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4 * This file is part of libFirm.
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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^+
51 #include "raw_bitset.h"
56 #include "becopyilp_t.h"
61 DEBUG_ONLY(static firm_dbg_module_t *dbg;)
63 typedef struct local_env_t {
66 const unsigned *allocatable_colors;
69 static unsigned check_alignment_constraints(ir_node *node)
71 const arch_register_req_t *req = arch_get_irn_register_req(node);
72 // For larger than 1 variables, support only aligned constraints
73 assert((arch_register_req_is(req, aligned) || req->width == 1) && "Unaligned large (width > 1) variables not supported");
74 return arch_register_req_is(req, aligned) && req->width > 1;
77 static void make_color_var_name(char *buf, size_t buf_size,
78 const ir_node *node, unsigned color)
80 unsigned node_idx = get_irn_idx(node);
81 snprintf(buf, buf_size, "x_%u_%u", node_idx, color);
84 static void build_coloring_cstr(ilp_env_t *ienv)
86 local_env_t *lenv = (local_env_t*)ienv->env;
87 be_ifg_t *ifg = ienv->co->cenv->ifg;
88 unsigned n_regs = arch_register_class_n_regs(ienv->co->cls);
89 const unsigned *allocatable_colors = lenv->allocatable_colors;
93 unsigned *const colors = rbitset_alloca(n_regs);
94 be_ifg_foreach_node(ifg, &iter, irn) {
95 const arch_register_req_t *req;
98 unsigned curr_node_color;
99 unsigned has_alignment_cstr;
101 if (sr_is_removed(ienv->sr, irn))
104 has_alignment_cstr = check_alignment_constraints(irn);
106 req = arch_get_irn_register_req(irn);
108 /* get assignable colors */
109 if (arch_register_req_is(req, limited)) {
110 rbitset_copy(colors, req->limited, n_regs);
112 rbitset_copy(colors, allocatable_colors, n_regs);
115 /* add the coloring constraint */
116 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 1.0);
118 curr_node_color = get_irn_col(irn);
119 for (col = 0; col < n_regs; ++col) {
122 if (!rbitset_is_set(colors, col)
123 || (has_alignment_cstr && ((col % req->width) != 0)))
126 make_color_var_name(buf, sizeof(buf), irn, col);
127 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
128 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
130 val = (col == curr_node_color) ? 1.0 : 0.0;
131 lpp_set_start_value(ienv->lp, var_idx, val);
133 lenv->last_x_var = var_idx;
134 if (lenv->first_x_var == -1)
135 lenv->first_x_var = var_idx;
138 /* add register constraint constraints */
139 for (col = 0; col < n_regs; ++col) {
142 if (rbitset_is_set(colors, col)
143 // for aligned variable, we set the unaligned part to 0
144 && (!has_alignment_cstr || ((col % req->width) == 0)))
147 make_color_var_name(buf, sizeof(buf), irn, col);
148 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 0.0);
149 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
150 lpp_set_start_value(ienv->lp, var_idx, 0.0);
151 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
153 lenv->last_x_var = var_idx;
158 static void build_interference_cstr(ilp_env_t *ienv)
160 lpp_t *lpp = ienv->lp;
161 local_env_t *lenv = (local_env_t*)ienv->env;
162 be_ifg_t *ifg = ienv->co->cenv->ifg;
163 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
164 ir_node **clique = ALLOCAN(ir_node*, n_colors);
165 const unsigned *allocatable_colors = lenv->allocatable_colors;
171 /* for each maximal clique */
172 be_ifg_foreach_clique(ifg, &iter, clique, &size) {
173 unsigned realsize = 0;
175 for (i=0; i<size; ++i) {
176 if (!sr_is_removed(ienv->sr, clique[i]))
184 for (col=0; col<n_colors; ++col) {
186 if (!rbitset_is_set(allocatable_colors, col))
189 cst_idx = lpp_add_cst(lpp, NULL, lpp_less_equal, 1.0);
191 /* for each member of this clique */
192 for (i=0; i<size; ++i) {
193 ir_node *irn = clique[i];
196 unsigned aligment_offset = 0;
198 if (sr_is_removed(ienv->sr, irn))
201 // Use the first part of the large registers for all
202 // interference, since it is the only colorable one.
203 if (check_alignment_constraints(irn)) {
204 const arch_register_req_t *req
205 = arch_get_irn_register_req(irn);
206 aligment_offset = col % req->width;
209 make_color_var_name(buf, sizeof(buf), irn,
210 col - aligment_offset);
211 var_idx = lpp_get_var_idx(lpp, buf);
212 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
218 static void make_affinity_var_name(char *buf, size_t buf_size,
219 const ir_node *node1, const ir_node *node2)
221 unsigned n1 = get_irn_idx(node1);
222 unsigned n2 = get_irn_idx(node2);
224 snprintf(buf, buf_size, "y_%u_%u", n1, n2);
226 snprintf(buf, buf_size, "y_%u_%u", n2, n1);
232 * TODO: Remove the dependency of the opt-units data structure
233 * by walking over all affinity edges. Graph structure
234 * does not provide this walker, yet.
