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 static firm_dbg_module_t *dbg = NULL;
33 #define MAX(a,b) ((a<b)?(b):(a))
34 #define EPSILON 0.00001
35 #define SLOTS_LIVING 32
37 typedef struct _simpl_t {
38 struct list_head chain;
42 typedef struct _problem_instance_t {
43 const copy_opt_t *co; /** the copy_opt problem */
44 /* problem size reduction removing simple nodes */
45 struct list_head simplicials; /**< holds all simpl_t's in right order to color*/
46 pset *removed; /**< holds all removed simplicial irns */
48 lpp_t *dilp; /**< problem formulation directly as milp */
50 lpp_t *curr_lp; /**< points to the problem currently used */
51 int cst_counter, last_x_var;
56 #define is_removed(irn) pset_find_ptr(pi->removed, irn)
58 #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))
61 * Some stuff for variable name handling.
63 #define mangle_cst(buf, prefix, nr) \
64 snprintf((buf), sizeof(buf), "%c%d", (prefix), (nr))
66 #define mangle_var(buf, prefix, node_nr, color) \
67 snprintf((buf), sizeof(buf), "%c%d_%d", (prefix), (node_nr), (color))
69 #define mangle_var_irn(buf, prefix, irn, color) \
70 mangle_var((buf), (prefix), get_irn_graph_nr(irn), (color))
72 #define split_var(var, nnr, col) \
73 sscanf(var, "x%d_%d", (nnr), (col))
77 * Checks if a node is simplicial in the graph
78 * heeding the already removed nodes.
80 static INLINE int pi_is_simplicial(problem_instance_t *pi, const if_node_t *ifn) {
82 if_node_t **all, *curr;
83 all = alloca(ifn_get_degree(ifn) * sizeof(*all));
85 /* get all non-removed neighbors */
86 foreach_neighb(ifn, curr)
87 if (!is_removed(curr))
90 /* check if these form a clique */
91 for (i=0; i<size; ++i)
92 for (o=i+1; o<size; ++o)
93 if (!ifg_has_edge(pi->co->chordal_env, all[i], all[o]))
96 /* all edges exist so this is a clique */
101 * Iterative finds and 'removes' from the graph all nodes which are
102 * simplicial AND not member of a equal-color-wish
104 static void pi_find_simplicials(problem_instance_t *pi) {
109 DBG((dbg, LEVEL_2, "Find simlicials...\n"));
111 if_nodes = be_ra_get_ifg_nodes(pi->co->chordal_env);
114 for (ifn = set_first(if_nodes); ifn; ifn = set_next(if_nodes)) {
115 ir_node *irn = get_irn_for_graph_nr(pi->co->chordal_env->irg, ifn->nnr);
116 if (!is_removed(irn) && !is_optimizable(pi->co->chordal_env->arch_env, irn) &&
117 !is_optimizable_arg(pi->co, irn) && pi_is_simplicial(pi, ifn)) {
118 simpl_t *s = xmalloc(sizeof(*s));
120 list_add(&s->chain, &pi->simplicials);
121 pset_insert_ptr(pi->removed, irn);
123 DBG((dbg, LEVEL_2, " Removed %n %d\n", irn, get_irn_graph_nr(irn)));
127 if (set_count(be_ra_get_ifg_nodes(pi->co->chordal_env)) == pset_count(pi->removed))
128 pi->all_simplicial = 1;
132 * Add coloring-force conditions
133 * Matrix A: knapsack constraint for each node
135 static void pi_add_constr_A(problem_instance_t *pi) {
138 DBG((dbg, LEVEL_2, "Add A constraints...\n"));
139 /* iterate over all blocks */
140 pmap_foreach(pi->co->chordal_env->border_heads, pme) {
141 struct list_head *head = pme->value;
143 bitset_t *pos_regs = bitset_alloca(pi->co->chordal_env->cls->n_regs);
145 list_for_each_entry_reverse(border_t, curr, head, list)
146 if (curr->is_def && curr->is_real && !is_removed(curr->irn)) {
147 int cst_idx, nnr, col;
149 nnr = get_irn_graph_nr(curr->irn);
150 mangle_cst(pi->buf, 'A', nnr);
151 cst_idx = lpp_add_cst(pi->curr_lp, pi->buf, lpp_equal, 1);
153 // iterate over all possible colors in order
154 bitset_clear_all(pos_regs);
155 arch_get_allocatable_regs(pi->co->chordal_env->arch_env, curr->irn, arch_pos_make_out(0), pi->co->chordal_env->cls, pos_regs);
156 bitset_foreach(pos_regs, col) {
158 mangle_var(pi->buf, 'x', nnr, col);
159 var_idx = lpp_add_var(pi->curr_lp, pi->buf, lpp_binary, 0);
160 pi->last_x_var = var_idx;
161 lpp_set_factor_fast(pi->curr_lp, cst_idx, var_idx, 1);
168 * Checks if all nodes in @p living are live in in block @p block.
