1 /*
2 * Copyright (C) 1995-2008 University of Karlsruhe. All right reserved.
3 *
4 * This file is part of libFirm.
5 *
6 * This file may be distributed and/or modified under the terms of the
7 * GNU General Public License version 2 as published by the Free Software
8 * Foundation and appearing in the file LICENSE.GPL included in the
9 * packaging of this file.
10 *
11 * Licensees holding valid libFirm Professional Edition licenses may use
12 * this file in accordance with the libFirm Commercial License.
13 * Agreement provided with the Software.
14 *
15 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
16 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR
17 * PURPOSE.
18 */
19
20 /**
21 * @file
22 * @brief ILP based copy minimization.
23 * @author Daniel Grund
24 * @date 28.02.2006
25 *
26 * ILP formalization using G=(V, E, Q):
27 * - 2 class of variables: coloring vars x_ic and equal color vars y_ij
28 * - Path constraints
29 * - Clique-star constraints
30 *
31 *
32 * \min \sum_{ (i,j) \in Q } w_ij y_ij
33 *
34 * \sum_c x_nc = 1 n \in N, c \in C
35 *
36 * x_nc = 0 n \in N, c \not\in C(n)
37 *
38 * \sum x_nc <= 1 x_nc \in Clique \in AllCliques, c \in C
39 *
40 * \sum_{e \in p} y_e >= 1 p \in P path constraints
41 *
42 * \sum_{e \in cs} y_e >= |cs| - 1 cs \in CP clique-star constraints
43 *
44 * x_nc, y_ij \in N, w_ij \in R^+
45 */
46 #include "config.h"
47
48 #include "bitset.h"
49 #include "raw_bitset.h"
50 #include "pdeq.h"
51
52 #include "util.h"
53 #include "irgwalk.h"
54 #include "becopyilp_t.h"
55 #include "beifg.h"
56 #include "besched.h"
57 #include "bemodule.h"
58
59 DEBUG_ONLY(static firm_dbg_module_t *dbg;)
60
61 typedef struct local_env_t {
62 int first_x_var;
63 int last_x_var;
64 const unsigned *allocatable_colors;
65 } local_env_t;
66
check_alignment_constraints(ir_node * node)67 static unsigned check_alignment_constraints(ir_node *node)
68 {
69 const arch_register_req_t *req = arch_get_irn_register_req(node);
70 // For larger than 1 variables, support only aligned constraints
71 assert(((!(req->type & arch_register_req_type_aligned)
72 && req->width == 1)
73 || (req->type & arch_register_req_type_aligned))
74 && "Unaligned large (width > 1) variables not supported");
75 return (req->type & arch_register_req_type_aligned) && req->width > 1;
76 }
77
make_color_var_name(char * buf,size_t buf_size,const ir_node * node,unsigned color)78 static void make_color_var_name(char *buf, size_t buf_size,
79 const ir_node *node, unsigned color)
80 {
81 unsigned node_idx = get_irn_idx(node);
82 snprintf(buf, buf_size, "x_%u_%u", node_idx, color);
83 }
84
build_coloring_cstr(ilp_env_t * ienv)85 static void build_coloring_cstr(ilp_env_t *ienv)
86 {
87 local_env_t *lenv = (local_env_t*)ienv->env;
88 be_ifg_t *ifg = ienv->co->cenv->ifg;
89 unsigned n_regs = arch_register_class_n_regs(ienv->co->cls);
90 const unsigned *allocatable_colors = lenv->allocatable_colors;
91 nodes_iter_t iter;
92 unsigned *colors;
93 ir_node *irn;
94 char buf[32];
95
96 rbitset_alloca(colors, n_regs);
97
98 be_ifg_foreach_node(ifg, &iter, irn) {
99 const arch_register_req_t *req;
100 unsigned col;
101 int cst_idx;
102 unsigned curr_node_color;
103 unsigned has_alignment_cstr;
104
105 if (sr_is_removed(ienv->sr, irn))
106 continue;
107
108 has_alignment_cstr = check_alignment_constraints(irn);
109
110 req = arch_get_irn_register_req(irn);
111
112 /* get assignable colors */
113 if (arch_register_req_is(req, limited)) {
114 rbitset_copy(colors, req->limited, n_regs);
115 } else {
116 rbitset_copy(colors, allocatable_colors, n_regs);
117 }
118
