nsz Git - libfirm/blob - heuristical.c

   1 #include "adt/array.h"
   2 #include "assert.h"
   3 #include "error.h"
   4
   5 #include "bucket.h"
   6 #include "heuristical.h"
   7 #if     KAPS_DUMP
   8 #include "html_dumper.h"
   9 #endif
  10 #include "kaps.h"
  11 #include "matrix.h"
  12 #include "pbqp_edge.h"
  13 #include "pbqp_edge_t.h"
  14 #include "pbqp_node.h"
  15 #include "pbqp_node_t.h"
  16 #include "vector.h"
  17
  18 static pbqp_edge **edge_bucket;
  19 static pbqp_node **node_buckets[4];
  20 static pbqp_node **reduced_bucket = NULL;
  21 static int         buckets_filled = 0;
  22
  23 #if KAPS_STATISTIC
  24 static int dump = 0;
  25 #endif
  26
  27 /* Forward declarations. */
  28 static void apply_Brute_Force(pbqp *pbqp);
  29
  30 static void insert_into_edge_bucket(pbqp_edge *edge)
  31 {
  32         if (edge_bucket_contains(edge_bucket, edge)) {
  33                 /* Edge is already inserted. */
  34                 return;
  35         }
  36
  37         edge_bucket_insert(&edge_bucket, edge);
  38 }
  39
  40 static void init_buckets(void)
  41 {
  42         int i;
  43
  44         edge_bucket_init(&edge_bucket);
  45         node_bucket_init(&reduced_bucket);
  46
  47         for (i = 0; i < 4; ++i) {
  48                 node_bucket_init(&node_buckets[i]);
  49         }
  50 }
  51
  52 static void free_buckets(void)
  53 {
  54         int i;
  55
  56         for (i = 0; i < 4; ++i) {
  57                 node_bucket_free(&node_buckets[i]);
  58         }
  59
  60         edge_bucket_free(&edge_bucket);
  61         node_bucket_free(&reduced_bucket);
  62
  63         buckets_filled = 0;
  64 }
  65
  66 static void fill_node_buckets(pbqp *pbqp)
  67 {
  68         unsigned node_index;
  69         unsigned node_len;
  70
  71         assert(pbqp);
  72         node_len = pbqp->num_nodes;
  73
  74         for (node_index = 0; node_index < node_len; ++node_index) {
  75                 unsigned   degree;
  76                 pbqp_node *node = get_node(pbqp, node_index);
  77
  78                 if (!node) continue;
  79
  80                 degree = pbqp_node_get_degree(node);
  81
  82                 /* We have only one bucket for nodes with arity >= 3. */
  83                 if (degree > 3) {
  84                         degree = 3;
  85                 }
  86
  87                 node_bucket_insert(&node_buckets[degree], node);
  88         }
  89
  90         buckets_filled = 1;
  91 }
  92
  93 static void normalize_towards_source(pbqp *pbqp, pbqp_edge *edge)
  94 {
  95         pbqp_matrix    *mat;
  96         pbqp_node      *src_node;
  97         pbqp_node      *tgt_node;
  98         vector         *src_vec;
  99         vector         *tgt_vec;
 100         int             src_len;
 101         int             tgt_len;
 102         int             src_index;
 103
 104         assert(pbqp);
 105         assert(edge);
 106
 107         src_node = edge->src;
 108         tgt_node = edge->tgt;
 109         assert(src_node);
 110         assert(tgt_node);
 111
 112         src_vec = src_node->costs;
 113         tgt_vec = tgt_node->costs;
 114         assert(src_vec);
 115         assert(tgt_vec);
 116
 117         src_len = src_vec->len;
 118         tgt_len = tgt_vec->len;
 119         assert(src_len > 0);
 120         assert(tgt_len > 0);
 121
 122         mat = edge->costs;
 123         assert(mat);
 124
 125         /* Normalize towards source node. */
 126         for (src_index = 0; src_index < src_len; ++src_index) {
 127                 num min = pbqp_matrix_get_row_min(mat, src_index, tgt_vec);
 128
 129                 if (min != 0) {
 130                         if (src_vec->entries[src_index].data == INF_COSTS) {
 131                                 pbqp_matrix_set_row_value(mat, src_index, 0);
 132                         } else {
 133                                 pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
 134                         }
 135                         src_vec->entries[src_index].data = pbqp_add(
 136                                         src_vec->entries[src_index].data, min);
 137
 138                         if (min == INF_COSTS) {
 139                                 unsigned edge_index;
 140                                 unsigned edge_len = pbqp_node_get_degree(src_node);
 141
 142                                 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
 143                                         pbqp_edge *edge_candidate = src_node->edges[edge_index];
 144                                         if (edge_candidate != edge) {
 145                                                 insert_into_edge_bucket(edge_candidate);
 146                                         }
 147                                 }
 148                         }
 149                 }
 150         }
 151 }
 152
 153 static void normalize_towards_target(pbqp *pbqp, pbqp_edge *edge)
 154 {
 155         pbqp_matrix    *mat;
 156         pbqp_node      *src_node;
 157         pbqp_node      *tgt_node;
 158         vector         *src_vec;
 159         vector         *tgt_vec;
 160         int             src_len;
 161         int             tgt_len;
 162         int             tgt_index;
 163
 164         assert(pbqp);
 165         assert(edge);
 166
 167         src_node = edge->src;
 168         tgt_node = edge->tgt;
 169         assert(src_node);