169 * @return 1 if all are live in
172 static INLINE int all_live_in(ir_node *block, pset *living) {
174 for (n = pset_first(living); n; n = pset_next(living))
175 if (!is_live_in(block, n)) {
183 * Finds cliques in the interference graph, considering only nodes
184 * for which the color @p color is possible. Finds only 'maximal-cliques',
185 * viz cliques which are not contained in another one.
186 * Matrix B: interference constraints using cliques
188 static void pi_add_constr_B(problem_instance_t *pi, int color) {
189 enum phase_t {growing, shrinking} phase = growing;
192 pset *living = pset_new_ptr(SLOTS_LIVING);
194 DBG((dbg, LEVEL_2, "Add B constraints (col = %d)...\n", color));
195 /* iterate over all blocks */
196 pmap_foreach(pi->co->chordal_env->border_heads, pme) {
197 ir_node *block = pme->key;
198 struct list_head *head = pme->value;
200 list_for_each_entry_reverse(border_t, b, head, list) {
201 const ir_node *irn = b->irn;
202 if (is_removed(irn) || !is_color_possible(irn, color))
206 DBG((dbg, LEVEL_2, "Def %n\n", irn));
207 pset_insert_ptr(living, irn);
209 } else { /* is_use */
210 DBG((dbg, LEVEL_2, "Use %n\n", irn));
212 /* before shrinking the set, store the current 'maximum' clique;
213 * do NOT if clique is a single node
214 * do NOT if all values are live_in (in this case they were contained in a live-out clique elsewhere) */
215 if (phase == growing && pset_count(living) >= 2 && !all_live_in(block, living)) {
218 mangle_cst(pi->buf, 'B', pi->cst_counter);
219 cst_idx = lpp_add_cst(pi->curr_lp, pi->buf, lpp_less, 1);
220 for (n = pset_first(living); n; n = pset_next(living)) {
222 mangle_var_irn(pi->buf, 'x', n, color);
223 var_idx = lpp_get_var_idx(pi->curr_lp, pi->buf);
224 lpp_set_factor_fast(pi->curr_lp, cst_idx, var_idx, 1);
228 pset_remove_ptr(living, irn);
233 assert(0 == pset_count(living));
238 * Generates constraints which interrelate x with y variables.
239 * x1 and x2 have the different colors ==> y_12 = 1
241 static void pi_add_constr_E(problem_instance_t *pi) {
243 bitset_t *root_regs, *arg_regs, *work_regs;
245 unsigned nregs = pi->co->chordal_env->cls->n_regs;
246 root_regs = bitset_alloca(nregs);
247 arg_regs = bitset_alloca(nregs);
248 work_regs = bitset_alloca(nregs);
250 DBG((dbg, LEVEL_2, "Add E constraints...\n"));
251 /* for all roots of optimization units */
252 list_for_each_entry(unit_t, curr, &pi->co->units, units) {
254 int rootnr, argnr, color;
258 root = curr->nodes[0];
259 rootnr = get_irn_graph_nr(root);
260 bitset_clear_all(root_regs);
261 arch_get_allocatable_regs(pi->co->chordal_env->arch_env, root, arch_pos_make_out(0), pi->co->chordal_env->cls, root_regs);
263 /* for all arguments of root */
264 for (i = 1; i < curr->node_count; ++i) {
265 arg = curr->nodes[i];
266 argnr = get_irn_graph_nr(arg);
267 bitset_clear_all(arg_regs);
268 arch_get_allocatable_regs(pi->co->chordal_env->arch_env, arg, arch_pos_make_out(0), pi->co->chordal_env->cls, arg_regs);
270 /* Introduce new variable and set factor in objective function */
271 mangle_var(buf, 'y', rootnr, argnr);
272 y_idx = lpp_add_var(pi->curr_lp, buf, lpp_continous, curr->costs[i]);
274 //BETTER: y vars as binary or continous vars ??
