2 * Minimizing copies with an exact algorithm using mixed integer programming (MIP).
3 * Problem statement as a 'quadratic 0-1 program with linear constraints' with
4 * n binary variables. Constraints are knapsack (enforce color for each node) and
5 * cliques of ifg (interference constraints).
6 * Transformation into a 'mixed integer program' with n binary variables and
7 * additional 2n real variables. Constraints are the above the transformed
8 * objective function and 'complementary conditions' for two var classes.
11 * NOTE: Unfortunately no good solver is available locally (or even for linking)
12 * We use CPLEX 9.0 which runs on a machine residing at the Rechenzentrum.
16 #include "becopyopt.h"
17 #include "becopystat.h"
19 #undef DUMP_MATRICES /**< dumps all matrices completely. only recommended for small problems */
20 #define DUMP_MILP /**< dumps the problem as Mixed Integer Linear Programming in "CPLEX"-MPS format. NOT fixed-column-MPS. */
21 #undef DO_SOLVE /**< solve the MPS output with CPLEX */
22 #undef DELETE_FILES /**< deletes all dumped files after use */
24 /* CPLEX-account related stuff */
25 #define SSH_USER_HOST "kb61@sp-smp.rz.uni-karlsruhe.de"
26 #define SSH_PASSWD_FILE "/ben/daniel/.smppw"
27 #define EXPECT_FILENAME "runme" /** name of the expect-script */
29 #define DEBUG_LVL 0 //SET_LEVEL_1
30 static firm_dbg_module_t *dbg = NULL;
32 #define SLOTS_NUM2POS 256
33 #define SLOTS_LIVING 32
35 /* get_weight represents the _gain_ if node n and m have the same color. */
36 #define get_weight(n,m) 1
39 * A type storing names of the x variables in the form x[NUMBER]_[COLOR]
41 typedef struct _x_name_t {
46 * For each node taking part in the opt-problem its position in the
47 * x-variable-vector is stored in a set. This set maps the node-nr (given by
48 * benumb) to the position in the vector.
50 typedef struct _num2pos_t {
55 * A type storing the unmodified '0-1 quadratic program' of the form
61 * This problem is called the original problem
63 typedef struct _problem_instance_t {
64 const copy_opt_t *co; /** the original copy_opt problem */
65 int x_dim, A_dim, B_dim; /**< number of: x variables (equals Q_dim), rows in A, rows in B */
66 x_name_t *x; /**< stores the names of the x variables. all possible colors for a node are ordered and occupy consecutive entries. lives in obstack ob. */
67 set *num2pos; /**< maps node numbers to positions in x. */
68 sp_matrix_t *Q, *A, *B; /**< the (sparse) matrices of this problem */
70 /* needed only for linearizations */
71 int bigM, maxQij, minQij;
73 /* overhead needed to build this */
79 /* Nodes have consecutive numbers so this hash shoud be fine */
80 #define HASH_NUM(num) num
82 static int set_cmp_num2pos(const void *x, const void *y, size_t size) {
83 return ((num2pos_t *)x)->num != ((num2pos_t *)y)->num;
87 * Sets the first position of node with number num to pos.
88 * See x_name_t *x in _problem_instance_t.
90 static INLINE void pi_set_first_pos(problem_instance_t *pi, int num, int pos) {
94 set_insert(pi->num2pos, &find, sizeof(find), HASH_NUM(num));
98 * Get position by number. (First possible color)
99 * returns -1 if not found.
101 static INLINE int pi_get_first_pos(problem_instance_t *pi, int num) {
102 num2pos_t find, *found;
104 found = set_find(pi->num2pos, &find, sizeof(find), HASH_NUM(num));
106 assert(pi->x[found->pos].n == num && (found->pos == 0 || pi->x[found->pos-1].n != num) && "pi->num2pos is broken!");
113 * Get position by number and color.
114 * returns -1 if not found.
116 static INLINE int pi_get_pos(problem_instance_t *pi, int num, int col) {
117 num2pos_t find, *found;
120 found = set_find(pi->num2pos, &find, sizeof(find), HASH_NUM(num));
124 while (pos < pi->x_dim && pi->x[pos].n == num && pi->x[pos].c < col)
127 if (pi->x[pos].n == num && pi->x[pos].c == col)
135 * Dump the raw matrices of the problem to a file for debugging.
