2 * Copyright (C) 1995-2008 University of Karlsruhe. All right reserved.
4 * This file is part of libFirm.
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12 * this file in accordance with the libFirm Commercial License.
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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^+
49 #include "raw_bitset.h"
54 #include "becopyilp_t.h"
59 DEBUG_ONLY(static firm_dbg_module_t *dbg;)
61 typedef struct local_env_t {
64 const unsigned *allocatable_colors;
67 static unsigned check_alignment_constraints(ir_node *node)
69 const arch_register_req_t *req = arch_get_irn_register_req(node);
70 // For larger than 1 variables, support only aligned constraints
71 assert(((!(req->type & arch_register_req_type_aligned)
73 || (req->type & arch_register_req_type_aligned))
74 && "Unaligned large (width > 1) variables not supported");
75 return (req->type & arch_register_req_type_aligned) && req->width > 1;
78 static void make_color_var_name(char *buf, size_t buf_size,
79 const ir_node *node, unsigned color)
81 unsigned node_idx = get_irn_idx(node);
82 snprintf(buf, buf_size, "x_%u_%u", node_idx, color);
85 static void build_coloring_cstr(ilp_env_t *ienv)
87 local_env_t *lenv = ienv->env;
88 be_ifg_t *ifg = ienv->co->cenv->ifg;
89 unsigned n_regs = arch_register_class_n_regs(ienv->co->cls);
90 const unsigned *allocatable_colors = lenv->allocatable_colors;
96 rbitset_alloca(colors, n_regs);
98 be_ifg_foreach_node(ifg, &iter, irn) {
99 const arch_register_req_t *req;
102 unsigned curr_node_color;
103 unsigned has_alignment_cstr;
105 if (sr_is_removed(ienv->sr, irn))
108 has_alignment_cstr = check_alignment_constraints(irn);
110 req = arch_get_irn_register_req(irn);
112 /* get assignable colors */
113 if (arch_register_req_is(req, limited)) {
114 rbitset_copy(colors, req->limited, n_regs);
116 rbitset_copy(colors, allocatable_colors, n_regs);
119 /* add the coloring constraint */
120 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 1.0);
122 curr_node_color = get_irn_col(irn);
123 for (col = 0; col < n_regs; ++col) {
126 if (!rbitset_is_set(colors, col)
127 || (has_alignment_cstr && ((col % req->width) != 0)))
130 make_color_var_name(buf, sizeof(buf), irn, col);
131 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
132 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
134 val = (col == curr_node_color) ? 1.0 : 0.0;
135 lpp_set_start_value(ienv->lp, var_idx, val);
137 lenv->last_x_var = var_idx;
138 if (lenv->first_x_var == -1)
139 lenv->first_x_var = var_idx;
142 /* add register constraint constraints */
143 for (col = 0; col < n_regs; ++col) {
146 if (rbitset_is_set(colors, col)
147 // for aligned variable, we set the unaligned part to 0
148 && (!has_alignment_cstr || ((col % req->width) == 0)))
151 // If it is possible to have only a part of a large variable that
152 // cannot be used, we should invalidate the whole piece.
153 // Since we do not think this can happen, we did implemented the
155 assert((!has_alignment_cstr
156 || rbitset_is_set(colors, col)
157 || !rbitset_is_set(colors, col - (col % req->width)))
158 && "Register constraints that invalidate just a part of "
159 "a large variable is not yet supported");
160 make_color_var_name(buf, sizeof(buf), irn, col);
161 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_equal, 0.0);
162 var_idx = lpp_add_var(ienv->lp, buf, lpp_binary, 0.0);
163 lpp_set_start_value(ienv->lp, var_idx, 0.0);
164 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1);
166 lenv->last_x_var = var_idx;
171 static void build_interference_cstr(ilp_env_t *ienv)
173 lpp_t *lpp = ienv->lp;
174 local_env_t *lenv = ienv->env;
175 be_ifg_t *ifg = ienv->co->cenv->ifg;
176 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
177 ir_node **clique = ALLOCAN(ir_node*, n_colors);
178 const unsigned *allocatable_colors = lenv->allocatable_colors;
184 /* for each maximal clique */
185 be_ifg_foreach_clique(ifg, &iter, clique, &size) {
186 unsigned realsize = 0;
188 for (i=0; i<size; ++i) {
189 if (!sr_is_removed(ienv->sr, clique[i]))
197 for (col=0; col<n_colors; ++col) {
199 if (!rbitset_is_set(allocatable_colors, col))
202 cst_idx = lpp_add_cst(lpp, NULL, lpp_less_equal, 1.0);
204 /* for each member of this clique */
205 for (i=0; i<size; ++i) {
206 ir_node *irn = clique[i];
209 unsigned aligment_offset = 0;
211 if (sr_is_removed(ienv->sr, irn))
214 // Use the first part of the large registers for all
215 // interference, since it is the only colorable one.
