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"
61 typedef struct local_env_t {
62 int first_x_var, last_x_var;
64 bitset_t *normal_colors;
66 DEBUG_ONLY(firm_dbg_module_t *dbg;)
69 static void build_coloring_cstr(ilp_env_t *ienv)
71 be_ifg_t *ifg = ienv->co->cenv->ifg;
77 colors = bitset_alloca(arch_register_class_n_regs(ienv->co->cls));
79 be_ifg_foreach_node(ifg, &iter, irn)
80 if (!sr_is_removed(ienv->sr, irn)) {
83 const arch_register_req_t *req;
84 int curr_node_color = get_irn_col(irn);
85 int node_nr = (int)get_irn_idx(irn);
86 local_env_t *lenv = ienv->env;
88 pmap_insert(lenv->nr_2_irn, INT_TO_PTR(node_nr), irn);
90 req = arch_get_irn_register_req(irn);
92 bitset_clear_all(colors);
94 /* get assignable colors */
95 if (arch_register_req_is(req, limited)) {
96 rbitset_copy_to_bitset(req->limited, colors);
98 bitset_copy(colors, lenv->normal_colors);
101 /* add the coloring constraint */
102 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 1.0);
104 bitset_foreach(colors, col) {
105 int var_idx = lpp_add_var(ienv->lp, name_cdd(buf, 'x', node_nr, (int)col), lpp_binary, 0.0);
106 lpp_set_start_value(ienv->lp, var_idx, (col == (unsigned) curr_node_color) ? 1.0 : 0.0);
107 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
109 lenv->last_x_var = var_idx;
110 if (lenv->first_x_var == -1)
111 lenv->first_x_var = var_idx;
114 /* add register constraint constraints */
115 bitset_foreach_clear(colors, col) {
116 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 0.0);
117 int var_idx = lpp_add_var(ienv->lp, name_cdd(buf, 'x', node_nr, (int)col), lpp_binary, 0.0);
118 lpp_set_start_value(ienv->lp, var_idx, 0.0);
119 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
121 lenv->last_x_var = var_idx;
126 static void build_interference_cstr(ilp_env_t *ienv)
128 lpp_t *lpp = ienv->lp;
129 local_env_t *lenv = ienv->env;
130 be_ifg_t *ifg = ienv->co->cenv->ifg;
131 int n_colors = lenv->n_colors;
133 ir_node **clique = ALLOCAN(ir_node*, n_colors);
140 /* for each maximal clique */
141 be_ifg_foreach_clique(ifg, &iter, clique, &size) {
144 for (i=0; i<size; ++i)
145 if (!sr_is_removed(ienv->sr, clique[i]))
152 for (col=0; col<n_colors; ++col) {
153 int cst_idx = lpp_add_cst(lpp, NULL, lpp_less_equal, 1.0);
155 /* for each member of this clique */
156 for (i=0; i<size; ++i) {
157 ir_node *irn = clique[i];
159 if (!sr_is_removed(ienv->sr, irn)) {
160 int var_idx = lpp_get_var_idx(lpp, name_cdd(buf, 'x', (int)get_irn_idx(irn), col));
161 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
170 * TODO: Remove the dependency of the opt-units data structure
171 * by walking over all affinity edges. Graph structure
172 * does not provide this walker, yet.
174 static void build_affinity_cstr(ilp_env_t *ienv)
176 local_env_t *lenv = ienv->env;
177 int n_colors = lenv->n_colors;
180 /* for all optimization units */
181 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
183 int root_nr, arg_nr, i, col, y_idx, root_idx, arg_idx;
185 int root_col, arg_col;
187 root = curr->nodes[0];
188 root_nr = (int) get_irn_idx(root);
189 root_col = get_irn_col(root);
191 for (i = 1; i < curr->node_count; ++i) {
192 arg = curr->nodes[i];
193 arg_nr = (int) get_irn_idx(arg);
194 arg_col = get_irn_col(arg);
196 /* add a new affinity variable */
197 y_idx = lpp_add_var(ienv->lp, name_cdd_sorted(buf, 'y', root_nr, arg_nr), lpp_binary, curr->costs[i]);
198 lpp_set_start_value(ienv->lp, y_idx, (root_col==arg_col) ? 0.0 : 1.0);
200 /* add constraints relating the affinity var to the color vars */
201 for (col=0; col<n_colors; ++col) {
202 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less_equal, 0.0);
203 root_idx = lpp_get_var_idx(ienv->lp, name_cdd(buf, 'x', root_nr, col));
204 arg_idx = lpp_get_var_idx(ienv->lp, name_cdd(buf, 'x', arg_nr, col));
206 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
207 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
208 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
215 * Helping stuff for build_clique_star_cstr
217 typedef struct edge_t {
221 static int compare_edge_t(const void *k1, const void *k2, size_t size)
223 const edge_t *e1 = k1;
224 const edge_t *e2 = k2;
227 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
230 #define HASH_EDGE(e) (hash_irn((e)->n1) ^ hash_irn((e)->n2))
232 static inline edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, int *counter)
236 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
244 return set_insert(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
247 static inline edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2)
251 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
258 return set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
261 static inline void remove_edge(set *edges, ir_node *n1, ir_node *n2, int *counter)
265 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
272 e = set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
280 #define pset_foreach(pset, irn) for (irn=pset_first(pset); irn; irn=pset_next(pset))
283 * Search for an interference clique and an external node
284 * with affinity edges to all nodes of the clique.