 170         assert(tgt_node);
 171
 172         src_vec = src_node->costs;
 173         tgt_vec = tgt_node->costs;
 174         assert(src_vec);
 175         assert(tgt_vec);
 176
 177         src_len = src_vec->len;
 178         tgt_len = tgt_vec->len;
 179         assert(src_len > 0);
 180         assert(tgt_len > 0);
 181
 182         mat = edge->costs;
 183         assert(mat);
 184
 185         for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
 186                 num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
 187
 188                 if (min != 0) {
 189                         if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
 190                                 pbqp_matrix_set_col_value(mat, tgt_index, 0);
 191                         } else {
 192                                 pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
 193                         }
 194                         tgt_vec->entries[tgt_index].data = pbqp_add(
 195                                         tgt_vec->entries[tgt_index].data, min);
 196
 197                         if (min == INF_COSTS) {
 198                                 unsigned edge_index;
 199                                 unsigned edge_len = pbqp_node_get_degree(tgt_node);
 200
 201                                 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
 202                                         pbqp_edge *edge_candidate = tgt_node->edges[edge_index];
 203                                         if (edge_candidate != edge) {
 204                                                 insert_into_edge_bucket(edge_candidate);
 205                                         }
 206                                 }
 207                         }
 208                 }
 209         }
 210 }
 211
 212 static void reorder_node(pbqp_node *node)
 213 {
 214         unsigned    degree     = pbqp_node_get_degree(node);
 215         /* Assume node lost one incident edge. */
 216         unsigned    old_degree = degree + 1;
 217
 218         if (!buckets_filled) return;
 219
 220         /* Same bucket as before */
 221         if (degree > 2) return;
 222
 223         if (!node_bucket_contains(node_buckets[old_degree], node)) {
 224                 /* Old arity is new arity, so we have nothing to do. */
 225                 assert(node_bucket_contains(node_buckets[degree], node));
 226                 return;
 227         }
 228
 229         /* Delete node from old bucket... */
 230         node_bucket_remove(&node_buckets[old_degree], node);
 231
 232         /* ..and add to new one. */
 233         node_bucket_insert(&node_buckets[degree], node);
 234 }
 235
 236 #if 0
 237 static void check_melting_possibility(pbqp *pbqp, pbqp_edge *edge)
 238 {
 239         pbqp_matrix    *mat;
 240         pbqp_node      *src_node;
 241         pbqp_node      *tgt_node;
 242         vector         *src_vec;
 243         vector         *tgt_vec;
 244         int             src_len;
 245         int             tgt_len;
 246         int             src_index;
 247         int             tgt_index;
 248
 249         assert(pbqp);
 250         assert(edge);
 251
 252         src_node = edge->src;
 253         tgt_node = edge->tgt;
 254         assert(src_node);
 255         assert(tgt_node);
 256
 257         src_vec = src_node->costs;
 258         tgt_vec = tgt_node->costs;
 259         assert(src_vec);
 260         assert(tgt_vec);
 261
 262         src_len = src_vec->len;
 263         tgt_len = tgt_vec->len;
 264         assert(src_len > 0);
 265         assert(tgt_len > 0);
 266
 267         mat = edge->costs;
 268         assert(mat);
 269
 270         if (src_len == 1 && tgt_len == 1) {
 271                 //panic("Something is wrong");
 272         }
 273
 274         int allRowsOk = 1;
 275         for (src_index = 0; src_index < src_len; ++src_index) {
 276                 int onlyOneZero = 0;
 277                 if (src_vec->entries[src_index].data == INF_COSTS) {
 278                         continue;
 279                 }
 280                 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
 281                         if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
 282                                 continue;
 283                         }
 284                         if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
 285                                 if (onlyOneZero) {
 286                                         onlyOneZero = 0;
 287                                         break;
 288                                 } else {
 289                                         onlyOneZero = 1;
 290                                         continue;
 291                                 }
 292                         }
 293                         if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
 294                                 continue;
 295                         }
 296                         onlyOneZero = 0;
 297                         break;
 298                 }
 299                 allRowsOk &= onlyOneZero;
 300         }
 301
 302         int allColsOk = 1;
 303         for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
 304                 int onlyOneZero = 0;
 305                 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
 306                         continue;
 307                 }
