nsz Git - libfirm/blob - heuristical.c

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