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 #include "html_dumper.h"
   8 #include "kaps.h"
   9 #include "matrix.h"
  10 #include "pbqp_edge.h"
  11 #include "pbqp_edge_t.h"
  12 #include "pbqp_node.h"
  13 #include "pbqp_node_t.h"
  14 #include "vector.h"
  15
  16 static pbqp_edge **edge_bucket;
  17 static pbqp_node **node_buckets[4];
  18 static pbqp_node **reduced_bucket = NULL;
  19 static int         buckets_filled = 0;
  20
  21 static void insert_into_edge_bucket(pbqp_edge *edge)
  22 {
  23         if (edge_bucket_contains(edge_bucket, edge)) {
  24                 /* Edge is already inserted. */
  25                 return;
  26         }
  27
  28         edge_bucket_insert(&edge_bucket, edge);
  29 }
  30
  31 static void init_buckets(void)
  32 {
  33         int i;
  34
  35         edge_bucket_init(&edge_bucket);
  36         node_bucket_init(&reduced_bucket);
  37
  38         for (i = 0; i < 4; ++i) {
  39                 node_bucket_init(&node_buckets[i]);
  40         }
  41 }
  42
  43 static void free_buckets(void)
  44 {
  45         int i;
  46
  47         for (i = 0; i < 4; ++i) {
  48                 node_bucket_free(&node_buckets[i]);
  49         }
  50
  51         edge_bucket_free(&edge_bucket);
  52         node_bucket_free(&reduced_bucket);
  53
  54         buckets_filled = 0;
  55 }
  56
  57 static void fill_node_buckets(pbqp *pbqp)
  58 {
  59         unsigned node_index;
  60         unsigned node_len;
  61
  62         assert(pbqp);
  63         node_len = pbqp->num_nodes;
  64
  65         for (node_index = 0; node_index < node_len; ++node_index) {
  66                 unsigned   arity;
  67                 pbqp_node *node = get_node(pbqp, node_index);
  68
  69                 if (!node) continue;
  70
  71                 arity = ARR_LEN(node->edges);
  72
  73                 /* We have only one bucket for nodes with arity >= 3. */
  74                 if (arity > 3) {
  75                         arity = 3;
  76                 }
  77
  78                 node_bucket_insert(&node_buckets[arity], node);
  79         }
  80
  81         buckets_filled = 1;
  82 }
  83
  84 static void normalize_towards_source(pbqp *pbqp, pbqp_edge *edge)
  85 {
  86         pbqp_matrix    *mat;
  87         pbqp_node      *src_node;
  88         pbqp_node      *tgt_node;
  89         vector         *src_vec;
  90         vector         *tgt_vec;
  91         int             src_len;
  92         int             tgt_len;
  93         int             src_index;
  94
  95         assert(pbqp);
  96         assert(edge);
  97
  98         src_node = edge->src;
  99         tgt_node = edge->tgt;
 100         assert(src_node);
 101         assert(tgt_node);
 102
 103         src_vec = src_node->costs;
 104         tgt_vec = tgt_node->costs;
 105         assert(src_vec);
 106         assert(tgt_vec);
 107
 108         src_len = src_vec->len;
 109         tgt_len = tgt_vec->len;
 110         assert(src_len > 0);
 111         assert(tgt_len > 0);
 112
 113         mat = edge->costs;
 114         assert(mat);
 115
 116         /* Normalize towards source node. */
 117         for (src_index = 0; src_index < src_len; ++src_index) {
 118                 num min = pbqp_matrix_get_row_min(mat, src_index, tgt_vec);
 119
 120                 if (min != 0) {
 121                         if (src_vec->entries[src_index].data == INF_COSTS) {
 122                                 pbqp_matrix_set_row_value(mat, src_index, 0);
 123                         } else {
 124                                 pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
 125                         }
 126                         src_vec->entries[src_index].data = pbqp_add(
 127                                         src_vec->entries[src_index].data, min);
 128
 129                         if (min == INF_COSTS) {
 130                                 unsigned edge_index;
 131                                 unsigned edge_len = ARR_LEN(src_node->edges);
 132
 133                                 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
 134                                         pbqp_edge *edge_candidate = src_node->edges[edge_index];
 135                                         if (edge_candidate != edge) {
 136                                                 insert_into_edge_bucket(edge_candidate);
 137                                         }
 138                                 }
 139                         }
 140                 }
 141         }
 142 }
 143
 144 static void normalize_towards_target(pbqp *pbqp, pbqp_edge *edge)
 145 {
 146         pbqp_matrix    *mat;
 147         pbqp_node      *src_node;
