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;
58 static void insert_into_edge_bucket(pbqp_edge *edge)
60 if (edge_bucket_contains(edge_bucket, edge)) {
61 /* Edge is already inserted. */
65 edge_bucket_insert(&edge_bucket, edge);
68 static void init_buckets(void)
72 edge_bucket_init(&edge_bucket);
73 node_bucket_init(&reduced_bucket);
75 for (i = 0; i < 4; ++i) {
76 node_bucket_init(&node_buckets[i]);
80 void free_buckets(void)
84 for (i = 0; i < 4; ++i) {
85 node_bucket_free(&node_buckets[i]);
88 edge_bucket_free(&edge_bucket);
89 node_bucket_free(&reduced_bucket);
94 void fill_node_buckets(pbqp *pbqp)
100 node_len = pbqp->num_nodes;
103 ir_timer_t *t_fill_buckets = ir_timer_register("be_pbqp_fill_buckets", "PBQP Fill Nodes into buckets");
104 ir_timer_reset_and_start(t_fill_buckets);
107 for (node_index = 0; node_index < node_len; ++node_index) {
109 pbqp_node *node = get_node(pbqp, node_index);
113 degree = pbqp_node_get_degree(node);
115 /* We have only one bucket for nodes with arity >= 3. */
120 node_bucket_insert(&node_buckets[degree], node);
126 ir_timer_stop(t_fill_buckets);
127 printf("%-20s: %8.3lf msec\n", ir_timer_get_description(t_fill_buckets), (double)ir_timer_elapsed_usec(t_fill_buckets) / 1000.0);
131 static void normalize_towards_source(pbqp_edge *edge)
144 src_node = edge->src;
145 tgt_node = edge->tgt;
149 src_vec = src_node->costs;
150 tgt_vec = tgt_node->costs;
154 src_len = src_vec->len;
155 tgt_len = tgt_vec->len;
162 /* Normalize towards source node. */
163 for (src_index = 0; src_index < src_len; ++src_index) {
164 num min = pbqp_matrix_get_row_min(mat, src_index, tgt_vec);
167 if (src_vec->entries[src_index].data == INF_COSTS) {
168 pbqp_matrix_set_row_value(mat, src_index, 0);
170 pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
172 src_vec->entries[src_index].data = pbqp_add(
173 src_vec->entries[src_index].data, min);
175 if (min == INF_COSTS) {
177 unsigned edge_len = pbqp_node_get_degree(src_node);
179 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
180 pbqp_edge *edge_candidate = src_node->edges[edge_index];
181 if (edge_candidate != edge) {
182 insert_into_edge_bucket(edge_candidate);
190 static void normalize_towards_target(pbqp_edge *edge)
203 src_node = edge->src;
204 tgt_node = edge->tgt;
208 src_vec = src_node->costs;
209 tgt_vec = tgt_node->costs;
213 src_len = src_vec->len;
214 tgt_len = tgt_vec->len;
221 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
222 num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
225 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
226 pbqp_matrix_set_col_value(mat, tgt_index, 0);
228 pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
230 tgt_vec->entries[tgt_index].data = pbqp_add(
231 tgt_vec->entries[tgt_index].data, min);
233 if (min == INF_COSTS) {
235 unsigned edge_len = pbqp_node_get_degree(tgt_node);
237 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
238 pbqp_edge *edge_candidate = tgt_node->edges[edge_index];
239 if (edge_candidate != edge) {
240 insert_into_edge_bucket(edge_candidate);
248 static void reorder_node(pbqp_node *node)
250 unsigned degree = pbqp_node_get_degree(node);
251 /* Assume node lost one incident edge. */
252 unsigned old_degree = degree + 1;
254 if (!buckets_filled) return;
256 /* Same bucket as before */
257 if (degree > 2) return;
259 if (!node_bucket_contains(node_buckets[old_degree], node)) {
260 /* Old arity is new arity, so we have nothing to do. */
261 assert(node_bucket_contains(node_buckets[degree], node));
265 /* Delete node from old bucket... */
266 node_bucket_remove(&node_buckets[old_degree], node);
268 /* ..and add to new one. */
269 node_bucket_insert(&node_buckets[degree], node);
273 static void check_melting_possibility(pbqp *pbqp, pbqp_edge *edge)
288 src_node = edge->src;
289 tgt_node = edge->tgt;
293 src_vec = src_node->costs;
294 tgt_vec = tgt_node->costs;
