isl_ast_codegen.c: refine_generic: hoist out gisting of bounds
[isl.git] / isl_ast_codegen.c
blob8e2560153d7020851fdad5b9f52944cba7aea302
1 /*
2 * Copyright 2012-2014 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 <limits.h>
11 #include <isl/aff.h>
12 #include <isl/set.h>
13 #include <isl/ilp.h>
14 #include <isl/union_map.h>
15 #include <isl_sort.h>
16 #include <isl_tarjan.h>
17 #include <isl_ast_private.h>
18 #include <isl_ast_build_expr.h>
19 #include <isl_ast_build_private.h>
20 #include <isl_ast_graft_private.h>
22 /* Data used in generate_domain.
24 * "build" is the input build.
25 * "list" collects the results.
27 struct isl_generate_domain_data {
28 isl_ast_build *build;
30 isl_ast_graft_list *list;
33 static __isl_give isl_ast_graft_list *generate_next_level(
34 __isl_take isl_union_map *executed,
35 __isl_take isl_ast_build *build);
36 static __isl_give isl_ast_graft_list *generate_code(
37 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build,
38 int internal);
40 /* Generate an AST for a single domain based on
41 * the (non single valued) inverse schedule "executed".
43 * We extend the schedule with the iteration domain
44 * and continue generating through a call to generate_code.
46 * In particular, if executed has the form
48 * S -> D
50 * then we continue generating code on
52 * [S -> D] -> D
54 * The extended inverse schedule is clearly single valued
55 * ensuring that the nested generate_code will not reach this function,
56 * but will instead create calls to all elements of D that need
57 * to be executed from the current schedule domain.
59 static int generate_non_single_valued(__isl_take isl_map *executed,
60 struct isl_generate_domain_data *data)
62 isl_map *identity;
63 isl_ast_build *build;
64 isl_ast_graft_list *list;
66 build = isl_ast_build_copy(data->build);
68 identity = isl_set_identity(isl_map_range(isl_map_copy(executed)));
69 executed = isl_map_domain_product(executed, identity);
70 build = isl_ast_build_set_single_valued(build, 1);
72 list = generate_code(isl_union_map_from_map(executed), build, 1);
74 data->list = isl_ast_graft_list_concat(data->list, list);
76 return 0;
79 /* Call the at_each_domain callback, if requested by the user,
80 * after recording the current inverse schedule in the build.
82 static __isl_give isl_ast_graft *at_each_domain(__isl_take isl_ast_graft *graft,
83 __isl_keep isl_map *executed, __isl_keep isl_ast_build *build)
85 if (!graft || !build)
86 return isl_ast_graft_free(graft);
87 if (!build->at_each_domain)
88 return graft;
90 build = isl_ast_build_copy(build);
91 build = isl_ast_build_set_executed(build,
92 isl_union_map_from_map(isl_map_copy(executed)));
93 if (!build)
94 return isl_ast_graft_free(graft);
96 graft->node = build->at_each_domain(graft->node,
97 build, build->at_each_domain_user);
98 isl_ast_build_free(build);
100 if (!graft->node)
101 graft = isl_ast_graft_free(graft);
103 return graft;
106 /* Generate an AST for a single domain based on
107 * the inverse schedule "executed" and add it to data->list.
109 * If there is more than one domain element associated to the current
110 * schedule "time", then we need to continue the generation process
111 * in generate_non_single_valued.
112 * Note that the inverse schedule being single-valued may depend
113 * on constraints that are only available in the original context
114 * domain specified by the user. We therefore first introduce
115 * the constraints from data->build->domain.
116 * On the other hand, we only perform the test after having taken the gist
117 * of the domain as the resulting map is the one from which the call
118 * expression is constructed. Using this map to construct the call
119 * expression usually yields simpler results.
120 * Because we perform the single-valuedness test on the gisted map,
121 * we may in rare cases fail to recognize that the inverse schedule
122 * is single-valued. This becomes problematic if this happens
123 * from the recursive call through generate_non_single_valued
124 * as we would then end up in an infinite recursion.
125 * We therefore check if we are inside a call to generate_non_single_valued
126 * and revert to the ungisted map if the gisted map turns out not to be
127 * single-valued.
129 * Otherwise, we generate a call expression for the single executed
130 * domain element and put a guard around it based on the (simplified)
131 * domain of "executed".
133 * If the user has set an at_each_domain callback, it is called
134 * on the constructed call expression node.
136 static int generate_domain(__isl_take isl_map *executed, void *user)
138 struct isl_generate_domain_data *data = user;
139 isl_ast_graft *graft;
140 isl_ast_graft_list *list;
141 isl_set *guard;
142 isl_map *map = NULL;
143 int empty, sv;
145 executed = isl_map_intersect_domain(executed,
146 isl_set_copy(data->build->domain));
147 empty = isl_map_is_empty(executed);
148 if (empty < 0)
149 goto error;
150 if (empty) {
151 isl_map_free(executed);
152 return 0;
155 executed = isl_map_coalesce(executed);
156 map = isl_map_copy(executed);
157 map = isl_ast_build_compute_gist_map_domain(data->build, map);
158 sv = isl_map_is_single_valued(map);
159 if (sv < 0)
160 goto error;
161 if (!sv) {
162 isl_map_free(map);
163 if (data->build->single_valued)
164 map = isl_map_copy(executed);
165 else
166 return generate_non_single_valued(executed, data);
168 guard = isl_map_domain(isl_map_copy(map));
169 guard = isl_set_compute_divs(guard);
170 guard = isl_set_coalesce(guard);
171 guard = isl_ast_build_compute_gist(data->build, guard);
172 graft = isl_ast_graft_alloc_domain(map, data->build);
173 graft = at_each_domain(graft, executed, data->build);
175 isl_map_free(executed);
176 graft = isl_ast_graft_add_guard(graft, guard, data->build);
178 list = isl_ast_graft_list_from_ast_graft(graft);
179 data->list = isl_ast_graft_list_concat(data->list, list);
181 return 0;
182 error:
183 isl_map_free(map);
184 isl_map_free(executed);
185 return -1;
188 /* Call build->create_leaf to a create "leaf" node in the AST,
189 * encapsulate the result in an isl_ast_graft and return the result
190 * as a 1-element list.
192 * Note that the node returned by the user may be an entire tree.
194 * Before we pass control to the user, we first clear some information
195 * from the build that is (presumbably) only meaningful
196 * for the current code generation.
197 * This includes the create_leaf callback itself, so we make a copy
198 * of the build first.
200 static __isl_give isl_ast_graft_list *call_create_leaf(
201 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
203 isl_ast_node *node;
204 isl_ast_graft *graft;
205 isl_ast_build *user_build;
207 user_build = isl_ast_build_copy(build);
208 user_build = isl_ast_build_set_executed(user_build, executed);
209 user_build = isl_ast_build_clear_local_info(user_build);
210 if (!user_build)
211 node = NULL;
212 else
213 node = build->create_leaf(user_build, build->create_leaf_user);
214 graft = isl_ast_graft_alloc(node, build);
215 isl_ast_build_free(build);
216 return isl_ast_graft_list_from_ast_graft(graft);
219 /* Generate an AST after having handled the complete schedule
220 * of this call to the code generator.
222 * If the user has specified a create_leaf callback, control
223 * is passed to the user in call_create_leaf.
225 * Otherwise, we generate one or more calls for each individual
226 * domain in generate_domain.
228 static __isl_give isl_ast_graft_list *generate_inner_level(
229 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
231 isl_ctx *ctx;
232 struct isl_generate_domain_data data = { build };
234 if (!build || !executed)
235 goto error;
237 if (build->create_leaf)
238 return call_create_leaf(executed, build);
240 ctx = isl_union_map_get_ctx(executed);
241 data.list = isl_ast_graft_list_alloc(ctx, 0);
242 if (isl_union_map_foreach_map(executed, &generate_domain, &data) < 0)
243 data.list = isl_ast_graft_list_free(data.list);
245 if (0)
246 error: data.list = NULL;
247 isl_ast_build_free(build);
248 isl_union_map_free(executed);
249 return data.list;
252 /* Call the before_each_for callback, if requested by the user.
254 static __isl_give isl_ast_node *before_each_for(__isl_take isl_ast_node *node,
255 __isl_keep isl_ast_build *build)
257 isl_id *id;
259 if (!node || !build)
260 return isl_ast_node_free(node);
261 if (!build->before_each_for)
262 return node;
263 id = build->before_each_for(build, build->before_each_for_user);
264 node = isl_ast_node_set_annotation(node, id);
265 return node;
268 /* Call the after_each_for callback, if requested by the user.
270 static __isl_give isl_ast_graft *after_each_for(__isl_take isl_ast_graft *graft,
271 __isl_keep isl_ast_build *build)
273 if (!graft || !build)
274 return isl_ast_graft_free(graft);
275 if (!build->after_each_for)
276 return graft;
277 graft->node = build->after_each_for(graft->node, build,
278 build->after_each_for_user);
279 if (!graft->node)
280 return isl_ast_graft_free(graft);
281 return graft;
284 /* Plug in all the know values of the current and outer dimensions
285 * in the domain of "executed". In principle, we only need to plug
286 * in the known value of the current dimension since the values of
287 * outer dimensions have been plugged in already.
288 * However, it turns out to be easier to just plug in all known values.
290 static __isl_give isl_union_map *plug_in_values(
291 __isl_take isl_union_map *executed, __isl_keep isl_ast_build *build)
293 return isl_ast_build_substitute_values_union_map_domain(build,
294 executed);
297 /* Check if the constraint "c" is a lower bound on dimension "pos",
298 * an upper bound, or independent of dimension "pos".
300 static int constraint_type(isl_constraint *c, int pos)
302 if (isl_constraint_is_lower_bound(c, isl_dim_set, pos))
303 return 1;
304 if (isl_constraint_is_upper_bound(c, isl_dim_set, pos))
305 return 2;
306 return 0;
309 /* Compare the types of the constraints "a" and "b",
310 * resulting in constraints that are independent of "depth"
311 * to be sorted before the lower bounds on "depth", which in
312 * turn are sorted before the upper bounds on "depth".
314 static int cmp_constraint(__isl_keep isl_constraint *a,
315 __isl_keep isl_constraint *b, void *user)
317 int *depth = user;
318 int t1 = constraint_type(a, *depth);
319 int t2 = constraint_type(b, *depth);
321 return t1 - t2;
324 /* Extract a lower bound on dimension "pos" from constraint "c".
326 * If the constraint is of the form
328 * a x + f(...) >= 0
330 * then we essentially return
332 * l = ceil(-f(...)/a)
334 * However, if the current dimension is strided, then we need to make
335 * sure that the lower bound we construct is of the form
337 * f + s a
339 * with f the offset and s the stride.
340 * We therefore compute
342 * f + s * ceil((l - f)/s)
344 static __isl_give isl_aff *lower_bound(__isl_keep isl_constraint *c,
345 int pos, __isl_keep isl_ast_build *build)
347 isl_aff *aff;
349 aff = isl_constraint_get_bound(c, isl_dim_set, pos);
350 aff = isl_aff_ceil(aff);
352 if (isl_ast_build_has_stride(build, pos)) {
353 isl_aff *offset;
354 isl_val *stride;
356 offset = isl_ast_build_get_offset(build, pos);
357 stride = isl_ast_build_get_stride(build, pos);
359 aff = isl_aff_sub(aff, isl_aff_copy(offset));
360 aff = isl_aff_scale_down_val(aff, isl_val_copy(stride));
361 aff = isl_aff_ceil(aff);
362 aff = isl_aff_scale_val(aff, stride);
363 aff = isl_aff_add(aff, offset);
366 aff = isl_ast_build_compute_gist_aff(build, aff);
368 return aff;
371 /* Return the exact lower bound (or upper bound if "upper" is set)
372 * of "domain" as a piecewise affine expression.
374 * If we are computing a lower bound (of a strided dimension), then
375 * we need to make sure it is of the form
377 * f + s a
379 * where f is the offset and s is the stride.
380 * We therefore need to include the stride constraint before computing
381 * the minimum.
383 static __isl_give isl_pw_aff *exact_bound(__isl_keep isl_set *domain,
384 __isl_keep isl_ast_build *build, int upper)
386 isl_set *stride;
387 isl_map *it_map;
388 isl_pw_aff *pa;
389 isl_pw_multi_aff *pma;
391 domain = isl_set_copy(domain);
392 if (!upper) {
393 stride = isl_ast_build_get_stride_constraint(build);
394 domain = isl_set_intersect(domain, stride);
396 it_map = isl_ast_build_map_to_iterator(build, domain);
397 if (upper)
398 pma = isl_map_lexmax_pw_multi_aff(it_map);
399 else
400 pma = isl_map_lexmin_pw_multi_aff(it_map);
401 pa = isl_pw_multi_aff_get_pw_aff(pma, 0);
402 isl_pw_multi_aff_free(pma);
403 pa = isl_ast_build_compute_gist_pw_aff(build, pa);
404 pa = isl_pw_aff_coalesce(pa);
406 return pa;
409 /* Extract a lower bound on dimension "pos" from each constraint
410 * in "constraints" and return the list of lower bounds.
411 * If "constraints" has zero elements, then we extract a lower bound
412 * from "domain" instead.
414 static __isl_give isl_pw_aff_list *lower_bounds(
415 __isl_keep isl_constraint_list *constraints, int pos,
416 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
418 isl_ctx *ctx;
419 isl_pw_aff_list *list;
420 int i, n;
422 if (!build)
423 return NULL;
425 n = isl_constraint_list_n_constraint(constraints);
426 if (n == 0) {
427 isl_pw_aff *pa;
428 pa = exact_bound(domain, build, 0);
429 return isl_pw_aff_list_from_pw_aff(pa);
432 ctx = isl_ast_build_get_ctx(build);
433 list = isl_pw_aff_list_alloc(ctx,n);
435 for (i = 0; i < n; ++i) {
436 isl_aff *aff;
437 isl_constraint *c;
439 c = isl_constraint_list_get_constraint(constraints, i);
440 aff = lower_bound(c, pos, build);
441 isl_constraint_free(c);
442 list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
445 return list;
448 /* Extract an upper bound on dimension "pos" from each constraint
449 * in "constraints" and return the list of upper bounds.
450 * If "constraints" has zero elements, then we extract an upper bound
451 * from "domain" instead.
453 static __isl_give isl_pw_aff_list *upper_bounds(
454 __isl_keep isl_constraint_list *constraints, int pos,
455 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
457 isl_ctx *ctx;
458 isl_pw_aff_list *list;
459 int i, n;
461 n = isl_constraint_list_n_constraint(constraints);
462 if (n == 0) {
463 isl_pw_aff *pa;
464 pa = exact_bound(domain, build, 1);
465 return isl_pw_aff_list_from_pw_aff(pa);
468 ctx = isl_ast_build_get_ctx(build);
469 list = isl_pw_aff_list_alloc(ctx,n);
471 for (i = 0; i < n; ++i) {
472 isl_aff *aff;
473 isl_constraint *c;
475 c = isl_constraint_list_get_constraint(constraints, i);
476 aff = isl_constraint_get_bound(c, isl_dim_set, pos);
477 isl_constraint_free(c);
478 aff = isl_aff_floor(aff);
479 list = isl_pw_aff_list_add(list, isl_pw_aff_from_aff(aff));
482 return list;
485 /* Callback for sorting the isl_pw_aff_list passed to reduce_list.
487 static int reduce_list_cmp(__isl_keep isl_pw_aff *a, __isl_keep isl_pw_aff *b,
488 void *user)
490 return isl_pw_aff_plain_cmp(a, b);
493 /* Return an isl_ast_expr that performs the reduction of type "type"
494 * on AST expressions corresponding to the elements in "list".
496 * The list is assumed to contain at least one element.
497 * If the list contains exactly one element, then the returned isl_ast_expr
498 * simply computes that affine expression.
499 * If the list contains more than one element, then we sort it
500 * using a fairly abitrary but hopefully reasonably stable order.
502 static __isl_give isl_ast_expr *reduce_list(enum isl_ast_op_type type,
503 __isl_keep isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
505 int i, n;
506 isl_ctx *ctx;
507 isl_ast_expr *expr;
509 if (!list)
510 return NULL;
512 n = isl_pw_aff_list_n_pw_aff(list);
514 if (n == 1)
515 return isl_ast_build_expr_from_pw_aff_internal(build,
516 isl_pw_aff_list_get_pw_aff(list, 0));
518 ctx = isl_pw_aff_list_get_ctx(list);
519 expr = isl_ast_expr_alloc_op(ctx, type, n);
520 if (!expr)
521 return NULL;
523 list = isl_pw_aff_list_copy(list);
524 list = isl_pw_aff_list_sort(list, &reduce_list_cmp, NULL);
525 if (!list)
526 return isl_ast_expr_free(expr);
528 for (i = 0; i < n; ++i) {
529 isl_ast_expr *expr_i;
531 expr_i = isl_ast_build_expr_from_pw_aff_internal(build,
532 isl_pw_aff_list_get_pw_aff(list, i));
533 if (!expr_i)
534 goto error;
535 expr->u.op.args[i] = expr_i;
538 isl_pw_aff_list_free(list);
539 return expr;
540 error:
541 isl_pw_aff_list_free(list);
542 isl_ast_expr_free(expr);
543 return NULL;
546 /* Add a guard to "graft" based on "bound" in the case of a degenerate
547 * level (including the special case of an eliminated level).