275 /* set starting value */
276 //lpp_set_start_value(pi->curr_lp, y_idx, (get_irn_col(pi->co, root) != get_irn_col(pi->co, arg)));
278 /* For all colors root and arg have in common, add 2 constraints to E */
279 bitset_copy(work_regs, root_regs);
280 bitset_and(work_regs, arg_regs);
281 bitset_foreach(work_regs, color) {
282 int root_idx, arg_idx, cst_idx;
283 mangle_var(buf, 'x', rootnr, color);
284 root_idx = lpp_get_var_idx(pi->curr_lp, buf);
285 mangle_var(buf, 'x', argnr, color);
286 arg_idx = lpp_get_var_idx(pi->curr_lp, buf);
288 /* add root-arg-y <= 0 */
289 mangle_cst(buf, 'E', cst_counter++);
290 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_less, 0);
291 lpp_set_factor_fast(pi->curr_lp, cst_idx, root_idx, 1);
292 lpp_set_factor_fast(pi->curr_lp, cst_idx, arg_idx, -1);
293 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, -1);
295 /* add arg-root-y <= 0 */
296 mangle_cst(buf, 'E', cst_counter++);
297 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_less, 0);
298 lpp_set_factor_fast(pi->curr_lp, cst_idx, root_idx, -1);
299 lpp_set_factor_fast(pi->curr_lp, cst_idx, arg_idx, 1);
300 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, -1);
302 /* For all colors root and arg have "disjunct", add 1 constraints to E.
303 * If root gets a color the arg is not possible to get then they will
304 * definetly get different colors. So y has to be 1.
305 * Vice versa for arg.
307 bitset_copy(work_regs, root_regs);
308 bitset_xor(work_regs, arg_regs);
309 bitset_foreach(work_regs, color) {
310 int root_idx, arg_idx, cst_idx;
311 mangle_var(buf, 'x', rootnr, color);
312 root_idx = lpp_get_var_idx(pi->curr_lp, buf);
313 mangle_var(buf, 'x', argnr, color);
314 arg_idx = lpp_get_var_idx(pi->curr_lp, buf);
316 mangle_cst(buf, 'E', cst_counter++);
317 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_less, 0);
318 if (bitset_is_set(root_regs, color)) {
319 /* add root-y <= 0 */
320 lpp_set_factor_fast(pi->curr_lp, cst_idx, root_idx, 1);
321 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, -1);
323 assert(bitset_is_set(arg_regs, color) && "bitset_xor is buggy");
325 lpp_set_factor_fast(pi->curr_lp, cst_idx, arg_idx, 1);
326 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, -1);
334 * Matrix S: maximum independent set constraints
335 * Generates lower bound-cuts for optimization units with inner interferences.
336 * Sum(y_{root, arg}, arg \in Args) <= max_indep_set_size - 1
338 static void pi_add_constr_S(problem_instance_t *pi) {
341 DBG((dbg, LEVEL_2, "Add S constraints...\n"));
343 /* for all optimization units */
344 list_for_each_entry(unit_t, curr, &pi->co->units, units) {
345 const ir_node *root, *arg;
347 int cst_idx, y_idx, i;
350 if (curr->minimal_costs == 0)
353 root = curr->nodes[0];
354 rootnr = get_irn_graph_nr(root);
355 mangle_cst(buf, 'S', cst_counter++);
356 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_greater, curr->minimal_costs);
358 /* for all arguments */
359 for (i = 1; i < curr->node_count; ++i) {
360 arg = curr->nodes[i];
361 argnr = get_irn_graph_nr(arg);
362 mangle_var(buf, 'y', rootnr, argnr);
363 y_idx = lpp_get_var_idx(pi->curr_lp, buf);
364 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, curr->costs[i]);
369 static INLINE int get_costs(problem_instance_t *pi, ir_node *phi, ir_node *irn) {
372 /* search optimization unit for phi */
373 list_for_each_entry(unit_t, curr, &pi->co->units, units)
374 if (curr->nodes[0] == phi) {
375 for (i=1; i<curr->node_count; ++i)
376 if (curr->nodes[i] == irn)
377 return curr->costs[i];
378 assert(0 && "irn must occur in this ou");
380 assert(0 && "phi must be found in a ou");
384 static void M_constr_walker(ir_node *block, void *env) {
385 problem_instance_t *pi = env;
386 int count, arity, row, col, other_row, *costs;
