4 * Copyright: (c) Universitaet Karlsruhe
5 * Licence: This file protected by GPL - GNU GENERAL PUBLIC LICENSE.
8 * ILP formalization using G=(V, E, Q):
9 * - 2 class of variables: coloring vars x_ic and equal color vars y_ij
11 * - Clique-star constraints
14 * \min \sum_{ (i,j) \in Q } w_ij y_ij
16 * \sum_c x_nc = 1 n \in N, c \in C
18 * x_nc = 0 n \in N, c \not\in C(n)
20 * \sum x_nc <= 1 x_nc \in Clique \in AllCliques, c \in C
22 * \sum_{e \in p} y_e >= 1 p \in P path constraints
24 * \sum_{e \in cs} y_e >= |cs| - 1 cs \in CP clique-star constraints
26 * x_nc, y_ij \in N, w_ij \in R^+
31 #endif /* HAVE_CONFIG_H */
40 #include "becopyilp_t.h"
42 #include "besched_t.h"
46 typedef struct _local_env_t {
47 firm_dbg_module_t *dbg;
49 int first_x_var, last_x_var;
53 static void build_coloring_cstr(ilp_env_t *ienv) {
54 be_ifg_t *ifg = ienv->co->cenv->ifg;
55 void *iter = be_ifg_nodes_iter_alloca(ifg);
60 colors = bitset_alloca(arch_register_class_n_regs(ienv->co->cls));
62 be_ifg_foreach_node(ifg, iter, irn)
63 if (!sr_is_removed(ienv->sr, irn)) {
65 arch_register_req_t req;
66 int curr_node_color = get_irn_col(ienv->co, irn);
67 int node_nr = (int)get_irn_node_nr(irn);
68 local_env_t *lenv = ienv->env;
70 pmap_insert(lenv->nr_2_irn, INT_TO_PTR(node_nr), irn);
72 arch_get_register_req(ienv->co->aenv, &req, irn, -1);
74 /* get assignable colors */
75 if (arch_register_req_is(&req, limited))
76 req.limited(req.limited_env, colors);
78 arch_put_non_ignore_regs(ienv->co->aenv, req.cls, colors);
80 /* add the coloring constraint */
81 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 1.0);
83 bitset_foreach(colors, col) {
84 int var_idx = lpp_add_var(ienv->lp, name_cdd(buf, 'x', node_nr, col), lpp_binary, 0.0);
85 lpp_set_start_value(ienv->lp, var_idx, (col == curr_node_color) ? 1.0 : 0.0);
86 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
88 lenv->last_x_var = var_idx;
89 if (lenv->first_x_var == -1)
90 lenv->first_x_var = var_idx;
93 /* add register constraint constraints */
94 bitset_foreach_clear(colors, col) {
95 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 0.0);
96 int var_idx = lpp_add_var(ienv->lp, name_cdd(buf, 'x', node_nr, col), lpp_binary, 0.0);
97 lpp_set_start_value(ienv->lp, var_idx, 0.0);
98 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
100 lenv->last_x_var = var_idx;
105 static void build_interference_cstr(ilp_env_t *ienv) {
106 lpp_t *lpp = ienv->lp;
107 be_ifg_t *ifg = ienv->co->cenv->ifg;
108 int n_colors = arch_register_class_n_regs(ienv->co->cls);
111 void *iter = be_ifg_cliques_iter_alloca(ifg);
112 ir_node **clique = alloca(sizeof(*clique) * n_colors);
117 /* for each maximal clique */
118 be_ifg_foreach_clique(ifg, iter, clique, &size) {
121 for (i=0; i<size; ++i)
122 if (!sr_is_removed(ienv->sr, clique[i]))
129 for (col=0; col<n_colors; ++col) {
130 int cst_idx = lpp_add_cst(lpp, NULL, lpp_less, 1.0);
132 /* for each member of this clique */
133 for (i=0; i<size; ++i) {
134 ir_node *irn = clique[i];
136 if (!sr_is_removed(ienv->sr, irn)) {
137 int var_idx = lpp_get_var_idx(lpp, name_cdd(buf, 'x', (int)get_irn_node_nr(irn), col));
138 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
147 * TODO: Remove the dependency of the opt-units data structure
148 * by walking over all affinity edges. Graph structure
149 * does not provide this walker, yet.