549 * We eliminate the current dimension, simplify the result in the current
550 * build and add the result as guards to the graft.
552 * Note that we cannot simply drop the constraints on the current dimension
553 * even in the eliminated case, because the single affine expression may
554 * not be explicitly available in "bounds". Moreover, the single affine
555 * expression may only be defined on a subset of the build domain,
556 * so we do in some cases need to insert a guard even in the eliminated case.
558 static __isl_give isl_ast_graft *add_degenerate_guard(
559 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
560 __isl_keep isl_ast_build *build)
562 int depth;
563 isl_set *dom;
565 depth = isl_ast_build_get_depth(build);
567 dom = isl_set_from_basic_set(isl_basic_set_copy(bounds));
568 dom = isl_set_eliminate(dom, isl_dim_set, depth, 1);
569 dom = isl_ast_build_compute_gist(build, dom);
571 graft = isl_ast_graft_add_guard(graft, dom, build);
573 return graft;
576 /* Add guards implied by the "generated constraints",
577 * but not (necessarily) enforced by the generated AST to "graft".
578 * In particular, if there is any stride constraints,
579 * then add the guard implied by those constraints.
580 * If we have generated a degenerate loop, then add the guard
581 * implied by "bounds" on the outer dimensions, i.e., the guard
582 * that ensures that the single value actually exists.
584 static __isl_give isl_ast_graft *add_implied_guards(
585 __isl_take isl_ast_graft *graft, int degenerate,
586 __isl_keep isl_basic_set *bounds, __isl_keep isl_ast_build *build)
588 int depth, has_stride;
589 isl_set *dom;
591 depth = isl_ast_build_get_depth(build);
592 has_stride = isl_ast_build_has_stride(build, depth);
593 if (!has_stride && !degenerate)
594 return graft;
596 if (degenerate) {
597 bounds = isl_basic_set_copy(bounds);
598 dom = isl_set_from_basic_set(bounds);
599 dom = isl_set_eliminate(dom, isl_dim_set, depth, 1);
600 dom = isl_ast_build_compute_gist(build, dom);
601 graft = isl_ast_graft_add_guard(graft, dom, build);
604 if (has_stride) {
605 dom = isl_ast_build_get_stride_constraint(build);
606 dom = isl_set_eliminate(dom, isl_dim_set, depth, 1);
607 dom = isl_ast_build_compute_gist(build, dom);
608 graft = isl_ast_graft_add_guard(graft, dom, build);
611 return graft;
614 /* Update "graft" based on "bounds" for the eliminated case.
616 * In the eliminated case, no for node is created, so we only need
617 * to check if "bounds" imply any guards that need to be inserted.
619 static __isl_give isl_ast_graft *refine_eliminated(
620 __isl_take isl_ast_graft *graft, __isl_keep isl_basic_set *bounds,
621 __isl_keep isl_ast_build *build)
623 return add_degenerate_guard(graft, bounds, build);
626 /* Update "graft" based on "sub_build" for the degenerate case.
628 * "build" is the build in which graft->node was created
629 * "sub_build" contains information about the current level itself,
630 * including the single value attained.
632 * We first set the initialization part of the for loop to the single
633 * value attained by the current dimension.
634 * The increment and condition are not strictly needed as the are known
635 * to be "1" and "iterator <= value" respectively.
637 static __isl_give isl_ast_graft *refine_degenerate(
638 __isl_take isl_ast_graft *graft, __isl_keep isl_ast_build *build,
639 __isl_keep isl_ast_build *sub_build)
641 isl_pw_aff *value;
643 if (!graft || !sub_build)
644 return isl_ast_graft_free(graft);
646 value = isl_pw_aff_copy(sub_build->value);
648 graft->node->u.f.init = isl_ast_build_expr_from_pw_aff_internal(build,
649 value);
650 if (!graft->node->u.f.init)
651 return isl_ast_graft_free(graft);
653 return graft;
656 /* Return the intersection of constraints in "list" as a set.
658 static __isl_give isl_set *intersect_constraints(
659 __isl_keep isl_constraint_list *list)
661 int i, n;
662 isl_basic_set *bset;
664 n = isl_constraint_list_n_constraint(list);
665 if (n < 1)
666 isl_die(isl_constraint_list_get_ctx(list), isl_error_internal,
667 "expecting at least one constraint", return NULL);
669 bset = isl_basic_set_from_constraint(
670 isl_constraint_list_get_constraint(list, 0));
671 for (i = 1; i < n; ++i) {
672 isl_basic_set *bset_i;
674 bset_i = isl_basic_set_from_constraint(
675 isl_constraint_list_get_constraint(list, i));
676 bset = isl_basic_set_intersect(bset, bset_i);
679 return isl_set_from_basic_set(bset);
682 /* Compute the constraints on the outer dimensions enforced by
683 * graft->node and add those constraints to graft->enforced,
684 * in case the upper bound is expressed as a set "upper".
686 * In particular, if l(...) is a lower bound in "lower", and
688 * -a i + f(...) >= 0 or a i <= f(...)
690 * is an upper bound ocnstraint on the current dimension i,
691 * then the for loop enforces the constraint
693 * -a l(...) + f(...) >= 0 or a l(...) <= f(...)
695 * We therefore simply take each lower bound in turn, plug it into
696 * the upper bounds and compute the intersection over all lower bounds.
698 * If a lower bound is a rational expression, then
699 * isl_basic_set_preimage_multi_aff will force this rational
700 * expression to have only integer values. However, the loop
701 * itself does not enforce this integrality constraint. We therefore
702 * use the ceil of the lower bounds instead of the lower bounds themselves.
703 * Other constraints will make sure that the for loop is only executed
704 * when each of the lower bounds attains an integral value.
705 * In particular, potentially rational values only occur in
706 * lower_bound if the offset is a (seemingly) rational expression,
707 * but then outer conditions will make sure that this rational expression
708 * only attains integer values.
710 static __isl_give isl_ast_graft *set_enforced_from_set(
711 __isl_take isl_ast_graft *graft,
712 __isl_keep isl_pw_aff_list *lower, int pos, __isl_keep isl_set *upper)
714 isl_space *space;
715 isl_basic_set *enforced;
716 isl_pw_multi_aff *pma;
717 int i, n;
719 if (!graft || !lower)
720 return isl_ast_graft_free(graft);
722 space = isl_set_get_space(upper);
723 enforced = isl_basic_set_universe(isl_space_copy(space));
725 space = isl_space_map_from_set(space);
726 pma = isl_pw_multi_aff_identity(space);
728 n = isl_pw_aff_list_n_pw_aff(lower);
729 for (i = 0; i < n; ++i) {
730 isl_pw_aff *pa;
731 isl_set *enforced_i;
732 isl_basic_set *hull;
733 isl_pw_multi_aff *pma_i;
735 pa = isl_pw_aff_list_get_pw_aff(lower, i);
736 pa = isl_pw_aff_ceil(pa);
737 pma_i = isl_pw_multi_aff_copy(pma);
738 pma_i = isl_pw_multi_aff_set_pw_aff(pma_i, pos, pa);
739 enforced_i = isl_set_copy(upper);
740 enforced_i = isl_set_preimage_pw_multi_aff(enforced_i, pma_i);
741 hull = isl_set_simple_hull(enforced_i);
742 enforced = isl_basic_set_intersect(enforced, hull);
745 isl_pw_multi_aff_free(pma);
747 graft = isl_ast_graft_enforce(graft, enforced);
749 return graft;
752 /* Compute the constraints on the outer dimensions enforced by
753 * graft->node and add those constraints to graft->enforced,
754 * in case the upper bound is expressed as
755 * a list of affine expressions "upper".
757 * The enforced condition is that each lower bound expression is less
758 * than or equal to each upper bound expression.
760 static __isl_give isl_ast_graft *set_enforced_from_list(
761 __isl_take isl_ast_graft *graft,
762 __isl_keep isl_pw_aff_list *lower, __isl_keep isl_pw_aff_list *upper)
764 isl_set *cond;
765 isl_basic_set *enforced;
767 lower = isl_pw_aff_list_copy(lower);
768 upper = isl_pw_aff_list_copy(upper);
769 cond = isl_pw_aff_list_le_set(lower, upper);
770 enforced = isl_set_simple_hull(cond);
771 graft = isl_ast_graft_enforce(graft, enforced);
773 return graft;
776 /* Does "aff" have a negative constant term?
778 static int aff_constant_is_negative(__isl_take isl_set *set,
779 __isl_take isl_aff *aff, void *user)
781 int *neg = user;
782 isl_val *v;
784 v = isl_aff_get_constant_val(aff);
785 *neg = isl_val_is_neg(v);
786 isl_val_free(v);
787 isl_set_free(set);
788 isl_aff_free(aff);
790 return *neg ? 0 : -1;
793 /* Does "pa" have a negative constant term over its entire domain?
795 static int pw_aff_constant_is_negative(__isl_take isl_pw_aff *pa, void *user)
797 int r;
798 int *neg = user;
800 r = isl_pw_aff_foreach_piece(pa, &aff_constant_is_negative, user);
801 isl_pw_aff_free(pa);
803 return *neg ? 0 : -1;
806 /* Does each element in "list" have a negative constant term?
808 * The callback terminates the iteration as soon an element has been
809 * found that does not have a negative constant term.
811 static int list_constant_is_negative(__isl_keep isl_pw_aff_list *list)
813 int neg = 1;
815 if (isl_pw_aff_list_foreach(list,
816 &pw_aff_constant_is_negative, &neg) < 0 && neg)
817 return -1;
819 return neg;
822 /* Add 1 to each of the elements in "list", where each of these elements
823 * is defined over the internal schedule space of "build".
825 static __isl_give isl_pw_aff_list *list_add_one(
826 __isl_take isl_pw_aff_list *list, __isl_keep isl_ast_build *build)
828 int i, n;
829 isl_space *space;
830 isl_aff *aff;
831 isl_pw_aff *one;
833 space = isl_ast_build_get_space(build, 1);
834 aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
835 aff = isl_aff_add_constant_si(aff, 1);
836 one = isl_pw_aff_from_aff(aff);
838 n = isl_pw_aff_list_n_pw_aff(list);
839 for (i = 0; i < n; ++i) {
840 isl_pw_aff *pa;
841 pa = isl_pw_aff_list_get_pw_aff(list, i);
842 pa = isl_pw_aff_add(pa, isl_pw_aff_copy(one));
843 list = isl_pw_aff_list_set_pw_aff(list, i, pa);
846 isl_pw_aff_free(one);
848 return list;
851 /* Set the condition part of the for node graft->node in case
852 * the upper bound is represented as a list of piecewise affine expressions.
854 * In particular, set the condition to
856 * iterator <= min(list of upper bounds)
858 * If each of the upper bounds has a negative constant term, then
859 * set the condition to
861 * iterator < min(list of (upper bound + 1)s)
864 static __isl_give isl_ast_graft *set_for_cond_from_list(
865 __isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *list,
866 __isl_keep isl_ast_build *build)
868 int neg;
869 isl_ast_expr *bound, *iterator, *cond;
870 enum isl_ast_op_type type = isl_ast_op_le;
872 if (!graft || !list)
873 return isl_ast_graft_free(graft);
875 neg = list_constant_is_negative(list);
876 if (neg < 0)
877 return isl_ast_graft_free(graft);
878 list = isl_pw_aff_list_copy(list);
879 if (neg) {
880 list = list_add_one(list, build);
881 type = isl_ast_op_lt;
884 bound = reduce_list(isl_ast_op_min, list, build);
885 iterator = isl_ast_expr_copy(graft->node->u.f.iterator);
886 cond = isl_ast_expr_alloc_binary(type, iterator, bound);
887 graft->node->u.f.cond = cond;
889 isl_pw_aff_list_free(list);
890 if (!graft->node->u.f.cond)
891 return isl_ast_graft_free(graft);
892 return graft;
895 /* Set the condition part of the for node graft->node in case
896 * the upper bound is represented as a set.
898 static __isl_give isl_ast_graft *set_for_cond_from_set(
899 __isl_take isl_ast_graft *graft, __isl_keep isl_set *set,
900 __isl_keep isl_ast_build *build)
902 isl_ast_expr *cond;
904 if (!graft)
905 return NULL;
907 cond = isl_ast_build_expr_from_set(build, isl_set_copy(set));
908 graft->node->u.f.cond = cond;
909 if (!graft->node->u.f.cond)
910 return isl_ast_graft_free(graft);
911 return graft;
914 /* Construct an isl_ast_expr for the increment (i.e., stride) of
915 * the current dimension.
917 static __isl_give isl_ast_expr *for_inc(__isl_keep isl_ast_build *build)
919 int depth;
920 isl_val *v;
921 isl_ctx *ctx;
923 if (!build)
924 return NULL;
925 ctx = isl_ast_build_get_ctx(build);
926 depth = isl_ast_build_get_depth(build);
928 if (!isl_ast_build_has_stride(build, depth))
929 return isl_ast_expr_alloc_int_si(ctx, 1);
931 v = isl_ast_build_get_stride(build, depth);
932 return isl_ast_expr_from_val(v);
935 /* Should we express the loop condition as
937 * iterator <= min(list of upper bounds)
939 * or as a conjunction of constraints?
941 * The first is constructed from a list of upper bounds.
942 * The second is constructed from a set.
944 * If there are no upper bounds in "constraints", then this could mean
945 * that "domain" simply doesn't have an upper bound or that we didn't
946 * pick any upper bound. In the first case, we want to generate the
947 * loop condition as a(n empty) conjunction of constraints
948 * In the second case, we will compute
949 * a single upper bound from "domain" and so we use the list form.
951 * If there are upper bounds in "constraints",
952 * then we use the list form iff the atomic_upper_bound option is set.
954 static int use_upper_bound_list(isl_ctx *ctx, int n_upper,
955 __isl_keep isl_set *domain, int depth)
957 if (n_upper > 0)
958 return isl_options_get_ast_build_atomic_upper_bound(ctx);
959 else
960 return isl_set_dim_has_upper_bound(domain, isl_dim_set, depth);
963 /* Fill in the expressions of the for node in graft->node.
965 * In particular,
966 * - set the initialization part of the loop to the maximum of the lower bounds
967 * - extract the increment from the stride of the current dimension
968 * - construct the for condition either based on a list of upper bounds
969 * or on a set of upper bound constraints.
971 static __isl_give isl_ast_graft *set_for_node_expressions(
972 __isl_take isl_ast_graft *graft, __isl_keep isl_pw_aff_list *lower,
973 int use_list, __isl_keep isl_pw_aff_list *upper_list,
974 __isl_keep isl_set *upper_set, __isl_keep isl_ast_build *build)
976 isl_ast_node *node;
978 if (!graft)
979 return NULL;
981 build = isl_ast_build_copy(build);
982 build = isl_ast_build_set_enforced(build,
983 isl_ast_graft_get_enforced(graft));
985 node = graft->node;
986 node->u.f.init = reduce_list(isl_ast_op_max, lower, build);
987 node->u.f.inc = for_inc(build);
989 if (use_list)
990 graft = set_for_cond_from_list(graft, upper_list, build);
991 else
992 graft = set_for_cond_from_set(graft, upper_set, build);
994 isl_ast_build_free(build);
996 if (!node->u.f.iterator || !node->u.f.init ||
997 !node->u.f.cond || !node->u.f.inc)
998 return isl_ast_graft_free(graft);
1000 return graft;
1003 /* Update "graft" based on "bounds" and "domain" for the generic,
1004 * non-degenerate, case.
1006 * "c_lower" and "c_upper" contain the lower and upper bounds
1007 * that the loop node should express.
1008 * "domain" is the subset of the intersection of the constraints
1009 * for which some code is executed.
1011 * There may be zero lower bounds or zero upper bounds in "constraints"
1012 * in case the list of constraints was created
1013 * based on the atomic option or based on separation with explicit bounds.
1014 * In that case, we use "domain" to derive lower and/or upper bounds.
1016 * We first compute a list of one or more lower bounds.
1018 * Then we decide if we want to express the condition as
1020 * iterator <= min(list of upper bounds)
1022 * or as a conjunction of constraints.
