2 * Copyright (C) 1995-2008 University of Karlsruhe. All right reserved.
4 * This file is part of libFirm.
6 * This file may be distributed and/or modified under the terms of the
7 * GNU General Public License version 2 as published by the Free Software
8 * Foundation and appearing in the file LICENSE.GPL included in the
9 * packaging of this file.
11 * Licensees holding valid libFirm Professional Edition licenses may use
12 * this file in accordance with the libFirm Commercial License.
13 * Agreement provided with the Software.
15 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
16 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22 * @brief Optimal reductions and helper functions.
24 * @author Sebastian Buchwald
29 #include "adt/array.h"
35 #include "html_dumper.h"
40 #include "pbqp_edge.h"
41 #include "pbqp_edge_t.h"
42 #include "pbqp_node.h"
43 #include "pbqp_node_t.h"
49 pbqp_edge **edge_bucket;
50 pbqp_node **node_buckets[4];
51 pbqp_node **reduced_bucket = NULL;
52 static int buckets_filled = 0;
54 static void insert_into_edge_bucket(pbqp_edge *edge)
56 if (edge_bucket_contains(edge_bucket, edge)) {
57 /* Edge is already inserted. */
61 edge_bucket_insert(&edge_bucket, edge);
64 static void init_buckets(void)
68 edge_bucket_init(&edge_bucket);
69 node_bucket_init(&reduced_bucket);
71 for (i = 0; i < 4; ++i) {
72 node_bucket_init(&node_buckets[i]);
76 void free_buckets(void)
80 for (i = 0; i < 4; ++i) {
81 node_bucket_free(&node_buckets[i]);
84 edge_bucket_free(&edge_bucket);
85 node_bucket_free(&reduced_bucket);
90 void fill_node_buckets(pbqp *pbqp)
96 node_len = pbqp->num_nodes;
99 ir_timer_t *t_fill_buckets = ir_timer_register("be_pbqp_fill_buckets", "PBQP Fill Nodes into buckets");
100 ir_timer_reset_and_start(t_fill_buckets);
103 for (node_index = 0; node_index < node_len; ++node_index) {
105 pbqp_node *node = get_node(pbqp, node_index);
109 degree = pbqp_node_get_degree(node);
111 /* We have only one bucket for nodes with arity >= 3. */
116 node_bucket_insert(&node_buckets[degree], node);
122 ir_timer_stop(t_fill_buckets);
123 printf("%-20s: %8.3lf msec\n", ir_timer_get_description(t_fill_buckets), (double)ir_timer_elapsed_usec(t_fill_buckets) / 1000.0);
127 static void normalize_towards_source(pbqp_edge *edge)
140 src_node = edge->src;
141 tgt_node = edge->tgt;
145 src_vec = src_node->costs;
146 tgt_vec = tgt_node->costs;
150 src_len = src_vec->len;
151 tgt_len = tgt_vec->len;
158 /* Normalize towards source node. */
159 for (src_index = 0; src_index < src_len; ++src_index) {
160 num min = pbqp_matrix_get_row_min(mat, src_index, tgt_vec);
163 if (src_vec->entries[src_index].data == INF_COSTS) {
164 pbqp_matrix_set_row_value(mat, src_index, 0);
166 pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
168 src_vec->entries[src_index].data = pbqp_add(
169 src_vec->entries[src_index].data, min);
171 if (min == INF_COSTS) {
173 unsigned edge_len = pbqp_node_get_degree(src_node);
175 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
176 pbqp_edge *edge_candidate = src_node->edges[edge_index];
177 if (edge_candidate != edge) {
178 insert_into_edge_bucket(edge_candidate);
186 static void normalize_towards_target(pbqp_edge *edge)
199 src_node = edge->src;
200 tgt_node = edge->tgt;
204 src_vec = src_node->costs;
205 tgt_vec = tgt_node->costs;
209 src_len = src_vec->len;
210 tgt_len = tgt_vec->len;
217 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
218 num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
221 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
222 pbqp_matrix_set_col_value(mat, tgt_index, 0);
224 pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
226 tgt_vec->entries[tgt_index].data = pbqp_add(
227 tgt_vec->entries[tgt_index].data, min);
229 if (min == INF_COSTS) {
231 unsigned edge_len = pbqp_node_get_degree(tgt_node);
233 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
234 pbqp_edge *edge_candidate = tgt_node->edges[edge_index];
235 if (edge_candidate != edge) {
236 insert_into_edge_bucket(edge_candidate);
244 void reorder_node(pbqp_node *node)
246 unsigned degree = pbqp_node_get_degree(node);
247 /* Assume node lost one incident edge. */
