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66f97d31 | 1 | /* Graph representation and manipulation functions. |
99dee823 | 2 | Copyright (C) 2007-2021 Free Software Foundation, Inc. |
66f97d31 ZD |
3 | |
4 | This file is part of GCC. | |
5 | ||
6 | GCC is free software; you can redistribute it and/or modify it under | |
7 | the terms of the GNU General Public License as published by the Free | |
9dcd6f09 | 8 | Software Foundation; either version 3, or (at your option) any later |
66f97d31 ZD |
9 | version. |
10 | ||
11 | GCC is distributed in the hope that it will be useful, but WITHOUT ANY | |
12 | WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
13 | FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
14 | for more details. | |
15 | ||
16 | You should have received a copy of the GNU General Public License | |
9dcd6f09 NC |
17 | along with GCC; see the file COPYING3. If not see |
18 | <http://www.gnu.org/licenses/>. */ | |
66f97d31 ZD |
19 | |
20 | #include "config.h" | |
21 | #include "system.h" | |
22 | #include "coretypes.h" | |
66f97d31 | 23 | #include "bitmap.h" |
66f97d31 ZD |
24 | #include "graphds.h" |
25 | ||
26 | /* Dumps graph G into F. */ | |
27 | ||
28 | void | |
29 | dump_graph (FILE *f, struct graph *g) | |
30 | { | |
31 | int i; | |
ae50c0cb | 32 | struct graph_edge *e; |
66f97d31 ZD |
33 | |
34 | for (i = 0; i < g->n_vertices; i++) | |
35 | { | |
36 | if (!g->vertices[i].pred | |
37 | && !g->vertices[i].succ) | |
38 | continue; | |
39 | ||
40 | fprintf (f, "%d (%d)\t<-", i, g->vertices[i].component); | |
41 | for (e = g->vertices[i].pred; e; e = e->pred_next) | |
42 | fprintf (f, " %d", e->src); | |
43 | fprintf (f, "\n"); | |
44 | ||
45 | fprintf (f, "\t->"); | |
46 | for (e = g->vertices[i].succ; e; e = e->succ_next) | |
47 | fprintf (f, " %d", e->dest); | |
48 | fprintf (f, "\n"); | |
49 | } | |
50 | } | |
51 | ||
52 | /* Creates a new graph with N_VERTICES vertices. */ | |
53 | ||
54 | struct graph * | |
55 | new_graph (int n_vertices) | |
56 | { | |
57 | struct graph *g = XNEW (struct graph); | |
58 | ||
2c41c19d | 59 | gcc_obstack_init (&g->ob); |
66f97d31 | 60 | g->n_vertices = n_vertices; |
2c41c19d RB |
61 | g->vertices = XOBNEWVEC (&g->ob, struct vertex, n_vertices); |
62 | memset (g->vertices, 0, sizeof (struct vertex) * n_vertices); | |
66f97d31 ZD |
63 | |
64 | return g; | |
65 | } | |
66 | ||
67 | /* Adds an edge from F to T to graph G. The new edge is returned. */ | |
68 | ||
ae50c0cb | 69 | struct graph_edge * |
66f97d31 ZD |
70 | add_edge (struct graph *g, int f, int t) |
71 | { | |
2c41c19d | 72 | struct graph_edge *e = XOBNEW (&g->ob, struct graph_edge); |
66f97d31 ZD |
73 | struct vertex *vf = &g->vertices[f], *vt = &g->vertices[t]; |
74 | ||
66f97d31 ZD |
75 | e->src = f; |
76 | e->dest = t; | |
77 | ||
78 | e->pred_next = vt->pred; | |
79 | vt->pred = e; | |
80 | ||
81 | e->succ_next = vf->succ; | |
82 | vf->succ = e; | |
83 | ||
04939ee6 | 84 | e->data = NULL; |
66f97d31 ZD |
85 | return e; |
86 | } | |
87 | ||
88 | /* Moves all the edges incident with U to V. */ | |
