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         unsigned bucket_len = edge_bucket_get_length(edge_bucket);
  24
  25         if (edge->bucket_index < bucket_len && edge_bucket[edge->bucket_index]
  26                         == edge)
  27                 /* Edge is already inserted. */
  28                 return;
  29
  30         edge->bucket_index = bucket_len;
  31         ARR_APP1(pbqp_edge *, edge_bucket, edge);
  32 }
  33
  34 static void init_buckets(void)
  35 {
  36         int i;
  37
  38         edge_bucket = NEW_ARR_F(pbqp_edge *, 0);
  39         reduced_bucket = NEW_ARR_F(pbqp_node *, 0);
  40
  41         for (i = 0; i < 4; ++i) {
  42                 node_buckets[i] = NEW_ARR_F(pbqp_node *, 0);
  43         }
  44 }
  45
  46 static void free_buckets(void)
  47 {
  48         int i;
  49
  50         for (i = 0; i < 4; ++i) {
  51                 DEL_ARR_F(node_buckets[i]);
  52                 node_buckets[i] = NULL;
  53         }
  54
  55         DEL_ARR_F(edge_bucket);
  56         edge_bucket = NULL;
  57
  58         DEL_ARR_F(reduced_bucket);
  59         reduced_bucket = NULL;
  60
  61         buckets_filled = 0;
  62 }
  63
  64 static void fill_node_buckets(pbqp *pbqp)
  65 {
  66         unsigned node_index;
  67         unsigned node_len;
  68
  69         assert(pbqp);
  70         node_len = pbqp->num_nodes;
  71
  72         for (node_index = 0; node_index < node_len; ++node_index) {
  73                 unsigned   arity;
  74                 pbqp_node *node = get_node(pbqp, node_index);
  75
  76                 if (!node) continue;
  77
  78                 arity = ARR_LEN(node->edges);
  79
  80                 /* We have only one bucket for nodes with arity >= 3. */
  81                 if (arity > 3) {
  82                         arity = 3;
  83                 }
  84
  85                 node->bucket_index = node_bucket_get_length(node_buckets[arity]);
  86
  87                 ARR_APP1(pbqp_node *, node_buckets[arity], 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 = ARR_LEN(src_node->edges);
 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 = ARR_LEN(tgt_node->edges);
 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    arity;
 215         unsigned    old_arity;
 216         unsigned    old_bucket_len;
 217         unsigned    old_bucket_index;
 218         pbqp_node **old_bucket;
 219         pbqp_node  *other;
 220
 221         if (!buckets_filled) return;
 222
 223         assert(node);
 224
 225         arity = ARR_LEN(node->edges);
 226
 227         /* Same bucket as before */
 228         if (arity > 2) return;
 229
 230         /* Assume node lost one incident edge. */
 231         old_arity        = arity + 1;
 232         old_bucket       = node_buckets[old_arity];
 233         old_bucket_len   = node_bucket_get_length(old_bucket);
 234         old_bucket_index = node->bucket_index;
 235
 236         if (old_bucket_len <= old_bucket_index || old_bucket[old_bucket_index]
 237                         != node) {
 238                 unsigned bucket_len = node_bucket_get_length(node_buckets[arity]);
 239
 240                 /* Old arity is new arity, so we have nothing to do. */
 241                 assert(old_bucket_index < bucket_len);
 242                 assert(node_buckets[arity][old_bucket_index] == node);
 243                 return;
 244         }
 245
 246         assert(old_bucket[old_bucket_index] == node);
 247
 248         /* Delete node from old bucket... */
 249         other                        = old_bucket[old_bucket_len - 1];
 250         other->bucket_index          = old_bucket_index;
 251         old_bucket[old_bucket_index] = other;
 252         ARR_SHRINKLEN(node_buckets[old_arity], old_bucket_len - 1);
 253
 254         /* ..and add to new one. */
 255         node->bucket_index = node_bucket_get_length(node_buckets[arity]);
 256         ARR_APP1(pbqp_node*, node_buckets[arity], node);
 257 }
 258
 259 static void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
 260 {
 261         pbqp_matrix    *mat;
 262         pbqp_node      *src_node;
 263         pbqp_node      *tgt_node;
 264         vector         *src_vec;
 265         vector         *tgt_vec;
 266         int             src_len;
 267         int             tgt_len;
 268
 269         assert(pbqp);
 270         assert(edge);
 271
 272         src_node = edge->src;
 273         tgt_node = edge->tgt;
 274         assert(src_node);
 275         assert(tgt_node);
 276
 277         /* If edge are already deleted, we have nothing to do. */
 278         if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
 279                 return;
 280
 281         if (pbqp->dump_file) {
 282                 char txt[100];
 283                 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
 284                 dump_section(pbqp->dump_file, 3, txt);
 285         }
 286
 287         src_vec = src_node->costs;
