1 /*
2  * Copyright (C) 1995-2008 University of Karlsruhe.  All right reserved.
3  *
4  * This file is part of libFirm.
5  *
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.
10  *
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.
14  *
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
17  * PURPOSE.
18  */
19 
20 /**
21  * @file
22  * @brief   Optimal reductions and helper functions.
23  * @date    28.12.2009
24  * @author  Sebastian Buchwald
25  */
26 #include "config.h"
27 
28 #include "adt/array.h"
29 #include "assert.h"
30 #include "error.h"
31 
32 #include "bucket.h"
33 #if KAPS_DUMP
34 #include "html_dumper.h"
35 #endif
36 #include "kaps.h"
37 #include "matrix.h"
38 #include "optimal.h"
39 #include "pbqp_edge.h"
40 #include "pbqp_edge_t.h"
41 #include "pbqp_node.h"
42 #include "pbqp_node_t.h"
43 #include "vector.h"
44 
45 #include "plist.h"
46 #include "timing.h"
47 
48 pbqp_edge_t **edge_bucket;
49 static pbqp_edge_t **rm_bucket;
50 pbqp_node_t **node_buckets[4];
51 pbqp_node_t **reduced_bucket = NULL;
52 pbqp_node_t  *merged_node = NULL;
53 static int  buckets_filled = 0;
54 
insert_into_edge_bucket(pbqp_edge_t * edge)55 static void insert_into_edge_bucket(pbqp_edge_t *edge)
56 {
57 	if (edge_bucket_contains(edge_bucket, edge)) {
58 		/* Edge is already inserted. */
59 		return;
60 	}
61 
62 	edge_bucket_insert(&edge_bucket, edge);
63 }
64 
insert_into_rm_bucket(pbqp_edge_t * edge)65 static void insert_into_rm_bucket(pbqp_edge_t *edge)
66 {
67 	if (edge_bucket_contains(rm_bucket, edge)) {
68 		/* Edge is already inserted. */
69 		return;
70 	}
71 
72 	edge_bucket_insert(&rm_bucket, edge);
73 }
74 
init_buckets(void)75 static void init_buckets(void)
76 {
77 	int i;
78 
79 	edge_bucket_init(&edge_bucket);
80 	edge_bucket_init(&rm_bucket);
81 	node_bucket_init(&reduced_bucket);
82 
83 	for (i = 0; i < 4; ++i) {
84 		node_bucket_init(&node_buckets[i]);
85 	}
86 }
87 
free_buckets(void)88 void free_buckets(void)
89 {
90 	int i;
91 
92 	for (i = 0; i < 4; ++i) {
93 		node_bucket_free(&node_buckets[i]);
94 	}
95 
96 	edge_bucket_free(&edge_bucket);
97 	edge_bucket_free(&rm_bucket);
98 	node_bucket_free(&reduced_bucket);
99 
100 	buckets_filled = 0;
101 }
102 
fill_node_buckets(pbqp_t * pbqp)103 void fill_node_buckets(pbqp_t *pbqp)
104 {
105 	unsigned node_index;
106 	unsigned node_len;
107 
108 	node_len = pbqp->num_nodes;
109 
110 	#if KAPS_TIMING
111 		ir_timer_t *t_fill_buckets = ir_timer_new();
112 		ir_timer_start(t_fill_buckets);
113 	#endif
114 
115 	for (node_index = 0; node_index < node_len; ++node_index) {
116 		unsigned     degree;
117 		pbqp_node_t *node = get_node(pbqp, node_index);
118 
119 		if (!node) continue;
120 
121 		degree = pbqp_node_get_degree(node);
122 
123 		/* We have only one bucket for nodes with arity >= 3. */
124 		if (degree > 3) {
125 			degree = 3;
126 		}
127 
128 		node_bucket_insert(&node_buckets[degree], node);
129 	}
130 
131 	buckets_filled = 1;
132 
133 	#if KAPS_TIMING
134 		ir_timer_stop(t_fill_buckets);
135 		printf("PBQP Fill Nodes into buckets: %10.3lf msec\n", (double)ir_timer_elapsed_usec(t_fill_buckets) / 1000.0);
136 	#endif
137 }
138 
normalize_towards_source(pbqp_edge_t * edge)139 static void normalize_towards_source(pbqp_edge_t *edge)
140 {
141 	pbqp_matrix_t  *mat;
142 	pbqp_node_t    *src_node;
143 	pbqp_node_t    *tgt_node;
144 	vector_t       *src_vec;
145 	vector_t       *tgt_vec;
146 	unsigned        src_len;
147 	unsigned        tgt_len;
148 	unsigned        src_index;
149 	unsigned        new_infinity = 0;
150 
151 	src_node = edge->src;
152 	tgt_node = edge->tgt;
153 
154 	src_vec = src_node->costs;
155 	tgt_vec = tgt_node->costs;
156 
157 	src_len = src_vec->len;
158 	tgt_len = tgt_vec->len;
159 	assert(src_len > 0);
160 	assert(tgt_len > 0);
161 
162 	mat = edge->costs;
163 
164 	/* Normalize towards source node. */
165 	for (src_index = 0; src_index < src_len; ++src_index) {
166 		num min = pbqp_matrix_get_row_min(mat, src_index, tgt_vec);
167 
168 		if (min != 0) {
169 			if (src_vec->entries[src_index].data == INF_COSTS) {
170 				pbqp_matrix_set_row_value(mat, src_index, 0);
171 				continue;
172 			}
173 
174 			pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
175 			src_vec->entries[src_index].data = pbqp_add(
176 					src_vec->entries[src_index].data, min);
177 
178 			if (min == INF_COSTS) {
179 				new_infinity = 1;
180 			}
181 		}
182 	}
183 
184 	if (new_infinity) {
185 		unsigned edge_index;
186 		unsigned edge_len = pbqp_node_get_degree(src_node);
187 
188 		for (edge_index = 0; edge_index < edge_len; ++edge_index) {
189 			pbqp_edge_t *edge_candidate = src_node->edges[edge_index];
190 
191 			if (edge_candidate != edge) {
192 				insert_into_edge_bucket(edge_candidate);
193 			}
194 		}
195 	}
196 }
197 
normalize_towards_target(pbqp_edge_t * edge)198 static void normalize_towards_target(pbqp_edge_t *edge)
199 {
200 	pbqp_matrix_t  *mat;
201 	pbqp_node_t    *src_node;
202 	pbqp_node_t    *tgt_node;
203 	vector_t       *src_vec;
204 	vector_t       *tgt_vec;
205 	unsigned        src_len;
206 	unsigned        tgt_len;
207 	unsigned        tgt_index;
208 	unsigned        new_infinity = 0;
209 
210 	src_node = edge->src;
211 	tgt_node = edge->tgt;
212 
213 	src_vec = src_node->costs;
214 	tgt_vec = tgt_node->costs;
215 
216 	src_len = src_vec->len;
217 	tgt_len = tgt_vec->len;
218 	assert(src_len > 0);
219 	assert(tgt_len > 0);
220 
221 	mat = edge->costs;
222 
223 	/* Normalize towards target node. */
224 	for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
225 		num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
226 