216 if (check_alignment_constraints(irn)) {
217 const arch_register_req_t *req
218 = arch_get_irn_register_req(irn);
219 aligment_offset = col % req->width;
222 make_color_var_name(buf, sizeof(buf), irn,
223 col - aligment_offset);
224 var_idx = lpp_get_var_idx(lpp, buf);
225 lpp_set_factor_fast(lpp, cst_idx, var_idx, 1);
231 static void make_affinity_var_name(char *buf, size_t buf_size,
232 const ir_node *node1, const ir_node *node2)
234 unsigned n1 = get_irn_idx(node1);
235 unsigned n2 = get_irn_idx(node2);
237 snprintf(buf, buf_size, "y_%u_%u", n1, n2);
239 snprintf(buf, buf_size, "y_%u_%u", n2, n1);
245 * TODO: Remove the dependency of the opt-units data structure
246 * by walking over all affinity edges. Graph structure
247 * does not provide this walker, yet.
249 static void build_affinity_cstr(ilp_env_t *ienv)
251 unsigned n_colors = arch_register_class_n_regs(ienv->co->cls);
254 /* for all optimization units */
255 list_for_each_entry(unit_t, curr, &ienv->co->units, units) {
256 ir_node *root = curr->nodes[0];
257 unsigned root_col = get_irn_col(root);
260 for (i = 1; i < curr->node_count; ++i) {
261 ir_node *arg = curr->nodes[i];
262 unsigned arg_col = get_irn_col(arg);
268 /* add a new affinity variable */
269 make_affinity_var_name(buf, sizeof(buf), arg, root);
270 y_idx = lpp_add_var(ienv->lp, buf, lpp_binary, curr->costs[i]);
271 val = (root_col == arg_col) ? 0.0 : 1.0;
272 lpp_set_start_value(ienv->lp, y_idx, val);
274 /* add constraints relating the affinity var to the color vars */
275 for (col=0; col<n_colors; ++col) {
276 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_less_equal, 0.0);
280 make_color_var_name(buf, sizeof(buf), root, col);
281 root_idx = lpp_get_var_idx(ienv->lp, buf);
282 make_color_var_name(buf, sizeof(buf), arg, col);
283 arg_idx = lpp_get_var_idx(ienv->lp, buf);
285 lpp_set_factor_fast(ienv->lp, cst_idx, root_idx, 1.0);
286 lpp_set_factor_fast(ienv->lp, cst_idx, arg_idx, -1.0);
287 lpp_set_factor_fast(ienv->lp, cst_idx, y_idx, -1.0);
294 * Helping stuff for build_clique_star_cstr
296 typedef struct edge_t {
301 static int compare_edge_t(const void *k1, const void *k2, size_t size)
303 const edge_t *e1 = k1;
304 const edge_t *e2 = k2;
307 return ! (e1->n1 == e2->n1 && e1->n2 == e2->n2);
310 #define HASH_EDGE(e) (hash_irn((e)->n1) ^ hash_irn((e)->n2))
312 static inline edge_t *add_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
316 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
324 return set_insert(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
327 static inline edge_t *find_edge(set *edges, ir_node *n1, ir_node *n2)
331 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
338 return set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
341 static inline void remove_edge(set *edges, ir_node *n1, ir_node *n2, size_t *counter)
345 if (PTR_TO_INT(n1) < PTR_TO_INT(n2)) {
352 e = set_find(edges, &new_edge, sizeof(new_edge), HASH_EDGE(&new_edge));
360 #define pset_foreach(pset, irn) for (irn=pset_first(pset); irn; irn=pset_next(pset))
363 * Search for an interference clique and an external node
364 * with affinity edges to all nodes of the clique.