 308                 for (src_index = 0; src_index < src_len; ++src_index) {
 309                         if (src_vec->entries[src_index].data == INF_COSTS) {
 310                                 continue;
 311                         }
 312                         if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
 313                                 if (onlyOneZero) {
 314                                         onlyOneZero = 0;
 315                                         break;
 316                                 } else {
 317                                         onlyOneZero = 1;
 318                                         continue;
 319                                 }
 320                         }
 321                         if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
 322                                 continue;
 323                         }
 324                         onlyOneZero = 0;
 325                         break;
 326                 }
 327                 allColsOk &= onlyOneZero;
 328         }
 329
 330         if (allRowsOk && allColsOk) {
 331                 panic("Hurray");
 332         }
 333 }
 334 #endif
 335
 336 static void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
 337 {
 338         pbqp_matrix    *mat;
 339         pbqp_node      *src_node;
 340         pbqp_node      *tgt_node;
 341         vector         *src_vec;
 342         vector         *tgt_vec;
 343         int             src_len;
 344         int             tgt_len;
 345
 346         assert(pbqp);
 347         assert(edge);
 348
 349         src_node = edge->src;
 350         tgt_node = edge->tgt;
 351         assert(src_node);
 352         assert(tgt_node);
 353
 354         /* If edge are already deleted, we have nothing to do. */
 355         if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
 356                 return;
 357
 358 #if     KAPS_DUMP
 359         if (pbqp->dump_file) {
 360                 char txt[100];
 361                 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
 362                 dump_section(pbqp->dump_file, 3, txt);
 363         }
 364 #endif
 365
 366         src_vec = src_node->costs;
 367         tgt_vec = tgt_node->costs;
 368         assert(src_vec);
 369         assert(tgt_vec);
 370
 371         src_len = src_vec->len;
 372         tgt_len = tgt_vec->len;
 373         assert(src_len > 0);
 374         assert(tgt_len > 0);
 375
 376         mat = edge->costs;
 377         assert(mat);
 378
 379 #if     KAPS_DUMP
 380         if (pbqp->dump_file) {
 381                 fputs("Input:<br>\n", pbqp->dump_file);
 382                 dump_simplifyedge(pbqp, edge);
 383         }
 384 #endif
 385
 386         normalize_towards_source(pbqp, edge);
 387         normalize_towards_target(pbqp, edge);
 388
 389 #if     KAPS_DUMP
 390         if (pbqp->dump_file) {
 391                 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
 392                 dump_simplifyedge(pbqp, edge);
 393         }
 394 #endif
 395
 396         if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
 397 #if     KAPS_DUMP
 398                 if (pbqp->dump_file) {
 399                         fputs("edge has been eliminated<br>\n", pbqp->dump_file);
 400                 }
 401 #endif
 402
 403 #if KAPS_STATISTIC
 404                 if (dump == 0) {
 405                         pbqp->num_edges++;
 406                 }
 407 #endif
 408
 409                 delete_edge(edge);
 410                 reorder_node(src_node);
 411                 reorder_node(tgt_node);
 412         }
 413 }
 414
 415 static void initial_simplify_edges(pbqp *pbqp)
 416 {
 417         unsigned node_index;
 418         unsigned node_len;
 419
 420         assert(pbqp);
 421
 422 #if     KAPS_DUMP
 423         if (pbqp->dump_file) {
 424                 pbqp_dump_input(pbqp);
 425                 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
 426         }
 427 #endif
 428
 429         node_len = pbqp->num_nodes;
 430
 431         init_buckets();
 432
 433         /* First simplify all edges. */
 434         for (node_index = 0; node_index < node_len; ++node_index) {
 435                 unsigned    edge_index;
 436                 pbqp_node  *node = get_node(pbqp, node_index);
 437                 pbqp_edge **edges;
 438                 unsigned    edge_len;
 439
 440                 if (!node) continue;
 441
 442                 edges = node->edges;
 443                 edge_len = pbqp_node_get_degree(node);
 444
 445                 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
 446                         pbqp_edge *edge = edges[edge_index];
 447
 448                         /* Simplify only once per edge. */
 449                         if (node != edge->src) continue;
 450
 451                         simplify_edge(pbqp, edge);
 452                 }
 453         }
 454 }
 455
 456 static num determine_solution(pbqp *pbqp)
 457 {
 458         unsigned node_index;
 459         unsigned node_len;
 460         num      solution   = 0;
 461 #if     KAPS_DUMP
 462         FILE     *file;
 463 #endif
 464
 465         assert(pbqp);
 466
 467 #if     KAPS_DUMP
 468         file = pbqp->dump_file;
 469
 470         if (file) {
 471                 dump_section(file, 1, "4. Determine Solution/Minimum");
 472                 dump_section(file, 2, "4.1. Trivial Solution");