227 		if (min != 0) {
228 			if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
229 				pbqp_matrix_set_col_value(mat, tgt_index, 0);
230 				continue;
231 			}
232 
233 			pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
234 			tgt_vec->entries[tgt_index].data = pbqp_add(
235 					tgt_vec->entries[tgt_index].data, min);
236 
237 			if (min == INF_COSTS) {
238 				new_infinity = 1;
239 			}
240 		}
241 	}
242 
243 	if (new_infinity) {
244 		unsigned edge_index;
245 		unsigned edge_len = pbqp_node_get_degree(tgt_node);
246 
247 		for (edge_index = 0; edge_index < edge_len; ++edge_index) {
248 			pbqp_edge_t *edge_candidate = tgt_node->edges[edge_index];
249 
250 			if (edge_candidate != edge) {
251 				insert_into_edge_bucket(edge_candidate);
252 			}
253 		}
254 	}
255 }
256 
257 /**
258  * Tries to apply RM for the source node of the given edge.
259  *
260  * Checks whether the source node of edge can be merged into the target node of
261  * edge, and performs the merge, if possible.
262  */
merge_source_into_target(pbqp_t * pbqp,pbqp_edge_t * edge)263 static void merge_source_into_target(pbqp_t *pbqp, pbqp_edge_t *edge)
264 {
265 	pbqp_matrix_t  *mat;
266 	pbqp_node_t    *src_node;
267 	pbqp_node_t    *tgt_node;
268 	vector_t       *src_vec;
269 	vector_t       *tgt_vec;
270 	unsigned       *mapping;
271 	unsigned        src_len;
272 	unsigned        tgt_len;
273 	unsigned        tgt_index;
274 	unsigned        edge_index;
275 	unsigned        edge_len;
276 
277 	src_node = edge->src;
278 	tgt_node = edge->tgt;
279 
280 	src_vec = src_node->costs;
281 	tgt_vec = tgt_node->costs;
282 
283 	src_len = src_vec->len;
284 	tgt_len = tgt_vec->len;
285 
286 	/* Matrizes are normalized. */
287 	assert(src_len > 1);
288 	assert(tgt_len > 1);
289 
290 	mat = edge->costs;
291 
292 	mapping = NEW_ARR_F(unsigned, tgt_len);
293 
294 	/* Check that each column has at most one zero entry. */
295 	for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
296 		unsigned onlyOneZero = 0;
297 		unsigned src_index;
298 
299 		if (tgt_vec->entries[tgt_index].data == INF_COSTS)
300 			continue;
301 
302 		for (src_index = 0; src_index < src_len; ++src_index) {
303 			if (src_vec->entries[src_index].data == INF_COSTS)
304 				continue;
305 
306 			if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS)
307 				continue;
308 
309 			/* Matrix entry is finite. */
310 			if (onlyOneZero) {
311 				DEL_ARR_F(mapping);
312 				return;
313 			}
314 
315 			onlyOneZero = 1;
316 			mapping[tgt_index] = src_index;
317 		}
318 	}
319 
320 	/* We know that we can merge the source node into the target node. */
321 	edge_len = pbqp_node_get_degree(src_node);
322 
323 #if KAPS_STATISTIC
324 	pbqp->num_rm++;
325 #endif
326 
327 #if KAPS_DUMP
328 	if (pbqp->dump_file) {
329 		char txt[100];
330 		sprintf(txt, "Merging n%d into n%d", src_node->index, tgt_node->index);
331 		pbqp_dump_section(pbqp->dump_file, 3, txt);
332 	}
333 #endif
334 
335 	/* Reconnect the source's edges with the target node. */
336 	for (edge_index = 0; edge_index < edge_len; ++edge_index) {
337 		pbqp_edge_t   *old_edge = src_node->edges[edge_index];
338 		pbqp_edge_t   *new_edge;
339 		pbqp_matrix_t *old_matrix;
340 		pbqp_matrix_t *new_matrix;
341 		pbqp_node_t   *other_node;
342 		vector_t      *other_vec;
343 		unsigned       other_len;
344 		unsigned       other_index;
345 
346 		assert(old_edge);
347 		if (old_edge == edge)
348 			continue;
349 
350 		old_matrix = old_edge->costs;
351 
352 		if (old_edge->tgt == src_node) {
353 			other_node = old_edge->src;
354 			other_len  = old_matrix->rows;
355 		}
356 		else {
357 			other_node = old_edge->tgt;
358 			other_len = old_matrix->cols;
359 		}
360 		other_vec = other_node->costs;
361 
362 		new_matrix = pbqp_matrix_alloc(pbqp, tgt_len, other_len);
363 
364 		/* Source node selects the column of the old_matrix. */
365 		if (old_edge->tgt == src_node) {
366 			for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
367 				unsigned src_index = mapping[tgt_index];
368 
369 				if (tgt_vec->entries[tgt_index].data == INF_COSTS)
370 					continue;
371 
372 				for (other_index = 0; other_index < other_len; ++other_index) {
373 					if (other_vec->entries[other_index].data == INF_COSTS)
374 						continue;
375 
376 					new_matrix->entries[tgt_index*other_len+other_index] = old_matrix->entries[other_index*src_len+src_index];
377 				}
378 			}
379 		}
380 		/* Source node selects the row of the old_matrix. */
381 		else {
382 			for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
383 				unsigned src_index = mapping[tgt_index];
384 
385 				if (tgt_vec->entries[tgt_index].data == INF_COSTS)
386 					continue;
387 
388 				for (other_index = 0; other_index < other_len; ++other_index) {
389 					if (other_vec->entries[other_index].data == INF_COSTS)
390 						continue;
391 
392 					new_matrix->entries[tgt_index*other_len+other_index] = old_matrix->entries[src_index*other_len+other_index];
393 				}
394 			}
395 		}
396 
397 		new_edge = get_edge(pbqp, tgt_node->index, other_node->index);
398 
399 		add_edge_costs(pbqp, tgt_node->index, other_node->index, new_matrix);
400 
401 		if (new_edge == NULL) {
402 			reorder_node_after_edge_insertion(tgt_node);
403 			reorder_node_after_edge_insertion(other_node);
404 		}
405 
406 		delete_edge(old_edge);
407 
408 		new_edge = get_edge(pbqp, tgt_node->index, other_node->index);
409 		simplify_edge(pbqp, new_edge);
410 
411 		insert_into_rm_bucket(new_edge);
412 	}
413 
414 #if KAPS_STATISTIC
415 	pbqp->num_r1--;
416 #endif
417 }
418 
419 /**
420  * Tries to apply RM for the target node of the given edge.