89 | ||
90 | void | |
91 | identify_vertices (struct graph *g, int v, int u) | |
92 | { | |
93 | struct vertex *vv = &g->vertices[v]; | |
94 | struct vertex *uu = &g->vertices[u]; | |
ae50c0cb | 95 | struct graph_edge *e, *next; |
66f97d31 ZD |
96 | |
97 | for (e = uu->succ; e; e = next) | |
98 | { | |
99 | next = e->succ_next; | |
100 | ||
101 | e->src = v; | |
102 | e->succ_next = vv->succ; | |
103 | vv->succ = e; | |
104 | } | |
105 | uu->succ = NULL; | |
106 | ||
107 | for (e = uu->pred; e; e = next) | |
108 | { | |
109 | next = e->pred_next; | |
110 | ||
111 | e->dest = v; | |
112 | e->pred_next = vv->pred; | |
113 | vv->pred = e; | |
114 | } | |
115 | uu->pred = NULL; | |
116 | } | |
117 | ||
118 | /* Helper function for graphds_dfs. Returns the source vertex of E, in the | |
119 | direction given by FORWARD. */ | |
120 | ||
121 | static inline int | |
ae50c0cb | 122 | dfs_edge_src (struct graph_edge *e, bool forward) |
66f97d31 ZD |
123 | { |
124 | return forward ? e->src : e->dest; | |
125 | } | |
126 | ||
127 | /* Helper function for graphds_dfs. Returns the destination vertex of E, in | |
128 | the direction given by FORWARD. */ | |
129 | ||
130 | static inline int | |
ae50c0cb | 131 | dfs_edge_dest (struct graph_edge *e, bool forward) |
66f97d31 ZD |
132 | { |
133 | return forward ? e->dest : e->src; | |
134 | } | |
135 | ||
136 | /* Helper function for graphds_dfs. Returns the first edge after E (including | |
04939ee6 BC |
137 | E), in the graph direction given by FORWARD, that belongs to SUBGRAPH. If |
138 | SKIP_EDGE_P is not NULL, it points to a callback function. Edge E will be | |
139 | skipped if callback function returns true. */ | |
66f97d31 | 140 | |
ae50c0cb | 141 | static inline struct graph_edge * |
04939ee6 BC |
142 | foll_in_subgraph (struct graph_edge *e, bool forward, bitmap subgraph, |
143 | skip_edge_callback skip_edge_p) | |
66f97d31 ZD |
144 | { |
145 | int d; | |
146 | ||
04939ee6 BC |
147 | if (!e) |
148 | return e; | |
149 | ||
150 | if (!subgraph && (!skip_edge_p || !skip_edge_p (e))) | |
66f97d31 ZD |
151 | return e; |
152 | ||
153 | while (e) | |
154 | { | |
155 | d = dfs_edge_dest (e, forward); | |
04939ee6 BC |
156 | /* Return edge if it belongs to subgraph and shouldn't be skipped. */ |
157 | if ((!subgraph || bitmap_bit_p (subgraph, d)) | |
158 | && (!skip_edge_p || !skip_edge_p (e))) | |
66f97d31 ZD |
159 | return e; |
160 | ||
161 | e = forward ? e->succ_next : e->pred_next; | |
162 | } | |
163 | ||
164 | return e; | |
165 | } | |
166 | ||
167 | /* Helper function for graphds_dfs. Select the first edge from V in G, in the | |
04939ee6 BC |
168 | direction given by FORWARD, that belongs to SUBGRAPH. If SKIP_EDGE_P is not |
169 | NULL, it points to a callback function. Edge E will be skipped if callback | |
170 | function returns true. */ | |
66f97d31 | 171 | |
ae50c0cb | 172 | static inline struct graph_edge * |
04939ee6 BC |
173 | dfs_fst_edge (struct graph *g, int v, bool forward, bitmap subgraph, |
174 | skip_edge_callback skip_edge_p) | |
