isl_basic_map_normalize: avoid invalid access on error
[isl.git] / isl_ast_codegen.c
blob1ada490b0a9727e57d267526b542f79f9c2c1259
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);
112 list = generate_code(isl_union_map_from_map(executed), build, 1);
114 data->list = isl_ast_graft_list_concat(data->list, list);
116 return 0;
119 /* Call the at_each_domain callback, if requested by the user,
120 * after recording the current inverse schedule in the build.
122 static __isl_give isl_ast_graft *at_each_domain(__isl_take isl_ast_graft *graft,
123 __isl_keep isl_map *executed, __isl_keep isl_ast_build *build)
125 if (!graft || !build)
126 return isl_ast_graft_free(graft);
127 if (!build->at_each_domain)
128 return graft;
130 build = isl_ast_build_copy(build);
131 build = isl_ast_build_set_executed(build,
132 isl_union_map_from_map(isl_map_copy(executed)));
133 if (!build)
134 return isl_ast_graft_free(graft);
136 graft->node = build->at_each_domain(graft->node,
137 build, build->at_each_domain_user);
138 isl_ast_build_free(build);
140 if (!graft->node)
141 graft = isl_ast_graft_free(graft);
143 return graft;
146 /* Generate an AST for a single domain based on
147 * the inverse schedule "executed".
149 * If there is more than one domain element associated to the current
150 * schedule "time", then we need to continue the generation process
151 * in generate_non_single_valued.
152 * Note that the inverse schedule being single-valued may depend
153 * on constraints that are only available in the original context
154 * domain specified by the user. We therefore first introduce
155 * the constraints from data->build->domain.
156 * On the other hand, we only perform the test after having taken the gist
157 * of the domain as the resulting map is the one from which the call
158 * expression is constructed.
160 * Otherwise, we generate a call expression for the single executed
161 * domain element and put a guard around it based on the (simplified)
162 * domain of "executed".
164 * If the user has set an at_each_domain callback, it is called
165 * on the constructed call expression node.
167 static int generate_domain(__isl_take isl_map *executed, void *user)
169 struct isl_generate_domain_data *data = user;
170 isl_ast_graft *graft;
171 isl_ast_graft_list *list;
172 isl_set *guard;
173 isl_map *map;
174 int sv;
176 executed = isl_map_intersect_domain(executed,
177 isl_set_copy(data->build->domain));
179 executed = isl_map_coalesce(executed);
180 map = isl_map_copy(executed);
181 map = isl_ast_build_compute_gist_map_domain(data->build, map);
182 sv = isl_map_is_single_valued(map);
183 if (sv < 0)
184 goto error;
185 if (!sv) {
186 isl_map_free(map);
187 return generate_non_single_valued(executed, data);
189 guard = isl_map_domain(isl_map_copy(map));
190 guard = isl_set_coalesce(guard);
191 guard = isl_ast_build_compute_gist(data->build, guard);
192 graft = isl_ast_graft_alloc_domain(map, data->build);
193 graft = at_each_domain(graft, executed, data->build);
195 isl_map_free(executed);
196 graft = isl_ast_graft_add_guard(graft, guard, data->build);
198 list = isl_ast_graft_list_from_ast_graft(graft);
199 data->list = isl_ast_graft_list_concat(data->list, list);
201 return 0;
202 error:
203 isl_map_free(map);
204 isl_map_free(executed);
205 return -1;
208 /* Call build->create_leaf to a create "leaf" node in the AST,
209 * encapsulate the result in an isl_ast_graft and return the result
210 * as a 1-element list.
212 * Note that the node returned by the user may be an entire tree.
214 * Before we pass control to the user, we first clear some information
215 * from the build that is (presumbably) only meaningful
216 * for the current code generation.
217 * This includes the create_leaf callback itself, so we make a copy
218 * of the build first.
220 static __isl_give isl_ast_graft_list *call_create_leaf(
221 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
223 isl_ast_node *node;
224 isl_ast_graft *graft;
225 isl_ast_build *user_build;
227 user_build = isl_ast_build_copy(build);
228 user_build = isl_ast_build_set_executed(user_build, executed);
229 user_build = isl_ast_build_clear_local_info(user_build);
230 if (!user_build)
231 node = NULL;
232 else
233 node = build->create_leaf(user_build, build->create_leaf_user);
234 graft = isl_ast_graft_alloc(node, build);
235 isl_ast_build_free(build);
236 return isl_ast_graft_list_from_ast_graft(graft);
239 /* Generate an AST after having handled the complete schedule
240 * of this call to the code generator.
242 * If the user has specified a create_leaf callback, control
243 * is passed to the user in call_create_leaf.
245 * Otherwise, we generate one or more calls for each individual
246 * domain in generate_domain.
248 static __isl_give isl_ast_graft_list *generate_inner_level(
249 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
251 isl_ctx *ctx;
252 struct isl_generate_domain_data data = { build };
254 if (!build || !executed)
255 goto error;
257 if (build->create_leaf)
258 return call_create_leaf(executed, build);
260 ctx = isl_union_map_get_ctx(executed);
261 data.list = isl_ast_graft_list_alloc(ctx, 0);
262 if (isl_union_map_foreach_map(executed, &generate_domain, &data) < 0)
263 data.list = isl_ast_graft_list_free(data.list);
265 if (0)
266 error: data.list = NULL;
267 isl_ast_build_free(build);
268 isl_union_map_free(executed);
269 return data.list;
272 /* Call the before_each_for callback, if requested by the user.
274 static __isl_give isl_ast_node *before_each_for(__isl_take isl_ast_node *node,
275 __isl_keep isl_ast_build *build)
277 isl_id *id;
279 if (!node || !build)
280 return isl_ast_node_free(node);
281 if (!build->before_each_for)
282 return node;
283 id = build->before_each_for(build, build->before_each_for_user);
284 node = isl_ast_node_set_annotation(node, id);
285 return node;
288 /* Call the after_each_for callback, if requested by the user.
290 static __isl_give isl_ast_graft *after_each_for(__isl_keep isl_ast_graft *graft,
291 __isl_keep isl_ast_build *build)
293 if (!graft || !build)
294 return isl_ast_graft_free(graft);
295 if (!build->after_each_for)
296 return graft;
297 graft->node = build->after_each_for(graft->node, build,
298 build->after_each_for_user);
299 if (!graft->node)
300 return isl_ast_graft_free(graft);
301 return graft;
304 /* Eliminate the schedule dimension "pos" from "executed" and return
305 * the result.
307 static __isl_give isl_union_map *eliminate(__isl_take isl_union_map *executed,
308 int pos, __isl_keep isl_ast_build *build)
310 isl_space *space;
311 isl_map *elim;
313 space = isl_ast_build_get_space(build, 1);
314 space = isl_space_map_from_set(space);
315 elim = isl_map_identity(space);
316 elim = isl_map_eliminate(elim, isl_dim_in, pos, 1);
318 executed = isl_union_map_apply_domain(executed,
319 isl_union_map_from_map(elim));
321 return executed;
324 /* Check if the constraint "c" is a lower bound on dimension "pos",
325 * an upper bound, or independent of dimension "pos".
327 static int constraint_type(isl_constraint *c, int pos)
329 if (isl_constraint_is_lower_bound(c, isl_dim_set, pos))
330 return 1;
331 if (isl_constraint_is_upper_bound(c, isl_dim_set, pos))
332 return 2;
333 return 0;
336 /* Compare the types of the constraints "a" and "b",
337 * resulting in constraints that are independent of "depth"
338 * to be sorted before the lower bounds on "depth", which in
339 * turn are sorted before the upper bounds on "depth".
341 static int cmp_constraint(const void *a, const void *b, void *user)
343 int *depth = user;
344 isl_constraint * const *c1 = a;
345 isl_constraint * const *c2 = b;
346 int t1 = constraint_type(*c1, *depth);
347 int t2 = constraint_type(*c2, *depth);
349 return t1 - t2;
352 /* Extract a lower bound on dimension "pos" from constraint "c".
354 * If the constraint is of the form
356 * a x + f(...) >= 0
358 * then we essentially return
360 * l = ceil(-f(...)/a)
362 * However, if the current dimension is strided, then we need to make
363 * sure that the lower bound we construct is of the form
365 * f + s a
367 * with f the offset and s the stride.
368 * We therefore compute
370 * f + s * ceil((l - f)/s)
372 static __isl_give isl_aff *lower_bound(__isl_keep isl_constraint *c,
373 int pos, __isl_keep isl_ast_build *build)
375 isl_aff *aff;
377 aff = isl_constraint_get_bound(c, isl_dim_set, pos);
378 aff = isl_aff_ceil(aff);
380 if (isl_ast_build_has_stride(build, pos)) {
381 isl_aff *offset;
382 isl_int stride;
384 isl_int_init(stride);
386 offset = isl_ast_build_get_offset(build, pos);
387 isl_ast_build_get_stride(build, pos, &stride);
389 aff = isl_aff_sub(aff, isl_aff_copy(offset));
390 aff = isl_aff_scale_down(aff, stride);
391 aff = isl_aff_ceil(aff);
392 aff = isl_aff_scale(aff, stride);
393 aff = isl_aff_add(aff, offset);
395 isl_int_clear(stride);
398 aff = isl_ast_build_compute_gist_aff(build, aff);
400 return aff;
403 /* Return the exact lower bound (or upper bound if "upper" is set)
404 * of "domain" as a piecewise affine expression.
406 * If we are computing a lower bound (of a strided dimension), then
407 * we need to make sure it is of the form
409 * f + s a
411 * where f is the offset and s is the stride.
412 * We therefore need to include the stride constraint before computing
413 * the minimum.
415 static __isl_give isl_pw_aff *exact_bound(__isl_keep isl_set *domain,
416 __isl_keep isl_ast_build *build, int upper)
418 isl_set *stride;
419 isl_map *it_map;
420 isl_pw_aff *pa;
421 isl_pw_multi_aff *pma;
423 domain = isl_set_copy(domain);
424 if (!upper) {
425 stride = isl_ast_build_get_stride_constraint(build);
426 domain = isl_set_intersect(domain, stride);
428 it_map = isl_ast_build_map_to_iterator(build, domain);
429 if (upper)
430 pma = isl_map_lexmax_pw_multi_aff(it_map);
431 else
432 pma = isl_map_lexmin_pw_multi_aff(it_map);
433 pa = isl_pw_multi_aff_get_pw_aff(pma, 0);
434 isl_pw_multi_aff_free(pma);
435 pa = isl_ast_build_compute_gist_pw_aff(build, pa);
436 pa = isl_pw_aff_coalesce(pa);
438 return pa;
441 /* Return a list of "n" lower bounds on dimension "pos"
442 * extracted from the "n" constraints starting at "constraint".
443 * If "n" is zero, then we extract a lower bound from "domain" instead.
445 static __isl_give isl_pw_aff_list *lower_bounds(
446 __isl_keep isl_constraint **constraint, int n, int pos,
447 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
449 isl_ctx *ctx;
450 isl_pw_aff_list *list;
451 int i;
453 if (!build)
454 return NULL;
456 if (n == 0) {
457 isl_pw_aff *pa;
458 pa = exact_bound(domain, build, 0);
459 return isl_pw_aff_list_from_pw_aff(pa);
462 ctx = isl_ast_build_get_ctx(build);
463 list = isl_pw_aff_list_alloc(ctx,n);
465 for (i = 0; i < n; ++i) {
466 isl_aff *aff;
468 aff = lower_bound(constraint[i], pos, build);
469 list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
472 return list;
475 /* Return a list of "n" upper bounds on dimension "pos"
476 * extracted from the "n" constraints starting at "constraint".
477 * If "n" is zero, then we extract an upper bound from "domain" instead.
479 static __isl_give isl_pw_aff_list *upper_bounds(
480 __isl_keep isl_constraint **constraint, int n, int pos,
481 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
483 isl_ctx *ctx;
484 isl_pw_aff_list *list;
485 int i;
487 if (n == 0) {
488 isl_pw_aff *pa;
489 pa = exact_bound(domain, build, 1);
490 return isl_pw_aff_list_from_pw_aff(pa);
493 ctx = isl_ast_build_get_ctx(build);
494 list = isl_pw_aff_list_alloc(ctx,n);
496 for (i = 0; i < n; ++i) {
497 isl_aff *aff;
499 aff = isl_constraint_get_bound(constraint[i], isl_dim_set, pos);
500 aff = isl_aff_floor(aff);
501 list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
504 return list;
507 /* Return an isl_ast_expr that performs the reduction of type "type"
508 * on AST expressions corresponding to the elements in "list".
510 * The list is assumed to contain at least one element.
511 * If the list contains exactly one element, then the returned isl_ast_expr
512 * simply computes that affine expression.
514 static __isl_give isl_ast_expr *reduce_list(enum isl_ast_op_type type,
515 __isl_keep isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
517 int i, n;
518 isl_ctx *ctx;
519 isl_ast_expr *expr;
521 if (!list)
522 return NULL;
524 n = isl_pw_aff_list_n_pw_aff(list);
526 if (n == 1)
527 return isl_ast_build_expr_from_pw_aff_internal(build,
528 isl_pw_aff_list_get_pw_aff(list, 0));
530 ctx = isl_pw_aff_list_get_ctx(list);
531 expr = isl_ast_expr_alloc_op(ctx, type, n);
532 if (!expr)
533 return NULL;
535 for (i = 0; i < n; ++i) {
536 isl_ast_expr *expr_i;
538 expr_i = isl_ast_build_expr_from_pw_aff_internal(build,
539 isl_pw_aff_list_get_pw_aff(list, i));
540 if (!expr_i)
541 return isl_ast_expr_free(expr);
542 expr->u.op.args[i] = expr_i;
545 return expr;
548 /* Add a guard to "graft" based on "bound" in the case of a degenerate
549 * level (including the special case of an eliminated level).
551 * We eliminate the current dimension, simplify the result in the current
552 * build and add the result as guards to the graft.
554 * Note that we cannot simply drop the constraints on the current dimension
555 * even in the eliminated case, because the single affine expression may
556 * not be explicitly available in "bounds". Moreover, the single affine
557 * expression may only be defined on a subset of the build domain,
558 * so we do in some cases need to insert a guard even in the eliminated case.
560 static __isl_give isl_ast_graft *add_degenerate_guard(
561 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
562 __isl_keep isl_ast_build *build)
564 int depth;
565 isl_set *dom;
567 depth = isl_ast_build_get_depth(build);
569 dom = isl_set_from_basic_set(isl_basic_set_copy(bounds));
570 if (isl_ast_build_has_stride(build, depth)) {
571 isl_set *stride;
573 stride = isl_ast_build_get_stride_constraint(build);
574 dom = isl_set_intersect(dom, stride);
576 dom = isl_set_eliminate(dom, isl_dim_set, depth, 1);
577 dom = isl_ast_build_compute_gist(build, dom);
579 graft = isl_ast_graft_add_guard(graft, dom, build);
581 return graft;
584 /* Update "graft" based on "bounds" for the eliminated case.