421  *
422  * Checks whether the target node of edge can be merged into the source node of
423  * edge, and performs the merge, if possible.
424  */
merge_target_into_source(pbqp_t * pbqp,pbqp_edge_t * edge)425 static void merge_target_into_source(pbqp_t *pbqp, pbqp_edge_t *edge)
426 {
427 	pbqp_matrix_t  *mat;
428 	pbqp_node_t    *src_node;
429 	pbqp_node_t    *tgt_node;
430 	vector_t       *src_vec;
431 	vector_t       *tgt_vec;
432 	unsigned       *mapping;
433 	unsigned        src_len;
434 	unsigned        tgt_len;
435 	unsigned        src_index;
436 	unsigned        edge_index;
437 	unsigned        edge_len;
438 
439 	src_node = edge->src;
440 	tgt_node = edge->tgt;
441 
442 	src_vec = src_node->costs;
443 	tgt_vec = tgt_node->costs;
444 
445 	src_len = src_vec->len;
446 	tgt_len = tgt_vec->len;
447 
448 	/* Matrizes are normalized. */
449 	assert(src_len > 1);
450 	assert(tgt_len > 1);
451 
452 	mat = edge->costs;
453 
454 	mapping = NEW_ARR_F(unsigned, src_len);
455 
456 	/* Check that each row has at most one zero entry. */
457 	for (src_index = 0; src_index < src_len; ++src_index) {
458 		unsigned onlyOneZero = 0;
459 		unsigned tgt_index;
460 
461 		if (src_vec->entries[src_index].data == INF_COSTS)
462 			continue;
463 
464 		for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
465 			if (tgt_vec->entries[tgt_index].data == INF_COSTS)
466 				continue;
467 
468 			if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS)
469 				continue;
470 
471 			/* Matrix entry is finite. */
472 			if (onlyOneZero) {
473 				DEL_ARR_F(mapping);
474 				return;
475 			}
476 
477 			onlyOneZero = 1;
478 			mapping[src_index] = tgt_index;
479 		}
480 	}
481 
482 	/* We know that we can merge the target node into the source node. */
483 	edge_len = pbqp_node_get_degree(tgt_node);
484 
485 #if KAPS_STATISTIC
486 	pbqp->num_rm++;
487 #endif
488 
489 #if KAPS_DUMP
490 	if (pbqp->dump_file) {
491 		char txt[100];
492 		sprintf(txt, "Merging n%d into n%d", tgt_node->index, src_node->index);
493 		pbqp_dump_section(pbqp->dump_file, 3, txt);
494 	}
495 #endif
496 
497 	/* Reconnect the target's edges with the source node. */
498 	for (edge_index = 0; edge_index < edge_len; ++edge_index) {
499 		pbqp_edge_t   *old_edge = tgt_node->edges[edge_index];
500 		pbqp_edge_t   *new_edge;
501 		pbqp_matrix_t *old_matrix;
502 		pbqp_matrix_t *new_matrix;
503 		pbqp_node_t   *other_node;
504 		vector_t      *other_vec;
505 		unsigned       other_len;
506 		unsigned       other_index;
507 
508 		assert(old_edge);
509 
510 		if (old_edge == edge)
511 			continue;
512 
513 		old_matrix = old_edge->costs;
514 
515 		if (old_edge->tgt == tgt_node) {
516 			other_node = old_edge->src;
517 			other_len  = old_matrix->rows;
518 		}
519 		else {
520 			other_node = old_edge->tgt;
521 			other_len = old_matrix->cols;
522 		}
523 		other_vec = other_node->costs;
524 
525 		new_matrix = pbqp_matrix_alloc(pbqp, src_len, other_len);
526 
527 		/* Target node selects the column of the old_matrix. */
528 		if (old_edge->tgt == tgt_node) {
529 			for (src_index = 0; src_index < src_len; ++src_index) {
530 				unsigned tgt_index = mapping[src_index];
531 
532 				if (src_vec->entries[src_index].data == INF_COSTS)
533 					continue;
534 
535 				for (other_index = 0; other_index < other_len; ++other_index) {
536 					if (other_vec->entries[other_index].data == INF_COSTS)
537 						continue;
538 
539 					new_matrix->entries[src_index*other_len+other_index] = old_matrix->entries[other_index*tgt_len+tgt_index];
540 				}
541 			}
542 		}
543 		/* Source node selects the row of the old_matrix. */
544 		else {
545 			for (src_index = 0; src_index < src_len; ++src_index) {
546 				unsigned tgt_index = mapping[src_index];
547 
548 				if (src_vec->entries[src_index].data == INF_COSTS)
549 					continue;
550 
551 				for (other_index = 0; other_index < other_len; ++other_index) {
552 					if (other_vec->entries[other_index].data == INF_COSTS)
553 						continue;
554 
555 					new_matrix->entries[src_index*other_len+other_index] = old_matrix->entries[tgt_index*other_len+other_index];
556 				}
557 			}
558 		}
559 
560 		new_edge = get_edge(pbqp, src_node->index, other_node->index);
561 
562 		add_edge_costs(pbqp, src_node->index, other_node->index, new_matrix);
563 
564 		if (new_edge == NULL) {
565 			reorder_node_after_edge_insertion(src_node);
566 			reorder_node_after_edge_insertion(other_node);
567 		}
568 
569 		delete_edge(old_edge);
570 
571 		new_edge = get_edge(pbqp, src_node->index, other_node->index);
572 		simplify_edge(pbqp, new_edge);
573 
574 		insert_into_rm_bucket(new_edge);
575 	}
576 
577 #if KAPS_STATISTIC
578 	pbqp->num_r1--;
579 #endif
580 }
581 
582 /**
583  * Merge neighbors into the given node.