66f97d31 | 175 | { |
ae50c0cb | 176 | struct graph_edge *e; |
66f97d31 ZD |
177 | |
178 | e = (forward ? g->vertices[v].succ : g->vertices[v].pred); | |
04939ee6 | 179 | return foll_in_subgraph (e, forward, subgraph, skip_edge_p); |
66f97d31 ZD |
180 | } |
181 | ||
182 | /* Helper function for graphds_dfs. Returns the next edge after E, in the | |
04939ee6 BC |
183 | graph direction given by FORWARD, that belongs to SUBGRAPH. If SKIP_EDGE_P |
184 | is not NULL, it points to a callback function. Edge E will be skipped if | |
185 | callback function returns true. */ | |
66f97d31 | 186 | |
ae50c0cb | 187 | static inline struct graph_edge * |
04939ee6 BC |
188 | dfs_next_edge (struct graph_edge *e, bool forward, bitmap subgraph, |
189 | skip_edge_callback skip_edge_p) | |
66f97d31 ZD |
190 | { |
191 | return foll_in_subgraph (forward ? e->succ_next : e->pred_next, | |
04939ee6 | 192 | forward, subgraph, skip_edge_p); |
66f97d31 ZD |
193 | } |
194 | ||
195 | /* Runs dfs search over vertices of G, from NQ vertices in queue QS. | |
196 | The vertices in postorder are stored into QT. If FORWARD is false, | |
197 | backward dfs is run. If SUBGRAPH is not NULL, it specifies the | |
198 | subgraph of G to run DFS on. Returns the number of the components | |
04939ee6 BC |
199 | of the graph (number of the restarts of DFS). If SKIP_EDGE_P is not |
200 | NULL, it points to a callback function. Edge E will be skipped if | |
201 | callback function returns true. */ | |
66f97d31 ZD |
202 | |
203 | int | |
9771b263 | 204 | graphds_dfs (struct graph *g, int *qs, int nq, vec<int> *qt, |
04939ee6 BC |
205 | bool forward, bitmap subgraph, |
206 | skip_edge_callback skip_edge_p) | |
66f97d31 ZD |
207 | { |
208 | int i, tick = 0, v, comp = 0, top; | |
ae50c0cb TN |
209 | struct graph_edge *e; |
210 | struct graph_edge **stack = XNEWVEC (struct graph_edge *, g->n_vertices); | |
66f97d31 ZD |
211 | bitmap_iterator bi; |
212 | unsigned av; | |
213 | ||
214 | if (subgraph) | |
215 | { | |
216 | EXECUTE_IF_SET_IN_BITMAP (subgraph, 0, av, bi) | |
217 | { | |
218 | g->vertices[av].component = -1; | |
219 | g->vertices[av].post = -1; | |
220 | } | |
221 | } | |
222 | else | |
223 | { | |
224 | for (i = 0; i < g->n_vertices; i++) | |
225 | { | |
226 | g->vertices[i].component = -1; | |
227 | g->vertices[i].post = -1; | |
228 | } | |
229 | } | |
230 | ||
231 | for (i = 0; i < nq; i++) | |
232 | { | |
233 | v = qs[i]; | |
234 | if (g->vertices[v].post != -1) | |
235 | continue; | |
236 | ||
237 | g->vertices[v].component = comp++; | |
04939ee6 | 238 | e = dfs_fst_edge (g, v, forward, subgraph, skip_edge_p); |
66f97d31 ZD |
239 | top = 0; |
240 | ||
241 | while (1) | |
242 | { | |
243 | while (e) | |
244 | { | |
245 | if (g->vertices[dfs_edge_dest (e, forward)].component | |
246 | == -1) | |
247 | break; | |
04939ee6 | 248 | e = dfs_next_edge (e, forward, subgraph, skip_edge_p); |
66f97d31 ZD |
249 | } |
250 | ||
251 | if (!e) | |
252 | { | |
253 | if (qt) | |
9771b263 | 254 | qt->safe_push (v); |
66f97d31 ZD |
255 | g->vertices[v].post = tick++; |