 288         tgt_vec = tgt_node->costs;
 289         assert(src_vec);
 290         assert(tgt_vec);
 291
 292         src_len = src_vec->len;
 293         tgt_len = tgt_vec->len;
 294         assert(src_len > 0);
 295         assert(tgt_len > 0);
 296
 297         mat = edge->costs;
 298         assert(mat);
 299
 300         if (pbqp->dump_file) {
 301                 fputs("Input:<br>\n", pbqp->dump_file);
 302                 dump_simplifyedge(pbqp, edge);
 303         }
 304
 305         normalize_towards_source(pbqp, edge);
 306         normalize_towards_target(pbqp, edge);
 307
 308         if (pbqp->dump_file) {
 309                 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
 310                 dump_simplifyedge(pbqp, edge);
 311         }
 312
 313         if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
 314                 if (pbqp->dump_file) {
 315                         fputs("edge has been eliminated<br>\n", pbqp->dump_file);
 316                 }
 317
 318                 delete_edge(edge);
 319                 reorder_node(src_node);
 320                 reorder_node(tgt_node);
 321         }
 322 }
 323
 324 void solve_pbqp_heuristical(pbqp *pbqp)
 325 {
 326         unsigned node_index;
 327         unsigned node_len;
 328
 329         assert(pbqp);
 330
 331         if (pbqp->dump_file) {
 332                 pbqp_dump_input(pbqp);
 333                 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
 334         }
 335
 336         node_len = pbqp->num_nodes;
 337
 338         init_buckets();
 339
 340         /* First simplify all edges. */
 341         for (node_index = 0; node_index < node_len; ++node_index) {
 342                 unsigned    edge_index;
 343                 pbqp_node  *node = get_node(pbqp, node_index);
 344                 pbqp_edge **edges;
 345                 unsigned    edge_len;
 346
 347                 if (!node) continue;
 348
 349                 edges = node->edges;
 350                 edge_len = ARR_LEN(edges);
 351
 352                 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
 353                         pbqp_edge *edge = edges[edge_index];
 354
 355                         /* Simplify only once per edge. */
 356                         if (node != edge->src) continue;
 357
 358                         simplify_edge(pbqp, edge);
 359                 }
 360         }
 361
 362         /* Put node into bucket representing their arity. */
 363         fill_node_buckets(pbqp);
 364
 365         for (;;) {
 366                 if (edge_bucket_get_length(edge_bucket) > 0) {
 367                         apply_edge(pbqp);
 368                 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
 369                         apply_RI(pbqp);
 370                 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
 371                         apply_RII(pbqp);
 372                 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
 373                         apply_RN(pbqp);
 374                 } else {
 375                         break;
 376                 }
 377         }
 378
 379         if (pbqp->dump_file) {
 380                 dump_section(pbqp->dump_file, 1, "4. Determine Solution/Minimum");
 381                 dump_section(pbqp->dump_file, 2, "4.1. Trivial Solution");
 382         }
 383
 384         /* Solve trivial nodes and calculate solution. */
 385         node_len = node_bucket_get_length(node_buckets[0]);
 386         for (node_index = 0; node_index < node_len; ++node_index) {
 387                 pbqp_node *node = node_buckets[0][node_index];
 388                 assert(node);
 389
 390                 node->solution = vector_get_min_index(node->costs);
 391                 pbqp->solution = pbqp_add(pbqp->solution,
 392                                 node->costs->entries[node->solution].data);
 393                 if (pbqp->dump_file) {
 394                         fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
 395                         dump_node(pbqp, node);
 396                 }
 397         }
 398
 399         if (pbqp->dump_file) {
 400                 dump_section(pbqp->dump_file, 2, "Minimum");
 401                 fprintf(pbqp->dump_file, "Minimum is equal to %lld.", pbqp->solution);
 402                 dump_section(pbqp->dump_file, 2, "Back Propagation");
 403         }
 404
 405         /* Solve reduced nodes. */
 406         node_len = node_bucket_get_length(reduced_bucket);
 407         for (node_index = node_len; node_index > 0; --node_index) {
 408                 pbqp_node *node = reduced_bucket[node_index - 1];
 409                 assert(node);
 410
 411                 switch (ARR_LEN(node->edges)) {
 412                         case 1:
 413                                 back_propagate_RI(pbqp, node);
 414                                 break;
 415                         case 2:
