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4 * This file is part of libFirm.
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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
22 * @brief ILP based copy minimization.
23 * @author Daniel Grund
26 * ILP formalization using G=(V, E, Q):
27 * - 2 class of variables: coloring vars x_ic and equal color vars y_ij
29 * - Clique-star constraints
32 * \min \sum_{ (i,j) \in Q } w_ij y_ij
34 * \sum_c x_nc = 1 n \in N, c \in C
36 * x_nc = 0 n \in N, c \not\in C(n)
38 * \sum x_nc <= 1 x_nc \in Clique \in AllCliques, c \in C
40 * \sum_{e \in p} y_e >= 1 p \in P path constraints
42 * \sum_{e \in cs} y_e >= |cs| - 1 cs \in CP clique-star constraints
44 * x_nc, y_ij \in N, w_ij \in R^+
49 #include "raw_bitset.h"
54 #include "becopyilp_t.h"
59 DEBUG_ONLY(static firm_dbg_module_t *dbg;)
61 typedef struct local_env_t {
64 const unsigned *allocatable_colors;
67 static void make_color_var_name(char *buf, size_t buf_size,
68 const ir_node *node, unsigned color)
70 unsigned node_idx = get_irn_idx(node);
71 snprintf(buf, buf_size, "x_%u_%u", node_idx, color);
74 static void build_coloring_cstr(ilp_env_t *ienv)
76 local_env_t *lenv = ienv->env;
77 be_ifg_t *ifg = ienv->co->cenv->ifg;
78 unsigned n_regs = arch_register_class_n_regs(ienv->co->cls);
79 const unsigned *allocatable_colors = lenv->allocatable_colors;
85 rbitset_alloca(colors, n_regs);
87 be_ifg_foreach_node(ifg, &iter, irn) {
88 const arch_register_req_t *req;
91 unsigned curr_node_color;
93 if (sr_is_removed(ienv->sr, irn))
96 req = arch_get_irn_register_req(irn);
98 /* get assignable colors */
99 if (arch_register_req_is(req, limited)) {
100 rbitset_copy(colors, req->limited, n_regs);
102 rbitset_copy(colors, allocatable_colors, n_regs);
105 /* add the coloring constraint */
106 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 1.0);
108 curr_node_color = get_irn_col(irn);
109 for (col = 0; col < n_regs; ++col) {
112 if (!rbitset_is_set(colors, col))
115 make_color_var_name(buf, sizeof(buf), irn, col);
116 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
117 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
119 val = (col == curr_node_color) ? 1.0 : 0.0;
120 lpp_set_start_value(ienv->lp, var_idx, val);
122 lenv->last_x_var = var_idx;
123 if (lenv->first_x_var == -1)
124 lenv->first_x_var = var_idx;
127 /* add register constraint constraints */
128 for (col = 0; col < n_regs; ++col) {
131 if (rbitset_is_set(colors, col))
134 make_color_var_name(buf, sizeof(buf), irn, col);
135 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 0.0);
136 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
137 lpp_set_start_value(ienv->lp, var_idx, 0.0);
138 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
140 lenv->last_x_var = var_idx;
145 static void build_interference_cstr(ilp_env_t *ienv)
147 lpp_t *lpp = ienv->lp;
148 local_env_t *lenv = ienv->env;
149 be_ifg_t *ifg = ienv->co->cenv->ifg;
150 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
151 ir_node **clique = ALLOCAN(ir_node*, n_colors);
152 const unsigned *allocatable_colors = lenv->allocatable_colors;
158 /* for each maximal clique */
159 be_ifg_foreach_clique(ifg, &iter, clique, &size) {
160 unsigned realsize = 0;
162 for (i=0; i<size; ++i) {
163 if (!sr_is_removed(ienv->sr, clique[i]))
171 for (col=0; col<n_colors; ++col) {
173 if (!rbitset_is_set(allocatable_colors, col))
176 cst_idx = lpp_add_cst(lpp, NULL, lpp_less_equal, 1.0);
178 /* for each member of this clique */
179 for (i=0; i<size; ++i) {
180 ir_node *irn = clique[i];
184 if (sr_is_removed(ienv->sr, irn))
187 make_color_var_name(buf, sizeof(buf), irn, col);
188 var_idx = lpp_get_var_idx(lpp, buf);
189 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
195 static void make_affinity_var_name(char *buf, size_t buf_size,
196 const ir_node *node1, const ir_node *node2)
198 unsigned n1 = get_irn_idx(node1);
199 unsigned n2 = get_irn_idx(node2);
201 snprintf(buf, buf_size, "y_%u_%u", n1, n2);
203 snprintf(buf, buf_size, "y_%u_%u", n2, n1);
209 * TODO: Remove the dependency of the opt-units data structure
210 * by walking over all affinity edges. Graph structure
211 * does not provide this walker, yet.