 473         }
 474 #endif
 475
 476         /* Solve trivial nodes and calculate solution. */
 477         node_len = node_bucket_get_length(node_buckets[0]);
 478
 479 #if KAPS_STATISTIC
 480         if (dump == 0) {
 481                 pbqp->num_r0 = node_len;
 482         }
 483 #endif
 484
 485         for (node_index = 0; node_index < node_len; ++node_index) {
 486                 pbqp_node *node = node_buckets[0][node_index];
 487                 assert(node);
 488
 489                 node->solution = vector_get_min_index(node->costs);
 490                 solution       = pbqp_add(solution,
 491                                 node->costs->entries[node->solution].data);
 492
 493 #if     KAPS_DUMP
 494                 if (file) {
 495                         fprintf(file, "node n%d is set to %d<br>\n", node->index, node->solution);
 496                         dump_node(file, node);
 497                 }
 498 #endif
 499         }
 500
 501 #if     KAPS_DUMP
 502         if (file) {
 503                 dump_section(file, 2, "Minimum");
 504                 fprintf(file, "Minimum is equal to %lld.", solution);
 505         }
 506 #endif
 507
 508         return solution;
 509 }
 510
 511 static void back_propagate(pbqp *pbqp)
 512 {
 513         unsigned node_index;
 514         unsigned node_len   = node_bucket_get_length(reduced_bucket);
 515
 516         assert(pbqp);
 517
 518 #if     KAPS_DUMP
 519         if (pbqp->dump_file) {
 520                 dump_section(pbqp->dump_file, 2, "Back Propagation");
 521         }
 522 #endif
 523
 524         for (node_index = node_len; node_index > 0; --node_index) {
 525                 pbqp_node *node = reduced_bucket[node_index - 1];
 526
 527                 switch (pbqp_node_get_degree(node)) {
 528                         case 1:
 529                                 back_propagate_RI(pbqp, node);
 530                                 break;
 531                         case 2:
 532                                 back_propagate_RII(pbqp, node);
 533                                 break;
 534                         default:
 535                                 panic("Only nodes with degree one or two should be in this bucket");
 536                                 break;
 537                 }
 538         }
 539 }
 540
 541 static void apply_heuristic_reductions(pbqp *pbqp)
 542 {
 543         for (;;) {
 544                 if (edge_bucket_get_length(edge_bucket) > 0) {
 545                         apply_edge(pbqp);
 546                 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
 547                         apply_RI(pbqp);
 548                 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
 549                         apply_RII(pbqp);
 550                 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
 551                         apply_RN(pbqp);
 552                 } else {
 553                         return;
 554                 }
 555         }
 556 }
 557
 558 void solve_pbqp_heuristical(pbqp *pbqp)
 559 {
 560         /* Reduce nodes degree ... */
 561         initial_simplify_edges(pbqp);
 562
 563         /* ... and put node into bucket representing their degree. */
 564         fill_node_buckets(pbqp);
 565
 566 #if KAPS_STATISTIC
 567         FILE *fh = fopen("solutions.pb", "a");
 568         fprintf(fh, "Solution");
 569         fclose(fh);
 570 #endif
 571
 572         apply_heuristic_reductions(pbqp);
 573
 574         pbqp->solution = determine_solution(pbqp);
 575
 576 #if KAPS_STATISTIC
 577         fh = fopen("solutions.pb", "a");
 578         fprintf(fh, ": %lld RE:%u R0:%u R1:%u R2:%u RN/BF:%u\n", pbqp->solution,
 579                                 pbqp->num_edges, pbqp->num_r0, pbqp->num_r1, pbqp->num_r2,
 580                                 pbqp->num_rn);
 581         fclose(fh);
 582 #endif
 583
 584         /* Solve reduced nodes. */
 585         back_propagate(pbqp);
 586
 587         free_buckets();
 588 }
 589
 590 void apply_edge(pbqp *pbqp)
 591 {
 592         pbqp_edge *edge = edge_bucket_pop(&edge_bucket);
 593
 594         simplify_edge(pbqp, edge);
 595 }
 596
 597 void apply_RI(pbqp *pbqp)
 598 {
 599         pbqp_node   *node       = node_bucket_pop(&node_buckets[1]);
 600         pbqp_edge   *edge       = node->edges[0];
 601         pbqp_matrix *mat        = edge->costs;
 602         int          is_src     = edge->src == node;
 603         pbqp_node   *other_node;
 604
 605         assert(pbqp_node_get_degree(node) == 1);
 606
 607         if (is_src) {
 608                 other_node = edge->tgt;
 609         } else {
 610                 other_node = edge->src;
 611         }
 612
 613 #if     KAPS_DUMP
 614         if (pbqp->dump_file) {
 615                 char     txt[100];
 616                 sprintf(txt, "RI-Reduction of Node n%d", node->index);
 617                 dump_section(pbqp->dump_file, 2, txt);
 618                 pbqp_dump_graph(pbqp);
 619                 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
 620                 dump_node(pbqp->dump_file, node);
 621                 dump_node(pbqp->dump_file, other_node);
 622                 dump_edge(pbqp->dump_file, edge);
 623         }
 624 #endif
 625
 626         if (is_src) {
 627                 pbqp_matrix_add_to_all_cols(mat, node->costs);
 628                 normalize_towards_target(pbqp, edge);
 629         } else {