1024 * The set of enforced constraints is then computed either based on
1025 * a list of upper bounds or on a set of upper bound constraints.
1026 * We do not compute any enforced constraints if we were forced
1027 * to compute a lower or upper bound using exact_bound. The domains
1028 * of the resulting expressions may imply some bounds on outer dimensions
1029 * that we do not want to appear in the enforced constraints since
1030 * they are not actually enforced by the corresponding code.
1032 * Finally, we fill in the expressions of the for node.
1034 static __isl_give isl_ast_graft *refine_generic_bounds(
1035 __isl_take isl_ast_graft *graft,
1036 __isl_take isl_constraint_list *c_lower,
1037 __isl_take isl_constraint_list *c_upper,
1038 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
1040 int depth;
1041 isl_ctx *ctx;
1042 isl_pw_aff_list *lower;
1043 int use_list;
1044 isl_set *upper_set = NULL;
1045 isl_pw_aff_list *upper_list = NULL;
1046 int n_lower, n_upper;
1048 if (!graft || !c_lower || !c_upper || !build)
1049 goto error;
1051 depth = isl_ast_build_get_depth(build);
1052 ctx = isl_ast_graft_get_ctx(graft);
1054 n_lower = isl_constraint_list_n_constraint(c_lower);
1055 n_upper = isl_constraint_list_n_constraint(c_upper);
1057 use_list = use_upper_bound_list(ctx, n_upper, domain, depth);
1059 lower = lower_bounds(c_lower, depth, domain, build);
1061 if (use_list)
1062 upper_list = upper_bounds(c_upper, depth, domain, build);
1063 else if (n_upper > 0)
1064 upper_set = intersect_constraints(c_upper);
1065 else
1066 upper_set = isl_set_universe(isl_set_get_space(domain));
1068 if (n_lower == 0 || n_upper == 0)
1070 else if (use_list)
1071 graft = set_enforced_from_list(graft, lower, upper_list);
1072 else
1073 graft = set_enforced_from_set(graft, lower, depth, upper_set);
1075 graft = set_for_node_expressions(graft, lower, use_list, upper_list,
1076 upper_set, build);
1078 isl_pw_aff_list_free(lower);
1079 isl_pw_aff_list_free(upper_list);
1080 isl_set_free(upper_set);
1081 isl_constraint_list_free(c_lower);
1082 isl_constraint_list_free(c_upper);
1084 return graft;
1085 error:
1086 isl_constraint_list_free(c_lower);
1087 isl_constraint_list_free(c_upper);
1088 return isl_ast_graft_free(graft);
1091 /* Internal data structure used inside count_constraints to keep
1092 * track of the number of constraints that are independent of dimension "pos",
1093 * the lower bounds in "pos" and the upper bounds in "pos".
1095 struct isl_ast_count_constraints_data {
1096 int pos;
1098 int n_indep;
1099 int n_lower;
1100 int n_upper;
1103 /* Increment data->n_indep, data->lower or data->upper depending
1104 * on whether "c" is independenct of dimensions data->pos,
1105 * a lower bound or an upper bound.
1107 static int count_constraints(__isl_take isl_constraint *c, void *user)
1109 struct isl_ast_count_constraints_data *data = user;
1111 if (isl_constraint_is_lower_bound(c, isl_dim_set, data->pos))
1112 data->n_lower++;
1113 else if (isl_constraint_is_upper_bound(c, isl_dim_set, data->pos))
1114 data->n_upper++;
1115 else
1116 data->n_indep++;
1118 isl_constraint_free(c);
1120 return 0;
1123 /* Update "graft" based on "bounds" and "domain" for the generic,
1124 * non-degenerate, case.
1126 * "list" respresent the list of bounds that need to be encoded by
1127 * the for loop (or a guard around the for loop).
1128 * "domain" is the subset of the intersection of the constraints
1129 * for which some code is executed.
1130 * "build" is the build in which graft->node was created.
1132 * We separate lower bounds, upper bounds and constraints that
1133 * are independent of the loop iterator.
1135 * The actual for loop bounds are generated in refine_generic_bounds.
1136 * If there are any constraints that are independent of the loop iterator,
1137 * we need to put a guard around the for loop (which may get hoisted up
1138 * to higher levels) and we call refine_generic_bounds in a build
1139 * where this guard is enforced.
1141 static __isl_give isl_ast_graft *refine_generic_split(
1142 __isl_take isl_ast_graft *graft, __isl_take isl_constraint_list *list,
1143 __isl_keep isl_set *domain, __isl_keep isl_ast_build *build)
1145 isl_ast_build *for_build;
1146 isl_set *guard;
1147 struct isl_ast_count_constraints_data data;
1148 isl_constraint_list *lower;
1149 isl_constraint_list *upper;
1151 if (!list)
1152 return isl_ast_graft_free(graft);
1154 data.pos = isl_ast_build_get_depth(build);
1156 list = isl_constraint_list_sort(list, &cmp_constraint, &data.pos);
1157 if (!list)
1158 return isl_ast_graft_free(graft);
1160 data.n_indep = data.n_lower = data.n_upper = 0;
1161 if (isl_constraint_list_foreach(list, &count_constraints, &data) < 0) {
1162 isl_constraint_list_free(list);
1163 return isl_ast_graft_free(graft);
1166 lower = isl_constraint_list_copy(list);
1167 lower = isl_constraint_list_drop(lower, 0, data.n_indep);
1168 upper = isl_constraint_list_copy(lower);
1169 lower = isl_constraint_list_drop(lower, data.n_lower, data.n_upper);
1170 upper = isl_constraint_list_drop(upper, 0, data.n_lower);
1172 if (data.n_indep == 0) {
1173 isl_constraint_list_free(list);
1174 return refine_generic_bounds(graft, lower, upper,
1175 domain, build);
1178 list = isl_constraint_list_drop(list, data.n_indep,
1179 data.n_lower + data.n_upper);
1180 guard = intersect_constraints(list);
1181 isl_constraint_list_free(list);
1183 for_build = isl_ast_build_copy(build);
1184 for_build = isl_ast_build_restrict_pending(for_build,
1185 isl_set_copy(guard));
1186 graft = refine_generic_bounds(graft, lower, upper, domain, for_build);
1187 isl_ast_build_free(for_build);
1189 graft = isl_ast_graft_add_guard(graft, guard, build);
1191 return graft;
1194 /* Update "graft" based on "bounds" and "domain" for the generic,
1195 * non-degenerate, case.
1197 * "bounds" respresent the bounds that need to be encoded by
1198 * the for loop (or a guard around the for loop).
1199 * "domain" is the subset of "bounds" for which some code is executed.
1200 * "build" is the build in which graft->node was created.
1202 * We break up "bounds" into a list of constraints and continue with
1203 * refine_generic_split.
1205 static __isl_give isl_ast_graft *refine_generic(
1206 __isl_take isl_ast_graft *graft,
1207 __isl_keep isl_basic_set *bounds, __isl_keep isl_set *domain,
1208 __isl_keep isl_ast_build *build)
1210 isl_constraint_list *list;
1212 if (!build || !graft)
1213 return isl_ast_graft_free(graft);
1215 list = isl_basic_set_get_constraint_list(bounds);
1217 graft = refine_generic_split(graft, list, domain, build);
1219 return graft;
1222 /* Create a for node for the current level.
1224 * Mark the for node degenerate if "degenerate" is set.
1226 static __isl_give isl_ast_node *create_for(__isl_keep isl_ast_build *build,
1227 int degenerate)
1229 int depth;
1230 isl_id *id;
1231 isl_ast_node *node;
1233 if (!build)
1234 return NULL;
1236 depth = isl_ast_build_get_depth(build);
1237 id = isl_ast_build_get_iterator_id(build, depth);
1238 node = isl_ast_node_alloc_for(id);
1239 if (degenerate)
1240 node = isl_ast_node_for_mark_degenerate(node);
1242 return node;
1245 /* If the ast_build_exploit_nested_bounds option is set, then return
1246 * the constraints enforced by all elements in "list".
1247 * Otherwise, return the universe.
1249 static __isl_give isl_basic_set *extract_shared_enforced(
1250 __isl_keep isl_ast_graft_list *list, __isl_keep isl_ast_build *build)
1252 isl_ctx *ctx;
1253 isl_space *space;
1255 if (!list)
1256 return NULL;
1258 ctx = isl_ast_graft_list_get_ctx(list);
1259 if (isl_options_get_ast_build_exploit_nested_bounds(ctx))
1260 return isl_ast_graft_list_extract_shared_enforced(list, build);
1262 space = isl_ast_build_get_space(build, 1);
1263 return isl_basic_set_universe(space);
1266 /* Create an AST node for the current dimension based on
1267 * the schedule domain "bounds" and return the node encapsulated
1268 * in an isl_ast_graft.
1270 * "executed" is the current inverse schedule, taking into account
1271 * the bounds in "bounds"
1272 * "domain" is the domain of "executed", with inner dimensions projected out.
1273 * It may be a strict subset of "bounds" in case "bounds" was created
1274 * based on the atomic option or based on separation with explicit bounds.
1276 * "domain" may satisfy additional equalities that result
1277 * from intersecting "executed" with "bounds" in add_node.
1278 * It may also satisfy some global constraints that were dropped out because
1279 * we performed separation with explicit bounds.
1280 * The very first step is then to copy these constraints to "bounds".
1282 * Since we may be calling before_each_for and after_each_for
1283 * callbacks, we record the current inverse schedule in the build.
1285 * We consider three builds,
1286 * "build" is the one in which the current level is created,
1287 * "body_build" is the build in which the next level is created,
1288 * "sub_build" is essentially the same as "body_build", except that
1289 * the depth has not been increased yet.
1291 * "build" already contains information (in strides and offsets)
1292 * about the strides at the current level, but this information is not
1293 * reflected in the build->domain.
1294 * We first add this information and the "bounds" to the sub_build->domain.
1295 * isl_ast_build_set_loop_bounds adds the stride information and
1296 * checks whether the current dimension attains
1297 * only a single value and whether this single value can be represented using
1298 * a single affine expression.
1299 * In the first case, the current level is considered "degenerate".
1300 * In the second, sub-case, the current level is considered "eliminated".
1301 * Eliminated levels don't need to be reflected in the AST since we can
1302 * simply plug in the affine expression. For degenerate, but non-eliminated,
1303 * levels, we do introduce a for node, but mark is as degenerate so that
1304 * it can be printed as an assignment of the single value to the loop
1305 * "iterator".
1307 * If the current level is eliminated, we explicitly plug in the value
1308 * for the current level found by isl_ast_build_set_loop_bounds in the
1309 * inverse schedule. This ensures that if we are working on a slice
1310 * of the domain based on information available in the inverse schedule
1311 * and the build domain, that then this information is also reflected
1312 * in the inverse schedule. This operation also eliminates the current
1313 * dimension from the inverse schedule making sure no inner dimensions depend
1314 * on the current dimension. Otherwise, we create a for node, marking
1315 * it degenerate if appropriate. The initial for node is still incomplete
1316 * and will be completed in either refine_degenerate or refine_generic.
1318 * We then generate a sequence of grafts for the next level,
1319 * create a surrounding graft for the current level and insert
1320 * the for node we created (if the current level is not eliminated).
1321 * Before creating a graft for the current level, we first extract
1322 * hoistable constraints from the child guards. These constraints
1323 * are used to simplify the child guards and then added to the guard
1324 * of the current graft.
1326 * Finally, we set the bounds of the for loop and insert guards
1327 * (either in the AST or in the graft) in one of
1328 * refine_eliminated, refine_degenerate or refine_generic.
1330 static __isl_give isl_ast_graft *create_node_scaled(
1331 __isl_take isl_union_map *executed,
1332 __isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
1333 __isl_take isl_ast_build *build)
1335 int depth;
1336 int degenerate, eliminated;
1337 isl_basic_set *hull;
1338 isl_basic_set *enforced;
1339 isl_set *hoisted;
1340 isl_ast_node *node = NULL;
1341 isl_ast_graft *graft;
1342 isl_ast_graft_list *children;
1343 isl_ast_build *sub_build;
1344 isl_ast_build *body_build;
1346 domain = isl_ast_build_eliminate_divs(build, domain);
1347 domain = isl_set_detect_equalities(domain);
1348 hull = isl_set_unshifted_simple_hull(isl_set_copy(domain));
1349 bounds = isl_basic_set_intersect(bounds, hull);
1350 build = isl_ast_build_set_executed(build, isl_union_map_copy(executed));
1352 depth = isl_ast_build_get_depth(build);
1353 sub_build = isl_ast_build_copy(build);
1354 sub_build = isl_ast_build_set_loop_bounds(sub_build,
1355 isl_basic_set_copy(bounds));
1356 degenerate = isl_ast_build_has_value(sub_build);
1357 eliminated = isl_ast_build_has_affine_value(sub_build, depth);
1358 if (degenerate < 0 || eliminated < 0)
1359 executed = isl_union_map_free(executed);
1360 if (eliminated)
1361 executed = plug_in_values(executed, sub_build);
1362 else
1363 node = create_for(build, degenerate);
1365 body_build = isl_ast_build_copy(sub_build);
1366 body_build = isl_ast_build_increase_depth(body_build);
1367 if (!eliminated)
1368 node = before_each_for(node, body_build);
1369 children = generate_next_level(executed,
1370 isl_ast_build_copy(body_build));
1372 enforced = extract_shared_enforced(children, build);
1373 hoisted = isl_ast_graft_list_extract_hoistable_guard(children, build);
1374 graft = isl_ast_graft_alloc_from_children(children, hoisted, enforced,
1375 build, sub_build);
1376 if (!eliminated)
1377 graft = isl_ast_graft_insert_for(graft, node);
1378 if (eliminated)
1379 graft = refine_eliminated(graft, bounds, build);
1380 else if (degenerate)
1381 graft = refine_degenerate(graft, build, sub_build);
1382 else {
1383 bounds = isl_ast_build_compute_gist_basic_set(build, bounds);
1384 graft = refine_generic(graft, bounds, domain, build);
1386 if (!eliminated) {
1387 graft = add_implied_guards(graft, degenerate, bounds, build);
1388 graft = after_each_for(graft, body_build);
1391 isl_ast_build_free(body_build);
1392 isl_ast_build_free(sub_build);
1393 isl_ast_build_free(build);
1394 isl_basic_set_free(bounds);
1395 isl_set_free(domain);
1397 return graft;
1400 /* Internal data structure for checking if all constraints involving
1401 * the input dimension "depth" are such that the other coefficients
1402 * are multiples of "m", reducing "m" if they are not.
1403 * If "m" is reduced all the way down to "1", then the check has failed
1404 * and we break out of the iteration.
1406 struct isl_check_scaled_data {
1407 int depth;
1408 isl_val *m;
1411 /* If constraint "c" involves the input dimension data->depth,
1412 * then make sure that all the other coefficients are multiples of data->m,
1413 * reducing data->m if needed.
1414 * Break out of the iteration if data->m has become equal to "1".
1416 static int constraint_check_scaled(__isl_take isl_constraint *c, void *user)
1418 struct isl_check_scaled_data *data = user;
1419 int i, j, n;
1420 enum isl_dim_type t[] = { isl_dim_param, isl_dim_in, isl_dim_out,
1421 isl_dim_div };
1423 if (!isl_constraint_involves_dims(c, isl_dim_in, data->depth, 1)) {
1424 isl_constraint_free(c);
1425 return 0;
1428 for (i = 0; i < 4; ++i) {
1429 n = isl_constraint_dim(c, t[i]);
1430 for (j = 0; j < n; ++j) {
1431 isl_val *d;
1433 if (t[i] == isl_dim_in && j == data->depth)
1434 continue;
1435 if (!isl_constraint_involves_dims(c, t[i], j, 1))
1436 continue;
1437 d = isl_constraint_get_coefficient_val(c, t[i], j);
1438 data->m = isl_val_gcd(data->m, d);
1439 if (isl_val_is_one(data->m))
1440 break;
1442 if (j < n)
1443 break;
1446 isl_constraint_free(c);
1448 return i < 4 ? -1 : 0;
1451 /* For each constraint of "bmap" that involves the input dimension data->depth,
1452 * make sure that all the other coefficients are multiples of data->m,
1453 * reducing data->m if needed.
1454 * Break out of the iteration if data->m has become equal to "1".
1456 static int basic_map_check_scaled(__isl_take isl_basic_map *bmap, void *user)
1458 int r;
1460 r = isl_basic_map_foreach_constraint(bmap,
1461 &constraint_check_scaled, user);
1462 isl_basic_map_free(bmap);
1464 return r;
1467 /* For each constraint of "map" that involves the input dimension data->depth,
1468 * make sure that all the other coefficients are multiples of data->m,
1469 * reducing data->m if needed.