151 static void build_affinity_cstr(ilp_env_t *ienv) {
153 int n_colors = arch_register_class_n_regs(ienv->co->cls);
155 /* for all optimization units */
156 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
158 int root_nr, arg_nr, i, col, y_idx, root_idx, arg_idx;
160 int root_col, arg_col;
162 root = curr->nodes[0];
163 root_nr = (int) get_irn_node_nr(root);
164 root_col = get_irn_col(ienv->co, root);
166 for (i = 1; i < curr->node_count; ++i) {
167 arg = curr->nodes[i];
168 arg_nr = (int) get_irn_node_nr(arg);
169 arg_col = get_irn_col(ienv->co, arg);
171 /* add a new affinity variable */
172 y_idx = lpp_add_var(ienv->lp, name_cdd_sorted(buf, 'y', root_nr, arg_nr), lpp_binary, curr->costs[i]);
173 lpp_set_start_value(ienv->lp, y_idx, (root_col==arg_col) ? 0.0 : 1.0);
175 /* add constraints relating the affinity var to the color vars */
176 for (col=0; col<n_colors; ++col) {
177 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less, 0.0);
178 root_idx = lpp_get_var_idx(ienv->lp, name_cdd(buf, 'x', root_nr, col));
179 arg_idx = lpp_get_var_idx(ienv->lp, name_cdd(buf, 'x', arg_nr, col));
181 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
182 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
183 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
190 * Helping stuff for build_clique_star_cstr
192 typedef struct _edge_t {
196 static int compare_edge_t(const void *k1, const void *k2, size_t size) {
197 const edge_t *e1 = k1;
198 const edge_t *e2 = k2;
200 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
203 #define HASH_EDGE(e) (HASH_PTR((e)->n1) ^ HASH_PTR((e)->n2))
205 static INLINE edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, int *counter) {
208 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
216 return set_insert(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
219 static INLINE edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2) {
222 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
229 return set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
232 static INLINE void remove_edge(set *edges, ir_node *n1, ir_node *n2, int *counter) {
235 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
242 e = set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
250 #define pset_foreach(pset, irn) for(irn=pset_first(pset); irn; irn=pset_next(pset))
253 * Search for an interference clique and an external node
254 * with affinity edges to all nodes of the clique.
255 * At most 1 node of the clique can be colored equally with the external node.
257 static void build_clique_star_cstr(ilp_env_t *ienv) {
258 affinity_node_t *aff;
260 /* for each node with affinity edges */
261 co_gs_foreach_aff_node(ienv->co, aff) {
264 ir_node *center = aff->irn;
267 int i, o, n_nodes, n_edges;
270 edges = new_set(compare_edge_t, 8);
272 /* get all affinity neighbours */
274 co_gs_foreach_neighb(aff, nbr) {
275 obstack_ptr_grow(&ob, nbr->irn);
278 nodes = obstack_finish(&ob);
280 /* get all interference edges between these */
282 for (i=0; i<n_nodes; ++i)
284 if (be_ifg_connected(ienv->co->cenv->ifg, nodes[i], nodes[o]))
285 add_edge(edges, nodes[i], nodes[o], &n_edges);
287 /* cover all these interference edges with maximal cliques */
290 pset *clique = pset_new_ptr(8);
293 /* get 2 starting nodes to form a clique */
294 for (e=set_first(edges); !e->n1; e=set_next(edges))
297 pset_insert_ptr(clique, e->n1);
298 pset_insert_ptr(clique, e->n2);
299 remove_edge(edges, e->n1, e->n2, &n_edges);
301 /* while the clique is growing */
305 /* search for a candidate to extend the clique */
306 for (i=0; i<n_nodes; ++i) {
307 ir_node *member, *cand = nodes[i];
310 /* if its already in the clique try the next */
311 if (pset_find_ptr(clique, cand))
314 /* are there all necessary interferences? */
316 pset_foreach(clique, member) {
317 if (!find_edge(edges, cand, member)) {
324 /* now we know if we have a clique extender */
326 /* first remove all covered edges */
327 pset_foreach(clique, member)
328 remove_edge(edges, cand, member, &n_edges);
330 /* insert into clique */
331 pset_insert_ptr(clique, cand);
338 /* now the clique is maximal. Finally add the constraint */
341 int var_idx, cst_idx, center_nr, member_nr;
344 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater, pset_count(clique)-1);
345 center_nr = get_irn_node_nr(center);
