bset = isl_basic_set_from_constraint(
656 isl_constraint_list_get_constraint(list, 0));
657 for (i = 1; i < n; ++i) {
658 isl_basic_set *bset_i;
660 bset_i = isl_basic_set_from_constraint(
661 isl_constraint_list_get_constraint(list, i));
662 bset = isl_basic_set_intersect(bset, bset_i);
665 return isl_set_from_basic_set(bset);
668 /* Compute the constraints on the outer dimensions enforced by
669 * graft->node and add those constraints to graft->enforced,
670 * in case the upper bound is expressed as a set "upper".
672 * In particular, if l(...) is a lower bound in "lower", and
674 * -a i + f(...) >= 0 or a i <= f(...)
676 * is an upper bound ocnstraint on the current dimension i,
677 * then the for loop enforces the constraint
679 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
681 * We therefore simply take each lower bound in turn, plug it into
682 * the upper bounds and compute the intersection over all lower bounds.
684 * If a lower bound is a rational expression, then
685 * isl_basic_set_preimage_multi_aff will force this rational
686 * expression to have only integer values. However, the loop
687 * itself does not enforce this integrality constraint. We therefore
688 * use the ceil of the lower bounds instead of the lower bounds themselves.
689 * Other constraints will make sure that the for loop is only executed
690 * when each of the lower bounds attains an integral value.
691 * In particular, potentially rational values only occur in
692 * lower_bound if the offset is a (seemingly) rational expression,
693 * but then outer conditions will make sure that this rational expression
694 * only attains integer values.
696 static __isl_give isl_ast_graft *set_enforced_from_set(
697 __isl_take isl_ast_graft *graft,
698 __isl_keep isl_pw_aff_list *lower, int pos, __isl_keep isl_set *upper)
701 isl_basic_set *enforced;
702 isl_pw_multi_aff *pma;
705 if (!graft || !lower)
706 return isl_ast_graft_free(graft);
708 space = isl_set_get_space(upper);
709 enforced = isl_basic_set_universe(isl_space_copy(space));
711 space = isl_space_map_from_set(space);
712 pma = isl_pw_multi_aff_identity(space);
714 n = isl_pw_aff_list_n_pw_aff(lower);
715 for (i = 0; i < n; ++i) {
719 isl_pw_multi_aff *pma_i;
721 pa = isl_pw_aff_list_get_pw_aff(lower, i);
722 pa = isl_pw_aff_ceil(pa);
723 pma_i = isl_pw_multi_aff_copy(pma);
724 pma_i = isl_pw_multi_aff_set_pw_aff(pma_i, pos, pa);
725 enforced_i = isl_set_copy(upper);
726 enforced_i = isl_set_preimage_pw_multi_aff(enforced_i, pma_i);
727 hull = isl_set_simple_hull(enforced_i);
728 enforced = isl_basic_set_intersect(enforced, hull);
731 isl_pw_multi_aff_free(pma);
733 graft = isl_ast_graft_enforce(graft, enforced);
738 /* Compute the constraints on the outer dimensions enforced by
739 * graft->node and add those constraints to graft->enforced,
740 * in case the upper bound is expressed as
741 * a list of affine expressions "upper".
743 * The enforced condition is that each lower bound expression is less
744 * than or equal to each upper bound expression.
746 static __isl_give isl_ast_graft *set_enforced_from_list(
747 __isl_take isl_ast_graft *graft,
748 __isl_keep isl_pw_aff_list *lower, __isl_keep isl_pw_aff_list *upper)
751 isl_basic_set *enforced;
753 lower = isl_pw_aff_list_copy(lower);
754 upper = isl_pw_aff_list_copy(upper);
755 cond = isl_pw_aff_list_le_set(lower, upper);
756 enforced = isl_set_simple_hull(cond);
757 graft = isl_ast_graft_enforce(graft, enforced);
762 /* Does "aff" have a negative constant term?
764 static int aff_constant_is_negative(__isl_take isl_set *set,
765 __isl_take isl_aff *aff, void *user)
771 isl_aff_get_constant(aff, &v);
772 *neg = isl_int_is_neg(v);
777 return *neg ? 0 : -1;
780 /* Does "pa" have a negative constant term over its entire domain?
782 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff *pa, void *user)
787 r = isl_pw_aff_foreach_piece(pa, &aff_constant_is_negative, user);
790 return *neg ? 0 : -1;
793 /* Does each element in "list" have a negative constant term?
795 * The callback terminates the iteration as soon an element has been
796 * found that does not have a negative constant term.
798 static int list_constant_is_negative(__isl_keep isl_pw_aff_list *list)
802 if (isl_pw_aff_list_foreach(list,
803 &pw_aff_constant_is_negative, &neg) < 0 && neg)
809 /* Add 1 to each of the elements in "list", where each of these elements
810 * is defined over the internal schedule space of "build".
812 static __isl_give isl_pw_aff_list *list_add_one(
813 __isl_take isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
820 space = isl_ast_build_get_space(build, 1);
821 aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
822 aff = isl_aff_add_constant_si(aff, 1);
823 one = isl_pw_aff_from_aff(aff);
825 n = isl_pw_aff_list_n_pw_aff(list);
826 for (i = 0; i < n; ++i) {
828 pa = isl_pw_aff_list_get_pw_aff(list, i);
829 pa = isl_pw_aff_add(pa, isl_pw_aff_copy(one));
830 list = isl_pw_aff_list_set_pw_aff(list, i, pa);
833 isl_pw_aff_free(one);
838 /* Set the condition part of the for node graft->node in case
839 * the upper bound is represented as a list of piecewise affine expressions.
841 * In particular, set the condition to
843 * iterator <= min(list of upper bounds)
845 * If each of the upper bounds has a negative constant term, then
846 * set the condition to
848 * iterator < min(list of (upper bound + 1)s)
851 static __isl_give isl_ast_graft *set_for_cond_from_list(
852 __isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *list,
853 __isl_keep isl_ast_build *build)
856 isl_ast_expr *bound, *iterator, *cond;
857 enum isl_ast_op_type type = isl_ast_op_le;
860 return isl_ast_graft_free(graft);
862 neg = list_constant_is_negative(list);
864 return isl_ast_graft_free(graft);
865 list = isl_pw_aff_list_copy(list);
867 list = list_add_one(list, build);
868 type = isl_ast_op_lt;
871 bound = reduce_list(isl_ast_op_min, list, build);
872 iterator = isl_ast_expr_copy(graft->node->u.f.iterator);
873 cond = isl_ast_expr_alloc_binary(type, iterator, bound);
874 graft->node->u.f.cond = cond;
876 isl_pw_aff_list_free(list);
877 if (!graft->node->u.f.cond)
878 return isl_ast_graft_free(graft);
882 /* Set the condition part of the for node graft->node in case
883 * the upper bound is represented as a set.
885 static __isl_give isl_ast_graft *set_for_cond_from_set(
886 __isl_take isl_ast_graft *graft, __isl_keep isl_set *set,
887 __isl_keep isl_ast_build *build)
894 cond = isl_ast_build_expr_from_set(build, isl_set_copy(set));
895 graft->node->u.f.cond = cond;
896 if (!graft->node->u.f.cond)
897 return isl_ast_graft_free(graft);
901 /* Construct an isl_ast_expr for the increment (i.e., stride) of
902 * the current dimension.
904 static __isl_give isl_ast_expr *for_inc(__isl_keep isl_ast_build *build)
912 ctx = isl_ast_build_get_ctx(build);
913 depth = isl_ast_build_get_depth(build);
915 if (!isl_ast_build_has_stride(build, depth))
916 return isl_ast_expr_alloc_int_si(ctx, 1);
918 v = isl_ast_build_get_stride(build, depth);
919 return isl_ast_expr_from_val(v);
922 /* Should we express the loop condition as
924 * iterator <= min(list of upper bounds)
926 * or as a conjunction of constraints?
928 * The first is constructed from a list of upper bounds.
929 * The second is constructed from a set.
931 * If there are no upper bounds in "constraints", then this could mean
932 * that "domain" simply doesn't have an upper bound or that we didn't
933 * pick any upper bound. In the first case, we want to generate the
934 * loop condition as a(n empty) conjunction of constraints
935 * In the second case, we will compute
936 * a single upper bound from "domain" and so we use the list form.
938 * If there are upper bounds in "constraints",
939 * then we use the list form iff the atomic_upper_bound option is set.
941 static int use_upper_bound_list(isl_ctx *ctx, int n_upper,
942 __isl_keep isl_set *domain, int depth)
945 return isl_options_get_ast_build_atomic_upper_bound(ctx);
947 return isl_set_dim_has_upper_bound(domain, isl_dim_set, depth);
950 /* Fill in the expressions of the for node in graft->node.
953 * - set the initialization part of the loop to the maximum of the lower bounds
954 * - set the size of the iterator based on the values attained by the iterator
955 * - extract the increment from the stride of the current dimension
956 * - construct the for condition either based on a list of upper bounds
957 * or on a set of upper bound constraints.
959 static __isl_give isl_ast_graft *set_for_node_expressions(
960 __isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *lower,
961 int use_list, __isl_keep isl_pw_aff_list *upper_list,
962 __isl_keep isl_set *upper_set, __isl_keep isl_ast_build *build)
969 build = isl_ast_build_copy(build);
970 build = isl_ast_build_set_enforced(build,
971 isl_ast_graft_get_enforced(graft));
974 node->u.f.init = reduce_list(isl_ast_op_max, lower, build);
975 node->u.f.inc = for_inc(build);
978 graft = set_for_cond_from_list(graft, upper_list, build);
980 graft = set_for_cond_from_set(graft, upper_set, build);
982 isl_ast_build_free(build);
984 if (!node->u.f.iterator || !node->u.f.init ||
985 !node->u.f.cond || !node->u.f.inc)
986 return isl_ast_graft_free(graft);
991 /* Update "graft" based on "bounds" and "domain" for the generic,
992 * non-degenerate, case.
994 * "c_lower" and "c_upper" contain the lower and upper bounds
995 * that the loop node should express.
996 * "domain" is the subset of the intersection of the constraints
997 * for which some code is executed.
999 * There may be zero lower bounds or zero upper bounds in "constraints"
1000 * in case the list of constraints was created
1001 * based on the atomic option or based on separation with explicit bounds.
1002 * In that case, we use "domain" to derive lower and/or upper bounds.
1004 * We first compute a list of one or more lower bounds.
1006 * Then we decide if we want to express the condition as
1008 * iterator <= min(list of upper bounds)
1010 * or as a conjunction of constraints.
1012 * The set of enforced constraints is then computed either based on
1013 * a list of upper bounds or on a set of upper bound constraints.
1014 * We do not compute any enforced constraints if we were forced
1015 * to compute a lower or upper bound using exact_bound. The domains
1016 * of the resulting expressions may imply some bounds on outer dimensions
1017 * that we do not want to appear in the enforced constraints since
1018 * they are not actually enforced by the corresponding code.
1020 * Finally, we fill in the expressions of the for node.
1022 static __isl_give isl_ast_graft *refine_generic_bounds(
1023 __isl_take isl_ast_graft *graft,
1024 __isl_take isl_constraint_list *c_lower,
1025 __isl_take isl_constraint_list *c_upper,
1026 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
1030 isl_pw_aff_list *lower;
1032 isl_set *upper_set = NULL;
1033 isl_pw_aff_list *upper_list = NULL;
1034 int n_lower, n_upper;
1036 if (!graft || !c_lower || !c_upper || !build)
1039 depth = isl_ast_build_get_depth(build);
1040 ctx = isl_ast_graft_get_ctx(graft);
1042 n_lower = isl_constraint_list_n_constraint(c_lower);
1043 n_upper = isl_constraint_list_n_constraint(c_upper);
1045 use_list = use_upper_bound_list(ctx, n_upper, domain, depth);
1047 lower = lower_bounds(c_lower, depth, domain, build);
1050 upper_list = upper_bounds(c_upper, depth, domain, build);
1051 else if (n_upper > 0)
1052 upper_set = intersect_constraints(c_upper);
1054 upper_set = isl_set_universe(isl_set_get_space(domain));
1056 if (n_lower == 0 || n_upper == 0)
1059 graft = set_enforced_from_list(graft, lower, upper_list);
1061 graft = set_enforced_from_set(graft, lower, depth, upper_set);
1063 graft = set_for_node_expressions(graft, lower, use_list, upper_list,
1066 isl_pw_aff_list_free(lower);
1067 isl_pw_aff_list_free(upper_list);
1068 isl_set_free(upper_set);
1069 isl_constraint_list_free(c_lower);
1070 isl_constraint_list_free(c_upper);
1074 isl_constraint_list_free(c_lower);
1075 isl_constraint_list_free(c_upper);
1076 return isl_ast_graft_free(graft);
1079 /* Internal data structure used inside count_constraints to keep
1080 * track of the number of constraints that are independent of dimension "pos",
1081 * the lower bounds in "pos" and the upper bounds in "pos".