1470 * Break out of the iteration if data->m has become equal to "1".
1472 static int map_check_scaled(__isl_take isl_map *map, void *user)
1474 int r;
1476 r = isl_map_foreach_basic_map(map, &basic_map_check_scaled, user);
1477 isl_map_free(map);
1479 return r;
1482 /* Create an AST node for the current dimension based on
1483 * the schedule domain "bounds" and return the node encapsulated
1484 * in an isl_ast_graft.
1486 * "executed" is the current inverse schedule, taking into account
1487 * the bounds in "bounds"
1488 * "domain" is the domain of "executed", with inner dimensions projected out.
1491 * Before moving on to the actual AST node construction in create_node_scaled,
1492 * we first check if the current dimension is strided and if we can scale
1493 * down this stride. Note that we only do this if the ast_build_scale_strides
1494 * option is set.
1496 * In particular, let the current dimension take on values
1498 * f + s a
1500 * with a an integer. We check if we can find an integer m that (obviously)
1501 * divides both f and s.
1503 * If so, we check if the current dimension only appears in constraints
1504 * where the coefficients of the other variables are multiples of m.
1505 * We perform this extra check to avoid the risk of introducing
1506 * divisions by scaling down the current dimension.
1508 * If so, we scale the current dimension down by a factor of m.
1509 * That is, we plug in
1511 * i = m i' (1)
1513 * Note that in principle we could always scale down strided loops
1514 * by plugging in
1516 * i = f + s i'
1518 * but this may result in i' taking on larger values than the original i,
1519 * due to the shift by "f".
1520 * By constrast, the scaling in (1) can only reduce the (absolute) value "i".
1522 static __isl_give isl_ast_graft *create_node(__isl_take isl_union_map *executed,
1523 __isl_take isl_basic_set *bounds, __isl_take isl_set *domain,
1524 __isl_take isl_ast_build *build)
1526 struct isl_check_scaled_data data;
1527 isl_ctx *ctx;
1528 isl_aff *offset;
1529 isl_val *d;
1531 ctx = isl_ast_build_get_ctx(build);
1532 if (!isl_options_get_ast_build_scale_strides(ctx))
1533 return create_node_scaled(executed, bounds, domain, build);
1535 data.depth = isl_ast_build_get_depth(build);
1536 if (!isl_ast_build_has_stride(build, data.depth))
1537 return create_node_scaled(executed, bounds, domain, build);
1539 offset = isl_ast_build_get_offset(build, data.depth);
1540 data.m = isl_ast_build_get_stride(build, data.depth);
1541 if (!data.m)
1542 offset = isl_aff_free(offset);
1543 offset = isl_aff_scale_down_val(offset, isl_val_copy(data.m));
1544 d = isl_aff_get_denominator_val(offset);
1545 if (!d)
1546 executed = isl_union_map_free(executed);
1548 if (executed && isl_val_is_divisible_by(data.m, d))
1549 data.m = isl_val_div(data.m, d);
1550 else {
1551 data.m = isl_val_set_si(data.m, 1);
1552 isl_val_free(d);
1555 if (!isl_val_is_one(data.m)) {
1556 if (isl_union_map_foreach_map(executed, &map_check_scaled,
1557 &data) < 0 &&
1558 !isl_val_is_one(data.m))
1559 executed = isl_union_map_free(executed);
1562 if (!isl_val_is_one(data.m)) {
1563 isl_space *space;
1564 isl_multi_aff *ma;
1565 isl_aff *aff;
1566 isl_map *map;
1567 isl_union_map *umap;
1569 space = isl_ast_build_get_space(build, 1);
1570 space = isl_space_map_from_set(space);
1571 ma = isl_multi_aff_identity(space);
1572 aff = isl_multi_aff_get_aff(ma, data.depth);
1573 aff = isl_aff_scale_val(aff, isl_val_copy(data.m));
1574 ma = isl_multi_aff_set_aff(ma, data.depth, aff);
1576 bounds = isl_basic_set_preimage_multi_aff(bounds,
1577 isl_multi_aff_copy(ma));
1578 domain = isl_set_preimage_multi_aff(domain,
1579 isl_multi_aff_copy(ma));
1580 map = isl_map_reverse(isl_map_from_multi_aff(ma));
1581 umap = isl_union_map_from_map(map);
1582 executed = isl_union_map_apply_domain(executed,
1583 isl_union_map_copy(umap));
1584 build = isl_ast_build_scale_down(build, isl_val_copy(data.m),
1585 umap);
1587 isl_aff_free(offset);
1588 isl_val_free(data.m);
1590 return create_node_scaled(executed, bounds, domain, build);
1593 /* Add the basic set to the list that "user" points to.
1595 static int collect_basic_set(__isl_take isl_basic_set *bset, void *user)
1597 isl_basic_set_list **list = user;
1599 *list = isl_basic_set_list_add(*list, bset);
1601 return 0;
1604 /* Extract the basic sets of "set" and collect them in an isl_basic_set_list.
1606 static __isl_give isl_basic_set_list *isl_basic_set_list_from_set(
1607 __isl_take isl_set *set)
1609 int n;
1610 isl_ctx *ctx;
1611 isl_basic_set_list *list;
1613 if (!set)
1614 return NULL;
1616 ctx = isl_set_get_ctx(set);
1618 n = isl_set_n_basic_set(set);
1619 list = isl_basic_set_list_alloc(ctx, n);
1620 if (isl_set_foreach_basic_set(set, &collect_basic_set, &list) < 0)
1621 list = isl_basic_set_list_free(list);
1623 isl_set_free(set);
1624 return list;
1627 /* Generate code for the schedule domain "bounds"
1628 * and add the result to "list".
1630 * We mainly detect strides here and check if the bounds do not
1631 * conflict with the current build domain
1632 * and then pass over control to create_node.
1634 * "bounds" reflects the bounds on the current dimension and possibly
1635 * some extra conditions on outer dimensions.
1636 * It does not, however, include any divs involving the current dimension,
1637 * so it does not capture any stride constraints.
1638 * We therefore need to compute that part of the schedule domain that
1639 * intersects with "bounds" and derive the strides from the result.
1641 static __isl_give isl_ast_graft_list *add_node(
1642 __isl_take isl_ast_graft_list *list, __isl_take isl_union_map *executed,
1643 __isl_take isl_basic_set *bounds, __isl_take isl_ast_build *build)
1645 isl_ast_graft *graft;
1646 isl_set *domain = NULL;
1647 isl_union_set *uset;
1648 int empty, disjoint;
1650 uset = isl_union_set_from_basic_set(isl_basic_set_copy(bounds));
1651 executed = isl_union_map_intersect_domain(executed, uset);
1652 empty = isl_union_map_is_empty(executed);
1653 if (empty < 0)
1654 goto error;
1655 if (empty)
1656 goto done;
1658 uset = isl_union_map_domain(isl_union_map_copy(executed));
1659 domain = isl_set_from_union_set(uset);
1660 domain = isl_ast_build_specialize(build, domain);
1662 domain = isl_set_compute_divs(domain);
1663 domain = isl_ast_build_eliminate_inner(build, domain);
1664 disjoint = isl_set_is_disjoint(domain, build->domain);
1665 if (disjoint < 0)
1666 goto error;
1667 if (disjoint)
1668 goto done;
1670 build = isl_ast_build_detect_strides(build, isl_set_copy(domain));
1672 graft = create_node(executed, bounds, domain,
1673 isl_ast_build_copy(build));
1674 list = isl_ast_graft_list_add(list, graft);
1675 isl_ast_build_free(build);
1676 return list;
1677 error:
1678 list = isl_ast_graft_list_free(list);
1679 done:
1680 isl_set_free(domain);
1681 isl_basic_set_free(bounds);
1682 isl_union_map_free(executed);
1683 isl_ast_build_free(build);
1684 return list;
1687 /* Does any element of i follow or coincide with any element of j
1688 * at the current depth for equal values of the outer dimensions?
1690 static int domain_follows_at_depth(__isl_keep isl_basic_set *i,
1691 __isl_keep isl_basic_set *j, void *user)
1693 int depth = *(int *) user;
1694 isl_basic_map *test;
1695 int empty;
1696 int l;
1698 test = isl_basic_map_from_domain_and_range(isl_basic_set_copy(i),
1699 isl_basic_set_copy(j));
1700 for (l = 0; l < depth; ++l)
1701 test = isl_basic_map_equate(test, isl_dim_in, l,
1702 isl_dim_out, l);
1703 test = isl_basic_map_order_ge(test, isl_dim_in, depth,
1704 isl_dim_out, depth);
1705 empty = isl_basic_map_is_empty(test);
1706 isl_basic_map_free(test);
1708 return empty < 0 ? -1 : !empty;
1711 /* Split up each element of "list" into a part that is related to "bset"
1712 * according to "gt" and a part that is not.
1713 * Return a list that consist of "bset" and all the pieces.
1715 static __isl_give isl_basic_set_list *add_split_on(
1716 __isl_take isl_basic_set_list *list, __isl_take isl_basic_set *bset,
1717 __isl_keep isl_basic_map *gt)
1719 int i, n;
1720 isl_basic_set_list *res;
1722 if (!list)
1723 bset = isl_basic_set_free(bset);
1725 gt = isl_basic_map_copy(gt);
1726 gt = isl_basic_map_intersect_domain(gt, isl_basic_set_copy(bset));
1727 n = isl_basic_set_list_n_basic_set(list);
1728 res = isl_basic_set_list_from_basic_set(bset);
1729 for (i = 0; res && i < n; ++i) {
1730 isl_basic_set *bset;
1731 isl_set *set1, *set2;
1732 isl_basic_map *bmap;
1733 int empty;
1735 bset = isl_basic_set_list_get_basic_set(list, i);
1736 bmap = isl_basic_map_copy(gt);
1737 bmap = isl_basic_map_intersect_range(bmap, bset);
1738 bset = isl_basic_map_range(bmap);
1739 empty = isl_basic_set_is_empty(bset);
1740 if (empty < 0)
1741 res = isl_basic_set_list_free(res);
1742 if (empty) {
1743 isl_basic_set_free(bset);
1744 bset = isl_basic_set_list_get_basic_set(list, i);
1745 res = isl_basic_set_list_add(res, bset);
1746 continue;
1749 res = isl_basic_set_list_add(res, isl_basic_set_copy(bset));
1750 set1 = isl_set_from_basic_set(bset);
1751 bset = isl_basic_set_list_get_basic_set(list, i);
1752 set2 = isl_set_from_basic_set(bset);
1753 set1 = isl_set_subtract(set2, set1);
1754 set1 = isl_set_make_disjoint(set1);
1756 res = isl_basic_set_list_concat(res,
1757 isl_basic_set_list_from_set(set1));
1759 isl_basic_map_free(gt);
1760 isl_basic_set_list_free(list);
1761 return res;
1764 static __isl_give isl_ast_graft_list *generate_sorted_domains(
1765 __isl_keep isl_basic_set_list *domain_list,
1766 __isl_keep isl_union_map *executed,
1767 __isl_keep isl_ast_build *build);
1769 /* Internal data structure for add_nodes.
1771 * "executed" and "build" are extra arguments to be passed to add_node.
1772 * "list" collects the results.
1774 struct isl_add_nodes_data {
1775 isl_union_map *executed;
1776 isl_ast_build *build;
1778 isl_ast_graft_list *list;
1781 /* Generate code for the schedule domains in "scc"
1782 * and add the results to "list".
1784 * The domains in "scc" form a strongly connected component in the ordering.
1785 * If the number of domains in "scc" is larger than 1, then this means
1786 * that we cannot determine a valid ordering for the domains in the component.
1787 * This should be fairly rare because the individual domains
1788 * have been made disjoint first.
1789 * The problem is that the domains may be integrally disjoint but not
1790 * rationally disjoint. For example, we may have domains
1792 * { [i,i] : 0 <= i <= 1 } and { [i,1-i] : 0 <= i <= 1 }
1794 * These two domains have an empty intersection, but their rational
1795 * relaxations do intersect. It is impossible to order these domains
1796 * in the second dimension because the first should be ordered before
1797 * the second for outer dimension equal to 0, while it should be ordered
1798 * after for outer dimension equal to 1.
1800 * This may happen in particular in case of unrolling since the domain
1801 * of each slice is replaced by its simple hull.
1803 * For each basic set i in "scc" and for each of the following basic sets j,
1804 * we split off that part of the basic set i that shares the outer dimensions
1805 * with j and lies before j in the current dimension.
1806 * We collect all the pieces in a new list that replaces "scc".
1808 * While the elements in "scc" should be disjoint, we double-check
1809 * this property to avoid running into an infinite recursion in case
1810 * they intersect due to some internal error.
1812 static int add_nodes(__isl_take isl_basic_set_list *scc, void *user)
1814 struct isl_add_nodes_data *data = user;
1815 int i, n, depth;
1816 isl_basic_set *bset, *first;
1817 isl_basic_set_list *list;
1818 isl_space *space;
1819 isl_basic_map *gt;
1821 n = isl_basic_set_list_n_basic_set(scc);
1822 bset = isl_basic_set_list_get_basic_set(scc, 0);
1823 if (n == 1) {
1824 isl_basic_set_list_free(scc);
1825 data->list = add_node(data->list,
1826 isl_union_map_copy(data->executed), bset,
1827 isl_ast_build_copy(data->build));
1828 return data->list ? 0 : -1;
1831 depth = isl_ast_build_get_depth(data->build);
1832 space = isl_basic_set_get_space(bset);
1833 space = isl_space_map_from_set(space);
1834 gt = isl_basic_map_universe(space);
1835 for (i = 0; i < depth; ++i)
1836 gt = isl_basic_map_equate(gt, isl_dim_in, i, isl_dim_out, i);
1837 gt = isl_basic_map_order_gt(gt, isl_dim_in, depth, isl_dim_out, depth);
1839 first = isl_basic_set_copy(bset);
1840 list = isl_basic_set_list_from_basic_set(bset);
1841 for (i = 1; i < n; ++i) {
1842 int disjoint;
1844 bset = isl_basic_set_list_get_basic_set(scc, i);
1846 disjoint = isl_basic_set_is_disjoint(bset, first);
1847 if (disjoint < 0)
1848 list = isl_basic_set_list_free(list);
1849 else if (!disjoint)
1850 isl_die(isl_basic_set_list_get_ctx(scc),
1851 isl_error_internal,
1852 "basic sets in scc are assumed to be disjoint",
1853 list = isl_basic_set_list_free(list));
1855 list = add_split_on(list, bset, gt);
1857 isl_basic_set_free(first);
1858 isl_basic_map_free(gt);
1859 isl_basic_set_list_free(scc);
1860 scc = list;
1861 data->list = isl_ast_graft_list_concat(data->list,
1862 generate_sorted_domains(scc, data->executed, data->build));
1863 isl_basic_set_list_free(scc);
1865 return data->list ? 0 : -1;
1868 /* Sort the domains in "domain_list" according to the execution order
1869 * at the current depth (for equal values of the outer dimensions),
1870 * generate code for each of them, collecting the results in a list.
1871 * If no code is generated (because the intersection of the inverse schedule
1872 * with the domains turns out to be empty), then an empty list is returned.
1874 * The caller is responsible for ensuring that the basic sets in "domain_list"
1875 * are pair-wise disjoint. It can, however, in principle happen that
1876 * two basic sets should be ordered one way for one value of the outer
1877 * dimensions and the other way for some other value of the outer dimensions.
1878 * We therefore play safe and look for strongly connected components.
1879 * The function add_nodes takes care of handling non-trivial components.
1881 static __isl_give isl_ast_graft_list *generate_sorted_domains(
1882 __isl_keep isl_basic_set_list *domain_list,
1883 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
1885 isl_ctx *ctx;
1886 struct isl_add_nodes_data data;
1887 int depth;
1888 int n;
1890 if (!domain_list)
1891 return NULL;
1893 ctx = isl_basic_set_list_get_ctx(domain_list);
1894 n = isl_basic_set_list_n_basic_set(domain_list);
1895 data.list = isl_ast_graft_list_alloc(ctx, n);
1896 if (n == 0)
1897 return data.list;
1898 if (n == 1)
1899 return add_node(data.list, isl_union_map_copy(executed),
1900 isl_basic_set_list_get_basic_set(domain_list, 0),
1901 isl_ast_build_copy(build));
1903 depth = isl_ast_build_get_depth(build);
1904 data.executed = executed;
1905 data.build = build;
1906 if (isl_basic_set_list_foreach_scc(domain_list,
1907 &domain_follows_at_depth, &depth,
1908 &add_nodes, &data) < 0)
1909 data.list = isl_ast_graft_list_free(data.list);
1911 return data.list;
1914 /* Do i and j share any values for the outer dimensions?