 148         pbqp_node      *tgt_node;
 149         vector         *src_vec;
 150         vector         *tgt_vec;
 151         int             src_len;
 152         int             tgt_len;
 153         int             tgt_index;
 154
 155         assert(pbqp);
 156         assert(edge);
 157
 158         src_node = edge->src;
 159         tgt_node = edge->tgt;
 160         assert(src_node);
 161         assert(tgt_node);
 162
 163         src_vec = src_node->costs;
 164         tgt_vec = tgt_node->costs;
 165         assert(src_vec);
 166         assert(tgt_vec);
 167
 168         src_len = src_vec->len;
 169         tgt_len = tgt_vec->len;
 170         assert(src_len > 0);
 171         assert(tgt_len > 0);
 172
 173         mat = edge->costs;
 174         assert(mat);
 175
 176         for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
 177                 num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
 178
 179                 if (min != 0) {
 180                         if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
 181                                 pbqp_matrix_set_col_value(mat, tgt_index, 0);
 182                         } else {
 183                                 pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
 184                         }
 185                         tgt_vec->entries[tgt_index].data = pbqp_add(
 186                                         tgt_vec->entries[tgt_index].data, min);
 187
 188                         if (min == INF_COSTS) {
 189                                 unsigned edge_index;
 190                                 unsigned edge_len = ARR_LEN(tgt_node->edges);
 191
 192                                 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
 193                                         pbqp_edge *edge_candidate = tgt_node->edges[edge_index];
 194                                         if (edge_candidate != edge) {
 195                                                 insert_into_edge_bucket(edge_candidate);
 196                                         }
 197                                 }
 198                         }
 199                 }
 200         }
 201 }
 202
 203 static void reorder_node(pbqp_node *node)
 204 {
 205         unsigned    arity;
 206         unsigned    old_arity;
 207         unsigned    old_bucket_len;
 208         unsigned    old_bucket_index;
 209         pbqp_node **old_bucket;
 210
 211         if (!buckets_filled) return;
 212
 213         assert(node);
 214
 215         arity = ARR_LEN(node->edges);
 216
 217         /* Same bucket as before */
 218         if (arity > 2) return;
 219
 220         /* Assume node lost one incident edge. */
 221         old_arity        = arity + 1;
 222         old_bucket       = node_buckets[old_arity];
 223         old_bucket_len   = node_bucket_get_length(old_bucket);
 224         old_bucket_index = node->bucket_index;
 225
 226         if (old_bucket_len <= old_bucket_index || old_bucket[old_bucket_index]
 227                         != node) {
 228                 unsigned bucket_len = node_bucket_get_length(node_buckets[arity]);
 229
 230                 /* Old arity is new arity, so we have nothing to do. */
 231                 assert(old_bucket_index < bucket_len);
 232                 assert(node_buckets[arity][old_bucket_index] == node);
 233                 return;
 234         }
 235
 236         assert(old_bucket[old_bucket_index] == node);
 237
 238         /* Delete node from old bucket... */
 239         node_bucket_remove(&node_buckets[old_arity], node);
 240
 241         /* ..and add to new one. */
 242         node->bucket_index = node_bucket_get_length(node_buckets[arity]);
 243         ARR_APP1(pbqp_node*, node_buckets[arity], node);
 244 }
 245
 246 static void check_melting_possibility(pbqp *pbqp, pbqp_edge *edge)
 247 {
 248         pbqp_matrix    *mat;
 249         pbqp_node      *src_node;
 250         pbqp_node      *tgt_node;
 251         vector         *src_vec;
 252         vector         *tgt_vec;
 253         int             src_len;
 254         int             tgt_len;
 255         int             src_index;
 256         int             tgt_index;
 257
 258         assert(pbqp);
 259         assert(edge);
 260
 261         src_node = edge->src;
 262         tgt_node = edge->tgt;
 263         assert(src_node);
 264         assert(tgt_node);
 265
 266         src_vec = src_node->costs;
 267         tgt_vec = tgt_node->costs;
 268         assert(src_vec);
 269         assert(tgt_vec);
 270
 271         src_len = src_vec->len;
 272         tgt_len = tgt_vec->len;
 273         assert(src_len > 0);