119 /* add the coloring constraint */
120 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 1.0);
121
122 curr_node_color = get_irn_col(irn);
123 for (col = 0; col < n_regs; ++col) {
124 int var_idx;
125 double val;
126 if (!rbitset_is_set(colors, col)
127 || (has_alignment_cstr && ((col % req->width) != 0)))
128 continue;
129
130 make_color_var_name(buf, sizeof(buf), irn, col);
131 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
132 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
133
134 val = (col == curr_node_color) ? 1.0 : 0.0;
135 lpp_set_start_value(ienv->lp, var_idx, val);
136
137 lenv->last_x_var = var_idx;
138 if (lenv->first_x_var == -1)
139 lenv->first_x_var = var_idx;
140 }
141
142 /* add register constraint constraints */
143 for (col = 0; col < n_regs; ++col) {
144 int cst_idx;
145 int var_idx;
146 if (rbitset_is_set(colors, col)
147 // for aligned variable, we set the unaligned part to 0
148 && (!has_alignment_cstr || ((col % req->width) == 0)))
149 continue;
150
151 make_color_var_name(buf, sizeof(buf), irn, col);
152 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 0.0);
153 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
154 lpp_set_start_value(ienv->lp, var_idx, 0.0);
155 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
156
157 lenv->last_x_var = var_idx;
158 }
159 }
160 }
161
build_interference_cstr(ilp_env_t * ienv)162 static void build_interference_cstr(ilp_env_t *ienv)
163 {
164 lpp_t *lpp = ienv->lp;
165 local_env_t *lenv = (local_env_t*)ienv->env;
166 be_ifg_t *ifg = ienv->co->cenv->ifg;
167 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
168 ir_node **clique = ALLOCAN(ir_node*, n_colors);
169 const unsigned *allocatable_colors = lenv->allocatable_colors;
170 cliques_iter_t iter;
171 int size;
172 unsigned col;
173 int i;
174
175 /* for each maximal clique */
176 be_ifg_foreach_clique(ifg, &iter, clique, &size) {
177 unsigned realsize = 0;
178
179 for (i=0; i<size; ++i) {
180 if (!sr_is_removed(ienv->sr, clique[i]))
181 ++realsize;
182 }
183
184 if (realsize < 2)
185 continue;
186
187 /* for all colors */
188 for (col=0; col<n_colors; ++col) {
189 int cst_idx;
190 if (!rbitset_is_set(allocatable_colors, col))
191 continue;
192
193 cst_idx = lpp_add_cst(lpp, NULL, lpp_less_equal, 1.0);
194
195 /* for each member of this clique */
196 for (i=0; i<size; ++i) {
197 ir_node *irn = clique[i];
198 char buf[32];
199 int var_idx;
200 unsigned aligment_offset = 0;
201
202 if (sr_is_removed(ienv->sr, irn))
203 continue;
204
205 // Use the first part of the large registers for all
206 // interference, since it is the only colorable one.
207 if (check_alignment_constraints(irn)) {
208 const arch_register_req_t *req
209 = arch_get_irn_register_req(irn);
210 aligment_offset = col % req->width;
211 }
212
213 make_color_var_name(buf, sizeof(buf), irn,
214 col - aligment_offset);
215 var_idx = lpp_get_var_idx(lpp, buf);
216 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
217 }
218 }
219 }
220 }
221
make_affinity_var_name(char * buf,size_t buf_size,const ir_node * node1,const ir_node * node2)222 static void make_affinity_var_name(char *buf, size_t buf_size,
223 const ir_node *node1, const ir_node *node2)
224 {
225 unsigned n1 = get_irn_idx(node1);
226 unsigned n2 = get_irn_idx(node2);
227 if (n1 < n2) {
228 snprintf(buf, buf_size, "y_%u_%u", n1, n2);
229 } else {
230 snprintf(buf, buf_size, "y_%u_%u", n2, n1);
231 }
232 }
233
234
235 /**
236 * TODO: Remove the dependency of the opt-units data structure
237 * by walking over all affinity edges. Graph structure
238 * does not provide this walker, yet.