586 * In the eliminated case, no for node is created, so we only need
587 * to check if "bounds" imply any guards that need to be inserted.
589 static __isl_give isl_ast_graft *refine_eliminated(
590 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
591 __isl_keep isl_ast_build *build)
593 return add_degenerate_guard(graft, bounds, build);
596 /* Update "graft" based on "bounds" and "sub_build" for the degenerate case.
598 * "build" is the build in which graft->node was created
599 * "sub_build" contains information about the current level itself,
600 * including the single value attained.
602 * We first set the initialization part of the for loop to the single
603 * value attained by the current dimension.
604 * The increment and condition are not strictly needed as the are known
605 * to be "1" and "iterator <= value" respectively.
606 * Then we set the size of the iterator and
607 * check if "bounds" imply any guards that need to be inserted.
609 static __isl_give isl_ast_graft *refine_degenerate(
610 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
611 __isl_keep isl_ast_build *build,
612 __isl_keep isl_ast_build *sub_build)
614 isl_pw_aff *value;
616 if (!graft || !sub_build)
617 return isl_ast_graft_free(graft);
619 value = isl_pw_aff_copy(sub_build->value);
621 graft->node->u.f.init = isl_ast_build_expr_from_pw_aff_internal(build,
622 value);
623 if (!graft->node->u.f.init)
624 return isl_ast_graft_free(graft);
626 graft = add_degenerate_guard(graft, bounds, build);
628 return graft;
631 /* Return the intersection of the "n" constraints starting at "constraint"
632 * as a set.
634 static __isl_give isl_set *intersect_constraints(isl_ctx *ctx,
635 __isl_keep isl_constraint **constraint, int n)
637 int i;
638 isl_basic_set *bset;
640 if (n < 1)
641 isl_die(ctx, isl_error_internal,
642 "expecting at least one constraint", return NULL);
644 bset = isl_basic_set_from_constraint(
645 isl_constraint_copy(constraint[0]));
646 for (i = 1; i < n; ++i) {
647 isl_basic_set *bset_i;
649 bset_i = isl_basic_set_from_constraint(
650 isl_constraint_copy(constraint[i]));
651 bset = isl_basic_set_intersect(bset, bset_i);
654 return isl_set_from_basic_set(bset);
657 /* Compute the constraints on the outer dimensions enforced by
658 * graft->node and add those constraints to graft->enforced,
659 * in case the upper bound is expressed as a set "upper".
661 * In particular, if l(...) is a lower bound in "lower", and
663 * -a i + f(...) >= 0 or a i <= f(...)
665 * is an upper bound ocnstraint on the current dimension i,
666 * then the for loop enforces the constraint
668 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
670 * We therefore simply take each lower bound in turn, plug it into
671 * the upper bounds and compute the intersection over all lower bounds.
673 * If a lower bound is a rational expression, then
674 * isl_basic_set_preimage_multi_aff will force this rational
675 * expression to have only integer values. However, the loop
676 * itself does not enforce this integrality constraint. We therefore
677 * use the ceil of the lower bounds instead of the lower bounds themselves.
678 * Other constraints will make sure that the for loop is only executed
679 * when each of the lower bounds attains an integral value.
680 * In particular, potentially rational values only occur in
681 * lower_bound if the offset is a (seemingly) rational expression,
682 * but then outer conditions will make sure that this rational expression
683 * only attains integer values.
685 static __isl_give isl_ast_graft *set_enforced_from_set(
686 __isl_take isl_ast_graft *graft,
687 __isl_keep isl_pw_aff_list *lower, int pos, __isl_keep isl_set *upper)
689 isl_space *space;
690 isl_basic_set *enforced;
691 isl_pw_multi_aff *pma;
692 int i, n;
694 if (!graft || !lower)
695 return isl_ast_graft_free(graft);
697 space = isl_set_get_space(upper);
698 enforced = isl_basic_set_universe(isl_space_copy(space));
700 space = isl_space_map_from_set(space);
701 pma = isl_pw_multi_aff_identity(space);
703 n = isl_pw_aff_list_n_pw_aff(lower);
704 for (i = 0; i < n; ++i) {
705 isl_pw_aff *pa;
706 isl_set *enforced_i;
707 isl_basic_set *hull;
708 isl_pw_multi_aff *pma_i;
710 pa = isl_pw_aff_list_get_pw_aff(lower, i);
711 pa = isl_pw_aff_ceil(pa);
712 pma_i = isl_pw_multi_aff_copy(pma);
713 pma_i = isl_pw_multi_aff_set_pw_aff(pma_i, pos, pa);
714 enforced_i = isl_set_copy(upper);
715 enforced_i = isl_set_preimage_pw_multi_aff(enforced_i, pma_i);
716 hull = isl_set_simple_hull(enforced_i);
717 enforced = isl_basic_set_intersect(enforced, hull);
720 isl_pw_multi_aff_free(pma);
722 graft = isl_ast_graft_enforce(graft, enforced);
724 return graft;
727 /* Compute the constraints on the outer dimensions enforced by
728 * graft->node and add those constraints to graft->enforced,
729 * in case the upper bound is expressed as
730 * a list of affine expressions "upper".
732 * The enforced condition is that each lower bound expression is less
733 * than or equal to each upper bound expression.
735 static __isl_give isl_ast_graft *set_enforced_from_list(
736 __isl_take isl_ast_graft *graft,
737 __isl_keep isl_pw_aff_list *lower, __isl_keep isl_pw_aff_list *upper)
739 isl_set *cond;
740 isl_basic_set *enforced;
742 lower = isl_pw_aff_list_copy(lower);
743 upper = isl_pw_aff_list_copy(upper);
744 cond = isl_pw_aff_list_le_set(lower, upper);
745 enforced = isl_set_simple_hull(cond);
746 graft = isl_ast_graft_enforce(graft, enforced);
748 return graft;
751 /* Does "aff" have a negative constant term?
753 static int aff_constant_is_negative(__isl_take isl_set *set,
754 __isl_take isl_aff *aff, void *user)
756 int *neg = user;
757 isl_int v;
759 isl_int_init(v);
760 isl_aff_get_constant(aff, &v);
761 *neg = isl_int_is_neg(v);
762 isl_int_clear(v);
763 isl_set_free(set);
764 isl_aff_free(aff);
766 return *neg ? 0 : -1;
769 /* Does "pa" have a negative constant term over its entire domain?
771 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff *pa, void *user)
773 int r;
774 int *neg = user;
776 r = isl_pw_aff_foreach_piece(pa, &aff_constant_is_negative, user);
777 isl_pw_aff_free(pa);
779 return *neg ? 0 : -1;
782 /* Does each element in "list" have a negative constant term?
784 * The callback terminates the iteration as soon an element has been
785 * found that does not have a negative constant term.
787 static int list_constant_is_negative(__isl_keep isl_pw_aff_list *list)
789 int neg = 1;
791 if (isl_pw_aff_list_foreach(list,
792 &pw_aff_constant_is_negative, &neg) < 0 && neg)
793 return -1;
795 return neg;
798 /* Add 1 to each of the elements in "list", where each of these elements
799 * is defined over the internal schedule space of "build".
801 static __isl_give isl_pw_aff_list *list_add_one(
802 __isl_take isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
804 int i, n;
805 isl_space *space;
806 isl_aff *aff;
807 isl_pw_aff *one;
809 space = isl_ast_build_get_space(build, 1);
810 aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
811 aff = isl_aff_add_constant_si(aff, 1);
812 one = isl_pw_aff_from_aff(aff);
814 n = isl_pw_aff_list_n_pw_aff(list);
815 for (i = 0; i < n; ++i) {
816 isl_pw_aff *pa;
817 pa = isl_pw_aff_list_get_pw_aff(list, i);
818 pa = isl_pw_aff_add(pa, isl_pw_aff_copy(one));
819 list = isl_pw_aff_list_set_pw_aff(list, i, pa);
822 isl_pw_aff_free(one);
824 return list;
827 /* Set the condition part of the for node graft->node in case
828 * the upper bound is represented as a list of piecewise affine expressions.
830 * In particular, set the condition to
832 * iterator <= min(list of upper bounds)
834 * If each of the upper bounds has a negative constant term, then
835 * set the condition to
837 * iterator < min(list of (upper bound + 1)s)
840 static __isl_give isl_ast_graft *set_for_cond_from_list(
841 __isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *list,
842 __isl_keep isl_ast_build *build)
844 int neg;
845 isl_ast_expr *bound, *iterator, *cond;
846 enum isl_ast_op_type type = isl_ast_op_le;
848 if (!graft || !list)
849 return isl_ast_graft_free(graft);
851 neg = list_constant_is_negative(list);
852 if (neg < 0)
853 return isl_ast_graft_free(graft);
854 list = isl_pw_aff_list_copy(list);
855 if (neg) {
856 list = list_add_one(list, build);
857 type = isl_ast_op_lt;
860 bound = reduce_list(isl_ast_op_min, list, build);
861 iterator = isl_ast_expr_copy(graft->node->u.f.iterator);
862 cond = isl_ast_expr_alloc_binary(type, iterator, bound);
863 graft->node->u.f.cond = cond;
865 isl_pw_aff_list_free(list);
866 if (!graft->node->u.f.cond)
867 return isl_ast_graft_free(graft);
868 return graft;
871 /* Set the condition part of the for node graft->node in case
872 * the upper bound is represented as a set.
874 static __isl_give isl_ast_graft *set_for_cond_from_set(
875 __isl_take isl_ast_graft *graft, __isl_keep isl_set *set,
876 __isl_keep isl_ast_build *build)
878 isl_ast_expr *cond;
880 if (!graft)
881 return NULL;
883 cond = isl_ast_build_expr_from_set(build, isl_set_copy(set));
884 graft->node->u.f.cond = cond;
885 if (!graft->node->u.f.cond)
886 return isl_ast_graft_free(graft);
887 return graft;
890 /* Construct an isl_ast_expr for the increment (i.e., stride) of
891 * the current dimension.
893 static __isl_give isl_ast_expr *for_inc(__isl_keep isl_ast_build *build)
895 int depth;
896 isl_int v;
897 isl_ctx *ctx;
898 isl_ast_expr *inc;
900 if (!build)
901 return NULL;
902 ctx = isl_ast_build_get_ctx(build);
903 depth = isl_ast_build_get_depth(build);
905 if (!isl_ast_build_has_stride(build, depth))
906 return isl_ast_expr_alloc_int_si(ctx, 1);
908 isl_int_init(v);
909 isl_ast_build_get_stride(build, depth, &v);
910 inc = isl_ast_expr_alloc_int(ctx, v);
911 isl_int_clear(v);
913 return inc;
916 /* Should we express the loop condition as
918 * iterator <= min(list of upper bounds)
920 * or as a conjunction of constraints?
922 * The first is constructed from a list of upper bounds.
923 * The second is constructed from a set.
925 * If there are no upper bounds in "constraints", then this could mean
926 * that "domain" simply doesn't have an upper bound or that we didn't
927 * pick any upper bound. In the first case, we want to generate the
928 * loop condition as a(n empty) conjunction of constraints
929 * In the second case, we will compute
930 * a single upper bound from "domain" and so we use the list form.
932 * If there are upper bounds in "constraints",
933 * then we use the list form iff the atomic_upper_bound option is set.
935 static int use_upper_bound_list(isl_ctx *ctx, int n_upper,
936 __isl_keep isl_set *domain, int depth)
938 if (n_upper > 0)
939 return isl_options_get_ast_build_atomic_upper_bound(ctx);
940 else
941 return isl_set_dim_has_upper_bound(domain, isl_dim_set, depth);
944 /* Fill in the expressions of the for node in graft->node.
946 * In particular,
947 * - set the initialization part of the loop to the maximum of the lower bounds
948 * - set the size of the iterator based on the values attained by the iterator
949 * - extract the increment from the stride of the current dimension
950 * - construct the for condition either based on a list of upper bounds
951 * or on a set of upper bound constraints.
953 static __isl_give isl_ast_graft *set_for_node_expressions(
954 __isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *lower,
955 int use_list, __isl_keep isl_pw_aff_list *upper_list,
956 __isl_keep isl_set *upper_set, __isl_keep isl_ast_build *build)
958 isl_ast_node *node;
960 if (!graft)
961 return NULL;
963 build = isl_ast_build_copy(build);
964 build = isl_ast_build_set_enforced(build,
965 isl_ast_graft_get_enforced(graft));
967 node = graft->node;
968 node->u.f.init = reduce_list(isl_ast_op_max, lower, build);
969 node->u.f.inc = for_inc(build);
971 if (use_list)
972 graft = set_for_cond_from_list(graft, upper_list, build);
973 else
974 graft = set_for_cond_from_set(graft, upper_set, build);
976 isl_ast_build_free(build);
978 if (!node->u.f.iterator || !node->u.f.init ||
979 !node->u.f.cond || !node->u.f.inc)
980 return isl_ast_graft_free(graft);
982 return graft;
985 /* Update "graft" based on "bounds" and "domain" for the generic,
986 * non-degenerate, case.
988 * "constraints" contains the "n_lower" lower and "n_upper" upper bounds
989 * that the loop node should express.
990 * "domain" is the subset of the intersection of the constraints
991 * for which some code is executed.
993 * There may be zero lower bounds or zero upper bounds in "constraints"
994 * in case the list of constraints was created
995 * based on the atomic option or based on separation with explicit bounds.
996 * In that case, we use "domain" to derive lower and/or upper bounds.
998 * We first compute a list of one or more lower bounds.
1000 * Then we decide if we want to express the condition as
1002 * iterator <= min(list of upper bounds)
1004 * or as a conjunction of constraints.
1006 * The set of enforced constraints is then computed either based on
1007 * a list of upper bounds or on a set of upper bound constraints.
1008 * We do not compute any enforced constraints if we were forced
1009 * to compute a lower or upper bound using exact_bound. The domains
1010 * of the resulting expressions may imply some bounds on outer dimensions
1011 * that we do not want to appear in the enforced constraints since
1012 * they are not actually enforced by the corresponding code.
1014 * Finally, we fill in the expressions of the for node.
1016 static __isl_give isl_ast_graft *refine_generic_bounds(
1017 __isl_take isl_ast_graft *graft,
1018 __isl_keep isl_constraint **constraint, int n_lower, int n_upper,
1019 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
1021 int depth;
1022 isl_ctx *ctx;
1023 isl_pw_aff_list *lower;
1024 int use_list;
1025 isl_set *upper_set = NULL;
1026 isl_pw_aff_list *upper_list = NULL;
1028 if (!graft || !build)
1029 return isl_ast_graft_free(graft);
1031 depth = isl_ast_build_get_depth(build);
1032 ctx = isl_ast_graft_get_ctx(graft);
1034 use_list = use_upper_bound_list(ctx, n_upper, domain, depth);
1036 lower = lower_bounds(constraint, n_lower, depth, domain, build);
1038 if (use_list)
1039 upper_list = upper_bounds(constraint + n_lower, n_upper, depth,
1040 domain, build);
1041 else if (n_upper > 0)
1042 upper_set = intersect_constraints(ctx, constraint + n_lower,
1043 n_upper);
1044 else
1045 upper_set = isl_set_universe(isl_set_get_space(domain));
1047 if (n_lower == 0 || n_upper == 0)
1049 else if (use_list)
1050 graft = set_enforced_from_list(graft, lower, upper_list);
1051 else
1052 graft = set_enforced_from_set(graft, lower, depth, upper_set);
1054 graft = set_for_node_expressions(graft, lower, use_list, upper_list,
1055 upper_set, build);
1057 isl_pw_aff_list_free(lower);
1058 isl_pw_aff_list_free(upper_list);
1059 isl_set_free(upper_set);
1061 return graft;
1064 /* How many constraints in the "constraint" array, starting at position "first"
1065 * are of the give type? "n" represents the total number of elements
1066 * in the array.