1083 struct isl_ast_count_constraints_data {
1091 /* Increment data->n_indep, data->lower or data->upper depending
1092 * on whether "c" is independenct of dimensions data->pos,
1093 * a lower bound or an upper bound.
1095 static int count_constraints(__isl_take isl_constraint *c, void *user)
1097 struct isl_ast_count_constraints_data *data = user;
1099 if (isl_constraint_is_lower_bound(c, isl_dim_set, data->pos))
1101 else if (isl_constraint_is_upper_bound(c, isl_dim_set, data->pos))
1106 isl_constraint_free(c);
1111 /* Update "graft" based on "bounds" and "domain" for the generic,
1112 * non-degenerate, case.
1114 * "list" respresent the list of bounds that need to be encoded by
1115 * the for loop (or a guard around the for loop).
1116 * "domain" is the subset of the intersection of the constraints
1117 * for which some code is executed.
1118 * "build" is the build in which graft->node was created.
1120 * We separate lower bounds, upper bounds and constraints that
1121 * are independent of the loop iterator.
1123 * The actual for loop bounds are generated in refine_generic_bounds.
1124 * If there are any constraints that are independent of the loop iterator,
1125 * we need to put a guard around the for loop (which may get hoisted up
1126 * to higher levels) and we call refine_generic_bounds in a build
1127 * where this guard is enforced.
1129 static __isl_give isl_ast_graft *refine_generic_split(
1130 __isl_take isl_ast_graft *graft, __isl_take isl_constraint_list *list,
1131 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
1133 isl_ast_build *for_build;
1135 struct isl_ast_count_constraints_data data;
1136 isl_constraint_list *lower;
1137 isl_constraint_list *upper;
1140 return isl_ast_graft_free(graft);
1142 data.pos = isl_ast_build_get_depth(build);
1144 list = isl_constraint_list_sort(list, &cmp_constraint, &data.pos);
1146 return isl_ast_graft_free(graft);
1148 data.n_indep = data.n_lower = data.n_upper = 0;
1149 if (isl_constraint_list_foreach(list, &count_constraints, &data) < 0) {
1150 isl_constraint_list_free(list);
1151 return isl_ast_graft_free(graft);
1154 lower = isl_constraint_list_copy(list);
1155 lower = isl_constraint_list_drop(lower, 0, data.n_indep);
1156 upper = isl_constraint_list_copy(lower);
1157 lower = isl_constraint_list_drop(lower, data.n_lower, data.n_upper);
1158 upper = isl_constraint_list_drop(upper, 0, data.n_lower);
1160 if (data.n_indep == 0) {
1161 isl_constraint_list_free(list);
1162 return refine_generic_bounds(graft, lower, upper,
1166 list = isl_constraint_list_drop(list, data.n_indep,
1167 data.n_lower + data.n_upper);
1168 guard = intersect_constraints(list);
1169 isl_constraint_list_free(list);
1171 for_build = isl_ast_build_copy(build);
1172 for_build = isl_ast_build_restrict_pending(for_build,
1173 isl_set_copy(guard));
1174 graft = refine_generic_bounds(graft, lower, upper, domain, for_build);
1175 isl_ast_build_free(for_build);
1177 graft = isl_ast_graft_add_guard(graft, guard, build);
1182 /* Add the guard implied by the current stride constraint (if any),
1183 * but not (necessarily) enforced by the generated AST to "graft".
1185 static __isl_give isl_ast_graft *add_stride_guard(
1186 __isl_take isl_ast_graft *graft, __isl_keep isl_ast_build *build)
1191 depth = isl_ast_build_get_depth(build);
1192 if (!isl_ast_build_has_stride(build, depth))
1195 dom = isl_ast_build_get_stride_constraint(build);
1196 dom = isl_set_eliminate(dom, isl_dim_set, depth, 1);
1197 dom = isl_ast_build_compute_gist(build, dom);
1199 graft = isl_ast_graft_add_guard(graft, dom, build);
1204 /* Update "graft" based on "bounds" and "domain" for the generic,
1205 * non-degenerate, case.
1207 * "bounds" respresent the bounds that need to be encoded by
1208 * the for loop (or a guard around the for loop).
1209 * "domain" is the subset of "bounds" for which some code is executed.
1210 * "build" is the build in which graft->node was created.
1212 * We break up "bounds" into a list of constraints and continue with
1213 * refine_generic_split.
1215 static __isl_give isl_ast_graft *refine_generic(
1216 __isl_take isl_ast_graft *graft,
1217 __isl_keep isl_basic_set *bounds, __isl_keep isl_set *domain,
1218 __isl_keep isl_ast_build *build)
1220 isl_constraint_list *list;
1222 if (!build || !graft)
1223 return isl_ast_graft_free(graft);
1225 bounds = isl_basic_set_copy(bounds);
1226 bounds = isl_ast_build_compute_gist_basic_set(build, bounds);
1227 list = isl_constraint_list_from_basic_set(bounds);
1229 graft = refine_generic_split(graft, list, domain, build);
1230 graft = add_stride_guard(graft, build);
1235 /* Create a for node for the current level.
1237 * Mark the for node degenerate if "degenerate" is set.
1239 static __isl_give isl_ast_node *create_for(__isl_keep isl_ast_build *build,
1249 depth = isl_ast_build_get_depth(build);
1250 id = isl_ast_build_get_iterator_id(build, depth);
1251 node = isl_ast_node_alloc_for(id);
1253 node = isl_ast_node_for_mark_degenerate(node);
1258 /* Create an AST node for the current dimension based on
1259 * the schedule domain "bounds" and return the node encapsulated
1260 * in an isl_ast_graft.
1262 * "executed" is the current inverse schedule, taking into account
1263 * the bounds in "bounds"
1264 * "domain" is the domain of "executed", with inner dimensions projected out.
1265 * It may be a strict subset of "bounds" in case "bounds" was created
1266 * based on the atomic option or based on separation with explicit bounds.
1268 * "domain" may satisfy additional equalities that result
1269 * from intersecting "executed" with "bounds" in add_node.
1270 * It may also satisfy some global constraints that were dropped out because
1271 * we performed separation with explicit bounds.
1272 * The very first step is then to copy these constraints to "bounds".
1274 * Since we may be calling before_each_for and after_each_for
1275 * callbacks, we record the current inverse schedule in the build.
1277 * We consider three builds,
1278 * "build" is the one in which the current level is created,
1279 * "body_build" is the build in which the next level is created,
1280 * "sub_build" is essentially the same as "body_build", except that
1281 * the depth has not been increased yet.
1283 * "build" already contains information (in strides and offsets)
1284 * about the strides at the current level, but this information is not
1285 * reflected in the build->domain.
1286 * We first add this information and the "bounds" to the sub_build->domain.
1287 * isl_ast_build_set_loop_bounds checks whether the current dimension attains
1288 * only a single value and whether this single value can be represented using
1289 * a single affine expression.
1290 * In the first case, the current level is considered "degenerate".
1291 * In the second, sub-case, the current level is considered "eliminated".
1292 * Eliminated level don't need to be reflected in the AST since we can
1293 * simply plug in the affine expression. For degenerate, but non-eliminated,
1294 * levels, we do introduce a for node, but mark is as degenerate so that
1295 * it can be printed as an assignment of the single value to the loop
1298 * If the current level is eliminated, we explicitly plug in the value
1299 * for the current level found by isl_ast_build_set_loop_bounds in the
1300 * inverse schedule. This ensures that if we are working on a slice
1301 * of the domain based on information available in the inverse schedule
1302 * and the build domain, that then this information is also reflected
1303 * in the inverse schedule. This operation also eliminates the current
1304 * dimension from the inverse schedule making sure no inner dimensions depend
1305 * on the current dimension. Otherwise, we create a for node, marking
1306 * it degenerate if appropriate. The initial for node is still incomplete
1307 * and will be completed in either refine_degenerate or refine_generic.
1309 * We then generate a sequence of grafts for the next level,
1310 * create a surrounding graft for the current level and insert
1311 * the for node we created (if the current level is not eliminated).
1313 * Finally, we set the bounds of the for loop and insert guards
1314 * (either in the AST or in the graft) in one of
1315 * refine_eliminated, refine_degenerate or refine_generic.
1317 static __isl_give isl_ast_graft *create_node_scaled(
1318 __isl_take isl_union_map *executed,
1319 __isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
1320 __isl_take isl_ast_build *build)
1323 int degenerate, eliminated;
1324 isl_basic_set *hull;
1325 isl_ast_node *node = NULL;
1326 isl_ast_graft *graft;
1327 isl_ast_graft_list *children;
1328 isl_ast_build *sub_build;
1329 isl_ast_build *body_build;
1331 domain = isl_ast_build_eliminate_divs(build, domain);
1332 domain = isl_set_detect_equalities(domain);
1333 hull = isl_set_unshifted_simple_hull(isl_set_copy(domain));
1334 bounds = isl_basic_set_intersect(bounds, hull);
1335 build = isl_ast_build_set_executed(build, isl_union_map_copy(executed));
1337 depth = isl_ast_build_get_depth(build);
1338 sub_build = isl_ast_build_copy(build);
1339 sub_build = isl_ast_build_include_stride(sub_build);
1340 sub_build = isl_ast_build_set_loop_bounds(sub_build,
1341 isl_basic_set_copy(bounds));
1342 degenerate = isl_ast_build_has_value(sub_build);
1343 eliminated = isl_ast_build_has_affine_value(sub_build, depth);
1344 if (degenerate < 0 || eliminated < 0)
1345 executed = isl_union_map_free(executed);
1347 executed = plug_in_values(executed, sub_build);
1349 node = create_for(build, degenerate);
1351 body_build = isl_ast_build_copy(sub_build);
1352 body_build = isl_ast_build_increase_depth(body_build);
1354 node = before_each_for(node, body_build);
1355 children = generate_next_level(executed,
1356 isl_ast_build_copy(body_build));
1358 graft = isl_ast_graft_alloc_level(children, build, sub_build);
1360 graft = isl_ast_graft_insert_for(graft, node);
1362 graft = refine_eliminated(graft, bounds, build);
1363 else if (degenerate)
1364 graft = refine_degenerate(graft, bounds, build, sub_build);
1366 graft = refine_generic(graft, bounds, domain, build);
1368 graft = after_each_for(graft, body_build);
1370 isl_ast_build_free(body_build);
1371 isl_ast_build_free(sub_build);
1372 isl_ast_build_free(build);
1373 isl_basic_set_free(bounds);
1374 isl_set_free(domain);
1379 /* Internal data structure for checking if all constraints involving
1380 * the input dimension "depth" are such that the other coefficients
1381 * are multiples of "m", reducing "m" if they are not.
1382 * If "m" is reduced all the way down to "1", then the check has failed
1383 * and we break out of the iteration.
1385 struct isl_check_scaled_data {
1390 /* If constraint "c" involves the input dimension data->depth,
1391 * then make sure that all the other coefficients are multiples of data->m,
1392 * reducing data->m if needed.
1393 * Break out of the iteration if data->m has become equal to "1".