137 static void pi_dump_matrices(problem_instance_t *pi) {
139 FILE *out = ffopen(pi->co->name, "matrix", "wt");
141 DBG((dbg, LEVEL_1, "Dumping raw...\n"));
142 fprintf(out, "\n\nx-names =\n");
143 for (i=0; i<pi->x_dim; ++i)
144 fprintf(out, "%5d %2d\n", pi->x[i].n, pi->x[i].c);
146 fprintf(out, "\n\n-Q =\n");
147 matrix_dump(pi->Q, out, -1);
149 fprintf(out, "\n\nA =\n");
150 matrix_dump(pi->A, out, 1);
152 fprintf(out, "\n\nB =\n");
153 matrix_dump(pi->B, out, 1);
161 * Dumps an mps file representing the problem. This is NOT the old-style,
162 * fixed-column format. Some white spaces are important, in general spaces
163 * are separators, MARKER-lines are used in COLUMN section to define binaries.
165 //BETTER use last 2 fields in COLUMNS section. See MPS docu for details
166 static void pi_dump_milp(problem_instance_t *pi) {
168 const matrix_elem_t *e;
169 FILE *out = ffopen(pi->co->name, "milp", "wt");
171 DBG((dbg, LEVEL_1, "Dumping milp...\n"));
172 max_abs_Qij = pi->maxQij;
173 if (-pi->minQij > max_abs_Qij)
174 max_abs_Qij = -pi->minQij;
175 pi->bigM = pi->A_dim * max_abs_Qij;
176 DBG((dbg, LEVEL_2, "BigM = %d\n", pi->bigM));
178 matrix_optimize(pi->Q);
179 bitset_t *good_row = bitset_alloca(pi->x_dim);
180 for (i=0; i<pi->x_dim; ++i)
181 if (matrix_row_first(pi->Q, i))
182 bitset_set(good_row, i);
184 fprintf(out, "NAME %s\n", pi->co->name);
186 fprintf(out, "ROWS\n");
187 fprintf(out, " N obj\n");
188 for (i=0; i<pi->x_dim; ++i)
189 if (bitset_is_set(good_row, i))
190 fprintf(out, " E cQ%d\n", i);
191 for (i=0; i<pi->A_dim; ++i)
192 fprintf(out, " E cA%d\n", i);
193 for (i=0; i<pi->B_dim; ++i)
194 fprintf(out, " L cB%d\n", i);
195 for (i=0; i<pi->x_dim; ++i)
196 if (bitset_is_set(good_row, i))
197 fprintf(out, " L cy%d\n", i);
199 fprintf(out, "COLUMNS\n");
200 /* the x vars come first */
201 /* mark them as binaries */
202 fprintf(out, " MARKI0\t'MARKER'\t'INTORG'\n");
203 for (i=0; i<pi->x_dim; ++i) {
204 /* participation in objective */
205 if (bitset_is_set(good_row, i))
206 fprintf(out, " x%d_%d\tobj\t%d\n", pi->x[i].n, pi->x[i].c, -pi->bigM);
208 matrix_foreach_in_col(pi->Q, i, e)
209 fprintf(out, " x%d_%d\tcQ%d\t%d\n", pi->x[i].n, pi->x[i].c, e->row, e->val);
211 matrix_foreach_in_col(pi->A, i, e)
212 fprintf(out, " x%d_%d\tcA%d\t%d\n", pi->x[i].n, pi->x[i].c, e->row, e->val);
214 matrix_foreach_in_col(pi->B, i, e)
215 fprintf(out, " x%d_%d\tcB%d\t%d\n", pi->x[i].n, pi->x[i].c, e->row, e->val);
217 if (bitset_is_set(good_row, i))
218 fprintf(out, " x%d_%d\tcy%d\t%d\n", pi->x[i].n, pi->x[i].c, i, 2*pi->bigM);
221 fprintf(out, " MARKI1\t'MARKER'\t'INTEND'\n"); /* end of marking */
223 /* next the s vars */
224 for (i=0; i<pi->x_dim; ++i)
225 if (bitset_is_set(good_row, i)) {
226 /* participation in objective */
227 fprintf(out, " s%d_%d\tobj\t%d\n", pi->x[i].n, pi->x[i].c, 1);
229 fprintf(out, " s%d_%d\tcQ%d\t%d\n", pi->x[i].n, pi->x[i].c, i, -1);
232 /* next the y vars */
233 for (i=0; i<pi->x_dim; ++i)
