4 * Copyright: (c) Universitaet Karlsruhe
5 * Licence: This file protected by GPL - GNU GENERAL PUBLIC LICENSE.
21 #include <lpp/lpp_net.h>
23 #include "becopyopt.h"
24 #include "becopystat.h"
25 #include "besched_t.h"
27 #define LPP_HOST "i44pc52"
28 #define LPP_SOLVER "cplex"
31 #define DEBUG_LVL SET_LEVEL_1
32 static firm_dbg_module_t *dbg = NULL;
34 #define MAX(a,b) ((a<b)?(b):(a))
35 #define EPSILON 0.00001
36 #define SLOTS_LIVING 32
38 typedef struct _simpl_t {
39 struct list_head chain;
43 typedef struct _problem_instance_t {
44 const copy_opt_t *co; /** the copy_opt problem */
45 /* problem size reduction removing simple nodes */
46 struct list_head simplicials; /**< holds all simpl_t's in right order to color*/
47 pset *removed; /**< holds all removed simplicial irns */
49 lpp_t *dilp; /**< problem formulation directly as milp */
51 lpp_t *curr_lp; /**< points to the problem currently used */
52 int cst_counter, last_x_var;
57 #define is_removed(irn) pset_find_ptr(pi->removed, irn)
59 #define is_color_possible(irn,color) arch_reg_is_allocatable(pi->co->chordal_env->arch_env, irn, arch_pos_make_out(0), arch_register_for_index(pi->co->chordal_env->cls, color))
62 * Some stuff for variable name handling.
64 #define mangle_cst(buf, prefix, nr) \
65 snprintf((buf), sizeof(buf), "%c%d", (prefix), (nr))
67 #define mangle_var(buf, prefix, node_nr, color) \
68 snprintf((buf), sizeof(buf), "%c%d_%d", (prefix), (node_nr), (color))
70 #define mangle_var_irn(buf, prefix, irn, color) \
71 mangle_var((buf), (prefix), get_irn_graph_nr(irn), (color))
73 #define split_var(var, nnr, col) \
74 sscanf(var, "x%d_%d", (nnr), (col))
78 * Checks if a node is simplicial in the graph
79 * heeding the already removed nodes.
81 static INLINE int pi_is_simplicial(problem_instance_t *pi, const if_node_t *ifn) {
83 if_node_t **all, *curr;
84 all = alloca(ifn_get_degree(ifn) * sizeof(*all));
86 /* get all non-removed neighbors */
87 foreach_neighb(ifn, curr)
88 if (!is_removed(curr))
91 /* check if these form a clique */
92 for (i=0; i<size; ++i)
93 for (o=i+1; o<size; ++o)
94 if (!ifg_has_edge(pi->co->chordal_env, all[i], all[o]))
97 /* all edges exist so this is a clique */
102 * Iterative finds and 'removes' from the graph all nodes which are
103 * simplicial AND not member of a equal-color-wish
105 static void pi_find_simplicials(problem_instance_t *pi) {
110 DBG((dbg, LEVEL_2, "Find simlicials...\n"));
112 if_nodes = be_ra_get_ifg_nodes(pi->co->chordal_env);
115 for (ifn = set_first(if_nodes); ifn; ifn = set_next(if_nodes)) {
116 ir_node *irn = get_irn_for_graph_nr(pi->co->chordal_env->irg, ifn->nnr);
117 if (!is_removed(irn) && !is_optimizable(pi->co->chordal_env->arch_env, irn) &&
118 !is_optimizable_arg(pi->co, irn) && pi_is_simplicial(pi, ifn)) {
119 simpl_t *s = xmalloc(sizeof(*s));
121 list_add(&s->chain, &pi->simplicials);
122 pset_insert_ptr(pi->removed, irn);
124 DBG((dbg, LEVEL_2, " Removed %n %d\n", irn, get_irn_graph_nr(irn)));
128 if (set_count(be_ra_get_ifg_nodes(pi->co->chordal_env)) == pset_count(pi->removed))
129 pi->all_simplicial = 1;