 630                 pbqp_matrix_add_to_all_rows(mat, node->costs);
 631                 normalize_towards_source(pbqp, edge);
 632         }
 633         disconnect_edge(other_node, edge);
 634
 635 #if     KAPS_DUMP
 636         if (pbqp->dump_file) {
 637                 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
 638                 dump_node(pbqp->dump_file, other_node);
 639         }
 640 #endif
 641
 642         reorder_node(other_node);
 643
 644 #if KAPS_STATISTIC
 645         if (dump == 0) {
 646                 pbqp->num_r1++;
 647         }
 648 #endif
 649
 650         /* Add node to back propagation list. */
 651         node_bucket_insert(&reduced_bucket, node);
 652 }
 653
 654 void apply_RII(pbqp *pbqp)
 655 {
 656         pbqp_node   *node       = node_bucket_pop(&node_buckets[2]);
 657         pbqp_edge   *src_edge   = node->edges[0];
 658         pbqp_edge   *tgt_edge   = node->edges[1];
 659         int          src_is_src = src_edge->src == node;
 660         int          tgt_is_src = tgt_edge->src == node;
 661         pbqp_matrix *src_mat;
 662         pbqp_matrix *tgt_mat;
 663         pbqp_node   *src_node;
 664         pbqp_node   *tgt_node;
 665         pbqp_matrix *mat;
 666         vector      *vec;
 667         vector      *node_vec;
 668         vector      *src_vec;
 669         vector      *tgt_vec;
 670         unsigned     col_index;
 671         unsigned     col_len;
 672         unsigned     row_index;
 673         unsigned     row_len;
 674         unsigned     node_len;
 675
 676         assert(pbqp);
 677         assert(pbqp_node_get_degree(node) == 2);
 678
 679         if (src_is_src) {
 680                 src_node = src_edge->tgt;
 681         } else {
 682                 src_node = src_edge->src;
 683         }
 684
 685         if (tgt_is_src) {
 686                 tgt_node = tgt_edge->tgt;
 687         } else {
 688                 tgt_node = tgt_edge->src;
 689         }
 690
 691         /* Swap nodes if necessary. */
 692         if (tgt_node->index < src_node->index) {
 693                 pbqp_node *tmp_node;
 694                 pbqp_edge *tmp_edge;
 695
 696                 tmp_node = src_node;
 697                 src_node = tgt_node;
 698                 tgt_node = tmp_node;
 699
 700                 tmp_edge = src_edge;
 701                 src_edge = tgt_edge;
 702                 tgt_edge = tmp_edge;
 703
 704                 src_is_src = src_edge->src == node;
 705                 tgt_is_src = tgt_edge->src == node;
 706         }
 707
 708 #if     KAPS_DUMP
 709         if (pbqp->dump_file) {
 710                 char     txt[100];
 711                 sprintf(txt, "RII-Reduction of Node n%d", node->index);
 712                 dump_section(pbqp->dump_file, 2, txt);
 713                 pbqp_dump_graph(pbqp);
 714                 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
 715                 dump_node(pbqp->dump_file, src_node);
 716                 dump_edge(pbqp->dump_file, src_edge);
 717                 dump_node(pbqp->dump_file, node);
 718                 dump_edge(pbqp->dump_file, tgt_edge);
 719                 dump_node(pbqp->dump_file, tgt_node);
 720         }
 721 #endif
 722
 723         src_mat = src_edge->costs;
 724         tgt_mat = tgt_edge->costs;
 725
 726         src_vec  = src_node->costs;
 727         tgt_vec  = tgt_node->costs;
 728         node_vec = node->costs;
 729
 730         row_len  = src_vec->len;
 731         col_len  = tgt_vec->len;
 732         node_len = node_vec->len;
 733
 734         mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
 735
 736         for (row_index = 0; row_index < row_len; ++row_index) {
 737                 for (col_index = 0; col_index < col_len; ++col_index) {
 738                         vec = vector_copy(pbqp, node_vec);
 739
 740                         if (src_is_src) {
 741                                 vector_add_matrix_col(vec, src_mat, row_index);
 742                         } else {
 743                                 vector_add_matrix_row(vec, src_mat, row_index);
 744                         }
 745
 746                         if (tgt_is_src) {
 747                                 vector_add_matrix_col(vec, tgt_mat, col_index);
 748                         } else {
 749                                 vector_add_matrix_row(vec, tgt_mat, col_index);
 750                         }
 751
 752                         mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
 753
 754                         obstack_free(&pbqp->obstack, vec);
 755                 }
 756         }
 757
 758         pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
 759
 760         /* Disconnect node. */
 761         disconnect_edge(src_node, src_edge);
 762         disconnect_edge(tgt_node, tgt_edge);
 763
 764 #if KAPS_STATISTIC
 765         if (dump == 0) {
 766                 pbqp->num_r2++;
 767         }
 768 #endif
 769
 770         /* Add node to back propagation list. */
 771         node_bucket_insert(&reduced_bucket, node);
 772
 773         if (edge == NULL) {
 774                 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
 775         } else {
 776                 pbqp_matrix_add(edge->costs, mat);
 777
 778                 /* Free local matrix. */
 779                 obstack_free(&pbqp->obstack, mat);
 780
 781                 reorder_node(src_node);
