isl_ast_graft.c: store_guard: coalesce guard after taking gist
[isl.git] / isl_ast_codegen.c
blobc5e9a39fb56ce187c432d124dc970b876debb76c
1 /*
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
8 */
10 #include <isl/aff.h>
11 #include <isl/set.h>
12 #include <isl/ilp.h>
13 #include <isl/union_map.h>
14 #include <isl_sort.h>
15 #include <isl_tarjan.h>
16 #include <isl_ast_private.h>
17 #include <isl_ast_build_expr.h>
18 #include <isl_ast_build_private.h>
19 #include <isl_ast_graft_private.h>
20 #include <isl_list_private.h>
22 /* Add the constraint to the list that "user" points to, if it is not
23 * a div constraint.
25 static int collect_constraint(__isl_take isl_constraint *constraint,
26 void *user)
28 isl_constraint_list **list = user;
30 if (isl_constraint_is_div_constraint(constraint))
31 isl_constraint_free(constraint);
32 else
33 *list = isl_constraint_list_add(*list, constraint);
35 return 0;
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)
44 int n;
45 isl_ctx *ctx;
46 isl_constraint_list *list;
48 if (!bset)
49 return NULL;
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);
60 return list;
63 /* Data used in generate_domain.
65 * "build" is the input build.
66 * "list" collects the results.
68 struct isl_generate_domain_data {
69 isl_ast_build *build;
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,
79 int internal);
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
89 * S -> D
91 * then we continue generating code on
93 * [S -> D] -> D
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)
103 isl_map *identity;
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);
117 return 0;
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)
129 return graft;
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)));
134 if (!build)
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);
141 if (!graft->node)
142 graft = isl_ast_graft_free(graft);
144 return 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
168 * single-valued.
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;
182 isl_set *guard;
183 isl_map *map;
184 int sv;
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);
193 if (sv < 0)
194 goto error;
195 if (!sv) {
196 isl_map_free(map);
197 if (data->build->single_valued)
198 map = isl_map_copy(executed);
199 else
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);
214 return 0;
215 error:
216 isl_map_free(map);
217 isl_map_free(executed);
218 return -1;
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)
236 isl_ast_node *node;
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);
243 if (!user_build)
244 node = NULL;
245 else
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)
264 isl_ctx *ctx;
265 struct isl_generate_domain_data data = { build };
267 if (!build || !executed)
268 goto error;
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);
278 if (0)
279 error: data.list = NULL;
280 isl_ast_build_free(build);
281 isl_union_map_free(executed);
282 return data.list;
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)
290 isl_id *id;
292 if (!node || !build)
293 return isl_ast_node_free(node);
294 if (!build->before_each_for)
295 return node;
296 id = build->before_each_for(build, build->before_each_for_user);
297 node = isl_ast_node_set_annotation(node, id);
298 return node;
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)
309 return graft;
310 graft->node = build->after_each_for(graft->node, build,
311 build->after_each_for_user);
312 if (!graft->node)
313 return isl_ast_graft_free(graft);
314 return graft;
317 /* Eliminate the schedule dimension "pos" from "executed" and return
318 * the result.
320 static __isl_give isl_union_map *eliminate(__isl_take isl_union_map *executed,
321 int pos, __isl_keep isl_ast_build *build)
323 isl_space *space;
324 isl_map *elim;
326 space = isl_ast_build_get_space(build, 1);
327 space = isl_space_map_from_set(space);
328 elim = isl_map_identity(space);
329 elim = isl_map_eliminate(elim, isl_dim_in, pos, 1);
331 executed = isl_union_map_apply_domain(executed,
332 isl_union_map_from_map(elim));
334 return executed;
337 /* Check if the constraint "c" is a lower bound on dimension "pos",
338 * an upper bound, or independent of dimension "pos".
340 static int constraint_type(isl_constraint *c, int pos)
342 if (isl_constraint_is_lower_bound(c, isl_dim_set, pos))
343 return 1;
344 if (isl_constraint_is_upper_bound(c, isl_dim_set, pos))
345 return 2;
346 return 0;
349 /* Compare the types of the constraints "a" and "b",
350 * resulting in constraints that are independent of "depth"
351 * to be sorted before the lower bounds on "depth", which in
352 * turn are sorted before the upper bounds on "depth".
354 static int cmp_constraint(const void *a, const void *b, void *user)
356 int *depth = user;
357 isl_constraint * const *c1 = a;
358 isl_constraint * const *c2 = b;
359 int t1 = constraint_type(*c1, *depth);
360 int t2 = constraint_type(*c2, *depth);
362 return t1 - t2;
365 /* Extract a lower bound on dimension "pos" from constraint "c".
367 * If the constraint is of the form
369 * a x + f(...) >= 0
371 * then we essentially return
373 * l = ceil(-f(...)/a)
375 * However, if the current dimension is strided, then we need to make
376 * sure that the lower bound we construct is of the form
378 * f + s a
380 * with f the offset and s the stride.
381 * We therefore compute
383 * f + s * ceil((l - f)/s)
385 static __isl_give isl_aff *lower_bound(__isl_keep isl_constraint *c,
386 int pos, __isl_keep isl_ast_build *build)
388 isl_aff *aff;
390 aff = isl_constraint_get_bound(c, isl_dim_set, pos);
391 aff = isl_aff_ceil(aff);
393 if (isl_ast_build_has_stride(build, pos)) {
394 isl_aff *offset;
395 isl_int stride;
397 isl_int_init(stride);
399 offset = isl_ast_build_get_offset(build, pos);
400 isl_ast_build_get_stride(build, pos, &stride);
402 aff = isl_aff_sub(aff, isl_aff_copy(offset));
403 aff = isl_aff_scale_down(aff, stride);
404 aff = isl_aff_ceil(aff);
405 aff = isl_aff_scale(aff, stride);
406 aff = isl_aff_add(aff, offset);
408 isl_int_clear(stride);
411 aff = isl_ast_build_compute_gist_aff(build, aff);
413 return aff;
416 /* Return the exact lower bound (or upper bound if "upper" is set)
417 * of "domain" as a piecewise affine expression.
419 * If we are computing a lower bound (of a strided dimension), then
420 * we need to make sure it is of the form
422 * f + s a
424 * where f is the offset and s is the stride.
425 * We therefore need to include the stride constraint before computing
426 * the minimum.
428 static __isl_give isl_pw_aff *exact_bound(__isl_keep isl_set *domain,
429 __isl_keep isl_ast_build *build, int upper)
431 isl_set *stride;
432 isl_map *it_map;
433 isl_pw_aff *pa;
434 isl_pw_multi_aff *pma;
436 domain = isl_set_copy(domain);
437 if (!upper) {
438 stride = isl_ast_build_get_stride_constraint(build);
439 domain = isl_set_intersect(domain, stride);
441 it_map = isl_ast_build_map_to_iterator(build, domain);
442 if (upper)
443 pma = isl_map_lexmax_pw_multi_aff(it_map);
444 else
445 pma = isl_map_lexmin_pw_multi_aff(it_map);
446 pa = isl_pw_multi_aff_get_pw_aff(pma, 0);
447 isl_pw_multi_aff_free(pma);
448 pa = isl_ast_build_compute_gist_pw_aff(build, pa);
449 pa = isl_pw_aff_coalesce(pa);
451 return pa;
454 /* Return a list of "n" lower bounds on dimension "pos"
455 * extracted from the "n" constraints starting at "constraint".
456 * If "n" is zero, then we extract a lower bound from "domain" instead.
458 static __isl_give isl_pw_aff_list *lower_bounds(
459 __isl_keep isl_constraint **constraint, int n, int pos,
460 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
462 isl_ctx *ctx;
463 isl_pw_aff_list *list;
464 int i;
466 if (!build)
467 return NULL;
469 if (n == 0) {
470 isl_pw_aff *pa;
471 pa = exact_bound(domain, build, 0);
472 return isl_pw_aff_list_from_pw_aff(pa);
475 ctx = isl_ast_build_get_ctx(build);
476 list = isl_pw_aff_list_alloc(ctx,n);
478 for (i = 0; i < n; ++i) {
479 isl_aff *aff;
481 aff = lower_bound(constraint[i], pos, build);
482 list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
485 return list;
488 /* Return a list of "n" upper bounds on dimension "pos"
489 * extracted from the "n" constraints starting at "constraint".
490 * If "n" is zero, then we extract an upper bound from "domain" instead.
492 static __isl_give isl_pw_aff_list *upper_bounds(
493 __isl_keep isl_constraint **constraint, int n, int pos,
494 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
496 isl_ctx *ctx;
497 isl_pw_aff_list *list;
498 int i;
500 if (n == 0) {
501 isl_pw_aff *pa;
502 pa = exact_bound(domain, build, 1);
503 return isl_pw_aff_list_from_pw_aff(pa);
506 ctx = isl_ast_build_get_ctx(build);
507 list = isl_pw_aff_list_alloc(ctx,n);
509 for (i = 0; i < n; ++i) {
510 isl_aff *aff;
512 aff = isl_constraint_get_bound(constraint[i], isl_dim_set, pos);
513 aff = isl_aff_floor(aff);
514 list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
517 return list;
520 /* Return an isl_ast_expr that performs the reduction of type "type"
521 * on AST expressions corresponding to the elements in "list".
523 * The list is assumed to contain at least one element.
524 * If the list contains exactly one element, then the returned isl_ast_expr
525 * simply computes that affine expression.
527 static __isl_give isl_ast_expr *reduce_list(enum isl_ast_op_type type,
528 __isl_keep isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
530 int i, n;
531 isl_ctx *ctx;
532 isl_ast_expr *expr;
534 if (!list)
535 return NULL;
537 n = isl_pw_aff_list_n_pw_aff(list);
539 if (n == 1)
540 return isl_ast_build_expr_from_pw_aff_internal(build,
541 isl_pw_aff_list_get_pw_aff(list, 0));
543 ctx = isl_pw_aff_list_get_ctx(list);
544 expr = isl_ast_expr_alloc_op(ctx, type, n);
545 if (!expr)
546 return NULL;
548 for (i = 0; i < n; ++i) {
549 isl_ast_expr *expr_i;
551 expr_i = isl_ast_build_expr_from_pw_aff_internal(build,
552 isl_pw_aff_list_get_pw_aff(list, i));
553 if (!expr_i)
554 return isl_ast_expr_free(expr);
555 expr->u.op.args[i] = expr_i;
558 return expr;
561 /* Add a guard to "graft" based on "bound" in the case of a degenerate
562 * level (including the special case of an eliminated level).
564 * We eliminate the current dimension, simplify the result in the current
565 * build and add the result as guards to the graft.
567 * Note that we cannot simply drop the constraints on the current dimension
568 * even in the eliminated case, because the single affine expression may
569 * not be explicitly available in "bounds". Moreover, the single affine
570 * expression may only be defined on a subset of the build domain,
571 * so we do in some cases need to insert a guard even in the eliminated case.
573 static __isl_give isl_ast_graft *add_degenerate_guard(
574 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
575 __isl_keep isl_ast_build *build)
577 int depth;
578 isl_set *dom;
580 depth = isl_ast_build_get_depth(build);
582 dom = isl_set_from_basic_set(isl_basic_set_copy(bounds));
583 if (isl_ast_build_has_stride(build, depth)) {
584 isl_set *stride;
586 stride = isl_ast_build_get_stride_constraint(build);
587 dom = isl_set_intersect(dom, stride);
589 dom = isl_set_eliminate(dom, isl_dim_set, depth, 1);
590 dom = isl_ast_build_compute_gist(build, dom);
592 graft = isl_ast_graft_add_guard(graft, dom, build);
594 return graft;
597 /* Update "graft" based on "bounds" for the eliminated case.
599 * In the eliminated case, no for node is created, so we only need
600 * to check if "bounds" imply any guards that need to be inserted.
602 static __isl_give isl_ast_graft *refine_eliminated(
603 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
604 __isl_keep isl_ast_build *build)
606 return add_degenerate_guard(graft, bounds, build);
609 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
611 * "build" is the build in which graft->node was created
612 * "sub_build" contains information about the current level itself,
613 * including the single value attained.
615 * We first set the initialization part of the for loop to the single
616 * value attained by the current dimension.
617 * The increment and condition are not strictly needed as the are known
618 * to be "1" and "iterator <= value" respectively.
619 * Then we set the size of the iterator and
620 * check if "bounds" imply any guards that need to be inserted.
622 static __isl_give isl_ast_graft *refine_degenerate(
623 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
624 __isl_keep isl_ast_build *build,
625 __isl_keep isl_ast_build *sub_build)
627 isl_pw_aff *value;
629 if (!graft || !sub_build)
630 return isl_ast_graft_free(graft);
632 value = isl_pw_aff_copy(sub_build->value);
634 graft->node->u.f.init = isl_ast_build_expr_from_pw_aff_internal(build,
635 value);
636 if (!graft->node->u.f.init)
637 return isl_ast_graft_free(graft);
639 graft = add_degenerate_guard(graft, bounds, build);
641 return graft;
644 /* Return the intersection of the "n" constraints starting at "constraint"
645 * as a set.
647 static __isl_give isl_set *intersect_constraints(isl_ctx *ctx,
648 __isl_keep isl_constraint **constraint, int n)
650 int i;
651 isl_basic_set *bset;
653 if (n < 1)
654 isl_die(ctx, isl_error_internal,
655 "expecting at least one constraint", return NULL);
657 bset = isl_basic_set_from_constraint(
658 isl_constraint_copy(constraint[0]));
659 for (i = 1; i < n; ++i) {
660 isl_basic_set *bset_i;
662 bset_i = isl_basic_set_from_constraint(
663 isl_constraint_copy(constraint[i]));
664 bset = isl_basic_set_intersect(bset, bset_i);
667 return isl_set_from_basic_set(bset);
670 /* Compute the constraints on the outer dimensions enforced by
671 * graft->node and add those constraints to graft->enforced,
672 * in case the upper bound is expressed as a set "upper".
674 * In particular, if l(...) is a lower bound in "lower", and
676 * -a i + f(...) >= 0 or a i <= f(...)
678 * is an upper bound ocnstraint on the current dimension i,
679 * then the for loop enforces the constraint
681 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
683 * We therefore simply take each lower bound in turn, plug it into
684 * the upper bounds and compute the intersection over all lower bounds.
686 * If a lower bound is a rational expression, then
687 * isl_basic_set_preimage_multi_aff will force this rational
688 * expression to have only integer values. However, the loop
689 * itself does not enforce this integrality constraint. We therefore
690 * use the ceil of the lower bounds instead of the lower bounds themselves.