387 ir_node **phis, *phi, *irn, **phi_matrix;
389 bitset_t *candidates;
391 /* Count all phi nodes of this block */
392 for (count=0, irn = sched_first(block); is_Phi(irn); irn = sched_next(irn))
395 /* We at least 2 phi nodes for this class of inequalities */
399 /* Build the \Phi-Matrix */
400 arity = get_irn_arity(sched_first(block));
401 phis = alloca(count * sizeof(*phis));
402 costs = alloca(count * sizeof(costs));
403 phi_matrix = alloca(count*arity * sizeof(*phi_matrix));
404 candidates = bitset_alloca(count);
406 phi = sched_first(block);
407 for (row=0; row<count; ++row) {
409 for (col=0; col<arity; ++col)
410 phi_matrix[row*arity + col] = get_irn_n(phi, col);
411 phi = sched_next(phi);
414 /* Now find the interesting patterns in the matrix:
415 * All nodes which are used at least twice in a column. */
417 for (col=0; col<arity; ++col) {
418 done = pset_new_ptr_default();
419 for (row=0; row<count; ++row) {
420 irn = phi_matrix[row*arity + col];
421 /* has the irn already been processed in this col? */
422 if (pset_find_ptr(done, irn))
425 pset_insert_ptr(done, irn);
427 /* insert irn in candidates */
428 bitset_clear_all(candidates);
429 bitset_set(candidates, row);
430 /* search the irn in the rows below */
431 for (other_row = row+1; other_row<count; ++other_row)
432 if (irn == phi_matrix[other_row*arity + col]) {
433 /* found the irn in the same col in another row */
434 bitset_set(candidates, other_row);
437 /* now we know all occurences of irn in this col */
438 if (bitset_popcnt(candidates) < 2)
441 /* compute the minimal costs (rhs) */
442 int phi_nr, sum=0, max=-1, minimal_costs;
443 bitset_foreach(candidates, phi_nr) {
444 costs[phi_nr] = get_costs(pi, phis[phi_nr], irn);
445 sum += costs[phi_nr];
446 max = MAX(max, costs[phi_nr]);
448 minimal_costs = sum - max;
450 /* generate an unequation finally.
451 * phis are indexed in the bitset,
452 * shared argument is irn
453 * rhs is minimal_costs */
457 int pos, irnnr, rootnr, cst_idx, y_idx, cst_counter = 0;
459 irnnr = get_irn_graph_nr(irn);
460 mangle_cst(buf, 'M', cst_counter++);
461 cst_idx = lpp_add_cst(pi->curr_lp, buf, lpp_greater, minimal_costs);
464 bitset_foreach(candidates, pos) {
466 rootnr = get_irn_graph_nr(root);
467 mangle_var(buf, 'y', rootnr, irnnr);
468 y_idx = lpp_get_var_idx(pi->curr_lp, buf);
469 lpp_set_factor_fast(pi->curr_lp, cst_idx, y_idx, costs[pos]);
473 del_pset(done); /* clear set for next row */
478 * Matrix M: Multi-Arg-Use. Interrelates different \phi-functions
479 * in the same block, iff they use the same arg at the same pos.
480 * Only one of the phis can get the arg.
482 static void pi_add_constr_M(problem_instance_t *pi) {
483 dom_tree_walk_irg(pi->co->chordal_env->irg, M_constr_walker, NULL, pi);
487 * Generate the initial problem matrices and vectors.
489 static problem_instance_t *new_pi(const copy_opt_t *co) {
490 problem_instance_t *pi;
493 DBG((dbg, LEVEL_2, "Generating new instance...\n"));
494 pi = xcalloc(1, sizeof(*pi));
496 pi->removed = pset_new_ptr_default();
497 INIT_LIST_HEAD(&pi->simplicials);
498 pi->dilp = new_lpp(co->name, lpp_minimize);
501 /* problem size reduction */
502 pi_find_simplicials(pi);
503 //BETTER If you wish to see it: dump_ifg_w/o_removed
504 if (pi->all_simplicial)
507 /* built objective abd constraints */
508 pi->curr_lp = pi->dilp;
510 for (col = 0; col < pi->co->chordal_env->cls->n_regs; ++col)
511 pi_add_constr_B(pi, col);
520 * Clean the problem instance
522 static void free_pi(problem_instance_t *pi) {
523 simpl_t *simpl, *tmp;
525 DBG((dbg, LEVEL_2, "Free instance...\n"));
527 list_for_each_entry_safe(simpl_t, simpl, tmp, &pi->simplicials, chain)
529 del_pset(pi->removed);
534 * Set starting values for the mip problem according
535 * to the current coloring of the graph.