239 */
build_affinity_cstr(ilp_env_t * ienv)240 static void build_affinity_cstr(ilp_env_t *ienv)
241 {
242 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
243
244 /* for all optimization units */
245 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
246 ir_node *root = curr->nodes[0];
247 unsigned root_col = get_irn_col(root);
248 int i;
249
250 for (i = 1; i < curr->node_count; ++i) {
251 ir_node *arg = curr->nodes[i];
252 unsigned arg_col = get_irn_col(arg);
253 double val;
254 char buf[32];
255 unsigned col;
256 int y_idx;
257
258 /* add a new affinity variable */
259 make_affinity_var_name(buf, sizeof(buf), arg, root);
260 y_idx = lpp_add_var(ienv->lp, buf, lpp_binary, curr->costs[i]);
261 val = (root_col == arg_col) ? 0.0 : 1.0;
262 lpp_set_start_value(ienv->lp, y_idx, val);
263
264 /* add constraints relating the affinity var to the color vars */
265 for (col=0; col<n_colors; ++col) {
266 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less_equal, 0.0);
267 int root_idx;
268 int arg_idx;
269
270 make_color_var_name(buf, sizeof(buf), root, col);
271 root_idx = lpp_get_var_idx(ienv->lp, buf);
272 make_color_var_name(buf, sizeof(buf), arg, col);
273 arg_idx = lpp_get_var_idx(ienv->lp, buf);
274
275 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
276 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
277 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
278 }
279 }
280 }
281 }
282
283 /**
284 * Helping stuff for build_clique_star_cstr
285 */
286 typedef struct edge_t {
287 ir_node *n1;
288 ir_node *n2;
289 } edge_t;
290
compare_edge_t(const void * k1,const void * k2,size_t size)291 static int compare_edge_t(const void *k1, const void *k2, size_t size)
292 {
293 const edge_t *e1 = (const edge_t*)k1;
294 const edge_t *e2 = (const edge_t*)k2;
295 (void) size;
296
297 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
298 }
299
300 #define HASH_EDGE(e) (hash_irn((e)->n1) ^ hash_irn((e)->n2))
301
add_edge(set * edges,ir_node * n1,ir_node * n2,size_t * counter)302 static inline edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
303 {
304 edge_t new_edge;
305
306 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
307 new_edge.n1 = n1;
308 new_edge.n2 = n2;
309 } else {
310 new_edge.n1 = n2;
311 new_edge.n2 = n1;
312 }
313 (*counter)++;
314 return set_insert(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
315 }
316
find_edge(set * edges,ir_node * n1,ir_node * n2)317 static inline edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2)
318 {
319 edge_t new_edge;
320
321 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
322 new_edge.n1 = n1;
323 new_edge.n2 = n2;
324 } else {
325 new_edge.n1 = n2;
326 new_edge.n2 = n1;
327 }
328 return set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
329 }
330
remove_edge(set * edges,ir_node * n1,ir_node * n2,size_t * counter)331 static inline void remove_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
332 {
333 edge_t new_edge, *e;
334
335 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
336 new_edge.n1 = n1;
337 new_edge.n2 = n2;
338 } else {
339 new_edge.n1 = n2;
340 new_edge.n2 = n1;
341 }
342 e = set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
343 if (e) {
344 e->n1 = NULL;
345 e->n2 = NULL;
346 (*counter)--;
347 }
348 }
349
350 #define pset_foreach(pset, irn) foreach_pset((pset), ir_node, (irn))
351
352 /**
353 * Search for an interference clique and an external node
354 * with affinity edges to all nodes of the clique.
355 * At most 1 node of the clique can be colored equally with the external node.