234 if (bitset_is_set(good_row, i)) {
236 fprintf(out, " y%d_%d\tcQ%d\t%d\n", pi->x[i].n, pi->x[i].c, i, -1);
238 fprintf(out, " y%d_%d\tcy%d\t%d\n", pi->x[i].n, pi->x[i].c, i, 1);
241 fprintf(out, "RHS\n");
242 for (i=0; i<pi->x_dim; ++i)
243 if (bitset_is_set(good_row, i))
244 fprintf(out, " rhs\tcQ%d\t%d\n", i, -pi->bigM);
245 for (i=0; i<pi->A_dim; ++i)
246 fprintf(out, " rhs\tcA%d\t%d\n", i, 1);
247 for (i=0; i<pi->B_dim; ++i)
248 fprintf(out, " rhs\tcB%d\t%d\n", i, 1);
249 for (i=0; i<pi->x_dim; ++i)
250 if (bitset_is_set(good_row, i))
251 fprintf(out, " rhs\tcy%d\t%d\n", i, 2*pi->bigM);
253 fprintf(out, "ENDATA\n");
260 * Dumps the known solution to a file to make use of it
261 * as a starting solution respectively as a bound
263 static void pi_dump_start_sol(problem_instance_t *pi) {
265 FILE *out = ffopen(pi->co->name, "mst", "wt");
266 fprintf(out, "NAME\n");
267 for (i=0; i<pi->x_dim; ++i) {
271 if (get_irn_color(get_irn_for_graph_nr(pi->co->irg, n)) == c)
275 fprintf(out, " x%d_%d\t%d\n", n, c, val);
277 fprintf(out, "ENDATA\n");
282 * Invoke an external solver
284 static void pi_solve_ilp(problem_instance_t *pi) {
288 DBG((dbg, LEVEL_1, "Solving with CPLEX@RZ...\n"));
289 /* write command file for CPLEX */
290 out = ffopen(pi->co->name, "cmd", "wt");
291 fprintf(out, "set logfile %s.sol\n", pi->co->name);
293 fprintf(out, "read %s.milp mps\n", pi->co->name);
296 fprintf(out, "read %s.miqp mps\n", pi->co->name);
298 fprintf(out, "read %s.mst\n", pi->co->name);
299 fprintf(out, "set mip strategy mipstart 1\n");
300 fprintf(out, "set mip emphasis 3\n");
301 fprintf(out, "optimize\n");
302 fprintf(out, "display solution variables 1-%d\n", pi->x_dim);
303 fprintf(out, "set logfile cplex.log\n");
304 fprintf(out, "quit\n");
307 /* write expect-file for copying problem to RZ */
308 pwfile = fopen(SSH_PASSWD_FILE, "rt");
309 fgets(passwd, sizeof(passwd), pwfile);
312 out = ffopen(EXPECT_FILENAME, "exp", "wt");
313 fprintf(out, "#! /usr/bin/expect\n");
314 fprintf(out, "spawn scp %s.miqp %s.milp %s.mst %s.cmd %s:\n", pi->co->name, pi->co->name, pi->co->name, pi->co->name, SSH_USER_HOST); /* copy problem files */
315 fprintf(out, "expect \"word:\"\nsend \"%s\\n\"\ninteract\n", passwd);
317 fprintf(out, "spawn ssh %s \"./cplex90 < %s.cmd\"\n", SSH_USER_HOST, pi->co->name); /* solve */
318 fprintf(out, "expect \"word:\"\nsend \"%s\\n\"\ninteract\n", passwd);
320 fprintf(out, "spawn scp %s:%s.sol .\n", SSH_USER_HOST, pi->co->name); /*copy back solution */
321 fprintf(out, "expect \"word:\"\nsend \"%s\\n\"\ninteract\n", passwd);
323 fprintf(out, "spawn ssh %s ./dell\n", SSH_USER_HOST); /* clean files on server */
324 fprintf(out, "expect \"word:\"\nsend \"%s\\n\"\ninteract\n", passwd);
327 /* call the expect script */
328 chmod(EXPECT_FILENAME ".exp", 0700);
329 system(EXPECT_FILENAME ".exp");
333 * Sets the colors of irns according to the values of variables found in the
334 * output file of the solver.