 416                                 back_propagate_RII(pbqp, node);
 417                                 break;
 418                         default:
 419                                 panic("Only nodes with degree one or two should be in this bucket");
 420                                 break;
 421                 }
 422         }
 423
 424         free_buckets();
 425 }
 426
 427 void apply_edge(pbqp *pbqp)
 428 {
 429         pbqp_edge *edge = edge_bucket_pop(&edge_bucket);
 430
 431         simplify_edge(pbqp, edge);
 432 }
 433
 434 void apply_RI(pbqp *pbqp)
 435 {
 436         pbqp_node   *node       = node_bucket_pop(&node_buckets[1]);
 437         pbqp_edge   *edge       = node->edges[0];
 438         pbqp_matrix *mat        = edge->costs;
 439         int          is_src     = edge->src == node;
 440         pbqp_node   *other_node;
 441
 442         if (is_src) {
 443                 other_node = edge->tgt;
 444         } else {
 445                 other_node = edge->src;
 446         }
 447
 448         if (pbqp->dump_file) {
 449                 char     txt[100];
 450                 sprintf(txt, "RI-Reduction of Node n%d", node->index);
 451                 dump_section(pbqp->dump_file, 2, txt);
 452                 pbqp_dump_graph(pbqp);
 453                 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
 454                 dump_node(pbqp, node);
 455                 dump_node(pbqp, other_node);
 456                 dump_edge(pbqp, edge);
 457         }
 458
 459         if (is_src) {
 460                 pbqp_matrix_add_to_all_cols(mat, node->costs);
 461                 normalize_towards_target(pbqp, edge);
 462         } else {
 463                 pbqp_matrix_add_to_all_rows(mat, node->costs);
 464                 normalize_towards_source(pbqp, edge);
 465         }
 466         disconnect_edge(other_node, edge);
 467
 468         if (pbqp->dump_file) {
 469                 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
 470                 dump_node(pbqp, other_node);
 471         }
 472
 473         reorder_node(other_node);
 474
 475         /* Add node to back propagation list. */
 476         node->bucket_index = node_bucket_get_length(reduced_bucket);
 477         ARR_APP1(pbqp_node *, reduced_bucket, node);
 478 }
 479
 480 void apply_RII(pbqp *pbqp)
 481 {
 482         pbqp_node  **bucket     = node_buckets[2];
 483         unsigned     bucket_len = node_bucket_get_length(bucket);
 484         pbqp_node   *node       = bucket[bucket_len - 1];
 485         pbqp_edge   *src_edge   = node->edges[0];
 486         pbqp_edge   *tgt_edge   = node->edges[1];
 487         int          src_is_src = src_edge->src == node;
 488         int          tgt_is_src = tgt_edge->src == node;
 489         pbqp_matrix *src_mat;
 490         pbqp_matrix *tgt_mat;
 491         pbqp_node   *src_node;
 492         pbqp_node   *tgt_node;
 493         pbqp_matrix *mat;
 494         vector      *vec;
 495         vector      *node_vec;
 496         vector      *src_vec;
 497         vector      *tgt_vec;
 498         unsigned     col_index;
 499         unsigned     col_len;
 500         unsigned     row_index;
 501         unsigned     row_len;
 502         unsigned     node_len;
 503
 504         assert(pbqp);
 505
 506         if (src_is_src) {
 507                 src_node = src_edge->tgt;
 508         } else {
 509                 src_node = src_edge->src;
 510         }
 511
 512         if (tgt_is_src) {
 513                 tgt_node = tgt_edge->tgt;
 514         } else {
 515                 tgt_node = tgt_edge->src;
 516         }
 517
 518         /* Swap nodes if necessary. */
 519         if (tgt_node->index < src_node->index) {
 520                 pbqp_node *tmp_node;
 521                 pbqp_edge *tmp_edge;
 522
 523                 tmp_node = src_node;
 524                 src_node = tgt_node;
 525                 tgt_node = tmp_node;
 526
 527                 tmp_edge = src_edge;
 528                 src_edge = tgt_edge;
 529                 tgt_edge = tmp_edge;
 530
 531                 src_is_src = src_edge->src == node;
 532                 tgt_is_src = tgt_edge->src == node;
 533         }
 534
 535         if (pbqp->dump_file) {
 536                 char     txt[100];
 537                 sprintf(txt, "RII-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, src_node);
 542                 dump_edge(pbqp, src_edge);
 543                 dump_node(pbqp, node);
 544                 dump_edge(pbqp, tgt_edge);
 545                 dump_node(pbqp, tgt_node);
 546         }
 547
 548         src_mat = src_edge->costs;
 549         tgt_mat = tgt_edge->costs;
 550
 551         src_vec  = src_node->costs;
 552         tgt_vec  = tgt_node->costs;
 553         node_vec = node->costs;
 554
 555         row_len  = src_vec->len;
 556         col_len  = tgt_vec->len;
 557         node_len = node_vec->len;
 558