1395 static int constraint_check_scaled(__isl_take isl_constraint *c, void *user)
1397 struct isl_check_scaled_data *data = user;
1399 enum isl_dim_type t[] = { isl_dim_param, isl_dim_in, isl_dim_out,
1402 if (!isl_constraint_involves_dims(c, isl_dim_in, data->depth, 1)) {
1403 isl_constraint_free(c);
1407 for (i = 0; i < 4; ++i) {
1408 n = isl_constraint_dim(c, t[i]);
1409 for (j = 0; j < n; ++j) {
1412 if (t[i] == isl_dim_in && j == data->depth)
1414 if (!isl_constraint_involves_dims(c, t[i], j, 1))
1416 d = isl_constraint_get_coefficient_val(c, t[i], j);
1417 data->m = isl_val_gcd(data->m, d);
1418 if (isl_val_is_one(data->m))
1425 isl_constraint_free(c);
1427 return i < 4 ? -1 : 0;
1430 /* For each constraint of "bmap" that involves the input dimension data->depth,
1431 * make sure that all the other coefficients are multiples of data->m,
1432 * reducing data->m if needed.
1433 * Break out of the iteration if data->m has become equal to "1".
1435 static int basic_map_check_scaled(__isl_take isl_basic_map *bmap, void *user)
1439 r = isl_basic_map_foreach_constraint(bmap,
1440 &constraint_check_scaled, user);
1441 isl_basic_map_free(bmap);
1446 /* For each constraint of "map" that involves the input dimension data->depth,
1447 * make sure that all the other coefficients are multiples of data->m,
1448 * reducing data->m if needed.
1449 * Break out of the iteration if data->m has become equal to "1".
1451 static int map_check_scaled(__isl_take isl_map *map, void *user)
1455 r = isl_map_foreach_basic_map(map, &basic_map_check_scaled, user);
1461 /* Create an AST node for the current dimension based on
1462 * the schedule domain "bounds" and return the node encapsulated
1463 * in an isl_ast_graft.
1465 * "executed" is the current inverse schedule, taking into account
1466 * the bounds in "bounds"
1467 * "domain" is the domain of "executed", with inner dimensions projected out.
1470 * Before moving on to the actual AST node construction in create_node_scaled,
1471 * we first check if the current dimension is strided and if we can scale
1472 * down this stride. Note that we only do this if the ast_build_scale_strides
1475 * In particular, let the current dimension take on values
1479 * with a an integer. We check if we can find an integer m that (obviouly)
1480 * divides both f and s.
1482 * If so, we check if the current dimension only appears in constraints
1483 * where the coefficients of the other variables are multiples of m.
1484 * We perform this extra check to avoid the risk of introducing
1485 * divisions by scaling down the current dimension.
1487 * If so, we scale the current dimension down by a factor of m.
1488 * That is, we plug in
1492 * Note that in principle we could always scale down strided loops
1497 * but this may result in i' taking on larger values than the original i,
1498 * due to the shift by "f".
1499 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1501 static __isl_give isl_ast_graft *create_node(__isl_take isl_union_map *executed,
1502 __isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
1503 __isl_take isl_ast_build *build)
1505 struct isl_check_scaled_data data;
1510 ctx = isl_ast_build_get_ctx(build);
1511 if (!isl_options_get_ast_build_scale_strides(ctx))
1512 return create_node_scaled(executed, bounds, domain, build);
1514 data.depth = isl_ast_build_get_depth(build);
1515 if (!isl_ast_build_has_stride(build, data.depth))
1516 return create_node_scaled(executed, bounds, domain, build);
1518 offset = isl_ast_build_get_offset(build, data.depth);
1519 data.m = isl_ast_build_get_stride(build, data.depth);
1521 offset = isl_aff_free(offset);
1522 offset = isl_aff_scale_down_val(offset, isl_val_copy(data.m));
1523 d = isl_aff_get_denominator_val(offset);
1525 executed = isl_union_map_free(executed);
1527 if (executed && isl_val_is_divisible_by(data.m, d))
1528 data.m = isl_val_div(data.m, d);
1530 data.m = isl_val_set_si(data.m, 1);
1534 if (!isl_val_is_one(data.m)) {
1535 if (isl_union_map_foreach_map(executed, &map_check_scaled,
1537 !isl_val_is_one(data.m))
1538 executed = isl_union_map_free(executed);
1541 if (!isl_val_is_one(data.m)) {
1546 isl_union_map *umap;
1548 space = isl_ast_build_get_space(build, 1);
1549 space = isl_space_map_from_set(space);
1550 ma = isl_multi_aff_identity(space);
1551 aff = isl_multi_aff_get_aff(ma, data.depth);
1552 aff = isl_aff_scale_val(aff, isl_val_copy(data.m));
1553 ma = isl_multi_aff_set_aff(ma, data.depth, aff);
1555 bounds = isl_basic_set_preimage_multi_aff(bounds,
1556 isl_multi_aff_copy(ma));
1557 domain = isl_set_preimage_multi_aff(domain,
1558 isl_multi_aff_copy(ma));
1559 map = isl_map_reverse(isl_map_from_multi_aff(ma));
1560 umap = isl_union_map_from_map(map);
1561 executed = isl_union_map_apply_domain(executed,
1562 isl_union_map_copy(umap));
1563 build = isl_ast_build_scale_down(build, isl_val_copy(data.m),
1566 isl_aff_free(offset);
1567 isl_val_free(data.m);
1569 return create_node_scaled(executed, bounds, domain, build);
1572 /* Add the basic set to the list that "user" points to.
1574 static int collect_basic_set(__isl_take isl_basic_set *bset, void *user)
1576 isl_basic_set_list **list = user;
1578 *list = isl_basic_set_list_add(*list, bset);
1583 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1585 static __isl_give isl_basic_set_list *isl_basic_set_list_from_set(
1586 __isl_take isl_set *set)
1590 isl_basic_set_list *list;
1595 ctx = isl_set_get_ctx(set);
1597 n = isl_set_n_basic_set(set);
1598 list = isl_basic_set_list_alloc(ctx, n);
1599 if (isl_set_foreach_basic_set(set, &collect_basic_set, &list) < 0)
1600 list = isl_basic_set_list_free(list);
1606 /* Generate code for the schedule domain "bounds"
1607 * and add the result to "list".
1609 * We mainly detect strides and additional equalities here
1610 * and then pass over control to create_node.
1612 * "bounds" reflects the bounds on the current dimension and possibly
1613 * some extra conditions on outer dimensions.
1614 * It does not, however, include any divs involving the current dimension,
1615 * so it does not capture any stride constraints.
1616 * We therefore need to compute that part of the schedule domain that
1617 * intersects with "bounds" and derive the strides from the result.
1619 static __isl_give isl_ast_graft_list *add_node(
1620 __isl_take isl_ast_graft_list *list, __isl_take isl_union_map *executed,
1621 __isl_take isl_basic_set *bounds, __isl_take isl_ast_build *build)
1623 isl_ast_graft *graft;
1624 isl_set *domain = NULL;
1625 isl_union_set *uset;
1628 uset = isl_union_set_from_basic_set(isl_basic_set_copy(bounds));
1629 executed = isl_union_map_intersect_domain(executed, uset);
1630 empty = isl_union_map_is_empty(executed);
1636 uset = isl_union_map_domain(isl_union_map_copy(executed));
1637 domain = isl_set_from_union_set(uset);
1638 domain = isl_ast_build_compute_gist(build, domain);
1639 empty = isl_set_is_empty(domain);
1645 domain = isl_ast_build_eliminate_inner(build, domain);
1646 build = isl_ast_build_detect_strides(build, isl_set_copy(domain));
1648 graft = create_node(executed, bounds, domain,
1649 isl_ast_build_copy(build));
1650 list = isl_ast_graft_list_add(list, graft);
1651 isl_ast_build_free(build);
1654 list = isl_ast_graft_list_free(list);
1656 isl_set_free(domain);
1657 isl_basic_set_free(bounds);
1658 isl_union_map_free(executed);
1659 isl_ast_build_free(build);
1663 /* Does any element of i follow or coincide with any element of j
1664 * at the current depth for equal values of the outer dimensions?
1666 static int domain_follows_at_depth(__isl_keep isl_basic_set *i,
1667 __isl_keep isl_basic_set *j, void *user)
1669 int depth = *(int *) user;
1670 isl_basic_map *test;
1674 test = isl_basic_map_from_domain_and_range(isl_basic_set_copy(i),
1675 isl_basic_set_copy(j));
1676 for (l = 0; l < depth; ++l)
1677 test = isl_basic_map_equate(test, isl_dim_in, l,
1679 test = isl_basic_map_order_ge(test, isl_dim_in, depth,
1680 isl_dim_out, depth);
1681 empty = isl_basic_map_is_empty(test);
1682 isl_basic_map_free(test);
1684 return empty < 0 ? -1 : !empty;
1687 /* Split up each element of "list" into a part that is related to "bset"
1688 * according to "gt" and a part that is not.
1689 * Return a list that consist of "bset" and all the pieces.
1691 static __isl_give isl_basic_set_list *add_split_on(
1692 __isl_take isl_basic_set_list *list, __isl_take isl_basic_set *bset,
1693 __isl_keep isl_basic_map *gt)
1696 isl_basic_set_list *res;
1698 gt = isl_basic_map_copy(gt);
1699 gt = isl_basic_map_intersect_domain(gt, isl_basic_set_copy(bset));
1700 n = isl_basic_set_list_n_basic_set(list);
1701 res = isl_basic_set_list_from_basic_set(bset);
1702 for (i = 0; res && i < n; ++i) {
1703 isl_basic_set *bset;
1704 isl_set *set1, *set2;
1705 isl_basic_map *bmap;
1708 bset = isl_basic_set_list_get_basic_set(list, i);
1709 bmap = isl_basic_map_copy(gt);
1710 bmap = isl_basic_map_intersect_range(bmap, bset);
1711 bset = isl_basic_map_range(bmap);
1712 empty = isl_basic_set_is_empty(bset);
1714 res = isl_basic_set_list_free(res);
1716 isl_basic_set_free(bset);
1717 bset = isl_basic_set_list_get_basic_set(list, i);
1718 res = isl_basic_set_list_add(res, bset);
1722 res = isl_basic_set_list_add(res, isl_basic_set_copy(bset));
1723 set1 = isl_set_from_basic_set(bset);
1724 bset = isl_basic_set_list_get_basic_set(list, i);
1725 set2 = isl_set_from_basic_set(bset);
1726 set1 = isl_set_subtract(set2, set1);
1727 set1 = isl_set_make_disjoint(set1);
1729 res = isl_basic_set_list_concat(res,
1730 isl_basic_set_list_from_set(set1));
1732 isl_basic_map_free(gt);
1733 isl_basic_set_list_free(list);
1737 static __isl_give isl_ast_graft_list *generate_sorted_domains(
1738 __isl_keep isl_basic_set_list *domain_list,
1739 __isl_keep isl_union_map *executed,
1740 __isl_keep isl_ast_build *build);
1742 /* Internal data structure for add_nodes.
1744 * "executed" and "build" are extra arguments to be passed to add_node.
1745 * "list" collects the results.
1747 struct isl_add_nodes_data {
1748 isl_union_map *executed;
1749 isl_ast_build *build;
1751 isl_ast_graft_list *list;
1754 /* Generate code for the schedule domains in "scc"
1755 * and add the results to "list".
1757 * The domains in "scc" form a strongly connected component in the ordering.
1758 * If the number of domains in "scc" is larger than 1, then this means
1759 * that we cannot determine a valid ordering for the domains in the component.
1760 * This should be fairly rare because the individual domains
1761 * have been made disjoint first.
1762 * The problem is that the domains may be integrally disjoint but not
1763 * rationally disjoint. For example, we may have domains
1765 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1767 * These two domains have an empty intersection, but their rational
1768 * relaxations do intersect. It is impossible to order these domains
1769 * in the second dimension because the first should be ordered before
1770 * the second for outer dimension equal to 0, while it should be ordered
1771 * after for outer dimension equal to 1.