584  */
apply_RM(pbqp_t * pbqp,pbqp_node_t * node)585 void apply_RM(pbqp_t *pbqp, pbqp_node_t *node)
586 {
587 	pbqp_edge_t **edges;
588 	unsigned      edge_index;
589 	unsigned      edge_len;
590 
591 	edges    = node->edges;
592 	edge_len = pbqp_node_get_degree(node);
593 
594 	/* Check all incident edges. */
595 	for (edge_index = 0; edge_index < edge_len; ++edge_index) {
596 		pbqp_edge_t *edge = edges[edge_index];
597 
598 		insert_into_rm_bucket(edge);
599 	}
600 
601 	/* ALAP: Merge neighbors into given node. */
602 	while(edge_bucket_get_length(rm_bucket) > 0) {
603 		pbqp_edge_t *edge = edge_bucket_pop(&rm_bucket);
604 
605 		/* If the edge is not deleted: Try a merge. */
606 		if (edge->src == node)
607 			merge_target_into_source(pbqp, edge);
608 		else if (edge->tgt == node)
609 			merge_source_into_target(pbqp, edge);
610 	}
611 
612 	merged_node = node;
613 }
614 
reorder_node_after_edge_deletion(pbqp_node_t * node)615 void reorder_node_after_edge_deletion(pbqp_node_t *node)
616 {
617 	unsigned    degree     = pbqp_node_get_degree(node);
618 	/* Assume node lost one incident edge. */
619 	unsigned    old_degree = degree + 1;
620 
621 	if (!buckets_filled) return;
622 
623 	/* Same bucket as before */
624 	if (degree > 2) return;
625 
626 	/* Delete node from old bucket... */
627 	node_bucket_remove(&node_buckets[old_degree], node);
628 
629 	/* ..and add to new one. */
630 	node_bucket_insert(&node_buckets[degree], node);
631 }
632 
reorder_node_after_edge_insertion(pbqp_node_t * node)633 void reorder_node_after_edge_insertion(pbqp_node_t *node)
634 {
635 	unsigned    degree     = pbqp_node_get_degree(node);
636 	/* Assume node lost one incident edge. */
637 	unsigned    old_degree = degree - 1;
638 
639 	if (!buckets_filled) return;
640 
641 	/* Same bucket as before */
642 	if (old_degree > 2) return;
643 
644 	/* Delete node from old bucket... */
645 	node_bucket_remove(&node_buckets[old_degree], node);
646 
647 	/* ..and add to new one. */
648 	node_bucket_insert(&node_buckets[degree], node);
649 }
650 
simplify_edge(pbqp_t * pbqp,pbqp_edge_t * edge)651 void simplify_edge(pbqp_t *pbqp, pbqp_edge_t *edge)
652 {
653 	pbqp_matrix_t *mat;
654 	pbqp_node_t   *src_node;
655 	pbqp_node_t   *tgt_node;
656 	vector_t      *src_vec;
657 	vector_t      *tgt_vec;
658 	int            src_len;
659 	int            tgt_len;
660 
661 	(void) pbqp;
662 
663 	src_node = edge->src;
664 	tgt_node = edge->tgt;
665 	assert(src_node);
666 	assert(tgt_node);
667 
668 	/* If edge are already deleted, we have nothing to do. */
669 	if (is_deleted(edge))
670 		return;
671 
672 #if KAPS_DUMP
673 	if (pbqp->dump_file) {
674 		char txt[100];
675 		sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
676 		pbqp_dump_section(pbqp->dump_file, 3, txt);
677 	}
678 #endif
679 
680 	src_vec = src_node->costs;
681 	tgt_vec = tgt_node->costs;
682 
683 	src_len = src_vec->len;
684 	tgt_len = tgt_vec->len;
685 	assert(src_len > 0);
686 	assert(tgt_len > 0);
687 
688 	mat = edge->costs;
689 
690 #if KAPS_DUMP
691 	if (pbqp->dump_file) {
692 		fputs("Input:<br>\n", pbqp->dump_file);
693 		pbqp_dump_simplifyedge(pbqp, edge);
694 	}
695 #endif
696 
697 	normalize_towards_source(edge);
698 	normalize_towards_target(edge);
699 
700 #if KAPS_DUMP
701 	if (pbqp->dump_file) {
702 		fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
703 		pbqp_dump_simplifyedge(pbqp, edge);
704 	}
705 #endif
706 
707 	if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
708 #if KAPS_DUMP
709 		if (pbqp->dump_file) {
710 			fputs("edge has been eliminated<br>\n", pbqp->dump_file);
711 		}
712 #endif
713 
714 #if KAPS_STATISTIC
715 		pbqp->num_edges++;
716 #endif
717 
718 		delete_edge(edge);
719 	}
720 }
721 
initial_simplify_edges(pbqp_t * pbqp)722 void initial_simplify_edges(pbqp_t *pbqp)
723 {
724 	unsigned node_index;
725 	unsigned node_len;
726 
727 	#if KAPS_TIMING
728 		ir_timer_t *t_int_simpl = ir_timer_new();
729 		ir_timer_start(t_int_simpl);
730 	#endif
731 
732 #if KAPS_DUMP
733 	if (pbqp->dump_file) {
734 		pbqp_dump_input(pbqp);
735 		pbqp_dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
736 	}
737 #endif
738 
739 	node_len = pbqp->num_nodes;
740 
741 	init_buckets();
742 
743 	/* First simplify all edges. */
744 	for (node_index = 0; node_index < node_len; ++node_index) {
745 		unsigned      edge_index;
746 		pbqp_node_t  *node = get_node(pbqp, node_index);
747 		pbqp_edge_t **edges;
748 		unsigned      edge_len;