 782                 reorder_node(tgt_node);
 783         }
 784
 785 #if     KAPS_DUMP
 786         if (pbqp->dump_file) {
 787                 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
 788                 dump_edge(pbqp->dump_file, edge);
 789         }
 790 #endif
 791
 792         /* Edge has changed so we simplify it. */
 793         simplify_edge(pbqp, edge);
 794 }
 795
 796 static void select_alternative(pbqp_node *node, unsigned selected_index)
 797 {
 798         unsigned  edge_index;
 799         unsigned  node_index;
 800         unsigned  node_len;
 801         vector   *node_vec;
 802         unsigned  max_degree = pbqp_node_get_degree(node);
 803
 804         assert(node);
 805         node->solution = selected_index;
 806         node_vec = node->costs;
 807         node_len = node_vec->len;
 808         assert(selected_index < node_len);
 809
 810         /* Set all other costs to infinity. */
 811         for (node_index = 0; node_index < node_len; ++node_index) {
 812                 if (node_index != selected_index) {
 813                         node_vec->entries[node_index].data = INF_COSTS;
 814                 }
 815         }
 816
 817         /* Add all incident edges to edge bucket, since they are now independent. */
 818         for (edge_index = 0; edge_index < max_degree; ++edge_index) {
 819                 insert_into_edge_bucket(node->edges[edge_index]);
 820         }
 821 }
 822
 823 static pbqp_node *get_node_with_max_degree(void)
 824 {
 825         pbqp_node  **bucket       = node_buckets[3];
 826         unsigned     bucket_len   = node_bucket_get_length(bucket);
 827         unsigned     bucket_index;
 828         unsigned     max_degree   = 0;
 829         pbqp_node   *result       = NULL;
 830
 831         for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
 832                 pbqp_node *candidate = bucket[bucket_index];
 833                 unsigned   degree    = pbqp_node_get_degree(candidate);
 834
 835                 if (degree > max_degree) {
 836                         result = candidate;
 837                         max_degree = degree;
 838                 }
 839         }
 840
 841         return result;
 842 }
 843
 844 static unsigned get_local_minimal_alternative(pbqp *pbqp, pbqp_node *node)
 845 {
 846         pbqp_edge   *edge;
 847         vector      *node_vec;
 848         vector      *vec;
 849         pbqp_matrix *mat;
 850         unsigned     edge_index;
 851         unsigned     max_degree   = 0;
 852         unsigned     node_index;
 853         unsigned     node_len;
 854         unsigned     min_index    = 0;
 855         num          min          = INF_COSTS;
 856         int          is_src;
 857
 858         assert(pbqp);
 859         assert(node);
 860         node_vec = node->costs;
 861         node_len = node_vec->len;
 862
 863         for (node_index = 0; node_index < node_len; ++node_index) {
 864                 num value = node_vec->entries[node_index].data;
 865
 866                 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
 867                         edge   = node->edges[edge_index];
 868                         mat    = edge->costs;
 869                         is_src = edge->src == node;
 870
 871                         if (is_src) {
 872                                 vec = vector_copy(pbqp, edge->tgt->costs);
 873                                 vector_add_matrix_row(vec, mat, node_index);
 874                         } else {
 875                                 vec = vector_copy(pbqp, edge->src->costs);
 876                                 vector_add_matrix_col(vec, mat, node_index);
 877                         }
 878
 879                         value = pbqp_add(value, vector_get_min(vec));
 880
 881                         obstack_free(&pbqp->obstack, vec);
 882                 }
 883
 884                 if (value < min) {
 885                         min = value;
 886                         min_index = node_index;
 887                 }
 888         }
 889
 890         return min_index;
 891 }
 892
 893 void apply_RN(pbqp *pbqp)
 894 {
 895         pbqp_node   *node         = NULL;
 896         unsigned     min_index    = 0;
 897
 898         assert(pbqp);
 899
 900         /* We want to reduce a node with maximum degree. */
 901         node = get_node_with_max_degree();
 902         assert(node);
 903         assert(pbqp_node_get_degree(node) > 2);
 904
 905 #if     KAPS_DUMP
 906         if (pbqp->dump_file) {
 907                 char     txt[100];
 908                 sprintf(txt, "RN-Reduction of Node n%d", node->index);
 909                 dump_section(pbqp->dump_file, 2, txt);
 910                 pbqp_dump_graph(pbqp);
 911         }
 912 #endif
 913
 914         min_index = get_local_minimal_alternative(pbqp, node);
 915
 916 #if     KAPS_DUMP
 917         if (pbqp->dump_file) {
 918                 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
 919                                         node->index, min_index);
 920         }
 921 #endif
 922
 923 #if KAPS_STATISTIC
 924         if (dump == 0) {
 925                 FILE *fh = fopen("solutions.pb", "a");
 926                 fprintf(fh, "[%u]", min_index);
 927                 fclose(fh);
 928                 pbqp->num_rn++;
 929         }
 930 #endif
 931
 932         /* Now that we found the local minimum set all other costs to infinity. */