691 * Other constraints will make sure that the for loop is only executed
692 * when each of the lower bounds attains an integral value.
693 * In particular, potentially rational values only occur in
694 * lower_bound if the offset is a (seemingly) rational expression,
695 * but then outer conditions will make sure that this rational expression
696 * only attains integer values.
698 static __isl_give isl_ast_graft *set_enforced_from_set(
699 __isl_take isl_ast_graft *graft,
700 __isl_keep isl_pw_aff_list *lower, int pos, __isl_keep isl_set *upper)
702 isl_space *space;
703 isl_basic_set *enforced;
704 isl_pw_multi_aff *pma;
705 int i, n;
707 if (!graft || !lower)
708 return isl_ast_graft_free(graft);
710 space = isl_set_get_space(upper);
711 enforced = isl_basic_set_universe(isl_space_copy(space));
713 space = isl_space_map_from_set(space);
714 pma = isl_pw_multi_aff_identity(space);
716 n = isl_pw_aff_list_n_pw_aff(lower);
717 for (i = 0; i < n; ++i) {
718 isl_pw_aff *pa;
719 isl_set *enforced_i;
720 isl_basic_set *hull;
721 isl_pw_multi_aff *pma_i;
723 pa = isl_pw_aff_list_get_pw_aff(lower, i);
724 pa = isl_pw_aff_ceil(pa);
725 pma_i = isl_pw_multi_aff_copy(pma);
726 pma_i = isl_pw_multi_aff_set_pw_aff(pma_i, pos, pa);
727 enforced_i = isl_set_copy(upper);
728 enforced_i = isl_set_preimage_pw_multi_aff(enforced_i, pma_i);
729 hull = isl_set_simple_hull(enforced_i);
730 enforced = isl_basic_set_intersect(enforced, hull);
733 isl_pw_multi_aff_free(pma);
735 graft = isl_ast_graft_enforce(graft, enforced);
737 return graft;
740 /* Compute the constraints on the outer dimensions enforced by
741 * graft->node and add those constraints to graft->enforced,
742 * in case the upper bound is expressed as
743 * a list of affine expressions "upper".
745 * The enforced condition is that each lower bound expression is less
746 * than or equal to each upper bound expression.
748 static __isl_give isl_ast_graft *set_enforced_from_list(
749 __isl_take isl_ast_graft *graft,
750 __isl_keep isl_pw_aff_list *lower, __isl_keep isl_pw_aff_list *upper)
752 isl_set *cond;
753 isl_basic_set *enforced;
755 lower = isl_pw_aff_list_copy(lower);
756 upper = isl_pw_aff_list_copy(upper);
757 cond = isl_pw_aff_list_le_set(lower, upper);
758 enforced = isl_set_simple_hull(cond);
759 graft = isl_ast_graft_enforce(graft, enforced);
761 return graft;
764 /* Does "aff" have a negative constant term?
766 static int aff_constant_is_negative(__isl_take isl_set *set,
767 __isl_take isl_aff *aff, void *user)
769 int *neg = user;
770 isl_int v;
772 isl_int_init(v);
773 isl_aff_get_constant(aff, &v);
774 *neg = isl_int_is_neg(v);
775 isl_int_clear(v);
776 isl_set_free(set);
777 isl_aff_free(aff);
779 return *neg ? 0 : -1;
782 /* Does "pa" have a negative constant term over its entire domain?
784 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff *pa, void *user)
786 int r;
787 int *neg = user;
789 r = isl_pw_aff_foreach_piece(pa, &aff_constant_is_negative, user);
790 isl_pw_aff_free(pa);
792 return *neg ? 0 : -1;
795 /* Does each element in "list" have a negative constant term?
797 * The callback terminates the iteration as soon an element has been
798 * found that does not have a negative constant term.
800 static int list_constant_is_negative(__isl_keep isl_pw_aff_list *list)
802 int neg = 1;
804 if (isl_pw_aff_list_foreach(list,
805 &pw_aff_constant_is_negative, &neg) < 0 && neg)
806 return -1;
808 return neg;
811 /* Add 1 to each of the elements in "list", where each of these elements
812 * is defined over the internal schedule space of "build".
814 static __isl_give isl_pw_aff_list *list_add_one(
815 __isl_take isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
817 int i, n;
818 isl_space *space;
819 isl_aff *aff;
820 isl_pw_aff *one;
822 space = isl_ast_build_get_space(build, 1);
823 aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
824 aff = isl_aff_add_constant_si(aff, 1);
825 one = isl_pw_aff_from_aff(aff);
827 n = isl_pw_aff_list_n_pw_aff(list);
828 for (i = 0; i < n; ++i) {
829 isl_pw_aff *pa;
830 pa = isl_pw_aff_list_get_pw_aff(list, i);
831 pa = isl_pw_aff_add(pa, isl_pw_aff_copy(one));
832 list = isl_pw_aff_list_set_pw_aff(list, i, pa);
835 isl_pw_aff_free(one);
837 return list;
840 /* Set the condition part of the for node graft->node in case
841 * the upper bound is represented as a list of piecewise affine expressions.
843 * In particular, set the condition to
845 * iterator <= min(list of upper bounds)
847 * If each of the upper bounds has a negative constant term, then
848 * set the condition to
850 * iterator < min(list of (upper bound + 1)s)
853 static __isl_give isl_ast_graft *set_for_cond_from_list(
854 __isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *list,
855 __isl_keep isl_ast_build *build)
857 int neg;
858 isl_ast_expr *bound, *iterator, *cond;
859 enum isl_ast_op_type type = isl_ast_op_le;
861 if (!graft || !list)
862 return isl_ast_graft_free(graft);
864 neg = list_constant_is_negative(list);
865 if (neg < 0)
866 return isl_ast_graft_free(graft);
867 list = isl_pw_aff_list_copy(list);
868 if (neg) {
869 list = list_add_one(list, build);
870 type = isl_ast_op_lt;
873 bound = reduce_list(isl_ast_op_min, list, build);
874 iterator = isl_ast_expr_copy(graft->node->u.f.iterator);
875 cond = isl_ast_expr_alloc_binary(type, iterator, bound);
876 graft->node->u.f.cond = cond;
878 isl_pw_aff_list_free(list);
879 if (!graft->node->u.f.cond)
880 return isl_ast_graft_free(graft);
881 return graft;
884 /* Set the condition part of the for node graft->node in case
885 * the upper bound is represented as a set.
887 static __isl_give isl_ast_graft *set_for_cond_from_set(
888 __isl_take isl_ast_graft *graft, __isl_keep isl_set *set,
889 __isl_keep isl_ast_build *build)
891 isl_ast_expr *cond;
893 if (!graft)
894 return NULL;
896 cond = isl_ast_build_expr_from_set(build, isl_set_copy(set));
897 graft->node->u.f.cond = cond;
898 if (!graft->node->u.f.cond)
899 return isl_ast_graft_free(graft);
900 return graft;
903 /* Construct an isl_ast_expr for the increment (i.e., stride) of
904 * the current dimension.
906 static __isl_give isl_ast_expr *for_inc(__isl_keep isl_ast_build *build)
908 int depth;
909 isl_int v;
910 isl_ctx *ctx;
911 isl_ast_expr *inc;
913 if (!build)
914 return NULL;
915 ctx = isl_ast_build_get_ctx(build);
916 depth = isl_ast_build_get_depth(build);
918 if (!isl_ast_build_has_stride(build, depth))
919 return isl_ast_expr_alloc_int_si(ctx, 1);
921 isl_int_init(v);
922 isl_ast_build_get_stride(build, depth, &v);
923 inc = isl_ast_expr_alloc_int(ctx, v);
924 isl_int_clear(v);
926 return inc;
929 /* Should we express the loop condition as
931 * iterator <= min(list of upper bounds)
933 * or as a conjunction of constraints?
935 * The first is constructed from a list of upper bounds.
936 * The second is constructed from a set.
938 * If there are no upper bounds in "constraints", then this could mean
939 * that "domain" simply doesn't have an upper bound or that we didn't
940 * pick any upper bound. In the first case, we want to generate the
941 * loop condition as a(n empty) conjunction of constraints
942 * In the second case, we will compute
943 * a single upper bound from "domain" and so we use the list form.
945 * If there are upper bounds in "constraints",
946 * then we use the list form iff the atomic_upper_bound option is set.
948 static int use_upper_bound_list(isl_ctx *ctx, int n_upper,
949 __isl_keep isl_set *domain, int depth)
951 if (n_upper > 0)
952 return isl_options_get_ast_build_atomic_upper_bound(ctx);
953 else
954 return isl_set_dim_has_upper_bound(domain, isl_dim_set, depth);
957 /* Fill in the expressions of the for node in graft->node.
959 * In particular,
960 * - set the initialization part of the loop to the maximum of the lower bounds
961 * - set the size of the iterator based on the values attained by the iterator
962 * - extract the increment from the stride of the current dimension
963 * - construct the for condition either based on a list of upper bounds
964 * or on a set of upper bound constraints.
966 static __isl_give isl_ast_graft *set_for_node_expressions(
967 __isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *lower,
968 int use_list, __isl_keep isl_pw_aff_list *upper_list,
969 __isl_keep isl_set *upper_set, __isl_keep isl_ast_build *build)
971 isl_ast_node *node;
973 if (!graft)
974 return NULL;
976 build = isl_ast_build_copy(build);
977 build = isl_ast_build_set_enforced(build,
978 isl_ast_graft_get_enforced(graft));
980 node = graft->node;
981 node->u.f.init = reduce_list(isl_ast_op_max, lower, build);
982 node->u.f.inc = for_inc(build);
984 if (use_list)
985 graft = set_for_cond_from_list(graft, upper_list, build);
986 else
987 graft = set_for_cond_from_set(graft, upper_set, build);
989 isl_ast_build_free(build);
991 if (!node->u.f.iterator || !node->u.f.init ||
992 !node->u.f.cond || !node->u.f.inc)
993 return isl_ast_graft_free(graft);
995 return graft;
998 /* Update "graft" based on "bounds" and "domain" for the generic,
999 * non-degenerate, case.
1001 * "constraints" contains the "n_lower" lower and "n_upper" upper bounds
1002 * that the loop node should express.
1003 * "domain" is the subset of the intersection of the constraints
1004 * for which some code is executed.
1006 * There may be zero lower bounds or zero upper bounds in "constraints"
1007 * in case the list of constraints was created
1008 * based on the atomic option or based on separation with explicit bounds.
1009 * In that case, we use "domain" to derive lower and/or upper bounds.
1011 * We first compute a list of one or more lower bounds.
1013 * Then we decide if we want to express the condition as
1015 * iterator <= min(list of upper bounds)
1017 * or as a conjunction of constraints.
1019 * The set of enforced constraints is then computed either based on
1020 * a list of upper bounds or on a set of upper bound constraints.
1021 * We do not compute any enforced constraints if we were forced
1022 * to compute a lower or upper bound using exact_bound. The domains
1023 * of the resulting expressions may imply some bounds on outer dimensions
1024 * that we do not want to appear in the enforced constraints since
1025 * they are not actually enforced by the corresponding code.
1027 * Finally, we fill in the expressions of the for node.
1029 static __isl_give isl_ast_graft *refine_generic_bounds(
1030 __isl_take isl_ast_graft *graft,
1031 __isl_keep isl_constraint **constraint, int n_lower, int n_upper,
1032 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
1034 int depth;
1035 isl_ctx *ctx;
1036 isl_pw_aff_list *lower;
1037 int use_list;
1038 isl_set *upper_set = NULL;
1039 isl_pw_aff_list *upper_list = NULL;
1041 if (!graft || !build)
1042 return isl_ast_graft_free(graft);
1044 depth = isl_ast_build_get_depth(build);
1045 ctx = isl_ast_graft_get_ctx(graft);
1047 use_list = use_upper_bound_list(ctx, n_upper, domain, depth);
1049 lower = lower_bounds(constraint, n_lower, depth, domain, build);
1051 if (use_list)
1052 upper_list = upper_bounds(constraint + n_lower, n_upper, depth,
1053 domain, build);
1054 else if (n_upper > 0)
1055 upper_set = intersect_constraints(ctx, constraint + n_lower,
1056 n_upper);
1057 else
1058 upper_set = isl_set_universe(isl_set_get_space(domain));
1060 if (n_lower == 0 || n_upper == 0)
1062 else if (use_list)
1063 graft = set_enforced_from_list(graft, lower, upper_list);
1064 else
1065 graft = set_enforced_from_set(graft, lower, depth, upper_set);
1067 graft = set_for_node_expressions(graft, lower, use_list, upper_list,
1068 upper_set, build);
1070 isl_pw_aff_list_free(lower);
1071 isl_pw_aff_list_free(upper_list);
1072 isl_set_free(upper_set);
1074 return graft;
1077 /* How many constraints in the "constraint" array, starting at position "first"
1078 * are of the give type? "n" represents the total number of elements
1079 * in the array.
1081 static int count_constraints(isl_constraint **constraint, int n, int first,
1082 int pos, int type)
1084 int i;
1086 constraint += first;
1088 for (i = 0; first + i < n; i++)
1089 if (constraint_type(constraint[i], pos) != type)
1090 break;
1092 return i;
1095 /* Update "graft" based on "bounds" and "domain" for the generic,
1096 * non-degenerate, case.
1098 * "list" respresent the list of bounds that need to be encoded by
1099 * the for loop (or a guard around the for loop).
1100 * "domain" is the subset of the intersection of the constraints
1101 * for which some code is executed.
1102 * "build" is the build in which graft->node was created.
1104 * We separate lower bounds, upper bounds and constraints that
1105 * are independent of the loop iterator.
1107 * The actual for loop bounds are generated in refine_generic_bounds.
1108 * If there are any constraints that are independent of the loop iterator,
1109 * we need to put a guard around the for loop (which may get hoisted up
1110 * to higher levels) and we call refine_generic_bounds in a build
1111 * where this guard is enforced.
