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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(((!(req->type & arch_register_req_type_aligned)
75 || (req->type & arch_register_req_type_aligned))
76 && "Unaligned large (width > 1) variables not supported");
77 return (req->type & arch_register_req_type_aligned) && req->width > 1;
80 static void make_color_var_name(char *buf, size_t buf_size,
81 const ir_node *node, unsigned color)
83 unsigned node_idx = get_irn_idx(node);
84 snprintf(buf, buf_size, "x_%u_%u", node_idx, color);
87 static void build_coloring_cstr(ilp_env_t *ienv)
89 local_env_t *lenv = (local_env_t*)ienv->env;
90 be_ifg_t *ifg = ienv->co->cenv->ifg;
91 unsigned n_regs = arch_register_class_n_regs(ienv->co->cls);
92 const unsigned *allocatable_colors = lenv->allocatable_colors;
98 rbitset_alloca(colors, n_regs);
100 be_ifg_foreach_node(ifg, &iter, irn) {
101 const arch_register_req_t *req;
104 unsigned curr_node_color;
105 unsigned has_alignment_cstr;
107 if (sr_is_removed(ienv->sr, irn))
110 has_alignment_cstr = check_alignment_constraints(irn);
112 req = arch_get_irn_register_req(irn);
114 /* get assignable colors */
115 if (arch_register_req_is(req, limited)) {
116 rbitset_copy(colors, req->limited, n_regs);
118 rbitset_copy(colors, allocatable_colors, n_regs);
121 /* add the coloring constraint */
122 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 1.0);
124 curr_node_color = get_irn_col(irn);
125 for (col = 0; col < n_regs; ++col) {
128 if (!rbitset_is_set(colors, col)
129 || (has_alignment_cstr && ((col % req->width) != 0)))
132 make_color_var_name(buf, sizeof(buf), irn, col);
133 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
134 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
136 val = (col == curr_node_color) ? 1.0 : 0.0;
137 lpp_set_start_value(ienv->lp, var_idx, val);
139 lenv->last_x_var = var_idx;
140 if (lenv->first_x_var == -1)
141 lenv->first_x_var = var_idx;
144 /* add register constraint constraints */
145 for (col = 0; col < n_regs; ++col) {
148 if (rbitset_is_set(colors, col)
149 // for aligned variable, we set the unaligned part to 0
150 && (!has_alignment_cstr || ((col % req->width) == 0)))
153 make_color_var_name(buf, sizeof(buf), irn, col);
154 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 0.0);
155 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
156 lpp_set_start_value(ienv->lp, var_idx, 0.0);
157 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
159 lenv->last_x_var = var_idx;
164 static void build_interference_cstr(ilp_env_t *ienv)
166 lpp_t *lpp = ienv->lp;
167 local_env_t *lenv = (local_env_t*)ienv->env;
168 be_ifg_t *ifg = ienv->co->cenv->ifg;
169 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
170 ir_node **clique = ALLOCAN(ir_node*, n_colors);
171 const unsigned *allocatable_colors = lenv->allocatable_colors;
177 /* for each maximal clique */
178 be_ifg_foreach_clique(ifg, &iter, clique, &size) {
179 unsigned realsize = 0;
181 for (i=0; i<size; ++i) {
182 if (!sr_is_removed(ienv->sr, clique[i]))
190 for (col=0; col<n_colors; ++col) {
192 if (!rbitset_is_set(allocatable_colors, col))
195 cst_idx = lpp_add_cst(lpp, NULL, lpp_less_equal, 1.0);
197 /* for each member of this clique */
198 for (i=0; i<size; ++i) {
199 ir_node *irn = clique[i];
202 unsigned aligment_offset = 0;
204 if (sr_is_removed(ienv->sr, irn))
207 // Use the first part of the large registers for all
208 // interference, since it is the only colorable one.
209 if (check_alignment_constraints(irn)) {
210 const arch_register_req_t *req
211 = arch_get_irn_register_req(irn);
212 aligment_offset = col % req->width;
215 make_color_var_name(buf, sizeof(buf), irn,
216 col - aligment_offset);
217 var_idx = lpp_get_var_idx(lpp, buf);
218 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
224 static void make_affinity_var_name(char *buf, size_t buf_size,
225 const ir_node *node1, const ir_node *node2)
227 unsigned n1 = get_irn_idx(node1);
228 unsigned n2 = get_irn_idx(node2);
230 snprintf(buf, buf_size, "y_%u_%u", n1, n2);
232 snprintf(buf, buf_size, "y_%u_%u", n2, n1);
238 * TODO: Remove the dependency of the opt-units data structure
239 * by walking over all affinity edges. Graph structure
240 * does not provide this walker, yet.