133 * Add coloring-force conditions
134 * Matrix A: knapsack constraint for each node
136 static void pi_add_constr_A(problem_instance_t *pi) {
139 DBG((dbg, LEVEL_2, "Add A constraints...\n"));
140 /* iterate over all blocks */
141 pmap_foreach(pi->co->chordal_env->border_heads, pme) {
142 struct list_head *head = pme->value;
144 bitset_t *pos_regs = bitset_alloca(pi->co->chordal_env->cls->n_regs);
146 list_for_each_entry_reverse(border_t, curr, head, list)
147 if (curr->is_def && curr->is_real && !is_removed(curr->irn)) {
148 int cst_idx, nnr, col;
150 nnr = get_irn_graph_nr(curr->irn);
151 mangle_cst(pi->buf, 'A', nnr);
152 cst_idx = lpp_add_cst(pi->curr_lp, pi->buf, lpp_equal, 1);
154 // iterate over all possible colors in order
155 bitset_clear_all(pos_regs);
156 arch_get_allocatable_regs(pi->co->chordal_env->arch_env, curr->irn, arch_pos_make_out(0), pi->co->chordal_env->cls, pos_regs);
157 bitset_foreach(pos_regs, col) {
159 mangle_var(pi->buf, 'x', nnr, col);
160 var_idx = lpp_add_var(pi->curr_lp, pi->buf, lpp_binary, 0);
161 pi->last_x_var = var_idx;
162 lpp_set_factor_fast(pi->curr_lp, cst_idx, var_idx, 1);
169 * Checks if all nodes in @p living are live in in block @p block.
170 * @return 1 if all are live in
173 static INLINE int all_live_in(ir_node *block, pset *living) {
175 for (n = pset_first(living); n; n = pset_next(living))
176 if (!is_live_in(block, n)) {
184 * Finds cliques in the interference graph, considering only nodes
185 * for which the color @p color is possible. Finds only 'maximal-cliques',
186 * viz cliques which are not contained in another one.
187 * Matrix B: interference constraints using cliques
189 static void pi_add_constr_B(problem_instance_t *pi, int color) {
190 enum phase_t {growing, shrinking} phase = growing;
193 pset *living = pset_new_ptr(SLOTS_LIVING);
195 DBG((dbg, LEVEL_2, "Add B constraints (col = %d)...\n", color));
196 /* iterate over all blocks */
197 pmap_foreach(pi->co->chordal_env->border_heads, pme) {
198 ir_node *block = pme->key;
199 struct list_head *head = pme->value;
201 list_for_each_entry_reverse(border_t, b, head, list) {
202 const ir_node *irn = b->irn;
203 if (is_removed(irn) || !is_color_possible(irn, color))
207 DBG((dbg, LEVEL_2, "Def %n\n", irn));
208 pset_insert_ptr(living, irn);
210 } else { /* is_use */
211 DBG((dbg, LEVEL_2, "Use %n\n", irn));
213 /* before shrinking the set, store the current 'maximum' clique;
214 * do NOT if clique is a single node
215 * do NOT if all values are live_in (in this case they were contained in a live-out clique elsewhere) */
216 if (phase == growing && pset_count(living) >= 2 && !all_live_in(block, living)) {
219 mangle_cst(pi->buf, 'B', pi->cst_counter);
220 cst_idx = lpp_add_cst(pi->curr_lp, pi->buf, lpp_less, 1);
221 for (n = pset_first(living); n; n = pset_next(living)) {
223 mangle_var_irn(pi->buf, 'x', n, color);
224 var_idx = lpp_get_var_idx(pi->curr_lp, pi->buf);
225 lpp_set_factor_fast(pi->curr_lp, cst_idx, var_idx, 1);
229 pset_remove_ptr(living, irn);
234 assert(0 == pset_count(living));
239 * Generates constraints which interrelate x with y variables.