1113 static __isl_give isl_ast_graft *refine_generic_split(
1114 __isl_take isl_ast_graft *graft, __isl_keep isl_constraint_list *list,
1115 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
1117 isl_ctx *ctx;
1118 isl_ast_build *for_build;
1119 isl_set *guard;
1120 int n_indep, n_lower, n_upper;
1121 int pos;
1122 int n;
1124 if (!list)
1125 return isl_ast_graft_free(graft);
1127 pos = isl_ast_build_get_depth(build);
1129 if (isl_sort(list->p, list->n, sizeof(isl_constraint *),
1130 &cmp_constraint, &pos) < 0)
1131 return isl_ast_graft_free(graft);
1133 n = list->n;
1134 n_indep = count_constraints(list->p, n, 0, pos, 0);
1135 n_lower = count_constraints(list->p, n, n_indep, pos, 1);
1136 n_upper = count_constraints(list->p, n, n_indep + n_lower, pos, 2);
1138 if (n_indep == 0)
1139 return refine_generic_bounds(graft,
1140 list->p + n_indep, n_lower, n_upper, domain, build);
1142 ctx = isl_ast_graft_get_ctx(graft);
1143 guard = intersect_constraints(ctx, list->p, n_indep);
1145 for_build = isl_ast_build_copy(build);
1146 for_build = isl_ast_build_restrict_pending(for_build,
1147 isl_set_copy(guard));
1148 graft = refine_generic_bounds(graft,
1149 list->p + n_indep, n_lower, n_upper, domain, for_build);
1150 isl_ast_build_free(for_build);
1152 graft = isl_ast_graft_add_guard(graft, guard, build);
1154 return graft;
1157 /* Update "graft" based on "bounds" and "domain" for the generic,
1158 * non-degenerate, case.
1160 * "bounds" respresent the bounds that need to be encoded by
1161 * the for loop (or a guard around the for loop).
1162 * "domain" is the subset of "bounds" for which some code is executed.
1163 * "build" is the build in which graft->node was created.
1165 * We break up "bounds" into a list of constraints and continue with
1166 * refine_generic_split.
1168 static __isl_give isl_ast_graft *refine_generic(
1169 __isl_take isl_ast_graft *graft,
1170 __isl_keep isl_basic_set *bounds, __isl_keep isl_set *domain,
1171 __isl_keep isl_ast_build *build)
1173 isl_constraint_list *list;
1175 if (!build || !graft)
1176 return isl_ast_graft_free(graft);
1178 bounds = isl_basic_set_copy(bounds);
1179 bounds = isl_ast_build_compute_gist_basic_set(build, bounds);
1180 list = isl_constraint_list_from_basic_set(bounds);
1182 graft = refine_generic_split(graft, list, domain, build);
1184 isl_constraint_list_free(list);
1185 return graft;
1188 /* Create a for node for the current level.
1190 * Mark the for node degenerate if "degenerate" is set.
1192 static __isl_give isl_ast_node *create_for(__isl_keep isl_ast_build *build,
1193 int degenerate)
1195 int depth;
1196 isl_id *id;
1197 isl_ast_node *node;
1199 if (!build)
1200 return NULL;
1202 depth = isl_ast_build_get_depth(build);
1203 id = isl_ast_build_get_iterator_id(build, depth);
1204 node = isl_ast_node_alloc_for(id);
1205 if (degenerate)
1206 node = isl_ast_node_for_mark_degenerate(node);
1208 return node;
1211 /* Create an AST node for the current dimension based on
1212 * the schedule domain "bounds" and return the node encapsulated
1213 * in an isl_ast_graft.
1215 * "executed" is the current inverse schedule, taking into account
1216 * the bounds in "bounds"
1217 * "domain" is the domain of "executed", with inner dimensions projected out.
1218 * It may be a strict subset of "bounds" in case "bounds" was created
1219 * based on the atomic option or based on separation with explicit bounds.
1221 * "domain" may satisfy additional equalities that result
1222 * from intersecting "executed" with "bounds" in add_node.
1223 * It may also satisfy some global constraints that were dropped out because
1224 * we performed separation with explicit bounds.
1225 * The very first step is then to copy these constraints to "bounds".
1227 * Since we may be calling before_each_for and after_each_for
1228 * callbacks, we record the current inverse schedule in the build.
1230 * We consider three builds,
1231 * "build" is the one in which the current level is created,
1232 * "body_build" is the build in which the next level is created,
1233 * "sub_build" is essentially the same as "body_build", except that
1234 * the depth has not been increased yet.
1236 * "build" already contains information (in strides and offsets)
1237 * about the strides at the current level, but this information is not
1238 * reflected in the build->domain.
1239 * We first add this information and the "bounds" to the sub_build->domain.
1240 * isl_ast_build_set_loop_bounds checks whether the current dimension attains
1241 * only a single value and whether this single value can be represented using
1242 * a single affine expression.
1243 * In the first case, the current level is considered "degenerate".
1244 * In the second, sub-case, the current level is considered "eliminated".
1245 * Eliminated level don't need to be reflected in the AST since we can
1246 * simply plug in the affine expression. For degenerate, but non-eliminated,
1247 * levels, we do introduce a for node, but mark is as degenerate so that
1248 * it can be printed as an assignment of the single value to the loop
1249 * "iterator".
1251 * If the current level is eliminated, we eliminate the current dimension
1252 * from the inverse schedule to make sure no inner dimensions depend
1253 * on the current dimension. Otherwise, we create a for node, marking
1254 * it degenerate if appropriate. The initial for node is still incomplete
1255 * and will be completed in either refine_degenerate or refine_generic.
1257 * We then generate a sequence of grafts for the next level,
1258 * create a surrounding graft for the current level and insert
1259 * the for node we created (if the current level is not eliminated).
1261 * Finally, we set the bounds of the for loop and insert guards
1262 * (either in the AST or in the graft) in one of
1263 * refine_eliminated, refine_degenerate or refine_generic.
1265 static __isl_give isl_ast_graft *create_node_scaled(
1266 __isl_take isl_union_map *executed,
1267 __isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
1268 __isl_take isl_ast_build *build)
1270 int depth;
1271 int degenerate, eliminated;
1272 isl_basic_set *hull;
1273 isl_ast_node *node = NULL;
1274 isl_ast_graft *graft;
1275 isl_ast_graft_list *children;
1276 isl_ast_build *sub_build;
1277 isl_ast_build *body_build;
1279 domain = isl_ast_build_eliminate_divs(build, domain);
1280 domain = isl_set_detect_equalities(domain);
1281 hull = isl_set_unshifted_simple_hull(isl_set_copy(domain));
1282 bounds = isl_basic_set_intersect(bounds, hull);
1283 build = isl_ast_build_set_executed(build, isl_union_map_copy(executed));
1285 depth = isl_ast_build_get_depth(build);
1286 sub_build = isl_ast_build_copy(build);
1287 sub_build = isl_ast_build_include_stride(sub_build);
1288 sub_build = isl_ast_build_set_loop_bounds(sub_build,
1289 isl_basic_set_copy(bounds));
1290 degenerate = isl_ast_build_has_value(sub_build);
1291 eliminated = isl_ast_build_has_affine_value(sub_build, depth);
1292 if (degenerate < 0 || eliminated < 0)
1293 executed = isl_union_map_free(executed);
1294 if (eliminated)
1295 executed = eliminate(executed, depth, build);
1296 else
1297 node = create_for(build, degenerate);
1299 body_build = isl_ast_build_copy(sub_build);
1300 body_build = isl_ast_build_increase_depth(body_build);
1301 if (!eliminated)
1302 node = before_each_for(node, body_build);
1303 children = generate_next_level(executed,
1304 isl_ast_build_copy(body_build));
1306 graft = isl_ast_graft_alloc_level(children, build, sub_build);
1307 if (!eliminated)
1308 graft = isl_ast_graft_insert_for(graft, node);
1309 if (eliminated)
1310 graft = refine_eliminated(graft, bounds, build);
1311 else if (degenerate)
1312 graft = refine_degenerate(graft, bounds, build, sub_build);
1313 else
1314 graft = refine_generic(graft, bounds, domain, build);
1315 if (!eliminated)
1316 graft = after_each_for(graft, body_build);
1318 isl_ast_build_free(body_build);
1319 isl_ast_build_free(sub_build);
1320 isl_ast_build_free(build);
1321 isl_basic_set_free(bounds);
1322 isl_set_free(domain);
1324 return graft;
1327 /* Internal data structure for checking if all constraints involving
1328 * the input dimension "depth" are such that the other coefficients
1329 * are multiples of "m", reducing "m" if they are not.
1330 * If "m" is reduced all the way down to "1", then the check has failed
1331 * and we break out of the iteration.
1332 * "d" is an initialized isl_int that can be used internally.
1334 struct isl_check_scaled_data {
1335 int depth;
1336 isl_int m, d;
1339 /* If constraint "c" involves the input dimension data->depth,
1340 * then make sure that all the other coefficients are multiples of data->m,
1341 * reducing data->m if needed.
1342 * Break out of the iteration if data->m has become equal to "1".
1344 static int constraint_check_scaled(__isl_take isl_constraint *c, void *user)
1346 struct isl_check_scaled_data *data = user;
1347 int i, j, n;
1348 enum isl_dim_type t[] = { isl_dim_param, isl_dim_in, isl_dim_out,
1349 isl_dim_div };
1351 if (!isl_constraint_involves_dims(c, isl_dim_in, data->depth, 1)) {
1352 isl_constraint_free(c);
1353 return 0;
1356 for (i = 0; i < 4; ++i) {
1357 n = isl_constraint_dim(c, t[i]);
1358 for (j = 0; j < n; ++j) {
1359 if (t[i] == isl_dim_in && j == data->depth)
1360 continue;
1361 if (!isl_constraint_involves_dims(c, t[i], j, 1))
1362 continue;
1363 isl_constraint_get_coefficient(c, t[i], j, &data->d);
1364 isl_int_gcd(data->m, data->m, data->d);
1365 if (isl_int_is_one(data->m))
1366 break;
1368 if (j < n)
1369 break;
1372 isl_constraint_free(c);
1374 return i < 4 ? -1 : 0;
1377 /* For each constraint of "bmap" that involves the input dimension data->depth,
1378 * make sure that all the other coefficients are multiples of data->m,
1379 * reducing data->m if needed.
1380 * Break out of the iteration if data->m has become equal to "1".
1382 static int basic_map_check_scaled(__isl_take isl_basic_map *bmap, void *user)
1384 int r;
1386 r = isl_basic_map_foreach_constraint(bmap,
1387 &constraint_check_scaled, user);
1388 isl_basic_map_free(bmap);
1390 return r;
1393 /* For each constraint of "map" that involves the input dimension data->depth,
1394 * make sure that all the other coefficients are multiples of data->m,
1395 * reducing data->m if needed.
1396 * Break out of the iteration if data->m has become equal to "1".
1398 static int map_check_scaled(__isl_take isl_map *map, void *user)
1400 int r;
1402 r = isl_map_foreach_basic_map(map, &basic_map_check_scaled, user);
1403 isl_map_free(map);
1405 return r;
1408 /* Create an AST node for the current dimension based on
1409 * the schedule domain "bounds" and return the node encapsulated
1410 * in an isl_ast_graft.
1412 * "executed" is the current inverse schedule, taking into account
1413 * the bounds in "bounds"
1414 * "domain" is the domain of "executed", with inner dimensions projected out.
1417 * Before moving on to the actual AST node construction in create_node_scaled,
1418 * we first check if the current dimension is strided and if we can scale
1419 * down this stride. Note that we only do this if the ast_build_scale_strides
1420 * option is set.
1422 * In particular, let the current dimension take on values
1424 * f + s a
1426 * with a an integer. We check if we can find an integer m that (obviouly)
1427 * divides both f and s.
1429 * If so, we check if the current dimension only appears in constraints
1430 * where the coefficients of the other variables are multiples of m.
1431 * We perform this extra check to avoid the risk of introducing
1432 * divisions by scaling down the current dimension.
1434 * If so, we scale the current dimension down by a factor of m.
1435 * That is, we plug in
1437 * i = m i' (1)
1439 * Note that in principle we could always scale down strided loops
1440 * by plugging in
1442 * i = f + s i'
1444 * but this may result in i' taking on larger values than the original i,
1445 * due to the shift by "f".
1446 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1448 static __isl_give isl_ast_graft *create_node(__isl_take isl_union_map *executed,
1449 __isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
1450 __isl_take isl_ast_build *build)
1452 struct isl_check_scaled_data data;
1453 isl_ctx *ctx;
1454 isl_aff *offset;
1456 ctx = isl_ast_build_get_ctx(build);
1457 if (!isl_options_get_ast_build_scale_strides(ctx))
1458 return create_node_scaled(executed, bounds, domain, build);
1460 data.depth = isl_ast_build_get_depth(build);
1461 if (!isl_ast_build_has_stride(build, data.depth))
1462 return create_node_scaled(executed, bounds, domain, build);
1464 isl_int_init(data.m);
1465 isl_int_init(data.d);
1467 offset = isl_ast_build_get_offset(build, data.depth);
1468 if (isl_ast_build_get_stride(build, data.depth, &data.m) < 0)
1469 offset = isl_aff_free(offset);
1470 offset = isl_aff_scale_down(offset, data.m);
1471 if (isl_aff_get_denominator(offset, &data.d) < 0)
1472 executed = isl_union_map_free(executed);
1474 if (executed && isl_int_is_divisible_by(data.m, data.d))
1475 isl_int_divexact(data.m, data.m, data.d);
1476 else
1477 isl_int_set_si(data.m, 1);
1479 if (!isl_int_is_one(data.m)) {
1480 if (isl_union_map_foreach_map(executed, &map_check_scaled,
1481 &data) < 0 &&
1482 !isl_int_is_one(data.m))
1483 executed = isl_union_map_free(executed);
1486 if (!isl_int_is_one(data.m)) {
1487 isl_space *space;
1488 isl_multi_aff *ma;
1489 isl_aff *aff;
1490 isl_map *map;
1491 isl_union_map *umap;
1493 space = isl_ast_build_get_space(build, 1);
1494 space = isl_space_map_from_set(space);
1495 ma = isl_multi_aff_identity(space);
1496 aff = isl_multi_aff_get_aff(ma, data.depth);
1497 aff = isl_aff_scale(aff, data.m);
1498 ma = isl_multi_aff_set_aff(ma, data.depth, aff);
1500 bounds = isl_basic_set_preimage_multi_aff(bounds,
1501 isl_multi_aff_copy(ma));
1502 domain = isl_set_preimage_multi_aff(domain,
1503 isl_multi_aff_copy(ma));
1504 map = isl_map_reverse(isl_map_from_multi_aff(ma));
1505 umap = isl_union_map_from_map(map);
1506 executed = isl_union_map_apply_domain(executed,
1507 isl_union_map_copy(umap));
1508 build = isl_ast_build_scale_down(build, data.m, umap);
1510 isl_aff_free(offset);
1512 isl_int_clear(data.d);
1513 isl_int_clear(data.m);
1515 return create_node_scaled(executed, bounds, domain, build);
1518 /* Add the basic set to the list that "user" points to.