 274         assert(tgt_len > 0);
 275
 276         mat = edge->costs;
 277         assert(mat);
 278
 279         if (src_len == 1 && tgt_len == 1) {
 280                 //panic("Something is wrong");
 281         }
 282
 283         int allRowsOk = 1;
 284         for (src_index = 0; src_index < src_len; ++src_index) {
 285                 int onlyOneZero = 0;
 286                 if (src_vec->entries[src_index].data == INF_COSTS) {
 287                         continue;
 288                 }
 289                 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
 290                         if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
 291                                 continue;
 292                         }
 293                         if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
 294                                 if (onlyOneZero) {
 295                                         onlyOneZero = 0;
 296                                         break;
 297                                 } else {
 298                                         onlyOneZero = 1;
 299                                         continue;
 300                                 }
 301                         }
 302                         if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
 303                                 continue;
 304                         }
 305                         onlyOneZero = 0;
 306                         break;
 307                 }
 308                 allRowsOk &= onlyOneZero;
 309         }
 310
 311         int allColsOk = 1;
 312         for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
 313                 int onlyOneZero = 0;
 314                 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
 315                         continue;
 316                 }
 317                 for (src_index = 0; src_index < src_len; ++src_index) {
 318                         if (src_vec->entries[src_index].data == INF_COSTS) {
 319                                 continue;
 320                         }
 321                         if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
 322                                 if (onlyOneZero) {
 323                                         onlyOneZero = 0;
 324                                         break;
 325                                 } else {
 326                                         onlyOneZero = 1;
 327                                         continue;
 328                                 }
 329                         }
 330                         if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
 331                                 continue;
 332                         }
 333                         onlyOneZero = 0;
 334                         break;
 335                 }
 336                 allColsOk &= onlyOneZero;
 337         }
 338
 339         if (allRowsOk && allColsOk) {
 340                 panic("Hurray");
 341         }
 342 }
 343
 344 static void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
 345 {
 346         pbqp_matrix    *mat;
 347         pbqp_node      *src_node;
 348         pbqp_node      *tgt_node;
 349         vector         *src_vec;
 350         vector         *tgt_vec;
 351         int             src_len;
 352         int             tgt_len;
 353
 354         assert(pbqp);
 355         assert(edge);
 356
 357         src_node = edge->src;
 358         tgt_node = edge->tgt;
 359         assert(src_node);
 360         assert(tgt_node);
 361
 362         /* If edge are already deleted, we have nothing to do. */
 363         if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
 364                 return;
 365
 366         if (pbqp->dump_file) {
 367                 char txt[100];
 368                 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
 369                 dump_section(pbqp->dump_file, 3, txt);
 370         }
 371
 372         src_vec = src_node->costs;
 373         tgt_vec = tgt_node->costs;
 374         assert(src_vec);
 375         assert(tgt_vec);
 376
 377         src_len = src_vec->len;
 378         tgt_len = tgt_vec->len;
 379         assert(src_len > 0);
 380         assert(tgt_len > 0);
 381
 382         mat = edge->costs;
 383         assert(mat);
 384
 385         if (pbqp->dump_file) {
 386                 fputs("Input:<br>\n", pbqp->dump_file);
 387                 dump_simplifyedge(pbqp, edge);
 388         }
 389
 390         normalize_towards_source(pbqp, edge);
 391         normalize_towards_target(pbqp, edge);
 392
 393         if (pbqp->dump_file) {
 394                 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