537 static void pi_set_start_sol(problem_instance_t *pi) {
540 DBG((dbg, LEVEL_2, "Set start solution...\n"));
541 for (i=1; i<=pi->last_x_var; ++i) {
544 /* get variable name */
545 lpp_get_var_name(pi->curr_lp, i, var_name, sizeof(var_name));
546 /* split into components */
547 if (split_var(var_name, &nnr, &col) == 2) {
548 assert(get_irn_col(pi->co, get_irn_for_graph_nr(pi->co->chordal_env->irg, nnr)) != -1);
549 val = (get_irn_col(pi->co, get_irn_for_graph_nr(pi->co->chordal_env->irg, nnr)) == col) ? 1 : 0;
550 lpp_set_start_value(pi->curr_lp, i, val);
552 fprintf(stderr, "Variable name is: %s\n", var_name);
553 assert(0 && "x vars always look like this 'x123_45'");
561 static void pi_solve_ilp(problem_instance_t *pi) {
562 pi_set_start_sol(pi);
563 lpp_solve_net(pi->curr_lp, LPP_HOST, LPP_SOLVER);
567 * Set the color of all simplicial nodes removed form
568 * the graph before transforming it to an ilp.
570 static void pi_set_simplicials(problem_instance_t *pi) {
571 simpl_t *simpl, *tmp;
572 bitset_t *used_cols = bitset_alloca(arch_register_class_n_regs(pi->co->chordal_env->cls));
574 DBG((dbg, LEVEL_2, "Set simplicials...\n"));
575 /* color the simplicial nodes in right order */
576 list_for_each_entry_safe(simpl_t, simpl, tmp, &pi->simplicials, chain) {
578 ir_node *other_irn, *irn;
579 if_node_t *other, *ifn;
581 /* get free color by inspecting all neighbors */
583 irn = get_irn_for_graph_nr(pi->co->chordal_env->irg, ifn->nnr);
584 bitset_clear_all(used_cols);
585 foreach_neighb(ifn, other) {
586 other_irn = get_irn_for_graph_nr(pi->co->chordal_env->irg, other->nnr);
587 if (!is_removed(other_irn)) /* only inspect nodes which are in graph right now */
588 bitset_set(used_cols, get_irn_col(pi->co, other_irn));
591 /* now all bits not set are possible colors */
592 free_col = bitset_next_clear(used_cols, 0);
593 assert(free_col != -1 && "No free color found. This can not be.");
594 set_irn_col(pi->co, irn, free_col);
595 pset_remove_ptr(pi->removed, irn); /* irn is back in graph again */
600 * Sets the colors of irns according to the values of variables
601 * provided by the solution of the solver.
603 static void pi_apply_solution(problem_instance_t *pi) {
606 lpp_sol_state_t state;
607 DBG((dbg, LEVEL_2, "Applying solution...\n"));
610 curr_vals[I_ILP_ITER] += lpp_get_iter_cnt(pi->curr_lp);
611 curr_vals[I_ILP_TIME] += lpp_get_sol_time(pi->curr_lp);
614 sol = xmalloc((pi->last_x_var+1) * sizeof(*sol));
615 state = lpp_get_solution(pi->curr_lp, sol, 1, pi->last_x_var);
616 if (state != lpp_optimal) {
617 printf("Solution state is not 'optimal': %d\n", state);
618 assert(state >= lpp_feasible && "The solution should at least be feasible!");
620 for (i=0; i<pi->last_x_var; ++i) {
624 if (sol[i] > 1-EPSILON) { /* split varibale name into components */
625 lpp_get_var_name(pi->curr_lp, 1+i, var_name, sizeof(var_name));
626 if (split_var(var_name, &nnr, &col) == 2) {
627 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]));
628 DBG((dbg, LEVEL_2, "x%d = %d\n", nnr, col));
629 set_irn_col(pi->co, get_irn_for_graph_nr(pi->co->chordal_env->irg, nnr), col);
631 assert(0 && "This should be a x-var");
636 void co_ilp_opt(copy_opt_t *co) {
637 problem_instance_t *pi;
639 dbg = firm_dbg_register("ir.be.copyoptilp");
640 if (!strcmp(co->name, DEBUG_IRG))
641 firm_dbg_set_mask(dbg, DEBUG_IRG_LVL_ILP);
643 firm_dbg_set_mask(dbg, DEBUG_LVL_ILP);
646 if (!pi->all_simplicial) {
649 snprintf(buf, sizeof(buf), "%s.mps", co->name);
650 lpp_dump(pi->curr_lp, buf);
653 pi_apply_solution(pi);
654 pi_set_simplicials(pi);