1068 static int count_constraints(isl_constraint **constraint, int n, int first,
1069 int pos, int type)
1071 int i;
1073 constraint += first;
1075 for (i = 0; first + i < n; i++)
1076 if (constraint_type(constraint[i], pos) != type)
1077 break;
1079 return i;
1082 /* Update "graft" based on "bounds" and "domain" for the generic,
1083 * non-degenerate, case.
1085 * "list" respresent the list of bounds that need to be encoded by
1086 * the for loop (or a guard around the for loop).
1087 * "domain" is the subset of the intersection of the constraints
1088 * for which some code is executed.
1089 * "build" is the build in which graft->node was created.
1091 * We separate lower bounds, upper bounds and constraints that
1092 * are independent of the loop iterator.
1094 * The actual for loop bounds are generated in refine_generic_bounds.
1095 * If there are any constraints that are independent of the loop iterator,
1096 * we need to put a guard around the for loop (which may get hoisted up
1097 * to higher levels) and we call refine_generic_bounds in a build
1098 * where this guard is enforced.
1100 static __isl_give isl_ast_graft *refine_generic_split(
1101 __isl_take isl_ast_graft *graft, __isl_keep isl_constraint_list *list,
1102 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
1104 isl_ctx *ctx;
1105 isl_ast_build *for_build;
1106 isl_set *guard;
1107 int n_indep, n_lower, n_upper;
1108 int pos;
1109 int n;
1111 if (!list)
1112 return isl_ast_graft_free(graft);
1114 pos = isl_ast_build_get_depth(build);
1116 if (isl_sort(list->p, list->n, sizeof(isl_constraint *),
1117 &cmp_constraint, &pos) < 0)
1118 return isl_ast_graft_free(graft);
1120 n = list->n;
1121 n_indep = count_constraints(list->p, n, 0, pos, 0);
1122 n_lower = count_constraints(list->p, n, n_indep, pos, 1);
1123 n_upper = count_constraints(list->p, n, n_indep + n_lower, pos, 2);
1125 if (n_indep == 0)
1126 return refine_generic_bounds(graft,
1127 list->p + n_indep, n_lower, n_upper, domain, build);
1129 ctx = isl_ast_graft_get_ctx(graft);
1130 guard = intersect_constraints(ctx, list->p, n_indep);
1132 for_build = isl_ast_build_copy(build);
1133 for_build = isl_ast_build_restrict_pending(for_build,
1134 isl_set_copy(guard));
1135 graft = refine_generic_bounds(graft,
1136 list->p + n_indep, n_lower, n_upper, domain, for_build);
1137 isl_ast_build_free(for_build);
1139 graft = isl_ast_graft_add_guard(graft, guard, build);
1141 return graft;
1144 /* Update "graft" based on "bounds" and "domain" for the generic,
1145 * non-degenerate, case.
1147 * "bounds" respresent the bounds that need to be encoded by
1148 * the for loop (or a guard around the for loop).
1149 * "domain" is the subset of "bounds" for which some code is executed.
1150 * "build" is the build in which graft->node was created.
1152 * We break up "bounds" into a list of constraints and continue with
1153 * refine_generic_split.
1155 static __isl_give isl_ast_graft *refine_generic(
1156 __isl_take isl_ast_graft *graft,
1157 __isl_keep isl_basic_set *bounds, __isl_keep isl_set *domain,
1158 __isl_keep isl_ast_build *build)
1160 isl_constraint_list *list;
1162 if (!build || !graft)
1163 return isl_ast_graft_free(graft);
1165 bounds = isl_basic_set_copy(bounds);
1166 bounds = isl_ast_build_compute_gist_basic_set(build, bounds);
1167 list = isl_constraint_list_from_basic_set(bounds);
1169 graft = refine_generic_split(graft, list, domain, build);
1171 isl_constraint_list_free(list);
1172 return graft;
1175 /* Create a for node for the current level.
1177 * Mark the for node degenerate if "degenerate" is set.
1179 static __isl_give isl_ast_node *create_for(__isl_keep isl_ast_build *build,
1180 int degenerate)
1182 int depth;
1183 isl_id *id;
1184 isl_ast_node *node;
1186 if (!build)
1187 return NULL;
1189 depth = isl_ast_build_get_depth(build);
1190 id = isl_ast_build_get_iterator_id(build, depth);
1191 node = isl_ast_node_alloc_for(id);
1192 if (degenerate)
1193 node = isl_ast_node_for_mark_degenerate(node);
1195 return node;
1198 /* Create an AST node for the current dimension based on
1199 * the schedule domain "bounds" and return the node encapsulated
1200 * in an isl_ast_graft.
1202 * "executed" is the current inverse schedule, taking into account
1203 * the bounds in "bounds"
1204 * "domain" is the domain of "executed", with inner dimensions projected out.
1205 * It may be a strict subset of "bounds" in case "bounds" was created
1206 * based on the atomic option or based on separation with explicit bounds.
1208 * "domain" may satisfy additional equalities that result
1209 * from intersecting "executed" with "bounds" in add_node.
1210 * It may also satisfy some global constraints that were dropped out because
1211 * we performed separation with explicit bounds.
1212 * The very first step is then to copy these constraints to "bounds".
1214 * Since we may be calling before_each_for and after_each_for
1215 * callbacks, we record the current inverse schedule in the build.
1217 * We consider three builds,
1218 * "build" is the one in which the current level is created,
1219 * "body_build" is the build in which the next level is created,
1220 * "sub_build" is essentially the same as "body_build", except that
1221 * the depth has not been increased yet.
1223 * "build" already contains information (in strides and offsets)
1224 * about the strides at the current level, but this information is not
1225 * reflected in the build->domain.
1226 * We first add this information and the "bounds" to the sub_build->domain.
1227 * isl_ast_build_set_loop_bounds checks whether the current dimension attains
1228 * only a single value and whether this single value can be represented using
1229 * a single affine expression.
1230 * In the first case, the current level is considered "degenerate".
1231 * In the second, sub-case, the current level is considered "eliminated".
1232 * Eliminated level don't need to be reflected in the AST since we can
1233 * simply plug in the affine expression. For degenerate, but non-eliminated,
1234 * levels, we do introduce a for node, but mark is as degenerate so that
1235 * it can be printed as an assignment of the single value to the loop
1236 * "iterator".
1238 * If the current level is eliminated, we eliminate the current dimension
1239 * from the inverse schedule to make sure no inner dimensions depend
1240 * on the current dimension. Otherwise, we create a for node, marking
1241 * it degenerate if appropriate. The initial for node is still incomplete
1242 * and will be completed in either refine_degenerate or refine_generic.
1244 * We then generate a sequence of grafts for the next level,
1245 * create a surrounding graft for the current level and insert
1246 * the for node we created (if the current level is not eliminated).
1248 * Finally, we set the bounds of the for loop and insert guards
1249 * (either in the AST or in the graft) in one of
1250 * refine_eliminated, refine_degenerate or refine_generic.
1252 static __isl_give isl_ast_graft *create_node_scaled(
1253 __isl_take isl_union_map *executed,
1254 __isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
1255 __isl_take isl_ast_build *build)
1257 int depth;
1258 int degenerate, eliminated;
1259 isl_basic_set *hull;
1260 isl_ast_node *node = NULL;
1261 isl_ast_graft *graft;
1262 isl_ast_graft_list *children;
1263 isl_ast_build *sub_build;
1264 isl_ast_build *body_build;
1266 domain = isl_ast_build_eliminate_divs(build, domain);
1267 domain = isl_set_detect_equalities(domain);
1268 hull = isl_set_unshifted_simple_hull(isl_set_copy(domain));
1269 bounds = isl_basic_set_intersect(bounds, hull);
1270 build = isl_ast_build_set_executed(build, isl_union_map_copy(executed));
1272 depth = isl_ast_build_get_depth(build);
1273 sub_build = isl_ast_build_copy(build);
1274 sub_build = isl_ast_build_include_stride(sub_build);
1275 sub_build = isl_ast_build_set_loop_bounds(sub_build,
1276 isl_basic_set_copy(bounds));
1277 degenerate = isl_ast_build_has_value(sub_build);
1278 eliminated = isl_ast_build_has_affine_value(sub_build, depth);
1279 if (degenerate < 0 || eliminated < 0)
1280 executed = isl_union_map_free(executed);
1281 if (eliminated)
1282 executed = eliminate(executed, depth, build);
1283 else
1284 node = create_for(build, degenerate);
1286 body_build = isl_ast_build_copy(sub_build);
1287 body_build = isl_ast_build_increase_depth(body_build);
1288 if (!eliminated)
1289 node = before_each_for(node, body_build);
1290 children = generate_next_level(executed,
1291 isl_ast_build_copy(body_build));
1293 graft = isl_ast_graft_alloc_level(children, sub_build);
1294 if (!eliminated)
1295 graft = isl_ast_graft_insert_for(graft, node);
1296 if (eliminated)
1297 graft = refine_eliminated(graft, bounds, build);
1298 else if (degenerate)
1299 graft = refine_degenerate(graft, bounds, build, sub_build);
1300 else
1301 graft = refine_generic(graft, bounds, domain, build);
1302 if (!eliminated)
1303 graft = after_each_for(graft, body_build);
1305 isl_ast_build_free(body_build);
1306 isl_ast_build_free(sub_build);
1307 isl_ast_build_free(build);
1308 isl_basic_set_free(bounds);
1309 isl_set_free(domain);
1311 return graft;
1314 /* Internal data structure for checking if all constraints involving
1315 * the input dimension "depth" are such that the other coefficients
1316 * are multiples of "m", reducing "m" if they are not.
1317 * If "m" is reduced all the way down to "1", then the check has failed
1318 * and we break out of the iteration.
1319 * "d" is an initialized isl_int that can be used internally.
1321 struct isl_check_scaled_data {
1322 int depth;
1323 isl_int m, d;
1326 /* If constraint "c" involves the input dimension data->depth,
1327 * then make sure that all the other coefficients are multiples of data->m,
1328 * reducing data->m if needed.
1329 * Break out of the iteration if data->m has become equal to "1".
1331 static int constraint_check_scaled(__isl_take isl_constraint *c, void *user)
1333 struct isl_check_scaled_data *data = user;
1334 int i, j, n;
1335 enum isl_dim_type t[] = { isl_dim_param, isl_dim_in, isl_dim_out,
1336 isl_dim_div };
1338 if (!isl_constraint_involves_dims(c, isl_dim_in, data->depth, 1)) {
1339 isl_constraint_free(c);
1340 return 0;
1343 for (i = 0; i < 4; ++i) {
1344 n = isl_constraint_dim(c, t[i]);
1345 for (j = 0; j < n; ++j) {
1346 if (t[i] == isl_dim_in && j == data->depth)
1347 continue;
1348 if (!isl_constraint_involves_dims(c, t[i], j, 1))
1349 continue;
1350 isl_constraint_get_coefficient(c, t[i], j, &data->d);
1351 isl_int_gcd(data->m, data->m, data->d);
1352 if (isl_int_is_one(data->m))
1353 break;
1355 if (j < n)
1356 break;
1359 isl_constraint_free(c);
1361 return i < 4 ? -1 : 0;
1364 /* For each constraint of "bmap" that involves the input dimension data->depth,
1365 * make sure that all the other coefficients are multiples of data->m,
1366 * reducing data->m if needed.
1367 * Break out of the iteration if data->m has become equal to "1".
1369 static int basic_map_check_scaled(__isl_take isl_basic_map *bmap, void *user)
1371 int r;
1373 r = isl_basic_map_foreach_constraint(bmap,
1374 &constraint_check_scaled, user);
1375 isl_basic_map_free(bmap);
1377 return r;
1380 /* For each constraint of "map" that involves the input dimension data->depth,
1381 * make sure that all the other coefficients are multiples of data->m,
1382 * reducing data->m if needed.
1383 * Break out of the iteration if data->m has become equal to "1".
1385 static int map_check_scaled(__isl_take isl_map *map, void *user)
1387 int r;
1389 r = isl_map_foreach_basic_map(map, &basic_map_check_scaled, user);
1390 isl_map_free(map);
1392 return r;
1395 /* Create an AST node for the current dimension based on
1396 * the schedule domain "bounds" and return the node encapsulated
1397 * in an isl_ast_graft.
1399 * "executed" is the current inverse schedule, taking into account
1400 * the bounds in "bounds"
1401 * "domain" is the domain of "executed", with inner dimensions projected out.
1404 * Before moving on to the actual AST node construction in create_node_scaled,
1405 * we first check if the current dimension is strided and if we can scale
1406 * down this stride. Note that we only do this if the ast_build_scale_strides
1407 * option is set.
1409 * In particular, let the current dimension take on values
1411 * f + s a
1413 * with a an integer. We check if we can find an integer m that (obviouly)
1414 * divides both f and s.
1416 * If so, we check if the current dimension only appears in constraints
1417 * where the coefficients of the other variables are multiples of m.
1418 * We perform this extra check to avoid the risk of introducing
1419 * divisions by scaling down the current dimension.
1421 * If so, we scale the current dimension down by a factor of m.
1422 * That is, we plug in
1424 * i = m i' (1)
1426 * Note that in principle we could always scale down strided loops
1427 * by plugging in
1429 * i = f + s i'
1431 * but this may result in i' taking on larger values than the original i,
1432 * due to the shift by "f".