213 static void build_affinity_cstr(ilp_env_t *ienv)
215 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
218 /* for all optimization units */
219 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
220 ir_node *root = curr->nodes[0];
221 unsigned root_col = get_irn_col(root);
224 for (i = 1; i < curr->node_count; ++i) {
225 ir_node *arg = curr->nodes[i];
226 unsigned arg_col = get_irn_col(arg);
232 /* add a new affinity variable */
233 make_affinity_var_name(buf, sizeof(buf), arg, root);
234 y_idx = lpp_add_var(ienv->lp, buf, lpp_binary, curr->costs[i]);
235 val = (root_col == arg_col) ? 0.0 : 1.0;
236 lpp_set_start_value(ienv->lp, y_idx, val);
238 /* add constraints relating the affinity var to the color vars */
239 for (col=0; col<n_colors; ++col) {
240 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less_equal, 0.0);
244 make_color_var_name(buf, sizeof(buf), root, col);
245 root_idx = lpp_get_var_idx(ienv->lp, buf);
246 make_color_var_name(buf, sizeof(buf), arg, col);
247 arg_idx = lpp_get_var_idx(ienv->lp, buf);
249 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
250 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
251 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
258 * Helping stuff for build_clique_star_cstr
260 typedef struct edge_t {
265 static int compare_edge_t(const void *k1, const void *k2, size_t size)
267 const edge_t *e1 = k1;
268 const edge_t *e2 = k2;
271 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
274 #define HASH_EDGE(e) (hash_irn((e)->n1) ^ hash_irn((e)->n2))
276 static inline edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
280 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
288 return set_insert(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
291 static inline edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2)
295 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
302 return set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
305 static inline void remove_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
309 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
316 e = set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
324 #define pset_foreach(pset, irn) for (irn=pset_first(pset); irn; irn=pset_next(pset))
327 * Search for an interference clique and an external node
328 * with affinity edges to all nodes of the clique.
329 * At most 1 node of the clique can be colored equally with the external node.
331 static void build_clique_star_cstr(ilp_env_t *ienv)
333 affinity_node_t *aff;
335 /* for each node with affinity edges */
336 co_gs_foreach_aff_node(ienv->co, aff) {
339 const ir_node *center = aff->irn;
345 if (arch_irn_is_ignore(aff->irn))
349 edges = new_set(compare_edge_t, 8);
351 /* get all affinity neighbours */
353 co_gs_foreach_neighb(aff, nbr) {
354 if (!arch_irn_is_ignore(nbr->irn)) {
355 obstack_ptr_grow(&ob, nbr->irn);
359 nodes = obstack_finish(&ob);
361 /* get all interference edges between these */
363 for (i=0; i<n_nodes; ++i) {
364 for (o=0; o<i; ++o) {
365 if (be_ifg_connected(ienv->co->cenv->ifg, nodes[i], nodes[o]))
366 add_edge(edges, nodes[i], nodes[o], &n_edges);
370 /* cover all these interference edges with maximal cliques */
373 pset *clique = pset_new_ptr(8);
376 /* get 2 starting nodes to form a clique */
377 for (e=set_first(edges); !e->n1; e=set_next(edges)) {
380 /* we could be stepped out of the loop before the set iterated to the end */
383 pset_insert_ptr(clique, e->n1);
384 pset_insert_ptr(clique, e->n2);
385 remove_edge(edges, e->n1, e->n2, &n_edges);
387 /* while the clique is growing */
391 /* search for a candidate to extend the clique */
392 for (i=0; i<n_nodes; ++i) {
393 ir_node *cand = nodes[i];
397 /* if its already in the clique try the next */
398 if (pset_find_ptr(clique, cand))
401 /* are there all necessary interferences? */
403 pset_foreach(clique, member) {
404 if (!find_edge(edges, cand, member)) {
411 /* now we know if we have a clique extender */
413 /* first remove all covered edges */
414 pset_foreach(clique, member)
415 remove_edge(edges, cand, member, &n_edges);
417 /* insert into clique */
418 pset_insert_ptr(clique, cand);
425 /* now the clique is maximal. Finally add the constraint */
432 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, pset_count(clique)-1);
434 pset_foreach(clique, member) {
435 make_affinity_var_name(buf, sizeof(buf), center, member);
436 var_idx = lpp_get_var_idx(ienv->lp, buf);
437 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
445 obstack_free(&ob, NULL);
449 static void extend_path(ilp_env_t *ienv, pdeq *path, const ir_node *irn)
451 be_ifg_t *ifg = ienv->co->cenv->ifg;
454 affinity_node_t *aff;
457 /* do not walk backwards or in circles */
458 if (pdeq_contains(path, irn))
461 if (arch_irn_is_ignore(irn))
464 /* insert the new irn */
465 pdeq_putr(path, irn);
467 /* check for forbidden interferences */
468 len = pdeq_len(path);
469 curr_path = ALLOCAN(ir_node*, len);
470 pdeq_copyl(path, (const void **)curr_path);
472 for (i=1; i<len; ++i) {
473 if (be_ifg_connected(ifg, irn, curr_path[i]))
477 /* check for terminating interference */
478 if (be_ifg_connected(ifg, irn, curr_path[0])) {
479 /* One node is not a path. */
480 /* And a path of length 2 is covered by a clique star constraint. */
482 /* finally build the constraint */
483 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, 1.0);
484 for (i=1; i<len; ++i) {
488 make_affinity_var_name(buf, sizeof(buf), curr_path[i-1], curr_path[i]);
489 var_idx = lpp_get_var_idx(ienv->lp, buf);
490 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
494 /* this path cannot be extended anymore */
498 /* recursively extend the path */
499 aff = get_affinity_info(ienv->co, irn);
500 co_gs_foreach_neighb(aff, nbr) {
501 extend_path(ienv, path, nbr->irn);
510 * Search a path of affinity edges, whose ends are connected
511 * by an interference edge and there are no other interference
513 * Then at least one of these affinity edges must break.