1520 static int collect_basic_set(__isl_take isl_basic_set *bset, void *user)
1522 isl_basic_set_list **list = user;
1524 *list = isl_basic_set_list_add(*list, bset);
1526 return 0;
1529 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1531 static __isl_give isl_basic_set_list *isl_basic_set_list_from_set(
1532 __isl_take isl_set *set)
1534 int n;
1535 isl_ctx *ctx;
1536 isl_basic_set_list *list;
1538 if (!set)
1539 return NULL;
1541 ctx = isl_set_get_ctx(set);
1543 n = isl_set_n_basic_set(set);
1544 list = isl_basic_set_list_alloc(ctx, n);
1545 if (isl_set_foreach_basic_set(set, &collect_basic_set, &list) < 0)
1546 list = isl_basic_set_list_free(list);
1548 isl_set_free(set);
1549 return list;
1552 /* Generate code for the schedule domain "bounds"
1553 * and add the result to "list".
1555 * We mainly detect strides and additional equalities here
1556 * and then pass over control to create_node.
1558 * "bounds" reflects the bounds on the current dimension and possibly
1559 * some extra conditions on outer dimensions.
1560 * It does not, however, include any divs involving the current dimension,
1561 * so it does not capture any stride constraints.
1562 * We therefore need to compute that part of the schedule domain that
1563 * intersects with "bounds" and derive the strides from the result.
1565 static __isl_give isl_ast_graft_list *add_node(
1566 __isl_take isl_ast_graft_list *list, __isl_take isl_union_map *executed,
1567 __isl_take isl_basic_set *bounds, __isl_take isl_ast_build *build)
1569 isl_ast_graft *graft;
1570 isl_set *domain = NULL;
1571 isl_union_set *uset;
1572 int empty;
1574 uset = isl_union_set_from_basic_set(isl_basic_set_copy(bounds));
1575 executed = isl_union_map_intersect_domain(executed, uset);
1576 empty = isl_union_map_is_empty(executed);
1577 if (empty < 0)
1578 goto error;
1579 if (empty)
1580 goto done;
1582 uset = isl_union_map_domain(isl_union_map_copy(executed));
1583 domain = isl_set_from_union_set(uset);
1584 domain = isl_ast_build_compute_gist(build, domain);
1585 empty = isl_set_is_empty(domain);
1586 if (empty < 0)
1587 goto error;
1588 if (empty)
1589 goto done;
1591 domain = isl_ast_build_eliminate_inner(build, domain);
1592 build = isl_ast_build_detect_strides(build, isl_set_copy(domain));
1594 graft = create_node(executed, bounds, domain,
1595 isl_ast_build_copy(build));
1596 list = isl_ast_graft_list_add(list, graft);
1597 isl_ast_build_free(build);
1598 return list;
1599 error:
1600 list = isl_ast_graft_list_free(list);
1601 done:
1602 isl_set_free(domain);
1603 isl_basic_set_free(bounds);
1604 isl_union_map_free(executed);
1605 isl_ast_build_free(build);
1606 return list;
1609 struct isl_domain_follows_at_depth_data {
1610 int depth;
1611 isl_basic_set **piece;
1614 /* Does any element of i follow or coincide with any element of j
1615 * at the current depth (data->depth) for equal values of the outer
1616 * dimensions?
1618 static int domain_follows_at_depth(int i, int j, void *user)
1620 struct isl_domain_follows_at_depth_data *data = user;
1621 isl_basic_map *test;
1622 int empty;
1623 int l;
1625 test = isl_basic_map_from_domain_and_range(
1626 isl_basic_set_copy(data->piece[i]),
1627 isl_basic_set_copy(data->piece[j]));
1628 for (l = 0; l < data->depth; ++l)
1629 test = isl_basic_map_equate(test, isl_dim_in, l,
1630 isl_dim_out, l);
1631 test = isl_basic_map_order_ge(test, isl_dim_in, data->depth,
1632 isl_dim_out, data->depth);
1633 empty = isl_basic_map_is_empty(test);
1634 isl_basic_map_free(test);
1636 return empty < 0 ? -1 : !empty;
1639 static __isl_give isl_ast_graft_list *generate_sorted_domains(
1640 __isl_keep isl_basic_set_list *domain_list,
1641 __isl_keep isl_union_map *executed,
1642 __isl_keep isl_ast_build *build);
1644 /* Generate code for the "n" schedule domains in "domain_list"
1645 * with positions specified by the entries of the "pos" array
1646 * and add the results to "list".
1648 * The "n" domains form a strongly connected component in the ordering.
1649 * If n is larger than 1, then this means that we cannot determine a valid
1650 * ordering for the n domains in the component. This should be fairly
1651 * rare because the individual domains have been made disjoint first.
1652 * The problem is that the domains may be integrally disjoint but not
1653 * rationally disjoint. For example, we may have domains
1655 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1657 * These two domains have an empty intersection, but their rational
1658 * relaxations do intersect. It is impossible to order these domains
1659 * in the second dimension because the first should be ordered before
1660 * the second for outer dimension equal to 0, while it should be ordered
1661 * after for outer dimension equal to 1.
1663 * This may happen in particular in case of unrolling since the domain
1664 * of each slice is replaced by its simple hull.
1666 * We collect the basic sets in the component, call isl_set_make_disjoint
1667 * and try again. Note that we rely here on isl_set_make_disjoint also
1668 * making the basic sets rationally disjoint. If the basic sets
1669 * are rationally disjoint, then the ordering problem does not occur.
1670 * To see this, there can only be a problem if there are points
1671 * (i,a) and (j,b) in one set and (i,c) and (j,d) in the other with
1672 * a < c and b > d. This means that either the interval spanned
1673 * by a en b lies inside that spanned by c and or the other way around.
1674 * In either case, there is a point inside both intervals with the
1675 * convex combination in terms of a and b and in terms of c and d.
1676 * Taking the same combination of i and j gives a point in the intersection.
1678 static __isl_give isl_ast_graft_list *add_nodes(
1679 __isl_take isl_ast_graft_list *list, int *pos, int n,
1680 __isl_keep isl_basic_set_list *domain_list,
1681 __isl_keep isl_union_map *executed,
1682 __isl_keep isl_ast_build *build)
1684 int i;
1685 isl_basic_set *bset;
1686 isl_set *set;
1688 bset = isl_basic_set_list_get_basic_set(domain_list, pos[0]);
1689 if (n == 1)
1690 return add_node(list, isl_union_map_copy(executed), bset,
1691 isl_ast_build_copy(build));
1693 set = isl_set_from_basic_set(bset);
1694 for (i = 1; i < n; ++i) {
1695 bset = isl_basic_set_list_get_basic_set(domain_list, pos[i]);
1696 set = isl_set_union(set, isl_set_from_basic_set(bset));
1699 set = isl_set_make_disjoint(set);
1700 if (isl_set_n_basic_set(set) == n)
1701 isl_die(isl_ast_graft_list_get_ctx(list), isl_error_internal,
1702 "unable to separate loop parts", goto error);
1703 domain_list = isl_basic_set_list_from_set(set);
1704 list = isl_ast_graft_list_concat(list,
1705 generate_sorted_domains(domain_list, executed, build));
1706 isl_basic_set_list_free(domain_list);
1708 return list;
1709 error:
1710 isl_set_free(set);
1711 return isl_ast_graft_list_free(list);
1714 /* Sort the domains in "domain_list" according to the execution order
1715 * at the current depth (for equal values of the outer dimensions),
1716 * generate code for each of them, collecting the results in a list.
1717 * If no code is generated (because the intersection of the inverse schedule
1718 * with the domains turns out to be empty), then an empty list is returned.
1720 * The caller is responsible for ensuring that the basic sets in "domain_list"
1721 * are pair-wise disjoint. It can, however, in principle happen that
1722 * two basic sets should be ordered one way for one value of the outer
1723 * dimensions and the other way for some other value of the outer dimensions.
1724 * We therefore play safe and look for strongly connected components.
1725 * The function add_nodes takes care of handling non-trivial components.
1727 static __isl_give isl_ast_graft_list *generate_sorted_domains(
1728 __isl_keep isl_basic_set_list *domain_list,
1729 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
1731 isl_ctx *ctx;
1732 isl_ast_graft_list *list;
1733 struct isl_domain_follows_at_depth_data data;
1734 struct isl_tarjan_graph *g;
1735 int i, n;
1737 if (!domain_list)
1738 return NULL;
1740 ctx = isl_basic_set_list_get_ctx(domain_list);
1741 n = isl_basic_set_list_n_basic_set(domain_list);
1742 list = isl_ast_graft_list_alloc(ctx, n);
1743 if (n == 0)
1744 return list;
1745 if (n == 1)
1746 return add_node(list, isl_union_map_copy(executed),
1747 isl_basic_set_list_get_basic_set(domain_list, 0),
1748 isl_ast_build_copy(build));
1750 data.depth = isl_ast_build_get_depth(build);
1751 data.piece = domain_list->p;
1752 g = isl_tarjan_graph_init(ctx, n, &domain_follows_at_depth, &data);
1753 if (!g)
1754 goto error;
1756 i = 0;
1757 while (list && n) {
1758 int first;
1760 if (g->order[i] == -1)
1761 isl_die(ctx, isl_error_internal, "cannot happen",
1762 goto error);
1763 first = i;
1764 while (g->order[i] != -1) {
1765 ++i; --n;
1767 list = add_nodes(list, g->order + first, i - first,
1768 domain_list, executed, build);
1769 ++i;
1772 if (0)
1773 error: list = isl_ast_graft_list_free(list);
1774 isl_tarjan_graph_free(g);
1776 return list;
1779 struct isl_shared_outer_data {
1780 int depth;
1781 isl_basic_set **piece;
1784 /* Do elements i and j share any values for the outer dimensions?
1786 static int shared_outer(int i, int j, void *user)
1788 struct isl_shared_outer_data *data = user;
1789 isl_basic_map *test;
1790 int empty;
1791 int l;
1793 test = isl_basic_map_from_domain_and_range(
1794 isl_basic_set_copy(data->piece[i]),
1795 isl_basic_set_copy(data->piece[j]));
1796 for (l = 0; l < data->depth; ++l)
1797 test = isl_basic_map_equate(test, isl_dim_in, l,
1798 isl_dim_out, l);
1799 empty = isl_basic_map_is_empty(test);
1800 isl_basic_map_free(test);
1802 return empty < 0 ? -1 : !empty;
1805 /* Call generate_sorted_domains on a list containing the elements
1806 * of "domain_list indexed by the first "n" elements of "pos".
1808 static __isl_give isl_ast_graft_list *generate_sorted_domains_part(
1809 __isl_keep isl_basic_set_list *domain_list, int *pos, int n,
1810 __isl_keep isl_union_map *executed,
1811 __isl_keep isl_ast_build *build)
1813 int i;
1814 isl_ctx *ctx;
1815 isl_basic_set_list *slice;
1816 isl_ast_graft_list *list;
1818 ctx = isl_ast_build_get_ctx(build);
1819 slice = isl_basic_set_list_alloc(ctx, n);
1820 for (i = 0; i < n; ++i) {
1821 isl_basic_set *bset;
1823 bset = isl_basic_set_copy(domain_list->p[pos[i]]);
1824 slice = isl_basic_set_list_add(slice, bset);
1827 list = generate_sorted_domains(slice, executed, build);
1828 isl_basic_set_list_free(slice);
1830 return list;
1833 /* Look for any (weakly connected) components in the "domain_list"
1834 * of domains that share some values of the outer dimensions.
1835 * That is, domains in different components do not share any values
1836 * of the outer dimensions. This means that these components
1837 * can be freely reordered.
1838 * Within each of the components, we sort the domains according
1839 * to the execution order at the current depth.
1841 * We fuse the result of each call to generate_sorted_domains_part
1842 * into a list with either zero or one graft and collect these (at most)
1843 * single element lists into a bigger list. This means that the elements of the
1844 * final list can be freely reordered. In particular, we sort them
1845 * according to an arbitrary but fixed ordering to ease merging of
1846 * graft lists from different components.
1848 static __isl_give isl_ast_graft_list *generate_parallel_domains(
1849 __isl_keep isl_basic_set_list *domain_list,
1850 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
1852 int i, n;
1853 isl_ctx *ctx;
1854 isl_ast_graft_list *list;
1855 struct isl_shared_outer_data data;
1856 struct isl_tarjan_graph *g;
1858 if (!domain_list)
1859 return NULL;
1861 n = isl_basic_set_list_n_basic_set(domain_list);
1862 if (n <= 1)
1863 return generate_sorted_domains(domain_list, executed, build);
1865 ctx = isl_basic_set_list_get_ctx(domain_list);
1867 data.depth = isl_ast_build_get_depth(build);
1868 data.piece = domain_list->p;
1869 g = isl_tarjan_graph_init(ctx, n, &shared_outer, &data);
1870 if (!g)
1871 return NULL;
1873 i = 0;
1874 do {
1875 int first;
1876 isl_ast_graft_list *list_c;
1878 if (g->order[i] == -1)
1879 isl_die(ctx, isl_error_internal, "cannot happen",
1880 break);
1881 first = i;
1882 while (g->order[i] != -1) {
1883 ++i; --n;
1885 if (first == 0 && n == 0) {
1886 isl_tarjan_graph_free(g);
1887 return generate_sorted_domains(domain_list,
1888 executed, build);
1890 list_c = generate_sorted_domains_part(domain_list,
1891 g->order + first, i - first, executed, build);
1892 list_c = isl_ast_graft_list_fuse(list_c, build);
1893 if (first == 0)
1894 list = list_c;
1895 else
1896 list = isl_ast_graft_list_concat(list, list_c);
1897 ++i;
1898 } while (list && n);
1900 if (n > 0)
1901 list = isl_ast_graft_list_free(list);
1903 list = isl_ast_graft_list_sort_guard(list);
1905 isl_tarjan_graph_free(g);
1907 return list;
1910 /* Internal data for separate_domain.
1912 * "explicit" is set if we only want to use explicit bounds.
1914 * "domain" collects the separated domains.
1916 struct isl_separate_domain_data {
1917 isl_ast_build *build;
1918 int explicit;
1919 isl_set *domain;
1922 /* Extract implicit bounds on the current dimension for the executed "map".
1924 * The domain of "map" may involve inner dimensions, so we
1925 * need to eliminate them.
1927 static __isl_give isl_set *implicit_bounds(__isl_take isl_map *map,
1928 __isl_keep isl_ast_build *build)
1930 isl_set *domain;
1932 domain = isl_map_domain(map);
1933 domain = isl_ast_build_eliminate(build, domain);
1935 return domain;
1938 /* Extract explicit bounds on the current dimension for the executed "map".
1940 * Rather than eliminating the inner dimensions as in implicit_bounds,
1941 * we simply drop any constraints involving those inner dimensions.