1433 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1435 static __isl_give isl_ast_graft *create_node(__isl_take isl_union_map *executed,
1436 __isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
1437 __isl_take isl_ast_build *build)
1439 struct isl_check_scaled_data data;
1440 isl_ctx *ctx;
1441 isl_aff *offset;
1443 ctx = isl_ast_build_get_ctx(build);
1444 if (!isl_options_get_ast_build_scale_strides(ctx))
1445 return create_node_scaled(executed, bounds, domain, build);
1447 data.depth = isl_ast_build_get_depth(build);
1448 if (!isl_ast_build_has_stride(build, data.depth))
1449 return create_node_scaled(executed, bounds, domain, build);
1451 isl_int_init(data.m);
1452 isl_int_init(data.d);
1454 offset = isl_ast_build_get_offset(build, data.depth);
1455 if (isl_ast_build_get_stride(build, data.depth, &data.m) < 0)
1456 offset = isl_aff_free(offset);
1457 offset = isl_aff_scale_down(offset, data.m);
1458 if (isl_aff_get_denominator(offset, &data.d) < 0)
1459 executed = isl_union_map_free(executed);
1461 if (executed && isl_int_is_divisible_by(data.m, data.d))
1462 isl_int_divexact(data.m, data.m, data.d);
1463 else
1464 isl_int_set_si(data.m, 1);
1466 if (!isl_int_is_one(data.m)) {
1467 if (isl_union_map_foreach_map(executed, &map_check_scaled,
1468 &data) < 0 &&
1469 !isl_int_is_one(data.m))
1470 executed = isl_union_map_free(executed);
1473 if (!isl_int_is_one(data.m)) {
1474 isl_space *space;
1475 isl_multi_aff *ma;
1476 isl_aff *aff;
1477 isl_map *map;
1478 isl_union_map *umap;
1480 space = isl_ast_build_get_space(build, 1);
1481 space = isl_space_map_from_set(space);
1482 ma = isl_multi_aff_identity(space);
1483 aff = isl_multi_aff_get_aff(ma, data.depth);
1484 aff = isl_aff_scale(aff, data.m);
1485 ma = isl_multi_aff_set_aff(ma, data.depth, aff);
1487 bounds = isl_basic_set_preimage_multi_aff(bounds,
1488 isl_multi_aff_copy(ma));
1489 domain = isl_set_preimage_multi_aff(domain,
1490 isl_multi_aff_copy(ma));
1491 map = isl_map_reverse(isl_map_from_multi_aff(ma));
1492 umap = isl_union_map_from_map(map);
1493 executed = isl_union_map_apply_domain(executed,
1494 isl_union_map_copy(umap));
1495 build = isl_ast_build_scale_down(build, data.m, umap);
1497 isl_aff_free(offset);
1499 isl_int_clear(data.d);
1500 isl_int_clear(data.m);
1502 return create_node_scaled(executed, bounds, domain, build);
1505 /* Add the basic set to the list that "user" points to.
1507 static int collect_basic_set(__isl_take isl_basic_set *bset, void *user)
1509 isl_basic_set_list **list = user;
1511 *list = isl_basic_set_list_add(*list, bset);
1513 return 0;
1516 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1518 static __isl_give isl_basic_set_list *isl_basic_set_list_from_set(
1519 __isl_take isl_set *set)
1521 int n;
1522 isl_ctx *ctx;
1523 isl_basic_set_list *list;
1525 if (!set)
1526 return NULL;
1528 ctx = isl_set_get_ctx(set);
1530 n = isl_set_n_basic_set(set);
1531 list = isl_basic_set_list_alloc(ctx, n);
1532 if (isl_set_foreach_basic_set(set, &collect_basic_set, &list) < 0)
1533 list = isl_basic_set_list_free(list);
1535 isl_set_free(set);
1536 return list;
1539 /* Generate code for the schedule domain "bounds"
1540 * and add the result to "list".
1542 * We mainly detect strides and additional equalities here
1543 * and then pass over control to create_node.
1545 * "bounds" reflects the bounds on the current dimension and possibly
1546 * some extra conditions on outer dimensions.
1547 * It does not, however, include any divs involving the current dimension,
1548 * so it does not capture any stride constraints.
1549 * We therefore need to compute that part of the schedule domain that
1550 * intersects with "bounds" and derive the strides from the result.
1552 static __isl_give isl_ast_graft_list *add_node(
1553 __isl_take isl_ast_graft_list *list, __isl_take isl_union_map *executed,
1554 __isl_take isl_basic_set *bounds, __isl_take isl_ast_build *build)
1556 isl_ast_graft *graft;
1557 isl_set *domain = NULL;
1558 isl_union_set *uset;
1559 int empty;
1561 uset = isl_union_set_from_basic_set(isl_basic_set_copy(bounds));
1562 executed = isl_union_map_intersect_domain(executed, uset);
1563 empty = isl_union_map_is_empty(executed);
1564 if (empty < 0)
1565 goto error;
1566 if (empty)
1567 goto done;
1569 uset = isl_union_map_domain(isl_union_map_copy(executed));
1570 domain = isl_set_from_union_set(uset);
1571 domain = isl_ast_build_compute_gist(build, domain);
1572 empty = isl_set_is_empty(domain);
1573 if (empty < 0)
1574 goto error;
1575 if (empty)
1576 goto done;
1578 domain = isl_ast_build_eliminate_inner(build, domain);
1579 build = isl_ast_build_detect_strides(build, isl_set_copy(domain));
1581 graft = create_node(executed, bounds, domain,
1582 isl_ast_build_copy(build));
1583 list = isl_ast_graft_list_add(list, graft);
1584 isl_ast_build_free(build);
1585 return list;
1586 error:
1587 list = isl_ast_graft_list_free(list);
1588 done:
1589 isl_set_free(domain);
1590 isl_basic_set_free(bounds);
1591 isl_union_map_free(executed);
1592 isl_ast_build_free(build);
1593 return list;
1596 struct isl_domain_follows_at_depth_data {
1597 int depth;
1598 isl_basic_set **piece;
1601 /* Does any element of i follow or coincide with any element of j
1602 * at the current depth (data->depth) for equal values of the outer
1603 * dimensions?
1605 static int domain_follows_at_depth(int i, int j, void *user)
1607 struct isl_domain_follows_at_depth_data *data = user;
1608 isl_basic_map *test;
1609 int empty;
1610 int l;
1612 test = isl_basic_map_from_domain_and_range(
1613 isl_basic_set_copy(data->piece[i]),
1614 isl_basic_set_copy(data->piece[j]));
1615 for (l = 0; l < data->depth; ++l)
1616 test = isl_basic_map_equate(test, isl_dim_in, l,
1617 isl_dim_out, l);
1618 test = isl_basic_map_order_ge(test, isl_dim_in, data->depth,
1619 isl_dim_out, data->depth);
1620 empty = isl_basic_map_is_empty(test);
1621 isl_basic_map_free(test);
1623 return empty < 0 ? -1 : !empty;
1626 static __isl_give isl_ast_graft_list *generate_sorted_domains(
1627 __isl_keep isl_basic_set_list *domain_list,
1628 __isl_keep isl_union_map *executed,
1629 __isl_keep isl_ast_build *build);
1631 /* Generate code for the "n" schedule domains in "domain_list"
1632 * with positions specified by the entries of the "pos" array
1633 * and add the results to "list".
1635 * The "n" domains form a strongly connected component in the ordering.
1636 * If n is larger than 1, then this means that we cannot determine a valid
1637 * ordering for the n domains in the component. This should be fairly
1638 * rare because the individual domains have been made disjoint first.
1639 * The problem is that the domains may be integrally disjoint but not
1640 * rationally disjoint. For example, we may have domains
1642 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1644 * These two domains have an empty intersection, but their rational
1645 * relaxations do intersect. It is impossible to order these domains
1646 * in the second dimension because the first should be ordered before
1647 * the second for outer dimension equal to 0, while it should be ordered
1648 * after for outer dimension equal to 1.
1650 * This may happen in particular in case of unrolling since the domain
1651 * of each slice is replaced by its simple hull.
1653 * We collect the basic sets in the component, call isl_set_make_disjoint
1654 * and try again. Note that we rely here on isl_set_make_disjoint also
1655 * making the basic sets rationally disjoint. If the basic sets
1656 * are rationally disjoint, then the ordering problem does not occur.
1657 * To see this, there can only be a problem if there are points
1658 * (i,a) and (j,b) in one set and (i,c) and (j,d) in the other with
1659 * a < c and b > d. This means that either the interval spanned
1660 * by a en b lies inside that spanned by c and or the other way around.
1661 * In either case, there is a point inside both intervals with the
1662 * convex combination in terms of a and b and in terms of c and d.
1663 * Taking the same combination of i and j gives a point in the intersection.
1665 static __isl_give isl_ast_graft_list *add_nodes(
1666 __isl_take isl_ast_graft_list *list, int *pos, int n,
1667 __isl_keep isl_basic_set_list *domain_list,
1668 __isl_keep isl_union_map *executed,
1669 __isl_keep isl_ast_build *build)
1671 int i;
1672 isl_basic_set *bset;
1673 isl_set *set;
1675 bset = isl_basic_set_list_get_basic_set(domain_list, pos[0]);
1676 if (n == 1)
1677 return add_node(list, isl_union_map_copy(executed), bset,
1678 isl_ast_build_copy(build));
1680 set = isl_set_from_basic_set(bset);
1681 for (i = 1; i < n; ++i) {
1682 bset = isl_basic_set_list_get_basic_set(domain_list, pos[i]);
1683 set = isl_set_union(set, isl_set_from_basic_set(bset));
1686 set = isl_set_make_disjoint(set);
1687 if (isl_set_n_basic_set(set) == n)
1688 isl_die(isl_ast_graft_list_get_ctx(list), isl_error_internal,
1689 "unable to separate loop parts", goto error);
1690 domain_list = isl_basic_set_list_from_set(set);
1691 list = isl_ast_graft_list_concat(list,
1692 generate_sorted_domains(domain_list, executed, build));
1693 isl_basic_set_list_free(domain_list);
1695 return list;
1696 error:
1697 isl_set_free(set);
1698 return isl_ast_graft_list_free(list);
1701 /* Sort the domains in "domain_list" according to the execution order
1702 * at the current depth (for equal values of the outer dimensions),
1703 * generate code for each of them, collecting the results in a list.
1704 * If no code is generated (because the intersection of the inverse schedule
1705 * with the domains turns out to be empty), then an empty list is returned.
1707 * The caller is responsible for ensuring that the basic sets in "domain_list"
1708 * are pair-wise disjoint. It can, however, in principle happen that
1709 * two basic sets should be ordered one way for one value of the outer
1710 * dimensions and the other way for some other value of the outer dimensions.
1711 * We therefore play safe and look for strongly connected components.
1712 * The function add_nodes takes care of handling non-trivial components.
1714 static __isl_give isl_ast_graft_list *generate_sorted_domains(
1715 __isl_keep isl_basic_set_list *domain_list,
1716 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
1718 isl_ctx *ctx;
1719 isl_ast_graft_list *list;
1720 struct isl_domain_follows_at_depth_data data;
1721 struct isl_tarjan_graph *g;
1722 int i, n;
1724 if (!domain_list)
1725 return NULL;
1727 ctx = isl_basic_set_list_get_ctx(domain_list);
1728 n = isl_basic_set_list_n_basic_set(domain_list);
1729 list = isl_ast_graft_list_alloc(ctx, n);
1730 if (n == 0)
1731 return list;
1732 if (n == 1)
1733 return add_node(list, isl_union_map_copy(executed),
1734 isl_basic_set_list_get_basic_set(domain_list, 0),
1735 isl_ast_build_copy(build));
1737 data.depth = isl_ast_build_get_depth(build);
1738 data.piece = domain_list->p;
1739 g = isl_tarjan_graph_init(ctx, n, &domain_follows_at_depth, &data);
1741 i = 0;
1742 while (list && n) {
1743 int first;
1745 if (g->order[i] == -1)
1746 isl_die(ctx, isl_error_internal, "cannot happen",
1747 goto error);
1748 first = i;
1749 while (g->order[i] != -1) {
1750 ++i; --n;
1752 list = add_nodes(list, g->order + first, i - first,
1753 domain_list, executed, build);
1754 ++i;
1757 if (0)
1758 error: list = isl_ast_graft_list_free(list);
1759 isl_tarjan_graph_free(g);
1761 return list;
1764 struct isl_shared_outer_data {
1765 int depth;
1766 isl_basic_set **piece;
1769 /* Do elements i and j share any values for the outer dimensions?
1771 static int shared_outer(int i, int j, void *user)
1773 struct isl_shared_outer_data *data = user;
1774 isl_basic_map *test;
1775 int empty;
1776 int l;
1778 test = isl_basic_map_from_domain_and_range(
1779 isl_basic_set_copy(data->piece[i]),
1780 isl_basic_set_copy(data->piece[j]));
1781 for (l = 0; l < data->depth; ++l)
1782 test = isl_basic_map_equate(test, isl_dim_in, l,
1783 isl_dim_out, l);
1784 empty = isl_basic_map_is_empty(test);
1785 isl_basic_map_free(test);
1787 return empty < 0 ? -1 : !empty;
1790 /* Call generate_sorted_domains on a list containing the elements
1791 * of "domain_list indexed by the first "n" elements of "pos".
1793 static __isl_give isl_ast_graft_list *generate_sorted_domains_part(
1794 __isl_keep isl_basic_set_list *domain_list, int *pos, int n,
1795 __isl_keep isl_union_map *executed,
1796 __isl_keep isl_ast_build *build)
1798 int i;
1799 isl_ctx *ctx;
1800 isl_basic_set_list *slice;
1801 isl_ast_graft_list *list;
1803 ctx = isl_ast_build_get_ctx(build);
1804 slice = isl_basic_set_list_alloc(ctx, n);
1805 for (i = 0; i < n; ++i) {
1806 isl_basic_set *bset;
1808 bset = isl_basic_set_copy(domain_list->p[pos[i]]);
1809 slice = isl_basic_set_list_add(slice, bset);
1812 list = generate_sorted_domains(slice, executed, build);
1813 isl_basic_set_list_free(slice);
1815 return list;
1818 /* Look for any (weakly connected) components in the "domain_list"
1819 * of domains that share some values of the outer dimensions.
1820 * That is, domains in different components do not share any values
1821 * of the outer dimensions. This means that these components
1822 * can be freely reorderd.
1823 * Within each of the components, we sort the domains according
1824 * to the execution order at the current depth.
1826 * We fuse the result of each call to generate_sorted_domains_part
1827 * into a list with either zero or one graft and collect these (at most)
1828 * single element lists into a bigger list. This means that the elements of the
1829 * final list can be freely reordered. In particular, we sort them
1830 * according to an arbitrary but fixed ordering to ease merging of
1831 * graft lists from different components.