242 static void build_affinity_cstr(ilp_env_t *ienv)
244 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
246 /* for all optimization units */
247 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
248 ir_node *root = curr->nodes[0];
249 unsigned root_col = get_irn_col(root);
252 for (i = 1; i < curr->node_count; ++i) {
253 ir_node *arg = curr->nodes[i];
254 unsigned arg_col = get_irn_col(arg);
260 /* add a new affinity variable */
261 make_affinity_var_name(buf, sizeof(buf), arg, root);
262 y_idx = lpp_add_var(ienv->lp, buf, lpp_binary, curr->costs[i]);
263 val = (root_col == arg_col) ? 0.0 : 1.0;
264 lpp_set_start_value(ienv->lp, y_idx, val);
266 /* add constraints relating the affinity var to the color vars */
267 for (col=0; col<n_colors; ++col) {
268 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less_equal, 0.0);
272 make_color_var_name(buf, sizeof(buf), root, col);
273 root_idx = lpp_get_var_idx(ienv->lp, buf);
274 make_color_var_name(buf, sizeof(buf), arg, col);
275 arg_idx = lpp_get_var_idx(ienv->lp, buf);
277 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
278 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
279 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
286 * Helping stuff for build_clique_star_cstr
288 typedef struct edge_t {
293 static int compare_edge_t(const void *k1, const void *k2, size_t size)
295 const edge_t *e1 = (const edge_t*)k1;
296 const edge_t *e2 = (const edge_t*)k2;
299 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
302 #define HASH_EDGE(e) (hash_irn((e)->n1) ^ hash_irn((e)->n2))
304 static inline edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
308 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
316 return set_insert(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
319 static inline edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2)
323 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
330 return set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
333 static inline void remove_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
337 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
344 e = set_find(edge_t, edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
352 #define pset_foreach(pset, irn) foreach_pset((pset), ir_node, (irn))
355 * Search for an interference clique and an external node
356 * with affinity edges to all nodes of the clique.
357 * At most 1 node of the clique can be colored equally with the external node.
359 static void build_clique_star_cstr(ilp_env_t *ienv)
361 /* for each node with affinity edges */
362 co_gs_foreach_aff_node(ienv->co, aff) {
364 const ir_node *center = aff->irn;
370 if (arch_irn_is_ignore(aff->irn))
374 edges = new_set(compare_edge_t, 8);
376 /* get all affinity neighbours */
378 co_gs_foreach_neighb(aff, nbr) {
379 if (!arch_irn_is_ignore(nbr->irn)) {
380 obstack_ptr_grow(&ob, nbr->irn);
384 nodes = (ir_node**)obstack_finish(&ob);
386 /* get all interference edges between these */
388 for (i=0; i<n_nodes; ++i) {
389 for (o=0; o<i; ++o) {
390 if (be_ifg_connected(ienv->co->cenv->ifg, nodes[i], nodes[o]))
391 add_edge(edges, nodes[i], nodes[o], &n_edges);
395 /* cover all these interference edges with maximal cliques */
398 pset *clique = pset_new_ptr(8);
401 /* get 2 starting nodes to form a clique */
402 for (e = set_first(edge_t, edges); !e->n1; e = set_next(edge_t, edges)) {}
404 /* we could be stepped out of the loop before the set iterated to the end */
407 pset_insert_ptr(clique, e->n1);
408 pset_insert_ptr(clique, e->n2);
409 remove_edge(edges, e->n1, e->n2, &n_edges);
411 /* while the clique is growing */
415 /* search for a candidate to extend the clique */
416 for (i=0; i<n_nodes; ++i) {
417 ir_node *cand = nodes[i];
420 /* if its already in the clique try the next */
421 if (pset_find_ptr(clique, cand))
424 /* are there all necessary interferences? */
426 pset_foreach(clique, member) {
427 if (!find_edge(edges, cand, member)) {
434 /* now we know if we have a clique extender */
436 /* first remove all covered edges */
437 pset_foreach(clique, member)
438 remove_edge(edges, cand, member, &n_edges);
440 /* insert into clique */
441 pset_insert_ptr(clique, cand);
448 /* now the clique is maximal. Finally add the constraint */
454 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, pset_count(clique)-1);
456 pset_foreach(clique, member) {
457 make_affinity_var_name(buf, sizeof(buf), center, member);
458 var_idx = lpp_get_var_idx(ienv->lp, buf);
459 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
467 obstack_free(&ob, NULL);
471 static void extend_path(ilp_env_t *ienv, pdeq *path, const ir_node *irn)
473 be_ifg_t *ifg = ienv->co->cenv->ifg;
476 affinity_node_t *aff;
478 /* do not walk backwards or in circles */
479 if (pdeq_contains(path, irn))
482 if (arch_irn_is_ignore(irn))
485 /* insert the new irn */
486 pdeq_putr(path, irn);
488 /* check for forbidden interferences */
489 len = pdeq_len(path);
490 curr_path = ALLOCAN(ir_node*, len);
491 pdeq_copyl(path, (const void **)curr_path);
493 for (i=1; i<len; ++i) {
494 if (be_ifg_connected(ifg, irn, curr_path[i]))
498 /* check for terminating interference */
499 if (be_ifg_connected(ifg, irn, curr_path[0])) {
500 /* One node is not a path. */
501 /* And a path of length 2 is covered by a clique star constraint. */
503 /* finally build the constraint */
504 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, 1.0);
505 for (i=1; i<len; ++i) {
509 make_affinity_var_name(buf, sizeof(buf), curr_path[i-1], curr_path[i]);
510 var_idx = lpp_get_var_idx(ienv->lp, buf);
511 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
515 /* this path cannot be extended anymore */
519 /* recursively extend the path */
520 aff = get_affinity_info(ienv->co, irn);
521 co_gs_foreach_neighb(aff, nbr) {
522 extend_path(ienv, path, nbr->irn);
531 * Search a path of affinity edges, whose ends are connected
532 * by an interference edge and there are no other interference
534 * Then at least one of these affinity edges must break.