240 * x1 and x2 have the different colors ==> y_12 = 1
242 static void pi_add_constr_E(problem_instance_t *pi) {
244 bitset_t *root_regs, *arg_regs, *work_regs;
246 unsigned nregs = pi->co->chordal_env->cls->n_regs;
247 root_regs = bitset_alloca(nregs);
248 arg_regs = bitset_alloca(nregs);
249 work_regs = bitset_alloca(nregs);
251 DBG((dbg, LEVEL_2, "Add E constraints...\n"));
252 /* for all roots of optimization units */
253 list_for_each_entry(unit_t, curr, &pi->co->units, units) {
255 int rootnr, argnr, color;
259 root = curr->nodes[0];
260 rootnr = get_irn_graph_nr(root);
261 bitset_clear_all(root_regs);
262 arch_get_allocatable_regs(pi->co->chordal_env->arch_env, root, arch_pos_make_out(0), pi->co->chordal_env->cls, root_regs);
264 /* for all arguments of root */
265 for (i = 1; i < curr->node_count; ++i) {
266 arg = curr->nodes[i];
267 argnr = get_irn_graph_nr(arg);
268 bitset_clear_all(arg_regs);
269 arch_get_allocatable_regs(pi->co->chordal_env->arch_env, arg, arch_pos_make_out(0), pi->co->chordal_env->cls, arg_regs);
271 /* Introduce new variable and set factor in objective function */
272 mangle_var(buf, 'y', rootnr, argnr);
273 y_idx = lpp_add_var(pi->curr_lp, buf, lpp_continous, curr->costs[i]);
275 //BETTER: y vars as binary or continous vars ??
276 /* set starting value */
277 //lpp_set_start_value(pi->curr_lp, y_idx, (get_irn_col(pi->co, root) != get_irn_col(pi->co, arg)));
279 /* For all colors root and arg have in common, add 2 constraints to E */
280 bitset_copy(work_regs, root_regs);
281 bitset_and(work_regs, arg_regs);
282 bitset_foreach(work_regs, color) {
283 int root_idx, arg_idx, cst_idx;
284 mangle_var(buf, 'x', rootnr, color);
285 root_idx = lpp_get_var_idx(pi->curr_lp, buf);
286 mangle_var(buf, 'x', argnr, color);
287 arg_idx = lpp_get_var_idx(pi->curr_lp, buf);
289 /* add root-arg-y <= 0 */
290 mangle_cst(buf, 'E', cst_counter++);
291 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_less, 0);
292 lpp_set_factor_fast(pi->curr_lp, cst_idx, root_idx, 1);
293 lpp_set_factor_fast(pi->curr_lp, cst_idx, arg_idx, -1);
294 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, -1);
296 /* add arg-root-y <= 0 */
297 mangle_cst(buf, 'E', cst_counter++);
298 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_less, 0);
299 lpp_set_factor_fast(pi->curr_lp, cst_idx, root_idx, -1);
300 lpp_set_factor_fast(pi->curr_lp, cst_idx, arg_idx, 1);
301 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, -1);
303 /* For all colors root and arg have "disjunct", add 1 constraints to E.
304 * If root gets a color the arg is not possible to get then they will
305 * definetly get different colors. So y has to be 1.
306 * Vice versa for arg.