1773 * This may happen in particular in case of unrolling since the domain
1774 * of each slice is replaced by its simple hull.
1776 * For each basic set i in "scc" and for each of the following basic sets j,
1777 * we split off that part of the basic set i that shares the outer dimensions
1778 * with j and lies before j in the current dimension.
1779 * We collect all the pieces in a new list that replaces "scc".
1781 static int add_nodes(__isl_take isl_basic_set_list *scc, void *user)
1783 struct isl_add_nodes_data *data = user;
1785 isl_basic_set *bset;
1786 isl_basic_set_list *list;
1790 n = isl_basic_set_list_n_basic_set(scc);
1791 bset = isl_basic_set_list_get_basic_set(scc, 0);
1793 isl_basic_set_list_free(scc);
1794 data->list = add_node(data->list,
1795 isl_union_map_copy(data->executed), bset,
1796 isl_ast_build_copy(data->build));
1797 return data->list ? 0 : -1;
1800 depth = isl_ast_build_get_depth(data->build);
1801 space = isl_basic_set_get_space(bset);
1802 space = isl_space_map_from_set(space);
1803 gt = isl_basic_map_universe(space);
1804 for (i = 0; i < depth; ++i)
1805 gt = isl_basic_map_equate(gt, isl_dim_in, i, isl_dim_out, i);
1806 gt = isl_basic_map_order_gt(gt, isl_dim_in, depth, isl_dim_out, depth);
1808 list = isl_basic_set_list_from_basic_set(bset);
1809 for (i = 1; i < n; ++i) {
1810 bset = isl_basic_set_list_get_basic_set(scc, i);
1811 list = add_split_on(list, bset, gt);
1813 isl_basic_map_free(gt);
1814 isl_basic_set_list_free(scc);
1816 data->list = isl_ast_graft_list_concat(data->list,
1817 generate_sorted_domains(scc, data->executed, data->build));
1818 isl_basic_set_list_free(scc);
1820 return data->list ? 0 : -1;
1823 /* Sort the domains in "domain_list" according to the execution order
1824 * at the current depth (for equal values of the outer dimensions),
1825 * generate code for each of them, collecting the results in a list.
1826 * If no code is generated (because the intersection of the inverse schedule
1827 * with the domains turns out to be empty), then an empty list is returned.
1829 * The caller is responsible for ensuring that the basic sets in "domain_list"
1830 * are pair-wise disjoint. It can, however, in principle happen that
1831 * two basic sets should be ordered one way for one value of the outer
1832 * dimensions and the other way for some other value of the outer dimensions.
1833 * We therefore play safe and look for strongly connected components.
1834 * The function add_nodes takes care of handling non-trivial components.
1836 static __isl_give isl_ast_graft_list *generate_sorted_domains(
1837 __isl_keep isl_basic_set_list *domain_list,
1838 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
1841 struct isl_add_nodes_data data;
1848 ctx = isl_basic_set_list_get_ctx(domain_list);
1849 n = isl_basic_set_list_n_basic_set(domain_list);
1850 data.list = isl_ast_graft_list_alloc(ctx, n);
1854 return add_node(data.list, isl_union_map_copy(executed),
1855 isl_basic_set_list_get_basic_set(domain_list, 0),
1856 isl_ast_build_copy(build));
1858 depth = isl_ast_build_get_depth(build);
1859 data.executed = executed;
1861 if (isl_basic_set_list_foreach_scc(domain_list,
1862 &domain_follows_at_depth, &depth,
1863 &add_nodes, &data) < 0)
1864 data.list = isl_ast_graft_list_free(data.list);
1869 /* Do i and j share any values for the outer dimensions?
1871 static int shared_outer(__isl_keep isl_basic_set *i,
1872 __isl_keep isl_basic_set *j, void *user)
1874 int depth = *(int *) user;
1875 isl_basic_map *test;
1879 test = isl_basic_map_from_domain_and_range(isl_basic_set_copy(i),
1880 isl_basic_set_copy(j));
1881 for (l = 0; l < depth; ++l)
1882 test = isl_basic_map_equate(test, isl_dim_in, l,
1884 empty = isl_basic_map_is_empty(test);
1885 isl_basic_map_free(test);
1887 return empty < 0 ? -1 : !empty;
1890 /* Internal data structure for generate_sorted_domains_wrap.
1892 * "n" is the total number of basic sets
1893 * "executed" and "build" are extra arguments to be passed
1894 * to generate_sorted_domains.
1896 * "single" is set to 1 by generate_sorted_domains_wrap if there
1897 * is only a single component.
1898 * "list" collects the results.
1900 struct isl_ast_generate_parallel_domains_data {
1902 isl_union_map *executed;
1903 isl_ast_build *build;
1906 isl_ast_graft_list *list;
1909 /* Call generate_sorted_domains on "scc", fuse the result into a list
1910 * with either zero or one graft and collect the these single element
1911 * lists into data->list.
1913 * If there is only one component, i.e., if the number of basic sets
1914 * in the current component is equal to the total number of basic sets,
1915 * then data->single is set to 1 and the result of generate_sorted_domains
1918 static int generate_sorted_domains_wrap(__isl_take isl_basic_set_list *scc,
1921 struct isl_ast_generate_parallel_domains_data *data = user;
1922 isl_ast_graft_list *list;
1924 list = generate_sorted_domains(scc, data->executed, data->build);
1925 data->single = isl_basic_set_list_n_basic_set(scc) == data->n;
1927 list = isl_ast_graft_list_fuse(list, data->build);
1931 data->list = isl_ast_graft_list_concat(data->list, list);
1933 isl_basic_set_list_free(scc);
1940 /* Look for any (weakly connected) components in the "domain_list"
1941 * of domains that share some values of the outer dimensions.
1942 * That is, domains in different components do not share any values
1943 * of the outer dimensions. This means that these components
1944 * can be freely reordered.
1945 * Within each of the components, we sort the domains according
1946 * to the execution order at the current depth.
1948 * If there is more than one component, then generate_sorted_domains_wrap
1949 * fuses the result of each call to generate_sorted_domains
1950 * into a list with either zero or one graft and collects these (at most)
1951 * single element lists into a bigger list. This means that the elements of the
1952 * final list can be freely reordered. In particular, we sort them
1953 * according to an arbitrary but fixed ordering to ease merging of
1954 * graft lists from different components.
1956 static __isl_give isl_ast_graft_list *generate_parallel_domains(
1957 __isl_keep isl_basic_set_list *domain_list,
1958 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
1961 struct isl_ast_generate_parallel_domains_data data;
1966 data.n = isl_basic_set_list_n_basic_set(domain_list);
1968 return generate_sorted_domains(domain_list, executed, build);
1970 depth = isl_ast_build_get_depth(build);
1972 data.executed = executed;
1975 if (isl_basic_set_list_foreach_scc(domain_list, &shared_outer, &depth,
1976 &generate_sorted_domains_wrap,
1978 data.list = isl_ast_graft_list_free(data.list);
1981 data.list = isl_ast_graft_list_sort_guard(data.list);
1986 /* Internal data for separate_domain.
1988 * "explicit" is set if we only want to use explicit bounds.
1990 * "domain" collects the separated domains.
1992 struct isl_separate_domain_data {
1993 isl_ast_build *build;
1998 /* Extract implicit bounds on the current dimension for the executed "map".
2000 * The domain of "map" may involve inner dimensions, so we
2001 * need to eliminate them.
2003 static __isl_give isl_set *implicit_bounds(__isl_take isl_map *map,
2004 __isl_keep isl_ast_build *build)
2008 domain = isl_map_domain(map);
2009 domain = isl_ast_build_eliminate(build, domain);
2014 /* Extract explicit bounds on the current dimension for the executed "map".
2016 * Rather than eliminating the inner dimensions as in implicit_bounds,
2017 * we simply drop any constraints involving those inner dimensions.
2018 * The idea is that most bounds that are implied by constraints on the
2019 * inner dimensions will be enforced by for loops and not by explicit guards.
2020 * There is then no need to separate along those bounds.
2022 static __isl_give isl_set *explicit_bounds(__isl_take isl_map *map,
2023 __isl_keep isl_ast_build *build)
2028 dim = isl_map_dim(map, isl_dim_out);
2029 map = isl_map_drop_constraints_involving_dims(map, isl_dim_out, 0, dim);
2031 domain = isl_map_domain(map);
2032 depth = isl_ast_build_get_depth(build);
2033 dim = isl_set_dim(domain, isl_dim_set);
2034 domain = isl_set_detect_equalities(domain);
2035 domain = isl_set_drop_constraints_involving_dims(domain,
2036 isl_dim_set, depth + 1, dim - (depth + 1));
2037 domain = isl_set_remove_divs_involving_dims(domain,
2038 isl_dim_set, depth, 1);
2039 domain = isl_set_remove_unknown_divs(domain);
2044 /* Split data->domain into pieces that intersect with the range of "map"
2045 * and pieces that do not intersect with the range of "map"
2046 * and then add that part of the range of "map" that does not intersect
2047 * with data->domain.
2049 static int separate_domain(__isl_take isl_map *map, void *user)
2051 struct isl_separate_domain_data *data = user;
2056 domain = explicit_bounds(map, data->build);
2058 domain = implicit_bounds(map, data->build);
2060 domain = isl_set_coalesce(domain);
2061 domain = isl_set_make_disjoint(domain);
2062 d1 = isl_set_subtract(isl_set_copy(domain), isl_set_copy(data->domain));
2063 d2 = isl_set_subtract(isl_set_copy(data->domain), isl_set_copy(domain));
2064 data->domain = isl_set_intersect(data->domain, domain);
2065 data->domain = isl_set_union(data->domain, d1);
2066 data->domain = isl_set_union(data->domain, d2);
2071 /* Separate the schedule domains of "executed".
2073 * That is, break up the domain of "executed" into basic sets,
2074 * such that for each basic set S, every element in S is associated with
2075 * the same domain spaces.
2077 * "space" is the (single) domain space of "executed".
2079 static __isl_give isl_set *separate_schedule_domains(
2080 __isl_take isl_space *space, __isl_take isl_union_map *executed,
2081 __isl_keep isl_ast_build *build)
2083 struct isl_separate_domain_data data = { build };
2086 ctx = isl_ast_build_get_ctx(build);
2087 data.explicit = isl_options_get_ast_build_separation_bounds(ctx) ==
2088 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT;
2089 data.domain = isl_set_empty(space);
2090 if (isl_union_map_foreach_map(executed, &separate_domain, &data) < 0)
2091 data.domain = isl_set_free(data.domain);
2093 isl_union_map_free(executed);
2097 /* Temporary data used during the search for a lower bound for unrolling.
2099 * "domain" is the original set for which to find a lower bound
2100 * "depth" is the dimension for which to find a lower boudn
2102 * "lower" is the best lower bound found so far. It is NULL if we have not
2104 * "n" is the corresponding size. If lower is NULL, then the value of n
2107 * "tmp" is a temporary initialized isl_int.
2109 struct isl_find_unroll_data {
2118 /* Check if we can use "c" as a lower bound and if it is better than
2119 * any previously found lower bound.
2121 * If "c" does not involve the dimension at the current depth,
2122 * then we cannot use it.