749 
750 		if (!node) continue;
751 
752 		edges = node->edges;
753 		edge_len = pbqp_node_get_degree(node);
754 
755 		for (edge_index = 0; edge_index < edge_len; ++edge_index) {
756 			pbqp_edge_t *edge = edges[edge_index];
757 
758 			/* Simplify only once per edge. */
759 			if (node != edge->src) continue;
760 
761 			simplify_edge(pbqp, edge);
762 		}
763 	}
764 
765 	#if KAPS_TIMING
766 		ir_timer_stop(t_int_simpl);
767 		printf("PBQP Initial simplify edges:  %10.3lf msec\n", (double)ir_timer_elapsed_usec(t_int_simpl) / 1000.0);
768 	#endif
769 }
770 
determine_solution(pbqp_t * pbqp)771 num determine_solution(pbqp_t *pbqp)
772 {
773 	unsigned node_index;
774 	unsigned node_len;
775 	num      solution   = 0;
776 
777 	#if KAPS_TIMING
778 		ir_timer_t *t_det_solution = ir_timer_new();
779 		ir_timer_reset_and_start(t_det_solution);
780 	#endif
781 
782 #if KAPS_DUMP
783 	FILE     *file;
784 #endif
785 
786 	(void) pbqp;
787 
788 #if KAPS_DUMP
789 	file = pbqp->dump_file;
790 
791 	if (file) {
792 		pbqp_dump_section(file, 1, "4. Determine Solution/Minimum");
793 		pbqp_dump_section(file, 2, "4.1. Trivial Solution");
794 	}
795 #endif
796 
797 	/* Solve trivial nodes and calculate solution. */
798 	node_len = node_bucket_get_length(node_buckets[0]);
799 
800 #if KAPS_STATISTIC
801 	pbqp->num_r0 = node_len;
802 #endif
803 
804 	for (node_index = 0; node_index < node_len; ++node_index) {
805 		pbqp_node_t *node = node_buckets[0][node_index];
806 
807 		node->solution = vector_get_min_index(node->costs);
808 		solution       = pbqp_add(solution,
809 				node->costs->entries[node->solution].data);
810 
811 #if KAPS_DUMP
812 		if (file) {
813 			fprintf(file, "node n%d is set to %d<br>\n", node->index, node->solution);
814 			pbqp_dump_node(file, node);
815 		}
816 #endif
817 	}
818 
819 #if KAPS_DUMP
820 	if (file) {
821 		pbqp_dump_section(file, 2, "Minimum");
822 #if KAPS_USE_UNSIGNED
823 		fprintf(file, "Minimum is equal to %u.", solution);
824 #else
825 		fprintf(file, "Minimum is equal to %lld.", solution);
826 #endif
827 	}
828 #endif
829 
830 	#if KAPS_TIMING
831 		ir_timer_stop(t_det_solution);
832 		printf("PBQP Determine Solution:      %10.3lf msec\n", (double)ir_timer_elapsed_usec(t_det_solution) / 1000.0);
833 	#endif
834 
835 	return solution;
836 }
837 
back_propagate_RI(pbqp_t * pbqp,pbqp_node_t * node)838 static void back_propagate_RI(pbqp_t *pbqp, pbqp_node_t *node)
839 {
840 	pbqp_edge_t   *edge;
841 	pbqp_node_t   *other;
842 	pbqp_matrix_t *mat;
843 	vector_t      *vec;
844 	int            is_src;
845 	(void) pbqp;
846 
847 	edge = node->edges[0];
848 	mat = edge->costs;
849 	is_src = edge->src == node;
850 	vec = node->costs;
851 
852 	if (is_src) {
853 		other = edge->tgt;
854 		node->solution = pbqp_matrix_get_col_min_index(mat, other->solution, vec);
855 	} else {
856 		other = edge->src;
857 		node->solution = pbqp_matrix_get_row_min_index(mat, other->solution, vec);
858 	}
859 
860 #if KAPS_DUMP
861 	if (pbqp->dump_file) {
862 		fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
863 	}
864 #endif
865 }
866 
back_propagate_RII(pbqp_t * pbqp,pbqp_node_t * node)867 static void back_propagate_RII(pbqp_t *pbqp, pbqp_node_t *node)
868 {
869 	pbqp_edge_t   *src_edge   = node->edges[0];
870 	pbqp_edge_t   *tgt_edge   = node->edges[1];
871 	int            src_is_src = src_edge->src == node;
872 	int            tgt_is_src = tgt_edge->src == node;
873 	pbqp_matrix_t *src_mat;
874 	pbqp_matrix_t *tgt_mat;
875 	pbqp_node_t   *src_node;
876 	pbqp_node_t   *tgt_node;
877 	vector_t      *vec;
878 	vector_t      *node_vec;
879 	unsigned       col_index;
880 	unsigned       row_index;
881 
882 	if (src_is_src) {
883 		src_node = src_edge->tgt;
884 	} else {
885 		src_node = src_edge->src;
886 	}
887 
888 	if (tgt_is_src) {
889 		tgt_node = tgt_edge->tgt;
890 	} else {
891 		tgt_node = tgt_edge->src;
892 	}
893 
894 	/* Swap nodes if necessary. */
895 	if (tgt_node->index < src_node->index) {
896 		pbqp_node_t *tmp_node;
897 		pbqp_edge_t *tmp_edge;
898 
899 		tmp_node = src_node;
900 		src_node = tgt_node;
901 		tgt_node = tmp_node;
902 
903 		tmp_edge = src_edge;
904 		src_edge = tgt_edge;
905 		tgt_edge = tmp_edge;
906 
907 		src_is_src = src_edge->src == node;
908 		tgt_is_src = tgt_edge->src == node;
909 	}
910 
911 	src_mat = src_edge->costs;
912 	tgt_mat = tgt_edge->costs;
913 
914 	node_vec = node->costs;
915 
916 	row_index = src_node->solution;