336 static void pi_apply_solution(problem_instance_t *pi) {
337 FILE *in = ffopen(pi->co->name, "sol", "rt");
341 DBG((dbg, LEVEL_1, "Applying solution...\n"));
344 int num = -1, col = -1, val = -1;
346 fgets(buf, sizeof(buf), in);
347 DBG((dbg, LEVEL_3, "Line: %s", buf));
349 if (strcmp(buf, "No integer feasible solution exists.") == 0)
350 assert(0 && "CPLEX says: No integer feasible solution exists!");
352 if (strcmp(buf, "TODO Out of memory") == 0) {}
359 if (sscanf(buf, "Solution time = %f sec. Iterations = %d", &sol_time, &iter) == 2) {
360 DBG((dbg, LEVEL_2, " Time: %f Iter: %d\n", sol_time, iter));
361 curr_vals[I_ILP_TIME] += 10 * sol_time;
362 curr_vals[I_ILP_ITER] += iter;
368 if (sscanf(buf, "x%d_%d %d", &num, &col, &val) == 3 && val == 1) {
369 DBG((dbg, LEVEL_2, " x%d_%d = %d\n", num, col, val));
370 set_irn_color(get_irn_for_graph_nr(pi->co->irg, num), col);
375 #endif /* DO_SOLVE */
378 static void pi_delete_files(problem_instance_t *pi) {
380 int end = snprintf(buf, sizeof(buf), "%s", pi->co->name);
381 DBG((dbg, LEVEL_1, "Deleting files...\n"));
383 snprintf(buf+end, sizeof(buf)-end, ".matrix");
387 snprintf(buf+end, sizeof(buf)-end, ".mps");
389 snprintf(buf+end, sizeof(buf)-end, ".mst");
391 snprintf(buf+end, sizeof(buf)-end, ".cmd");
393 remove(EXPECT_FILENAME ".exp");
396 snprintf(buf+end, sizeof(buf)-end, ".sol");
403 * Collects all irns in currently processed register class
405 static void pi_collect_x_names(ir_node *block, void *env) {
406 problem_instance_t *pi = env;
407 struct list_head *head = &get_ra_block_info(block)->border_head;
409 bitset_t *pos_regs = bitset_alloca(pi->co->cls->n_regs);
411 list_for_each_entry_reverse(border_t, curr, head, list)
412 if (curr->is_def && curr->is_real) {
414 pi->A_dim++; /* one knapsack constraint for each node */
416 xx.n = get_irn_graph_nr(curr->irn);
417 pi_set_first_pos(pi, xx.n, pi->x_dim);
419 // iterate over all possible colors in order
420 bitset_clear_all(pos_regs);
421 pi->co->isa->get_allocatable_regs(curr->irn, pi->co->cls, pos_regs);
422 bitset_foreach(pos_regs, xx.c) {
423 DBG((dbg, LEVEL_2, "Adding %n %d\n", curr->irn, xx.c));
424 obstack_grow(&pi->ob, &xx, sizeof(xx));
425 pi->x_dim++; /* one x variable for each node and color */
431 * Checks if all nodes in living are live_out in block block.
433 static INLINE int all_live_in(ir_node *block, pset *living) {
435 for (n = pset_first(living); n; n = pset_next(living))
436 if (!is_live_in(block, n)) {
444 * Finds cliques in the interference graph, considering only nodes
445 * for which the color pi->curr_color is possible. Finds only 'maximal-cliques',
446 * viz cliques which are not conatained in another one.
447 * This is used for the matrix B.
449 static void pi_clique_finder(ir_node *block, void *env) {
450 problem_instance_t *pi = env;
451 enum phase_t {growing, shrinking} phase = growing;
452 struct list_head *head = &get_ra_block_info(block)->border_head;
454 pset *living = pset_new_ptr(SLOTS_LIVING);
456 list_for_each_entry_reverse(border_t, b, head, list) {
457 const ir_node *irn = b->irn;
460 DBG((dbg, LEVEL_2, "Def %n\n", irn));
461 pset_insert_ptr(living, irn);
463 } else { /* is_use */
464 DBG((dbg, LEVEL_2, "Use %n\n", irn));
466 /* before shrinking the set, store the current 'maximum' clique;
467 * do NOT if clique is a single node
468 * do NOT if all values are live_in (in this case they were contained in a live-out clique elsewhere) */
469 if (phase == growing && pset_count(living) >= 2 && !all_live_in(block, living)) {
471 for (n = pset_first(living); n; n = pset_next(living)) {
472 int pos = pi_get_pos(pi, get_irn_graph_nr(n), pi->curr_color);
473 matrix_set(pi->B, pi->curr_row, pos, 1);
474 DBG((dbg, LEVEL_2, "B[%d, %d] := %d\n", pi->curr_row, pos, 1));
478 pset_remove_ptr(living, irn);
487 * Generate the initial problem matrices and vectors.