2123 * Otherwise, let "c" be of the form
2127 * We compute the maximal value of
2129 * -ceil(f(j)/a)) + i + 1
2131 * over the domain. If there is such a value "n", then we know
2133 * -ceil(f(j)/a)) + i + 1 <= n
2137 * i < ceil(f(j)/a)) + n
2139 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2140 * We just need to check if we have found any lower bound before and
2141 * if the new lower bound is better (smaller n) than the previously found
2144 static int update_unrolling_lower_bound(struct isl_find_unroll_data *data,
2145 __isl_keep isl_constraint *c)
2147 isl_aff *aff, *lower;
2148 enum isl_lp_result res;
2150 if (!isl_constraint_is_lower_bound(c, isl_dim_set, data->depth))
2153 lower = isl_constraint_get_bound(c, isl_dim_set, data->depth);
2154 lower = isl_aff_ceil(lower);
2155 aff = isl_aff_copy(lower);
2156 aff = isl_aff_neg(aff);
2157 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, data->depth, 1);
2158 aff = isl_aff_add_constant_si(aff, 1);
2159 res = isl_set_max(data->domain, aff, &data->tmp);
2162 if (res == isl_lp_error)
2164 if (res == isl_lp_unbounded) {
2165 isl_aff_free(lower);
2169 if (isl_int_cmp_si(data->tmp, INT_MAX) <= 0 &&
2170 (!data->lower || isl_int_cmp_si(data->tmp, *data->n) < 0)) {
2171 isl_aff_free(data->lower);
2172 data->lower = lower;
2173 *data->n = isl_int_get_si(data->tmp);
2175 isl_aff_free(lower);
2179 isl_aff_free(lower);
2183 /* Check if we can use "c" as a lower bound and if it is better than
2184 * any previously found lower bound.
2186 static int constraint_find_unroll(__isl_take isl_constraint *c, void *user)
2188 struct isl_find_unroll_data *data;
2191 data = (struct isl_find_unroll_data *) user;
2192 r = update_unrolling_lower_bound(data, c);
2193 isl_constraint_free(c);
2198 /* Look for a lower bound l(i) on the dimension at "depth"
2199 * and a size n such that "domain" is a subset of
2201 * { [i] : l(i) <= i_d < l(i) + n }
2203 * where d is "depth" and l(i) depends only on earlier dimensions.
2204 * Furthermore, try and find a lower bound such that n is as small as possible.
2205 * In particular, "n" needs to be finite.
2207 * Inner dimensions have been eliminated from "domain" by the caller.
2209 * We first construct a collection of lower bounds on the input set
2210 * by computing its simple hull. We then iterate through them,
2211 * discarding those that we cannot use (either because they do not
2212 * involve the dimension at "depth" or because they have no corresponding
2213 * upper bound, meaning that "n" would be unbounded) and pick out the
2214 * best from the remaining ones.
2216 * If we cannot find a suitable lower bound, then we consider that
2219 static __isl_give isl_aff *find_unroll_lower_bound(__isl_keep isl_set *domain,
2222 struct isl_find_unroll_data data = { domain, depth, NULL, n };
2223 isl_basic_set *hull;
2225 isl_int_init(data.tmp);
2226 hull = isl_set_simple_hull(isl_set_copy(domain));
2228 if (isl_basic_set_foreach_constraint(hull,
2229 &constraint_find_unroll, &data) < 0)
2232 isl_basic_set_free(hull);
2233 isl_int_clear(data.tmp);
2236 isl_die(isl_set_get_ctx(domain), isl_error_invalid,
2237 "cannot find lower bound for unrolling", return NULL);
2241 isl_basic_set_free(hull);
2242 isl_int_clear(data.tmp);
2243 return isl_aff_free(data.lower);
2246 /* Return the constraint
2248 * i_"depth" = aff + offset
2250 static __isl_give isl_constraint *at_offset(int depth, __isl_keep isl_aff *aff,
2253 aff = isl_aff_copy(aff);
2254 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, depth, -1);
2255 aff = isl_aff_add_constant_si(aff, offset);
2256 return isl_equality_from_aff(aff);
2259 /* Return a list of basic sets, one for each value of the current dimension
2261 * The divs that involve the current dimension have not been projected out
2264 * Since we are going to be iterating over the individual values,
2265 * we first check if there are any strides on the current dimension.
2266 * If there is, we rewrite the current dimension i as
2268 * i = stride i' + offset
2270 * and then iterate over individual values of i' instead.
2272 * We then look for a lower bound on i' and a size such that the domain
2275 * { [j,i'] : l(j) <= i' < l(j) + n }
2277 * and then take slices of the domain at values of i'
2278 * between l(j) and l(j) + n - 1.
2280 * We compute the unshifted simple hull of each slice to ensure that
2281 * we have a single basic set per offset. The slicing constraint
2282 * may get simplified away before the unshifted simple hull is taken
2283 * and may therefore in some rare cases disappear from the result.
2284 * We therefore explicitly add the constraint back after computing
2285 * the unshifted simple hull to ensure that the basic sets
2286 * remain disjoint. The constraints that are dropped by taking the hull
2287 * will be taken into account at the next level, as in the case of the
2290 * Finally, we map i' back to i and add each basic set to the list.
2292 static __isl_give isl_basic_set_list *do_unroll(__isl_take isl_set *domain,
2293 __isl_keep isl_ast_build *build)
2299 isl_basic_set_list *list;
2300 isl_multi_aff *expansion;
2301 isl_basic_map *bmap;
2306 ctx = isl_set_get_ctx(domain);
2307 depth = isl_ast_build_get_depth(build);
2308 build = isl_ast_build_copy(build);
2309 domain = isl_ast_build_eliminate_inner(build, domain);
2310 build = isl_ast_build_detect_strides(build, isl_set_copy(domain));
2311 expansion = isl_ast_build_get_stride_expansion(build);
2313 domain = isl_set_preimage_multi_aff(domain,
2314 isl_multi_aff_copy(expansion));
2315 domain = isl_ast_build_eliminate_divs(build, domain);
2317 isl_ast_build_free(build);
2319 list = isl_basic_set_list_alloc(ctx, 0);
2321 lower = find_unroll_lower_bound(domain, depth, &n);
2323 list = isl_basic_set_list_free(list);
2325 bmap = isl_basic_map_from_multi_aff(expansion);
2327 for (i = 0; list && i < n; ++i) {
2329 isl_basic_set *bset;
2330 isl_constraint *slice;
2332 slice = at_offset(depth, lower, i);
2333 set = isl_set_copy(domain);
2334 set = isl_set_add_constraint(set, isl_constraint_copy(slice));
2335 bset = isl_set_unshifted_simple_hull(set);
2336 bset = isl_basic_set_add_constraint(bset, slice);
2337 bset = isl_basic_set_apply(bset, isl_basic_map_copy(bmap));
2338 list = isl_basic_set_list_add(list, bset);
2341 isl_aff_free(lower);
2342 isl_set_free(domain);
2343 isl_basic_map_free(bmap);
2348 /* Data structure for storing the results and the intermediate objects
2349 * of compute_domains.
2351 * "list" is the main result of the function and contains a list
2352 * of disjoint basic sets for which code should be generated.
2354 * "executed" and "build" are inputs to compute_domains.
2355 * "schedule_domain" is the domain of "executed".
2357 * "option" constains the domains at the current depth that should by
2358 * atomic, separated or unrolled. These domains are as specified by
2359 * the user, except that inner dimensions have been eliminated and
2360 * that they have been made pair-wise disjoint.
2362 * "sep_class" contains the user-specified split into separation classes
2363 * specialized to the current depth.
2364 * "done" contains the union of the separation domains that have already
2366 * "atomic" contains the domain that has effectively been made atomic.
2367 * This domain may be larger than the intersection of option[atomic]
2368 * and the schedule domain.
2370 struct isl_codegen_domains {
2371 isl_basic_set_list *list;
2373 isl_union_map *executed;
2374 isl_ast_build *build;
2375 isl_set *schedule_domain;
2384 /* Add domains to domains->list for each individual value of the current
2385 * dimension, for that part of the schedule domain that lies in the
2386 * intersection of the option domain and the class domain.
2388 * "domain" is the intersection of the class domain and the schedule domain.
2389 * The divs that involve the current dimension have not been projected out
2392 * We first break up the unroll option domain into individual pieces
2393 * and then handle each of them separately. The unroll option domain
2394 * has been made disjoint in compute_domains_init_options,
2396 * Note that we actively want to combine different pieces of the
2397 * schedule domain that have the same value at the current dimension.
2398 * We therefore need to break up the unroll option domain before
2399 * intersecting with class and schedule domain, hoping that the
2400 * unroll option domain specified by the user is relatively simple.
2402 static int compute_unroll_domains(struct isl_codegen_domains *domains,
2403 __isl_keep isl_set *domain)
2405 isl_set *unroll_domain;
2406 isl_basic_set_list *unroll_list;
2410 empty = isl_set_is_empty(domains->option[unroll]);
2416 unroll_domain = isl_set_copy(domains->option[unroll]);
2417 unroll_list = isl_basic_set_list_from_set(unroll_domain);
2419 n = isl_basic_set_list_n_basic_set(unroll_list);
2420 for (i = 0; i < n; ++i) {
2421 isl_basic_set *bset;
2422 isl_basic_set_list *list;
2424 bset = isl_basic_set_list_get_basic_set(unroll_list, i);
2425 unroll_domain = isl_set_from_basic_set(bset);
2426 unroll_domain = isl_set_intersect(unroll_domain,
2427 isl_set_copy(domain));
2429 empty = isl_set_is_empty(unroll_domain);
2430 if (empty >= 0 && empty) {
2431 isl_set_free(unroll_domain);
2435 list = do_unroll(unroll_domain, domains->build);
2436 domains->list = isl_basic_set_list_concat(domains->list, list);
2439 isl_basic_set_list_free(unroll_list);
2444 /* Construct a single basic set that includes the intersection of
2445 * the schedule domain, the atomic option domain and the class domain.
2446 * Add the resulting basic set to domains->list and save a copy
2447 * in domains->atomic for use in compute_partial_domains.
2449 * We construct a single domain rather than trying to combine
2450 * the schedule domains of individual domains because we are working
2451 * within a single component so that non-overlapping schedule domains
2452 * should already have been separated.
2453 * Note, though, that this does not take into account the class domain.
2454 * So, it is possible for a class domain to carve out a piece of the
2455 * schedule domain with independent pieces and then we would only
2456 * generate a single domain for them. If this proves to be problematic
2457 * for some users, then this function will have to be adjusted.
2459 * "domain" is the intersection of the schedule domain and the class domain,
2460 * with inner dimensions projected out.
2462 static int compute_atomic_domain(struct isl_codegen_domains *domains,
2463 __isl_keep isl_set *domain)
2465 isl_basic_set *bset;
2466 isl_set *atomic_domain;
2469 atomic_domain = isl_set_copy(domains->option[atomic]);
2470 atomic_domain = isl_set_intersect(atomic_domain, isl_set_copy(domain));
2471 empty = isl_set_is_empty(atomic_domain);
2472 if (empty < 0 || empty) {
2473 domains->atomic = atomic_domain;
2474 return empty < 0 ? -1 : 0;
2477 atomic_domain = isl_set_coalesce(atomic_domain);
2478 bset = isl_set_unshifted_simple_hull(atomic_domain);
2479 domains->atomic = isl_set_from_basic_set(isl_basic_set_copy(bset));
2480 domains->list = isl_basic_set_list_add(domains->list, bset);
2485 /* Split up the schedule domain into uniform basic sets,
2486 * in the sense that each element in a basic set is associated to
2487 * elements of the same domains, and add the result to domains->list.
2488 * Do this for that part of the schedule domain that lies in the
2489 * intersection of "class_domain" and the separate option domain.
2491 * "class_domain" may or may not include the constraints
2492 * of the schedule domain, but this does not make a difference
2493 * since we are going to intersect it with the domain of the inverse schedule.
2494 * If it includes schedule domain constraints, then they may involve
2495 * inner dimensions, but we will eliminate them in separation_domain.
2497 static int compute_separate_domain(struct isl_codegen_domains *domains,
2498 __isl_keep isl_set *class_domain)
2502 isl_union_map *executed;
2503 isl_basic_set_list *list;
2506 domain = isl_set_copy(domains->option[separate]);
2507 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2508 executed = isl_union_map_copy(domains->executed);
2509 executed = isl_union_map_intersect_domain(executed,
2510 isl_union_set_from_set(domain));
2511 empty = isl_union_map_is_empty(executed);
2512 if (empty < 0 || empty) {
2513 isl_union_map_free(executed);
2514 return empty < 0 ? -1 : 0;
2517 space = isl_set_get_space(class_domain);
2518 domain = separate_schedule_domains(space, executed, domains->build);
2520 list = isl_basic_set_list_from_set(domain);
2521 domains->list = isl_basic_set_list_concat(domains->list, list);
2526 /* Split up the domain at the current depth into disjoint
2527 * basic sets for which code should be generated separately
2528 * for the given separation class domain.