 395                 dump_simplifyedge(pbqp, edge);
 396         }
 397
 398         if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
 399                 if (pbqp->dump_file) {
 400                         fputs("edge has been eliminated<br>\n", pbqp->dump_file);
 401                 }
 402
 403                 delete_edge(edge);
 404                 reorder_node(src_node);
 405                 reorder_node(tgt_node);
 406         } else {
 407                 //check_melting_possibility(pbqp, edge);
 408         }
 409 }
 410
 411 void solve_pbqp_heuristical(pbqp *pbqp)
 412 {
 413         unsigned node_index;
 414         unsigned node_len;
 415
 416         assert(pbqp);
 417
 418         if (pbqp->dump_file) {
 419                 pbqp_dump_input(pbqp);
 420                 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
 421         }
 422
 423         node_len = pbqp->num_nodes;
 424
 425         init_buckets();
 426
 427         /* First simplify all edges. */
 428         for (node_index = 0; node_index < node_len; ++node_index) {
 429                 unsigned    edge_index;
 430                 pbqp_node  *node = get_node(pbqp, node_index);
 431                 pbqp_edge **edges;
 432                 unsigned    edge_len;
 433
 434                 if (!node) continue;
 435
 436                 edges = node->edges;
 437                 edge_len = ARR_LEN(edges);
 438
 439                 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
 440                         pbqp_edge *edge = edges[edge_index];
 441
 442                         /* Simplify only once per edge. */
 443                         if (node != edge->src) continue;
 444
 445                         simplify_edge(pbqp, edge);
 446                 }
 447         }
 448
 449         /* Put node into bucket representing their arity. */
 450         fill_node_buckets(pbqp);
 451
 452         for (;;) {
 453                 if (edge_bucket_get_length(edge_bucket) > 0) {
 454                         apply_edge(pbqp);
 455                 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
 456                         apply_RI(pbqp);
 457                 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
 458                         apply_RII(pbqp);
 459                 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
 460                         apply_RN(pbqp);
 461                 } else {
 462                         break;
 463                 }
 464         }
 465
 466         if (pbqp->dump_file) {
 467                 dump_section(pbqp->dump_file, 1, "4. Determine Solution/Minimum");
 468                 dump_section(pbqp->dump_file, 2, "4.1. Trivial Solution");
 469         }
 470
 471         /* Solve trivial nodes and calculate solution. */
 472         node_len = node_bucket_get_length(node_buckets[0]);
 473         for (node_index = 0; node_index < node_len; ++node_index) {
 474                 pbqp_node *node = node_buckets[0][node_index];
 475                 assert(node);
 476
 477                 node->solution = vector_get_min_index(node->costs);
 478                 pbqp->solution = pbqp_add(pbqp->solution,
 479                                 node->costs->entries[node->solution].data);
 480                 if (pbqp->dump_file) {
 481                         fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
 482                         dump_node(pbqp, node);
 483                 }
 484         }
 485
 486         if (pbqp->dump_file) {
 487                 dump_section(pbqp->dump_file, 2, "Minimum");
 488                 fprintf(pbqp->dump_file, "Minimum is equal to %lld.", pbqp->solution);
 489                 dump_section(pbqp->dump_file, 2, "Back Propagation");
 490         }
 491
 492         /* Solve reduced nodes. */
 493         node_len = node_bucket_get_length(reduced_bucket);
 494         for (node_index = node_len; node_index > 0; --node_index) {
 495                 pbqp_node *node = reduced_bucket[node_index - 1];
 496                 assert(node);
 497
 498                 switch (ARR_LEN(node->edges)) {
 499                         case 1:
 500                                 back_propagate_RI(pbqp, node);
 501                                 break;
 502                         case 2:
 503                                 back_propagate_RII(pbqp, node);
 504                                 break;
 505                         default:
 506                                 panic("Only nodes with degree one or two should be in this bucket");
 507                                 break;
 508                 }
 509         }
 510
 511         free_buckets();
 512 }
 513
 514 void apply_edge(pbqp *pbqp)