248 unsigned old_degree = degree + 1;
250 if (!buckets_filled) return;
252 /* Same bucket as before */
253 if (degree > 2) return;
255 if (!node_bucket_contains(node_buckets[old_degree], node)) {
256 /* Old arity is new arity, so we have nothing to do. */
257 assert(node_bucket_contains(node_buckets[degree], node));
261 /* Delete node from old bucket... */
262 node_bucket_remove(&node_buckets[old_degree], node);
264 /* ..and add to new one. */
265 node_bucket_insert(&node_buckets[degree], node);
269 void check_melting_possibility(pbqp *pbqp, pbqp_edge *edge)
284 src_node = edge->src;
285 tgt_node = edge->tgt;
289 src_vec = src_node->costs;
290 tgt_vec = tgt_node->costs;
294 src_len = src_vec->len;
295 tgt_len = tgt_vec->len;
302 if (src_len == 1 && tgt_len == 1) {
303 //panic("Something is wrong");
307 for (src_index = 0; src_index < src_len; ++src_index) {
309 if (src_vec->entries[src_index].data == INF_COSTS) {
312 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
313 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
316 if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
325 if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
331 allRowsOk &= onlyOneZero;
335 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
337 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
340 for (src_index = 0; src_index < src_len; ++src_index) {
341 if (src_vec->entries[src_index].data == INF_COSTS) {
344 if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
353 if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
359 allColsOk &= onlyOneZero;
362 if (allRowsOk || allColsOk) {
368 void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
381 src_node = edge->src;
382 tgt_node = edge->tgt;
386 /* If edge are already deleted, we have nothing to do. */
387 if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
391 if (pbqp->dump_file) {
393 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
394 dump_section(pbqp->dump_file, 3, txt);
398 src_vec = src_node->costs;
399 tgt_vec = tgt_node->costs;
403 src_len = src_vec->len;
404 tgt_len = tgt_vec->len;
412 if (pbqp->dump_file) {
413 fputs("Input:<br>\n", pbqp->dump_file);
414 dump_simplifyedge(pbqp, edge);
418 normalize_towards_source(edge);
419 normalize_towards_target(edge);
422 if (pbqp->dump_file) {
423 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
424 dump_simplifyedge(pbqp, edge);
428 if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
430 if (pbqp->dump_file) {
431 fputs("edge has been eliminated<br>\n", pbqp->dump_file);
440 reorder_node(src_node);
441 reorder_node(tgt_node);
445 void initial_simplify_edges(pbqp *pbqp)
453 ir_timer_t *t_int_simpl = ir_timer_register("be_pbqp_init_simp", "PBQP Initial simplify edges");
454 ir_timer_reset_and_start(t_int_simpl);
458 if (pbqp->dump_file) {
459 pbqp_dump_input(pbqp);
460 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
464 node_len = pbqp->num_nodes;
468 /* First simplify all edges. */
469 for (node_index = 0; node_index < node_len; ++node_index) {
471 pbqp_node *node = get_node(pbqp, node_index);
478 edge_len = pbqp_node_get_degree(node);
480 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
481 pbqp_edge *edge = edges[edge_index];
483 /* Simplify only once per edge. */
484 if (node != edge->src) continue;
486 simplify_edge(pbqp, edge);
491 ir_timer_stop(t_int_simpl);
492 printf("%-20s: %8.3lf msec\n", ir_timer_get_description(t_int_simpl), (double)ir_timer_elapsed_usec(t_int_simpl) / 1000.0);
496 num determine_solution(pbqp *pbqp)
503 ir_timer_t *t_det_solution = ir_timer_register("be_det_solution", "PBQP Determine Solution");
504 ir_timer_reset_and_start(t_det_solution);
514 file = pbqp->dump_file;
517 dump_section(file, 1, "4. Determine Solution/Minimum");
518 dump_section(file, 2, "4.1. Trivial Solution");
522 /* Solve trivial nodes and calculate solution. */
523 node_len = node_bucket_get_length(node_buckets[0]);
526 pbqp->num_r0 = node_len;
529 for (node_index = 0; node_index < node_len; ++node_index) {
530 pbqp_node *node = node_buckets[0][node_index];
533 node->solution = vector_get_min_index(node->costs);