 933         select_alternative(node, min_index);
 934 }
 935
 936 static void apply_brute_force_reductions(pbqp *pbqp)
 937 {
 938         for (;;) {
 939                 if (edge_bucket_get_length(edge_bucket) > 0) {
 940                         apply_edge(pbqp);
 941                 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
 942                         apply_RI(pbqp);
 943                 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
 944                         apply_RII(pbqp);
 945                 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
 946                         apply_Brute_Force(pbqp);
 947                 } else {
 948                         return;
 949                 }
 950         }
 951 }
 952
 953 static unsigned get_minimal_alternative(pbqp *pbqp, pbqp_node *node)
 954 {
 955         vector      *node_vec;
 956         unsigned     node_index;
 957         unsigned     node_len;
 958         unsigned     min_index    = 0;
 959         num          min          = INF_COSTS;
 960         unsigned     bucket_index;
 961
 962         assert(pbqp);
 963         assert(node);
 964         node_vec     = node->costs;
 965         node_len     = node_vec->len;
 966         bucket_index = node->bucket_index;
 967
 968         for (node_index = 0; node_index < node_len; ++node_index) {
 969                 pbqp_node_bucket bucket_deg3;
 970                 num              value;
 971                 unsigned         bucket_0_length;
 972                 unsigned         bucket_red_length;
 973
 974                 char *tmp = obstack_finish(&pbqp->obstack);
 975
 976                 node_bucket_init(&bucket_deg3);
 977
 978                 /* Some node buckets and the edge bucket should be empty. */
 979                 assert(node_bucket_get_length(node_buckets[1]) == 0);
 980                 assert(node_bucket_get_length(node_buckets[2]) == 0);
 981                 assert(edge_bucket_get_length(edge_bucket)     == 0);
 982
 983                 /* char *tmp = obstack_finish(&pbqp->obstack); */
 984
 985                 /* Save current PBQP state. */
 986                 node_bucket_copy(&bucket_deg3, node_buckets[3]);
 987                 node_bucket_shrink(&node_buckets[3], 0);
 988                 node_bucket_deep_copy(pbqp, &node_buckets[3], bucket_deg3);
 989                 node_bucket_update(pbqp, node_buckets[3]);
 990                 bucket_0_length   = node_bucket_get_length(node_buckets[0]);
 991                 bucket_red_length = node_bucket_get_length(reduced_bucket);
 992
 993                 /* Select alternative and solve PBQP recursively. */
 994                 select_alternative(node_buckets[3][bucket_index], node_index);
 995                 apply_brute_force_reductions(pbqp);
 996
 997                 value = determine_solution(pbqp);
 998
 999                 if (value < min) {
1000                         min = value;
1001                         min_index = node_index;
1002                 }
1003
1004                 /* Some node buckets and the edge bucket should still be empty. */
1005                 assert(node_bucket_get_length(node_buckets[1]) == 0);
1006                 assert(node_bucket_get_length(node_buckets[2]) == 0);
1007                 assert(edge_bucket_get_length(edge_bucket)     == 0);
1008
1009                 /* Clear modified buckets... */
1010                 node_bucket_shrink(&node_buckets[3], 0);
1011
1012                 /* ... and restore old PBQP state. */
1013                 node_bucket_shrink(&node_buckets[0], bucket_0_length);
1014                 node_bucket_shrink(&reduced_bucket, bucket_red_length);
1015                 node_bucket_copy(&node_buckets[3], bucket_deg3);
1016                 node_bucket_update(pbqp, node_buckets[3]);
1017
1018                 /* Free copies. */
1019                 /* obstack_free(&pbqp->obstack, tmp); */
1020                 node_bucket_free(&bucket_deg3);
1021
1022                 obstack_free(&pbqp->obstack, tmp);
1023         }
1024
1025         return min_index;
1026 }
1027
1028 void apply_Brute_Force(pbqp *pbqp)
1029 {
1030         pbqp_node   *node         = NULL;
1031         unsigned     min_index    = 0;
1032
1033         assert(pbqp);
1034
1035         /* We want to reduce a node with maximum degree. */
1036         node = get_node_with_max_degree();
1037         assert(node);
1038         assert(pbqp_node_get_degree(node) > 2);
1039
1040 #if     KAPS_DUMP
1041         if (pbqp->dump_file) {
1042                 char     txt[100];
1043                 sprintf(txt, "BF-Reduction of Node n%d", node->index);
1044                 dump_section(pbqp->dump_file, 2, txt);
1045                 pbqp_dump_graph(pbqp);
1046         }
1047 #endif
1048
1049 #if KAPS_STATISTIC
1050         dump++;
1051 #endif
1052
1053         min_index = get_minimal_alternative(pbqp, node);
1054         node = pbqp->nodes[node->index];
1055
1056 #if     KAPS_DUMP
1057         if (pbqp->dump_file) {
1058                 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
1059                                         node->index, min_index);
1060         }
1061 #endif
1062
1063 #if KAPS_STATISTIC
1064         dump--;
1065         if (dump == 0) {
1066                 FILE *fh = fopen("solutions.pb", "a");
1067                 fprintf(fh, "[%u]", min_index);
1068                 fclose(fh);
