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^+
37 #include "raw_bitset.h"
42 #include "becopyilp_t.h"
47 DEBUG_ONLY(static firm_dbg_module_t *dbg;)
49 typedef struct local_env_t {
52 const unsigned *allocatable_colors;
55 static unsigned check_alignment_constraints(ir_node *node)
57 const arch_register_req_t *req = arch_get_irn_register_req(node);
58 // For larger than 1 variables, support only aligned constraints
59 assert((arch_register_req_is(req, aligned) || req->width == 1) && "Unaligned large (width > 1) variables not supported");
60 return arch_register_req_is(req, aligned) && req->width > 1;
63 static void make_color_var_name(char *buf, size_t buf_size,
64 const ir_node *node, unsigned color)
66 unsigned node_idx = get_irn_idx(node);
67 snprintf(buf, buf_size, "x_%u_%u", node_idx, color);
70 static void build_coloring_cstr(ilp_env_t *ienv)
72 local_env_t *lenv = (local_env_t*)ienv->env;
73 be_ifg_t *ifg = ienv->co->cenv->ifg;
74 unsigned n_regs = arch_register_class_n_regs(ienv->co->cls);
75 const unsigned *allocatable_colors = lenv->allocatable_colors;
79 unsigned *const colors = rbitset_alloca(n_regs);
80 be_ifg_foreach_node(ifg, &iter, irn) {
81 const arch_register_req_t *req;
84 unsigned curr_node_color;
85 unsigned has_alignment_cstr;
87 if (sr_is_removed(ienv->sr, irn))
90 has_alignment_cstr = check_alignment_constraints(irn);
92 req = arch_get_irn_register_req(irn);
94 /* get assignable colors */
95 if (arch_register_req_is(req, limited)) {
96 rbitset_copy(colors, req->limited, n_regs);
98 rbitset_copy(colors, allocatable_colors, n_regs);
101 /* add the coloring constraint */
102 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 1.0);
104 curr_node_color = get_irn_col(irn);
105 for (col = 0; col < n_regs; ++col) {
108 if (!rbitset_is_set(colors, col)
109 || (has_alignment_cstr && ((col % req->width) != 0)))
112 make_color_var_name(buf, sizeof(buf), irn, col);
113 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
114 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
116 val = (col == curr_node_color) ? 1.0 : 0.0;
117 lpp_set_start_value(ienv->lp, var_idx, val);
119 lenv->last_x_var = var_idx;
120 if (lenv->first_x_var == -1)
121 lenv->first_x_var = var_idx;
124 /* add register constraint constraints */
125 for (col = 0; col < n_regs; ++col) {
128 if (rbitset_is_set(colors, col)
129 // for aligned variable, we set the unaligned part to 0
130 && (!has_alignment_cstr || ((col % req->width) == 0)))
133 make_color_var_name(buf, sizeof(buf), irn, col);
134 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 0.0);
135 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
136 lpp_set_start_value(ienv->lp, var_idx, 0.0);
137 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
139 lenv->last_x_var = var_idx;
144 static void build_interference_cstr(ilp_env_t *ienv)
146 lpp_t *lpp = ienv->lp;
147 local_env_t *lenv = (local_env_t*)ienv->env;
148 be_ifg_t *ifg = ienv->co->cenv->ifg;
149 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
150 ir_node **clique = ALLOCAN(ir_node*, n_colors);
151 const unsigned *allocatable_colors = lenv->allocatable_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) {
172 if (!rbitset_is_set(allocatable_colors, col))
175 cst_idx = lpp_add_cst(lpp, NULL, lpp_less_equal, 1.0);
177 /* for each member of this clique */
178 for (i=0; i<size; ++i) {
179 ir_node *irn = clique[i];
182 unsigned aligment_offset = 0;
184 if (sr_is_removed(ienv->sr, irn))
187 // Use the first part of the large registers for all
188 // interference, since it is the only colorable one.
189 if (check_alignment_constraints(irn)) {
190 const arch_register_req_t *req
191 = arch_get_irn_register_req(irn);
192 aligment_offset = col % req->width;
195 make_color_var_name(buf, sizeof(buf), irn,
196 col - aligment_offset);
197 var_idx = lpp_get_var_idx(lpp, buf);
198 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
204 static void make_affinity_var_name(char *buf, size_t buf_size,
205 const ir_node *node1, const ir_node *node2)
207 unsigned n1 = get_irn_idx(node1);
208 unsigned n2 = get_irn_idx(node2);
210 snprintf(buf, buf_size, "y_%u_%u", n1, n2);
212 snprintf(buf, buf_size, "y_%u_%u", n2, n1);
218 * TODO: Remove the dependency of the opt-units data structure
219 * by walking over all affinity edges. Graph structure
220 * does not provide this walker, yet.