308 bitset_copy(work_regs, root_regs);
309 bitset_xor(work_regs, arg_regs);
310 bitset_foreach(work_regs, color) {
311 int root_idx, arg_idx, cst_idx;
312 mangle_var(buf, 'x', rootnr, color);
313 root_idx = lpp_get_var_idx(pi->curr_lp, buf);
314 mangle_var(buf, 'x', argnr, color);
315 arg_idx = lpp_get_var_idx(pi->curr_lp, buf);
317 mangle_cst(buf, 'E', cst_counter++);
318 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_less, 0);
319 if (bitset_is_set(root_regs, color)) {
320 /* add root-y <= 0 */
321 lpp_set_factor_fast(pi->curr_lp, cst_idx, root_idx, 1);
322 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, -1);
324 assert(bitset_is_set(arg_regs, color) && "bitset_xor is buggy");
326 lpp_set_factor_fast(pi->curr_lp, cst_idx, arg_idx, 1);
327 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, -1);
335 * Matrix S: maximum independent set constraints
336 * Generates lower bound-cuts for optimization units with inner interferences.
337 * Sum(y_{root, arg}, arg \in Args) <= max_indep_set_size - 1
339 static void pi_add_constr_S(problem_instance_t *pi) {
342 DBG((dbg, LEVEL_2, "Add S constraints...\n"));
344 /* for all optimization units */
345 list_for_each_entry(unit_t, curr, &pi->co->units, units) {
346 const ir_node *root, *arg;
348 int cst_idx, y_idx, i;
351 if (curr->minimal_costs == 0)
354 root = curr->nodes[0];
355 rootnr = get_irn_graph_nr(root);
356 mangle_cst(buf, 'S', cst_counter++);
357 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_greater, curr->minimal_costs);
359 /* for all arguments */
360 for (i = 1; i < curr->node_count; ++i) {
361 arg = curr->nodes[i];
362 argnr = get_irn_graph_nr(arg);
363 mangle_var(buf, 'y', rootnr, argnr);
364 y_idx = lpp_get_var_idx(pi->curr_lp, buf);
365 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, curr->costs[i]);
370 static INLINE int get_costs(problem_instance_t *pi, ir_node *phi, ir_node *irn) {
373 /* search optimization unit for phi */
374 list_for_each_entry(unit_t, curr, &pi->co->units, units)
375 if (curr->nodes[0] == phi) {
376 for (i=1; i<curr->node_count; ++i)
377 if (curr->nodes[i] == irn)
378 return curr->costs[i];
379 assert(0 && "irn must occur in this ou");
381 assert(0 && "phi must be found in a ou");
385 static void M_constr_walker(ir_node *block, void *env) {
386 problem_instance_t *pi = env;
387 int count, arity, row, col, other_row, *costs;
388 ir_node **phis, *phi, *irn, **phi_matrix;
390 bitset_t *candidates;
392 /* Count all phi nodes of this block */
393 for (count=0, irn = sched_first(block); is_Phi(irn); irn = sched_next(irn))
396 /* We at least 2 phi nodes for this class of inequalities */
400 /* Build the \Phi-Matrix */
401 arity = get_irn_arity(sched_first(block));
402 phis = alloca(count * sizeof(*phis));
403 costs = alloca(count * sizeof(costs));
404 phi_matrix = alloca(count*arity * sizeof(*phi_matrix));
405 candidates = bitset_alloca(count);
407 phi = sched_first(block);
408 for (row=0; row<count; ++row) {
410 for (col=0; col<arity; ++col)
411 phi_matrix[row*arity + col] = get_irn_n(phi, col);
412 phi = sched_next(phi);
415 /* Now find the interesting patterns in the matrix:
416 * All nodes which are used at least twice in a column. */
418 for (col=0; col<arity; ++col) {
419 done = pset_new_ptr_default();
420 for (row=0; row<count; ++row) {
421 irn = phi_matrix[row*arity + col];
422 /* has the irn already been processed in this col? */
423 if (pset_find_ptr(done, irn))
426 pset_insert_ptr(done, irn);
428 /* insert irn in candidates */
429 bitset_clear_all(candidates);
430 bitset_set(candidates, row);
431 /* search the irn in the rows below */
432 for (other_row = row+1; other_row<count; ++other_row)
433 if (irn == phi_matrix[other_row*arity + col]) {
434 /* found the irn in the same col in another row */
435 bitset_set(candidates, other_row);
438 /* now we know all occurences of irn in this col */
439 if (bitset_popcnt(candidates) < 2)
442 /* compute the minimal costs (rhs) */
443 int phi_nr, sum=0, max=-1, minimal_costs;
444 bitset_foreach(candidates, phi_nr) {
445 costs[phi_nr] = get_costs(pi, phis[phi_nr], irn);
446 sum += costs[phi_nr];
447 max = MAX(max, costs[phi_nr]);
449 minimal_costs = sum - max;
451 /* generate an unequation finally.