347 pset_foreach(clique, member) {
348 member_nr = get_irn_node_nr(member);
349 var_idx = lpp_get_var_idx(ienv->lp, name_cdd_sorted(buf, 'y', center_nr, member_nr));
350 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
358 obstack_free(&ob, NULL);
363 static void extend_path(ilp_env_t *ienv, pdeq *path, ir_node *irn) {
364 be_ifg_t *ifg = ienv->co->cenv->ifg;
367 affinity_node_t *aff;
370 /* do not walk backwards or in circles */
371 if (pdeq_contains(path, irn))
374 /* insert the new irn */
375 pdeq_putr(path, irn);
379 /* check for forbidden interferences */
380 len = pdeq_len(path);
381 curr_path = alloca(len * sizeof(*curr_path));
382 pdeq_copyl(path, (const void **)curr_path);
384 for (i=1; i<len; ++i)
385 if (be_ifg_connected(ifg, irn, curr_path[i]))
390 /* check for terminating interference */
391 if (be_ifg_connected(ifg, irn, curr_path[0])) {
393 /* One node is not a path. */
394 /* And a path of length 2 is covered by a clique star constraint. */
396 /* finally build the constraint */
397 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater, 1.0);
398 for (i=1; i<len; ++i) {
400 int nr_1 = get_irn_node_nr(curr_path[i-1]);
401 int nr_2 = get_irn_node_nr(curr_path[i]);
402 int var_idx = lpp_get_var_idx(ienv->lp, name_cdd_sorted(buf, 'y', nr_1, nr_2));
403 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
407 /* this path cannot be extended anymore */
413 /* recursively extend the path */
414 aff = get_affinity_info(ienv->co, irn);
415 co_gs_foreach_neighb(aff, nbr)
416 extend_path(ienv, path, nbr->irn);
426 * Search a path of affinity edges, whose ends are connected
427 * by an interference edge and there are no other interference
429 * Then at least one of these affinity edges must break.
431 static void build_path_cstr(ilp_env_t *ienv) {
432 affinity_node_t *aff_info;
434 /* for each node with affinity edges */
435 co_gs_foreach_aff_node(ienv->co, aff_info) {
436 pdeq *path = new_pdeq();
438 extend_path(ienv, path, aff_info->irn);
444 static void ilp2_build(ilp_env_t *ienv) {
445 local_env_t *lenv = ienv->env;
448 ienv->lp = new_lpp(ienv->co->name, lpp_minimize);
449 build_coloring_cstr(ienv);
450 build_interference_cstr(ienv);
451 build_affinity_cstr(ienv);
452 build_clique_star_cstr(ienv);
453 build_path_cstr(ienv);
455 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
456 lpp_set_bound(ienv->lp, lower_bound);
457 lpp_set_time_limit(ienv->lp, lenv->time_limit);
460 static void ilp2_apply(ilp_env_t *ienv) {
461 local_env_t *lenv = ienv->env;
463 lpp_sol_state_t state;
466 /* first check if there was sth. to optimize */
467 if (lenv->first_x_var >= 0) {
469 count = lenv->last_x_var - lenv->first_x_var + 1;
470 sol = xmalloc(count * sizeof(sol[0]));
471 state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
472 if (state != lpp_optimal) {
473 printf("WARNING %s: Solution state is not 'optimal': %d\n", ienv->co->name, state);
474 assert(state >= lpp_feasible && "The solution should at least be feasible!");
477 for (i=0; i<count; ++i) {
481 if (sol[i] > 1-EPSILON) { /* split variable name into components */
482 lpp_get_var_name(ienv->lp, lenv->first_x_var+i, var_name, sizeof(var_name));
484 if (sscanf(var_name, "x_%d_%d", &nodenr, &color) == 2) {
485 ir_node *irn = pmap_get(lenv->nr_2_irn, INT_TO_PTR(nodenr));
486 assert(irn && "This node number must be present in the map");
488 set_irn_col(ienv->co, irn, color);
490 assert(0 && "This should be a x-var");
496 /* TODO adapt to multiple possible ILPs */
497 copystat_add_ilp_time((int)(1000.0*lpp_get_sol_time(pi->curr_lp))); //now we have ms
498 copystat_add_ilp_vars(lpp_get_var_count(pi->curr_lp));
499 copystat_add_ilp_csts(lpp_get_cst_count(pi->curr_lp));
500 copystat_add_ilp_iter(lpp_get_iter_cnt(pi->curr_lp));
504 int co_solve_ilp2(copy_opt_t *co, double time_limit) {
505 lpp_sol_state_t sol_state;
509 ASSERT_OU_AVAIL(co); //See build_clique_st
512 my.time_limit = time_limit;
515 my.nr_2_irn = pmap_create();
516 FIRM_DBG_REGISTER(my.dbg, "ir.be.coilp2");
517 firm_dbg_set_mask(my.dbg, DEBUG_LVL);
519 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
521 sol_state = ilp_go(ienv);
523 pmap_destroy(my.nr_2_irn);
526 return sol_state == lpp_optimal;
531 static void only_that_you_can_compile_without_WITH_ILP_defined(void) {
534 #endif /* WITH_ILP */