236 static void build_affinity_cstr(ilp_env_t *ienv)
238 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
240 /* for all optimization units */
241 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
242 ir_node *root = curr->nodes[0];
243 unsigned root_col = get_irn_col(root);
246 for (i = 1; i < curr->node_count; ++i) {
247 ir_node *arg = curr->nodes[i];
248 unsigned arg_col = get_irn_col(arg);
254 /* add a new affinity variable */
255 make_affinity_var_name(buf, sizeof(buf), arg, root);
256 y_idx = lpp_add_var(ienv->lp, buf, lpp_binary, curr->costs[i]);
257 val = (root_col == arg_col) ? 0.0 : 1.0;
258 lpp_set_start_value(ienv->lp, y_idx, val);
260 /* add constraints relating the affinity var to the color vars */
261 for (col=0; col<n_colors; ++col) {
262 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less_equal, 0.0);
266 make_color_var_name(buf, sizeof(buf), root, col);
267 root_idx = lpp_get_var_idx(ienv->lp, buf);
268 make_color_var_name(buf, sizeof(buf), arg, col);
269 arg_idx = lpp_get_var_idx(ienv->lp, buf);
271 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
272 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
273 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
280 * Helping stuff for build_clique_star_cstr
282 typedef struct edge_t {
287 static int compare_edge_t(const void *k1, const void *k2, size_t size)
289 const edge_t *e1 = (const edge_t*)k1;
290 const edge_t *e2 = (const edge_t*)k2;
293 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
296 #define HASH_EDGE(e) (hash_irn((e)->n1) ^ hash_irn((e)->n2))
298 static inline edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
302 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
310 return set_insert(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
313 static inline edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2)
317 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
324 return set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
327 static inline void remove_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
331 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
338 e = set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
346 #define pset_foreach(pset, irn) foreach_pset((pset), ir_node, (irn))
349 * Search for an interference clique and an external node
350 * with affinity edges to all nodes of the clique.
351 * At most 1 node of the clique can be colored equally with the external node.
353 static void build_clique_star_cstr(ilp_env_t *ienv)
355 /* for each node with affinity edges */
356 co_gs_foreach_aff_node(ienv->co, aff) {
358 const ir_node *center = aff->irn;
364 if (arch_irn_is_ignore(aff->irn))
368 edges = new_set(compare_edge_t, 8);
370 /* get all affinity neighbours */
372 co_gs_foreach_neighb(aff, nbr) {
373 if (!arch_irn_is_ignore(nbr->irn)) {
374 obstack_ptr_grow(&ob, nbr->irn);
378 nodes = (ir_node**)obstack_finish(&ob);
380 /* get all interference edges between these */
382 for (i=0; i<n_nodes; ++i) {
383 for (o=0; o<i; ++o) {
384 if (be_ifg_connected(ienv->co->cenv->ifg, nodes[i], nodes[o]))
385 add_edge(edges, nodes[i], nodes[o], &n_edges);
389 /* cover all these interference edges with maximal cliques */
392 pset *clique = pset_new_ptr(8);
395 /* get 2 starting nodes to form a clique */
396 for (e = set_first(edge_t, edges); !e->n1; e = set_next(edge_t, edges)) {}
398 /* we could be stepped out of the loop before the set iterated to the end */
401 pset_insert_ptr(clique, e->n1);
402 pset_insert_ptr(clique, e->n2);
403 remove_edge(edges, e->n1, e->n2, &n_edges);
405 /* while the clique is growing */
409 /* search for a candidate to extend the clique */
410 for (i=0; i<n_nodes; ++i) {
411 ir_node *cand = nodes[i];
414 /* if its already in the clique try the next */
415 if (pset_find_ptr(clique, cand))
418 /* are there all necessary interferences? */
420 pset_foreach(clique, member) {
421 if (!find_edge(edges, cand, member)) {
428 /* now we know if we have a clique extender */
430 /* first remove all covered edges */
431 pset_foreach(clique, member)
432 remove_edge(edges, cand, member, &n_edges);
434 /* insert into clique */
435 pset_insert_ptr(clique, cand);
442 /* now the clique is maximal. Finally add the constraint */
448 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, pset_count(clique)-1);
450 pset_foreach(clique, member) {