 515 {
 516         pbqp_edge *edge = edge_bucket_pop(&edge_bucket);
 517
 518         simplify_edge(pbqp, edge);
 519 }
 520
 521 void apply_RI(pbqp *pbqp)
 522 {
 523         pbqp_node   *node       = node_bucket_pop(&node_buckets[1]);
 524         pbqp_edge   *edge       = node->edges[0];
 525         pbqp_matrix *mat        = edge->costs;
 526         int          is_src     = edge->src == node;
 527         pbqp_node   *other_node;
 528
 529         if (is_src) {
 530                 other_node = edge->tgt;
 531         } else {
 532                 other_node = edge->src;
 533         }
 534
 535         if (pbqp->dump_file) {
 536                 char     txt[100];
 537                 sprintf(txt, "RI-Reduction of Node n%d", node->index);
 538                 dump_section(pbqp->dump_file, 2, txt);
 539                 pbqp_dump_graph(pbqp);
 540                 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
 541                 dump_node(pbqp, node);
 542                 dump_node(pbqp, other_node);
 543                 dump_edge(pbqp, edge);
 544         }
 545
 546         if (is_src) {
 547                 pbqp_matrix_add_to_all_cols(mat, node->costs);
 548                 normalize_towards_target(pbqp, edge);
 549         } else {
 550                 pbqp_matrix_add_to_all_rows(mat, node->costs);
 551                 normalize_towards_source(pbqp, edge);
 552         }
 553         disconnect_edge(other_node, edge);
 554
 555         if (pbqp->dump_file) {
 556                 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
 557                 dump_node(pbqp, other_node);
 558         }
 559
 560         reorder_node(other_node);
 561
 562         /* Add node to back propagation list. */
 563         node_bucket_insert(&reduced_bucket, node);
 564 }
 565
 566 void apply_RII(pbqp *pbqp)
 567 {
 568         pbqp_node   *node       = node_bucket_pop(&node_buckets[2]);
 569         pbqp_edge   *src_edge   = node->edges[0];
 570         pbqp_edge   *tgt_edge   = node->edges[1];
 571         int          src_is_src = src_edge->src == node;
 572         int          tgt_is_src = tgt_edge->src == node;
 573         pbqp_matrix *src_mat;
 574         pbqp_matrix *tgt_mat;
 575         pbqp_node   *src_node;
 576         pbqp_node   *tgt_node;
 577         pbqp_matrix *mat;
 578         vector      *vec;
 579         vector      *node_vec;
 580         vector      *src_vec;
 581         vector      *tgt_vec;
 582         unsigned     col_index;
 583         unsigned     col_len;
 584         unsigned     row_index;
 585         unsigned     row_len;
 586         unsigned     node_len;
 587
 588         assert(pbqp);
 589
 590         if (src_is_src) {
 591                 src_node = src_edge->tgt;
 592         } else {
 593                 src_node = src_edge->src;
 594         }
 595
 596         if (tgt_is_src) {
 597                 tgt_node = tgt_edge->tgt;
 598         } else {
 599                 tgt_node = tgt_edge->src;
 600         }
 601
 602         /* Swap nodes if necessary. */
 603         if (tgt_node->index < src_node->index) {
 604                 pbqp_node *tmp_node;
 605                 pbqp_edge *tmp_edge;
 606
 607                 tmp_node = src_node;
 608                 src_node = tgt_node;
 609                 tgt_node = tmp_node;
 610
 611                 tmp_edge = src_edge;
 612                 src_edge = tgt_edge;
 613                 tgt_edge = tmp_edge;
 614
 615                 src_is_src = src_edge->src == node;
 616                 tgt_is_src = tgt_edge->src == node;
 617         }
 618
 619         if (pbqp->dump_file) {
 620                 char     txt[100];
 621                 sprintf(txt, "RII-Reduction of Node n%d", node->index);
 622                 dump_section(pbqp->dump_file, 2, txt);
 623                 pbqp_dump_graph(pbqp);
 624                 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
 625                 dump_node(pbqp, src_node);
 626                 dump_edge(pbqp, src_edge);
 627                 dump_node(pbqp, node);
 628                 dump_edge(pbqp, tgt_edge);
 629                 dump_node(pbqp, tgt_node);
 630         }
 631
 632         src_mat = src_edge->costs;
 633         tgt_mat = tgt_edge->costs;
 634
 635         src_vec  = src_node->costs;
 636         tgt_vec  = tgt_node->costs;
 637         node_vec = node->costs;
 638
 639         row_len  = src_vec->len;
 640         col_len  = tgt_vec->len;
 641         node_len = node_vec->len;
 642
 643         mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
 644
 645         for (row_index = 0; row_index < row_len; ++row_index) {