1916 static int shared_outer(__isl_keep isl_basic_set *i,
1917 __isl_keep isl_basic_set *j, void *user)
1919 int depth = *(int *) user;
1920 isl_basic_map *test;
1921 int empty;
1922 int l;
1924 test = isl_basic_map_from_domain_and_range(isl_basic_set_copy(i),
1925 isl_basic_set_copy(j));
1926 for (l = 0; l < depth; ++l)
1927 test = isl_basic_map_equate(test, isl_dim_in, l,
1928 isl_dim_out, l);
1929 empty = isl_basic_map_is_empty(test);
1930 isl_basic_map_free(test);
1932 return empty < 0 ? -1 : !empty;
1935 /* Internal data structure for generate_sorted_domains_wrap.
1937 * "n" is the total number of basic sets
1938 * "executed" and "build" are extra arguments to be passed
1939 * to generate_sorted_domains.
1941 * "single" is set to 1 by generate_sorted_domains_wrap if there
1942 * is only a single component.
1943 * "list" collects the results.
1945 struct isl_ast_generate_parallel_domains_data {
1946 int n;
1947 isl_union_map *executed;
1948 isl_ast_build *build;
1950 int single;
1951 isl_ast_graft_list *list;
1954 /* Call generate_sorted_domains on "scc", fuse the result into a list
1955 * with either zero or one graft and collect the these single element
1956 * lists into data->list.
1958 * If there is only one component, i.e., if the number of basic sets
1959 * in the current component is equal to the total number of basic sets,
1960 * then data->single is set to 1 and the result of generate_sorted_domains
1961 * is not fused.
1963 static int generate_sorted_domains_wrap(__isl_take isl_basic_set_list *scc,
1964 void *user)
1966 struct isl_ast_generate_parallel_domains_data *data = user;
1967 isl_ast_graft_list *list;
1969 list = generate_sorted_domains(scc, data->executed, data->build);
1970 data->single = isl_basic_set_list_n_basic_set(scc) == data->n;
1971 if (!data->single)
1972 list = isl_ast_graft_list_fuse(list, data->build);
1973 if (!data->list)
1974 data->list = list;
1975 else
1976 data->list = isl_ast_graft_list_concat(data->list, list);
1978 isl_basic_set_list_free(scc);
1979 if (!data->list)
1980 return -1;
1982 return 0;
1985 /* Look for any (weakly connected) components in the "domain_list"
1986 * of domains that share some values of the outer dimensions.
1987 * That is, domains in different components do not share any values
1988 * of the outer dimensions. This means that these components
1989 * can be freely reordered.
1990 * Within each of the components, we sort the domains according
1991 * to the execution order at the current depth.
1993 * If there is more than one component, then generate_sorted_domains_wrap
1994 * fuses the result of each call to generate_sorted_domains
1995 * into a list with either zero or one graft and collects these (at most)
1996 * single element lists into a bigger list. This means that the elements of the
1997 * final list can be freely reordered. In particular, we sort them
1998 * according to an arbitrary but fixed ordering to ease merging of
1999 * graft lists from different components.
2001 static __isl_give isl_ast_graft_list *generate_parallel_domains(
2002 __isl_keep isl_basic_set_list *domain_list,
2003 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
2005 int depth;
2006 struct isl_ast_generate_parallel_domains_data data;
2008 if (!domain_list)
2009 return NULL;
2011 data.n = isl_basic_set_list_n_basic_set(domain_list);
2012 if (data.n <= 1)
2013 return generate_sorted_domains(domain_list, executed, build);
2015 depth = isl_ast_build_get_depth(build);
2016 data.list = NULL;
2017 data.executed = executed;
2018 data.build = build;
2019 data.single = 0;
2020 if (isl_basic_set_list_foreach_scc(domain_list, &shared_outer, &depth,
2021 &generate_sorted_domains_wrap,
2022 &data) < 0)
2023 data.list = isl_ast_graft_list_free(data.list);
2025 if (!data.single)
2026 data.list = isl_ast_graft_list_sort_guard(data.list);
2028 return data.list;
2031 /* Internal data for separate_domain.
2033 * "explicit" is set if we only want to use explicit bounds.
2035 * "domain" collects the separated domains.
2037 struct isl_separate_domain_data {
2038 isl_ast_build *build;
2039 int explicit;
2040 isl_set *domain;
2043 /* Extract implicit bounds on the current dimension for the executed "map".
2045 * The domain of "map" may involve inner dimensions, so we
2046 * need to eliminate them.
2048 static __isl_give isl_set *implicit_bounds(__isl_take isl_map *map,
2049 __isl_keep isl_ast_build *build)
2051 isl_set *domain;
2053 domain = isl_map_domain(map);
2054 domain = isl_ast_build_eliminate(build, domain);
2056 return domain;
2059 /* Extract explicit bounds on the current dimension for the executed "map".
2061 * Rather than eliminating the inner dimensions as in implicit_bounds,
2062 * we simply drop any constraints involving those inner dimensions.
2063 * The idea is that most bounds that are implied by constraints on the
2064 * inner dimensions will be enforced by for loops and not by explicit guards.
2065 * There is then no need to separate along those bounds.
2067 static __isl_give isl_set *explicit_bounds(__isl_take isl_map *map,
2068 __isl_keep isl_ast_build *build)
2070 isl_set *domain;
2071 int depth, dim;
2073 dim = isl_map_dim(map, isl_dim_out);
2074 map = isl_map_drop_constraints_involving_dims(map, isl_dim_out, 0, dim);
2076 domain = isl_map_domain(map);
2077 depth = isl_ast_build_get_depth(build);
2078 dim = isl_set_dim(domain, isl_dim_set);
2079 domain = isl_set_detect_equalities(domain);
2080 domain = isl_set_drop_constraints_involving_dims(domain,
2081 isl_dim_set, depth + 1, dim - (depth + 1));
2082 domain = isl_set_remove_divs_involving_dims(domain,
2083 isl_dim_set, depth, 1);
2084 domain = isl_set_remove_unknown_divs(domain);
2086 return domain;
2089 /* Split data->domain into pieces that intersect with the range of "map"
2090 * and pieces that do not intersect with the range of "map"
2091 * and then add that part of the range of "map" that does not intersect
2092 * with data->domain.
2094 static int separate_domain(__isl_take isl_map *map, void *user)
2096 struct isl_separate_domain_data *data = user;
2097 isl_set *domain;
2098 isl_set *d1, *d2;
2100 if (data->explicit)
2101 domain = explicit_bounds(map, data->build);
2102 else
2103 domain = implicit_bounds(map, data->build);
2105 domain = isl_set_coalesce(domain);
2106 domain = isl_set_make_disjoint(domain);
2107 d1 = isl_set_subtract(isl_set_copy(domain), isl_set_copy(data->domain));
2108 d2 = isl_set_subtract(isl_set_copy(data->domain), isl_set_copy(domain));
2109 data->domain = isl_set_intersect(data->domain, domain);
2110 data->domain = isl_set_union(data->domain, d1);
2111 data->domain = isl_set_union(data->domain, d2);
2113 return 0;
2116 /* Separate the schedule domains of "executed".
2118 * That is, break up the domain of "executed" into basic sets,
2119 * such that for each basic set S, every element in S is associated with
2120 * the same domain spaces.
2122 * "space" is the (single) domain space of "executed".
2124 static __isl_give isl_set *separate_schedule_domains(
2125 __isl_take isl_space *space, __isl_take isl_union_map *executed,
2126 __isl_keep isl_ast_build *build)
2128 struct isl_separate_domain_data data = { build };
2129 isl_ctx *ctx;
2131 ctx = isl_ast_build_get_ctx(build);
2132 data.explicit = isl_options_get_ast_build_separation_bounds(ctx) ==
2133 ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT;
2134 data.domain = isl_set_empty(space);
2135 if (isl_union_map_foreach_map(executed, &separate_domain, &data) < 0)
2136 data.domain = isl_set_free(data.domain);
2138 isl_union_map_free(executed);
2139 return data.domain;
2142 /* Temporary data used during the search for a lower bound for unrolling.
2144 * "domain" is the original set for which to find a lower bound
2145 * "depth" is the dimension for which to find a lower boudn
2147 * "lower" is the best lower bound found so far. It is NULL if we have not
2148 * found any yet.
2149 * "n" is the corresponding size. If lower is NULL, then the value of n
2150 * is undefined.
2152 struct isl_find_unroll_data {
2153 isl_set *domain;
2154 int depth;
2156 isl_aff *lower;
2157 int *n;
2160 /* Check if we can use "c" as a lower bound and if it is better than
2161 * any previously found lower bound.
2163 * If "c" does not involve the dimension at the current depth,
2164 * then we cannot use it.
2165 * Otherwise, let "c" be of the form
2167 * i >= f(j)/a
2169 * We compute the maximal value of
2171 * -ceil(f(j)/a)) + i + 1
2173 * over the domain. If there is such a value "n", then we know
2175 * -ceil(f(j)/a)) + i + 1 <= n
2177 * or
2179 * i < ceil(f(j)/a)) + n
2181 * meaning that we can use ceil(f(j)/a)) as a lower bound for unrolling.
2182 * We just need to check if we have found any lower bound before and
2183 * if the new lower bound is better (smaller n) than the previously found
2184 * lower bounds.
2186 static int update_unrolling_lower_bound(struct isl_find_unroll_data *data,
2187 __isl_keep isl_constraint *c)
2189 isl_aff *aff, *lower;
2190 isl_val *max;
2192 if (!isl_constraint_is_lower_bound(c, isl_dim_set, data->depth))
2193 return 0;
2195 lower = isl_constraint_get_bound(c, isl_dim_set, data->depth);
2196 lower = isl_aff_ceil(lower);
2197 aff = isl_aff_copy(lower);
2198 aff = isl_aff_neg(aff);
2199 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, data->depth, 1);
2200 aff = isl_aff_add_constant_si(aff, 1);
2201 max = isl_set_max_val(data->domain, aff);
2202 isl_aff_free(aff);
2204 if (!max)
2205 goto error;
2206 if (isl_val_is_infty(max)) {
2207 isl_val_free(max);
2208 isl_aff_free(lower);
2209 return 0;
2212 if (isl_val_cmp_si(max, INT_MAX) <= 0 &&
2213 (!data->lower || isl_val_cmp_si(max, *data->n) < 0)) {
2214 isl_aff_free(data->lower);
2215 data->lower = lower;
2216 *data->n = isl_val_get_num_si(max);
2217 } else
2218 isl_aff_free(lower);
2219 isl_val_free(max);
2221 return 1;
2222 error:
2223 isl_aff_free(lower);
2224 return -1;
2227 /* Check if we can use "c" as a lower bound and if it is better than
2228 * any previously found lower bound.
2230 static int constraint_find_unroll(__isl_take isl_constraint *c, void *user)
2232 struct isl_find_unroll_data *data;
2233 int r;
2235 data = (struct isl_find_unroll_data *) user;
2236 r = update_unrolling_lower_bound(data, c);
2237 isl_constraint_free(c);
2239 return r;
2242 /* Look for a lower bound l(i) on the dimension at "depth"
2243 * and a size n such that "domain" is a subset of
2245 * { [i] : l(i) <= i_d < l(i) + n }
2247 * where d is "depth" and l(i) depends only on earlier dimensions.
2248 * Furthermore, try and find a lower bound such that n is as small as possible.
2249 * In particular, "n" needs to be finite.
2251 * Inner dimensions have been eliminated from "domain" by the caller.
2253 * We first construct a collection of lower bounds on the input set
2254 * by computing its simple hull. We then iterate through them,
2255 * discarding those that we cannot use (either because they do not
2256 * involve the dimension at "depth" or because they have no corresponding
2257 * upper bound, meaning that "n" would be unbounded) and pick out the
2258 * best from the remaining ones.
2260 * If we cannot find a suitable lower bound, then we consider that
2261 * to be an error.
2263 static __isl_give isl_aff *find_unroll_lower_bound(__isl_keep isl_set *domain,
2264 int depth, int *n)
2266 struct isl_find_unroll_data data = { domain, depth, NULL, n };
2267 isl_basic_set *hull;
2269 hull = isl_set_simple_hull(isl_set_copy(domain));
2271 if (isl_basic_set_foreach_constraint(hull,
2272 &constraint_find_unroll, &data) < 0)
2273 goto error;
2275 isl_basic_set_free(hull);
2277 if (!data.lower)
2278 isl_die(isl_set_get_ctx(domain), isl_error_invalid,
2279 "cannot find lower bound for unrolling", return NULL);
2281 return data.lower;
2282 error:
2283 isl_basic_set_free(hull);
2284 return isl_aff_free(data.lower);
2287 /* Return the constraint
2289 * i_"depth" = aff + offset
2291 static __isl_give isl_constraint *at_offset(int depth, __isl_keep isl_aff *aff,
2292 int offset)
2294 aff = isl_aff_copy(aff);
2295 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, depth, -1);
2296 aff = isl_aff_add_constant_si(aff, offset);
2297 return isl_equality_from_aff(aff);
2300 /* Data structure for storing the results and the intermediate objects
2301 * of compute_domains.
2303 * "list" is the main result of the function and contains a list
2304 * of disjoint basic sets for which code should be generated.
2306 * "executed" and "build" are inputs to compute_domains.
2307 * "schedule_domain" is the domain of "executed".
2309 * "option" constains the domains at the current depth that should by
2310 * atomic, separated or unrolled. These domains are as specified by
2311 * the user, except that inner dimensions have been eliminated and
2312 * that they have been made pair-wise disjoint.
2314 * "sep_class" contains the user-specified split into separation classes
2315 * specialized to the current depth.
2316 * "done" contains the union of the separation domains that have already
2317 * been handled.
2319 struct isl_codegen_domains {
2320 isl_basic_set_list *list;
2322 isl_union_map *executed;
2323 isl_ast_build *build;
2324 isl_set *schedule_domain;
2326 isl_set *option[3];
2328 isl_map *sep_class;
2329 isl_set *done;
2332 /* Extend domains->list with a list of basic sets, one for each value
2333 * of the current dimension in "domain" and remove the corresponding
2334 * sets from the class domain. Return the updated class domain.
2335 * The divs that involve the current dimension have not been projected out
2336 * from this domain.
2338 * Since we are going to be iterating over the individual values,
2339 * we first check if there are any strides on the current dimension.
2340 * If there is, we rewrite the current dimension i as
2342 * i = stride i' + offset
2344 * and then iterate over individual values of i' instead.
2346 * We then look for a lower bound on i' and a size such that the domain
2347 * is a subset of
2349 * { [j,i'] : l(j) <= i' < l(j) + n }
2351 * and then take slices of the domain at values of i'
2352 * between l(j) and l(j) + n - 1.
2354 * We compute the unshifted simple hull of each slice to ensure that
2355 * we have a single basic set per offset. The slicing constraint
2356 * may get simplified away before the unshifted simple hull is taken
2357 * and may therefore in some rare cases disappear from the result.
2358 * We therefore explicitly add the constraint back after computing
2359 * the unshifted simple hull to ensure that the basic sets
2360 * remain disjoint. The constraints that are dropped by taking the hull
2361 * will be taken into account at the next level, as in the case of the
2362 * atomic option.
2364 * Finally, we map i' back to i and add each basic set to the list.
2365 * Since we may have dropped some constraints, we intersect with
2366 * the class domain again to ensure that each element in the list
2367 * is disjoint from the other class domains.