298 src_len = src_vec->len;
299 tgt_len = tgt_vec->len;
306 if (src_len == 1 && tgt_len == 1) {
307 //panic("Something is wrong");
311 for (src_index = 0; src_index < src_len; ++src_index) {
313 if (src_vec->entries[src_index].data == INF_COSTS) {
316 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
317 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
320 if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
329 if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
335 allRowsOk &= onlyOneZero;
339 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
341 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
344 for (src_index = 0; src_index < src_len; ++src_index) {
345 if (src_vec->entries[src_index].data == INF_COSTS) {
348 if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
357 if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
363 allColsOk &= onlyOneZero;
366 if (allRowsOk && allColsOk) {
372 void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
385 src_node = edge->src;
386 tgt_node = edge->tgt;
390 /* If edge are already deleted, we have nothing to do. */
391 if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
395 if (pbqp->dump_file) {
397 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
398 dump_section(pbqp->dump_file, 3, txt);
402 src_vec = src_node->costs;
403 tgt_vec = tgt_node->costs;
407 src_len = src_vec->len;
408 tgt_len = tgt_vec->len;
416 if (pbqp->dump_file) {
417 fputs("Input:<br>\n", pbqp->dump_file);
418 dump_simplifyedge(pbqp, edge);
422 normalize_towards_source(edge);
423 normalize_towards_target(edge);
426 if (pbqp->dump_file) {
427 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
428 dump_simplifyedge(pbqp, edge);
432 if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
434 if (pbqp->dump_file) {
435 fputs("edge has been eliminated<br>\n", pbqp->dump_file);
446 reorder_node(src_node);
447 reorder_node(tgt_node);
451 void initial_simplify_edges(pbqp *pbqp)
459 ir_timer_t *t_int_simpl = ir_timer_register("be_pbqp_init_simp", "PBQP Initial simplify edges");
460 ir_timer_reset_and_start(t_int_simpl);
464 if (pbqp->dump_file) {
465 pbqp_dump_input(pbqp);
466 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
470 node_len = pbqp->num_nodes;
474 /* First simplify all edges. */
475 for (node_index = 0; node_index < node_len; ++node_index) {
477 pbqp_node *node = get_node(pbqp, node_index);
484 edge_len = pbqp_node_get_degree(node);
486 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
487 pbqp_edge *edge = edges[edge_index];
489 /* Simplify only once per edge. */
490 if (node != edge->src) continue;
492 simplify_edge(pbqp, edge);
497 ir_timer_stop(t_int_simpl);
498 printf("%-20s: %8.3lf msec\n", ir_timer_get_description(t_int_simpl), (double)ir_timer_elapsed_usec(t_int_simpl) / 1000.0);
502 num determine_solution(pbqp *pbqp)
509 ir_timer_t *t_det_solution = ir_timer_register("be_det_solution", "PBQP Determine Solution");
510 ir_timer_reset_and_start(t_det_solution);
520 file = pbqp->dump_file;
523 dump_section(file, 1, "4. Determine Solution/Minimum");
524 dump_section(file, 2, "4.1. Trivial Solution");
528 /* Solve trivial nodes and calculate solution. */
529 node_len = node_bucket_get_length(node_buckets[0]);
533 pbqp->num_r0 = node_len;
537 for (node_index = 0; node_index < node_len; ++node_index) {
538 pbqp_node *node = node_buckets[0][node_index];
541 node->solution = vector_get_min_index(node->costs);
542 solution = pbqp_add(solution,
543 node->costs->entries[node->solution].data);
547 fprintf(file, "node n%d is set to %d<br>\n", node->index, node->solution);
548 dump_node(file, node);
555 dump_section(file, 2, "Minimum");
556 #if KAPS_USE_UNSIGNED
557 fprintf(file, "Minimum is equal to %u.", solution);
559 fprintf(file, "Minimum is equal to %lld.", solution);
565 ir_timer_stop(t_det_solution);
566 printf("%-20s: %8.3lf msec\n", ir_timer_get_description(t_det_solution), (double)ir_timer_elapsed_usec(t_det_solution) / 1000.0);