534 solution = pbqp_add(solution,
535 node->costs->entries[node->solution].data);
539 fprintf(file, "node n%d is set to %d<br>\n", node->index, node->solution);
540 dump_node(file, node);
547 dump_section(file, 2, "Minimum");
548 #if KAPS_USE_UNSIGNED
549 fprintf(file, "Minimum is equal to %u.", solution);
551 fprintf(file, "Minimum is equal to %lld.", solution);
557 ir_timer_stop(t_det_solution);
558 printf("%-20s: %8.3lf msec\n", ir_timer_get_description(t_det_solution), (double)ir_timer_elapsed_usec(t_det_solution) / 1000.0);
564 static void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
575 edge = node->edges[0];
577 is_src = edge->src == node;
584 node->solution = pbqp_matrix_get_col_min_index(mat, other->solution, vec);
589 node->solution = pbqp_matrix_get_row_min_index(mat, other->solution, vec);
593 if (pbqp->dump_file) {
594 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
599 static void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
601 pbqp_edge *src_edge = node->edges[0];
602 pbqp_edge *tgt_edge = node->edges[1];
603 int src_is_src = src_edge->src == node;
604 int tgt_is_src = tgt_edge->src == node;
605 pbqp_matrix *src_mat;
606 pbqp_matrix *tgt_mat;
617 src_node = src_edge->tgt;
619 src_node = src_edge->src;
623 tgt_node = tgt_edge->tgt;
625 tgt_node = tgt_edge->src;
628 /* Swap nodes if necessary. */
629 if (tgt_node->index < src_node->index) {
641 src_is_src = src_edge->src == node;
642 tgt_is_src = tgt_edge->src == node;
645 src_mat = src_edge->costs;
646 tgt_mat = tgt_edge->costs;
648 node_vec = node->costs;
650 row_index = src_node->solution;
651 col_index = tgt_node->solution;
653 vec = vector_copy(pbqp, node_vec);
656 vector_add_matrix_col(vec, src_mat, row_index);
658 vector_add_matrix_row(vec, src_mat, row_index);
662 vector_add_matrix_col(vec, tgt_mat, col_index);
664 vector_add_matrix_row(vec, tgt_mat, col_index);
667 node->solution = vector_get_min_index(vec);
670 if (pbqp->dump_file) {
671 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
675 obstack_free(&pbqp->obstack, vec);
678 void back_propagate(pbqp *pbqp)
681 unsigned node_len = node_bucket_get_length(reduced_bucket);
686 if (pbqp->dump_file) {
687 dump_section(pbqp->dump_file, 2, "Back Propagation");
691 for (node_index = node_len; node_index > 0; --node_index) {
692 pbqp_node *node = reduced_bucket[node_index - 1];
694 switch (pbqp_node_get_degree(node)) {
696 back_propagate_RI(pbqp, node);
699 back_propagate_RII(pbqp, node);
702 panic("Only nodes with degree one or two should be in this bucket");
708 void apply_edge(pbqp *pbqp)
710 pbqp_edge *edge = edge_bucket_pop(&edge_bucket);
712 simplify_edge(pbqp, edge);
715 void apply_RI(pbqp *pbqp)
717 pbqp_node *node = node_bucket_pop(&node_buckets[1]);
718 pbqp_edge *edge = node->edges[0];
719 pbqp_matrix *mat = edge->costs;
720 int is_src = edge->src == node;
721 pbqp_node *other_node;
724 assert(pbqp_node_get_degree(node) == 1);
727 other_node = edge->tgt;
729 other_node = edge->src;
733 if (pbqp->dump_file) {
735 sprintf(txt, "RI-Reduction of Node n%d", node->index);
736 dump_section(pbqp->dump_file, 2, txt);
737 pbqp_dump_graph(pbqp);
738 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
739 dump_node(pbqp->dump_file, node);
740 dump_node(pbqp->dump_file, other_node);
741 dump_edge(pbqp->dump_file, edge);
746 pbqp_matrix_add_to_all_cols(mat, node->costs);
747 normalize_towards_target(edge);
749 pbqp_matrix_add_to_all_rows(mat, node->costs);
750 normalize_towards_source(edge);
752 disconnect_edge(other_node, edge);
755 if (pbqp->dump_file) {
756 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
757 dump_node(pbqp->dump_file, other_node);
761 reorder_node(other_node);
767 /* Add node to back propagation list. */
768 node_bucket_insert(&reduced_bucket, node);
771 void apply_RII(pbqp *pbqp)
773 pbqp_node *node = node_bucket_pop(&node_buckets[2]);
774 pbqp_edge *src_edge = node->edges[0];
775 pbqp_edge *tgt_edge = node->edges[1];
776 int src_is_src = src_edge->src == node;
777 int tgt_is_src = tgt_edge->src == node;
778 pbqp_matrix *src_mat;
779 pbqp_matrix *tgt_mat;
794 assert(pbqp_node_get_degree(node) == 2);