2369 static __isl_give isl_set *do_unroll(struct isl_codegen_domains *domains,
2370 __isl_take isl_set *domain, __isl_take isl_set *class_domain)
2372 int i, n;
2373 int depth;
2374 isl_ctx *ctx;
2375 isl_aff *lower;
2376 isl_multi_aff *expansion;
2377 isl_basic_map *bmap;
2378 isl_set *unroll_domain;
2379 isl_ast_build *build;
2381 if (!domain)
2382 return isl_set_free(class_domain);
2384 ctx = isl_set_get_ctx(domain);
2385 depth = isl_ast_build_get_depth(domains->build);
2386 build = isl_ast_build_copy(domains->build);
2387 domain = isl_ast_build_eliminate_inner(build, domain);
2388 build = isl_ast_build_detect_strides(build, isl_set_copy(domain));
2389 expansion = isl_ast_build_get_stride_expansion(build);
2391 domain = isl_set_preimage_multi_aff(domain,
2392 isl_multi_aff_copy(expansion));
2393 domain = isl_ast_build_eliminate_divs(build, domain);
2395 isl_ast_build_free(build);
2397 lower = find_unroll_lower_bound(domain, depth, &n);
2398 if (!lower)
2399 class_domain = isl_set_free(class_domain);
2401 bmap = isl_basic_map_from_multi_aff(expansion);
2403 unroll_domain = isl_set_empty(isl_set_get_space(domain));
2405 for (i = 0; class_domain && i < n; ++i) {
2406 isl_set *set;
2407 isl_basic_set *bset;
2408 isl_constraint *slice;
2409 isl_basic_set_list *list;
2411 slice = at_offset(depth, lower, i);
2412 set = isl_set_copy(domain);
2413 set = isl_set_add_constraint(set, isl_constraint_copy(slice));
2414 bset = isl_set_unshifted_simple_hull(set);
2415 bset = isl_basic_set_add_constraint(bset, slice);
2416 bset = isl_basic_set_apply(bset, isl_basic_map_copy(bmap));
2417 set = isl_set_from_basic_set(bset);
2418 unroll_domain = isl_set_union(unroll_domain, isl_set_copy(set));
2419 set = isl_set_intersect(set, isl_set_copy(class_domain));
2420 set = isl_set_make_disjoint(set);
2421 list = isl_basic_set_list_from_set(set);
2422 domains->list = isl_basic_set_list_concat(domains->list, list);
2425 class_domain = isl_set_subtract(class_domain, unroll_domain);
2427 isl_aff_free(lower);
2428 isl_set_free(domain);
2429 isl_basic_map_free(bmap);
2431 return class_domain;
2434 /* Add domains to domains->list for each individual value of the current
2435 * dimension, for that part of the schedule domain that lies in the
2436 * intersection of the option domain and the class domain.
2437 * Remove the corresponding sets from the class domain and
2438 * return the updated class domain.
2440 * We first break up the unroll option domain into individual pieces
2441 * and then handle each of them separately. The unroll option domain
2442 * has been made disjoint in compute_domains_init_options,
2444 * Note that we actively want to combine different pieces of the
2445 * schedule domain that have the same value at the current dimension.
2446 * We therefore need to break up the unroll option domain before
2447 * intersecting with class and schedule domain, hoping that the
2448 * unroll option domain specified by the user is relatively simple.
2450 static __isl_give isl_set *compute_unroll_domains(
2451 struct isl_codegen_domains *domains, __isl_take isl_set *class_domain)
2453 isl_set *unroll_domain;
2454 isl_basic_set_list *unroll_list;
2455 int i, n;
2456 int empty;
2458 empty = isl_set_is_empty(domains->option[unroll]);
2459 if (empty < 0)
2460 return isl_set_free(class_domain);
2461 if (empty)
2462 return class_domain;
2464 unroll_domain = isl_set_copy(domains->option[unroll]);
2465 unroll_list = isl_basic_set_list_from_set(unroll_domain);
2467 n = isl_basic_set_list_n_basic_set(unroll_list);
2468 for (i = 0; i < n; ++i) {
2469 isl_basic_set *bset;
2471 bset = isl_basic_set_list_get_basic_set(unroll_list, i);
2472 unroll_domain = isl_set_from_basic_set(bset);
2473 unroll_domain = isl_set_intersect(unroll_domain,
2474 isl_set_copy(class_domain));
2475 unroll_domain = isl_set_intersect(unroll_domain,
2476 isl_set_copy(domains->schedule_domain));
2478 empty = isl_set_is_empty(unroll_domain);
2479 if (empty >= 0 && empty) {
2480 isl_set_free(unroll_domain);
2481 continue;
2484 class_domain = do_unroll(domains, unroll_domain, class_domain);
2487 isl_basic_set_list_free(unroll_list);
2489 return class_domain;
2492 /* Try and construct a single basic set that includes the intersection of
2493 * the schedule domain, the atomic option domain and the class domain.
2494 * Add the resulting basic set(s) to domains->list and remove them
2495 * from class_domain. Return the updated class domain.
2497 * We construct a single domain rather than trying to combine
2498 * the schedule domains of individual domains because we are working
2499 * within a single component so that non-overlapping schedule domains
2500 * should already have been separated.
2501 * We do however need to make sure that this single domains is a subset
2502 * of the class domain so that it would not intersect with any other
2503 * class domains. This means that we may end up splitting up the atomic
2504 * domain in case separation classes are being used.
2506 * "domain" is the intersection of the schedule domain and the class domain,
2507 * with inner dimensions projected out.
2509 static __isl_give isl_set *compute_atomic_domain(
2510 struct isl_codegen_domains *domains, __isl_take isl_set *class_domain)
2512 isl_basic_set *bset;
2513 isl_basic_set_list *list;
2514 isl_set *domain, *atomic_domain;
2515 int empty;
2517 domain = isl_set_copy(domains->option[atomic]);
2518 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2519 domain = isl_set_intersect(domain,
2520 isl_set_copy(domains->schedule_domain));
2521 empty = isl_set_is_empty(domain);
2522 if (empty < 0)
2523 class_domain = isl_set_free(class_domain);
2524 if (empty) {
2525 isl_set_free(domain);
2526 return class_domain;
2529 domain = isl_ast_build_eliminate(domains->build, domain);
2530 domain = isl_set_coalesce(domain);
2531 bset = isl_set_unshifted_simple_hull(domain);
2532 domain = isl_set_from_basic_set(bset);
2533 atomic_domain = isl_set_copy(domain);
2534 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2535 class_domain = isl_set_subtract(class_domain, atomic_domain);
2536 domain = isl_set_make_disjoint(domain);
2537 list = isl_basic_set_list_from_set(domain);
2538 domains->list = isl_basic_set_list_concat(domains->list, list);
2540 return class_domain;
2543 /* Split up the schedule domain into uniform basic sets,
2544 * in the sense that each element in a basic set is associated to
2545 * elements of the same domains, and add the result to domains->list.
2546 * Do this for that part of the schedule domain that lies in the
2547 * intersection of "class_domain" and the separate option domain.
2549 * "class_domain" may or may not include the constraints
2550 * of the schedule domain, but this does not make a difference
2551 * since we are going to intersect it with the domain of the inverse schedule.
2552 * If it includes schedule domain constraints, then they may involve
2553 * inner dimensions, but we will eliminate them in separation_domain.
2555 static int compute_separate_domain(struct isl_codegen_domains *domains,
2556 __isl_keep isl_set *class_domain)
2558 isl_space *space;
2559 isl_set *domain;
2560 isl_union_map *executed;
2561 isl_basic_set_list *list;
2562 int empty;
2564 domain = isl_set_copy(domains->option[separate]);
2565 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2566 executed = isl_union_map_copy(domains->executed);
2567 executed = isl_union_map_intersect_domain(executed,
2568 isl_union_set_from_set(domain));
2569 empty = isl_union_map_is_empty(executed);
2570 if (empty < 0 || empty) {
2571 isl_union_map_free(executed);
2572 return empty < 0 ? -1 : 0;
2575 space = isl_set_get_space(class_domain);
2576 domain = separate_schedule_domains(space, executed, domains->build);
2578 list = isl_basic_set_list_from_set(domain);
2579 domains->list = isl_basic_set_list_concat(domains->list, list);
2581 return 0;
2584 /* Split up the domain at the current depth into disjoint
2585 * basic sets for which code should be generated separately
2586 * for the given separation class domain.
2588 * If any separation classes have been defined, then "class_domain"
2589 * is the domain of the current class and does not refer to inner dimensions.
2590 * Otherwise, "class_domain" is the universe domain.
2592 * We first make sure that the class domain is disjoint from
2593 * previously considered class domains.
2595 * The separate domains can be computed directly from the "class_domain".
2597 * The unroll, atomic and remainder domains need the constraints
2598 * from the schedule domain.
2600 * For unrolling, the actual schedule domain is needed (with divs that
2601 * may refer to the current dimension) so that stride detection can be
2602 * performed.
2604 * For atomic and remainder domains, inner dimensions and divs involving
2605 * the current dimensions should be eliminated.
2606 * In case we are working within a separation class, we need to intersect
2607 * the result with the current "class_domain" to ensure that the domains
2608 * are disjoint from those generated from other class domains.
2610 * The domain that has been made atomic may be larger than specified
2611 * by the user since it needs to be representable as a single basic set.
2612 * This possibly larger domain is removed from class_domain by
2613 * compute_atomic_domain. It is computed first so that the extended domain
2614 * would not overlap with any domains computed before.
2615 * Similary, the unrolled domains may have some constraints removed and
2616 * may therefore also be larger than specified by the user.
2618 * If anything is left after handling separate, unroll and atomic,
2619 * we split it up into basic sets and append the basic sets to domains->list.
2621 static int compute_partial_domains(struct isl_codegen_domains *domains,
2622 __isl_take isl_set *class_domain)
2624 isl_basic_set_list *list;
2625 isl_set *domain;
2627 class_domain = isl_set_subtract(class_domain,
2628 isl_set_copy(domains->done));
2629 domains->done = isl_set_union(domains->done,
2630 isl_set_copy(class_domain));
2632 class_domain = compute_atomic_domain(domains, class_domain);
2633 class_domain = compute_unroll_domains(domains, class_domain);
2635 domain = isl_set_copy(class_domain);
2637 if (compute_separate_domain(domains, domain) < 0)
2638 goto error;
2639 domain = isl_set_subtract(domain,
2640 isl_set_copy(domains->option[separate]));
2642 domain = isl_set_intersect(domain,
2643 isl_set_copy(domains->schedule_domain));
2645 domain = isl_ast_build_eliminate(domains->build, domain);
2646 domain = isl_set_intersect(domain, isl_set_copy(class_domain));
2648 domain = isl_set_coalesce(domain);
2649 domain = isl_set_make_disjoint(domain);
2651 list = isl_basic_set_list_from_set(domain);
2652 domains->list = isl_basic_set_list_concat(domains->list, list);
2654 isl_set_free(class_domain);
2656 return 0;
2657 error:
2658 isl_set_free(domain);
2659 isl_set_free(class_domain);
2660 return -1;
2663 /* Split up the domain at the current depth into disjoint
2664 * basic sets for which code should be generated separately
2665 * for the separation class identified by "pnt".
2667 * We extract the corresponding class domain from domains->sep_class,
2668 * eliminate inner dimensions and pass control to compute_partial_domains.
2670 static int compute_class_domains(__isl_take isl_point *pnt, void *user)
2672 struct isl_codegen_domains *domains = user;
2673 isl_set *class_set;
2674 isl_set *domain;
2675 int disjoint;
2677 class_set = isl_set_from_point(pnt);
2678 domain = isl_map_domain(isl_map_intersect_range(
2679 isl_map_copy(domains->sep_class), class_set));
2680 domain = isl_ast_build_compute_gist(domains->build, domain);
2681 domain = isl_ast_build_eliminate(domains->build, domain);
2683 disjoint = isl_set_plain_is_disjoint(domain, domains->schedule_domain);
2684 if (disjoint < 0)
2685 return -1;
2686 if (disjoint) {
2687 isl_set_free(domain);
2688 return 0;
2691 return compute_partial_domains(domains, domain);
2694 /* Extract the domains at the current depth that should be atomic,
2695 * separated or unrolled and store them in option.
2697 * The domains specified by the user might overlap, so we make
2698 * them disjoint by subtracting earlier domains from later domains.
2700 static void compute_domains_init_options(isl_set *option[3],
2701 __isl_keep isl_ast_build *build)
2703 enum isl_ast_build_domain_type type, type2;
2705 for (type = atomic; type <= separate; ++type) {
2706 option[type] = isl_ast_build_get_option_domain(build, type);
2707 for (type2 = atomic; type2 < type; ++type2)
2708 option[type] = isl_set_subtract(option[type],
2709 isl_set_copy(option[type2]));
2712 option[unroll] = isl_set_coalesce(option[unroll]);
2713 option[unroll] = isl_set_make_disjoint(option[unroll]);
2716 /* Split up the domain at the current depth into disjoint
2717 * basic sets for which code should be generated separately,
2718 * based on the user-specified options.
2719 * Return the list of disjoint basic sets.
2721 * There are three kinds of domains that we need to keep track of.
2722 * - the "schedule domain" is the domain of "executed"
2723 * - the "class domain" is the domain corresponding to the currrent
2724 * separation class
2725 * - the "option domain" is the domain corresponding to one of the options
2726 * atomic, unroll or separate
2728 * We first consider the individial values of the separation classes
2729 * and split up the domain for each of them separately.
2730 * Finally, we consider the remainder. If no separation classes were
2731 * specified, then we call compute_partial_domains with the universe
2732 * "class_domain". Otherwise, we take the "schedule_domain" as "class_domain",
2733 * with inner dimensions removed. We do this because we want to
2734 * avoid computing the complement of the class domains (i.e., the difference
2735 * between the universe and domains->done).
2737 static __isl_give isl_basic_set_list *compute_domains(
2738 __isl_keep isl_union_map *executed, __isl_keep isl_ast_build *build)
2740 struct isl_codegen_domains domains;
2741 isl_ctx *ctx;
2742 isl_set *domain;
2743 isl_union_set *schedule_domain;
2744 isl_set *classes;
2745 isl_space *space;
2746 int n_param;
2747 enum isl_ast_build_domain_type type;
2748 int empty;
2750 if (!executed)
2751 return NULL;
2753 ctx = isl_union_map_get_ctx(executed);
2754 domains.list = isl_basic_set_list_alloc(ctx, 0);
2756 schedule_domain = isl_union_map_domain(isl_union_map_copy(executed));
2757 domain = isl_set_from_union_set(schedule_domain);
2759 compute_domains_init_options(domains.option, build);
2761 domains.sep_class = isl_ast_build_get_separation_class(build);
2762 classes = isl_map_range(isl_map_copy(domains.sep_class));
2763 n_param = isl_set_dim(classes, isl_dim_param);
2764 classes = isl_set_project_out(classes, isl_dim_param, 0, n_param);
2766 space = isl_set_get_space(domain);
2767 domains.build = build;
2768 domains.schedule_domain = isl_set_copy(domain);
2769 domains.executed = executed;
2770 domains.done = isl_set_empty(space);
2772 if (isl_set_foreach_point(classes, &compute_class_domains, &domains) < 0)
2773 domains.list = isl_basic_set_list_free(domains.list);
2774 isl_set_free(classes);
2776 empty = isl_set_is_empty(domains.done);
2777 if (empty < 0) {
2778 domains.list = isl_basic_set_list_free(domains.list);
2779 domain = isl_set_free(domain);
2780 } else if (empty) {
2781 isl_set_free(domain);
2782 domain = isl_set_universe(isl_set_get_space(domains.done));
2783 } else {
2784 domain = isl_ast_build_eliminate(build, domain);
2786 if (compute_partial_domains(&domains, domain) < 0)
2787 domains.list = isl_basic_set_list_free(domains.list);
2789 isl_set_free(domains.schedule_domain);
2790 isl_set_free(domains.done);
2791 isl_map_free(domains.sep_class);
2792 for (type = atomic; type <= separate; ++type)
2793 isl_set_free(domains.option[type]);
2795 return domains.list;
2798 /* Generate code for a single component, after shifting (if any)
2799 * has been applied.
2801 * We first split up the domain at the current depth into disjoint
2802 * basic sets based on the user-specified options.
2803 * Then we generated code for each of them and concatenate the results.
2805 static __isl_give isl_ast_graft_list *generate_shifted_component(
2806 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
2808 isl_basic_set_list *domain_list;
2809 isl_ast_graft_list *list = NULL;
2811 domain_list = compute_domains(executed, build);
2812 list = generate_parallel_domains(domain_list, executed, build);
2814 isl_basic_set_list_free(domain_list);
2815 isl_union_map_free(executed);
2816 isl_ast_build_free(build);
2818 return list;
2821 struct isl_set_map_pair {
2822 isl_set *set;
2823 isl_map *map;
2826 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2827 * of indices into the "domain" array,
2828 * return the union of the "map" fields of the elements
2829 * indexed by the first "n" elements of "order".
2831 static __isl_give isl_union_map *construct_component_executed(
2832 struct isl_set_map_pair *domain, int *order, int n)
2834 int i;
2835 isl_map *map;
2836 isl_union_map *executed;
2838 map = isl_map_copy(domain[order[0]].map);
2839 executed = isl_union_map_from_map(map);
2840 for (i = 1; i < n; ++i) {
2841 map = isl_map_copy(domain[order[i]].map);
2842 executed = isl_union_map_add_map(executed, map);
2845 return executed;
2848 /* Generate code for a single component, after shifting (if any)
2849 * has been applied.
2851 * The component inverse schedule is specified as the "map" fields
2852 * of the elements of "domain" indexed by the first "n" elements of "order".
2854 static __isl_give isl_ast_graft_list *generate_shifted_component_from_list(
2855 struct isl_set_map_pair *domain, int *order, int n,
2856 __isl_take isl_ast_build *build)
2858 isl_union_map *executed;
2860 executed = construct_component_executed(domain, order, n);
2861 return generate_shifted_component(executed, build);
2864 /* Does set dimension "pos" of "set" have an obviously fixed value?
