2 * Copyright (C) 1995-2008 University of Karlsruhe. All right reserved.
4 * This file is part of libFirm.
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12 * this file in accordance with the libFirm Commercial License.
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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 {
65 unsigned *normal_colors;
68 static void make_color_var_name(char *buf, size_t buf_size,
69 const ir_node *node, unsigned color)
71 unsigned node_idx = get_irn_idx(node);
72 snprintf(buf, buf_size, "x_%u_%u", node_idx, color);
75 static void build_coloring_cstr(ilp_env_t *ienv)
77 local_env_t *lenv = ienv->env;
78 be_ifg_t *ifg = ienv->co->cenv->ifg;
79 unsigned n_regs = arch_register_class_n_regs(ienv->co->cls);
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, lenv->normal_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 = lenv->n_colors;
151 ir_node **clique = ALLOCAN(ir_node*, n_colors);
157 /* for each maximal clique */
158 be_ifg_foreach_clique(ifg, &iter, clique, &size) {
159 unsigned realsize = 0;
161 for (i=0; i<size; ++i) {
162 if (!sr_is_removed(ienv->sr, clique[i]))
170 for (col=0; col<n_colors; ++col) {
171 int cst_idx = lpp_add_cst(lpp, NULL, lpp_less_equal, 1.0);
173 /* for each member of this clique */
174 for (i=0; i<size; ++i) {
175 ir_node *irn = clique[i];
179 if (sr_is_removed(ienv->sr, irn))
182 make_color_var_name(buf, sizeof(buf), irn, col);
183 var_idx = lpp_get_var_idx(lpp, buf);
184 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
190 static void make_affinity_var_name(char *buf, size_t buf_size,
191 const ir_node *node1, const ir_node *node2)
193 unsigned n1 = get_irn_idx(node1);
194 unsigned n2 = get_irn_idx(node2);
196 snprintf(buf, buf_size, "y_%u_%u", n1, n2);
198 snprintf(buf, buf_size, "y_%u_%u", n2, n1);
204 * TODO: Remove the dependency of the opt-units data structure
205 * by walking over all affinity edges. Graph structure
206 * does not provide this walker, yet.
208 static void build_affinity_cstr(ilp_env_t *ienv)
210 local_env_t *lenv = ienv->env;
211 unsigned n_colors = lenv->n_colors;
214 /* for all optimization units */
215 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
216 ir_node *root = curr->nodes[0];
217 unsigned root_col = get_irn_col(root);
220 for (i = 1; i < curr->node_count; ++i) {
221 ir_node *arg = curr->nodes[i];
222 unsigned arg_col = get_irn_col(arg);
228 /* add a new affinity variable */
229 make_affinity_var_name(buf, sizeof(buf), arg, root);
230 y_idx = lpp_add_var(ienv->lp, buf, lpp_binary, curr->costs[i]);
231 val = (root_col == arg_col) ? 0.0 : 1.0;
232 lpp_set_start_value(ienv->lp, y_idx, val);
234 /* add constraints relating the affinity var to the color vars */
235 for (col=0; col<n_colors; ++col) {
236 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less_equal, 0.0);
240 make_color_var_name(buf, sizeof(buf), root, col);
241 root_idx = lpp_get_var_idx(ienv->lp, buf);
242 make_color_var_name(buf, sizeof(buf), arg, col);
243 arg_idx = lpp_get_var_idx(ienv->lp, buf);
245 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
246 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
247 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
254 * Helping stuff for build_clique_star_cstr
256 typedef struct edge_t {
261 static int compare_edge_t(const void *k1, const void *k2, size_t size)
263 const edge_t *e1 = k1;
264 const edge_t *e2 = k2;
267 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
270 #define HASH_EDGE(e) (hash_irn((e)->n1) ^ hash_irn((e)->n2))
272 static inline edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
276 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
284 return set_insert(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
287 static inline edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2)
291 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
298 return set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
301 static inline void remove_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
305 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
312 e = set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
320 #define pset_foreach(pset, irn) for (irn=pset_first(pset); irn; irn=pset_next(pset))
323 * Search for an interference clique and an external node
324 * with affinity edges to all nodes of the clique.
325 * At most 1 node of the clique can be colored equally with the external node.