356 */
build_clique_star_cstr(ilp_env_t * ienv)357 static void build_clique_star_cstr(ilp_env_t *ienv)
358 {
359 /* for each node with affinity edges */
360 co_gs_foreach_aff_node(ienv->co, aff) {
361 struct obstack ob;
362 const ir_node *center = aff->irn;
363 ir_node **nodes;
364 set *edges;
365 int i, o, n_nodes;
366 size_t n_edges;
367
368 if (arch_irn_is_ignore(aff->irn))
369 continue;
370
371 obstack_init(&ob);
372 edges = new_set(compare_edge_t, 8);
373
374 /* get all affinity neighbours */
375 n_nodes = 0;
376 co_gs_foreach_neighb(aff, nbr) {
377 if (!arch_irn_is_ignore(nbr->irn)) {
378 obstack_ptr_grow(&ob, nbr->irn);
379 ++n_nodes;
380 }
381 }
382 nodes = (ir_node**)obstack_finish(&ob);
383
384 /* get all interference edges between these */
385 n_edges = 0;
386 for (i=0; i<n_nodes; ++i) {
387 for (o=0; o<i; ++o) {
388 if (be_ifg_connected(ienv->co->cenv->ifg, nodes[i], nodes[o]))
389 add_edge(edges, nodes[i], nodes[o], &n_edges);
390 }
391 }
392
393 /* cover all these interference edges with maximal cliques */
394 while (n_edges) {
395 edge_t *e;
396 pset *clique = pset_new_ptr(8);
397 bool growed;
398
399 /* get 2 starting nodes to form a clique */
400 for (e = set_first(edge_t, edges); !e->n1; e = set_next(edge_t, edges)) {}
401
402 /* we could be stepped out of the loop before the set iterated to the end */
403 set_break(edges);
404
405 pset_insert_ptr(clique, e->n1);
406 pset_insert_ptr(clique, e->n2);
407 remove_edge(edges, e->n1, e->n2, &n_edges);
408
409 /* while the clique is growing */
410 do {
411 growed = false;
412
413 /* search for a candidate to extend the clique */
414 for (i=0; i<n_nodes; ++i) {
415 ir_node *cand = nodes[i];
416 bool is_cand;
417
418 /* if its already in the clique try the next */
419 if (pset_find_ptr(clique, cand))
420 continue;
421
422 /* are there all necessary interferences? */
423 is_cand = true;
424 pset_foreach(clique, member) {
425 if (!find_edge(edges, cand, member)) {
426 is_cand = false;
427 pset_break(clique);
428 break;
429 }
430 }
431
432 /* now we know if we have a clique extender */
433 if (is_cand) {
434 /* first remove all covered edges */
435 pset_foreach(clique, member)
436 remove_edge(edges, cand, member, &n_edges);
437
438 /* insert into clique */
439 pset_insert_ptr(clique, cand);
440 growed = true;
441 break;
442 }
443 }
444 } while (growed);
445
446 /* now the clique is maximal. Finally add the constraint */
447 {
448 int var_idx;
449 int cst_idx;
450 char buf[32];
451
452 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, pset_count(clique)-1);
453
454 pset_foreach(clique, member) {
455 make_affinity_var_name(buf, sizeof(buf), center, member);
456 var_idx = lpp_get_var_idx(ienv->lp, buf);
457 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
458 }
459 }
460
461 del_pset(clique);
462 }
463
464 del_set(edges);
465 obstack_free(&ob, NULL);
466 }
467 }
468
extend_path(ilp_env_t * ienv,pdeq * path,const ir_node * irn)469 static void extend_path(ilp_env_t *ienv, pdeq *path, const ir_node *irn)
470 {
471 be_ifg_t *ifg = ienv->co->cenv->ifg;
472 int i, len;
473 ir_node **curr_path;
474 affinity_node_t *aff;
475
476 /* do not walk backwards or in circles */
477 if (pdeq_contains(path, irn))
478 return;
479
480 if (arch_irn_is_ignore(irn))
481 return;
482
483 /* insert the new irn */
484 pdeq_putr(path, irn);
485
486 /* check for forbidden interferences */
487 len = pdeq_len(path);
488 curr_path = ALLOCAN(ir_node*, len);
489 pdeq_copyl(path, (const void **)curr_path);
490
491 for (i=1; i<len; ++i) {
492 if (be_ifg_connected(ifg, irn, curr_path[i]))
493 goto end;
494 }
495
496 /* check for terminating interference */
497 if (be_ifg_connected(ifg, irn, curr_path[0])) {
498 /* One node is not a path. */
499 /* And a path of length 2 is covered by a clique star constraint. */
500 if (len > 2) {
501 /* finally build the constraint */
502 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, 1.0);
503 for (i=1; i<len; ++i) {
504 char buf[32];
505 int var_idx;
506
507 make_affinity_var_name(buf, sizeof(buf), curr_path[i-1], curr_path[i]);
508 var_idx = lpp_get_var_idx(ienv->lp, buf);
509 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
510 }
511 }
512
513 /* this path cannot be extended anymore */
514 goto end;
515 }
516
517 /* recursively extend the path */
518 aff = get_affinity_info(ienv->co, irn);
519 co_gs_foreach_neighb(aff, nbr) {
520 extend_path(ienv, path, nbr->irn);
521 }
522
523 end:
524 /* remove the irn */
525 pdeq_getr(path);
526 }
527
528 /**
529 * Search a path of affinity edges, whose ends are connected
530 * by an interference edge and there are no other interference
531 * edges in between.
532 * Then at least one of these affinity edges must break.