917 	col_index = tgt_node->solution;
918 
919 	vec = vector_copy(pbqp, node_vec);
920 
921 	if (src_is_src) {
922 		vector_add_matrix_col(vec, src_mat, row_index);
923 	} else {
924 		vector_add_matrix_row(vec, src_mat, row_index);
925 	}
926 
927 	if (tgt_is_src) {
928 		vector_add_matrix_col(vec, tgt_mat, col_index);
929 	} else {
930 		vector_add_matrix_row(vec, tgt_mat, col_index);
931 	}
932 
933 	node->solution = vector_get_min_index(vec);
934 
935 #if KAPS_DUMP
936 	if (pbqp->dump_file) {
937 		fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
938 	}
939 #endif
940 
941 	obstack_free(&pbqp->obstack, vec);
942 }
943 
back_propagate(pbqp_t * pbqp)944 void back_propagate(pbqp_t *pbqp)
945 {
946 	unsigned node_index;
947 	unsigned node_len   = node_bucket_get_length(reduced_bucket);
948 
949 #if KAPS_DUMP
950 	if (pbqp->dump_file) {
951 		pbqp_dump_section(pbqp->dump_file, 2, "Back Propagation");
952 	}
953 #endif
954 
955 	for (node_index = node_len; node_index > 0; --node_index) {
956 		pbqp_node_t *node = reduced_bucket[node_index - 1];
957 
958 		switch (pbqp_node_get_degree(node)) {
959 			case 1:
960 				back_propagate_RI(pbqp, node);
961 				break;
962 			case 2:
963 				back_propagate_RII(pbqp, node);
964 				break;
965 			default:
966 				panic("Only nodes with degree one or two should be in this bucket");
967 		}
968 	}
969 }
970 
apply_edge(pbqp_t * pbqp)971 void apply_edge(pbqp_t *pbqp)
972 {
973 	pbqp_edge_t *edge = edge_bucket_pop(&edge_bucket);
974 
975 	simplify_edge(pbqp, edge);
976 }
977 
apply_RI(pbqp_t * pbqp)978 void apply_RI(pbqp_t *pbqp)
979 {
980 	pbqp_node_t   *node   = node_bucket_pop(&node_buckets[1]);
981 	pbqp_edge_t   *edge   = node->edges[0];
982 	pbqp_matrix_t *mat    = edge->costs;
983 	int            is_src = edge->src == node;
984 	pbqp_node_t   *other_node;
985 
986 	(void) pbqp;
987 	assert(pbqp_node_get_degree(node) == 1);
988 
989 	if (is_src) {
990 		other_node = edge->tgt;
991 	} else {
992 		other_node = edge->src;
993 	}
994 
995 #if KAPS_DUMP
996 	if (pbqp->dump_file) {
997 		char     txt[100];
998 		sprintf(txt, "RI-Reduction of Node n%d", node->index);
999 		pbqp_dump_section(pbqp->dump_file, 2, txt);
1000 		pbqp_dump_graph(pbqp);
1001 		fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
1002 		pbqp_dump_node(pbqp->dump_file, node);
1003 		pbqp_dump_node(pbqp->dump_file, other_node);
1004 		pbqp_dump_edge(pbqp->dump_file, edge);
1005 	}
1006 #endif
1007 
1008 	if (is_src) {
1009 		pbqp_matrix_add_to_all_cols(mat, node->costs);
1010 		normalize_towards_target(edge);
1011 	} else {
1012 		pbqp_matrix_add_to_all_rows(mat, node->costs);
1013 		normalize_towards_source(edge);
1014 	}
1015 	disconnect_edge(other_node, edge);
1016 
1017 #if KAPS_DUMP
1018 	if (pbqp->dump_file) {
1019 		fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
1020 		pbqp_dump_node(pbqp->dump_file, other_node);
1021 	}
1022 #endif
1023 
1024 	reorder_node_after_edge_deletion(other_node);
1025 
1026 #if KAPS_STATISTIC
1027 	pbqp->num_r1++;
1028 #endif
1029 
1030 	/* Add node to back propagation list. */
1031 	node_bucket_insert(&reduced_bucket, node);
1032 }
1033 
apply_RII(pbqp_t * pbqp)1034 void apply_RII(pbqp_t *pbqp)
1035 {
1036 	pbqp_node_t   *node       = node_bucket_pop(&node_buckets[2]);
1037 	pbqp_edge_t   *src_edge   = node->edges[0];
1038 	pbqp_edge_t   *tgt_edge   = node->edges[1];
1039 	int            src_is_src = src_edge->src == node;
1040 	int            tgt_is_src = tgt_edge->src == node;
1041 	pbqp_matrix_t *src_mat;
1042 	pbqp_matrix_t *tgt_mat;
1043 	pbqp_node_t   *src_node;
1044 	pbqp_node_t   *tgt_node;
1045 	pbqp_edge_t   *edge;
1046 	pbqp_matrix_t *mat;
1047 	vector_t      *vec;
1048 	vector_t      *node_vec;
1049 	vector_t      *src_vec;
1050 	vector_t      *tgt_vec;
1051 	unsigned       col_index;
1052 	unsigned       col_len;
1053 	unsigned       row_index;
1054 	unsigned       row_len;
1055 
1056 	assert(pbqp_node_get_degree(node) == 2);
1057 
1058 	if (src_is_src) {
1059 		src_node = src_edge->tgt;
1060 	} else {
1061 		src_node = src_edge->src;
1062 	}
1063 
1064 	if (tgt_is_src) {
1065 		tgt_node = tgt_edge->tgt;
1066 	} else {
1067 		tgt_node = tgt_edge->src;
1068 	}
1069 
1070 	/* Swap nodes if necessary. */
1071 	if (tgt_node->index < src_node->index) {
1072 		pbqp_node_t *tmp_node;
1073 		pbqp_edge_t *tmp_edge;
1074 
1075 		tmp_node = src_node;
1076 		src_node = tgt_node;
1077 		tgt_node = tmp_node;
1078 
1079 		tmp_edge = src_edge;