285 * At most 1 node of the clique can be colored equally with the external node.
287 static void build_clique_star_cstr(ilp_env_t *ienv)
289 affinity_node_t *aff;
291 /* for each node with affinity edges */
292 co_gs_foreach_aff_node(ienv->co, aff) {
295 const ir_node *center = aff->irn;
298 int i, o, n_nodes, n_edges;
300 if (arch_irn_is_ignore(aff->irn))
304 edges = new_set(compare_edge_t, 8);
306 /* get all affinity neighbours */
308 co_gs_foreach_neighb(aff, nbr) {
309 if (!arch_irn_is_ignore(nbr->irn)) {
310 obstack_ptr_grow(&ob, nbr->irn);
314 nodes = obstack_finish(&ob);
316 /* get all interference edges between these */
318 for (i=0; i<n_nodes; ++i)
320 if (be_ifg_connected(ienv->co->cenv->ifg, nodes[i], nodes[o]))
321 add_edge(edges, nodes[i], nodes[o], &n_edges);
323 /* cover all these interference edges with maximal cliques */
326 pset *clique = pset_new_ptr(8);
329 /* get 2 starting nodes to form a clique */
330 for (e=set_first(edges); !e->n1; e=set_next(edges)) {
333 /* we could be stepped out of the loop before the set iterated to the end */
336 pset_insert_ptr(clique, e->n1);
337 pset_insert_ptr(clique, e->n2);
338 remove_edge(edges, e->n1, e->n2, &n_edges);
340 /* while the clique is growing */
344 /* search for a candidate to extend the clique */
345 for (i=0; i<n_nodes; ++i) {
346 ir_node *member, *cand = nodes[i];
349 /* if its already in the clique try the next */
350 if (pset_find_ptr(clique, cand))
353 /* are there all necessary interferences? */
355 pset_foreach(clique, member) {
356 if (!find_edge(edges, cand, member)) {
363 /* now we know if we have a clique extender */
365 /* first remove all covered edges */
366 pset_foreach(clique, member)
367 remove_edge(edges, cand, member, &n_edges);
369 /* insert into clique */
370 pset_insert_ptr(clique, cand);
377 /* now the clique is maximal. Finally add the constraint */
380 int var_idx, cst_idx, center_nr, member_nr;
383 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, pset_count(clique)-1);
384 center_nr = get_irn_idx(center);
386 pset_foreach(clique, member) {
387 member_nr = get_irn_idx(member);
388 var_idx = lpp_get_var_idx(ienv->lp, name_cdd_sorted(buf, 'y', center_nr, member_nr));
389 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
397 obstack_free(&ob, NULL);
402 static void extend_path(ilp_env_t *ienv, pdeq *path, const ir_node *irn)
404 be_ifg_t *ifg = ienv->co->cenv->ifg;
407 affinity_node_t *aff;
410 /* do not walk backwards or in circles */
411 if (pdeq_contains(path, irn))
414 if (arch_irn_is_ignore(irn))
417 /* insert the new irn */
418 pdeq_putr(path, irn);
422 /* check for forbidden interferences */
423 len = pdeq_len(path);
424 curr_path = ALLOCAN(ir_node*, len);
425 pdeq_copyl(path, (const void **)curr_path);
427 for (i=1; i<len; ++i)
428 if (be_ifg_connected(ifg, irn, curr_path[i]))
433 /* check for terminating interference */
434 if (be_ifg_connected(ifg, irn, curr_path[0])) {
436 /* One node is not a path. */
437 /* And a path of length 2 is covered by a clique star constraint. */
439 /* finally build the constraint */
440 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, 1.0);
441 for (i=1; i<len; ++i) {
443 int nr_1 = get_irn_idx(curr_path[i-1]);
444 int nr_2 = get_irn_idx(curr_path[i]);
445 int var_idx = lpp_get_var_idx(ienv->lp, name_cdd_sorted(buf, 'y', nr_1, nr_2));
446 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
450 /* this path cannot be extended anymore */
456 /* recursively extend the path */
457 aff = get_affinity_info(ienv->co, irn);
458 co_gs_foreach_neighb(aff, nbr)
459 extend_path(ienv, path, nbr->irn);
469 * Search a path of affinity edges, whose ends are connected
470 * by an interference edge and there are no other interference
472 * Then at least one of these affinity edges must break.