572 static void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
583 edge = node->edges[0];
585 is_src = edge->src == node;
592 node->solution = pbqp_matrix_get_col_min_index(mat, other->solution, vec);
597 node->solution = pbqp_matrix_get_row_min_index(mat, other->solution, vec);
601 if (pbqp->dump_file) {
602 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
607 static void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
609 pbqp_edge *src_edge = node->edges[0];
610 pbqp_edge *tgt_edge = node->edges[1];
611 int src_is_src = src_edge->src == node;
612 int tgt_is_src = tgt_edge->src == node;
613 pbqp_matrix *src_mat;
614 pbqp_matrix *tgt_mat;
625 src_node = src_edge->tgt;
627 src_node = src_edge->src;
631 tgt_node = tgt_edge->tgt;
633 tgt_node = tgt_edge->src;
636 /* Swap nodes if necessary. */
637 if (tgt_node->index < src_node->index) {
649 src_is_src = src_edge->src == node;
650 tgt_is_src = tgt_edge->src == node;
653 src_mat = src_edge->costs;
654 tgt_mat = tgt_edge->costs;
656 node_vec = node->costs;
658 row_index = src_node->solution;
659 col_index = tgt_node->solution;
661 vec = vector_copy(pbqp, node_vec);
664 vector_add_matrix_col(vec, src_mat, row_index);
666 vector_add_matrix_row(vec, src_mat, row_index);
670 vector_add_matrix_col(vec, tgt_mat, col_index);
672 vector_add_matrix_row(vec, tgt_mat, col_index);
675 node->solution = vector_get_min_index(vec);
678 if (pbqp->dump_file) {
679 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
683 obstack_free(&pbqp->obstack, vec);
686 void back_propagate(pbqp *pbqp)
689 unsigned node_len = node_bucket_get_length(reduced_bucket);
694 if (pbqp->dump_file) {
695 dump_section(pbqp->dump_file, 2, "Back Propagation");
699 for (node_index = node_len; node_index > 0; --node_index) {
700 pbqp_node *node = reduced_bucket[node_index - 1];
702 switch (pbqp_node_get_degree(node)) {
704 back_propagate_RI(pbqp, node);
707 back_propagate_RII(pbqp, node);
710 panic("Only nodes with degree one or two should be in this bucket");
716 void apply_edge(pbqp *pbqp)
718 pbqp_edge *edge = edge_bucket_pop(&edge_bucket);
720 simplify_edge(pbqp, edge);
723 void apply_RI(pbqp *pbqp)
725 pbqp_node *node = node_bucket_pop(&node_buckets[1]);
726 pbqp_edge *edge = node->edges[0];
727 pbqp_matrix *mat = edge->costs;
728 int is_src = edge->src == node;
729 pbqp_node *other_node;
732 assert(pbqp_node_get_degree(node) == 1);
735 other_node = edge->tgt;
737 other_node = edge->src;
741 if (pbqp->dump_file) {
743 sprintf(txt, "RI-Reduction of Node n%d", node->index);
744 dump_section(pbqp->dump_file, 2, txt);
745 pbqp_dump_graph(pbqp);
746 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
747 dump_node(pbqp->dump_file, node);
748 dump_node(pbqp->dump_file, other_node);
749 dump_edge(pbqp->dump_file, edge);
754 pbqp_matrix_add_to_all_cols(mat, node->costs);
755 normalize_towards_target(edge);
757 pbqp_matrix_add_to_all_rows(mat, node->costs);
758 normalize_towards_source(edge);
760 disconnect_edge(other_node, edge);
763 if (pbqp->dump_file) {
764 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
765 dump_node(pbqp->dump_file, other_node);
769 reorder_node(other_node);
777 /* Add node to back propagation list. */
778 node_bucket_insert(&reduced_bucket, node);
781 void apply_RII(pbqp *pbqp)
783 pbqp_node *node = node_bucket_pop(&node_buckets[2]);
784 pbqp_edge *src_edge = node->edges[0];
785 pbqp_edge *tgt_edge = node->edges[1];
786 int src_is_src = src_edge->src == node;
787 int tgt_is_src = tgt_edge->src == node;
788 pbqp_matrix *src_mat;
789 pbqp_matrix *tgt_mat;
804 assert(pbqp_node_get_degree(node) == 2);
807 src_node = src_edge->tgt;
809 src_node = src_edge->src;
813 tgt_node = tgt_edge->tgt;
815 tgt_node = tgt_edge->src;
818 /* Swap nodes if necessary. */
819 if (tgt_node->index < src_node->index) {
831 src_is_src = src_edge->src == node;