1833 static __isl_give isl_ast_graft_list *generate_parallel_domains(
1834 __isl_keep isl_basic_set_list *domain_list,
1835 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
1837 int i, n;
1838 isl_ctx *ctx;
1839 isl_ast_graft_list *list;
1840 struct isl_shared_outer_data data;
1841 struct isl_tarjan_graph *g;
1843 if (!domain_list)
1844 return NULL;
1846 n = isl_basic_set_list_n_basic_set(domain_list);
1847 if (n <= 1)
1848 return generate_sorted_domains(domain_list, executed, build);
1850 ctx = isl_basic_set_list_get_ctx(domain_list);
1852 data.depth = isl_ast_build_get_depth(build);
1853 data.piece = domain_list->p;
1854 g = isl_tarjan_graph_init(ctx, n, &shared_outer, &data);
1855 if (!g)
1856 return NULL;
1858 i = 0;
1859 do {
1860 int first;
1861 isl_ast_graft_list *list_c;
1863 if (g->order[i] == -1)
1864 isl_die(ctx, isl_error_internal, "cannot happen",
1865 break);
1866 first = i;
1867 while (g->order[i] != -1) {
1868 ++i; --n;
1870 if (first == 0 && n == 0) {
1871 isl_tarjan_graph_free(g);
1872 return generate_sorted_domains(domain_list,
1873 executed, build);
1875 list_c = generate_sorted_domains_part(domain_list,
1876 g->order + first, i - first, executed, build);
1877 list_c = isl_ast_graft_list_fuse(list_c, build);
1878 if (first == 0)
1879 list = list_c;
1880 else
1881 list = isl_ast_graft_list_concat(list, list_c);
1882 ++i;
1883 } while (list && n);
1885 if (n > 0)
1886 list = isl_ast_graft_list_free(list);
1888 list = isl_ast_graft_list_sort(list);
1890 isl_tarjan_graph_free(g);
1892 return list;
1895 /* Internal data for separate_domain.
1897 * "explicit" is set if we only want to use explicit bounds.
1899 * "domain" collects the separated domains.
1901 struct isl_separate_domain_data {
1902 isl_ast_build *build;
1903 int explicit;
1904 isl_set *domain;
1907 /* Extract implicit bounds on the current dimension for the executed "map".
1909 * The domain of "map" may involve inner dimensions, so we
1910 * need to eliminate them.
1912 static __isl_give isl_set *implicit_bounds(__isl_take isl_map *map,
1913 __isl_keep isl_ast_build *build)
1915 isl_set *domain;
1917 domain = isl_map_domain(map);
1918 domain = isl_ast_build_eliminate(build, domain);
1920 return domain;
1923 /* Extract explicit bounds on the current dimension for the executed "map".
1925 * Rather than eliminating the inner dimensions as in implicit_bounds,
1926 * we simply drop any constraints involving those inner dimensions.
1927 * The idea is that most bounds that are implied by constraints on the
1928 * inner dimensions will be enforced by for loops and not by explicit guards.
1929 * There is then no need to separate along those bounds.
1931 static __isl_give isl_set *explicit_bounds(__isl_take isl_map *map,
1932 __isl_keep isl_ast_build *build)
1934 isl_set *domain;
1935 int depth, dim;
1937 dim = isl_map_dim(map, isl_dim_out);
1938 map = isl_map_drop_constraints_involving_dims(map, isl_dim_out, 0, dim);
1940 domain = isl_map_domain(map);
1941 depth = isl_ast_build_get_depth(build);
1942 dim = isl_set_dim(domain, isl_dim_set);
1943 domain = isl_set_detect_equalities(domain);
1944 domain = isl_set_drop_constraints_involving_dims(domain,
1945 isl_dim_set, depth + 1, dim - (depth + 1));
1946 domain = isl_set_remove_divs_involving_dims(domain,
1947 isl_dim_set, depth, 1);
1948 domain = isl_set_remove_unknown_divs(domain);
1950 return domain;
1953 /* Split data->domain into pieces that intersect with the range of "map"
1954 * and pieces that do not intersect with the range of "map"
1955 * and then add that part of the range of "map" that does not intersect
1956 * with data->domain.
1958 static int separate_domain(__isl_take isl_map *map, void *user)
1960 struct isl_separate_domain_data *data = user;
1961 isl_set *domain;
1962 isl_set *d1, *d2;
1964 if (data->explicit)
1965 domain = explicit_bounds(map, data->build);
1966 else
1967 domain = implicit_bounds(map, data->build);
1969 domain = isl_set_coalesce(domain);
1970 domain = isl_set_make_disjoint(domain);
1971 d1 = isl_set_subtract(isl_set_copy(domain), isl_set_copy(data->domain));
1972 d2 = isl_set_subtract(isl_set_copy(data->domain), isl_set_copy(domain));
1973 data->domain = isl_set_intersect(data->domain, domain);
1974 data->domain = isl_set_union(data->domain, d1);
1975 data->domain = isl_set_union(data->domain, d2);
1977 return 0;
1980 /* Separate the schedule domains of "executed".
1982 * That is, break up the domain of "executed" into basic sets,
1983 * such that for each basic set S, every element in S is associated with
1984 * the same domain spaces.
1986 * "space" is the (single) domain space of "executed".
1988 static __isl_give isl_set *separate_schedule_domains(
1989 __isl_take isl_space *space, __isl_take isl_union_map *executed,
1990 __isl_keep isl_ast_build *build)
1992 struct isl_separate_domain_data data = { build };
1993 isl_ctx *ctx;
1995 ctx = isl_ast_build_get_ctx(build);
1996 data.explicit = isl_options_get_ast_build_separation_bounds(ctx) ==
1997 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT;
1998 data.domain = isl_set_empty(space);
1999 if (isl_union_map_foreach_map(executed, &separate_domain, &data) < 0)
2000 data.domain = isl_set_free(data.domain);
2002 isl_union_map_free(executed);
2003 return data.domain;
2006 /* Temporary data used during the search for a lower bound for unrolling.
2008 * "domain" is the original set for which to find a lower bound
2009 * "depth" is the dimension for which to find a lower boudn
2011 * "lower" is the best lower bound found so far. It is NULL if we have not
2012 * found any yet.
2013 * "n" is the corresponding size. If lower is NULL, then the value of n
2014 * is undefined.
2016 * "tmp" is a temporary initialized isl_int.
2018 struct isl_find_unroll_data {
2019 isl_set *domain;
2020 int depth;
2022 isl_aff *lower;
2023 int *n;
2024 isl_int tmp;
2027 /* Check if we can use "c" as a lower bound and if it is better than
2028 * any previously found lower bound.
2030 * If "c" does not involve the dimension at the current depth,
2031 * then we cannot use it.
2032 * Otherwise, let "c" be of the form
2034 * i >= f(j)/a
2036 * We compute the maximal value of
2038 * -ceil(f(j)/a)) + i + 1
2040 * over the domain. If there is such a value "n", then we know
2042 * -ceil(f(j)/a)) + i + 1 <= n
2044 * or
2046 * i < ceil(f(j)/a)) + n
2048 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2049 * We just need to check if we have found any lower bound before and
2050 * if the new lower bound is better (smaller n) than the previously found
2051 * lower bounds.
2053 static int update_unrolling_lower_bound(struct isl_find_unroll_data *data,
2054 __isl_keep isl_constraint *c)
2056 isl_aff *aff, *lower;
2057 enum isl_lp_result res;
2059 if (!isl_constraint_is_lower_bound(c, isl_dim_set, data->depth))
2060 return 0;
2062 lower = isl_constraint_get_bound(c, isl_dim_set, data->depth);
2063 lower = isl_aff_ceil(lower);
2064 aff = isl_aff_copy(lower);
2065 aff = isl_aff_neg(aff);
2066 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, data->depth, 1);
2067 aff = isl_aff_add_constant_si(aff, 1);
2068 res = isl_set_max(data->domain, aff, &data->tmp);
2069 isl_aff_free(aff);
2071 if (res == isl_lp_error)
2072 goto error;
2073 if (res == isl_lp_unbounded) {
2074 isl_aff_free(lower);
2075 return 0;
2078 if (!data->lower || isl_int_cmp_si(data->tmp, *data->n) < 0) {
2079 isl_aff_free(data->lower);
2080 data->lower = lower;
2081 *data->n = isl_int_get_si(data->tmp);
2082 } else
2083 isl_aff_free(lower);
2085 return 1;
2086 error:
2087 isl_aff_free(lower);
2088 return -1;
2091 /* Check if we can use "c" as a lower bound and if it is better than
2092 * any previously found lower bound.
2094 static int constraint_find_unroll(__isl_take isl_constraint *c, void *user)
2096 struct isl_find_unroll_data *data;
2097 int r;
2099 data = (struct isl_find_unroll_data *) user;
2100 r = update_unrolling_lower_bound(data, c);
2101 isl_constraint_free(c);
2103 return r;
2106 /* Look for a lower bound l(i) on the dimension at "depth"
2107 * and a size n such that "domain" is a subset of
2109 * { [i] : l(i) <= i_d < l(i) + n }
2111 * where d is "depth" and l(i) depends only on earlier dimensions.
2112 * Furthermore, try and find a lower bound such that n is as small as possible.
2113 * In particular, "n" needs to be finite.
2115 * Inner dimensions have been eliminated from "domain" by the caller.
2117 * We first construct a collection of lower bounds on the input set
2118 * by computing its simple hull. We then iterate through them,
2119 * discarding those that we cannot use (either because they do not
2120 * involve the dimension at "depth" or because they have no corresponding
2121 * upper bound, meaning that "n" would be unbounded) and pick out the
2122 * best from the remaining ones.
2124 * If we cannot find a suitable lower bound, then we consider that
2125 * to be an error.
2127 static __isl_give isl_aff *find_unroll_lower_bound(__isl_keep isl_set *domain,
2128 int depth, int *n)
2130 struct isl_find_unroll_data data = { domain, depth, NULL, n };
2131 isl_basic_set *hull;
2133 isl_int_init(data.tmp);
2134 hull = isl_set_simple_hull(isl_set_copy(domain));
2136 if (isl_basic_set_foreach_constraint(hull,
2137 &constraint_find_unroll, &data) < 0)
2138 goto error;
2140 isl_basic_set_free(hull);
2141 isl_int_clear(data.tmp);
2143 if (!data.lower)
2144 isl_die(isl_set_get_ctx(domain), isl_error_invalid,
2145 "cannot find lower bound for unrolling", return NULL);
2147 return data.lower;
2148 error:
2149 isl_basic_set_free(hull);
2150 isl_int_clear(data.tmp);
2151 return isl_aff_free(data.lower);
2154 /* Intersect "set" with the constraint
2156 * i_"depth" = aff + offset
2158 static __isl_give isl_set *at_offset(__isl_take isl_set *set, int depth,
2159 __isl_keep isl_aff *aff, int offset)
2161 isl_constraint *eq;
2163 aff = isl_aff_copy(aff);
2164 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, depth, -1);
2165 aff = isl_aff_add_constant_si(aff, offset);
2166 eq = isl_equality_from_aff(aff);
2167 set = isl_set_add_constraint(set, eq);
2169 return set;
2172 /* Return a list of basic sets, one for each value of the current dimension
2173 * in "domain".
2174 * The divs that involve the current dimension have not been projected out
2175 * from this domain.
2177 * Since we are going to be iterating over the individual values,
2178 * we first check if there are any strides on the current dimension.
2179 * If there is, we rewrite the current dimension i as
2181 * i = stride i' + offset
2183 * and then iterate over individual values of i' instead.
2185 * We then look for a lower bound on i' and a size such that the domain
2186 * is a subset of
2188 * { [j,i'] : l(j) <= i' < l(j) + n }
2190 * and then take slices of the domain at values of i'
2191 * between l(j) and l(j) + n - 1.
2193 * We compute the unshifted simple hull of each slice to ensure that
2194 * we have a single basic set per offset. The slicing constraint
2195 * is preserved by taking the unshifted simple hull, so these basic sets
2196 * remain disjoint. The constraints that are dropped by taking the hull
2197 * will be taken into account at the next level, as in the case of the
2198 * atomic option.
2200 * Finally, we map i' back to i and add each basic set to the list.
2202 static __isl_give isl_basic_set_list *do_unroll(__isl_take isl_set *domain,
2203 __isl_keep isl_ast_build *build)
2205 int i, n;
2206 int depth;
2207 isl_ctx *ctx;
2208 isl_aff *lower;
2209 isl_basic_set_list *list;
2210 isl_multi_aff *expansion;
2211 isl_basic_map *bmap;
2213 if (!domain)
2214 return NULL;
2216 ctx = isl_set_get_ctx(domain);
2217 depth = isl_ast_build_get_depth(build);
2218 build = isl_ast_build_copy(build);
2219 domain = isl_ast_build_eliminate_inner(build, domain);
2220 build = isl_ast_build_detect_strides(build, isl_set_copy(domain));
2221 expansion = isl_ast_build_get_stride_expansion(build);
2223 domain = isl_set_preimage_multi_aff(domain,
2224 isl_multi_aff_copy(expansion));
2225 domain = isl_ast_build_eliminate_divs(build, domain);
2227 isl_ast_build_free(build);
2229 list = isl_basic_set_list_alloc(ctx, 0);
2231 lower = find_unroll_lower_bound(domain, depth, &n);
2232 if (!lower)
2233 list = isl_basic_set_list_free(list);
2235 bmap = isl_basic_map_from_multi_aff(expansion);
2237 for (i = 0; list && i < n; ++i) {
2238 isl_set *set;
2239 isl_basic_set *bset;
2241 set = at_offset(isl_set_copy(domain), depth, lower, i);
2242 bset = isl_set_unshifted_simple_hull(set);
2243 bset = isl_basic_set_apply(bset, isl_basic_map_copy(bmap));
2244 list = isl_basic_set_list_add(list, bset);
2247 isl_aff_free(lower);
2248 isl_set_free(domain);
2249 isl_basic_map_free(bmap);
2251 return list;
2254 /* Data structure for storing the results and the intermediate objects
2255 * of compute_domains.
2257 * "list" is the main result of the function and contains a list
2258 * of disjoint basic sets for which code should be generated.
2260 * "executed" and "build" are inputs to compute_domains.
2261 * "schedule_domain" is the domain of "executed".
2263 * "option" constains the domains at the current depth that should by
2264 * atomic, separated or unrolled. These domains are as specified by
2265 * the user, except that inner dimensions have been eliminated and
2266 * that they have been made pair-wise disjoint.
2268 * "sep_class" contains the user-specified split into separation classes
2269 * specialized to the current depth.
2270 * "done" contains the union of th separation domains that have already
2271 * been handled.
2273 struct isl_codegen_domains {
2274 isl_basic_set_list *list;
2276 isl_union_map *executed;
2277 isl_ast_build *build;
2278 isl_set *schedule_domain;
2280 isl_set *option[3];
2282 isl_map *sep_class;
2283 isl_set *done;
2286 /* Add domains to domains->list for each individual value of the current
2287 * dimension, for that part of the schedule domain that lies in the
2288 * intersection of the option domain and the class domain.
2290 * "domain" is the intersection of the class domain and the schedule domain.
2291 * The divs that involve the current dimension have not been projected out
2292 * from this domain.
2294 * We first break up the unroll option domain into individual pieces
2295 * and then handle each of them separately. The unroll option domain
2296 * has been made disjoint in compute_domains_init_options,
2298 * Note that we actively want to combine different pieces of the
2299 * schedule domain that have the same value at the current dimension.
2300 * We therefore need to break up the unroll option domain before
2301 * intersecting with class and schedule domain, hoping that the
2302 * unroll option domain specified by the user is relatively simple.