2530 * If any separation classes have been defined, then "class_domain"
2531 * is the domain of the current class and does not refer to inner dimensions.
2532 * Otherwise, "class_domain" is the universe domain.
2534 * We first make sure that the class domain is disjoint from
2535 * previously considered class domains.
2537 * The separate domains can be computed directly from the "class_domain".
2539 * The unroll, atomic and remainder domains need the constraints
2540 * from the schedule domain.
2542 * For unrolling, the actual schedule domain is needed (with divs that
2543 * may refer to the current dimension) so that stride detection can be
2546 * For atomic and remainder domains, inner dimensions and divs involving
2547 * the current dimensions should be eliminated.
2548 * In case we are working within a separation class, we need to intersect
2549 * the result with the current "class_domain" to ensure that the domains
2550 * are disjoint from those generated from other class domains.
2552 * The domain that has been made atomic may be larger than specified
2553 * by the user since it needs to be representable as a single basic set.
2554 * This possibly larger domain is stored in domains->atomic by
2555 * compute_atomic_domain.
2557 * If anything is left after handling separate, unroll and atomic,
2558 * we split it up into basic sets and append the basic sets to domains->list.
2560 static int compute_partial_domains(struct isl_codegen_domains *domains,
2561 __isl_take isl_set *class_domain)
2563 isl_basic_set_list *list;
2566 class_domain = isl_set_subtract(class_domain,
2567 isl_set_copy(domains->done));
2568 domains->done = isl_set_union(domains->done,
2569 isl_set_copy(class_domain));
2571 domain = isl_set_copy(class_domain);
2573 if (compute_separate_domain(domains, domain) < 0)
2575 domain = isl_set_subtract(domain,
2576 isl_set_copy(domains->option[separate]));
2578 domain = isl_set_intersect(domain,
2579 isl_set_copy(domains->schedule_domain));
2581 if (compute_unroll_domains(domains, domain) < 0)
2583 domain = isl_set_subtract(domain,
2584 isl_set_copy(domains->option[unroll]));
2586 domain = isl_ast_build_eliminate(domains->build, domain);
2587 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2589 if (compute_atomic_domain(domains, domain) < 0)
2590 domain = isl_set_free(domain);
2591 domain = isl_set_subtract(domain, domains->atomic);
2593 domain = isl_set_coalesce(domain);
2594 domain = isl_set_make_disjoint(domain);
2596 list = isl_basic_set_list_from_set(domain);
2597 domains->list = isl_basic_set_list_concat(domains->list, list);
2599 isl_set_free(class_domain);
2603 isl_set_free(domain);
2604 isl_set_free(class_domain);
2608 /* Split up the domain at the current depth into disjoint
2609 * basic sets for which code should be generated separately
2610 * for the separation class identified by "pnt".
2612 * We extract the corresponding class domain from domains->sep_class,
2613 * eliminate inner dimensions and pass control to compute_partial_domains.
2615 static int compute_class_domains(__isl_take isl_point *pnt, void *user)
2617 struct isl_codegen_domains *domains = user;
2622 class_set = isl_set_from_point(pnt);
2623 domain = isl_map_domain(isl_map_intersect_range(
2624 isl_map_copy(domains->sep_class), class_set));
2625 domain = isl_ast_build_compute_gist(domains->build, domain);
2626 domain = isl_ast_build_eliminate(domains->build, domain);
2628 disjoint = isl_set_plain_is_disjoint(domain, domains->schedule_domain);
2632 isl_set_free(domain);
2636 return compute_partial_domains(domains, domain);
2639 /* Extract the domains at the current depth that should be atomic,
2640 * separated or unrolled and store them in option.
2642 * The domains specified by the user might overlap, so we make
2643 * them disjoint by subtracting earlier domains from later domains.
2645 static void compute_domains_init_options(isl_set *option[3],
2646 __isl_keep isl_ast_build *build)
2648 enum isl_ast_build_domain_type type, type2;
2650 for (type = atomic; type <= separate; ++type) {
2651 option[type] = isl_ast_build_get_option_domain(build, type);
2652 for (type2 = atomic; type2 < type; ++type2)
2653 option[type] = isl_set_subtract(option[type],
2654 isl_set_copy(option[type2]));
2657 option[unroll] = isl_set_coalesce(option[unroll]);
2658 option[unroll] = isl_set_make_disjoint(option[unroll]);
2661 /* Split up the domain at the current depth into disjoint
2662 * basic sets for which code should be generated separately,
2663 * based on the user-specified options.
2664 * Return the list of disjoint basic sets.
2666 * There are three kinds of domains that we need to keep track of.
2667 * - the "schedule domain" is the domain of "executed"
2668 * - the "class domain" is the domain corresponding to the currrent
2670 * - the "option domain" is the domain corresponding to one of the options
2671 * atomic, unroll or separate
2673 * We first consider the individial values of the separation classes
2674 * and split up the domain for each of them separately.
2675 * Finally, we consider the remainder. If no separation classes were
2676 * specified, then we call compute_partial_domains with the universe
2677 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2678 * with inner dimensions removed. We do this because we want to
2679 * avoid computing the complement of the class domains (i.e., the difference
2680 * between the universe and domains->done).
2682 static __isl_give isl_basic_set_list *compute_domains(
2683 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
2685 struct isl_codegen_domains domains;
2688 isl_union_set *schedule_domain;
2692 enum isl_ast_build_domain_type type;
2698 ctx = isl_union_map_get_ctx(executed);
2699 domains.list = isl_basic_set_list_alloc(ctx, 0);
2701 schedule_domain = isl_union_map_domain(isl_union_map_copy(executed));
2702 domain = isl_set_from_union_set(schedule_domain);
2704 compute_domains_init_options(domains.option, build);
2706 domains.sep_class = isl_ast_build_get_separation_class(build);
2707 classes = isl_map_range(isl_map_copy(domains.sep_class));
2708 n_param = isl_set_dim(classes, isl_dim_param);
2709 classes = isl_set_project_out(classes, isl_dim_param, 0, n_param);
2711 space = isl_set_get_space(domain);
2712 domains.build = build;
2713 domains.schedule_domain = isl_set_copy(domain);
2714 domains.executed = executed;
2715 domains.done = isl_set_empty(space);
2717 if (isl_set_foreach_point(classes, &compute_class_domains, &domains) < 0)
2718 domains.list = isl_basic_set_list_free(domains.list);
2719 isl_set_free(classes);
2721 empty = isl_set_is_empty(domains.done);
2723 domains.list = isl_basic_set_list_free(domains.list);
2724 domain = isl_set_free(domain);
2726 isl_set_free(domain);
2727 domain = isl_set_universe(isl_set_get_space(domains.done));
2729 domain = isl_ast_build_eliminate(build, domain);
2731 if (compute_partial_domains(&domains, domain) < 0)
2732 domains.list = isl_basic_set_list_free(domains.list);
2734 isl_set_free(domains.schedule_domain);
2735 isl_set_free(domains.done);
2736 isl_map_free(domains.sep_class);
2737 for (type = atomic; type <= separate; ++type)
2738 isl_set_free(domains.option[type]);
2740 return domains.list;
2743 /* Generate code for a single component, after shifting (if any)
2746 * We first split up the domain at the current depth into disjoint
2747 * basic sets based on the user-specified options.
2748 * Then we generated code for each of them and concatenate the results.
2750 static __isl_give isl_ast_graft_list *generate_shifted_component(
2751 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
2753 isl_basic_set_list *domain_list;
2754 isl_ast_graft_list *list = NULL;
2756 domain_list = compute_domains(executed, build);
2757 list = generate_parallel_domains(domain_list, executed, build);
2759 isl_basic_set_list_free(domain_list);
2760 isl_union_map_free(executed);
2761 isl_ast_build_free(build);
2766 struct isl_set_map_pair {
2771 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2772 * of indices into the "domain" array,
2773 * return the union of the "map" fields of the elements
2774 * indexed by the first "n" elements of "order".
2776 static __isl_give isl_union_map *construct_component_executed(
2777 struct isl_set_map_pair *domain, int *order, int n)
2781 isl_union_map *executed;
2783 map = isl_map_copy(domain[order[0]].map);
2784 executed = isl_union_map_from_map(map);
2785 for (i = 1; i < n; ++i) {
2786 map = isl_map_copy(domain[order[i]].map);
2787 executed = isl_union_map_add_map(executed, map);
2793 /* Generate code for a single component, after shifting (if any)
2796 * The component inverse schedule is specified as the "map" fields
2797 * of the elements of "domain" indexed by the first "n" elements of "order".
2799 static __isl_give isl_ast_graft_list *generate_shifted_component_from_list(
2800 struct isl_set_map_pair *domain, int *order, int n,
2801 __isl_take isl_ast_build *build)
2803 isl_union_map *executed;
2805 executed = construct_component_executed(domain, order, n);
2806 return generate_shifted_component(executed, build);
2809 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2810 * of indices into the "domain" array,
2811 * do all (except for at most one) of the "set" field of the elements
2812 * indexed by the first "n" elements of "order" have a fixed value
2813 * at position "depth"?
2815 static int at_most_one_non_fixed(struct isl_set_map_pair *domain,
2816 int *order, int n, int depth)
2821 for (i = 0; i < n; ++i) {
2824 f = isl_set_plain_is_fixed(domain[order[i]].set,
2825 isl_dim_set, depth, NULL);
2838 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2839 * of indices into the "domain" array,
2840 * eliminate the inner dimensions from the "set" field of the elements
2841 * indexed by the first "n" elements of "order", provided the current
2842 * dimension does not have a fixed value.
2844 * Return the index of the first element in "order" with a corresponding
2845 * "set" field that does not have an (obviously) fixed value.
2847 static int eliminate_non_fixed(struct isl_set_map_pair *domain,
2848 int *order, int n, int depth, __isl_keep isl_ast_build *build)
2853 for (i = n - 1; i >= 0; --i) {
2855 f = isl_set_plain_is_fixed(domain[order[i]].set,
2856 isl_dim_set, depth, NULL);
2861 domain[order[i]].set = isl_ast_build_eliminate_inner(build,
2862 domain[order[i]].set);
2869 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2870 * of indices into the "domain" array,
2871 * find the element of "domain" (amongst those indexed by the first "n"
2872 * elements of "order") with the "set" field that has the smallest
2873 * value for the current iterator.
2875 * Note that the domain with the smallest value may depend on the parameters
2876 * and/or outer loop dimension. Since the result of this function is only
2877 * used as heuristic, we only make a reasonable attempt at finding the best
2878 * domain, one that should work in case a single domain provides the smallest
2879 * value for the current dimension over all values of the parameters
2880 * and outer dimensions.
2882 * In particular, we compute the smallest value of the first domain
2883 * and replace it by that of any later domain if that later domain
2884 * has a smallest value that is smaller for at least some value
2885 * of the parameters and outer dimensions.
2887 static int first_offset(struct isl_set_map_pair *domain, int *order, int n,
2888 __isl_keep isl_ast_build *build)
2894 min_first = isl_ast_build_map_to_iterator(build,
2895 isl_set_copy(domain[order[0]].set));
2896 min_first = isl_map_lexmin(min_first);
2898 for (i = 1; i < n; ++i) {
2899 isl_map *min, *test;
2902 min = isl_ast_build_map_to_iterator(build,
2903 isl_set_copy(domain[order[i]].set));
2904 min = isl_map_lexmin(min);
2905 test = isl_map_copy(min);
2906 test = isl_map_apply_domain(isl_map_copy(min_first), test);
2907 test = isl_map_order_lt(test, isl_dim_in, 0, isl_dim_out, 0);
2908 empty = isl_map_is_empty(test);
2910 if (empty >= 0 && !empty) {
2911 isl_map_free(min_first);
2921 isl_map_free(min_first);
2923 return i < n ? -1 : first;
2926 /* Construct a shifted inverse schedule based on the original inverse schedule,
2927 * the stride and the offset.