1942 * The idea is that most bounds that are implied by constraints on the
1943 * inner dimensions will be enforced by for loops and not by explicit guards.
1944 * There is then no need to separate along those bounds.
1946 static __isl_give isl_set *explicit_bounds(__isl_take isl_map *map,
1947 __isl_keep isl_ast_build *build)
1949 isl_set *domain;
1950 int depth, dim;
1952 dim = isl_map_dim(map, isl_dim_out);
1953 map = isl_map_drop_constraints_involving_dims(map, isl_dim_out, 0, dim);
1955 domain = isl_map_domain(map);
1956 depth = isl_ast_build_get_depth(build);
1957 dim = isl_set_dim(domain, isl_dim_set);
1958 domain = isl_set_detect_equalities(domain);
1959 domain = isl_set_drop_constraints_involving_dims(domain,
1960 isl_dim_set, depth + 1, dim - (depth + 1));
1961 domain = isl_set_remove_divs_involving_dims(domain,
1962 isl_dim_set, depth, 1);
1963 domain = isl_set_remove_unknown_divs(domain);
1965 return domain;
1968 /* Split data->domain into pieces that intersect with the range of "map"
1969 * and pieces that do not intersect with the range of "map"
1970 * and then add that part of the range of "map" that does not intersect
1971 * with data->domain.
1973 static int separate_domain(__isl_take isl_map *map, void *user)
1975 struct isl_separate_domain_data *data = user;
1976 isl_set *domain;
1977 isl_set *d1, *d2;
1979 if (data->explicit)
1980 domain = explicit_bounds(map, data->build);
1981 else
1982 domain = implicit_bounds(map, data->build);
1984 domain = isl_set_coalesce(domain);
1985 domain = isl_set_make_disjoint(domain);
1986 d1 = isl_set_subtract(isl_set_copy(domain), isl_set_copy(data->domain));
1987 d2 = isl_set_subtract(isl_set_copy(data->domain), isl_set_copy(domain));
1988 data->domain = isl_set_intersect(data->domain, domain);
1989 data->domain = isl_set_union(data->domain, d1);
1990 data->domain = isl_set_union(data->domain, d2);
1992 return 0;
1995 /* Separate the schedule domains of "executed".
1997 * That is, break up the domain of "executed" into basic sets,
1998 * such that for each basic set S, every element in S is associated with
1999 * the same domain spaces.
2001 * "space" is the (single) domain space of "executed".
2003 static __isl_give isl_set *separate_schedule_domains(
2004 __isl_take isl_space *space, __isl_take isl_union_map *executed,
2005 __isl_keep isl_ast_build *build)
2007 struct isl_separate_domain_data data = { build };
2008 isl_ctx *ctx;
2010 ctx = isl_ast_build_get_ctx(build);
2011 data.explicit = isl_options_get_ast_build_separation_bounds(ctx) ==
2012 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT;
2013 data.domain = isl_set_empty(space);
2014 if (isl_union_map_foreach_map(executed, &separate_domain, &data) < 0)
2015 data.domain = isl_set_free(data.domain);
2017 isl_union_map_free(executed);
2018 return data.domain;
2021 /* Temporary data used during the search for a lower bound for unrolling.
2023 * "domain" is the original set for which to find a lower bound
2024 * "depth" is the dimension for which to find a lower boudn
2026 * "lower" is the best lower bound found so far. It is NULL if we have not
2027 * found any yet.
2028 * "n" is the corresponding size. If lower is NULL, then the value of n
2029 * is undefined.
2031 * "tmp" is a temporary initialized isl_int.
2033 struct isl_find_unroll_data {
2034 isl_set *domain;
2035 int depth;
2037 isl_aff *lower;
2038 int *n;
2039 isl_int tmp;
2042 /* Check if we can use "c" as a lower bound and if it is better than
2043 * any previously found lower bound.
2045 * If "c" does not involve the dimension at the current depth,
2046 * then we cannot use it.
2047 * Otherwise, let "c" be of the form
2049 * i >= f(j)/a
2051 * We compute the maximal value of
2053 * -ceil(f(j)/a)) + i + 1
2055 * over the domain. If there is such a value "n", then we know
2057 * -ceil(f(j)/a)) + i + 1 <= n
2059 * or
2061 * i < ceil(f(j)/a)) + n
2063 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2064 * We just need to check if we have found any lower bound before and
2065 * if the new lower bound is better (smaller n) than the previously found
2066 * lower bounds.
2068 static int update_unrolling_lower_bound(struct isl_find_unroll_data *data,
2069 __isl_keep isl_constraint *c)
2071 isl_aff *aff, *lower;
2072 enum isl_lp_result res;
2074 if (!isl_constraint_is_lower_bound(c, isl_dim_set, data->depth))
2075 return 0;
2077 lower = isl_constraint_get_bound(c, isl_dim_set, data->depth);
2078 lower = isl_aff_ceil(lower);
2079 aff = isl_aff_copy(lower);
2080 aff = isl_aff_neg(aff);
2081 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, data->depth, 1);
2082 aff = isl_aff_add_constant_si(aff, 1);
2083 res = isl_set_max(data->domain, aff, &data->tmp);
2084 isl_aff_free(aff);
2086 if (res == isl_lp_error)
2087 goto error;
2088 if (res == isl_lp_unbounded) {
2089 isl_aff_free(lower);
2090 return 0;
2093 if (!data->lower || isl_int_cmp_si(data->tmp, *data->n) < 0) {
2094 isl_aff_free(data->lower);
2095 data->lower = lower;
2096 *data->n = isl_int_get_si(data->tmp);
2097 } else
2098 isl_aff_free(lower);
2100 return 1;
2101 error:
2102 isl_aff_free(lower);
2103 return -1;
2106 /* Check if we can use "c" as a lower bound and if it is better than
2107 * any previously found lower bound.
2109 static int constraint_find_unroll(__isl_take isl_constraint *c, void *user)
2111 struct isl_find_unroll_data *data;
2112 int r;
2114 data = (struct isl_find_unroll_data *) user;
2115 r = update_unrolling_lower_bound(data, c);
2116 isl_constraint_free(c);
2118 return r;
2121 /* Look for a lower bound l(i) on the dimension at "depth"
2122 * and a size n such that "domain" is a subset of
2124 * { [i] : l(i) <= i_d < l(i) + n }
2126 * where d is "depth" and l(i) depends only on earlier dimensions.
2127 * Furthermore, try and find a lower bound such that n is as small as possible.
2128 * In particular, "n" needs to be finite.
2130 * Inner dimensions have been eliminated from "domain" by the caller.
2132 * We first construct a collection of lower bounds on the input set
2133 * by computing its simple hull. We then iterate through them,
2134 * discarding those that we cannot use (either because they do not
2135 * involve the dimension at "depth" or because they have no corresponding
2136 * upper bound, meaning that "n" would be unbounded) and pick out the
2137 * best from the remaining ones.
2139 * If we cannot find a suitable lower bound, then we consider that
2140 * to be an error.
2142 static __isl_give isl_aff *find_unroll_lower_bound(__isl_keep isl_set *domain,
2143 int depth, int *n)
2145 struct isl_find_unroll_data data = { domain, depth, NULL, n };
2146 isl_basic_set *hull;
2148 isl_int_init(data.tmp);
2149 hull = isl_set_simple_hull(isl_set_copy(domain));
2151 if (isl_basic_set_foreach_constraint(hull,
2152 &constraint_find_unroll, &data) < 0)
2153 goto error;
2155 isl_basic_set_free(hull);
2156 isl_int_clear(data.tmp);
2158 if (!data.lower)
2159 isl_die(isl_set_get_ctx(domain), isl_error_invalid,
2160 "cannot find lower bound for unrolling", return NULL);
2162 return data.lower;
2163 error:
2164 isl_basic_set_free(hull);
2165 isl_int_clear(data.tmp);
2166 return isl_aff_free(data.lower);
2169 /* Return the constraint
2171 * i_"depth" = aff + offset
2173 static __isl_give isl_constraint *at_offset(int depth, __isl_keep isl_aff *aff,
2174 int offset)
2176 aff = isl_aff_copy(aff);
2177 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, depth, -1);
2178 aff = isl_aff_add_constant_si(aff, offset);
2179 return isl_equality_from_aff(aff);
2182 /* Return a list of basic sets, one for each value of the current dimension
2183 * in "domain".
2184 * The divs that involve the current dimension have not been projected out
2185 * from this domain.
2187 * Since we are going to be iterating over the individual values,
2188 * we first check if there are any strides on the current dimension.
2189 * If there is, we rewrite the current dimension i as
2191 * i = stride i' + offset
2193 * and then iterate over individual values of i' instead.
2195 * We then look for a lower bound on i' and a size such that the domain
2196 * is a subset of
2198 * { [j,i'] : l(j) <= i' < l(j) + n }
2200 * and then take slices of the domain at values of i'
2201 * between l(j) and l(j) + n - 1.
2203 * We compute the unshifted simple hull of each slice to ensure that
2204 * we have a single basic set per offset. The slicing constraint
2205 * may get simplified away before the unshifted simple hull is taken
2206 * and may therefore in some rare cases disappear from the result.
2207 * We therefore explicitly add the constraint back after computing
2208 * the unshifted simple hull to ensure that the basic sets
2209 * remain disjoint. The constraints that are dropped by taking the hull
2210 * will be taken into account at the next level, as in the case of the
2211 * atomic option.
2213 * Finally, we map i' back to i and add each basic set to the list.
2215 static __isl_give isl_basic_set_list *do_unroll(__isl_take isl_set *domain,
2216 __isl_keep isl_ast_build *build)
2218 int i, n;
2219 int depth;
2220 isl_ctx *ctx;
2221 isl_aff *lower;
2222 isl_basic_set_list *list;
2223 isl_multi_aff *expansion;
2224 isl_basic_map *bmap;
2226 if (!domain)
2227 return NULL;
2229 ctx = isl_set_get_ctx(domain);
2230 depth = isl_ast_build_get_depth(build);
2231 build = isl_ast_build_copy(build);
2232 domain = isl_ast_build_eliminate_inner(build, domain);
2233 build = isl_ast_build_detect_strides(build, isl_set_copy(domain));
2234 expansion = isl_ast_build_get_stride_expansion(build);
2236 domain = isl_set_preimage_multi_aff(domain,
2237 isl_multi_aff_copy(expansion));
2238 domain = isl_ast_build_eliminate_divs(build, domain);
2240 isl_ast_build_free(build);
2242 list = isl_basic_set_list_alloc(ctx, 0);
2244 lower = find_unroll_lower_bound(domain, depth, &n);
2245 if (!lower)
2246 list = isl_basic_set_list_free(list);
2248 bmap = isl_basic_map_from_multi_aff(expansion);
2250 for (i = 0; list && i < n; ++i) {
2251 isl_set *set;
2252 isl_basic_set *bset;
2253 isl_constraint *slice;
2255 slice = at_offset(depth, lower, i);
2256 set = isl_set_copy(domain);
2257 set = isl_set_add_constraint(set, isl_constraint_copy(slice));
2258 bset = isl_set_unshifted_simple_hull(set);
2259 bset = isl_basic_set_add_constraint(bset, slice);
2260 bset = isl_basic_set_apply(bset, isl_basic_map_copy(bmap));
2261 list = isl_basic_set_list_add(list, bset);
2264 isl_aff_free(lower);
2265 isl_set_free(domain);
2266 isl_basic_map_free(bmap);
2268 return list;
2271 /* Data structure for storing the results and the intermediate objects
2272 * of compute_domains.
2274 * "list" is the main result of the function and contains a list
2275 * of disjoint basic sets for which code should be generated.
2277 * "executed" and "build" are inputs to compute_domains.
2278 * "schedule_domain" is the domain of "executed".
2280 * "option" constains the domains at the current depth that should by
2281 * atomic, separated or unrolled. These domains are as specified by
2282 * the user, except that inner dimensions have been eliminated and
2283 * that they have been made pair-wise disjoint.
2285 * "sep_class" contains the user-specified split into separation classes
2286 * specialized to the current depth.
2287 * "done" contains the union of th separation domains that have already
2288 * been handled.
2290 struct isl_codegen_domains {
2291 isl_basic_set_list *list;
2293 isl_union_map *executed;
2294 isl_ast_build *build;
2295 isl_set *schedule_domain;
2297 isl_set *option[3];
2299 isl_map *sep_class;
2300 isl_set *done;
2303 /* Add domains to domains->list for each individual value of the current
2304 * dimension, for that part of the schedule domain that lies in the
2305 * intersection of the option domain and the class domain.
2307 * "domain" is the intersection of the class domain and the schedule domain.
2308 * The divs that involve the current dimension have not been projected out
2309 * from this domain.
2311 * We first break up the unroll option domain into individual pieces
2312 * and then handle each of them separately. The unroll option domain
2313 * has been made disjoint in compute_domains_init_options,
2315 * Note that we actively want to combine different pieces of the
2316 * schedule domain that have the same value at the current dimension.
2317 * We therefore need to break up the unroll option domain before
2318 * intersecting with class and schedule domain, hoping that the
2319 * unroll option domain specified by the user is relatively simple.
2321 static int compute_unroll_domains(struct isl_codegen_domains *domains,
2322 __isl_keep isl_set *domain)
2324 isl_set *unroll_domain;
2325 isl_basic_set_list *unroll_list;
2326 int i, n;
2327 int empty;
2329 empty = isl_set_is_empty(domains->option[unroll]);
2330 if (empty < 0)
2331 return -1;
2332 if (empty)
2333 return 0;
2335 unroll_domain = isl_set_copy(domains->option[unroll]);
2336 unroll_list = isl_basic_set_list_from_set(unroll_domain);
2338 n = isl_basic_set_list_n_basic_set(unroll_list);
2339 for (i = 0; i < n; ++i) {
2340 isl_basic_set *bset;
2341 isl_basic_set_list *list;
2343 bset = isl_basic_set_list_get_basic_set(unroll_list, i);
2344 unroll_domain = isl_set_from_basic_set(bset);
2345 unroll_domain = isl_set_intersect(unroll_domain,
2346 isl_set_copy(domain));
2348 empty = isl_set_is_empty(unroll_domain);
2349 if (empty >= 0 && empty) {
2350 isl_set_free(unroll_domain);
2351 continue;
2354 list = do_unroll(unroll_domain, domains->build);
2355 domains->list = isl_basic_set_list_concat(domains->list, list);
2358 isl_basic_set_list_free(unroll_list);
2360 return 0;
2363 /* Construct a single basic set that includes the intersection of
2364 * the schedule domain, the atomic option domain and the class domain.