797 src_node = src_edge->tgt;
799 src_node = src_edge->src;
803 tgt_node = tgt_edge->tgt;
805 tgt_node = tgt_edge->src;
808 /* Swap nodes if necessary. */
809 if (tgt_node->index < src_node->index) {
821 src_is_src = src_edge->src == node;
822 tgt_is_src = tgt_edge->src == node;
826 if (pbqp->dump_file) {
828 sprintf(txt, "RII-Reduction of Node n%d", node->index);
829 dump_section(pbqp->dump_file, 2, txt);
830 pbqp_dump_graph(pbqp);
831 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
832 dump_node(pbqp->dump_file, src_node);
833 dump_edge(pbqp->dump_file, src_edge);
834 dump_node(pbqp->dump_file, node);
835 dump_edge(pbqp->dump_file, tgt_edge);
836 dump_node(pbqp->dump_file, tgt_node);
840 src_mat = src_edge->costs;
841 tgt_mat = tgt_edge->costs;
843 src_vec = src_node->costs;
844 tgt_vec = tgt_node->costs;
845 node_vec = node->costs;
847 row_len = src_vec->len;
848 col_len = tgt_vec->len;
849 node_len = node_vec->len;
851 mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
853 for (row_index = 0; row_index < row_len; ++row_index) {
854 for (col_index = 0; col_index < col_len; ++col_index) {
855 vec = vector_copy(pbqp, node_vec);
858 vector_add_matrix_col(vec, src_mat, row_index);
860 vector_add_matrix_row(vec, src_mat, row_index);
864 vector_add_matrix_col(vec, tgt_mat, col_index);
866 vector_add_matrix_row(vec, tgt_mat, col_index);
869 mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
871 obstack_free(&pbqp->obstack, vec);
875 pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
877 /* Disconnect node. */
878 disconnect_edge(src_node, src_edge);
879 disconnect_edge(tgt_node, tgt_edge);
885 /* Add node to back propagation list. */
886 node_bucket_insert(&reduced_bucket, node);
889 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
892 pbqp_matrix_add(edge->costs, mat);
894 /* Free local matrix. */
895 obstack_free(&pbqp->obstack, mat);
897 reorder_node(src_node);
898 reorder_node(tgt_node);
902 if (pbqp->dump_file) {
903 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
904 dump_edge(pbqp->dump_file, edge);
908 /* Edge has changed so we simplify it. */
909 simplify_edge(pbqp, edge);
912 void select_alternative(pbqp_node *node, unsigned selected_index)
918 unsigned max_degree = pbqp_node_get_degree(node);
921 node->solution = selected_index;
922 node_vec = node->costs;
923 node_len = node_vec->len;
924 assert(selected_index < node_len);
926 /* Set all other costs to infinity. */
927 for (node_index = 0; node_index < node_len; ++node_index) {
928 if (node_index != selected_index) {
929 node_vec->entries[node_index].data = INF_COSTS;
933 /* Add all incident edges to edge bucket, since they are now independent. */
934 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
935 insert_into_edge_bucket(node->edges[edge_index]);
939 pbqp_node *get_node_with_max_degree(void)
941 pbqp_node **bucket = node_buckets[3];
942 unsigned bucket_len = node_bucket_get_length(bucket);
943 unsigned bucket_index;
944 unsigned max_degree = 0;
945 pbqp_node *result = NULL;
947 for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
948 pbqp_node *candidate = bucket[bucket_index];
949 unsigned degree = pbqp_node_get_degree(candidate);
951 if (degree > max_degree) {
960 unsigned get_local_minimal_alternative(pbqp *pbqp, pbqp_node *node)
970 unsigned min_index = 0;
976 node_vec = node->costs;
977 node_len = node_vec->len;
978 max_degree = pbqp_node_get_degree(node);
980 for (node_index = 0; node_index < node_len; ++node_index) {
981 num value = node_vec->entries[node_index].data;
983 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
984 edge = node->edges[edge_index];
986 is_src = edge->src == node;
989 vec = vector_copy(pbqp, edge->tgt->costs);
990 vector_add_matrix_row(vec, mat, node_index);
992 vec = vector_copy(pbqp, edge->src->costs);
993 vector_add_matrix_col(vec, mat, node_index);
996 value = pbqp_add(value, vector_get_min(vec));
998 obstack_free(&pbqp->obstack, vec);
1003 min_index = node_index;
1010 int node_is_reduced(pbqp_node *node)
1012 if (!reduced_bucket) return 0;
1014 if (pbqp_node_get_degree(node) == 0) return 1;
1016 return node_bucket_contains(reduced_bucket, node);