222 static void build_affinity_cstr(ilp_env_t *ienv)
224 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
226 /* for all optimization units */
227 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
228 ir_node *root = curr->nodes[0];
229 unsigned root_col = get_irn_col(root);
232 for (i = 1; i < curr->node_count; ++i) {
233 ir_node *arg = curr->nodes[i];
234 unsigned arg_col = get_irn_col(arg);
240 /* add a new affinity variable */
241 make_affinity_var_name(buf, sizeof(buf), arg, root);
242 y_idx = lpp_add_var(ienv->lp, buf, lpp_binary, curr->costs[i]);
243 val = (root_col == arg_col) ? 0.0 : 1.0;
244 lpp_set_start_value(ienv->lp, y_idx, val);
246 /* add constraints relating the affinity var to the color vars */
247 for (col=0; col<n_colors; ++col) {
248 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less_equal, 0.0);
252 make_color_var_name(buf, sizeof(buf), root, col);
253 root_idx = lpp_get_var_idx(ienv->lp, buf);
254 make_color_var_name(buf, sizeof(buf), arg, col);
255 arg_idx = lpp_get_var_idx(ienv->lp, buf);
257 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
258 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
259 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
266 * Helping stuff for build_clique_star_cstr
268 typedef struct edge_t {
273 static int compare_edge_t(const void *k1, const void *k2, size_t size)
275 const edge_t *e1 = (const edge_t*)k1;
276 const edge_t *e2 = (const edge_t*)k2;
279 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
282 #define HASH_EDGE(e) (hash_irn((e)->n1) ^ hash_irn((e)->n2))
284 static inline edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
288 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
296 return set_insert(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
299 static inline edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2)
303 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
310 return set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
313 static inline void remove_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
317 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
324 e = set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
332 #define pset_foreach(pset, irn) foreach_pset((pset), ir_node, (irn))
335 * Search for an interference clique and an external node
336 * with affinity edges to all nodes of the clique.
337 * At most 1 node of the clique can be colored equally with the external node.
339 static void build_clique_star_cstr(ilp_env_t *ienv)
341 /* for each node with affinity edges */
342 co_gs_foreach_aff_node(ienv->co, aff) {
344 const ir_node *center = aff->irn;
350 if (arch_irn_is_ignore(aff->irn))
354 edges = new_set(compare_edge_t, 8);
356 /* get all affinity neighbours */
358 co_gs_foreach_neighb(aff, nbr) {
359 if (!arch_irn_is_ignore(nbr->irn)) {
360 obstack_ptr_grow(&ob, nbr->irn);
364 nodes = (ir_node**)obstack_finish(&ob);
366 /* get all interference edges between these */
368 for (i=0; i<n_nodes; ++i) {
369 for (o=0; o<i; ++o) {
370 if (be_ifg_connected(ienv->co->cenv->ifg, nodes[i], nodes[o]))
371 add_edge(edges, nodes[i], nodes[o], &n_edges);
375 /* cover all these interference edges with maximal cliques */
378 pset *clique = pset_new_ptr(8);
381 /* get 2 starting nodes to form a clique */
382 for (e = set_first(edge_t, edges); !e->n1; e = set_next(edge_t, edges)) {}
384 /* we could be stepped out of the loop before the set iterated to the end */
387 pset_insert_ptr(clique, e->n1);
388 pset_insert_ptr(clique, e->n2);
389 remove_edge(edges, e->n1, e->n2, &n_edges);
391 /* while the clique is growing */
395 /* search for a candidate to extend the clique */
396 for (i=0; i<n_nodes; ++i) {
397 ir_node *cand = nodes[i];
400 /* if its already in the clique try the next */
401 if (pset_find_ptr(clique, cand))
404 /* are there all necessary interferences? */
406 pset_foreach(clique, member) {
407 if (!find_edge(edges, cand, member)) {
414 /* now we know if we have a clique extender */
416 /* first remove all covered edges */
417 pset_foreach(clique, member)
418 remove_edge(edges, cand, member, &n_edges);
420 /* insert into clique */
421 pset_insert_ptr(clique, cand);
428 /* now the clique is maximal. Finally add the constraint */
434 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, pset_count(clique)-1);
436 pset_foreach(clique, member) {
437 make_affinity_var_name(buf, sizeof(buf), center, member);
438 var_idx = lpp_get_var_idx(ienv->lp, buf);
439 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
447 obstack_free(&ob, NULL);
451 static void extend_path(ilp_env_t *ienv, pdeq *path, const ir_node *irn)
453 be_ifg_t *ifg = ienv->co->cenv->ifg;
456 affinity_node_t *aff;
458 /* do not walk backwards or in circles */
459 if (pdeq_contains(path, irn))
462 if (arch_irn_is_ignore(irn))
465 /* insert the new irn */
466 pdeq_putr(path, irn);
468 /* check for forbidden interferences */
469 len = pdeq_len(path);
470 curr_path = ALLOCAN(ir_node*, len);
471 pdeq_copyl(path, (const void **)curr_path);
473 for (i=1; i<len; ++i) {
474 if (be_ifg_connected(ifg, irn, curr_path[i]))
478 /* check for terminating interference */
479 if (be_ifg_connected(ifg, irn, curr_path[0])) {
480 /* One node is not a path. */
481 /* And a path of length 2 is covered by a clique star constraint. */
483 /* finally build the constraint */
484 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, 1.0);
485 for (i=1; i<len; ++i) {
489 make_affinity_var_name(buf, sizeof(buf), curr_path[i-1], curr_path[i]);
490 var_idx = lpp_get_var_idx(ienv->lp, buf);
491 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
495 /* this path cannot be extended anymore */
499 /* recursively extend the path */
500 aff = get_affinity_info(ienv->co, irn);
501 co_gs_foreach_neighb(aff, nbr) {
502 extend_path(ienv, path, nbr->irn);
511 * Search a path of affinity edges, whose ends are connected
512 * by an interference edge and there are no other interference
514 * Then at least one of these affinity edges must break.