2365 * Add the resulting basic set to domains->list.
2367 * We construct a single domain rather than trying to combine
2368 * the schedule domains of individual domains because we are working
2369 * within a single component so that non-overlapping schedule domains
2370 * should already have been separated.
2371 * Note, though, that this does not take into account the class domain.
2372 * So, it is possible for a class domain to carve out a piece of the
2373 * schedule domain with independent pieces and then we would only
2374 * generate a single domain for them. If this proves to be problematic
2375 * for some users, then this function will have to be adjusted.
2377 * "domain" is the intersection of the schedule domain and the class domain,
2378 * with inner dimensions projected out.
2380 static int compute_atomic_domain(struct isl_codegen_domains *domains,
2381 __isl_keep isl_set *domain)
2383 isl_basic_set *bset;
2384 isl_set *atomic_domain;
2385 int empty;
2387 atomic_domain = isl_set_copy(domains->option[atomic]);
2388 atomic_domain = isl_set_intersect(atomic_domain, isl_set_copy(domain));
2389 empty = isl_set_is_empty(atomic_domain);
2390 if (empty < 0 || empty) {
2391 isl_set_free(atomic_domain);
2392 return empty < 0 ? -1 : 0;
2395 atomic_domain = isl_set_coalesce(atomic_domain);
2396 bset = isl_set_unshifted_simple_hull(atomic_domain);
2397 domains->list = isl_basic_set_list_add(domains->list, bset);
2399 return 0;
2402 /* Split up the schedule domain into uniform basic sets,
2403 * in the sense that each element in a basic set is associated to
2404 * elements of the same domains, and add the result to domains->list.
2405 * Do this for that part of the schedule domain that lies in the
2406 * intersection of "class_domain" and the separate option domain.
2408 * "class_domain" may or may not include the constraints
2409 * of the schedule domain, but this does not make a difference
2410 * since we are going to intersect it with the domain of the inverse schedule.
2411 * If it includes schedule domain constraints, then they may involve
2412 * inner dimensions, but we will eliminate them in separation_domain.
2414 static int compute_separate_domain(struct isl_codegen_domains *domains,
2415 __isl_keep isl_set *class_domain)
2417 isl_space *space;
2418 isl_set *domain;
2419 isl_union_map *executed;
2420 isl_basic_set_list *list;
2421 int empty;
2423 domain = isl_set_copy(domains->option[separate]);
2424 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2425 executed = isl_union_map_copy(domains->executed);
2426 executed = isl_union_map_intersect_domain(executed,
2427 isl_union_set_from_set(domain));
2428 empty = isl_union_map_is_empty(executed);
2429 if (empty < 0 || empty) {
2430 isl_union_map_free(executed);
2431 return empty < 0 ? -1 : 0;
2434 space = isl_set_get_space(class_domain);
2435 domain = separate_schedule_domains(space, executed, domains->build);
2437 list = isl_basic_set_list_from_set(domain);
2438 domains->list = isl_basic_set_list_concat(domains->list, list);
2440 return 0;
2443 /* Split up the domain at the current depth into disjoint
2444 * basic sets for which code should be generated separately
2445 * for the given separation class domain.
2447 * If any separation classes have been defined, then "class_domain"
2448 * is the domain of the current class and does not refer to inner dimensions.
2449 * Otherwise, "class_domain" is the universe domain.
2451 * We first make sure that the class domain is disjoint from
2452 * previously considered class domains.
2454 * The separate domains can be computed directly from the "class_domain".
2456 * The unroll, atomic and remainder domains need the constraints
2457 * from the schedule domain.
2459 * For unrolling, the actual schedule domain is needed (with divs that
2460 * may refer to the current dimension) so that stride detection can be
2461 * performed.
2463 * For atomic and remainder domains, inner dimensions and divs involving
2464 * the current dimensions should be eliminated.
2465 * In case we are working within a separation class, we need to intersect
2466 * the result with the current "class_domain" to ensure that the domains
2467 * are disjoint from those generated from other class domains.
2469 * If anything is left after handling separate, unroll and atomic,
2470 * we split it up into basic sets and append the basic sets to domains->list.
2472 static int compute_partial_domains(struct isl_codegen_domains *domains,
2473 __isl_take isl_set *class_domain)
2475 isl_basic_set_list *list;
2476 isl_set *domain;
2478 class_domain = isl_set_subtract(class_domain,
2479 isl_set_copy(domains->done));
2480 domains->done = isl_set_union(domains->done,
2481 isl_set_copy(class_domain));
2483 domain = isl_set_copy(class_domain);
2485 if (compute_separate_domain(domains, domain) < 0)
2486 goto error;
2487 domain = isl_set_subtract(domain,
2488 isl_set_copy(domains->option[separate]));
2490 domain = isl_set_intersect(domain,
2491 isl_set_copy(domains->schedule_domain));
2493 if (compute_unroll_domains(domains, domain) < 0)
2494 goto error;
2495 domain = isl_set_subtract(domain,
2496 isl_set_copy(domains->option[unroll]));
2498 domain = isl_ast_build_eliminate(domains->build, domain);
2499 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2501 if (compute_atomic_domain(domains, domain) < 0)
2502 goto error;
2503 domain = isl_set_subtract(domain,
2504 isl_set_copy(domains->option[atomic]));
2506 domain = isl_set_coalesce(domain);
2507 domain = isl_set_make_disjoint(domain);
2509 list = isl_basic_set_list_from_set(domain);
2510 domains->list = isl_basic_set_list_concat(domains->list, list);
2512 isl_set_free(class_domain);
2514 return 0;
2515 error:
2516 isl_set_free(domain);
2517 isl_set_free(class_domain);
2518 return -1;
2521 /* Split up the domain at the current depth into disjoint
2522 * basic sets for which code should be generated separately
2523 * for the separation class identified by "pnt".
2525 * We extract the corresponding class domain from domains->sep_class,
2526 * eliminate inner dimensions and pass control to compute_partial_domains.
2528 static int compute_class_domains(__isl_take isl_point *pnt, void *user)
2530 struct isl_codegen_domains *domains = user;
2531 isl_set *class_set;
2532 isl_set *domain;
2533 int disjoint;
2535 class_set = isl_set_from_point(pnt);
2536 domain = isl_map_domain(isl_map_intersect_range(
2537 isl_map_copy(domains->sep_class), class_set));
2538 domain = isl_ast_build_compute_gist(domains->build, domain);
2539 domain = isl_ast_build_eliminate(domains->build, domain);
2541 disjoint = isl_set_plain_is_disjoint(domain, domains->schedule_domain);
2542 if (disjoint < 0)
2543 return -1;
2544 if (disjoint) {
2545 isl_set_free(domain);
2546 return 0;
2549 return compute_partial_domains(domains, domain);
2552 /* Extract the domains at the current depth that should be atomic,
2553 * separated or unrolled and store them in option.
2555 * The domains specified by the user might overlap, so we make
2556 * them disjoint by subtracting earlier domains from later domains.
2558 static void compute_domains_init_options(isl_set *option[3],
2559 __isl_keep isl_ast_build *build)
2561 enum isl_ast_build_domain_type type, type2;
2563 for (type = atomic; type <= separate; ++type) {
2564 option[type] = isl_ast_build_get_option_domain(build, type);
2565 for (type2 = atomic; type2 < type; ++type2)
2566 option[type] = isl_set_subtract(option[type],
2567 isl_set_copy(option[type2]));
2570 option[unroll] = isl_set_coalesce(option[unroll]);
2571 option[unroll] = isl_set_make_disjoint(option[unroll]);
2574 /* Split up the domain at the current depth into disjoint
2575 * basic sets for which code should be generated separately,
2576 * based on the user-specified options.
2577 * Return the list of disjoint basic sets.
2579 * There are three kinds of domains that we need to keep track of.
2580 * - the "schedule domain" is the domain of "executed"
2581 * - the "class domain" is the domain corresponding to the currrent
2582 * separation class
2583 * - the "option domain" is the domain corresponding to one of the options
2584 * atomic, unroll or separate
2586 * We first consider the individial values of the separation classes
2587 * and split up the domain for each of them separately.
2588 * Finally, we consider the remainder. If no separation classes were
2589 * specified, then we call compute_partial_domains with the universe
2590 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2591 * with inner dimensions removed. We do this because we want to
2592 * avoid computing the complement of the class domains (i.e., the difference
2593 * between the universe and domains->done).
2595 static __isl_give isl_basic_set_list *compute_domains(
2596 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
2598 struct isl_codegen_domains domains;
2599 isl_ctx *ctx;
2600 isl_set *domain;
2601 isl_union_set *schedule_domain;
2602 isl_set *classes;
2603 isl_space *space;
2604 int n_param;
2605 enum isl_ast_build_domain_type type;
2606 int empty;
2608 if (!executed)
2609 return NULL;
2611 ctx = isl_union_map_get_ctx(executed);
2612 domains.list = isl_basic_set_list_alloc(ctx, 0);
2614 schedule_domain = isl_union_map_domain(isl_union_map_copy(executed));
2615 domain = isl_set_from_union_set(schedule_domain);
2617 compute_domains_init_options(domains.option, build);
2619 domains.sep_class = isl_ast_build_get_separation_class(build);
2620 classes = isl_map_range(isl_map_copy(domains.sep_class));
2621 n_param = isl_set_dim(classes, isl_dim_param);
2622 classes = isl_set_project_out(classes, isl_dim_param, 0, n_param);
2624 space = isl_set_get_space(domain);
2625 domains.build = build;
2626 domains.schedule_domain = isl_set_copy(domain);
2627 domains.executed = executed;
2628 domains.done = isl_set_empty(space);
2630 if (isl_set_foreach_point(classes, &compute_class_domains, &domains) < 0)
2631 domains.list = isl_basic_set_list_free(domains.list);
2632 isl_set_free(classes);
2634 empty = isl_set_is_empty(domains.done);
2635 if (empty < 0) {
2636 domains.list = isl_basic_set_list_free(domains.list);
2637 domain = isl_set_free(domain);
2638 } else if (empty) {
2639 isl_set_free(domain);
2640 domain = isl_set_universe(isl_set_get_space(domains.done));
2641 } else {
2642 domain = isl_ast_build_eliminate(build, domain);
2644 if (compute_partial_domains(&domains, domain) < 0)
2645 domains.list = isl_basic_set_list_free(domains.list);
2647 isl_set_free(domains.schedule_domain);
2648 isl_set_free(domains.done);
2649 isl_map_free(domains.sep_class);
2650 for (type = atomic; type <= separate; ++type)
2651 isl_set_free(domains.option[type]);
2653 return domains.list;
2656 /* Generate code for a single component, after shifting (if any)
2657 * has been applied.
2659 * We first split up the domain at the current depth into disjoint
2660 * basic sets based on the user-specified options.
2661 * Then we generated code for each of them and concatenate the results.
2663 static __isl_give isl_ast_graft_list *generate_shifted_component(
2664 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
2666 isl_basic_set_list *domain_list;
2667 isl_ast_graft_list *list = NULL;
2669 domain_list = compute_domains(executed, build);
2670 list = generate_parallel_domains(domain_list, executed, build);
2672 isl_basic_set_list_free(domain_list);
2673 isl_union_map_free(executed);
2674 isl_ast_build_free(build);
2676 return list;
2679 struct isl_set_map_pair {
2680 isl_set *set;
2681 isl_map *map;
2684 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2685 * of indices into the "domain" array,
2686 * return the union of the "map" fields of the elements
2687 * indexed by the first "n" elements of "order".
2689 static __isl_give isl_union_map *construct_component_executed(
2690 struct isl_set_map_pair *domain, int *order, int n)
2692 int i;
2693 isl_map *map;
2694 isl_union_map *executed;
2696 map = isl_map_copy(domain[order[0]].map);
2697 executed = isl_union_map_from_map(map);
2698 for (i = 1; i < n; ++i) {
2699 map = isl_map_copy(domain[order[i]].map);
2700 executed = isl_union_map_add_map(executed, map);
2703 return executed;
2706 /* Generate code for a single component, after shifting (if any)
2707 * has been applied.
2709 * The component inverse schedule is specified as the "map" fields
2710 * of the elements of "domain" indexed by the first "n" elements of "order".
2712 static __isl_give isl_ast_graft_list *generate_shifted_component_from_list(
2713 struct isl_set_map_pair *domain, int *order, int n,
2714 __isl_take isl_ast_build *build)
2716 isl_union_map *executed;
2718 executed = construct_component_executed(domain, order, n);
2719 return generate_shifted_component(executed, build);
2722 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2723 * of indices into the "domain" array,
2724 * do all (except for at most one) of the "set" field of the elements
2725 * indexed by the first "n" elements of "order" have a fixed value
2726 * at position "depth"?
2728 static int at_most_one_non_fixed(struct isl_set_map_pair *domain,
2729 int *order, int n, int depth)
2731 int i;
2732 int non_fixed = -1;
2734 for (i = 0; i < n; ++i) {
2735 int f;
2737 f = isl_set_plain_is_fixed(domain[order[i]].set,
2738 isl_dim_set, depth, NULL);
2739 if (f < 0)
2740 return -1;
2741 if (f)
2742 continue;
2743 if (non_fixed >= 0)
2744 return 0;
2745 non_fixed = i;
2748 return 1;
2751 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2752 * of indices into the "domain" array,
2753 * eliminate the inner dimensions from the "set" field of the elements
2754 * indexed by the first "n" elements of "order", provided the current
2755 * dimension does not have a fixed value.
2757 * Return the index of the first element in "order" with a corresponding
2758 * "set" field that does not have an (obviously) fixed value.
2760 static int eliminate_non_fixed(struct isl_set_map_pair *domain,
2761 int *order, int n, int depth, __isl_keep isl_ast_build *build)
2763 int i;
2764 int base = -1;
2766 for (i = n - 1; i >= 0; --i) {
2767 int f;
2768 f = isl_set_plain_is_fixed(domain[order[i]].set,
2769 isl_dim_set, depth, NULL);
2770 if (f < 0)
2771 return -1;
2772 if (f)
2773 continue;
2774 domain[order[i]].set = isl_ast_build_eliminate_inner(build,
2775 domain[order[i]].set);
2776 base = i;
2779 return base;
2782 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2783 * of indices into the "domain" array,
2784 * find the element of "domain" (amongst those indexed by the first "n"
2785 * elements of "order") with the "set" field that has the smallest
2786 * value for the current iterator.
2788 * Note that the domain with the smallest value may depend on the parameters
2789 * and/or outer loop dimension. Since the result of this function is only
2790 * used as heuristic, we only make a reasonable attempt at finding the best
2791 * domain, one that should work in case a single domain provides the smallest
2792 * value for the current dimension over all values of the parameters
2793 * and outer dimensions.