 646                 for (col_index = 0; col_index < col_len; ++col_index) {
 647                         vec = vector_copy(pbqp, node_vec);
 648
 649                         if (src_is_src) {
 650                                 vector_add_matrix_col(vec, src_mat, row_index);
 651                         } else {
 652                                 vector_add_matrix_row(vec, src_mat, row_index);
 653                         }
 654
 655                         if (tgt_is_src) {
 656                                 vector_add_matrix_col(vec, tgt_mat, col_index);
 657                         } else {
 658                                 vector_add_matrix_row(vec, tgt_mat, col_index);
 659                         }
 660
 661                         mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
 662
 663                         obstack_free(&pbqp->obstack, vec);
 664                 }
 665         }
 666
 667         pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
 668
 669         /* Disconnect node. */
 670         disconnect_edge(src_node, src_edge);
 671         disconnect_edge(tgt_node, tgt_edge);
 672
 673         /* Add node to back propagation list. */
 674         node_bucket_insert(&reduced_bucket, node);
 675
 676         if (edge == NULL) {
 677                 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
 678         } else {
 679                 pbqp_matrix_add(edge->costs, mat);
 680
 681                 /* Free local matrix. */
 682                 obstack_free(&pbqp->obstack, mat);
 683
 684                 reorder_node(src_node);
 685                 reorder_node(tgt_node);
 686         }
 687
 688         if (pbqp->dump_file) {
 689                 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
 690                 dump_edge(pbqp, edge);
 691         }
 692
 693         /* Edge has changed so we simplify it. */
 694         simplify_edge(pbqp, edge);
 695 }
 696
 697 void apply_RN(pbqp *pbqp)
 698 {
 699         pbqp_node  **bucket       = node_buckets[3];
 700         unsigned     bucket_len   = node_bucket_get_length(bucket);
 701         unsigned     bucket_index;
 702         pbqp_node   *node         = NULL;
 703         pbqp_edge   *edge;
 704         vector      *node_vec;
 705         vector      *vec;
 706         pbqp_matrix *mat;
 707         unsigned     edge_index;
 708         unsigned     max_degree   = 0;
 709         unsigned     node_index;
 710         unsigned     node_len;
 711         unsigned     min_index    = 0;
 712         num          min          = INF_COSTS;
 713         int          is_src;
 714
 715         assert(pbqp);
 716
 717         /* Search for node with maximum degree. */
 718         for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
 719                 pbqp_node *candidate = bucket[bucket_index];
 720                 unsigned   degree    = ARR_LEN(candidate->edges);
 721
 722                 if (degree > max_degree) {
 723                         node = candidate;
 724                         max_degree = degree;
 725                 }
 726         }
 727         assert(node);
 728         node_vec = node->costs;
 729         node_len = node_vec->len;
 730
 731         if (pbqp->dump_file) {
 732                 char     txt[100];
 733                 sprintf(txt, "RN-Reduction of Node n%d", node->index);
 734                 dump_section(pbqp->dump_file, 2, txt);
 735                 pbqp_dump_graph(pbqp);
 736         }
 737
 738         for (node_index = 0; node_index < node_len; ++node_index) {
 739                 num value = node_vec->entries[node_index].data;
 740
 741                 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
 742                         edge   = node->edges[edge_index];
 743                         mat    = edge->costs;
 744                         is_src = edge->src == node;
 745
 746                         if (is_src) {
 747                                 vec = vector_copy(pbqp, edge->tgt->costs);
 748                                 vector_add_matrix_row(vec, mat, node_index);
 749                         } else {
 750                                 vec = vector_copy(pbqp, edge->src->costs);
 751                                 vector_add_matrix_col(vec, mat, node_index);
 752                         }
 753
 754                         value = pbqp_add(value, vector_get_min(vec));
 755
 756                         obstack_free(&pbqp->obstack, vec);
 757                 }
 758
 759                 if (value < min) {
 760                         min = value;
 761                         min_index = node_index;
 762                 }
 763         }
 764
 765         if (pbqp->dump_file) {