365 * At most 1 node of the clique can be colored equally with the external node.
367 static void build_clique_star_cstr(ilp_env_t *ienv)
369 affinity_node_t *aff;
371 /* for each node with affinity edges */
372 co_gs_foreach_aff_node(ienv->co, aff) {
375 const ir_node *center = aff->irn;
381 if (arch_irn_is_ignore(aff->irn))
385 edges = new_set(compare_edge_t, 8);
387 /* get all affinity neighbours */
389 co_gs_foreach_neighb(aff, nbr) {
390 if (!arch_irn_is_ignore(nbr->irn)) {
391 obstack_ptr_grow(&ob, nbr->irn);
395 nodes = obstack_finish(&ob);
397 /* get all interference edges between these */
399 for (i=0; i<n_nodes; ++i) {
400 for (o=0; o<i; ++o) {
401 if (be_ifg_connected(ienv->co->cenv->ifg, nodes[i], nodes[o]))
402 add_edge(edges, nodes[i], nodes[o], &n_edges);
406 /* cover all these interference edges with maximal cliques */
409 pset *clique = pset_new_ptr(8);
412 /* get 2 starting nodes to form a clique */
413 for (e=set_first(edges); !e->n1; e=set_next(edges)) {
416 /* we could be stepped out of the loop before the set iterated to the end */
419 pset_insert_ptr(clique, e->n1);
420 pset_insert_ptr(clique, e->n2);
421 remove_edge(edges, e->n1, e->n2, &n_edges);
423 /* while the clique is growing */
427 /* search for a candidate to extend the clique */
428 for (i=0; i<n_nodes; ++i) {
429 ir_node *cand = nodes[i];
433 /* if its already in the clique try the next */
434 if (pset_find_ptr(clique, cand))
437 /* are there all necessary interferences? */
439 pset_foreach(clique, member) {
440 if (!find_edge(edges, cand, member)) {
447 /* now we know if we have a clique extender */
449 /* first remove all covered edges */
450 pset_foreach(clique, member)
451 remove_edge(edges, cand, member, &n_edges);
453 /* insert into clique */
454 pset_insert_ptr(clique, cand);
461 /* now the clique is maximal. Finally add the constraint */
468 cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, pset_count(clique)-1);
470 pset_foreach(clique, member) {
471 make_affinity_var_name(buf, sizeof(buf), center, member);
472 var_idx = lpp_get_var_idx(ienv->lp, buf);
473 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
481 obstack_free(&ob, NULL);
485 static void extend_path(ilp_env_t *ienv, pdeq *path, const ir_node *irn)
487 be_ifg_t *ifg = ienv->co->cenv->ifg;
490 affinity_node_t *aff;
493 /* do not walk backwards or in circles */
494 if (pdeq_contains(path, irn))
497 if (arch_irn_is_ignore(irn))
500 /* insert the new irn */
501 pdeq_putr(path, irn);
503 /* check for forbidden interferences */
504 len = pdeq_len(path);
505 curr_path = ALLOCAN(ir_node*, len);
506 pdeq_copyl(path, (const void **)curr_path);
508 for (i=1; i<len; ++i) {
509 if (be_ifg_connected(ifg, irn, curr_path[i]))
513 /* check for terminating interference */
514 if (be_ifg_connected(ifg, irn, curr_path[0])) {
515 /* One node is not a path. */
516 /* And a path of length 2 is covered by a clique star constraint. */
518 /* finally build the constraint */
519 int cst_idx = lpp_add_cst(ienv->lp, NULL, lpp_greater_equal, 1.0);
520 for (i=1; i<len; ++i) {
524 make_affinity_var_name(buf, sizeof(buf), curr_path[i-1], curr_path[i]);
525 var_idx = lpp_get_var_idx(ienv->lp, buf);
526 lpp_set_factor_fast(ienv->lp, cst_idx, var_idx, 1.0);
530 /* this path cannot be extended anymore */
534 /* recursively extend the path */
535 aff = get_affinity_info(ienv->co, irn);
536 co_gs_foreach_neighb(aff, nbr) {
537 extend_path(ienv, path, nbr->irn);
546 * Search a path of affinity edges, whose ends are connected
547 * by an interference edge and there are no other interference
549 * Then at least one of these affinity edges must break.