2866 static int dim_is_fixed(__isl_keep isl_set *set, int pos)
2868 int fixed;
2869 isl_val *v;
2871 v = isl_set_plain_get_val_if_fixed(set, isl_dim_set, pos);
2872 if (!v)
2873 return -1;
2874 fixed = !isl_val_is_nan(v);
2875 isl_val_free(v);
2877 return fixed;
2880 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2881 * of indices into the "domain" array,
2882 * do all (except for at most one) of the "set" field of the elements
2883 * indexed by the first "n" elements of "order" have a fixed value
2884 * at position "depth"?
2886 static int at_most_one_non_fixed(struct isl_set_map_pair *domain,
2887 int *order, int n, int depth)
2889 int i;
2890 int non_fixed = -1;
2892 for (i = 0; i < n; ++i) {
2893 int f;
2895 f = dim_is_fixed(domain[order[i]].set, depth);
2896 if (f < 0)
2897 return -1;
2898 if (f)
2899 continue;
2900 if (non_fixed >= 0)
2901 return 0;
2902 non_fixed = i;
2905 return 1;
2908 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2909 * of indices into the "domain" array,
2910 * eliminate the inner dimensions from the "set" field of the elements
2911 * indexed by the first "n" elements of "order", provided the current
2912 * dimension does not have a fixed value.
2914 * Return the index of the first element in "order" with a corresponding
2915 * "set" field that does not have an (obviously) fixed value.
2917 static int eliminate_non_fixed(struct isl_set_map_pair *domain,
2918 int *order, int n, int depth, __isl_keep isl_ast_build *build)
2920 int i;
2921 int base = -1;
2923 for (i = n - 1; i >= 0; --i) {
2924 int f;
2925 f = dim_is_fixed(domain[order[i]].set, depth);
2926 if (f < 0)
2927 return -1;
2928 if (f)
2929 continue;
2930 domain[order[i]].set = isl_ast_build_eliminate_inner(build,
2931 domain[order[i]].set);
2932 base = i;
2935 return base;
2938 /* Given an array "domain" of isl_set_map_pairs and an array "order"
2939 * of indices into the "domain" array,
2940 * find the element of "domain" (amongst those indexed by the first "n"
2941 * elements of "order") with the "set" field that has the smallest
2942 * value for the current iterator.
2944 * Note that the domain with the smallest value may depend on the parameters
2945 * and/or outer loop dimension. Since the result of this function is only
2946 * used as heuristic, we only make a reasonable attempt at finding the best
2947 * domain, one that should work in case a single domain provides the smallest
2948 * value for the current dimension over all values of the parameters
2949 * and outer dimensions.
2951 * In particular, we compute the smallest value of the first domain
2952 * and replace it by that of any later domain if that later domain
2953 * has a smallest value that is smaller for at least some value
2954 * of the parameters and outer dimensions.
2956 static int first_offset(struct isl_set_map_pair *domain, int *order, int n,
2957 __isl_keep isl_ast_build *build)
2959 int i;
2960 isl_map *min_first;
2961 int first = 0;
2963 min_first = isl_ast_build_map_to_iterator(build,
2964 isl_set_copy(domain[order[0]].set));
2965 min_first = isl_map_lexmin(min_first);
2967 for (i = 1; i < n; ++i) {
2968 isl_map *min, *test;
2969 int empty;
2971 min = isl_ast_build_map_to_iterator(build,
2972 isl_set_copy(domain[order[i]].set));
2973 min = isl_map_lexmin(min);
2974 test = isl_map_copy(min);
2975 test = isl_map_apply_domain(isl_map_copy(min_first), test);
2976 test = isl_map_order_lt(test, isl_dim_in, 0, isl_dim_out, 0);
2977 empty = isl_map_is_empty(test);
2978 isl_map_free(test);
2979 if (empty >= 0 && !empty) {
2980 isl_map_free(min_first);
2981 first = i;
2982 min_first = min;
2983 } else
2984 isl_map_free(min);
2986 if (empty < 0)
2987 break;
2990 isl_map_free(min_first);
2992 return i < n ? -1 : first;
2995 /* Construct a shifted inverse schedule based on the original inverse schedule,
2996 * the stride and the offset.
2998 * The original inverse schedule is specified as the "map" fields
2999 * of the elements of "domain" indexed by the first "n" elements of "order".
3001 * "stride" and "offset" are such that the difference
3002 * between the values of the current dimension of domain "i"
3003 * and the values of the current dimension for some reference domain are
3004 * equal to
3006 * stride * integer + offset[i]
3008 * Moreover, 0 <= offset[i] < stride.
3010 * For each domain, we create a map
3012 * { [..., j, ...] -> [..., j - offset[i], offset[i], ....] }
3014 * where j refers to the current dimension and the other dimensions are
3015 * unchanged, and apply this map to the original schedule domain.
3017 * For example, for the original schedule
3019 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3021 * and assuming the offset is 0 for the A domain and 1 for the B domain,
3022 * we apply the mapping
3024 * { [j] -> [j, 0] }
3026 * to the schedule of the "A" domain and the mapping
3028 * { [j - 1] -> [j, 1] }
3030 * to the schedule of the "B" domain.
3033 * Note that after the transformation, the differences between pairs
3034 * of values of the current dimension over all domains are multiples
3035 * of stride and that we have therefore exposed the stride.
3038 * To see that the mapping preserves the lexicographic order,
3039 * first note that each of the individual maps above preserves the order.
3040 * If the value of the current iterator is j1 in one domain and j2 in another,
3041 * then if j1 = j2, we know that the same map is applied to both domains
3042 * and the order is preserved.
3043 * Otherwise, let us assume, without loss of generality, that j1 < j2.
3044 * If c1 >= c2 (with c1 and c2 the corresponding offsets), then
3046 * j1 - c1 < j2 - c2
3048 * and the order is preserved.
3049 * If c1 < c2, then we know
3051 * 0 <= c2 - c1 < s
3053 * We also have
3055 * j2 - j1 = n * s + r
3057 * with n >= 0 and 0 <= r < s.
3058 * In other words, r = c2 - c1.
3059 * If n > 0, then
3061 * j1 - c1 < j2 - c2
3063 * If n = 0, then
3065 * j1 - c1 = j2 - c2
3067 * and so
3069 * (j1 - c1, c1) << (j2 - c2, c2)
3071 * with "<<" the lexicographic order, proving that the order is preserved
3072 * in all cases.
3074 static __isl_give isl_union_map *contruct_shifted_executed(
3075 struct isl_set_map_pair *domain, int *order, int n,
3076 __isl_keep isl_val *stride, __isl_keep isl_multi_val *offset,
3077 __isl_take isl_ast_build *build)
3079 int i;
3080 isl_union_map *executed;
3081 isl_space *space;
3082 isl_map *map;
3083 int depth;
3084 isl_constraint *c;
3086 depth = isl_ast_build_get_depth(build);
3087 space = isl_ast_build_get_space(build, 1);
3088 executed = isl_union_map_empty(isl_space_copy(space));
3089 space = isl_space_map_from_set(space);
3090 map = isl_map_identity(isl_space_copy(space));
3091 map = isl_map_eliminate(map, isl_dim_out, depth, 1);
3092 map = isl_map_insert_dims(map, isl_dim_out, depth + 1, 1);
3093 space = isl_space_insert_dims(space, isl_dim_out, depth + 1, 1);
3095 c = isl_equality_alloc(isl_local_space_from_space(space));
3096 c = isl_constraint_set_coefficient_si(c, isl_dim_in, depth, 1);
3097 c = isl_constraint_set_coefficient_si(c, isl_dim_out, depth, -1);
3099 for (i = 0; i < n; ++i) {
3100 isl_map *map_i;
3101 isl_val *v;
3103 v = isl_multi_val_get_val(offset, i);
3104 if (!v)
3105 break;
3106 map_i = isl_map_copy(map);
3107 map_i = isl_map_fix_val(map_i, isl_dim_out, depth + 1,
3108 isl_val_copy(v));
3109 v = isl_val_neg(v);
3110 c = isl_constraint_set_constant_val(c, v);
3111 map_i = isl_map_add_constraint(map_i, isl_constraint_copy(c));
3113 map_i = isl_map_apply_domain(isl_map_copy(domain[order[i]].map),
3114 map_i);
3115 executed = isl_union_map_add_map(executed, map_i);
3118 isl_constraint_free(c);
3119 isl_map_free(map);
3121 if (i < n)
3122 executed = isl_union_map_free(executed);
3124 return executed;
3127 /* Generate code for a single component, after exposing the stride,
3128 * given that the schedule domain is "shifted strided".
3130 * The component inverse schedule is specified as the "map" fields
3131 * of the elements of "domain" indexed by the first "n" elements of "order".
3133 * The schedule domain being "shifted strided" means that the differences
3134 * between the values of the current dimension of domain "i"
3135 * and the values of the current dimension for some reference domain are
3136 * equal to
3138 * stride * integer + offset[i]
3140 * We first look for the domain with the "smallest" value for the current
3141 * dimension and adjust the offsets such that the offset of the "smallest"
3142 * domain is equal to zero. The other offsets are reduced modulo stride.
3144 * Based on this information, we construct a new inverse schedule in
3145 * contruct_shifted_executed that exposes the stride.
3146 * Since this involves the introduction of a new schedule dimension,
3147 * the build needs to be changed accodingly.
3148 * After computing the AST, the newly introduced dimension needs
3149 * to be removed again from the list of grafts. We do this by plugging
3150 * in a mapping that represents the new schedule domain in terms of the
3151 * old schedule domain.
3153 static __isl_give isl_ast_graft_list *generate_shift_component(
3154 struct isl_set_map_pair *domain, int *order, int n,
3155 __isl_keep isl_val *stride, __isl_keep isl_multi_val *offset,
3156 __isl_take isl_ast_build *build)
3158 isl_ast_graft_list *list;
3159 int first;
3160 int depth;
3161 isl_ctx *ctx;
3162 isl_val *val;
3163 isl_multi_val *mv;
3164 isl_space *space;
3165 isl_multi_aff *ma, *zero;
3166 isl_union_map *executed;
3168 ctx = isl_ast_build_get_ctx(build);
3169 depth = isl_ast_build_get_depth(build);
3171 first = first_offset(domain, order, n, build);
3172 if (first < 0)
3173 goto error;
3175 mv = isl_multi_val_copy(offset);
3176 val = isl_multi_val_get_val(offset, first);
3177 val = isl_val_neg(val);
3178 mv = isl_multi_val_add_val(mv, val);
3179 mv = isl_multi_val_mod_val(mv, isl_val_copy(stride));
3181 executed = contruct_shifted_executed(domain, order, n, stride, mv,
3182 build);
3183 space = isl_ast_build_get_space(build, 1);
3184 space = isl_space_map_from_set(space);
3185 ma = isl_multi_aff_identity(isl_space_copy(space));
3186 space = isl_space_from_domain(isl_space_domain(space));
3187 space = isl_space_add_dims(space, isl_dim_out, 1);
3188 zero = isl_multi_aff_zero(space);
3189 ma = isl_multi_aff_range_splice(ma, depth + 1, zero);
3190 build = isl_ast_build_insert_dim(build, depth + 1);
3191 list = generate_shifted_component(executed, build);
3193 list = isl_ast_graft_list_preimage_multi_aff(list, ma);
3195 isl_multi_val_free(mv);
3197 return list;
3198 error:
3199 isl_ast_build_free(build);
3200 return NULL;
3203 /* Generate code for a single component.
3205 * The component inverse schedule is specified as the "map" fields
3206 * of the elements of "domain" indexed by the first "n" elements of "order".
3208 * This function may modify the "set" fields of "domain".
3210 * Before proceeding with the actual code generation for the component,
3211 * we first check if there are any "shifted" strides, meaning that
3212 * the schedule domains of the individual domains are all strided,
3213 * but that they have different offsets, resulting in the union
3214 * of schedule domains not being strided anymore.
3216 * The simplest example is the schedule
3218 * { A[i] -> [2i]: 0 <= i < 10; B[i] -> [2i+1] : 0 <= i < 10 }
3220 * Both schedule domains are strided, but their union is not.
3221 * This function detects such cases and then rewrites the schedule to
3223 * { A[i] -> [2i, 0]: 0 <= i < 10; B[i] -> [2i, 1] : 0 <= i < 10 }
3225 * In the new schedule, the schedule domains have the same offset (modulo
3226 * the stride), ensuring that the union of schedule domains is also strided.
3229 * If there is only a single domain in the component, then there is
3230 * nothing to do. Similarly, if the current schedule dimension has
3231 * a fixed value for almost all domains then there is nothing to be done.
3232 * In particular, we need at least two domains where the current schedule
3233 * dimension does not have a fixed value.
3234 * Finally, if any of the options refer to the current schedule dimension,
3235 * then we bail out as well. It would be possible to reformulate the options
3236 * in terms of the new schedule domain, but that would introduce constraints
3237 * that separate the domains in the options and that is something we would
3238 * like to avoid.
3241 * To see if there is any shifted stride, we look at the differences
3242 * between the values of the current dimension in pairs of domains
3243 * for equal values of outer dimensions. These differences should be
3244 * of the form
3246 * m x + r
3248 * with "m" the stride and "r" a constant. Note that we cannot perform
3249 * this analysis on individual domains as the lower bound in each domain
3250 * may depend on parameters or outer dimensions and so the current dimension
3251 * itself may not have a fixed remainder on division by the stride.
3253 * In particular, we compare the first domain that does not have an
3254 * obviously fixed value for the current dimension to itself and all
3255 * other domains and collect the offsets and the gcd of the strides.
3256 * If the gcd becomes one, then we failed to find shifted strides.
3257 * If the gcd is zero, then the differences were all fixed, meaning
3258 * that some domains had non-obviously fixed values for the current dimension.
3259 * If all the offsets are the same (for those domains that do not have
3260 * an obviously fixed value for the current dimension), then we do not
3261 * apply the transformation.
3262 * If none of the domains were skipped, then there is nothing to do.
3263 * If some of them were skipped, then if we apply separation, the schedule
3264 * domain should get split in pieces with a (non-shifted) stride.
3266 * Otherwise, we apply a shift to expose the stride in
3267 * generate_shift_component.
3269 static __isl_give isl_ast_graft_list *generate_component(
3270 struct isl_set_map_pair *domain, int *order, int n,
3271 __isl_take isl_ast_build *build)
3273 int i, d;
3274 int depth;
3275 isl_ctx *ctx;
3276 isl_map *map;
3277 isl_set *deltas;
3278 isl_val *gcd = NULL;
3279 isl_multi_val *mv;
3280 int fixed, skip;
3281 int base;
3282 isl_ast_graft_list *list;
3283 int res = 0;
3285 depth = isl_ast_build_get_depth(build);
3287 skip = n == 1;
3288 if (skip >= 0 && !skip)
3289 skip = at_most_one_non_fixed(domain, order, n, depth);
3290 if (skip >= 0 && !skip)
3291 skip = isl_ast_build_options_involve_depth(build);
3292 if (skip < 0)
3293 goto error;
3294 if (skip)
3295 return generate_shifted_component_from_list(domain,
3296 order, n, build);
3298 base = eliminate_non_fixed(domain, order, n, depth, build);
3299 if (base < 0)
3300 goto error;
3302 ctx = isl_ast_build_get_ctx(build);
3304 mv = isl_multi_val_zero(isl_space_set_alloc(ctx, 0, n));
3306 fixed = 1;
3307 for (i = 0; i < n; ++i) {
3308 isl_val *r, *m;
3310 map = isl_map_from_domain_and_range(
3311 isl_set_copy(domain[order[base]].set),
3312 isl_set_copy(domain[order[i]].set));
3313 for (d = 0; d < depth; ++d)
3314 map = isl_map_equate(map, isl_dim_in, d,
3315 isl_dim_out, d);
3316 deltas = isl_map_deltas(map);
3317 res = isl_set_dim_residue_class_val(deltas, depth, &m, &r);
3318 isl_set_free(deltas);
3319 if (res < 0)
3320 break;
3322 if (i == 0)
3323 gcd = m;
3324 else
3325 gcd = isl_val_gcd(gcd, m);
3326 if (isl_val_is_one(gcd)) {
3327 isl_val_free(r);
3328 break;
3330 mv = isl_multi_val_set_val(mv, i, r);
3332 res = dim_is_fixed(domain[order[i]].set, depth);
3333 if (res < 0)
3334 break;
3335 if (res)
3336 continue;
3338 if (fixed && i > base) {
3339 isl_val *a, *b;
3340 a = isl_multi_val_get_val(mv, i);
3341 b = isl_multi_val_get_val(mv, base);
3342 if (isl_val_ne(a, b))
3343 fixed = 0;
3344 isl_val_free(a);
3345 isl_val_free(b);
3349 if (res < 0 || !gcd) {
3350 isl_ast_build_free(build);
3351 list = NULL;
3352 } else if (i < n || fixed || isl_val_is_zero(gcd)) {
3353 list = generate_shifted_component_from_list(domain,
3354 order, n, build);
3355 } else {
3356 list = generate_shift_component(domain, order, n, gcd, mv,
3357 build);
3360 isl_val_free(gcd);
3361 isl_multi_val_free(mv);
3363 return list;
3364 error:
3365 isl_ast_build_free(build);
3366 return NULL;
3369 /* Store both "map" itself and its domain in the
3370 * structure pointed to by *next and advance to the next array element.