1080 		src_edge = tgt_edge;
1081 		tgt_edge = tmp_edge;
1082 
1083 		src_is_src = src_edge->src == node;
1084 		tgt_is_src = tgt_edge->src == node;
1085 	}
1086 
1087 #if KAPS_DUMP
1088 	if (pbqp->dump_file) {
1089 		char     txt[100];
1090 		sprintf(txt, "RII-Reduction of Node n%d", node->index);
1091 		pbqp_dump_section(pbqp->dump_file, 2, txt);
1092 		pbqp_dump_graph(pbqp);
1093 		fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
1094 		pbqp_dump_node(pbqp->dump_file, src_node);
1095 		pbqp_dump_edge(pbqp->dump_file, src_edge);
1096 		pbqp_dump_node(pbqp->dump_file, node);
1097 		pbqp_dump_edge(pbqp->dump_file, tgt_edge);
1098 		pbqp_dump_node(pbqp->dump_file, tgt_node);
1099 	}
1100 #endif
1101 
1102 	src_mat = src_edge->costs;
1103 	tgt_mat = tgt_edge->costs;
1104 
1105 	src_vec  = src_node->costs;
1106 	tgt_vec  = tgt_node->costs;
1107 	node_vec = node->costs;
1108 
1109 	row_len  = src_vec->len;
1110 	col_len  = tgt_vec->len;
1111 
1112 	mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
1113 
1114 	for (row_index = 0; row_index < row_len; ++row_index) {
1115 		for (col_index = 0; col_index < col_len; ++col_index) {
1116 			vec = vector_copy(pbqp, node_vec);
1117 
1118 			if (src_is_src) {
1119 				vector_add_matrix_col(vec, src_mat, row_index);
1120 			} else {
1121 				vector_add_matrix_row(vec, src_mat, row_index);
1122 			}
1123 
1124 			if (tgt_is_src) {
1125 				vector_add_matrix_col(vec, tgt_mat, col_index);
1126 			} else {
1127 				vector_add_matrix_row(vec, tgt_mat, col_index);
1128 			}
1129 
1130 			mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
1131 
1132 			obstack_free(&pbqp->obstack, vec);
1133 		}
1134 	}
1135 
1136 	edge = get_edge(pbqp, src_node->index, tgt_node->index);
1137 
1138 	/* Disconnect node. */
1139 	disconnect_edge(src_node, src_edge);
1140 	disconnect_edge(tgt_node, tgt_edge);
1141 
1142 #if KAPS_STATISTIC
1143 	pbqp->num_r2++;
1144 #endif
1145 
1146 	/* Add node to back propagation list. */
1147 	node_bucket_insert(&reduced_bucket, node);
1148 
1149 	if (edge == NULL) {
1150 		edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
1151 	} else {
1152 		// matrix
1153 		pbqp_matrix_add(edge->costs, mat);
1154 
1155 		/* Free local matrix. */
1156 		obstack_free(&pbqp->obstack, mat);
1157 
1158 		reorder_node_after_edge_deletion(src_node);
1159 		reorder_node_after_edge_deletion(tgt_node);
1160 	}
1161 
1162 #if KAPS_DUMP
1163 	if (pbqp->dump_file) {
1164 		fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
1165 		pbqp_dump_edge(pbqp->dump_file, edge);
1166 	}
1167 #endif
1168 
1169 	/* Edge has changed so we simplify it. */
1170 	simplify_edge(pbqp, edge);
1171 }
1172 
select_column(pbqp_edge_t * edge,unsigned col_index)1173 static void select_column(pbqp_edge_t *edge, unsigned col_index)
1174 {
1175 	pbqp_matrix_t  *mat;
1176 	pbqp_node_t    *src_node;
1177 	pbqp_node_t    *tgt_node;
1178 	vector_t       *src_vec;
1179 	vector_t       *tgt_vec;
1180 	unsigned        src_len;
1181 	unsigned        tgt_len;
1182 	unsigned        src_index;
1183 	unsigned        new_infinity = 0;
1184 
1185 	src_node = edge->src;
1186 	tgt_node = edge->tgt;
1187 
1188 	src_vec = src_node->costs;
1189 	tgt_vec = tgt_node->costs;
1190 
1191 	src_len = src_vec->len;
1192 	tgt_len = tgt_vec->len;
1193 	assert(src_len > 0);
1194 	assert(tgt_len > 0);
1195 
1196 	mat = edge->costs;
1197 
1198 	for (src_index = 0; src_index < src_len; ++src_index) {
1199 		num elem = mat->entries[src_index * tgt_len + col_index];
1200 
1201 		if (elem != 0) {
1202 			if (elem == INF_COSTS && src_vec->entries[src_index].data != INF_COSTS)
1203 				new_infinity = 1;
1204 
1205 			src_vec->entries[src_index].data = pbqp_add(
1206 					src_vec->entries[src_index].data, elem);
1207 		}
1208 	}
1209 
1210 	if (new_infinity) {
1211 		unsigned edge_index;
1212 		unsigned edge_len = pbqp_node_get_degree(src_node);
1213 
1214 		for (edge_index = 0; edge_index < edge_len; ++edge_index) {
1215 			pbqp_edge_t *edge_candidate = src_node->edges[edge_index];
1216 
1217 			if (edge_candidate != edge) {
1218 				insert_into_edge_bucket(edge_candidate);
1219 			}
1220 		}
1221 	}
1222 
1223 	delete_edge(edge);
1224 }
1225 
select_row(pbqp_edge_t * edge,unsigned row_index)1226 static void select_row(pbqp_edge_t *edge, unsigned row_index)
1227 {
1228 	pbqp_matrix_t  *mat;
1229 	pbqp_node_t    *tgt_node;
1230 	vector_t       *tgt_vec;
1231 	unsigned        tgt_len;