533 */
build_path_cstr(ilp_env_t * ienv)534 static void build_path_cstr(ilp_env_t *ienv)
535 {
536 /* for each node with affinity edges */
537 co_gs_foreach_aff_node(ienv->co, aff_info) {
538 pdeq *path = new_pdeq();
539
540 extend_path(ienv, path, aff_info->irn);
541
542 del_pdeq(path);
543 }
544 }
545
ilp2_build(ilp_env_t * ienv)546 static void ilp2_build(ilp_env_t *ienv)
547 {
548 int lower_bound;
549
550 ienv->lp = lpp_new(ienv->co->name, lpp_minimize);
551 build_coloring_cstr(ienv);
552 build_interference_cstr(ienv);
553 build_affinity_cstr(ienv);
554 build_clique_star_cstr(ienv);
555 build_path_cstr(ienv);
556
557 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
558 lpp_set_bound(ienv->lp, lower_bound);
559 }
560
ilp2_apply(ilp_env_t * ienv)561 static void ilp2_apply(ilp_env_t *ienv)
562 {
563 local_env_t *lenv = (local_env_t*)ienv->env;
564 ir_graph *irg = ienv->co->irg;
565
566 /* first check if there was sth. to optimize */
567 if (lenv->first_x_var >= 0) {
568 int count = lenv->last_x_var - lenv->first_x_var + 1;
569 double *sol = XMALLOCN(double, count);
570 lpp_sol_state_t state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
571 int i;
572
573 if (state != lpp_optimal) {
574 printf("WARNING %s: Solution state is not 'optimal': %d\n",
575 ienv->co->name, (int)state);
576 if (state < lpp_feasible) {
577 panic("Copy coalescing solution not feasible!");
578 }
579 }
580
581 for (i=0; i<count; ++i) {
582 unsigned nodenr;
583 unsigned color;
584 char var_name[32];
585 if (sol[i] <= 1-EPSILON)
586 continue;
587 /* split variable name into components */
588 lpp_get_var_name(ienv->lp, lenv->first_x_var+i, var_name, sizeof(var_name));
589
590 if (sscanf(var_name, "x_%u_%u", &nodenr, &color) == 2) {
591 ir_node *irn = get_idx_irn(irg, nodenr);
592 set_irn_col(ienv->co->cls, irn, color);
593 } else {
594 panic("This should be a x-var");
595 }
596 }
597
598 xfree(sol);
599 }
600
601 #ifdef COPYOPT_STAT
602 /* TODO adapt to multiple possible ILPs */
603 copystat_add_ilp_time((int)(1000.0*lpp_get_sol_time(pi->curr_lp))); //now we have ms
604 copystat_add_ilp_vars(lpp_get_var_count(pi->curr_lp));
605 copystat_add_ilp_csts(lpp_get_cst_count(pi->curr_lp));
606 copystat_add_ilp_iter(lpp_get_iter_cnt(pi->curr_lp));
607 #endif
608 }
609
610 /**
611 * Solves the problem using mixed integer programming
612 * @returns 1 iff solution state was optimal
613 * Uses the OU and the GRAPH data structure
614 * Dependency of the OU structure can be removed
615 */
co_solve_ilp2(copy_opt_t * co)616 static int co_solve_ilp2(copy_opt_t *co)
617 {
618 unsigned *allocatable_colors;
619 unsigned n_regs = arch_register_class_n_regs(co->cls);
620 lpp_sol_state_t sol_state;
621 ilp_env_t *ienv;
622 local_env_t my;
623
624 ASSERT_OU_AVAIL(co); //See build_clique_st
625 ASSERT_GS_AVAIL(co);
626
627 my.first_x_var = -1;
628 my.last_x_var = -1;
629 FIRM_DBG_REGISTER(dbg, "firm.be.coilp2");
630
631 rbitset_alloca(allocatable_colors, n_regs);
632 be_set_allocatable_regs(co->irg, co->cls, allocatable_colors);
633 my.allocatable_colors = allocatable_colors;
634
635 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
636
637 sol_state = ilp_go(ienv);
638
639 free_ilp_env(ienv);
640
641 return sol_state == lpp_optimal;
642 }
643
BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)644 BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)
645 void be_init_copyilp2(void)
646 {
647 static co_algo_info copyheur = {
648 co_solve_ilp2, 1
649 };
650
651 be_register_copyopt("ilp", ©heur);
652 }
653