327 static void build_clique_star_cstr(ilp_env_t *ienv)
329 affinity_node_t *aff;
331 /* for each node with affinity edges */
332 co_gs_foreach_aff_node(ienv->co, aff) {
335 const ir_node *center = aff->irn;
341 if (arch_irn_is_ignore(aff->irn))
345 edges = new_set(compare_edge_t, 8);
347 /* get all affinity neighbours */
349 co_gs_foreach_neighb(aff, nbr) {
350 if (!arch_irn_is_ignore(nbr->irn)) {
351 obstack_ptr_grow(&ob, nbr->irn);
355 nodes = obstack_finish(&ob);
357 /* get all interference edges between these */
359 for (i=0; i<n_nodes; ++i) {
360 for (o=0; o<i; ++o) {
361 if (be_ifg_connected(ienv->co->cenv->ifg, nodes[i], nodes[o]))
362 add_edge(edges, nodes[i], nodes[o], &n_edges);
366 /* cover all these interference edges with maximal cliques */
369 pset *clique = pset_new_ptr(8);
372 /* get 2 starting nodes to form a clique */
373 for (e=set_first(edges); !e->n1; e=set_next(edges)) {
376 /* we could be stepped out of the loop before the set iterated to the end */
379 pset_insert_ptr(clique, e->n1);
380 pset_insert_ptr(clique, e->n2);
381 remove_edge(edges, e->n1, e->n2, &n_edges);
383 /* while the clique is growing */
387 /* search for a candidate to extend the clique */
388 for (i=0; i<n_nodes; ++i) {
389 ir_node *cand = nodes[i];
393 /* if its already in the clique try the next */
394 if (pset_find_ptr(clique, cand))
397 /* are there all necessary interferences? */
399 pset_foreach(clique, member) {
400 if (!find_edge(edges, cand, member)) {
407 /* now we know if we have a clique extender */
409 /* first remove all covered edges */
410 pset_foreach(clique, member)
411 remove_edge(edges, cand, member, &n_edges);
413 /* insert into clique */
414 pset_insert_ptr(clique, cand);
421 /* now the clique is maximal. Finally add the constraint */
428 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, pset_count(clique)-1);
430 pset_foreach(clique, member) {
431 make_affinity_var_name(buf, sizeof(buf), center, member);
432 var_idx = lpp_get_var_idx(ienv->lp, buf);
433 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
441 obstack_free(&ob, NULL);
445 static void extend_path(ilp_env_t *ienv, pdeq *path, const ir_node *irn)
447 be_ifg_t *ifg = ienv->co->cenv->ifg;
450 affinity_node_t *aff;
453 /* do not walk backwards or in circles */
454 if (pdeq_contains(path, irn))
457 if (arch_irn_is_ignore(irn))
460 /* insert the new irn */
461 pdeq_putr(path, irn);
463 /* check for forbidden interferences */
464 len = pdeq_len(path);
465 curr_path = ALLOCAN(ir_node*, len);
466 pdeq_copyl(path, (const void **)curr_path);
468 for (i=1; i<len; ++i) {
469 if (be_ifg_connected(ifg, irn, curr_path[i]))
473 /* check for terminating interference */
474 if (be_ifg_connected(ifg, irn, curr_path[0])) {
475 /* One node is not a path. */
476 /* And a path of length 2 is covered by a clique star constraint. */
478 /* finally build the constraint */
479 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, 1.0);
480 for (i=1; i<len; ++i) {
484 make_affinity_var_name(buf, sizeof(buf), curr_path[i-1], curr_path[i]);
485 var_idx = lpp_get_var_idx(ienv->lp, buf);
486 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
490 /* this path cannot be extended anymore */
494 /* recursively extend the path */
495 aff = get_affinity_info(ienv->co, irn);
496 co_gs_foreach_neighb(aff, nbr) {
497 extend_path(ienv, path, nbr->irn);
506 * Search a path of affinity edges, whose ends are connected
507 * by an interference edge and there are no other interference
509 * Then at least one of these affinity edges must break.
511 static void build_path_cstr(ilp_env_t *ienv)
513 affinity_node_t *aff_info;
515 /* for each node with affinity edges */
516 co_gs_foreach_aff_node(ienv->co, aff_info) {
517 pdeq *path = new_pdeq();
519 extend_path(ienv, path, aff_info->irn);
525 static void ilp2_build(ilp_env_t *ienv)
529 ienv->lp = lpp_new(ienv->co->name, lpp_minimize);
530 build_coloring_cstr(ienv);
531 build_interference_cstr(ienv);
532 build_affinity_cstr(ienv);
533 build_clique_star_cstr(ienv);
534 build_path_cstr(ienv);
536 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
537 lpp_set_bound(ienv->lp, lower_bound);
540 static void ilp2_apply(ilp_env_t *ienv)
542 local_env_t *lenv = ienv->env;
543 ir_graph *irg = ienv->co->irg;
545 /* first check if there was sth. to optimize */
546 if (lenv->first_x_var >= 0) {
547 int count = lenv->last_x_var - lenv->first_x_var + 1;
548 double *sol = XMALLOCN(double, count);
549 lpp_sol_state_t state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
552 if (state != lpp_optimal) {
553 printf("WARNING %s: Solution state is not 'optimal': %d\n",
554 ienv->co->name, (int)state);
555 if (state < lpp_feasible) {
556 panic("Copy coalescing solution not feasible!");
560 for (i=0; i<count; ++i) {
564 if (sol[i] <= 1-EPSILON)
566 /* split variable name into components */
567 lpp_get_var_name(ienv->lp, lenv->first_x_var+i, var_name, sizeof(var_name));
569 if (sscanf(var_name, "x_%u_%u", &nodenr, &color) == 2) {
570 ir_node *irn = get_idx_irn(irg, nodenr);
571 set_irn_col(ienv->co->cls, irn, color);
573 panic("This should be a x-var");
581 /* TODO adapt to multiple possible ILPs */
582 copystat_add_ilp_time((int)(1000.0*lpp_get_sol_time(pi->curr_lp))); //now we have ms
583 copystat_add_ilp_vars(lpp_get_var_count(pi->curr_lp));
584 copystat_add_ilp_csts(lpp_get_cst_count(pi->curr_lp));
585 copystat_add_ilp_iter(lpp_get_iter_cnt(pi->curr_lp));
590 * Solves the problem using mixed integer programming
591 * @returns 1 iff solution state was optimal
592 * Uses the OU and the GRAPH data structure
593 * Dependency of the OU structure can be removed
595 static int co_solve_ilp2(copy_opt_t *co)
597 unsigned n_regs = arch_register_class_n_regs(co->cls);
598 lpp_sol_state_t sol_state;
602 ASSERT_OU_AVAIL(co); //See build_clique_st
607 FIRM_DBG_REGISTER(dbg, "firm.be.coilp2");
609 rbitset_alloca(my.normal_colors, n_regs);
610 be_set_allocatable_regs(co->irg, co->cls, my.normal_colors);
611 my.n_colors = rbitset_popcount(my.normal_colors, n_regs);
613 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
615 sol_state = ilp_go(ienv);
619 return sol_state == lpp_optimal;
622 BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)
623 void be_init_copyilp2(void)
625 static co_algo_info copyheur = {
629 be_register_copyopt("ilp", ©heur);