2304 static int compute_unroll_domains(struct isl_codegen_domains *domains,
2305 __isl_keep isl_set *domain)
2307 isl_set *unroll_domain;
2308 isl_basic_set_list *unroll_list;
2309 int i, n;
2310 int empty;
2312 empty = isl_set_is_empty(domains->option[unroll]);
2313 if (empty < 0)
2314 return -1;
2315 if (empty)
2316 return 0;
2318 unroll_domain = isl_set_copy(domains->option[unroll]);
2319 unroll_list = isl_basic_set_list_from_set(unroll_domain);
2321 n = isl_basic_set_list_n_basic_set(unroll_list);
2322 for (i = 0; i < n; ++i) {
2323 isl_basic_set *bset;
2324 isl_basic_set_list *list;
2326 bset = isl_basic_set_list_get_basic_set(unroll_list, i);
2327 unroll_domain = isl_set_from_basic_set(bset);
2328 unroll_domain = isl_set_intersect(unroll_domain,
2329 isl_set_copy(domain));
2331 empty = isl_set_is_empty(unroll_domain);
2332 if (empty >= 0 && empty) {
2333 isl_set_free(unroll_domain);
2334 continue;
2337 list = do_unroll(unroll_domain, domains->build);
2338 domains->list = isl_basic_set_list_concat(domains->list, list);
2341 isl_basic_set_list_free(unroll_list);
2343 return 0;
2346 /* Construct a single basic set that includes the intersection of
2347 * the schedule domain, the atomic option domain and the class domain.
2348 * Add the resulting basic set to domains->list.
2350 * We construct a single domain rather than trying to combine
2351 * the schedule domains of individual domains because we are working
2352 * within a single component so that non-overlapping schedule domains
2353 * should already have been separated.
2354 * Note, though, that this does not take into account the class domain.
2355 * So, it is possible for a class domain to carve out a piece of the
2356 * schedule domain with independent pieces and then we would only
2357 * generate a single domain for them. If this proves to be problematic
2358 * for some users, then this function will have to be adjusted.
2360 * "domain" is the intersection of the schedule domain and the class domain,
2361 * with inner dimensions projected out.
2363 static int compute_atomic_domain(struct isl_codegen_domains *domains,
2364 __isl_keep isl_set *domain)
2366 isl_basic_set *bset;
2367 isl_set *atomic_domain;
2368 int empty;
2370 atomic_domain = isl_set_copy(domains->option[atomic]);
2371 atomic_domain = isl_set_intersect(atomic_domain, isl_set_copy(domain));
2372 empty = isl_set_is_empty(atomic_domain);
2373 if (empty < 0 || empty) {
2374 isl_set_free(atomic_domain);
2375 return empty < 0 ? -1 : 0;
2378 atomic_domain = isl_set_coalesce(atomic_domain);
2379 bset = isl_set_unshifted_simple_hull(atomic_domain);
2380 domains->list = isl_basic_set_list_add(domains->list, bset);
2382 return 0;
2385 /* Split up the schedule domain into uniform basic sets,
2386 * in the sense that each element in a basic set is associated to
2387 * elements of the same domains, and add the result to domains->list.
2388 * Do this for that part of the schedule domain that lies in the
2389 * intersection of "class_domain" and the separate option domain.
2391 * "class_domain" may or may not include the constraints
2392 * of the schedule domain, but this does not make a difference
2393 * since we are going to intersect it with the domain of the inverse schedule.
2394 * If it includes schedule domain constraints, then they may involve
2395 * inner dimensions, but we will eliminate them in separation_domain.
2397 static int compute_separate_domain(struct isl_codegen_domains *domains,
2398 __isl_keep isl_set *class_domain)
2400 isl_space *space;
2401 isl_set *domain;
2402 isl_union_map *executed;
2403 isl_basic_set_list *list;
2404 int empty;
2406 domain = isl_set_copy(domains->option[separate]);
2407 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2408 executed = isl_union_map_copy(domains->executed);
2409 executed = isl_union_map_intersect_domain(executed,
2410 isl_union_set_from_set(domain));
2411 empty = isl_union_map_is_empty(executed);
2412 if (empty < 0 || empty) {
2413 isl_union_map_free(executed);
2414 return empty < 0 ? -1 : 0;
2417 space = isl_set_get_space(class_domain);
2418 domain = separate_schedule_domains(space, executed, domains->build);
2420 list = isl_basic_set_list_from_set(domain);
2421 domains->list = isl_basic_set_list_concat(domains->list, list);
2423 return 0;
2426 /* Split up the domain at the current depth into disjoint
2427 * basic sets for which code should be generated separately
2428 * for the given separation class domain.
2430 * If any separation classes have been defined, then "class_domain"
2431 * is the domain of the current class and does not refer to inner dimensions.
2432 * Otherwise, "class_domain" is the universe domain.
2434 * We first make sure that the class domain is disjoint from
2435 * previously considered class domains.
2437 * The separate domains can be computed directly from the "class_domain".
2439 * The unroll, atomic and remainder domains need the constraints
2440 * from the schedule domain.
2442 * For unrolling, the actual schedule domain is needed (with divs that
2443 * may refer to the current dimension) so that stride detection can be
2444 * performed.
2446 * For atomic and remainder domains, inner dimensions and divs involving
2447 * the current dimensions should be eliminated.
2448 * In case we are working within a separation class, we need to intersect
2449 * the result with the current "class_domain" to ensure that the domains
2450 * are disjoint from those generated from other class domains.
2452 * If anything is left after handling separate, unroll and atomic,
2453 * we split it up into basic sets and append the basic sets to domains->list.
2455 static int compute_partial_domains(struct isl_codegen_domains *domains,
2456 __isl_take isl_set *class_domain)
2458 isl_basic_set_list *list;
2459 isl_set *domain;
2461 class_domain = isl_set_subtract(class_domain,
2462 isl_set_copy(domains->done));
2463 domains->done = isl_set_union(domains->done,
2464 isl_set_copy(class_domain));
2466 domain = isl_set_copy(class_domain);
2468 if (compute_separate_domain(domains, domain) < 0)
2469 goto error;
2470 domain = isl_set_subtract(domain,
2471 isl_set_copy(domains->option[separate]));
2473 domain = isl_set_intersect(domain,
2474 isl_set_copy(domains->schedule_domain));
2476 if (compute_unroll_domains(domains, domain) < 0)
2477 goto error;
2478 domain = isl_set_subtract(domain,
2479 isl_set_copy(domains->option[unroll]));
2481 domain = isl_ast_build_eliminate(domains->build, domain);
2482 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2484 if (compute_atomic_domain(domains, domain) < 0)
2485 goto error;
2486 domain = isl_set_subtract(domain,
2487 isl_set_copy(domains->option[atomic]));
2489 domain = isl_set_coalesce(domain);
2490 domain = isl_set_make_disjoint(domain);
2492 list = isl_basic_set_list_from_set(domain);
2493 domains->list = isl_basic_set_list_concat(domains->list, list);
2495 isl_set_free(class_domain);
2497 return 0;
2498 error:
2499 isl_set_free(domain);
2500 isl_set_free(class_domain);
2501 return -1;
2504 /* Split up the domain at the current depth into disjoint
2505 * basic sets for which code should be generated separately
2506 * for the separation class identified by "pnt".
2508 * We extract the corresponding class domain from domains->sep_class,
2509 * eliminate inner dimensions and pass control to compute_partial_domains.
2511 static int compute_class_domains(__isl_take isl_point *pnt, void *user)
2513 struct isl_codegen_domains *domains = user;
2514 isl_set *class_set;
2515 isl_set *domain;
2516 int disjoint;
2518 class_set = isl_set_from_point(pnt);
2519 domain = isl_map_domain(isl_map_intersect_range(
2520 isl_map_copy(domains->sep_class), class_set));
2521 domain = isl_ast_build_eliminate(domains->build, domain);
2523 disjoint = isl_set_plain_is_disjoint(domain, domains->schedule_domain);
2524 if (disjoint < 0)
2525 return -1;
2526 if (disjoint) {
2527 isl_set_free(domain);
2528 return 0;
2531 return compute_partial_domains(domains, domain);
2534 /* Extract the domains at the current depth that should be atomic,
2535 * separated or unrolled and store them in option.
2537 * The domains specified by the user might overlap, so we make
2538 * them disjoint by subtracting earlier domains from later domains.
2540 static void compute_domains_init_options(isl_set *option[3],
2541 __isl_keep isl_ast_build *build)
2543 enum isl_ast_build_domain_type type, type2;
2545 for (type = atomic; type <= separate; ++type) {
2546 option[type] = isl_ast_build_get_option_domain(build, type);
2547 for (type2 = atomic; type2 < type; ++type2)
2548 option[type] = isl_set_subtract(option[type],
2549 isl_set_copy(option[type2]));
2552 option[unroll] = isl_set_coalesce(option[unroll]);
2553 option[unroll] = isl_set_make_disjoint(option[unroll]);
2556 /* Split up the domain at the current depth into disjoint
2557 * basic sets for which code should be generated separately,
2558 * based on the user-specified options.
2559 * Return the list of disjoint basic sets.
2561 * There are three kinds of domains that we need to keep track of.
2562 * - the "schedule domain" is the domain of "executed"
2563 * - the "class domain" is the domain corresponding to the currrent
2564 * separation class
2565 * - the "option domain" is the domain corresponding to one of the options
2566 * atomic, unroll or separate
2568 * We first consider the individial values of the separation classes
2569 * and split up the domain for each of them separately.
2570 * Finally, we consider the remainder. If no separation classes were
2571 * specified, then we call compute_partial_domains with the universe
2572 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2573 * with inner dimensions removed. We do this because we want to
2574 * avoid computing the complement of the class domains (i.e., the difference
2575 * between the universe and domains->done).
2577 static __isl_give isl_basic_set_list *compute_domains(
2578 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
2580 struct isl_codegen_domains domains;
2581 isl_ctx *ctx;
2582 isl_set *domain;
2583 isl_union_set *schedule_domain;
2584 isl_set *classes;
2585 isl_space *space;
2586 int n_param;
2587 enum isl_ast_build_domain_type type;
2588 int empty;
2590 if (!executed)
2591 return NULL;
2593 ctx = isl_union_map_get_ctx(executed);
2594 domains.list = isl_basic_set_list_alloc(ctx, 0);
2596 schedule_domain = isl_union_map_domain(isl_union_map_copy(executed));
2597 domain = isl_set_from_union_set(schedule_domain);
2599 compute_domains_init_options(domains.option, build);
2601 domains.sep_class = isl_ast_build_get_separation_class(build);
2602 classes = isl_map_range(isl_map_copy(domains.sep_class));
2603 n_param = isl_set_dim(classes, isl_dim_param);
2604 classes = isl_set_project_out(classes, isl_dim_param, 0, n_param);
2606 space = isl_set_get_space(domain);
2607 domains.build = build;
2608 domains.schedule_domain = isl_set_copy(domain);
2609 domains.executed = executed;
2610 domains.done = isl_set_empty(space);
2612 if (isl_set_foreach_point(classes, &compute_class_domains, &domains) < 0)
2613 domains.list = isl_basic_set_list_free(domains.list);
2614 isl_set_free(classes);
2616 empty = isl_set_is_empty(domains.done);
2617 if (empty < 0) {
2618 domains.list = isl_basic_set_list_free(domains.list);
2619 domain = isl_set_free(domain);
2620 } else if (empty) {
2621 isl_set_free(domain);
2622 domain = isl_set_universe(isl_set_get_space(domains.done));
2623 } else {
2624 domain = isl_ast_build_eliminate(build, domain);
2626 if (compute_partial_domains(&domains, domain) < 0)
2627 domains.list = isl_basic_set_list_free(domains.list);
2629 isl_set_free(domains.schedule_domain);
2630 isl_set_free(domains.done);
2631 isl_map_free(domains.sep_class);
2632 for (type = atomic; type <= separate; ++type)
2633 isl_set_free(domains.option[type]);
2635 return domains.list;
2638 /* Generate code for a single component, after shifting (if any)
2639 * has been applied.
2641 * We first split up the domain at the current depth into disjoint
2642 * basic sets based on the user-specified options.
2643 * Then we generated code for each of them and concatenate the results.
2645 static __isl_give isl_ast_graft_list *generate_shifted_component(
2646 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
2648 isl_basic_set_list *domain_list;
2649 isl_ast_graft_list *list = NULL;
2651 domain_list = compute_domains(executed, build);
2652 list = generate_parallel_domains(domain_list, executed, build);
2654 isl_basic_set_list_free(domain_list);
2655 isl_union_map_free(executed);
2656 isl_ast_build_free(build);
2658 return list;
2661 struct isl_set_map_pair {
2662 isl_set *set;
2663 isl_map *map;
2666 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2667 * of indices into the "domain" array,
2668 * return the union of the "map" fields of the elements
2669 * indexed by the first "n" elements of "order".
2671 static __isl_give isl_union_map *construct_component_executed(
2672 struct isl_set_map_pair *domain, int *order, int n)
2674 int i;
2675 isl_map *map;
2676 isl_union_map *executed;
2678 map = isl_map_copy(domain[order[0]].map);
2679 executed = isl_union_map_from_map(map);
2680 for (i = 1; i < n; ++i) {
2681 map = isl_map_copy(domain[order[i]].map);
2682 executed = isl_union_map_add_map(executed, map);
2685 return executed;
2688 /* Generate code for a single component, after shifting (if any)
2689 * has been applied.
2691 * The component inverse schedule is specified as the "map" fields
2692 * of the elements of "domain" indexed by the first "n" elements of "order".
2694 static __isl_give isl_ast_graft_list *generate_shifted_component_from_list(
2695 struct isl_set_map_pair *domain, int *order, int n,
2696 __isl_take isl_ast_build *build)
2698 isl_union_map *executed;
2700 executed = construct_component_executed(domain, order, n);
2701 return generate_shifted_component(executed, build);
2704 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2705 * of indices into the "domain" array,
2706 * do all (except for at most one) of the "set" field of the elements
2707 * indexed by the first "n" elements of "order" have a fixed value
2708 * at position "depth"?
2710 static int at_most_one_non_fixed(struct isl_set_map_pair *domain,
2711 int *order, int n, int depth)
2713 int i;
2714 int non_fixed = -1;
2716 for (i = 0; i < n; ++i) {
2717 int f;
2719 f = isl_set_plain_is_fixed(domain[order[i]].set,
2720 isl_dim_set, depth, NULL);
2721 if (f < 0)
2722 return -1;
2723 if (f)
2724 continue;
2725 if (non_fixed >= 0)
2726 return 0;
2727 non_fixed = i;
2730 return 1;
2733 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2734 * of indices into the "domain" array,
2735 * eliminate the inner dimensions from the "set" field of the elements
2736 * indexed by the first "n" elements of "order", provided the current
2737 * dimension does not have a fixed value.
2739 * Return the index of the first element in "order" with a corresponding
2740 * "set" field that does not have an (obviously) fixed value.