2795 * In particular, we compute the smallest value of the first domain
2796 * and replace it by that of any later domain if that later domain
2797 * has a smallest value that is smaller for at least some value
2798 * of the parameters and outer dimensions.
2800 static int first_offset(struct isl_set_map_pair *domain, int *order, int n,
2801 __isl_keep isl_ast_build *build)
2803 int i;
2804 isl_map *min_first;
2805 int first = 0;
2807 min_first = isl_ast_build_map_to_iterator(build,
2808 isl_set_copy(domain[order[0]].set));
2809 min_first = isl_map_lexmin(min_first);
2811 for (i = 1; i < n; ++i) {
2812 isl_map *min, *test;
2813 int empty;
2815 min = isl_ast_build_map_to_iterator(build,
2816 isl_set_copy(domain[order[i]].set));
2817 min = isl_map_lexmin(min);
2818 test = isl_map_copy(min);
2819 test = isl_map_apply_domain(isl_map_copy(min_first), test);
2820 test = isl_map_order_lt(test, isl_dim_in, 0, isl_dim_out, 0);
2821 empty = isl_map_is_empty(test);
2822 isl_map_free(test);
2823 if (empty >= 0 && !empty) {
2824 isl_map_free(min_first);
2825 first = i;
2826 min_first = min;
2827 } else
2828 isl_map_free(min);
2830 if (empty < 0)
2831 break;
2834 isl_map_free(min_first);
2836 return i < n ? -1 : first;
2839 /* Construct a shifted inverse schedule based on the original inverse schedule,
2840 * the stride and the offset.
2842 * The original inverse schedule is specified as the "map" fields
2843 * of the elements of "domain" indexed by the first "n" elements of "order".
2845 * "stride" and "offset" are such that the difference
2846 * between the values of the current dimension of domain "i"
2847 * and the values of the current dimension for some reference domain are
2848 * equal to
2850 * stride * integer + offset[i]
2852 * Moreover, 0 <= offset[i] < stride.
2854 * For each domain, we create a map
2856 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2858 * where j refers to the current dimension and the other dimensions are
2859 * unchanged, and apply this map to the original schedule domain.
2861 * For example, for the original schedule
2863 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2865 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2866 * we apply the mapping
2868 * { [j] -> [j, 0] }
2870 * to the schedule of the "A" domain and the mapping
2872 * { [j - 1] -> [j, 1] }
2874 * to the schedule of the "B" domain.
2877 * Note that after the transformation, the differences between pairs
2878 * of values of the current dimension over all domains are multiples
2879 * of stride and that we have therefore exposed the stride.
2882 * To see that the mapping preserves the lexicographic order,
2883 * first note that each of the individual maps above preserves the order.
2884 * If the value of the current iterator is j1 in one domain and j2 in another,
2885 * then if j1 = j2, we know that the same map is applied to both domains
2886 * and the order is preserved.
2887 * Otherwise, let us assume, without loss of generality, that j1 < j2.
2888 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
2890 * j1 - c1 < j2 - c2
2892 * and the order is preserved.
2893 * If c1 < c2, then we know
2895 * 0 <= c2 - c1 < s
2897 * We also have
2899 * j2 - j1 = n * s + r
2901 * with n >= 0 and 0 <= r < s.
2902 * In other words, r = c2 - c1.
2903 * If n > 0, then
2905 * j1 - c1 < j2 - c2
2907 * If n = 0, then
2909 * j1 - c1 = j2 - c2
2911 * and so
2913 * (j1 - c1, c1) << (j2 - c2, c2)
2915 * with "<<" the lexicographic order, proving that the order is preserved
2916 * in all cases.
2918 static __isl_give isl_union_map *contruct_shifted_executed(
2919 struct isl_set_map_pair *domain, int *order, int n, isl_int stride,
2920 __isl_keep isl_vec *offset, __isl_keep isl_ast_build *build)
2922 int i;
2923 isl_int v;
2924 isl_union_map *executed;
2925 isl_space *space;
2926 isl_map *map;
2927 int depth;
2928 isl_constraint *c;
2930 depth = isl_ast_build_get_depth(build);
2931 space = isl_ast_build_get_space(build, 1);
2932 executed = isl_union_map_empty(isl_space_copy(space));
2933 space = isl_space_map_from_set(space);
2934 map = isl_map_identity(isl_space_copy(space));
2935 map = isl_map_eliminate(map, isl_dim_out, depth, 1);
2936 map = isl_map_insert_dims(map, isl_dim_out, depth + 1, 1);
2937 space = isl_space_insert_dims(space, isl_dim_out, depth + 1, 1);
2939 c = isl_equality_alloc(isl_local_space_from_space(space));
2940 c = isl_constraint_set_coefficient_si(c, isl_dim_in, depth, 1);
2941 c = isl_constraint_set_coefficient_si(c, isl_dim_out, depth, -1);
2943 isl_int_init(v);
2945 for (i = 0; i < n; ++i) {
2946 isl_map *map_i;
2948 if (isl_vec_get_element(offset, i, &v) < 0)
2949 break;
2950 map_i = isl_map_copy(map);
2951 map_i = isl_map_fix(map_i, isl_dim_out, depth + 1, v);
2952 isl_int_neg(v, v);
2953 c = isl_constraint_set_constant(c, v);
2954 map_i = isl_map_add_constraint(map_i, isl_constraint_copy(c));
2956 map_i = isl_map_apply_domain(isl_map_copy(domain[order[i]].map),
2957 map_i);
2958 executed = isl_union_map_add_map(executed, map_i);
2961 isl_constraint_free(c);
2962 isl_map_free(map);
2964 isl_int_clear(v);
2966 if (i < n)
2967 executed = isl_union_map_free(executed);
2969 return executed;
2972 /* Generate code for a single component, after exposing the stride,
2973 * given that the schedule domain is "shifted strided".
2975 * The component inverse schedule is specified as the "map" fields
2976 * of the elements of "domain" indexed by the first "n" elements of "order".
2978 * The schedule domain being "shifted strided" means that the differences
2979 * between the values of the current dimension of domain "i"
2980 * and the values of the current dimension for some reference domain are
2981 * equal to
2983 * stride * integer + offset[i]
2985 * We first look for the domain with the "smallest" value for the current
2986 * dimension and adjust the offsets such that the offset of the "smallest"
2987 * domain is equal to zero. The other offsets are reduced modulo stride.
2989 * Based on this information, we construct a new inverse schedule in
2990 * contruct_shifted_executed that exposes the stride.
2991 * Since this involves the introduction of a new schedule dimension,
2992 * the build needs to be changed accodingly.
2993 * After computing the AST, the newly introduced dimension needs
2994 * to be removed again from the list of grafts. We do this by plugging
2995 * in a mapping that represents the new schedule domain in terms of the
2996 * old schedule domain.
2998 static __isl_give isl_ast_graft_list *generate_shift_component(
2999 struct isl_set_map_pair *domain, int *order, int n, isl_int stride,
3000 __isl_keep isl_vec *offset, __isl_take isl_ast_build *build)
3002 isl_ast_graft_list *list;
3003 int first;
3004 int depth;
3005 isl_ctx *ctx;
3006 isl_int val;
3007 isl_vec *v;
3008 isl_space *space;
3009 isl_multi_aff *ma, *zero;
3010 isl_union_map *executed;
3012 ctx = isl_ast_build_get_ctx(build);
3013 depth = isl_ast_build_get_depth(build);
3015 first = first_offset(domain, order, n, build);
3016 if (first < 0)
3017 return isl_ast_build_free(build);
3019 isl_int_init(val);
3020 v = isl_vec_alloc(ctx, n);
3021 if (isl_vec_get_element(offset, first, &val) < 0)
3022 v = isl_vec_free(v);
3023 isl_int_neg(val, val);
3024 v = isl_vec_set(v, val);
3025 v = isl_vec_add(v, isl_vec_copy(offset));
3026 v = isl_vec_fdiv_r(v, stride);
3028 executed = contruct_shifted_executed(domain, order, n, stride, v,
3029 build);
3030 space = isl_ast_build_get_space(build, 1);
3031 space = isl_space_map_from_set(space);
3032 ma = isl_multi_aff_identity(isl_space_copy(space));
3033 space = isl_space_from_domain(isl_space_domain(space));
3034 space = isl_space_add_dims(space, isl_dim_out, 1);
3035 zero = isl_multi_aff_zero(space);
3036 ma = isl_multi_aff_range_splice(ma, depth + 1, zero);
3037 build = isl_ast_build_insert_dim(build, depth + 1);
3038 list = generate_shifted_component(executed, build);
3040 list = isl_ast_graft_list_preimage_multi_aff(list, ma);
3042 isl_vec_free(v);
3043 isl_int_clear(val);
3045 return list;
3048 /* Generate code for a single component.
3050 * The component inverse schedule is specified as the "map" fields
3051 * of the elements of "domain" indexed by the first "n" elements of "order".
3053 * This function may modify the "set" fields of "domain".
3055 * Before proceeding with the actual code generation for the component,
3056 * we first check if there are any "shifted" strides, meaning that
3057 * the schedule domains of the individual domains are all strided,
3058 * but that they have different offsets, resulting in the union
3059 * of schedule domains not being strided anymore.
3061 * The simplest example is the schedule
3063 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3065 * Both schedule domains are strided, but their union is not.
3066 * This function detects such cases and then rewrites the schedule to
3068 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3070 * In the new schedule, the schedule domains have the same offset (modulo
3071 * the stride), ensuring that the union of schedule domains is also strided.
3074 * If there is only a single domain in the component, then there is
3075 * nothing to do. Similarly, if the current schedule dimension has
3076 * a fixed value for almost all domains then there is nothing to be done.
3077 * In particular, we need at least two domains where the current schedule
3078 * dimension does not have a fixed value.
3079 * Finally, if any of the options refer to the current schedule dimension,
3080 * then we bail out as well. It would be possible to reformulate the options
3081 * in terms of the new schedule domain, but that would introduce constraints
3082 * that separate the domains in the options and that is something we would
3083 * like to avoid.
3086 * To see if there is any shifted stride, we look at the differences
3087 * between the values of the current dimension in pairs of domains
3088 * for equal values of outer dimensions. These differences should be
3089 * of the form
3091 * m x + r
3093 * with "m" the stride and "r" a constant. Note that we cannot perform
3094 * this analysis on individual domains as the lower bound in each domain
3095 * may depend on parameters or outer dimensions and so the current dimension
3096 * itself may not have a fixed remainder on division by the stride.
3098 * In particular, we compare the first domain that does not have an
3099 * obviously fixed value for the current dimension to itself and all
3100 * other domains and collect the offsets and the gcd of the strides.
3101 * If the gcd becomes one, then we failed to find shifted strides.
3102 * If all the offsets are the same (for those domains that do not have
3103 * an obviously fixed value for the current dimension), then we do not
3104 * apply the transformation.
3105 * If none of the domains were skipped, then there is nothing to do.
3106 * If some of them were skipped, then if we apply separation, the schedule
3107 * domain should get split in pieces with a (non-shifted) stride.
3109 * Otherwise, we apply a shift to expose the stride in
3110 * generate_shift_component.
3112 static __isl_give isl_ast_graft_list *generate_component(
3113 struct isl_set_map_pair *domain, int *order, int n,
3114 __isl_take isl_ast_build *build)
3116 int i, d;
3117 int depth;
3118 isl_ctx *ctx;
3119 isl_map *map;
3120 isl_set *deltas;
3121 isl_int m, r, gcd;
3122 isl_vec *v;
3123 int fixed, skip;
3124 int base;
3125 isl_ast_graft_list *list;
3126 int res = 0;
3128 depth = isl_ast_build_get_depth(build);
3130 skip = n == 1;
3131 if (skip >= 0 && !skip)
3132 skip = at_most_one_non_fixed(domain, order, n, depth);
3133 if (skip >= 0 && !skip)
3134 skip = isl_ast_build_options_involve_depth(build);
3135 if (skip < 0)
3136 return isl_ast_build_free(build);
3137 if (skip)
3138 return generate_shifted_component_from_list(domain,
3139 order, n, build);
3141 base = eliminate_non_fixed(domain, order, n, depth, build);
3142 if (base < 0)
3143 return isl_ast_build_free(build);
3145 ctx = isl_ast_build_get_ctx(build);
3147 isl_int_init(m);
3148 isl_int_init(r);
3149 isl_int_init(gcd);
3150 v = isl_vec_alloc(ctx, n);
3152 fixed = 1;
3153 for (i = 0; i < n; ++i) {
3154 map = isl_map_from_domain_and_range(
3155 isl_set_copy(domain[order[base]].set),
3156 isl_set_copy(domain[order[i]].set));
3157 for (d = 0; d < depth; ++d)
3158 map = isl_map_equate(map, isl_dim_in, d,
3159 isl_dim_out, d);
3160 deltas = isl_map_deltas(map);
3161 res = isl_set_dim_residue_class(deltas, depth, &m, &r);
3162 isl_set_free(deltas);
3163 if (res < 0)
3164 break;
3166 if (i == 0)
3167 isl_int_set(gcd, m);
3168 else
3169 isl_int_gcd(gcd, gcd, m);
3170 if (isl_int_is_one(gcd))
3171 break;
3172 v = isl_vec_set_element(v, i, r);
3174 res = isl_set_plain_is_fixed(domain[order[i]].set,
3175 isl_dim_set, depth, NULL);
3176 if (res < 0)
3177 break;
3178 if (res)
3179 continue;
3181 if (fixed && i > base) {
3182 isl_vec_get_element(v, base, &m);
3183 if (isl_int_ne(m, r))
3184 fixed = 0;
3188 if (res < 0) {
3189 isl_ast_build_free(build);
3190 list = NULL;
3191 } else if (i < n || fixed) {
3192 list = generate_shifted_component_from_list(domain,
3193 order, n, build);
3194 } else {
3195 list = generate_shift_component(domain, order, n, gcd, v,
3196 build);
3199 isl_vec_free(v);
3200 isl_int_clear(gcd);
3201 isl_int_clear(r);
3202 isl_int_clear(m);
3204 return list;
3207 /* Store both "map" itself and its domain in the
3208 * structure pointed to by *next and advance to the next array element.
3210 static int extract_domain(__isl_take isl_map *map, void *user)
3212 struct isl_set_map_pair **next = user;
3214 (*next)->map = isl_map_copy(map);
3215 (*next)->set = isl_map_domain(map);
3216 (*next)++;
3218 return 0;
3221 /* Internal data for any_scheduled_after.