551 static void build_path_cstr(ilp_env_t *ienv)
553 affinity_node_t *aff_info;
555 /* for each node with affinity edges */
556 co_gs_foreach_aff_node(ienv->co, aff_info) {
557 pdeq *path = new_pdeq();
559 extend_path(ienv, path, aff_info->irn);
565 static void ilp2_build(ilp_env_t *ienv)
569 ienv->lp = lpp_new(ienv->co->name, lpp_minimize);
570 build_coloring_cstr(ienv);
571 build_interference_cstr(ienv);
572 build_affinity_cstr(ienv);
573 build_clique_star_cstr(ienv);
574 build_path_cstr(ienv);
576 lower_bound = co_get_lower_bound(ienv->co) - co_get_inevit_copy_costs(ienv->co);
577 lpp_set_bound(ienv->lp, lower_bound);
580 static void ilp2_apply(ilp_env_t *ienv)
582 local_env_t *lenv = ienv->env;
583 ir_graph *irg = ienv->co->irg;
585 /* first check if there was sth. to optimize */
586 if (lenv->first_x_var >= 0) {
587 int count = lenv->last_x_var - lenv->first_x_var + 1;
588 double *sol = XMALLOCN(double, count);
589 lpp_sol_state_t state = lpp_get_solution(ienv->lp, sol, lenv->first_x_var, lenv->last_x_var);
592 if (state != lpp_optimal) {
593 printf("WARNING %s: Solution state is not 'optimal': %d\n",
594 ienv->co->name, (int)state);
595 if (state < lpp_feasible) {
596 panic("Copy coalescing solution not feasible!");
600 for (i=0; i<count; ++i) {
604 if (sol[i] <= 1-EPSILON)
606 /* split variable name into components */
607 lpp_get_var_name(ienv->lp, lenv->first_x_var+i, var_name, sizeof(var_name));
609 if (sscanf(var_name, "x_%u_%u", &nodenr, &color) == 2) {
610 ir_node *irn = get_idx_irn(irg, nodenr);
611 set_irn_col(ienv->co->cls, irn, color);
613 panic("This should be a x-var");
621 /* TODO adapt to multiple possible ILPs */
622 copystat_add_ilp_time((int)(1000.0*lpp_get_sol_time(pi->curr_lp))); //now we have ms
623 copystat_add_ilp_vars(lpp_get_var_count(pi->curr_lp));
624 copystat_add_ilp_csts(lpp_get_cst_count(pi->curr_lp));
625 copystat_add_ilp_iter(lpp_get_iter_cnt(pi->curr_lp));
630 * Solves the problem using mixed integer programming
631 * @returns 1 iff solution state was optimal
632 * Uses the OU and the GRAPH data structure
633 * Dependency of the OU structure can be removed
635 static int co_solve_ilp2(copy_opt_t *co)
637 unsigned *allocatable_colors;
638 unsigned n_regs = arch_register_class_n_regs(co->cls);
639 lpp_sol_state_t sol_state;
643 ASSERT_OU_AVAIL(co); //See build_clique_st
648 FIRM_DBG_REGISTER(dbg, "firm.be.coilp2");
650 rbitset_alloca(allocatable_colors, n_regs);
651 be_set_allocatable_regs(co->irg, co->cls, allocatable_colors);
652 my.allocatable_colors = allocatable_colors;
654 ienv = new_ilp_env(co, ilp2_build, ilp2_apply, &my);
656 sol_state = ilp_go(ienv);
660 return sol_state == lpp_optimal;
663 BE_REGISTER_MODULE_CONSTRUCTOR(be_init_copyilp2)
664 void be_init_copyilp2(void)
666 static co_algo_info copyheur = {
670 be_register_copyopt("ilp", ©heur);