2742 static int eliminate_non_fixed(struct isl_set_map_pair *domain,
2743 int *order, int n, int depth, __isl_keep isl_ast_build *build)
2745 int i;
2746 int base = -1;
2748 for (i = n - 1; i >= 0; --i) {
2749 int f;
2750 f = isl_set_plain_is_fixed(domain[order[i]].set,
2751 isl_dim_set, depth, NULL);
2752 if (f < 0)
2753 return -1;
2754 if (f)
2755 continue;
2756 domain[order[i]].set = isl_ast_build_eliminate_inner(build,
2757 domain[order[i]].set);
2758 base = i;
2761 return base;
2764 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2765 * of indices into the "domain" array,
2766 * find the element of "domain" (amongst those indexed by the first "n"
2767 * elements of "order") with the "set" field that has the smallest
2768 * value for the current iterator.
2770 * Note that the domain with the smallest value may depend on the parameters
2771 * and/or outer loop dimension. Since the result of this function is only
2772 * used as heuristic, we only make a reasonable attempt at finding the best
2773 * domain, one that should work in case a single domain provides the smallest
2774 * value for the current dimension over all values of the parameters
2775 * and outer dimensions.
2777 * In particular, we compute the smallest value of the first domain
2778 * and replace it by that of any later domain if that later domain
2779 * has a smallest value that is smaller for at least some value
2780 * of the parameters and outer dimensions.
2782 static int first_offset(struct isl_set_map_pair *domain, int *order, int n,
2783 __isl_keep isl_ast_build *build)
2785 int i;
2786 isl_map *min_first;
2787 int first = 0;
2789 min_first = isl_ast_build_map_to_iterator(build,
2790 isl_set_copy(domain[order[0]].set));
2791 min_first = isl_map_lexmin(min_first);
2793 for (i = 1; i < n; ++i) {
2794 isl_map *min, *test;
2795 int empty;
2797 min = isl_ast_build_map_to_iterator(build,
2798 isl_set_copy(domain[order[i]].set));
2799 min = isl_map_lexmin(min);
2800 test = isl_map_copy(min);
2801 test = isl_map_apply_domain(isl_map_copy(min_first), test);
2802 test = isl_map_order_lt(test, isl_dim_in, 0, isl_dim_out, 0);
2803 empty = isl_map_is_empty(test);
2804 isl_map_free(test);
2805 if (empty >= 0 && !empty) {
2806 isl_map_free(min_first);
2807 first = i;
2808 min_first = min;
2809 } else
2810 isl_map_free(min);
2812 if (empty < 0)
2813 break;
2816 isl_map_free(min_first);
2818 return i < n ? -1 : first;
2821 /* Construct a shifted inverse schedule based on the original inverse schedule,
2822 * the stride and the offset.
2824 * The original inverse schedule is specified as the "map" fields
2825 * of the elements of "domain" indexed by the first "n" elements of "order".
2827 * "stride" and "offset" are such that the difference
2828 * between the values of the current dimension of domain "i"
2829 * and the values of the current dimension for some reference domain are
2830 * equal to
2832 * stride * integer + offset[i]
2834 * Moreover, 0 <= offset[i] < stride.
2836 * For each domain, we create a map
2838 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
2840 * where j refers to the current dimension and the other dimensions are
2841 * unchanged, and apply this map to the original schedule domain.
2843 * For example, for the original schedule
2845 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
2847 * and assuming the offset is 0 for the A domain and 1 for the B domain,
2848 * we apply the mapping
2850 * { [j] -> [j, 0] }
2852 * to the schedule of the "A" domain and the mapping
2854 * { [j - 1] -> [j, 1] }
2856 * to the schedule of the "B" domain.
2859 * Note that after the transformation, the differences between pairs
2860 * of values of the current dimension over all domains are multiples
2861 * of stride and that we have therefore exposed the stride.
2864 * To see that the mapping preserves the lexicographic order,
2865 * first note that each of the individual maps above preserves the order.
2866 * If the value of the current iterator is j1 in one domain and j2 in another,
2867 * then if j1 = j2, we know that the same map is applied to both domains
2868 * and the order is preserved.
2869 * Otherwise, let us assume, without loss of generality, that j1 < j2.
2870 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
2872 * j1 - c1 < j2 - c2
2874 * and the order is preserved.
2875 * If c1 < c2, then we know
2877 * 0 <= c2 - c1 < s
2879 * We also have
2881 * j2 - j1 = n * s + r
2883 * with n >= 0 and 0 <= r < s.
2884 * In other words, r = c2 - c1.
2885 * If n > 0, then
2887 * j1 - c1 < j2 - c2
2889 * If n = 0, then
2891 * j1 - c1 = j2 - c2
2893 * and so
2895 * (j1 - c1, c1) << (j2 - c2, c2)
2897 * with "<<" the lexicographic order, proving that the order is preserved
2898 * in all cases.
2900 static __isl_give isl_union_map *contruct_shifted_executed(
2901 struct isl_set_map_pair *domain, int *order, int n, isl_int stride,
2902 __isl_keep isl_vec *offset, __isl_keep isl_ast_build *build)
2904 int i;
2905 isl_int v;
2906 isl_union_map *executed;
2907 isl_space *space;
2908 isl_map *map;
2909 int depth;
2910 isl_constraint *c;
2912 depth = isl_ast_build_get_depth(build);
2913 space = isl_ast_build_get_space(build, 1);
2914 executed = isl_union_map_empty(isl_space_copy(space));
2915 space = isl_space_map_from_set(space);
2916 map = isl_map_identity(isl_space_copy(space));
2917 map = isl_map_eliminate(map, isl_dim_out, depth, 1);
2918 map = isl_map_insert_dims(map, isl_dim_out, depth + 1, 1);
2919 space = isl_space_insert_dims(space, isl_dim_out, depth + 1, 1);
2921 c = isl_equality_alloc(isl_local_space_from_space(space));
2922 c = isl_constraint_set_coefficient_si(c, isl_dim_in, depth, 1);
2923 c = isl_constraint_set_coefficient_si(c, isl_dim_out, depth, -1);
2925 isl_int_init(v);
2927 for (i = 0; i < n; ++i) {
2928 isl_map *map_i;
2930 if (isl_vec_get_element(offset, i, &v) < 0)
2931 break;
2932 map_i = isl_map_copy(map);
2933 map_i = isl_map_fix(map_i, isl_dim_out, depth + 1, v);
2934 isl_int_neg(v, v);
2935 c = isl_constraint_set_constant(c, v);
2936 map_i = isl_map_add_constraint(map_i, isl_constraint_copy(c));
2938 map_i = isl_map_apply_domain(isl_map_copy(domain[order[i]].map),
2939 map_i);
2940 executed = isl_union_map_add_map(executed, map_i);
2943 isl_constraint_free(c);
2944 isl_map_free(map);
2946 isl_int_clear(v);
2948 if (i < n)
2949 executed = isl_union_map_free(executed);
2951 return executed;
2954 /* Generate code for a single component, after exposing the stride,
2955 * given that the schedule domain is "shifted strided".
2957 * The component inverse schedule is specified as the "map" fields
2958 * of the elements of "domain" indexed by the first "n" elements of "order".
2960 * The schedule domain being "shifted strided" means that the differences
2961 * between the values of the current dimension of domain "i"
2962 * and the values of the current dimension for some reference domain are
2963 * equal to
2965 * stride * integer + offset[i]
2967 * We first look for the domain with the "smallest" value for the current
2968 * dimension and adjust the offsets such that the offset of the "smallest"
2969 * domain is equal to zero. The other offsets are reduced modulo stride.
2971 * Based on this information, we construct a new inverse schedule in
2972 * contruct_shifted_executed that exposes the stride.
2973 * Since this involves the introduction of a new schedule dimension,
2974 * the build needs to be changed accodingly.
2975 * After computing the AST, the newly introduced dimension needs
2976 * to be removed again from the list of grafts. We do this by plugging
2977 * in a mapping that represents the new schedule domain in terms of the
2978 * old schedule domain.
2980 static __isl_give isl_ast_graft_list *generate_shift_component(
2981 struct isl_set_map_pair *domain, int *order, int n, isl_int stride,
2982 __isl_keep isl_vec *offset, __isl_take isl_ast_build *build)
2984 isl_ast_graft_list *list;
2985 int first;
2986 int depth;
2987 isl_ctx *ctx;
2988 isl_int val;
2989 isl_vec *v;
2990 isl_space *space;
2991 isl_multi_aff *ma, *zero;
2992 isl_union_map *executed;
2994 ctx = isl_ast_build_get_ctx(build);
2995 depth = isl_ast_build_get_depth(build);
2997 first = first_offset(domain, order, n, build);
2998 if (first < 0)
2999 return isl_ast_build_free(build);
3001 isl_int_init(val);
3002 v = isl_vec_alloc(ctx, n);
3003 if (isl_vec_get_element(offset, first, &val) < 0)
3004 v = isl_vec_free(v);
3005 isl_int_neg(val, val);
3006 v = isl_vec_set(v, val);
3007 v = isl_vec_add(v, isl_vec_copy(offset));
3008 v = isl_vec_fdiv_r(v, stride);
3010 executed = contruct_shifted_executed(domain, order, n, stride, v,
3011 build);
3012 space = isl_ast_build_get_space(build, 1);
3013 space = isl_space_map_from_set(space);
3014 ma = isl_multi_aff_identity(isl_space_copy(space));
3015 space = isl_space_from_domain(isl_space_domain(space));
3016 space = isl_space_add_dims(space, isl_dim_out, 1);
3017 zero = isl_multi_aff_zero(space);
3018 ma = isl_multi_aff_range_splice(ma, depth + 1, zero);
3019 build = isl_ast_build_insert_dim(build, depth + 1);
3020 list = generate_shifted_component(executed, build);
3022 list = isl_ast_graft_list_preimage_multi_aff(list, ma);
3024 isl_vec_free(v);
3025 isl_int_clear(val);
3027 return list;
3030 /* Generate code for a single component.
3032 * The component inverse schedule is specified as the "map" fields
3033 * of the elements of "domain" indexed by the first "n" elements of "order".
3035 * This function may modify the "set" fields of "domain".
3037 * Before proceeding with the actual code generation for the component,
3038 * we first check if there are any "shifted" strides, meaning that
3039 * the schedule domains of the individual domains are all strided,
3040 * but that they have different offsets, resulting in the union
3041 * of schedule domains not being strided anymore.
3043 * The simplest example is the schedule
3045 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3047 * Both schedule domains are strided, but their union is not.
3048 * This function detects such cases and then rewrites the schedule to
3050 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3052 * In the new schedule, the schedule domains have the same offset (modulo
3053 * the stride), ensuring that the union of schedule domains is also strided.
3056 * If there is only a single domain in the component, then there is
3057 * nothing to do. Similarly, if the current schedule dimension has
3058 * a fixed value for almost all domains then there is nothing to be done.
3059 * In particular, we need at least two domains where the current schedule
3060 * dimension does not have a fixed value.
3061 * Finally, if any of the options refer to the current schedule dimension,
3062 * then we bail out as well. It would be possible to reformulate the options
3063 * in terms of the new schedule domain, but that would introduce constraints
3064 * that separate the domains in the options and that is something we would
3065 * like to avoid.
3068 * To see if there is any shifted stride, we look at the differences
3069 * between the values of the current dimension in pairs of domains
3070 * for equal values of outer dimensions. These differences should be
3071 * of the form
3073 * m x + r
3075 * with "m" the stride and "r" a constant. Note that we cannot perform
3076 * this analysis on individual domains as the lower bound in each domain
3077 * may depend on parameters or outer dimensions and so the current dimension
3078 * itself may not have a fixed remainder on division by the stride.
3080 * In particular, we compare the first domain that does not have an
3081 * obviously fixed value for the current dimension to itself and all
3082 * other domains and collect the offsets and the gcd of the strides.
3083 * If the gcd becomes one, then we failed to find shifted strides.
3084 * If all the offsets are the same (for those domains that do not have
3085 * an obviously fixed value for the current dimension), then we do not
3086 * apply the transformation.
3087 * If none of the domains were skipped, then there is nothing to do.
3088 * If some of them were skipped, then if we apply separation, the schedule
3089 * domain should get split in pieces with a (non-shifted) stride.
3091 * Otherwise, we apply a shift to expose the stride in
3092 * generate_shift_component.
3094 static __isl_give isl_ast_graft_list *generate_component(
3095 struct isl_set_map_pair *domain, int *order, int n,
3096 __isl_take isl_ast_build *build)
3098 int i, d;
3099 int depth;
3100 isl_ctx *ctx;
3101 isl_map *map;
3102 isl_set *deltas;
3103 isl_int m, r, gcd;
3104 isl_vec *v;
3105 int fixed, skip;
3106 int base;
3107 isl_ast_graft_list *list;
3108 int res = 0;
3110 depth = isl_ast_build_get_depth(build);
3112 skip = n == 1;
3113 if (skip >= 0 && !skip)
3114 skip = at_most_one_non_fixed(domain, order, n, depth);
3115 if (skip >= 0 && !skip)
3116 skip = isl_ast_build_options_involve_depth(build);
3117 if (skip < 0)
3118 return isl_ast_build_free(build);
3119 if (skip)
3120 return generate_shifted_component_from_list(domain,
3121 order, n, build);
3123 base = eliminate_non_fixed(domain, order, n, depth, build);
3124 if (base < 0)
3125 return isl_ast_build_free(build);
3127 ctx = isl_ast_build_get_ctx(build);
3129 isl_int_init(m);
3130 isl_int_init(r);
3131 isl_int_init(gcd);
3132 v = isl_vec_alloc(ctx, n);
3134 fixed = 1;
3135 for (i = 0; i < n; ++i) {
3136 map = isl_map_from_domain_and_range(
3137 isl_set_copy(domain[order[base]].set),
3138 isl_set_copy(domain[order[i]].set));
3139 for (d = 0; d < depth; ++d)
3140 map = isl_map_equate(map, isl_dim_in, d,
3141 isl_dim_out, d);
3142 deltas = isl_map_deltas(map);
3143 res = isl_set_dim_residue_class(deltas, depth, &m, &r);
3144 isl_set_free(deltas);
3145 if (res < 0)
3146 break;
3148 if (i == 0)
3149 isl_int_set(gcd, m);
3150 else
3151 isl_int_gcd(gcd, gcd, m);
3152 if (isl_int_is_one(gcd))
3153 break;
3154 v = isl_vec_set_element(v, i, r);
3156 res = isl_set_plain_is_fixed(domain[order[i]].set,
3157 isl_dim_set, depth, NULL);
3158 if (res < 0)
3159 break;
3160 if (res)
3161 continue;
3163 if (fixed && i > base) {
3164 isl_vec_get_element(v, base, &m);
3165 if (isl_int_ne(m, r))
3166 fixed = 0;
3170 if (res < 0) {
3171 isl_ast_build_free(build);
3172 list = NULL;
3173 } else if (i < n || fixed) {
3174 list = generate_shifted_component_from_list(domain,
3175 order, n, build);
3176 } else {
3177 list = generate_shift_component(domain, order, n, gcd, v,
3178 build);
3181 isl_vec_free(v);
3182 isl_int_clear(gcd);
3183 isl_int_clear(r);
3184 isl_int_clear(m);
3186 return list;
3189 /* Store both "map" itself and its domain in the
3190 * structure pointed to by *next and advance to the next array element.
