2 * This file is part of libFirm.
3 * Copyright (C) 2012 University of Karlsruhe.
8 * @brief ILP based copy minimization.
12 * ILP formalization using G=(V, E, Q):
13 * - 2 class of variables: coloring vars x_ic and equal color vars y_ij
15 * - Clique-star constraints
18 * \min \sum_{ (i,j) \in Q } w_ij y_ij
20 * \sum_c x_nc = 1 n \in N, c \in C
22 * x_nc = 0 n \in N, c \not\in C(n)
24 * \sum x_nc <= 1 x_nc \in Clique \in AllCliques, c \in C
26 * \sum_{e \in p} y_e >= 1 p \in P path constraints
28 * \sum_{e \in cs} y_e >= |cs| - 1 cs \in CP clique-star constraints
30 * x_nc, y_ij \in N, w_ij \in R^+
35 #include "beintlive_t.h"
39 #include "raw_bitset.h"
44 #include "becopyilp_t.h"
49 DEBUG_ONLY(static firm_dbg_module_t *dbg;)
51 typedef struct local_env_t {
54 const unsigned *allocatable_colors;
57 static unsigned check_alignment_constraints(ir_node *node)
59 const arch_register_req_t *req = arch_get_irn_register_req(node);
60 // For larger than 1 variables, support only aligned constraints
61 assert((arch_register_req_is(req, aligned) || req->width == 1) && "Unaligned large (width > 1) variables not supported");
62 return arch_register_req_is(req, aligned) && req->width > 1;
65 static void make_color_var_name(char *buf, size_t buf_size,
66 const ir_node *node, unsigned color)
68 unsigned node_idx = get_irn_idx(node);
69 snprintf(buf, buf_size, "x_%u_%u", node_idx, color);
72 static void build_coloring_cstr(ilp_env_t *ienv)
74 local_env_t *lenv = (local_env_t*)ienv->env;
75 be_ifg_t *ifg = ienv->co->cenv->ifg;
76 unsigned n_regs = arch_register_class_n_regs(ienv->co->cls);
77 const unsigned *allocatable_colors = lenv->allocatable_colors;
80 unsigned *const colors = rbitset_alloca(n_regs);
81 be_ifg_foreach_node(ifg, irn) {
82 const arch_register_req_t *req;
85 unsigned curr_node_color;
86 unsigned has_alignment_cstr;
88 if (sr_is_removed(ienv, irn))
91 has_alignment_cstr = check_alignment_constraints(irn);
93 req = arch_get_irn_register_req(irn);
95 /* get assignable colors */
96 if (arch_register_req_is(req, limited)) {
97 rbitset_copy(colors, req->limited, n_regs);
99 rbitset_copy(colors, allocatable_colors, n_regs);
102 /* add the coloring constraint */
103 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 1.0);
105 curr_node_color = get_irn_col(irn);
106 for (col = 0; col < n_regs; ++col) {
109 if (!rbitset_is_set(colors, col)
110 || (has_alignment_cstr && ((col % req->width) != 0)))
113 make_color_var_name(buf, sizeof(buf), irn, col);
114 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
115 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
117 val = (col == curr_node_color) ? 1.0 : 0.0;
118 lpp_set_start_value(ienv->lp, var_idx, val);
120 lenv->last_x_var = var_idx;
121 if (lenv->first_x_var == -1)
122 lenv->first_x_var = var_idx;
125 /* add register constraint constraints */
126 for (col = 0; col < n_regs; ++col) {
129 if (rbitset_is_set(colors, col)
130 // for aligned variable, we set the unaligned part to 0
131 && (!has_alignment_cstr || ((col % req->width) == 0)))
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 = (local_env_t*)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, 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];
183 unsigned aligment_offset = 0;
185 if (sr_is_removed(ienv, irn))
188 // Use the first part of the large registers for all
189 // interference, since it is the only colorable one.