2929 * The original inverse schedule is specified as the "map" fields
2930 * of the elements of "domain" indexed by the first "n" elements of "order".
2932 * "stride" and "offset" are such that the difference
2933 * between the values of the current dimension of domain "i"
2934 * and the values of the current dimension for some reference domain are
2937 * stride * integer + offset[i]
2939 * Moreover, 0 <= offset[i] < stride.
2941 * For each domain, we create a map
2943 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2945 * where j refers to the current dimension and the other dimensions are
2946 * unchanged, and apply this map to the original schedule domain.
2948 * For example, for the original schedule
2950 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2952 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2953 * we apply the mapping
2957 * to the schedule of the "A" domain and the mapping
2959 * { [j - 1] -> [j, 1] }
2961 * to the schedule of the "B" domain.
2964 * Note that after the transformation, the differences between pairs
2965 * of values of the current dimension over all domains are multiples
2966 * of stride and that we have therefore exposed the stride.
2969 * To see that the mapping preserves the lexicographic order,
2970 * first note that each of the individual maps above preserves the order.
2971 * If the value of the current iterator is j1 in one domain and j2 in another,
2972 * then if j1 = j2, we know that the same map is applied to both domains
2973 * and the order is preserved.
2974 * Otherwise, let us assume, without loss of generality, that j1 < j2.
2975 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
2979 * and the order is preserved.
2980 * If c1 < c2, then we know
2986 * j2 - j1 = n * s + r
2988 * with n >= 0 and 0 <= r < s.
2989 * In other words, r = c2 - c1.
3000 * (j1 - c1, c1) << (j2 - c2, c2)
3002 * with "<<" the lexicographic order, proving that the order is preserved
3005 static __isl_give isl_union_map *contruct_shifted_executed(
3006 struct isl_set_map_pair *domain, int *order, int n, isl_int stride,
3007 __isl_keep isl_vec *offset, __isl_keep isl_ast_build *build)
3011 isl_union_map *executed;
3017 depth = isl_ast_build_get_depth(build);
3018 space = isl_ast_build_get_space(build, 1);
3019 executed = isl_union_map_empty(isl_space_copy(space));
3020 space = isl_space_map_from_set(space);
3021 map = isl_map_identity(isl_space_copy(space));
3022 map = isl_map_eliminate(map, isl_dim_out, depth, 1);
3023 map = isl_map_insert_dims(map, isl_dim_out, depth + 1, 1);
3024 space = isl_space_insert_dims(space, isl_dim_out, depth + 1, 1);
3026 c = isl_equality_alloc(isl_local_space_from_space(space));
3027 c = isl_constraint_set_coefficient_si(c, isl_dim_in, depth, 1);
3028 c = isl_constraint_set_coefficient_si(c, isl_dim_out, depth, -1);
3032 for (i = 0; i < n; ++i) {
3035 if (isl_vec_get_element(offset, i, &v) < 0)
3037 map_i = isl_map_copy(map);
3038 map_i = isl_map_fix(map_i, isl_dim_out, depth + 1, v);
3040 c = isl_constraint_set_constant(c, v);
3041 map_i = isl_map_add_constraint(map_i, isl_constraint_copy(c));
3043 map_i = isl_map_apply_domain(isl_map_copy(domain[order[i]].map),
3045 executed = isl_union_map_add_map(executed, map_i);
3048 isl_constraint_free(c);
3054 executed = isl_union_map_free(executed);
3059 /* Generate code for a single component, after exposing the stride,
3060 * given that the schedule domain is "shifted strided".
3062 * The component inverse schedule is specified as the "map" fields
3063 * of the elements of "domain" indexed by the first "n" elements of "order".
3065 * The schedule domain being "shifted strided" means that the differences
3066 * between the values of the current dimension of domain "i"
3067 * and the values of the current dimension for some reference domain are
3070 * stride * integer + offset[i]
3072 * We first look for the domain with the "smallest" value for the current
3073 * dimension and adjust the offsets such that the offset of the "smallest"
3074 * domain is equal to zero. The other offsets are reduced modulo stride.
3076 * Based on this information, we construct a new inverse schedule in
3077 * contruct_shifted_executed that exposes the stride.
3078 * Since this involves the introduction of a new schedule dimension,
3079 * the build needs to be changed accodingly.
3080 * After computing the AST, the newly introduced dimension needs
3081 * to be removed again from the list of grafts. We do this by plugging
3082 * in a mapping that represents the new schedule domain in terms of the
3083 * old schedule domain.
3085 static __isl_give isl_ast_graft_list *generate_shift_component(
3086 struct isl_set_map_pair *domain, int *order, int n, isl_int stride,
3087 __isl_keep isl_vec *offset, __isl_take isl_ast_build *build)
3089 isl_ast_graft_list *list;
3096 isl_multi_aff *ma, *zero;
3097 isl_union_map *executed;
3099 ctx = isl_ast_build_get_ctx(build);
3100 depth = isl_ast_build_get_depth(build);
3102 first = first_offset(domain, order, n, build);
3104 return isl_ast_build_free(build);
3107 v = isl_vec_alloc(ctx, n);
3108 if (isl_vec_get_element(offset, first, &val) < 0)
3109 v = isl_vec_free(v);
3110 isl_int_neg(val, val);
3111 v = isl_vec_set(v, val);
3112 v = isl_vec_add(v, isl_vec_copy(offset));
3113 v = isl_vec_fdiv_r(v, stride);
3115 executed = contruct_shifted_executed(domain, order, n, stride, v,
3117 space = isl_ast_build_get_space(build, 1);
3118 space = isl_space_map_from_set(space);
3119 ma = isl_multi_aff_identity(isl_space_copy(space));
3120 space = isl_space_from_domain(isl_space_domain(space));
3121 space = isl_space_add_dims(space, isl_dim_out, 1);
3122 zero = isl_multi_aff_zero(space);
3123 ma = isl_multi_aff_range_splice(ma, depth + 1, zero);
3124 build = isl_ast_build_insert_dim(build, depth + 1);
3125 list = generate_shifted_component(executed, build);
3127 list = isl_ast_graft_list_preimage_multi_aff(list, ma);
3135 /* Generate code for a single component.
3137 * The component inverse schedule is specified as the "map" fields
3138 * of the elements of "domain" indexed by the first "n" elements of "order".
3140 * This function may modify the "set" fields of "domain".
3142 * Before proceeding with the actual code generation for the component,
3143 * we first check if there are any "shifted" strides, meaning that
3144 * the schedule domains of the individual domains are all strided,
3145 * but that they have different offsets, resulting in the union
3146 * of schedule domains not being strided anymore.
3148 * The simplest example is the schedule
3150 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3152 * Both schedule domains are strided, but their union is not.
3153 * This function detects such cases and then rewrites the schedule to
3155 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3157 * In the new schedule, the schedule domains have the same offset (modulo
3158 * the stride), ensuring that the union of schedule domains is also strided.
3161 * If there is only a single domain in the component, then there is
3162 * nothing to do. Similarly, if the current schedule dimension has
3163 * a fixed value for almost all domains then there is nothing to be done.
3164 * In particular, we need at least two domains where the current schedule
3165 * dimension does not have a fixed value.
3166 * Finally, if any of the options refer to the current schedule dimension,
3167 * then we bail out as well. It would be possible to reformulate the options
3168 * in terms of the new schedule domain, but that would introduce constraints
3169 * that separate the domains in the options and that is something we would
3173 * To see if there is any shifted stride, we look at the differences
3174 * between the values of the current dimension in pairs of domains
3175 * for equal values of outer dimensions. These differences should be
3180 * with "m" the stride and "r" a constant. Note that we cannot perform
3181 * this analysis on individual domains as the lower bound in each domain
3182 * may depend on parameters or outer dimensions and so the current dimension
3183 * itself may not have a fixed remainder on division by the stride.
3185 * In particular, we compare the first domain that does not have an
3186 * obviously fixed value for the current dimension to itself and all
3187 * other domains and collect the offsets and the gcd of the strides.
3188 * If the gcd becomes one, then we failed to find shifted strides.
3189 * If all the offsets are the same (for those domains that do not have
3190 * an obviously fixed value for the current dimension), then we do not
3191 * apply the transformation.
3192 * If none of the domains were skipped, then there is nothing to do.
3193 * If some of them were skipped, then if we apply separation, the schedule
3194 * domain should get split in pieces with a (non-shifted) stride.
3196 * Otherwise, we apply a shift to expose the stride in
3197 * generate_shift_component.
3199 static __isl_give isl_ast_graft_list *generate_component(
3200 struct isl_set_map_pair *domain, int *order, int n,
3201 __isl_take isl_ast_build *build)
3212 isl_ast_graft_list *list;
3215 depth = isl_ast_build_get_depth(build);
3218 if (skip >= 0 && !skip)
3219 skip = at_most_one_non_fixed(domain, order, n, depth);
3220 if (skip >= 0 && !skip)
3221 skip = isl_ast_build_options_involve_depth(build);
3223 return isl_ast_build_free(build);
3225 return generate_shifted_component_from_list(domain,
3228 base = eliminate_non_fixed(domain, order, n, depth, build);
3230 return isl_ast_build_free(build);
3232 ctx = isl_ast_build_get_ctx(build);
3237 v = isl_vec_alloc(ctx, n);
3240 for (i = 0; i < n; ++i) {
3241 map = isl_map_from_domain_and_range(
3242 isl_set_copy(domain[order[base]].set),
3243 isl_set_copy(domain[order[i]].set));
3244 for (d = 0; d < depth; ++d)
3245 map = isl_map_equate(map, isl_dim_in, d,
3247 deltas = isl_map_deltas(map);
3248 res = isl_set_dim_residue_class(deltas, depth, &m, &r);
3249 isl_set_free(deltas);
3254 isl_int_set(gcd, m);
3256 isl_int_gcd(gcd, gcd, m);
3257 if (isl_int_is_one(gcd))
3259 v = isl_vec_set_element(v, i, r);
3261 res = isl_set_plain_is_fixed(domain[order[i]].set,
3262 isl_dim_set, depth, NULL);
3268 if (fixed && i > base) {
3269 isl_vec_get_element(v, base, &m);
3270 if (isl_int_ne(m, r))
3276 isl_ast_build_free(build);
3278 } else if (i < n || fixed) {
3279 list = generate_shifted_component_from_list(domain,
3282 list = generate_shift_component(domain, order, n, gcd, v,
3294 /* Store both "map" itself and its domain in the
3295 * structure pointed to by *next and advance to the next array element.
3297 static int extract_domain(__isl_take isl_map *map, void *user)
3299 struct isl_set_map_pair **next = user;
3301 (*next)->map = isl_map_copy(map);
3302 (*next)->set = isl_map_domain(map);
3308 /* Internal data for any_scheduled_after.
3310 * "depth" is the number of loops that have already been generated
3311 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3312 * "domain" is an array of set-map pairs corresponding to the different
3313 * iteration domains. The set is the schedule domain, i.e., the domain
3314 * of the inverse schedule, while the map is the inverse schedule itself.
3316 struct isl_any_scheduled_after_data {
3318 int group_coscheduled;
3319 struct isl_set_map_pair *domain;
3322 /* Is any element of domain "i" scheduled after any element of domain "j"
3323 * (for a common iteration of the first data->depth loops)?
3325 * data->domain[i].set contains the domain of the inverse schedule
3326 * for domain "i", i.e., elements in the schedule domain.
3328 * If data->group_coscheduled is set, then we also return 1 if there
3329 * is any pair of elements in the two domains that are scheduled together.
3331 static int any_scheduled_after(int i, int j, void *user)
3333 struct isl_any_scheduled_after_data *data = user;
3334 int dim = isl_set_dim(data->domain[i].set, isl_dim_set);
3337 for (pos = data->depth; pos < dim; ++pos) {
3340 follows = isl_set_follows_at(data->domain[i].set,
3341 data->domain[j].set, pos);
3351 return data->group_coscheduled;
3354 /* Look for independent components at the current depth and generate code
3355 * for each component separately. The resulting lists of grafts are
3356 * merged in an attempt to combine grafts with identical guards.