1232 	unsigned        tgt_index;
1233 	unsigned        new_infinity = 0;
1234 
1235 	tgt_node = edge->tgt;
1236 
1237 	tgt_vec = tgt_node->costs;
1238 
1239 	tgt_len = tgt_vec->len;
1240 	assert(tgt_len > 0);
1241 
1242 	mat = edge->costs;
1243 
1244 	for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
1245 		num elem = mat->entries[row_index * tgt_len + tgt_index];
1246 
1247 		if (elem != 0) {
1248 			if (elem == INF_COSTS && tgt_vec->entries[tgt_index].data != INF_COSTS)
1249 				new_infinity = 1;
1250 
1251 			tgt_vec->entries[tgt_index].data = pbqp_add(
1252 					tgt_vec->entries[tgt_index].data, elem);
1253 		}
1254 	}
1255 
1256 	if (new_infinity) {
1257 		unsigned edge_index;
1258 		unsigned edge_len = pbqp_node_get_degree(tgt_node);
1259 
1260 		for (edge_index = 0; edge_index < edge_len; ++edge_index) {
1261 			pbqp_edge_t *edge_candidate = tgt_node->edges[edge_index];
1262 
1263 			if (edge_candidate != edge) {
1264 				insert_into_edge_bucket(edge_candidate);
1265 			}
1266 		}
1267 	}
1268 
1269 	delete_edge(edge);
1270 }
1271 
select_alternative(pbqp_node_t * node,unsigned selected_index)1272 void select_alternative(pbqp_node_t *node, unsigned selected_index)
1273 {
1274 	unsigned  edge_index;
1275 	unsigned  node_index;
1276 	unsigned  node_len;
1277 	vector_t *node_vec;
1278 	unsigned  max_degree = pbqp_node_get_degree(node);
1279 
1280 	node->solution = selected_index;
1281 	node_vec = node->costs;
1282 	node_len = node_vec->len;
1283 	assert(selected_index < node_len);
1284 
1285 	/* Set all other costs to infinity. */
1286 	for (node_index = 0; node_index < node_len; ++node_index) {
1287 		if (node_index != selected_index) {
1288 			node_vec->entries[node_index].data = INF_COSTS;
1289 		}
1290 	}
1291 
1292 	/* Select corresponding row/column for incident edges. */
1293 	for (edge_index = 0; edge_index < max_degree; ++edge_index) {
1294 		pbqp_edge_t *edge = node->edges[edge_index];
1295 
1296 		if (edge->src == node)
1297 			select_row(edge, selected_index);
1298 		else
1299 			select_column(edge, selected_index);
1300 	}
1301 }
1302 
get_node_with_max_degree(void)1303 pbqp_node_t *get_node_with_max_degree(void)
1304 {
1305 	pbqp_node_t **bucket       = node_buckets[3];
1306 	unsigned      bucket_len   = node_bucket_get_length(bucket);
1307 	unsigned      bucket_index;
1308 	unsigned      max_degree   = 0;
1309 	pbqp_node_t  *result       = NULL;
1310 
1311 	for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
1312 		pbqp_node_t *candidate = bucket[bucket_index];
1313 		unsigned     degree    = pbqp_node_get_degree(candidate);
1314 
1315 		if (degree > max_degree) {
1316 			result = candidate;
1317 			max_degree = degree;
1318 		}
1319 	}
1320 
1321 	return result;
1322 }
1323 
get_local_minimal_alternative(pbqp_t * pbqp,pbqp_node_t * node)1324 unsigned get_local_minimal_alternative(pbqp_t *pbqp, pbqp_node_t *node)
1325 {
1326 	pbqp_edge_t   *edge;
1327 	vector_t      *node_vec;
1328 	vector_t      *vec;
1329 	pbqp_matrix_t *mat;
1330 	unsigned       edge_index;
1331 	unsigned       max_degree;
1332 	unsigned       node_index;
1333 	unsigned       node_len;
1334 	unsigned       min_index    = 0;
1335 	num            min          = INF_COSTS;
1336 	int            is_src;
1337 
1338 	node_vec   = node->costs;
1339 	node_len   = node_vec->len;
1340 	max_degree = pbqp_node_get_degree(node);
1341 
1342 	for (node_index = 0; node_index < node_len; ++node_index) {
1343 		num value = node_vec->entries[node_index].data;
1344 
1345 		for (edge_index = 0; edge_index < max_degree; ++edge_index) {
1346 			edge   = node->edges[edge_index];
1347 			mat    = edge->costs;
1348 			is_src = edge->src == node;
1349 
1350 			if (is_src) {
1351 				vec = vector_copy(pbqp, edge->tgt->costs);
1352 				vector_add_matrix_row(vec, mat, node_index);
1353 			} else {
1354 				vec = vector_copy(pbqp, edge->src->costs);
1355 				vector_add_matrix_col(vec, mat, node_index);
1356 			}
1357 
1358 			value = pbqp_add(value, vector_get_min(vec));
1359 
1360 			obstack_free(&pbqp->obstack, vec);
1361 		}
1362 
1363 		if (value < min) {
1364 			min = value;
1365 			min_index = node_index;
1366 		}
1367 	}
1368 
1369 	return min_index;
1370 }
1371 
node_is_reduced(pbqp_node_t * node)1372 int node_is_reduced(pbqp_node_t *node)
1373 {
1374 	if (!reduced_bucket) return 0;
1375 
1376 	if (pbqp_node_get_degree(node) == 0) return 1;
1377 
1378 	return node_bucket_contains(reduced_bucket, node);
1379 }
1380