451 make_affinity_var_name(buf, sizeof(buf), center, member);
452 var_idx = lpp_get_var_idx(ienv->lp, buf);
453 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
461 obstack_free(&ob, NULL);
465 static void extend_path(ilp_env_t *ienv, pdeq *path, const ir_node *irn)
467 be_ifg_t *ifg = ienv->co->cenv->ifg;
470 affinity_node_t *aff;
472 /* do not walk backwards or in circles */
473 if (pdeq_contains(path, irn))
476 if (arch_irn_is_ignore(irn))
479 /* insert the new irn */
480 pdeq_putr(path, irn);
482 /* check for forbidden interferences */
483 len = pdeq_len(path);
484 curr_path = ALLOCAN(ir_node*, len);
485 pdeq_copyl(path, (const void **)curr_path);
487 for (i=1; i<len; ++i) {
488 if (be_ifg_connected(ifg, irn, curr_path[i]))
492 /* check for terminating interference */
493 if (be_ifg_connected(ifg, irn, curr_path[0])) {
494 /* One node is not a path. */
495 /* And a path of length 2 is covered by a clique star constraint. */
497 /* finally build the constraint */
498 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, 1.0);
499 for (i=1; i<len; ++i) {
503 make_affinity_var_name(buf, sizeof(buf), curr_path[i-1], curr_path[i]);
504 var_idx = lpp_get_var_idx(ienv->lp, buf);
505 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
509 /* this path cannot be extended anymore */
513 /* recursively extend the path */
514 aff = get_affinity_info(ienv->co, irn);
515 co_gs_foreach_neighb(aff, nbr) {
516 extend_path(ienv, path, nbr->irn);
525 * Search a path of affinity edges, whose ends are connected
526 * by an interference edge and there are no other interference
528 * Then at least one of these affinity edges must break.
530 static void build_path_cstr(ilp_env_t *ienv)
532 /* for each node with affinity edges */
533 co_gs_foreach_aff_node(ienv->co, aff_info) {
534 pdeq *path = new_pdeq();
536 extend_path(ienv, path, aff_info->irn);
542 static void ilp2_build(ilp_env_t *ienv)
546 ienv->lp = lpp_new(ienv->co->name, lpp_minimize);
547 build_coloring_cstr(ienv);
548 build_interference_cstr(ienv);
549 build_affinity_cstr(ienv);
550 build_clique_star_cstr(ienv);
551 build_path_cstr(ienv);
553 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
554 lpp_set_bound(ienv->lp, lower_bound);
557 static void ilp2_apply(ilp_env_t *ienv)
559 local_env_t *lenv = (local_env_t*)ienv->env;
560 ir_graph *irg = ienv->co->irg;
562 /* first check if there was sth. to optimize */
563 if (lenv->first_x_var >= 0) {
564 int count = lenv->last_x_var - lenv->first_x_var + 1;
565 double *sol = XMALLOCN(double, count);
566 lpp_sol_state_t state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
569 if (state != lpp_optimal) {
570 printf("WARNING %s: Solution state is not 'optimal': %d\n",
571 ienv->co->name, (int)state);
572 if (state < lpp_feasible) {
573 panic("Copy coalescing solution not feasible!");
577 for (i=0; i<count; ++i) {
581 if (sol[i] <= 1-EPSILON)
583 /* split variable name into components */
584 lpp_get_var_name(ienv->lp, lenv->first_x_var+i, var_name, sizeof(var_name));
586 if (sscanf(var_name, "x_%u_%u", &nodenr, &color) == 2) {
587 ir_node *irn = get_idx_irn(irg, nodenr);
588 set_irn_col(ienv->co->cls, irn, color);
590 panic("This should be a x-var");
598 /* TODO adapt to multiple possible ILPs */
599 copystat_add_ilp_time((int)(1000.0*lpp_get_sol_time(pi->curr_lp))); //now we have ms
600 copystat_add_ilp_vars(lpp_get_var_count(pi->curr_lp));
601 copystat_add_ilp_csts(lpp_get_cst_count(pi->curr_lp));
602 copystat_add_ilp_iter(lpp_get_iter_cnt(pi->curr_lp));
607 * Solves the problem using mixed integer programming
608 * @returns 1 iff solution state was optimal
609 * Uses the OU and the GRAPH data structure
610 * Dependency of the OU structure can be removed
612 static int co_solve_ilp2(copy_opt_t *co)
614 unsigned n_regs = arch_register_class_n_regs(co->cls);
615 lpp_sol_state_t sol_state;
619 ASSERT_OU_AVAIL(co); //See build_clique_st
624 FIRM_DBG_REGISTER(dbg, "firm.be.coilp2");
626 unsigned *const allocatable_colors = rbitset_alloca(n_regs);
627 be_set_allocatable_regs(co->irg, co->cls, allocatable_colors);
628 my.allocatable_colors = allocatable_colors;
630 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
632 sol_state = ilp_go(ienv);
636 return sol_state == lpp_optimal;
639 BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)
640 void be_init_copyilp2(void)
642 static co_algo_info copyheur = {
646 be_register_copyopt("ilp", ©heur);