190 if (check_alignment_constraints(irn)) {
191 const arch_register_req_t *req
192 = arch_get_irn_register_req(irn);
193 aligment_offset = col % req->width;
196 make_color_var_name(buf, sizeof(buf), irn,
197 col - aligment_offset);
198 var_idx = lpp_get_var_idx(lpp, buf);
199 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
205 static void make_affinity_var_name(char *buf, size_t buf_size,
206 const ir_node *node1, const ir_node *node2)
208 unsigned n1 = get_irn_idx(node1);
209 unsigned n2 = get_irn_idx(node2);
211 snprintf(buf, buf_size, "y_%u_%u", n1, n2);
213 snprintf(buf, buf_size, "y_%u_%u", n2, n1);
219 * TODO: Remove the dependency of the opt-units data structure
220 * by walking over all affinity edges. Graph structure
221 * does not provide this walker, yet.
223 static void build_affinity_cstr(ilp_env_t *ienv)
225 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
227 /* for all optimization units */
228 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
229 ir_node *root = curr->nodes[0];
230 unsigned root_col = get_irn_col(root);
233 for (i = 1; i < curr->node_count; ++i) {
234 ir_node *arg = curr->nodes[i];
235 unsigned arg_col = get_irn_col(arg);
241 /* add a new affinity variable */
242 make_affinity_var_name(buf, sizeof(buf), arg, root);
243 y_idx = lpp_add_var(ienv->lp, buf, lpp_binary, curr->costs[i]);
244 val = (root_col == arg_col) ? 0.0 : 1.0;
245 lpp_set_start_value(ienv->lp, y_idx, val);
247 /* add constraints relating the affinity var to the color vars */
248 for (col=0; col<n_colors; ++col) {
249 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less_equal, 0.0);
253 make_color_var_name(buf, sizeof(buf), root, col);
254 root_idx = lpp_get_var_idx(ienv->lp, buf);
255 make_color_var_name(buf, sizeof(buf), arg, col);
256 arg_idx = lpp_get_var_idx(ienv->lp, buf);
258 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
259 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
260 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
267 * Helping stuff for build_clique_star_cstr
269 typedef struct edge_t {
274 static int compare_edge_t(const void *k1, const void *k2, size_t size)
276 const edge_t *e1 = (const edge_t*)k1;
277 const edge_t *e2 = (const edge_t*)k2;
280 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
283 #define HASH_EDGE(e) (hash_irn((e)->n1) ^ hash_irn((e)->n2))
285 static inline edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
289 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
297 return set_insert(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
300 static inline edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2)
304 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
311 return set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
314 static inline void remove_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
318 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
325 e = set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
333 #define pset_foreach(pset, irn) foreach_pset((pset), ir_node, (irn))
336 * Search for an interference clique and an external node
337 * with affinity edges to all nodes of the clique.
338 * At most 1 node of the clique can be colored equally with the external node.
340 static void build_clique_star_cstr(ilp_env_t *ienv)
342 /* for each node with affinity edges */
343 be_lv_t *const lv = be_get_irg_liveness(ienv->co->irg);
344 co_gs_foreach_aff_node(ienv->co, aff) {
346 const ir_node *center = aff->irn;
352 if (arch_irn_is_ignore(aff->irn))
356 edges = new_set(compare_edge_t, 8);
358 /* get all affinity neighbours */
360 co_gs_foreach_neighb(aff, nbr) {
361 if (!arch_irn_is_ignore(nbr->irn)) {
362 obstack_ptr_grow(&ob, nbr->irn);
366 nodes = (ir_node**)obstack_finish(&ob);
368 /* get all interference edges between these */
370 for (i=0; i<n_nodes; ++i) {
371 for (o=0; o<i; ++o) {
372 if (be_values_interfere(lv, nodes[i], nodes[o]))
373 add_edge(edges, nodes[i], nodes[o], &n_edges);
377 /* cover all these interference edges with maximal cliques */
380 pset *clique = pset_new_ptr(8);
383 /* get 2 starting nodes to form a clique */
384 for (e = set_first(edge_t, edges); !e->n1; e = set_next(edge_t, edges)) {}
386 /* we could be stepped out of the loop before the set iterated to the end */
389 pset_insert_ptr(clique, e->n1);