 559         mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
 560
 561         for (row_index = 0; row_index < row_len; ++row_index) {
 562                 for (col_index = 0; col_index < col_len; ++col_index) {
 563                         vec = vector_copy(pbqp, node_vec);
 564
 565                         if (src_is_src) {
 566                                 vector_add_matrix_col(vec, src_mat, row_index);
 567                         } else {
 568                                 vector_add_matrix_row(vec, src_mat, row_index);
 569                         }
 570
 571                         if (tgt_is_src) {
 572                                 vector_add_matrix_col(vec, tgt_mat, col_index);
 573                         } else {
 574                                 vector_add_matrix_row(vec, tgt_mat, col_index);
 575                         }
 576
 577                         mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
 578
 579                         obstack_free(&pbqp->obstack, vec);
 580                 }
 581         }
 582
 583         pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
 584
 585         /* Disconnect node. */
 586         disconnect_edge(src_node, src_edge);
 587         disconnect_edge(tgt_node, tgt_edge);
 588
 589         /* Remove node from bucket... */
 590         ARR_SHRINKLEN(bucket, (int)bucket_len - 1);
 591
 592         /* ...and add it to back propagation list. */
 593         node->bucket_index = node_bucket_get_length(reduced_bucket);
 594         ARR_APP1(pbqp_node *, reduced_bucket, node);
 595
 596         if (edge == NULL) {
 597                 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
 598         } else {
 599                 pbqp_matrix_add(edge->costs, mat);
 600
 601                 /* Free local matrix. */
 602                 obstack_free(&pbqp->obstack, mat);
 603
 604                 reorder_node(src_node);
 605                 reorder_node(tgt_node);
 606         }
 607
 608         if (pbqp->dump_file) {
 609                 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
 610                 dump_edge(pbqp, edge);
 611         }
 612
 613         /* Edge has changed so we simplify it. */
 614         simplify_edge(pbqp, edge);
 615 }
 616
 617 void apply_RN(pbqp *pbqp)
 618 {
 619         pbqp_node  **bucket       = node_buckets[3];
 620         unsigned     bucket_len   = node_bucket_get_length(bucket);
 621         unsigned     bucket_index;
 622         pbqp_node   *node         = NULL;
 623         pbqp_edge   *edge;
 624         vector      *node_vec;
 625         vector      *vec;
 626         pbqp_matrix *mat;
 627         unsigned     edge_index;
 628         unsigned     max_degree   = 0;
 629         unsigned     node_index;
 630         unsigned     node_len;
 631         unsigned     min_index    = 0;
 632         num          min          = INF_COSTS;
 633         int          is_src;
 634
 635         assert(pbqp);
 636
 637         /* Search for node with maximum degree. */
 638         for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
 639                 pbqp_node *candidate = bucket[bucket_index];
 640                 unsigned   degree    = ARR_LEN(candidate->edges);
 641
 642                 if (degree > max_degree) {
 643                         node = candidate;
 644                         max_degree = degree;
 645                 }
 646         }
 647         assert(node);
 648         node_vec = node->costs;
 649         node_len = node_vec->len;
 650
 651         if (pbqp->dump_file) {
 652                 char     txt[100];
 653                 sprintf(txt, "RN-Reduction of Node n%d", node->index);
 654                 dump_section(pbqp->dump_file, 2, txt);
 655                 pbqp_dump_graph(pbqp);
 656         }
 657
 658         for (node_index = 0; node_index < node_len; ++node_index) {
 659                 num value = node_vec->entries[node_index].data;
 660
 661                 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
 662                         edge   = node->edges[edge_index];
 663                         mat    = edge->costs;
 664                         is_src = edge->src == node;
 665
 666                         if (is_src) {
 667                                 vec = vector_copy(pbqp, edge->tgt->costs);
 668                                 vector_add_matrix_row(vec, mat, node_index);
 669                         } else {
 670                                 vec = vector_copy(pbqp, edge->src->costs);
 671                                 vector_add_matrix_col(vec, mat, node_index);
 672                         }
 673
 674                         value = pbqp_add(value, vector_get_min(vec));
 675
 676                         obstack_free(&pbqp->obstack, vec);
 677                 }
 678
 679                 if (value < min) {
 680                         min = value;
 681                         min_index = node_index;