516 static void build_path_cstr(ilp_env_t *ienv)
518 /* for each node with affinity edges */
519 co_gs_foreach_aff_node(ienv->co, aff_info) {
520 pdeq *path = new_pdeq();
522 extend_path(ienv, path, aff_info->irn);
528 static void ilp2_build(ilp_env_t *ienv)
532 ienv->lp = lpp_new(ienv->co->name, lpp_minimize);
533 build_coloring_cstr(ienv);
534 build_interference_cstr(ienv);
535 build_affinity_cstr(ienv);
536 build_clique_star_cstr(ienv);
537 build_path_cstr(ienv);
539 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
540 lpp_set_bound(ienv->lp, lower_bound);
543 static void ilp2_apply(ilp_env_t *ienv)
545 local_env_t *lenv = (local_env_t*)ienv->env;
546 ir_graph *irg = ienv->co->irg;
548 /* first check if there was sth. to optimize */
549 if (lenv->first_x_var >= 0) {
550 int count = lenv->last_x_var - lenv->first_x_var + 1;
551 double *sol = XMALLOCN(double, count);
552 lpp_sol_state_t state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
555 if (state != lpp_optimal) {
556 printf("WARNING %s: Solution state is not 'optimal': %d\n",
557 ienv->co->name, (int)state);
558 if (state < lpp_feasible) {
559 panic("Copy coalescing solution not feasible!");
563 for (i=0; i<count; ++i) {
567 if (sol[i] <= 1-EPSILON)
569 /* split variable name into components */
570 lpp_get_var_name(ienv->lp, lenv->first_x_var+i, var_name, sizeof(var_name));
572 if (sscanf(var_name, "x_%u_%u", &nodenr, &color) == 2) {
573 ir_node *irn = get_idx_irn(irg, nodenr);
574 set_irn_col(ienv->co->cls, irn, color);
576 panic("This should be a x-var");
584 /* TODO adapt to multiple possible ILPs */
585 copystat_add_ilp_time((int)(1000.0*lpp_get_sol_time(pi->curr_lp))); //now we have ms
586 copystat_add_ilp_vars(lpp_get_var_count(pi->curr_lp));
587 copystat_add_ilp_csts(lpp_get_cst_count(pi->curr_lp));
588 copystat_add_ilp_iter(lpp_get_iter_cnt(pi->curr_lp));
593 * Solves the problem using mixed integer programming
594 * @returns 1 iff solution state was optimal
595 * Uses the OU and the GRAPH data structure
596 * Dependency of the OU structure can be removed
598 static int co_solve_ilp2(copy_opt_t *co)
600 unsigned n_regs = arch_register_class_n_regs(co->cls);
601 lpp_sol_state_t sol_state;
605 ASSERT_OU_AVAIL(co); //See build_clique_st
610 FIRM_DBG_REGISTER(dbg, "firm.be.coilp2");
612 unsigned *const allocatable_colors = rbitset_alloca(n_regs);
613 be_set_allocatable_regs(co->irg, co->cls, allocatable_colors);
614 my.allocatable_colors = allocatable_colors;
616 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
618 sol_state = ilp_go(ienv);
622 return sol_state == lpp_optimal;
625 BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)
626 void be_init_copyilp2(void)
628 static co_algo_info copyheur = {
632 be_register_copyopt("ilp", ©heur);