489 static problem_instance_t *new_pi(const copy_opt_t *co) {
490 DBG((dbg, LEVEL_1, "Generating new instance...\n"));
491 problem_instance_t *pi = calloc(1, sizeof(*pi));
493 pi->num2pos = new_set(set_cmp_num2pos, SLOTS_NUM2POS);
497 * one entry per node and possible color */
498 obstack_init(&pi->ob);
499 dom_tree_walk_irg(co->irg, pi_collect_x_names, NULL, pi);
500 pi->x = obstack_finish(&pi->ob);
503 * weights for the 'same-color-optimization' target */
506 pi->Q = new_matrix(pi->x_dim, pi->x_dim);
508 list_for_each_entry(unit_t, curr, &co->units, units) {
509 const ir_node *root, *arg;
511 unsigned rootpos, argpos;
514 root = curr->nodes[0];
515 rootnr = get_irn_graph_nr(root);
516 rootpos = pi_get_first_pos(pi, rootnr);
517 for (i = 1; i < curr->node_count; ++i) {
518 int weight = -get_weight(root, arg);
519 arg = curr->nodes[i];
520 argnr = get_irn_graph_nr(arg);
521 argpos = pi_get_first_pos(pi, argnr);
523 DBG((dbg, LEVEL_2, "Q[%n, %n] := %d\n", root, arg, weight));
524 /* for all colors root and arg have in common, set the weight for
525 * this pair in the objective function matrix Q */
526 while (rootpos < pi->x_dim && argpos < pi->x_dim &&
527 pi->x[rootpos].n == rootnr && pi->x[argpos].n == argnr) {
528 if (pi->x[rootpos].c < pi->x[argpos].c)
530 else if (pi->x[rootpos].c > pi->x[argpos].c)
533 matrix_set(pi->Q, rootpos++, argpos++, weight);
535 if (weight < pi->minQij) {
536 DBG((dbg, LEVEL_2, "minQij = %d\n", weight));
539 if (weight > pi->maxQij) {
540 DBG((dbg, LEVEL_2, "maxQij = %d\n", weight));
550 * knapsack constraint for each node */
552 int row = 0, col = 0;
553 pi->A = new_matrix(pi->A_dim, pi->x_dim);
554 while (col < pi->x_dim) {
555 int curr_n = pi->x[col].n;
556 while (col < pi->x_dim && pi->x[col].n == curr_n) {
557 DBG((dbg, LEVEL_2, "A[%d, %d] := %d\n", row, col, 1));
558 matrix_set(pi->A, row, col++, 1);
562 assert(row == pi->A_dim);
566 * interference constraints using exactly those cliques not contained in others. */
568 int color, expected_clipques = pi->A_dim/4 * pi->co->cls->n_regs;
569 pi->B = new_matrix(expected_clipques, pi->x_dim);
570 for (color = 0; color < pi->co->cls->n_regs; ++color) {
571 pi->curr_color = color;
572 dom_tree_walk_irg(pi->co->irg, pi_clique_finder, NULL, pi);
574 pi->B_dim = matrix_get_rowcount(pi->B);
581 * clean the problem instance
583 static void free_pi(problem_instance_t *pi) {
584 DBG((dbg, LEVEL_1, "Generating new instance...\n"));
588 del_set(pi->num2pos);
589 obstack_free(&pi->ob, NULL);
593 void co_ilp_opt(copy_opt_t *co) {
594 dbg = firm_dbg_register("ir.be.copyoptilp");
595 firm_dbg_set_mask(dbg, DEBUG_LVL);
596 if (!strcmp(co->name, DEBUG_IRG))
597 firm_dbg_set_mask(dbg, -1);
599 problem_instance_t *pi = new_pi(co);
600 DBG((dbg, 0, "\t\t\t %5d %5d %5d\n", pi->x_dim, pi->A_dim, pi->B_dim));
604 pi_dump_matrices(pi);
612 pi_dump_start_sol(pi);
614 pi_apply_solution(pi);