1069                 pbqp->num_bf++;
1070         }
1071 #endif
1072
1073         /* Now that we found the minimum set all other costs to infinity. */
1074         select_alternative(node, min_index);
1075 }
1076
1077 void solve_pbqp_brute_force(pbqp *pbqp)
1078 {
1079         /* Reduce nodes degree ... */
1080         initial_simplify_edges(pbqp);
1081
1082         /* ... and put node into bucket representing their degree. */
1083         fill_node_buckets(pbqp);
1084
1085 #if KAPS_STATISTIC
1086         FILE *fh = fopen("solutions.pb", "a");
1087         fprintf(fh, "Solution");
1088         fclose(fh);
1089 #endif
1090
1091         apply_brute_force_reductions(pbqp);
1092
1093         pbqp->solution = determine_solution(pbqp);
1094
1095 #if KAPS_STATISTIC
1096         fh = fopen("solutions.pb", "a");
1097         fprintf(fh, ": %lld RE:%u R0:%u R1:%u R2:%u RN/BF:%u\n", pbqp->solution,
1098                         pbqp->num_edges, pbqp->num_r0, pbqp->num_r1, pbqp->num_r2,
1099                         pbqp->num_bf);
1100         fclose(fh);
1101 #endif
1102
1103         /* Solve reduced nodes. */
1104         back_propagate(pbqp);
1105
1106         free_buckets();
1107 }
1108
1109 void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
1110 {
1111         pbqp_edge   *edge;
1112         pbqp_node   *other;
1113         pbqp_matrix *mat;
1114         vector      *vec;
1115         int          is_src;
1116
1117         assert(pbqp);
1118         assert(node);
1119
1120         edge = node->edges[0];
1121         mat = edge->costs;
1122         is_src = edge->src == node;
1123         vec = node->costs;
1124
1125         if (is_src) {
1126                 other = edge->tgt;
1127                 assert(other);
1128
1129                 /* Update pointer for brute force solver. */
1130                 other = pbqp->nodes[other->index];
1131
1132                 node->solution = pbqp_matrix_get_col_min_index(mat, other->solution, vec);
1133         } else {
1134                 other = edge->src;
1135                 assert(other);
1136
1137                 /* Update pointer for brute force solver. */
1138                 other = pbqp->nodes[other->index];
1139
1140                 node->solution = pbqp_matrix_get_row_min_index(mat, other->solution, vec);
1141         }
1142
1143 #if     KAPS_DUMP
1144         if (pbqp->dump_file) {
1145                 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
1146         }
1147 #endif
1148 }
1149
1150 void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
1151 {
1152         pbqp_edge   *src_edge   = node->edges[0];
1153         pbqp_edge   *tgt_edge   = node->edges[1];
1154         int          src_is_src = src_edge->src == node;
1155         int          tgt_is_src = tgt_edge->src == node;
1156         pbqp_matrix *src_mat;
1157         pbqp_matrix *tgt_mat;
1158         pbqp_node   *src_node;
1159         pbqp_node   *tgt_node;
1160         vector      *vec;
1161         vector      *node_vec;
1162         unsigned     col_index;
1163         unsigned     row_index;
1164
1165         assert(pbqp);
1166
1167         if (src_is_src) {
1168                 src_node = src_edge->tgt;
1169         } else {
1170                 src_node = src_edge->src;
1171         }
1172
1173         if (tgt_is_src) {
1174                 tgt_node = tgt_edge->tgt;
1175         } else {
1176                 tgt_node = tgt_edge->src;
1177         }
1178
1179         /* Swap nodes if necessary. */
1180         if (tgt_node->index < src_node->index) {
1181                 pbqp_node *tmp_node;
1182                 pbqp_edge *tmp_edge;
1183
1184                 tmp_node = src_node;
1185                 src_node = tgt_node;
1186                 tgt_node = tmp_node;
1187
1188                 tmp_edge = src_edge;
1189                 src_edge = tgt_edge;
1190                 tgt_edge = tmp_edge;
1191
1192                 src_is_src = src_edge->src == node;
1193                 tgt_is_src = tgt_edge->src == node;
1194         }
1195
1196         /* Update pointer for brute force solver. */
1197         src_node = pbqp->nodes[src_node->index];
1198         tgt_node = pbqp->nodes[tgt_node->index];
1199
1200         src_mat = src_edge->costs;
1201         tgt_mat = tgt_edge->costs;
1202
1203         node_vec = node->costs;
1204
1205         row_index = src_node->solution;
1206         col_index = tgt_node->solution;
1207
1208         vec = vector_copy(pbqp, node_vec);
1209
1210         if (src_is_src) {
1211                 vector_add_matrix_col(vec, src_mat, row_index);
1212         } else {
1213                 vector_add_matrix_row(vec, src_mat, row_index);
1214         }
1215
1216         if (tgt_is_src) {
1217                 vector_add_matrix_col(vec, tgt_mat, col_index);
1218         } else {
1219                 vector_add_matrix_row(vec, tgt_mat, col_index);
1220         }
1221
1222         node->solution = vector_get_min_index(vec);
1223
1224 #if     KAPS_DUMP
1225         if (pbqp->dump_file) {
1226                 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
1227         }
1228 #endif
1229
1230         obstack_free(&pbqp->obstack, vec);
1231 }
1232
1233 int node_is_reduced(pbqp_node *node)
1234 {
1235         if (!reduced_bucket) return 0;
1236
1237         if (pbqp_node_get_degree(node) == 0) return 1;
1238
1239         return node_bucket_contains(reduced_bucket, node);
1240 }