3358 * Code for two domains can be generated separately if all the elements
3359 * of one domain are scheduled before (or together with) all the elements
3360 * of the other domain. We therefore consider the graph with as nodes
3361 * the domains and an edge between two nodes if any element of the first
3362 * node is scheduled after any element of the second node.
3363 * If the ast_build_group_coscheduled is set, then we also add an edge if
3364 * there is any pair of elements in the two domains that are scheduled
3366 * Code is then generated (by generate_component)
3367 * for each of the strongly connected components in this graph
3368 * in their topological order.
3370 * Since the test is performed on the domain of the inverse schedules of
3371 * the different domains, we precompute these domains and store
3372 * them in data.domain.
3374 static __isl_give isl_ast_graft_list *generate_components(
3375 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
3378 isl_ctx *ctx = isl_ast_build_get_ctx(build);
3379 int n = isl_union_map_n_map(executed);
3380 struct isl_any_scheduled_after_data data;
3381 struct isl_set_map_pair *next;
3382 struct isl_tarjan_graph *g = NULL;
3383 isl_ast_graft_list *list = NULL;
3386 data.domain = isl_calloc_array(ctx, struct isl_set_map_pair, n);
3392 if (isl_union_map_foreach_map(executed, &extract_domain, &next) < 0)
3397 data.depth = isl_ast_build_get_depth(build);
3398 data.group_coscheduled = isl_options_get_ast_build_group_coscheduled(ctx);
3399 g = isl_tarjan_graph_init(ctx, n, &any_scheduled_after, &data);
3401 list = isl_ast_graft_list_alloc(ctx, 0);
3405 isl_ast_graft_list *list_c;
3408 if (g->order[i] == -1)
3409 isl_die(ctx, isl_error_internal, "cannot happen",
3412 while (g->order[i] != -1) {
3416 list_c = generate_component(data.domain,
3417 g->order + first, i - first,
3418 isl_ast_build_copy(build));
3419 list = isl_ast_graft_list_merge(list, list_c, build);
3425 error: list = isl_ast_graft_list_free(list);
3426 isl_tarjan_graph_free(g);
3427 for (i = 0; i < n_domain; ++i) {
3428 isl_map_free(data.domain[i].map);
3429 isl_set_free(data.domain[i].set);
3432 isl_union_map_free(executed);
3433 isl_ast_build_free(build);
3438 /* Generate code for the next level (and all inner levels).
3440 * If "executed" is empty, i.e., no code needs to be generated,
3441 * then we return an empty list.
3443 * If we have already generated code for all loop levels, then we pass
3444 * control to generate_inner_level.
3446 * If "executed" lives in a single space, i.e., if code needs to be
3447 * generated for a single domain, then there can only be a single
3448 * component and we go directly to generate_shifted_component.
3449 * Otherwise, we call generate_components to detect the components
3450 * and to call generate_component on each of them separately.
3452 static __isl_give isl_ast_graft_list *generate_next_level(
3453 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
3457 if (!build || !executed)
3460 if (isl_union_map_is_empty(executed)) {
3461 isl_ctx *ctx = isl_ast_build_get_ctx(build);
3462 isl_union_map_free(executed);
3463 isl_ast_build_free(build);
3464 return isl_ast_graft_list_alloc(ctx, 0);
3467 depth = isl_ast_build_get_depth(build);
3468 if (depth >= isl_set_dim(build->domain, isl_dim_set))
3469 return generate_inner_level(executed, build);
3471 if (isl_union_map_n_map(executed) == 1)
3472 return generate_shifted_component(executed, build);
3474 return generate_components(executed, build);
3476 isl_union_map_free(executed);
3477 isl_ast_build_free(build);
3481 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3482 * internal, executed and build are the inputs to generate_code.
3483 * list collects the output.
3485 struct isl_generate_code_data {
3487 isl_union_map *executed;
3488 isl_ast_build *build;
3490 isl_ast_graft_list *list;
3493 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3497 * with E the external build schedule and S the additional schedule "space",
3498 * reformulate the inverse schedule in terms of the internal schedule domain,
3503 * We first obtain a mapping
3507 * take the inverse and the product with S -> S, resulting in
3509 * [I -> S] -> [E -> S]
3511 * Applying the map to the input produces the desired result.
3513 static __isl_give isl_union_map *internal_executed(
3514 __isl_take isl_union_map *executed, __isl_keep isl_space *space,
3515 __isl_keep isl_ast_build *build)
3519 proj = isl_ast_build_get_schedule_map(build);
3520 proj = isl_map_reverse(proj);
3521 space = isl_space_map_from_set(isl_space_copy(space));
3522 id = isl_map_identity(space);
3523 proj = isl_map_product(proj, id);
3524 executed = isl_union_map_apply_domain(executed,
3525 isl_union_map_from_map(proj));
3529 /* Generate an AST that visits the elements in the range of data->executed
3530 * in the relative order specified by the corresponding image element(s)
3531 * for those image elements that belong to "set".
3532 * Add the result to data->list.
3534 * The caller ensures that "set" is a universe domain.
3535 * "space" is the space of the additional part of the schedule.
3536 * It is equal to the space of "set" if build->domain is parametric.
3537 * Otherwise, it is equal to the range of the wrapped space of "set".
3539 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3540 * was called from an outside user (data->internal not set), then
3541 * the (inverse) schedule refers to the external build domain and needs to
3542 * be transformed to refer to the internal build domain.
3544 * The build is extended to include the additional part of the schedule.
3545 * If the original build space was not parametric, then the options
3546 * in data->build refer only to the additional part of the schedule
3547 * and they need to be adjusted to refer to the complete AST build
3550 * After having adjusted inverse schedule and build, we start generating
3551 * code with the outer loop of the current code generation
3552 * in generate_next_level.
3554 * If the original build space was not parametric, we undo the embedding
3555 * on the resulting isl_ast_node_list so that it can be used within
3556 * the outer AST build.
3558 static int generate_code_in_space(struct isl_generate_code_data *data,
3559 __isl_take isl_set *set, __isl_take isl_space *space)
3561 isl_union_map *executed;
3562 isl_ast_build *build;
3563 isl_ast_graft_list *list;
3566 executed = isl_union_map_copy(data->executed);
3567 executed = isl_union_map_intersect_domain(executed,
3568 isl_union_set_from_set(set));
3570 embed = !isl_set_is_params(data->build->domain);
3571 if (embed && !data->internal)
3572 executed = internal_executed(executed, space, data->build);
3574 build = isl_ast_build_copy(data->build);
3575 build = isl_ast_build_product(build, space);
3577 list = generate_next_level(executed, build);
3579 list = isl_ast_graft_list_unembed(list, embed);
3581 data->list = isl_ast_graft_list_concat(data->list, list);
3586 /* Generate an AST that visits the elements in the range of data->executed
3587 * in the relative order specified by the corresponding domain element(s)
3588 * for those domain elements that belong to "set".
3589 * Add the result to data->list.
3591 * The caller ensures that "set" is a universe domain.
3593 * If the build space S is not parametric, then the space of "set"
3594 * need to be a wrapped relation with S as domain. That is, it needs
3599 * Check this property and pass control to generate_code_in_space
3601 * If the build space is not parametric, then T is the space of "set".
3603 static int generate_code_set(__isl_take isl_set *set, void *user)
3605 struct isl_generate_code_data *data = user;
3606 isl_space *space, *build_space;
3609 space = isl_set_get_space(set);
3611 if (isl_set_is_params(data->build->domain))
3612 return generate_code_in_space(data, set, space);
3614 build_space = isl_ast_build_get_space(data->build, data->internal);
3615 space = isl_space_unwrap(space);
3616 is_domain = isl_space_is_domain(build_space, space);
3617 isl_space_free(build_space);
3618 space = isl_space_range(space);
3623 isl_die(isl_set_get_ctx(set), isl_error_invalid,
3624 "invalid nested schedule space", goto error);
3626 return generate_code_in_space(data, set, space);
3629 isl_space_free(space);
3633 /* Generate an AST that visits the elements in the range of "executed"
3634 * in the relative order specified by the corresponding domain element(s).
3636 * "build" is an isl_ast_build that has either been constructed by
3637 * isl_ast_build_from_context or passed to a callback set by
3638 * isl_ast_build_set_create_leaf.
3639 * In the first case, the space of the isl_ast_build is typically
3640 * a parametric space, although this is currently not enforced.
3641 * In the second case, the space is never a parametric space.
3642 * If the space S is not parametric, then the domain space(s) of "executed"
3643 * need to be wrapped relations with S as domain.
3645 * If the domain of "executed" consists of several spaces, then an AST
3646 * is generated for each of them (in arbitrary order) and the results
3649 * If "internal" is set, then the domain "S" above refers to the internal
3650 * schedule domain representation. Otherwise, it refers to the external
3651 * representation, as returned by isl_ast_build_get_schedule_space.
3653 * We essentially run over all the spaces in the domain of "executed"
3654 * and call generate_code_set on each of them.
3656 static __isl_give isl_ast_graft_list *generate_code(
3657 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build,
3661 struct isl_generate_code_data data = { 0 };
3663 isl_union_set *schedule_domain;
3664 isl_union_map *universe;
3668 space = isl_ast_build_get_space(build, 1);
3669 space = isl_space_align_params(space,
3670 isl_union_map_get_space(executed));
3671 space = isl_space_align_params(space,
3672 isl_union_map_get_space(build->options));
3673 build = isl_ast_build_align_params(build, isl_space_copy(space));
3674 executed = isl_union_map_align_params(executed, space);
3675 if (!executed || !build)
3678 ctx = isl_ast_build_get_ctx(build);
3680 data.internal = internal;
3681 data.executed = executed;
3683 data.list = isl_ast_graft_list_alloc(ctx, 0);
3685 universe = isl_union_map_universe(isl_union_map_copy(executed));
3686 schedule_domain = isl_union_map_domain(universe);
3687 if (isl_union_set_foreach_set(schedule_domain, &generate_code_set,
3689 data.list = isl_ast_graft_list_free(data.list);
3691 isl_union_set_free(schedule_domain);
3692 isl_union_map_free(executed);
3694 isl_ast_build_free(build);
3697 isl_union_map_free(executed);
3698 isl_ast_build_free(build);
3702 /* Generate an AST that visits the elements in the domain of "schedule"
3703 * in the relative order specified by the corresponding image element(s).
3705 * "build" is an isl_ast_build that has either been constructed by
3706 * isl_ast_build_from_context or passed to a callback set by
3707 * isl_ast_build_set_create_leaf.
3708 * In the first case, the space of the isl_ast_build is typically
3709 * a parametric space, although this is currently not enforced.
3710 * In the second case, the space is never a parametric space.
3711 * If the space S is not parametric, then the range space(s) of "schedule"
3712 * need to be wrapped relations with S as domain.
3714 * If the range of "schedule" consists of several spaces, then an AST
3715 * is generated for each of them (in arbitrary order) and the results
3718 * We first initialize the local copies of the relevant options.
3719 * We do this here rather than when the isl_ast_build is created
3720 * because the options may have changed between the construction
3721 * of the isl_ast_build and the call to isl_generate_code.
3723 * The main computation is performed on an inverse schedule (with
3724 * the schedule domain in the domain and the elements to be executed
3725 * in the range) called "executed".
3727 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
3728 __isl_keep isl_ast_build *build, __isl_take isl_union_map *schedule)
3730 isl_ast_graft_list *list;
3732 isl_union_map *executed;
3734 build = isl_ast_build_copy(build);
3735 build = isl_ast_build_set_single_valued(build, 0);
3736 executed = isl_union_map_reverse(schedule);
3737 list = generate_code(executed, isl_ast_build_copy(build), 0);
3738 node = isl_ast_node_from_graft_list(list, build);
3739 isl_ast_build_free(build);