474 static void build_path_cstr(ilp_env_t *ienv)
476 affinity_node_t *aff_info;
478 /* for each node with affinity edges */
479 co_gs_foreach_aff_node(ienv->co, aff_info) {
480 pdeq *path = new_pdeq();
482 extend_path(ienv, path, aff_info->irn);
488 static void ilp2_build(ilp_env_t *ienv)
492 ienv->lp = lpp_new(ienv->co->name, lpp_minimize);
493 build_coloring_cstr(ienv);
494 build_interference_cstr(ienv);
495 build_affinity_cstr(ienv);
496 build_clique_star_cstr(ienv);
497 build_path_cstr(ienv);
499 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
500 lpp_set_bound(ienv->lp, lower_bound);
503 static void ilp2_apply(ilp_env_t *ienv)
505 local_env_t *lenv = ienv->env;
508 /* first check if there was sth. to optimize */
509 if (lenv->first_x_var >= 0) {
510 int count = lenv->last_x_var - lenv->first_x_var + 1;
511 double *sol = XMALLOCN(double, count);
512 lpp_sol_state_t state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
514 if (state != lpp_optimal) {
515 printf("WARNING %s: Solution state is not 'optimal': %d\n",
516 ienv->co->name, (int)state);
517 if (state < lpp_feasible) {
518 panic("Copy coalescing solution not feasible!");
522 for (i=0; i<count; ++i) {
526 if (sol[i] > 1-EPSILON) { /* split variable name into components */
527 lpp_get_var_name(ienv->lp, lenv->first_x_var+i, var_name, sizeof(var_name));
529 if (sscanf(var_name, "x_%d_%d", &nodenr, &color) == 2) {
530 ir_node *irn = pmap_get(lenv->nr_2_irn, INT_TO_PTR(nodenr));
531 assert(irn && "This node number must be present in the map");
533 set_irn_col(ienv->co, irn, color);
535 assert(0 && "This should be a x-var");
543 /* TODO adapt to multiple possible ILPs */
544 copystat_add_ilp_time((int)(1000.0*lpp_get_sol_time(pi->curr_lp))); //now we have ms
545 copystat_add_ilp_vars(lpp_get_var_count(pi->curr_lp));
546 copystat_add_ilp_csts(lpp_get_cst_count(pi->curr_lp));
547 copystat_add_ilp_iter(lpp_get_iter_cnt(pi->curr_lp));
552 * Solves the problem using mixed integer programming
553 * @returns 1 iff solution state was optimal
554 * Uses the OU and the GRAPH data structure
555 * Dependency of the OU structure can be removed
557 static int co_solve_ilp2(copy_opt_t *co)
559 lpp_sol_state_t sol_state;
563 ASSERT_OU_AVAIL(co); //See build_clique_st
568 my.nr_2_irn = pmap_create();
569 FIRM_DBG_REGISTER(my.dbg, "firm.be.coilp2");
571 my.normal_colors = bitset_alloca(arch_register_class_n_regs(co->cls));
572 bitset_clear_all(my.normal_colors);
573 be_put_allocatable_regs(co->irg, co->cls, my.normal_colors);
574 my.n_colors = bitset_popcount(my.normal_colors);
576 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
578 sol_state = ilp_go(ienv);
580 pmap_destroy(my.nr_2_irn);
583 return sol_state == lpp_optimal;
586 BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)
587 void be_init_copyilp2(void)
589 static co_algo_info copyheur = {
593 be_register_copyopt("ilp", ©heur);