515 static void build_path_cstr(ilp_env_t *ienv)
517 affinity_node_t *aff_info;
519 /* for each node with affinity edges */
520 co_gs_foreach_aff_node(ienv->co, aff_info) {
521 pdeq *path = new_pdeq();
523 extend_path(ienv, path, aff_info->irn);
529 static void ilp2_build(ilp_env_t *ienv)
533 ienv->lp = lpp_new(ienv->co->name, lpp_minimize);
534 build_coloring_cstr(ienv);
535 build_interference_cstr(ienv);
536 build_affinity_cstr(ienv);
537 build_clique_star_cstr(ienv);
538 build_path_cstr(ienv);
540 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
541 lpp_set_bound(ienv->lp, lower_bound);
544 static void ilp2_apply(ilp_env_t *ienv)
546 local_env_t *lenv = ienv->env;
547 ir_graph *irg = ienv->co->irg;
549 /* first check if there was sth. to optimize */
550 if (lenv->first_x_var >= 0) {
551 int count = lenv->last_x_var - lenv->first_x_var + 1;
552 double *sol = XMALLOCN(double, count);
553 lpp_sol_state_t state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
556 if (state != lpp_optimal) {
557 printf("WARNING %s: Solution state is not 'optimal': %d\n",
558 ienv->co->name, (int)state);
559 if (state < lpp_feasible) {
560 panic("Copy coalescing solution not feasible!");
564 for (i=0; i<count; ++i) {
568 if (sol[i] <= 1-EPSILON)
570 /* split variable name into components */
571 lpp_get_var_name(ienv->lp, lenv->first_x_var+i, var_name, sizeof(var_name));
573 if (sscanf(var_name, "x_%u_%u", &nodenr, &color) == 2) {
574 ir_node *irn = get_idx_irn(irg, nodenr);
575 set_irn_col(ienv->co->cls, irn, color);
577 panic("This should be a x-var");
585 /* TODO adapt to multiple possible ILPs */
586 copystat_add_ilp_time((int)(1000.0*lpp_get_sol_time(pi->curr_lp))); //now we have ms
587 copystat_add_ilp_vars(lpp_get_var_count(pi->curr_lp));
588 copystat_add_ilp_csts(lpp_get_cst_count(pi->curr_lp));
589 copystat_add_ilp_iter(lpp_get_iter_cnt(pi->curr_lp));
594 * Solves the problem using mixed integer programming
595 * @returns 1 iff solution state was optimal
596 * Uses the OU and the GRAPH data structure
597 * Dependency of the OU structure can be removed
599 static int co_solve_ilp2(copy_opt_t *co)
601 unsigned *allocatable_colors;
602 unsigned n_regs = arch_register_class_n_regs(co->cls);
603 lpp_sol_state_t sol_state;
607 ASSERT_OU_AVAIL(co); //See build_clique_st
612 FIRM_DBG_REGISTER(dbg, "firm.be.coilp2");
614 rbitset_alloca(allocatable_colors, n_regs);
615 be_set_allocatable_regs(co->irg, co->cls, allocatable_colors);
616 my.allocatable_colors = allocatable_colors;
618 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
620 sol_state = ilp_go(ienv);
624 return sol_state == lpp_optimal;
627 BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)
628 void be_init_copyilp2(void)
630 static co_algo_info copyheur = {
634 be_register_copyopt("ilp", ©heur);