3223 * "depth" is the number of loops that have already been generated
3224 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3225 * "domain" is an array of set-map pairs corresponding to the different
3226 * iteration domains. The set is the schedule domain, i.e., the domain
3227 * of the inverse schedule, while the map is the inverse schedule itself.
3229 struct isl_any_scheduled_after_data {
3230 int depth;
3231 int group_coscheduled;
3232 struct isl_set_map_pair *domain;
3235 /* Is any element of domain "i" scheduled after any element of domain "j"
3236 * (for a common iteration of the first data->depth loops)?
3238 * data->domain[i].set contains the domain of the inverse schedule
3239 * for domain "i", i.e., elements in the schedule domain.
3241 * If data->group_coscheduled is set, then we also return 1 if there
3242 * is any pair of elements in the two domains that are scheduled together.
3244 static int any_scheduled_after(int i, int j, void *user)
3246 struct isl_any_scheduled_after_data *data = user;
3247 int dim = isl_set_dim(data->domain[i].set, isl_dim_set);
3248 int pos;
3250 for (pos = data->depth; pos < dim; ++pos) {
3251 int follows;
3253 follows = isl_set_follows_at(data->domain[i].set,
3254 data->domain[j].set, pos);
3256 if (follows < -1)
3257 return -1;
3258 if (follows > 0)
3259 return 1;
3260 if (follows < 0)
3261 return 0;
3264 return data->group_coscheduled;
3267 /* Look for independent components at the current depth and generate code
3268 * for each component separately. The resulting lists of grafts are
3269 * merged in an attempt to combine grafts with identical guards.
3271 * Code for two domains can be generated separately if all the elements
3272 * of one domain are scheduled before (or together with) all the elements
3273 * of the other domain. We therefore consider the graph with as nodes
3274 * the domains and an edge between two nodes if any element of the first
3275 * node is scheduled after any element of the second node.
3276 * If the ast_build_group_coscheduled is set, then we also add an edge if
3277 * there is any pair of elements in the two domains that are scheduled
3278 * together.
3279 * Code is then generated (by generate_component)
3280 * for each of the strongly connected components in this graph
3281 * in their topological order.
3283 * Since the test is performed on the domain of the inverse schedules of
3284 * the different domains, we precompute these domains and store
3285 * them in data.domain.
3287 static __isl_give isl_ast_graft_list *generate_components(
3288 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
3290 int i;
3291 isl_ctx *ctx = isl_ast_build_get_ctx(build);
3292 int n = isl_union_map_n_map(executed);
3293 struct isl_any_scheduled_after_data data;
3294 struct isl_set_map_pair *next;
3295 struct isl_tarjan_graph *g = NULL;
3296 isl_ast_graft_list *list = NULL;
3297 int n_domain = 0;
3299 data.domain = isl_calloc_array(ctx, struct isl_set_map_pair, n);
3300 if (!data.domain)
3301 goto error;
3302 n_domain = n;
3304 next = data.domain;
3305 if (isl_union_map_foreach_map(executed, &extract_domain, &next) < 0)
3306 goto error;
3308 if (!build)
3309 goto error;
3310 data.depth = isl_ast_build_get_depth(build);
3311 data.group_coscheduled = isl_options_get_ast_build_group_coscheduled(ctx);
3312 g = isl_tarjan_graph_init(ctx, n, &any_scheduled_after, &data);
3314 list = isl_ast_graft_list_alloc(ctx, 0);
3316 i = 0;
3317 while (list && n) {
3318 isl_ast_graft_list *list_c;
3319 int first = i;
3321 if (g->order[i] == -1)
3322 isl_die(ctx, isl_error_internal, "cannot happen",
3323 goto error);
3324 ++i; --n;
3325 while (g->order[i] != -1) {
3326 ++i; --n;
3329 list_c = generate_component(data.domain,
3330 g->order + first, i - first,
3331 isl_ast_build_copy(build));
3332 list = isl_ast_graft_list_merge(list, list_c, build);
3334 ++i;
3337 if (0)
3338 error: list = isl_ast_graft_list_free(list);
3339 isl_tarjan_graph_free(g);
3340 for (i = 0; i < n_domain; ++i) {
3341 isl_map_free(data.domain[i].map);
3342 isl_set_free(data.domain[i].set);
3344 free(data.domain);
3345 isl_union_map_free(executed);
3346 isl_ast_build_free(build);
3348 return list;
3351 /* Generate code for the next level (and all inner levels).
3353 * If "executed" is empty, i.e., no code needs to be generated,
3354 * then we return an empty list.
3356 * If we have already generated code for all loop levels, then we pass
3357 * control to generate_inner_level.
3359 * If "executed" lives in a single space, i.e., if code needs to be
3360 * generated for a single domain, then there can only be a single
3361 * component and we go directly to generate_shifted_component.
3362 * Otherwise, we call generate_components to detect the components
3363 * and to call generate_component on each of them separately.
3365 static __isl_give isl_ast_graft_list *generate_next_level(
3366 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
3368 int depth;
3370 if (!build || !executed)
3371 goto error;
3373 if (isl_union_map_is_empty(executed)) {
3374 isl_ctx *ctx = isl_ast_build_get_ctx(build);
3375 isl_union_map_free(executed);
3376 isl_ast_build_free(build);
3377 return isl_ast_graft_list_alloc(ctx, 0);
3380 depth = isl_ast_build_get_depth(build);
3381 if (depth >= isl_set_dim(build->domain, isl_dim_set))
3382 return generate_inner_level(executed, build);
3384 if (isl_union_map_n_map(executed) == 1)
3385 return generate_shifted_component(executed, build);
3387 return generate_components(executed, build);
3388 error:
3389 isl_union_map_free(executed);
3390 isl_ast_build_free(build);
3391 return NULL;
3394 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3395 * internal, executed and build are the inputs to generate_code.
3396 * list collects the output.
3398 struct isl_generate_code_data {
3399 int internal;
3400 isl_union_map *executed;
3401 isl_ast_build *build;
3403 isl_ast_graft_list *list;
3406 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3408 * [E -> S] -> D
3410 * with E the external build schedule and S the additional schedule "space",
3411 * reformulate the inverse schedule in terms of the internal schedule domain,
3412 * i.e., return
3414 * [I -> S] -> D
3416 * We first obtain a mapping
3418 * I -> E
3420 * take the inverse and the product with S -> S, resulting in
3422 * [I -> S] -> [E -> S]
3424 * Applying the map to the input produces the desired result.
3426 static __isl_give isl_union_map *internal_executed(
3427 __isl_take isl_union_map *executed, __isl_keep isl_space *space,
3428 __isl_keep isl_ast_build *build)
3430 isl_map *id, *proj;
3432 proj = isl_ast_build_get_schedule_map(build);
3433 proj = isl_map_reverse(proj);
3434 space = isl_space_map_from_set(isl_space_copy(space));
3435 id = isl_map_identity(space);
3436 proj = isl_map_product(proj, id);
3437 executed = isl_union_map_apply_domain(executed,
3438 isl_union_map_from_map(proj));
3439 return executed;
3442 /* Generate an AST that visits the elements in the range of data->executed
3443 * in the relative order specified by the corresponding image element(s)
3444 * for those image elements that belong to "set".
3445 * Add the result to data->list.
3447 * The caller ensures that "set" is a universe domain.
3448 * "space" is the space of the additional part of the schedule.
3449 * It is equal to the space of "set" if build->domain is parametric.
3450 * Otherwise, it is equal to the range of the wrapped space of "set".
3452 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3453 * was called from an outside user (data->internal not set), then
3454 * the (inverse) schedule refers to the external build domain and needs to
3455 * be transformed to refer to the internal build domain.
3457 * The build is extended to include the additional part of the schedule.
3458 * If the original build space was not parametric, then the options
3459 * in data->build refer only to the additional part of the schedule
3460 * and they need to be adjusted to refer to the complete AST build
3461 * domain.
3463 * After having adjusted inverse schedule and build, we start generating
3464 * code with the outer loop of the current code generation
3465 * in generate_next_level.
3467 * If the original build space was not parametric, we undo the embedding
3468 * on the resulting isl_ast_node_list so that it can be used within
3469 * the outer AST build.
3471 static int generate_code_in_space(struct isl_generate_code_data *data,
3472 __isl_take isl_set *set, __isl_take isl_space *space)
3474 isl_union_map *executed;
3475 isl_ast_build *build;
3476 isl_ast_graft_list *list;
3477 int embed;
3479 executed = isl_union_map_copy(data->executed);
3480 executed = isl_union_map_intersect_domain(executed,
3481 isl_union_set_from_set(set));
3483 embed = !isl_set_is_params(data->build->domain);
3484 if (embed && !data->internal)
3485 executed = internal_executed(executed, space, data->build);
3487 build = isl_ast_build_copy(data->build);
3488 build = isl_ast_build_product(build, space);
3490 list = generate_next_level(executed, build);
3492 list = isl_ast_graft_list_unembed(list, embed);
3494 data->list = isl_ast_graft_list_concat(data->list, list);
3496 return 0;
3499 /* Generate an AST that visits the elements in the range of data->executed
3500 * in the relative order specified by the corresponding domain element(s)
3501 * for those domain elements that belong to "set".
3502 * Add the result to data->list.
3504 * The caller ensures that "set" is a universe domain.
3506 * If the build space S is not parametric, then the space of "set"
3507 * need to be a wrapped relation with S as domain. That is, it needs
3508 * to be of the form
3510 * [S -> T]
3512 * Check this property and pass control to generate_code_in_space
3513 * passing along T.
3514 * If the build space is not parametric, then T is the space of "set".
3516 static int generate_code_set(__isl_take isl_set *set, void *user)
3518 struct isl_generate_code_data *data = user;
3519 isl_space *space, *build_space;
3520 int is_domain;
3522 space = isl_set_get_space(set);
3524 if (isl_set_is_params(data->build->domain))
3525 return generate_code_in_space(data, set, space);
3527 build_space = isl_ast_build_get_space(data->build, data->internal);
3528 space = isl_space_unwrap(space);
3529 is_domain = isl_space_is_domain(build_space, space);
3530 isl_space_free(build_space);
3531 space = isl_space_range(space);
3533 if (is_domain < 0)
3534 goto error;
3535 if (!is_domain)
3536 isl_die(isl_set_get_ctx(set), isl_error_invalid,
3537 "invalid nested schedule space", goto error);
3539 return generate_code_in_space(data, set, space);
3540 error:
3541 isl_set_free(set);
3542 isl_space_free(space);
3543 return -1;
3546 /* Generate an AST that visits the elements in the range of "executed"
3547 * in the relative order specified by the corresponding domain element(s).
3549 * "build" is an isl_ast_build that has either been constructed by
3550 * isl_ast_build_from_context or passed to a callback set by
3551 * isl_ast_build_set_create_leaf.
3552 * In the first case, the space of the isl_ast_build is typically
3553 * a parametric space, although this is currently not enforced.
3554 * In the second case, the space is never a parametric space.
3555 * If the space S is not parametric, then the domain space(s) of "executed"
3556 * need to be wrapped relations with S as domain.
3558 * If the domain of "executed" consists of several spaces, then an AST
3559 * is generated for each of them (in arbitrary order) and the results
3560 * are concatenated.
3562 * If "internal" is set, then the domain "S" above refers to the internal
3563 * schedule domain representation. Otherwise, it refers to the external
3564 * representation, as returned by isl_ast_build_get_schedule_space.
3566 * We essentially run over all the spaces in the domain of "executed"
3567 * and call generate_code_set on each of them.
3569 static __isl_give isl_ast_graft_list *generate_code(
3570 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build,
3571 int internal)
3573 isl_ctx *ctx;
3574 struct isl_generate_code_data data = { 0 };
3575 isl_space *space;
3576 isl_union_set *schedule_domain;
3577 isl_union_map *universe;
3579 if (!build)
3580 goto error;
3581 space = isl_ast_build_get_space(build, 1);
3582 space = isl_space_align_params(space,
3583 isl_union_map_get_space(executed));
3584 space = isl_space_align_params(space,
3585 isl_union_map_get_space(build->options));
3586 build = isl_ast_build_align_params(build, isl_space_copy(space));
3587 executed = isl_union_map_align_params(executed, space);
3588 if (!executed || !build)
3589 goto error;
3591 ctx = isl_ast_build_get_ctx(build);
3593 data.internal = internal;
3594 data.executed = executed;
3595 data.build = build;
3596 data.list = isl_ast_graft_list_alloc(ctx, 0);
3598 universe = isl_union_map_universe(isl_union_map_copy(executed));
3599 schedule_domain = isl_union_map_domain(universe);
3600 if (isl_union_set_foreach_set(schedule_domain, &generate_code_set,
3601 &data) < 0)
3602 data.list = isl_ast_graft_list_free(data.list);
3604 isl_union_set_free(schedule_domain);
3605 isl_union_map_free(executed);
3607 isl_ast_build_free(build);
3608 return data.list;
3609 error:
3610 isl_union_map_free(executed);
3611 isl_ast_build_free(build);
3612 return NULL;
3615 /* Generate an AST that visits the elements in the domain of "schedule"
3616 * in the relative order specified by the corresponding image element(s).
3618 * "build" is an isl_ast_build that has either been constructed by
3619 * isl_ast_build_from_context or passed to a callback set by
3620 * isl_ast_build_set_create_leaf.
3621 * In the first case, the space of the isl_ast_build is typically
3622 * a parametric space, although this is currently not enforced.
3623 * In the second case, the space is never a parametric space.
3624 * If the space S is not parametric, then the range space(s) of "schedule"
3625 * need to be wrapped relations with S as domain.
3627 * If the range of "schedule" consists of several spaces, then an AST
3628 * is generated for each of them (in arbitrary order) and the results
3629 * are concatenated.
3631 * We first initialize the local copies of the relevant options.
3632 * We do this here rather than when the isl_ast_build is created
3633 * because the options may have changed between the construction
3634 * of the isl_ast_build and the call to isl_generate_code.
3636 * The main computation is performed on an inverse schedule (with
3637 * the schedule domain in the domain and the elements to be executed
3638 * in the range) called "executed".
3640 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
3641 __isl_keep isl_ast_build *build, __isl_take isl_union_map *schedule)
3643 isl_ast_graft_list *list;
3644 isl_ast_node *node;
3645 isl_union_map *executed;
3647 build = isl_ast_build_copy(build);
3648 build = isl_ast_build_set_single_valued(build, 0);
3649 executed = isl_union_map_reverse(schedule);
3650 list = generate_code(executed, isl_ast_build_copy(build), 0);
3651 node = isl_ast_node_from_graft_list(list, build);
3652 isl_ast_build_free(build);
3654 return node;