 766                 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
 767                                         node->index, min_index);
 768                 fprintf(pbqp->dump_file, "Minimal cost of RN reduction: %lld<br>\n",
 769                                                         min);
 770         }
 771
 772         node->solution = min_index;
 773
 774         /* Now that we found the local minimum set all other costs to infinity. */
 775         for (node_index = 0; node_index < node_len; ++node_index) {
 776                 if (node_index != min_index) {
 777                         node_vec->entries[node_index].data = INF_COSTS;
 778                 }
 779         }
 780
 781         /* Add all incident edges to edge bucket, since they are now independent. */
 782         for (edge_index = 0; edge_index < max_degree; ++edge_index) {
 783                 insert_into_edge_bucket(node->edges[edge_index]);
 784         }
 785 }
 786
 787 void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
 788 {
 789         pbqp_edge   *edge;
 790         pbqp_node   *other;
 791         pbqp_matrix *mat;
 792         vector      *vec;
 793         int          is_src;
 794
 795         assert(pbqp);
 796         assert(node);
 797
 798         edge = node->edges[0];
 799         mat = edge->costs;
 800         is_src = edge->src == node;
 801         vec = node->costs;
 802
 803         if (is_src) {
 804                 other = edge->tgt;
 805                 assert(other);
 806                 vector_add_matrix_col(vec, mat, other->solution);
 807         } else {
 808                 other = edge->src;
 809                 assert(other);
 810                 vector_add_matrix_row(vec, mat, other->solution);
 811         }
 812
 813         node->solution = vector_get_min_index(vec);
 814         if (pbqp->dump_file) {
 815                 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
 816         }
 817 }
 818
 819 void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
 820 {
 821         pbqp_edge   *src_edge   = node->edges[0];
 822         pbqp_edge   *tgt_edge   = node->edges[1];
 823         int          src_is_src = src_edge->src == node;
 824         int          tgt_is_src = tgt_edge->src == node;
 825         pbqp_matrix *src_mat;
 826         pbqp_matrix *tgt_mat;
 827         pbqp_node   *src_node;
 828         pbqp_node   *tgt_node;
 829         vector      *vec;
 830         vector      *node_vec;
 831         unsigned     col_index;
 832         unsigned     row_index;
 833
 834         assert(pbqp);
 835
 836         if (src_is_src) {
 837                 src_node = src_edge->tgt;
 838         } else {
 839                 src_node = src_edge->src;
 840         }
 841
 842         if (tgt_is_src) {
 843                 tgt_node = tgt_edge->tgt;
 844         } else {
 845                 tgt_node = tgt_edge->src;
 846         }
 847
 848         /* Swap nodes if necessary. */
 849         if (tgt_node->index < src_node->index) {
 850                 pbqp_node *tmp_node;
 851                 pbqp_edge *tmp_edge;
 852
 853                 tmp_node = src_node;
 854                 src_node = tgt_node;
 855                 tgt_node = tmp_node;
 856
 857                 tmp_edge = src_edge;
 858                 src_edge = tgt_edge;
 859                 tgt_edge = tmp_edge;
 860
 861                 src_is_src = src_edge->src == node;
 862                 tgt_is_src = tgt_edge->src == node;
 863         }
 864
 865         src_mat = src_edge->costs;
 866         tgt_mat = tgt_edge->costs;
 867
 868         node_vec = node->costs;
 869
 870         row_index = src_node->solution;
 871         col_index = tgt_node->solution;
 872
 873         vec = vector_copy(pbqp, node_vec);
 874
 875         if (src_is_src) {
 876                 vector_add_matrix_col(vec, src_mat, row_index);
 877         } else {
 878                 vector_add_matrix_row(vec, src_mat, row_index);
 879         }
 880
 881         if (tgt_is_src) {
 882                 vector_add_matrix_col(vec, tgt_mat, col_index);
 883         } else {
 884                 vector_add_matrix_row(vec, tgt_mat, col_index);
 885         }
 886
 887         node->solution = vector_get_min_index(vec);
 888         if (pbqp->dump_file) {
 889                 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
 890         }
 891
 892         obstack_free(&pbqp->obstack, vec);
 893 }
 894
 895 int node_is_reduced(pbqp_node *node)
 896 {
 897         if (!reduced_bucket) return 0;
 898
 899         assert(node);
 900         if (ARR_LEN(node->edges) == 0) return 1;
 901
 902         return node_bucket_contains(reduced_bucket, node);
 903 }