 682                 }
 683         }
 684
 685         if (pbqp->dump_file) {
 686                 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
 687                                         node->index, min_index);
 688                 fprintf(pbqp->dump_file, "Minimal cost of RN reduction: %lld<br>\n",
 689                                                         min);
 690         }
 691
 692         node->solution = min_index;
 693
 694         /* Now that we found the local minimum set all other costs to infinity. */
 695         for (node_index = 0; node_index < node_len; ++node_index) {
 696                 if (node_index != min_index) {
 697                         node_vec->entries[node_index].data = INF_COSTS;
 698                 }
 699         }
 700
 701         /* Add all incident edges to edge bucket, since they are now independent. */
 702         for (edge_index = 0; edge_index < max_degree; ++edge_index) {
 703                 insert_into_edge_bucket(node->edges[edge_index]);
 704         }
 705 }
 706
 707 void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
 708 {
 709         pbqp_edge   *edge;
 710         pbqp_node   *other;
 711         pbqp_matrix *mat;
 712         vector      *vec;
 713         int          is_src;
 714
 715         assert(pbqp);
 716         assert(node);
 717
 718         edge = node->edges[0];
 719         mat = edge->costs;
 720         is_src = edge->src == node;
 721         vec = node->costs;
 722
 723         if (is_src) {
 724                 other = edge->tgt;
 725                 assert(other);
 726                 vector_add_matrix_col(vec, mat, other->solution);
 727         } else {
 728                 other = edge->src;
 729                 assert(other);
 730                 vector_add_matrix_row(vec, mat, other->solution);
 731         }
 732
 733         node->solution = vector_get_min_index(vec);
 734         if (pbqp->dump_file) {
 735                 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
 736         }
 737 }
 738
 739 void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
 740 {
 741         pbqp_edge   *src_edge   = node->edges[0];
 742         pbqp_edge   *tgt_edge   = node->edges[1];
 743         int          src_is_src = src_edge->src == node;
 744         int          tgt_is_src = tgt_edge->src == node;
 745         pbqp_matrix *src_mat;
 746         pbqp_matrix *tgt_mat;
 747         pbqp_node   *src_node;
 748         pbqp_node   *tgt_node;
 749         vector      *vec;
 750         vector      *node_vec;
 751         unsigned     col_index;
 752         unsigned     row_index;
 753
 754         assert(pbqp);
 755
 756         if (src_is_src) {
 757                 src_node = src_edge->tgt;
 758         } else {
 759                 src_node = src_edge->src;
 760         }
 761
 762         if (tgt_is_src) {
 763                 tgt_node = tgt_edge->tgt;
 764         } else {
 765                 tgt_node = tgt_edge->src;
 766         }
 767
 768         /* Swap nodes if necessary. */
 769         if (tgt_node->index < src_node->index) {
 770                 pbqp_node *tmp_node;
 771                 pbqp_edge *tmp_edge;
 772
 773                 tmp_node = src_node;
 774                 src_node = tgt_node;
 775                 tgt_node = tmp_node;
 776
 777                 tmp_edge = src_edge;
 778                 src_edge = tgt_edge;
 779                 tgt_edge = tmp_edge;
 780
 781                 src_is_src = src_edge->src == node;
 782                 tgt_is_src = tgt_edge->src == node;
 783         }
 784
 785         src_mat = src_edge->costs;
 786         tgt_mat = tgt_edge->costs;
 787
 788         node_vec = node->costs;
 789
 790         row_index = src_node->solution;
 791         col_index = tgt_node->solution;
 792
 793         vec = vector_copy(pbqp, node_vec);
 794
 795         if (src_is_src) {
 796                 vector_add_matrix_col(vec, src_mat, row_index);
 797         } else {
 798                 vector_add_matrix_row(vec, src_mat, row_index);
 799         }
 800
 801         if (tgt_is_src) {
 802                 vector_add_matrix_col(vec, tgt_mat, col_index);
 803         } else {
 804                 vector_add_matrix_row(vec, tgt_mat, col_index);
 805         }
 806
 807         node->solution = vector_get_min_index(vec);
 808         if (pbqp->dump_file) {
 809                 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
 810         }
 811
 812         obstack_free(&pbqp->obstack, vec);
 813 }
 814
 815 int node_is_reduced(pbqp_node *node)
 816 {
 817         if (!reduced_bucket) return 0;
 818
 819         assert(node);
 820         if (ARR_LEN(node->edges) == 0) return 1;
 821
 822         unsigned bucket_length = node_bucket_get_length(reduced_bucket);
 823         unsigned bucket_index  = node->bucket_index;
 824
 825         return bucket_index < bucket_length && reduced_bucket[bucket_index] == node;
 826 }