3372 static int extract_domain(__isl_take isl_map *map, void *user)
3374 struct isl_set_map_pair **next = user;
3376 (*next)->map = isl_map_copy(map);
3377 (*next)->set = isl_map_domain(map);
3378 (*next)++;
3380 return 0;
3383 /* Internal data for any_scheduled_after.
3385 * "depth" is the number of loops that have already been generated
3386 * "group_coscheduled" is a local copy of options->ast_build_group_coscheduled
3387 * "domain" is an array of set-map pairs corresponding to the different
3388 * iteration domains. The set is the schedule domain, i.e., the domain
3389 * of the inverse schedule, while the map is the inverse schedule itself.
3391 struct isl_any_scheduled_after_data {
3392 int depth;
3393 int group_coscheduled;
3394 struct isl_set_map_pair *domain;
3397 /* Is any element of domain "i" scheduled after any element of domain "j"
3398 * (for a common iteration of the first data->depth loops)?
3400 * data->domain[i].set contains the domain of the inverse schedule
3401 * for domain "i", i.e., elements in the schedule domain.
3403 * If data->group_coscheduled is set, then we also return 1 if there
3404 * is any pair of elements in the two domains that are scheduled together.
3406 static int any_scheduled_after(int i, int j, void *user)
3408 struct isl_any_scheduled_after_data *data = user;
3409 int dim = isl_set_dim(data->domain[i].set, isl_dim_set);
3410 int pos;
3412 for (pos = data->depth; pos < dim; ++pos) {
3413 int follows;
3415 follows = isl_set_follows_at(data->domain[i].set,
3416 data->domain[j].set, pos);
3418 if (follows < -1)
3419 return -1;
3420 if (follows > 0)
3421 return 1;
3422 if (follows < 0)
3423 return 0;
3426 return data->group_coscheduled;
3429 /* Look for independent components at the current depth and generate code
3430 * for each component separately. The resulting lists of grafts are
3431 * merged in an attempt to combine grafts with identical guards.
3433 * Code for two domains can be generated separately if all the elements
3434 * of one domain are scheduled before (or together with) all the elements
3435 * of the other domain. We therefore consider the graph with as nodes
3436 * the domains and an edge between two nodes if any element of the first
3437 * node is scheduled after any element of the second node.
3438 * If the ast_build_group_coscheduled is set, then we also add an edge if
3439 * there is any pair of elements in the two domains that are scheduled
3440 * together.
3441 * Code is then generated (by generate_component)
3442 * for each of the strongly connected components in this graph
3443 * in their topological order.
3445 * Since the test is performed on the domain of the inverse schedules of
3446 * the different domains, we precompute these domains and store
3447 * them in data.domain.
3449 static __isl_give isl_ast_graft_list *generate_components(
3450 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
3452 int i;
3453 isl_ctx *ctx = isl_ast_build_get_ctx(build);
3454 int n = isl_union_map_n_map(executed);
3455 struct isl_any_scheduled_after_data data;
3456 struct isl_set_map_pair *next;
3457 struct isl_tarjan_graph *g = NULL;
3458 isl_ast_graft_list *list = NULL;
3459 int n_domain = 0;
3461 data.domain = isl_calloc_array(ctx, struct isl_set_map_pair, n);
3462 if (!data.domain)
3463 goto error;
3464 n_domain = n;
3466 next = data.domain;
3467 if (isl_union_map_foreach_map(executed, &extract_domain, &next) < 0)
3468 goto error;
3470 if (!build)
3471 goto error;
3472 data.depth = isl_ast_build_get_depth(build);
3473 data.group_coscheduled = isl_options_get_ast_build_group_coscheduled(ctx);
3474 g = isl_tarjan_graph_init(ctx, n, &any_scheduled_after, &data);
3475 if (!g)
3476 goto error;
3478 list = isl_ast_graft_list_alloc(ctx, 0);
3480 i = 0;
3481 while (list && n) {
3482 isl_ast_graft_list *list_c;
3483 int first = i;
3485 if (g->order[i] == -1)
3486 isl_die(ctx, isl_error_internal, "cannot happen",
3487 goto error);
3488 ++i; --n;
3489 while (g->order[i] != -1) {
3490 ++i; --n;
3493 list_c = generate_component(data.domain,
3494 g->order + first, i - first,
3495 isl_ast_build_copy(build));
3496 list = isl_ast_graft_list_merge(list, list_c, build);
3498 ++i;
3501 if (0)
3502 error: list = isl_ast_graft_list_free(list);
3503 isl_tarjan_graph_free(g);
3504 for (i = 0; i < n_domain; ++i) {
3505 isl_map_free(data.domain[i].map);
3506 isl_set_free(data.domain[i].set);
3508 free(data.domain);
3509 isl_union_map_free(executed);
3510 isl_ast_build_free(build);
3512 return list;
3515 /* Generate code for the next level (and all inner levels).
3517 * If "executed" is empty, i.e., no code needs to be generated,
3518 * then we return an empty list.
3520 * If we have already generated code for all loop levels, then we pass
3521 * control to generate_inner_level.
3523 * If "executed" lives in a single space, i.e., if code needs to be
3524 * generated for a single domain, then there can only be a single
3525 * component and we go directly to generate_shifted_component.
3526 * Otherwise, we call generate_components to detect the components
3527 * and to call generate_component on each of them separately.
3529 static __isl_give isl_ast_graft_list *generate_next_level(
3530 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build)
3532 int depth;
3534 if (!build || !executed)
3535 goto error;
3537 if (isl_union_map_is_empty(executed)) {
3538 isl_ctx *ctx = isl_ast_build_get_ctx(build);
3539 isl_union_map_free(executed);
3540 isl_ast_build_free(build);
3541 return isl_ast_graft_list_alloc(ctx, 0);
3544 depth = isl_ast_build_get_depth(build);
3545 if (depth >= isl_ast_build_dim(build, isl_dim_set))
3546 return generate_inner_level(executed, build);
3548 if (isl_union_map_n_map(executed) == 1)
3549 return generate_shifted_component(executed, build);
3551 return generate_components(executed, build);
3552 error:
3553 isl_union_map_free(executed);
3554 isl_ast_build_free(build);
3555 return NULL;
3558 /* Internal data structure used by isl_ast_build_ast_from_schedule.
3559 * internal, executed and build are the inputs to generate_code.
3560 * list collects the output.
3562 struct isl_generate_code_data {
3563 int internal;
3564 isl_union_map *executed;
3565 isl_ast_build *build;
3567 isl_ast_graft_list *list;
3570 /* Given an inverse schedule in terms of the external build schedule, i.e.,
3572 * [E -> S] -> D
3574 * with E the external build schedule and S the additional schedule "space",
3575 * reformulate the inverse schedule in terms of the internal schedule domain,
3576 * i.e., return
3578 * [I -> S] -> D
3580 * We first obtain a mapping
3582 * I -> E
3584 * take the inverse and the product with S -> S, resulting in
3586 * [I -> S] -> [E -> S]
3588 * Applying the map to the input produces the desired result.
3590 static __isl_give isl_union_map *internal_executed(
3591 __isl_take isl_union_map *executed, __isl_keep isl_space *space,
3592 __isl_keep isl_ast_build *build)
3594 isl_map *id, *proj;
3596 proj = isl_ast_build_get_schedule_map(build);
3597 proj = isl_map_reverse(proj);
3598 space = isl_space_map_from_set(isl_space_copy(space));
3599 id = isl_map_identity(space);
3600 proj = isl_map_product(proj, id);
3601 executed = isl_union_map_apply_domain(executed,
3602 isl_union_map_from_map(proj));
3603 return executed;
3606 /* Generate an AST that visits the elements in the range of data->executed
3607 * in the relative order specified by the corresponding domain element(s)
3608 * for those domain elements that belong to "set".
3609 * Add the result to data->list.
3611 * The caller ensures that "set" is a universe domain.
3612 * "space" is the space of the additional part of the schedule.
3613 * It is equal to the space of "set" if build->domain is parametric.
3614 * Otherwise, it is equal to the range of the wrapped space of "set".
3616 * If the build space is not parametric and if isl_ast_build_ast_from_schedule
3617 * was called from an outside user (data->internal not set), then
3618 * the (inverse) schedule refers to the external build domain and needs to
3619 * be transformed to refer to the internal build domain.
3621 * If the build space is parametric, then we add some of the parameter
3622 * constraints to the executed relation. Adding these constraints
3623 * allows for an earlier detection of conflicts in some cases.
3624 * However, we do not want to divide the executed relation into
3625 * more disjuncts than necessary. We therefore approximate
3626 * the constraints on the parameters by a single disjunct set.
3628 * The build is extended to include the additional part of the schedule.
3629 * If the original build space was not parametric, then the options
3630 * in data->build refer only to the additional part of the schedule
3631 * and they need to be adjusted to refer to the complete AST build
3632 * domain.
3634 * After having adjusted inverse schedule and build, we start generating
3635 * code with the outer loop of the current code generation
3636 * in generate_next_level.
3638 * If the original build space was not parametric, we undo the embedding
3639 * on the resulting isl_ast_node_list so that it can be used within
3640 * the outer AST build.
3642 static int generate_code_in_space(struct isl_generate_code_data *data,
3643 __isl_take isl_set *set, __isl_take isl_space *space)
3645 isl_union_map *executed;
3646 isl_ast_build *build;
3647 isl_ast_graft_list *list;
3648 int embed;
3650 executed = isl_union_map_copy(data->executed);
3651 executed = isl_union_map_intersect_domain(executed,
3652 isl_union_set_from_set(set));
3654 embed = !isl_set_is_params(data->build->domain);
3655 if (embed && !data->internal)
3656 executed = internal_executed(executed, space, data->build);
3657 if (!embed) {
3658 isl_set *domain;
3659 domain = isl_ast_build_get_domain(data->build);
3660 domain = isl_set_from_basic_set(isl_set_simple_hull(domain));
3661 executed = isl_union_map_intersect_params(executed, domain);
3664 build = isl_ast_build_copy(data->build);
3665 build = isl_ast_build_product(build, space);
3667 list = generate_next_level(executed, build);
3669 list = isl_ast_graft_list_unembed(list, embed);
3671 data->list = isl_ast_graft_list_concat(data->list, list);
3673 return 0;
3676 /* Generate an AST that visits the elements in the range of data->executed
3677 * in the relative order specified by the corresponding domain element(s)
3678 * for those domain elements that belong to "set".
3679 * Add the result to data->list.
3681 * The caller ensures that "set" is a universe domain.
3683 * If the build space S is not parametric, then the space of "set"
3684 * need to be a wrapped relation with S as domain. That is, it needs
3685 * to be of the form
3687 * [S -> T]
3689 * Check this property and pass control to generate_code_in_space
3690 * passing along T.
3691 * If the build space is not parametric, then T is the space of "set".
3693 static int generate_code_set(__isl_take isl_set *set, void *user)
3695 struct isl_generate_code_data *data = user;
3696 isl_space *space, *build_space;
3697 int is_domain;
3699 space = isl_set_get_space(set);
3701 if (isl_set_is_params(data->build->domain))
3702 return generate_code_in_space(data, set, space);
3704 build_space = isl_ast_build_get_space(data->build, data->internal);
3705 space = isl_space_unwrap(space);
3706 is_domain = isl_space_is_domain(build_space, space);
3707 isl_space_free(build_space);
3708 space = isl_space_range(space);
3710 if (is_domain < 0)
3711 goto error;
3712 if (!is_domain)
3713 isl_die(isl_set_get_ctx(set), isl_error_invalid,
3714 "invalid nested schedule space", goto error);
3716 return generate_code_in_space(data, set, space);
3717 error:
3718 isl_set_free(set);
3719 isl_space_free(space);
3720 return -1;
3723 /* Generate an AST that visits the elements in the range of "executed"
3724 * in the relative order specified by the corresponding domain element(s).
3726 * "build" is an isl_ast_build that has either been constructed by
3727 * isl_ast_build_from_context or passed to a callback set by
3728 * isl_ast_build_set_create_leaf.
3729 * In the first case, the space of the isl_ast_build is typically
3730 * a parametric space, although this is currently not enforced.
3731 * In the second case, the space is never a parametric space.
3732 * If the space S is not parametric, then the domain space(s) of "executed"
3733 * need to be wrapped relations with S as domain.
3735 * If the domain of "executed" consists of several spaces, then an AST
3736 * is generated for each of them (in arbitrary order) and the results
3737 * are concatenated.
3739 * If "internal" is set, then the domain "S" above refers to the internal
3740 * schedule domain representation. Otherwise, it refers to the external
3741 * representation, as returned by isl_ast_build_get_schedule_space.
3743 * We essentially run over all the spaces in the domain of "executed"
3744 * and call generate_code_set on each of them.
3746 static __isl_give isl_ast_graft_list *generate_code(
3747 __isl_take isl_union_map *executed, __isl_take isl_ast_build *build,
3748 int internal)
3750 isl_ctx *ctx;
3751 struct isl_generate_code_data data = { 0 };
3752 isl_space *space;
3753 isl_union_set *schedule_domain;
3754 isl_union_map *universe;
3756 if (!build)
3757 goto error;
3758 space = isl_ast_build_get_space(build, 1);
3759 space = isl_space_align_params(space,
3760 isl_union_map_get_space(executed));
3761 space = isl_space_align_params(space,
3762 isl_union_map_get_space(build->options));
3763 build = isl_ast_build_align_params(build, isl_space_copy(space));
3764 executed = isl_union_map_align_params(executed, space);
3765 if (!executed || !build)
3766 goto error;
3768 ctx = isl_ast_build_get_ctx(build);
3770 data.internal = internal;
3771 data.executed = executed;
3772 data.build = build;
3773 data.list = isl_ast_graft_list_alloc(ctx, 0);
3775 universe = isl_union_map_universe(isl_union_map_copy(executed));
3776 schedule_domain = isl_union_map_domain(universe);
3777 if (isl_union_set_foreach_set(schedule_domain, &generate_code_set,
3778 &data) < 0)
3779 data.list = isl_ast_graft_list_free(data.list);
3781 isl_union_set_free(schedule_domain);
3782 isl_union_map_free(executed);
3784 isl_ast_build_free(build);
3785 return data.list;
3786 error:
3787 isl_union_map_free(executed);
3788 isl_ast_build_free(build);
3789 return NULL;
3792 /* Generate an AST that visits the elements in the domain of "schedule"
3793 * in the relative order specified by the corresponding image element(s).
3795 * "build" is an isl_ast_build that has either been constructed by
3796 * isl_ast_build_from_context or passed to a callback set by
3797 * isl_ast_build_set_create_leaf.
3798 * In the first case, the space of the isl_ast_build is typically
3799 * a parametric space, although this is currently not enforced.
3800 * In the second case, the space is never a parametric space.
3801 * If the space S is not parametric, then the range space(s) of "schedule"
3802 * need to be wrapped relations with S as domain.
3804 * If the range of "schedule" consists of several spaces, then an AST
3805 * is generated for each of them (in arbitrary order) and the results
3806 * are concatenated.
3808 * We first initialize the local copies of the relevant options.
3809 * We do this here rather than when the isl_ast_build is created
3810 * because the options may have changed between the construction
3811 * of the isl_ast_build and the call to isl_generate_code.
3813 * The main computation is performed on an inverse schedule (with
3814 * the schedule domain in the domain and the elements to be executed
3815 * in the range) called "executed".
3817 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
3818 __isl_keep isl_ast_build *build, __isl_take isl_union_map *schedule)
3820 isl_ast_graft_list *list;
3821 isl_ast_node *node;
3822 isl_union_map *executed;
3824 build = isl_ast_build_copy(build);
3825 build = isl_ast_build_set_single_valued(build, 0);
3826 schedule = isl_union_map_coalesce(schedule);
3827 executed = isl_union_map_reverse(schedule);
3828 list = generate_code(executed, isl_ast_build_copy(build), 0);
3829 node = isl_ast_node_from_graft_list(list, build);
3830 isl_ast_build_free(build);
3832 return node;