452 * phis are indexed in the bitset,
453 * shared argument is irn
454 * rhs is minimal_costs */
458 int pos, irnnr, rootnr, cst_idx, y_idx, cst_counter = 0;
460 irnnr = get_irn_graph_nr(irn);
461 mangle_cst(buf, 'M', cst_counter++);
462 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_greater, minimal_costs);
465 bitset_foreach(candidates, pos) {
467 rootnr = get_irn_graph_nr(root);
468 mangle_var(buf, 'y', rootnr, irnnr);
469 y_idx = lpp_get_var_idx(pi->curr_lp, buf);
470 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, costs[pos]);
474 del_pset(done); /* clear set for next row */
479 * Matrix M: Multi-Arg-Use. Interrelates different \phi-functions
480 * in the same block, iff they use the same arg at the same pos.
481 * Only one of the phis can get the arg.
483 static void pi_add_constr_M(problem_instance_t *pi) {
484 dom_tree_walk_irg(pi->co->chordal_env->irg, M_constr_walker, NULL, pi);
488 * Generate the initial problem matrices and vectors.
490 static problem_instance_t *new_pi(const copy_opt_t *co) {
491 problem_instance_t *pi;
494 DBG((dbg, LEVEL_2, "Generating new instance...\n"));
495 pi = xcalloc(1, sizeof(*pi));
497 pi->removed = pset_new_ptr_default();
498 INIT_LIST_HEAD(&pi->simplicials);
499 pi->dilp = new_lpp(co->name, lpp_minimize);
502 /* problem size reduction */
503 pi_find_simplicials(pi);
504 //BETTER If you wish to see it: dump_ifg_w/o_removed
505 if (pi->all_simplicial)
508 /* built objective abd constraints */
509 pi->curr_lp = pi->dilp;
511 for (col = 0; col < pi->co->chordal_env->cls->n_regs; ++col)
512 pi_add_constr_B(pi, col);
521 * Clean the problem instance
523 static void free_pi(problem_instance_t *pi) {
524 simpl_t *simpl, *tmp;
526 DBG((dbg, LEVEL_2, "Free instance...\n"));
528 list_for_each_entry_safe(simpl_t, simpl, tmp, &pi->simplicials, chain)
530 del_pset(pi->removed);
535 * Set starting values for the mip problem according
536 * to the current coloring of the graph.
538 static void pi_set_start_sol(problem_instance_t *pi) {
541 DBG((dbg, LEVEL_2, "Set start solution...\n"));
542 for (i=1; i<=pi->last_x_var; ++i) {
545 /* get variable name */
546 lpp_get_var_name(pi->curr_lp, i, var_name, sizeof(var_name));
547 /* split into components */
548 if (split_var(var_name, &nnr, &col) == 2) {
549 assert(get_irn_col(pi->co, get_irn_for_graph_nr(pi->co->chordal_env->irg, nnr)) != -1);
550 val = (get_irn_col(pi->co, get_irn_for_graph_nr(pi->co->chordal_env->irg, nnr)) == col) ? 1 : 0;
551 lpp_set_start_value(pi->curr_lp, i, val);
553 fprintf(stderr, "Variable name is: %s\n", var_name);
554 assert(0 && "x vars always look like this 'x123_45'");
562 static void pi_solve_ilp(problem_instance_t *pi) {
563 pi_set_start_sol(pi);
564 lpp_solve_net(pi->curr_lp, LPP_HOST, LPP_SOLVER);
568 * Set the color of all simplicial nodes removed form
569 * the graph before transforming it to an ilp.