536 static void build_path_cstr(ilp_env_t *ienv)
538 /* for each node with affinity edges */
539 co_gs_foreach_aff_node(ienv->co, aff_info) {
540 pdeq *path = new_pdeq();
542 extend_path(ienv, path, aff_info->irn);
548 static void ilp2_build(ilp_env_t *ienv)
552 ienv->lp = lpp_new(ienv->co->name, lpp_minimize);
553 build_coloring_cstr(ienv);
554 build_interference_cstr(ienv);
555 build_affinity_cstr(ienv);
556 build_clique_star_cstr(ienv);
557 build_path_cstr(ienv);
559 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
560 lpp_set_bound(ienv->lp, lower_bound);
563 static void ilp2_apply(ilp_env_t *ienv)
565 local_env_t *lenv = (local_env_t*)ienv->env;
566 ir_graph *irg = ienv->co->irg;
568 /* first check if there was sth. to optimize */
569 if (lenv->first_x_var >= 0) {
570 int count = lenv->last_x_var - lenv->first_x_var + 1;
571 double *sol = XMALLOCN(double, count);
572 lpp_sol_state_t state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
575 if (state != lpp_optimal) {
576 printf("WARNING %s: Solution state is not 'optimal': %d\n",
577 ienv->co->name, (int)state);
578 if (state < lpp_feasible) {
579 panic("Copy coalescing solution not feasible!");
583 for (i=0; i<count; ++i) {
587 if (sol[i] <= 1-EPSILON)
589 /* split variable name into components */
590 lpp_get_var_name(ienv->lp, lenv->first_x_var+i, var_name, sizeof(var_name));
592 if (sscanf(var_name, "x_%u_%u", &nodenr, &color) == 2) {
593 ir_node *irn = get_idx_irn(irg, nodenr);
594 set_irn_col(ienv->co->cls, irn, color);
596 panic("This should be a x-var");
604 /* TODO adapt to multiple possible ILPs */
605 copystat_add_ilp_time((int)(1000.0*lpp_get_sol_time(pi->curr_lp))); //now we have ms
606 copystat_add_ilp_vars(lpp_get_var_count(pi->curr_lp));
607 copystat_add_ilp_csts(lpp_get_cst_count(pi->curr_lp));
608 copystat_add_ilp_iter(lpp_get_iter_cnt(pi->curr_lp));
613 * Solves the problem using mixed integer programming
614 * @returns 1 iff solution state was optimal
615 * Uses the OU and the GRAPH data structure
616 * Dependency of the OU structure can be removed
618 static int co_solve_ilp2(copy_opt_t *co)
620 unsigned *allocatable_colors;
621 unsigned n_regs = arch_register_class_n_regs(co->cls);
622 lpp_sol_state_t sol_state;
626 ASSERT_OU_AVAIL(co); //See build_clique_st
631 FIRM_DBG_REGISTER(dbg, "firm.be.coilp2");
633 rbitset_alloca(allocatable_colors, n_regs);
634 be_set_allocatable_regs(co->irg, co->cls, allocatable_colors);
635 my.allocatable_colors = allocatable_colors;
637 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
639 sol_state = ilp_go(ienv);
643 return sol_state == lpp_optimal;
646 BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)
647 void be_init_copyilp2(void)
649 static co_algo_info copyheur = {
653 be_register_copyopt("ilp", ©heur);