832 tgt_is_src = tgt_edge->src == node;
836 if (pbqp->dump_file) {
838 sprintf(txt, "RII-Reduction of Node n%d", node->index);
839 dump_section(pbqp->dump_file, 2, txt);
840 pbqp_dump_graph(pbqp);
841 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
842 dump_node(pbqp->dump_file, src_node);
843 dump_edge(pbqp->dump_file, src_edge);
844 dump_node(pbqp->dump_file, node);
845 dump_edge(pbqp->dump_file, tgt_edge);
846 dump_node(pbqp->dump_file, tgt_node);
850 src_mat = src_edge->costs;
851 tgt_mat = tgt_edge->costs;
853 src_vec = src_node->costs;
854 tgt_vec = tgt_node->costs;
855 node_vec = node->costs;
857 row_len = src_vec->len;
858 col_len = tgt_vec->len;
859 node_len = node_vec->len;
861 mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
863 for (row_index = 0; row_index < row_len; ++row_index) {
864 for (col_index = 0; col_index < col_len; ++col_index) {
865 vec = vector_copy(pbqp, node_vec);
868 vector_add_matrix_col(vec, src_mat, row_index);
870 vector_add_matrix_row(vec, src_mat, row_index);
874 vector_add_matrix_col(vec, tgt_mat, col_index);
876 vector_add_matrix_row(vec, tgt_mat, col_index);
879 mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
881 obstack_free(&pbqp->obstack, vec);
885 pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
887 /* Disconnect node. */
888 disconnect_edge(src_node, src_edge);
889 disconnect_edge(tgt_node, tgt_edge);
897 /* Add node to back propagation list. */
898 node_bucket_insert(&reduced_bucket, node);
901 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
904 pbqp_matrix_add(edge->costs, mat);
906 /* Free local matrix. */
907 obstack_free(&pbqp->obstack, mat);
909 reorder_node(src_node);
910 reorder_node(tgt_node);
914 if (pbqp->dump_file) {
915 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
916 dump_edge(pbqp->dump_file, edge);
920 /* Edge has changed so we simplify it. */
921 simplify_edge(pbqp, edge);
924 void select_alternative(pbqp_node *node, unsigned selected_index)
930 unsigned max_degree = pbqp_node_get_degree(node);
933 node->solution = selected_index;
934 node_vec = node->costs;
935 node_len = node_vec->len;
936 assert(selected_index < node_len);
938 /* Set all other costs to infinity. */
939 for (node_index = 0; node_index < node_len; ++node_index) {
940 if (node_index != selected_index) {
941 node_vec->entries[node_index].data = INF_COSTS;
945 /* Add all incident edges to edge bucket, since they are now independent. */
946 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
947 insert_into_edge_bucket(node->edges[edge_index]);
951 pbqp_node *get_node_with_max_degree(void)
953 pbqp_node **bucket = node_buckets[3];
954 unsigned bucket_len = node_bucket_get_length(bucket);
955 unsigned bucket_index;
956 unsigned max_degree = 0;
957 pbqp_node *result = NULL;
959 for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
960 pbqp_node *candidate = bucket[bucket_index];
961 unsigned degree = pbqp_node_get_degree(candidate);
963 if (degree > max_degree) {
972 unsigned get_local_minimal_alternative(pbqp *pbqp, pbqp_node *node)
979 unsigned max_degree = 0;
982 unsigned min_index = 0;
988 node_vec = node->costs;
989 node_len = node_vec->len;
991 for (node_index = 0; node_index < node_len; ++node_index) {
992 num value = node_vec->entries[node_index].data;
994 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
995 edge = node->edges[edge_index];
997 is_src = edge->src == node;
1000 vec = vector_copy(pbqp, edge->tgt->costs);
1001 vector_add_matrix_row(vec, mat, node_index);
1003 vec = vector_copy(pbqp, edge->src->costs);
1004 vector_add_matrix_col(vec, mat, node_index);
1007 value = pbqp_add(value, vector_get_min(vec));
1009 obstack_free(&pbqp->obstack, vec);
1014 min_index = node_index;
1021 int node_is_reduced(pbqp_node *node)
1023 if (!reduced_bucket) return 0;
1025 if (pbqp_node_get_degree(node) == 0) return 1;
1027 return node_bucket_contains(reduced_bucket, node);