3192 static int extract_domain(__isl_take isl_map *map, void *user)
3194 struct isl_set_map_pair **next = user;
3196 (*next)->map = isl_map_copy(map);
3197 (*next)->set = isl_map_domain(map);
3198 (*next)++;
3200 return 0;
3203 /* Internal data for any_scheduled_after.
3205 * "depth" is the number of loops that have already been generated
3206 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3207 * "domain" is an array of set-map pairs corresponding to the different
3208 * iteration domains. The set is the schedule domain, i.e., the domain
3209 * of the inverse schedule, while the map is the inverse schedule itself.
3211 struct isl_any_scheduled_after_data {
3212 int depth;
3213 int group_coscheduled;
3214 struct isl_set_map_pair *domain;
3217 /* Is any element of domain "i" scheduled after any element of domain "j"
3218 * (for a common iteration of the first data->depth loops)?
3220 * data->domain[i].set contains the domain of the inverse schedule
3221 * for domain "i", i.e., elements in the schedule domain.
3223 * If data->group_coscheduled is set, then we also return 1 if there
3224 * is any pair of elements in the two domains that are scheduled together.
3226 static int any_scheduled_after(int i, int j, void *user)
3228 struct isl_any_scheduled_after_data *data = user;
3229 int dim = isl_set_dim(data->domain[i].set, isl_dim_set);
3230 int pos;
3232 for (pos = data->depth; pos < dim; ++pos) {
3233 int follows;
3235 follows = isl_set_follows_at(data->domain[i].set,
3236 data->domain[j].set, pos);
3238 if (follows < -1)
3239 return -1;
3240 if (follows > 0)
3241 return 1;
3242 if (follows < 0)
3243 return 0;
3246 return data->group_coscheduled;
3249 /* Look for independent components at the current depth and generate code
3250 * for each component separately. The resulting lists of grafts are
3251 * merged in an attempt to combine grafts with identical guards.
3253 * Code for two domains can be generated separately if all the elements
3254 * of one domain are scheduled before (or together with) all the elements
3255 * of the other domain. We therefore consider the graph with as nodes
3256 * the domains and an edge between two nodes if any element of the first
3257 * node is scheduled after any element of the second node.
3258 * If the ast_build_group_coscheduled is set, then we also add an edge if
3259 * there is any pair of elements in the two domains that are scheduled
3260 * together.
3261 * Code is then generated (by generate_component)
3262 * for each of the strongly connected components in this graph
3263 * in their topological order.
3265 * Since the test is performed on the domain of the inverse schedules of
3266 * the different domains, we precompute these domains and store
3267 * them in data.domain.
3269 static __isl_give isl_ast_graft_list *generate_components(
3270 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
3272 int i;
3273 isl_ctx *ctx = isl_ast_build_get_ctx(build);
3274 int n = isl_union_map_n_map(executed);
3275 struct isl_any_scheduled_after_data data;
3276 struct isl_set_map_pair *next;
3277 struct isl_tarjan_graph *g = NULL;
3278 isl_ast_graft_list *list = NULL;
3279 int n_domain = 0;
3281 data.domain = isl_calloc_array(ctx, struct isl_set_map_pair, n);
3282 if (!data.domain)
3283 goto error;
3284 n_domain = n;
3286 next = data.domain;
3287 if (isl_union_map_foreach_map(executed, &extract_domain, &next) < 0)
3288 goto error;
3290 if (!build)
3291 goto error;
3292 data.depth = isl_ast_build_get_depth(build);
3293 data.group_coscheduled = isl_options_get_ast_build_group_coscheduled(ctx);
3294 g = isl_tarjan_graph_init(ctx, n, &any_scheduled_after, &data);
3296 list = isl_ast_graft_list_alloc(ctx, 0);
3298 i = 0;
3299 while (list && n) {
3300 isl_ast_graft_list *list_c;
3301 int first = i;
3303 if (g->order[i] == -1)
3304 isl_die(ctx, isl_error_internal, "cannot happen",
3305 goto error);
3306 ++i; --n;
3307 while (g->order[i] != -1) {
3308 ++i; --n;
3311 list_c = generate_component(data.domain,
3312 g->order + first, i - first,
3313 isl_ast_build_copy(build));
3314 list = isl_ast_graft_list_merge(list, list_c, build);
3316 ++i;
3319 if (0)
3320 error: list = isl_ast_graft_list_free(list);
3321 isl_tarjan_graph_free(g);
3322 for (i = 0; i < n_domain; ++i) {
3323 isl_map_free(data.domain[i].map);
3324 isl_set_free(data.domain[i].set);
3326 free(data.domain);
3327 isl_union_map_free(executed);
3328 isl_ast_build_free(build);
3330 return list;
3333 /* Generate code for the next level (and all inner levels).
3335 * If "executed" is empty, i.e., no code needs to be generated,
3336 * then we return an empty list.
3338 * If we have already generated code for all loop levels, then we pass
3339 * control to generate_inner_level.
3341 * If "executed" lives in a single space, i.e., if code needs to be
3342 * generated for a single domain, then there can only be a single
3343 * component and we go directly to generate_shifted_component.
3344 * Otherwise, we call generate_components to detect the components
3345 * and to call generate_component on each of them separately.
3347 static __isl_give isl_ast_graft_list *generate_next_level(
3348 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
3350 int depth;
3352 if (!build || !executed)
3353 goto error;
3355 if (isl_union_map_is_empty(executed)) {
3356 isl_ctx *ctx = isl_ast_build_get_ctx(build);
3357 isl_union_map_free(executed);
3358 isl_ast_build_free(build);
3359 return isl_ast_graft_list_alloc(ctx, 0);
3362 depth = isl_ast_build_get_depth(build);
3363 if (depth >= isl_set_dim(build->domain, isl_dim_set))
3364 return generate_inner_level(executed, build);
3366 if (isl_union_map_n_map(executed) == 1)
3367 return generate_shifted_component(executed, build);
3369 return generate_components(executed, build);
3370 error:
3371 isl_union_map_free(executed);
3372 isl_ast_build_free(build);
3373 return NULL;
3376 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3377 * internal, executed and build are the inputs to generate_code.
3378 * list collects the output.
3380 struct isl_generate_code_data {
3381 int internal;
3382 isl_union_map *executed;
3383 isl_ast_build *build;
3385 isl_ast_graft_list *list;
3388 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3390 * [E -> S] -> D
3392 * with E the external build schedule and S the additional schedule "space",
3393 * reformulate the inverse schedule in terms of the internal schedule domain,
3394 * i.e., return
3396 * [I -> S] -> D
3398 * We first obtain a mapping
3400 * I -> E
3402 * take the inverse and the product with S -> S, resulting in
3404 * [I -> S] -> [E -> S]
3406 * Applying the map to the input produces the desired result.
3408 static __isl_give isl_union_map *internal_executed(
3409 __isl_take isl_union_map *executed, __isl_keep isl_space *space,
3410 __isl_keep isl_ast_build *build)
3412 isl_map *id, *proj;
3414 proj = isl_ast_build_get_schedule_map(build);
3415 proj = isl_map_reverse(proj);
3416 space = isl_space_map_from_set(isl_space_copy(space));
3417 id = isl_map_identity(space);
3418 proj = isl_map_product(proj, id);
3419 executed = isl_union_map_apply_domain(executed,
3420 isl_union_map_from_map(proj));
3421 return executed;
3424 /* Generate an AST that visits the elements in the range of data->executed
3425 * in the relative order specified by the corresponding image element(s)
3426 * for those image elements that belong to "set".
3427 * Add the result to data->list.
3429 * The caller ensures that "set" is a universe domain.
3430 * "space" is the space of the additional part of the schedule.
3431 * It is equal to the space of "set" if build->domain is parametric.
3432 * Otherwise, it is equal to the range of the wrapped space of "set".
3434 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3435 * was called from an outside user (data->internal not set), then
3436 * the (inverse) schedule refers to the external build domain and needs to
3437 * be transformed to refer to the internal build domain.
3439 * The build is extended to include the additional part of the schedule.
3440 * If the original build space was not parametric, then the options
3441 * in data->build refer only to the additional part of the schedule
3442 * and they need to be adjusted to refer to the complete AST build
3443 * domain.
3445 * After having adjusted inverse schedule and build, we start generating
3446 * code with the outer loop of the current code generation
3447 * in generate_next_level.
3449 * If the original build space was not parametric, we undo the embedding
3450 * on the resulting isl_ast_node_list so that it can be used within
3451 * the outer AST build.
3453 static int generate_code_in_space(struct isl_generate_code_data *data,
3454 __isl_take isl_set *set, __isl_take isl_space *space)
3456 isl_union_map *executed;
3457 isl_ast_build *build;
3458 isl_ast_graft_list *list;
3459 int embed;
3461 executed = isl_union_map_copy(data->executed);
3462 executed = isl_union_map_intersect_domain(executed,
3463 isl_union_set_from_set(set));
3465 embed = !isl_set_is_params(data->build->domain);
3466 if (embed && !data->internal)
3467 executed = internal_executed(executed, space, data->build);
3469 build = isl_ast_build_copy(data->build);
3470 build = isl_ast_build_product(build, space);
3472 list = generate_next_level(executed, build);
3474 list = isl_ast_graft_list_unembed(list, embed);
3476 data->list = isl_ast_graft_list_concat(data->list, list);
3478 return 0;
3481 /* Generate an AST that visits the elements in the range of data->executed
3482 * in the relative order specified by the corresponding domain element(s)
3483 * for those domain elements that belong to "set".
3484 * Add the result to data->list.
3486 * The caller ensures that "set" is a universe domain.
3488 * If the build space S is not parametric, then the space of "set"
3489 * need to be a wrapped relation with S as domain. That is, it needs
3490 * to be of the form
3492 * [S -> T]
3494 * Check this property and pass control to generate_code_in_space
3495 * passing along T.
3496 * If the build space is not parametric, then T is the space of "set".
3498 static int generate_code_set(__isl_take isl_set *set, void *user)
3500 struct isl_generate_code_data *data = user;
3501 isl_space *space, *build_space;
3502 int is_domain;
3504 space = isl_set_get_space(set);
3506 if (isl_set_is_params(data->build->domain))
3507 return generate_code_in_space(data, set, space);
3509 build_space = isl_ast_build_get_space(data->build, data->internal);
3510 space = isl_space_unwrap(space);
3511 is_domain = isl_space_is_domain(build_space, space);
3512 isl_space_free(build_space);
3513 space = isl_space_range(space);
3515 if (is_domain < 0)
3516 goto error;
3517 if (!is_domain)
3518 isl_die(isl_set_get_ctx(set), isl_error_invalid,
3519 "invalid nested schedule space", goto error);
3521 return generate_code_in_space(data, set, space);
3522 error:
3523 isl_set_free(set);
3524 isl_space_free(space);
3525 return -1;
3528 /* Generate an AST that visits the elements in the range of "executed"
3529 * in the relative order specified by the corresponding domain element(s).
3531 * "build" is an isl_ast_build that has either been constructed by
3532 * isl_ast_build_from_context or passed to a callback set by
3533 * isl_ast_build_set_create_leaf.
3534 * In the first case, the space of the isl_ast_build is typically
3535 * a parametric space, although this is currently not enforced.
3536 * In the second case, the space is never a parametric space.
3537 * If the space S is not parametric, then the domain space(s) of "executed"
3538 * need to be wrapped relations with S as domain.
3540 * If the domain of "executed" consists of several spaces, then an AST
3541 * is generated for each of them (in arbitrary order) and the results
3542 * are concatenated.
3544 * If "internal" is set, then the domain "S" above refers to the internal
3545 * schedule domain representation. Otherwise, it refers to the external
3546 * representation, as returned by isl_ast_build_get_schedule_space.
3548 * We essentially run over all the spaces in the domain of "executed"
3549 * and call generate_code_set on each of them.
3551 static __isl_give isl_ast_graft_list *generate_code(
3552 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build,
3553 int internal)
3555 isl_ctx *ctx;
3556 struct isl_generate_code_data data = { 0 };
3557 isl_space *space;
3558 isl_union_set *schedule_domain;
3559 isl_union_map *universe;
3561 if (!build)
3562 goto error;
3563 space = isl_ast_build_get_space(build, 1);
3564 space = isl_space_align_params(space,
3565 isl_union_map_get_space(executed));
3566 space = isl_space_align_params(space,
3567 isl_union_map_get_space(build->options));
3568 build = isl_ast_build_align_params(build, isl_space_copy(space));
3569 executed = isl_union_map_align_params(executed, space);
3570 if (!executed || !build)
3571 goto error;
3573 ctx = isl_ast_build_get_ctx(build);
3575 data.internal = internal;
3576 data.executed = executed;
3577 data.build = build;
3578 data.list = isl_ast_graft_list_alloc(ctx, 0);
3580 universe = isl_union_map_universe(isl_union_map_copy(executed));
3581 schedule_domain = isl_union_map_domain(universe);
3582 if (isl_union_set_foreach_set(schedule_domain, &generate_code_set,
3583 &data) < 0)
3584 data.list = isl_ast_graft_list_free(data.list);
3586 isl_union_set_free(schedule_domain);
3587 isl_union_map_free(executed);
3589 isl_ast_build_free(build);
3590 return data.list;
3591 error:
3592 isl_union_map_free(executed);
3593 isl_ast_build_free(build);
3594 return NULL;
3597 /* Generate an AST that visits the elements in the domain of "schedule"
3598 * in the relative order specified by the corresponding image element(s).
3600 * "build" is an isl_ast_build that has either been constructed by
3601 * isl_ast_build_from_context or passed to a callback set by
3602 * isl_ast_build_set_create_leaf.
3603 * In the first case, the space of the isl_ast_build is typically
3604 * a parametric space, although this is currently not enforced.
3605 * In the second case, the space is never a parametric space.
3606 * If the space S is not parametric, then the range space(s) of "schedule"
3607 * need to be wrapped relations with S as domain.
3609 * If the range of "schedule" consists of several spaces, then an AST
3610 * is generated for each of them (in arbitrary order) and the results
3611 * are concatenated.
3613 * We first initialize the local copies of the relevant options.
3614 * We do this here rather than when the isl_ast_build is created
3615 * because the options may have changed between the construction
3616 * of the isl_ast_build and the call to isl_generate_code.
3618 * The main computation is performed on an inverse schedule (with
3619 * the schedule domain in the domain and the elements to be executed
3620 * in the range) called "executed".
3622 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
3623 __isl_keep isl_ast_build *build, __isl_take isl_union_map *schedule)
3625 isl_ast_graft_list *list;
3626 isl_ast_node *node;
3627 isl_union_map *executed;
3629 executed = isl_union_map_reverse(schedule);
3630 list = generate_code(executed, isl_ast_build_copy(build), 0);
3631 node = isl_ast_node_from_graft_list(list, build);
3633 return node;