571 static void pi_set_simplicials(problem_instance_t *pi) {
572 simpl_t *simpl, *tmp;
573 bitset_t *used_cols = bitset_alloca(arch_register_class_n_regs(pi->co->chordal_env->cls));
575 DBG((dbg, LEVEL_2, "Set simplicials...\n"));
576 /* color the simplicial nodes in right order */
577 list_for_each_entry_safe(simpl_t, simpl, tmp, &pi->simplicials, chain) {
579 ir_node *other_irn, *irn;
580 if_node_t *other, *ifn;
582 /* get free color by inspecting all neighbors */
584 irn = get_irn_for_graph_nr(pi->co->chordal_env->irg, ifn->nnr);
585 bitset_clear_all(used_cols);
586 foreach_neighb(ifn, other) {
587 other_irn = get_irn_for_graph_nr(pi->co->chordal_env->irg, other->nnr);
588 if (!is_removed(other_irn)) /* only inspect nodes which are in graph right now */
589 bitset_set(used_cols, get_irn_col(pi->co, other_irn));
592 /* now all bits not set are possible colors */
593 free_col = bitset_next_clear(used_cols, 0);
594 assert(free_col != -1 && "No free color found. This can not be.");
595 set_irn_col(pi->co, irn, free_col);
596 pset_remove_ptr(pi->removed, irn); /* irn is back in graph again */
601 * Sets the colors of irns according to the values of variables
602 * provided by the solution of the solver.
604 static void pi_apply_solution(problem_instance_t *pi) {
607 lpp_sol_state_t state;
608 DBG((dbg, LEVEL_2, "Applying solution...\n"));
611 curr_vals[I_ILP_ITER] += lpp_get_iter_cnt(pi->curr_lp);
612 curr_vals[I_ILP_TIME] += lpp_get_sol_time(pi->curr_lp);
615 sol = xmalloc((pi->last_x_var+1) * sizeof(*sol));
616 state = lpp_get_solution(pi->curr_lp, sol, 1, pi->last_x_var);
617 if (state != lpp_optimal) {
618 printf("Solution state is not 'optimal': %d\n", state);
619 assert(state >= lpp_feasible && "The solution should at least be feasible!");
621 for (i=0; i<pi->last_x_var; ++i) {
625 if (sol[i] > 1-EPSILON) { /* split varibale name into components */
626 lpp_get_var_name(pi->curr_lp, 1+i, var_name, sizeof(var_name));
627 if (split_var(var_name, &nnr, &col) == 2) {
628 DBG((dbg, LEVEL_2, "Irn %n Idx %d Var %s Val %f\n", get_irn_for_graph_nr(pi->co->chordal_env->irg, nnr), i, var_name, sol[i]));
629 DBG((dbg, LEVEL_2, "x%d = %d\n", nnr, col));
630 set_irn_col(pi->co, get_irn_for_graph_nr(pi->co->chordal_env->irg, nnr), col);
632 assert(0 && "This should be a x-var");
637 void co_ilp_opt(copy_opt_t *co) {
638 problem_instance_t *pi;
640 dbg = firm_dbg_register("ir.be.copyoptilp");
641 if (!strcmp(co->name, DEBUG_IRG))
642 firm_dbg_set_mask(dbg, DEBUG_LVL_ILP);
644 firm_dbg_set_mask(dbg, DEBUG_LVL);
647 if (!pi->all_simplicial) {
650 snprintf(buf, sizeof(buf), "%s.mps", co->name);
651 lpp_dump(pi->curr_lp, buf);
654 pi_apply_solution(pi);
655 pi_set_simplicials(pi);