390 pset_insert_ptr(clique, e->n2);
391 remove_edge(edges, e->n1, e->n2, &n_edges);
393 /* while the clique is growing */
397 /* search for a candidate to extend the clique */
398 for (i=0; i<n_nodes; ++i) {
399 ir_node *cand = nodes[i];
402 /* if its already in the clique try the next */
403 if (pset_find_ptr(clique, cand))
406 /* are there all necessary interferences? */
408 pset_foreach(clique, member) {
409 if (!find_edge(edges, cand, member)) {
416 /* now we know if we have a clique extender */
418 /* first remove all covered edges */
419 pset_foreach(clique, member)
420 remove_edge(edges, cand, member, &n_edges);
422 /* insert into clique */
423 pset_insert_ptr(clique, cand);
430 /* now the clique is maximal. Finally add the constraint */
436 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, pset_count(clique)-1);
438 pset_foreach(clique, member) {
439 make_affinity_var_name(buf, sizeof(buf), center, member);
440 var_idx = lpp_get_var_idx(ienv->lp, buf);
441 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
449 obstack_free(&ob, NULL);
453 static void extend_path(ilp_env_t *ienv, pdeq *path, const ir_node *irn)
457 affinity_node_t *aff;
459 /* do not walk backwards or in circles */
460 if (pdeq_contains(path, irn))
463 if (arch_irn_is_ignore(irn))
466 /* insert the new irn */
467 pdeq_putr(path, irn);
469 /* check for forbidden interferences */
470 len = pdeq_len(path);
471 curr_path = ALLOCAN(ir_node*, len);
472 pdeq_copyl(path, (const void **)curr_path);
474 be_lv_t *const lv = be_get_irg_liveness(ienv->co->irg);
475 for (i=1; i<len; ++i) {
476 if (be_values_interfere(lv, irn, curr_path[i]))
480 /* check for terminating interference */
481 if (be_values_interfere(lv, irn, curr_path[0])) {
482 /* One node is not a path. */
483 /* And a path of length 2 is covered by a clique star constraint. */
485 /* finally build the constraint */
486 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, 1.0);
487 for (i=1; i<len; ++i) {
491 make_affinity_var_name(buf, sizeof(buf), curr_path[i-1], curr_path[i]);
492 var_idx = lpp_get_var_idx(ienv->lp, buf);
493 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
497 /* this path cannot be extended anymore */
501 /* recursively extend the path */
502 aff = get_affinity_info(ienv->co, irn);
503 co_gs_foreach_neighb(aff, nbr) {
504 extend_path(ienv, path, nbr->irn);
513 * Search a path of affinity edges, whose ends are connected
514 * by an interference edge and there are no other interference
516 * Then at least one of these affinity edges must break.
518 static void build_path_cstr(ilp_env_t *ienv)
520 /* for each node with affinity edges */
521 co_gs_foreach_aff_node(ienv->co, aff_info) {
522 pdeq *path = new_pdeq();
524 extend_path(ienv, path, aff_info->irn);
530 static void ilp2_build(ilp_env_t *ienv)
534 ienv->lp = lpp_new("copyilp", lpp_minimize);
535 build_coloring_cstr(ienv);
536 build_interference_cstr(ienv);
537 build_affinity_cstr(ienv);
538 build_clique_star_cstr(ienv);
539 build_path_cstr(ienv);
541 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
542 lpp_set_bound(ienv->lp, lower_bound);
545 static void ilp2_apply(ilp_env_t *ienv)
547 local_env_t *lenv = (local_env_t*)ienv->env;
548 ir_graph *irg = ienv->co->irg;
550 /* first check if there was sth. to optimize */
551 if (lenv->first_x_var >= 0) {
552 int count = lenv->last_x_var - lenv->first_x_var + 1;
553 double *sol = XMALLOCN(double, count);
554 lpp_sol_state_t state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
557 if (state != lpp_optimal) {
558 ir_printf("WARNING: Solution state of %F register class %s is not 'optimal': %d\n", ienv->co->irg, ienv->co->cls->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 n_regs = arch_register_class_n_regs(co->cls);
602 lpp_sol_state_t sol_state;
606 ASSERT_OU_AVAIL(co); //See build_clique_st
611 FIRM_DBG_REGISTER(dbg, "firm.be.coilp2");
613 unsigned *const allocatable_colors = rbitset_alloca(n_regs);
614 be_set_allocatable_regs(co->irg, co->cls, allocatable_colors);
615 my.allocatable_colors = allocatable_colors;
617 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
619 sol_state = ilp_go(ienv);
623 return sol_state == lpp_optimal;
626 BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)
627 void be_init_copyilp2(void)
629 static co_algo_info copyheur = {
633 be_register_copyopt("ilp", ©heur);