256 | ||
257 | if (!top) | |
258 | break; | |
259 | ||
260 | e = stack[--top]; | |
261 | v = dfs_edge_src (e, forward); | |
04939ee6 | 262 | e = dfs_next_edge (e, forward, subgraph, skip_edge_p); |
66f97d31 ZD |
263 | continue; |
264 | } | |
265 | ||
266 | stack[top++] = e; | |
267 | v = dfs_edge_dest (e, forward); | |
04939ee6 | 268 | e = dfs_fst_edge (g, v, forward, subgraph, skip_edge_p); |
66f97d31 ZD |
269 | g->vertices[v].component = comp - 1; |
270 | } | |
271 | } | |
272 | ||
273 | free (stack); | |
274 | ||
275 | return comp; | |
276 | } | |
277 | ||
278 | /* Determines the strongly connected components of G, using the algorithm of | |
279 | Tarjan -- first determine the postorder dfs numbering in reversed graph, | |
280 | then run the dfs on the original graph in the order given by decreasing | |
281 | numbers assigned by the previous pass. If SUBGRAPH is not NULL, it | |
282 | specifies the subgraph of G whose strongly connected components we want | |
04939ee6 BC |
283 | to determine. If SKIP_EDGE_P is not NULL, it points to a callback function. |
284 | Edge E will be skipped if callback function returns true. | |
b8698a0f | 285 | |
66f97d31 ZD |
286 | After running this function, v->component is the number of the strongly |
287 | connected component for each vertex of G. Returns the number of the | |
288 | sccs of G. */ | |
289 | ||
290 | int | |
04939ee6 BC |
291 | graphds_scc (struct graph *g, bitmap subgraph, |
292 | skip_edge_callback skip_edge_p) | |
66f97d31 ZD |
293 | { |
294 | int *queue = XNEWVEC (int, g->n_vertices); | |
6e1aa848 | 295 | vec<int> postorder = vNULL; |
66f97d31 ZD |
296 | int nq, i, comp; |
297 | unsigned v; | |
298 | bitmap_iterator bi; | |
299 | ||
300 | if (subgraph) | |
301 | { | |
302 | nq = 0; | |
303 | EXECUTE_IF_SET_IN_BITMAP (subgraph, 0, v, bi) | |
304 | { | |
305 | queue[nq++] = v; | |
306 | } | |
307 | } | |
308 | else | |
309 | { | |
310 | for (i = 0; i < g->n_vertices; i++) | |
311 | queue[i] = i; | |
312 | nq = g->n_vertices; | |
313 | } | |
314 | ||
04939ee6 | 315 | graphds_dfs (g, queue, nq, &postorder, false, subgraph, skip_edge_p); |
9771b263 | 316 | gcc_assert (postorder.length () == (unsigned) nq); |
66f97d31 ZD |
317 | |
318 | for (i = 0; i < nq; i++) | |
9771b263 | 319 | queue[i] = postorder[nq - i - 1]; |
04939ee6 | 320 | comp = graphds_dfs (g, queue, nq, NULL, true, subgraph, skip_edge_p); |
66f97d31 ZD |
321 | |
322 | free (queue); | |
9771b263 | 323 | postorder.release (); |
66f97d31 ZD |
324 | |
325 | return comp; | |
326 | } | |
327 | ||
04939ee6 | 328 | /* Runs CALLBACK for all edges in G. DATA is private data for CALLBACK. */ |
66f97d31 ZD |
329 | |
330 | void | |
04939ee6 | 331 | for_each_edge (struct graph *g, graphds_edge_callback callback, void *data) |
66f97d31 | 332 | { |
ae50c0cb | 333 | struct graph_edge *e; |
66f97d31 ZD |
334 | int i; |
335 | ||
336 | for (i = 0; i < g->n_vertices; i++) | |
337 | for (e = g->vertices[i].succ; e; e = e->succ_next) | |
04939ee6 | 338 | callback (g, e, data); |
66f97d31 ZD |
339 | } |
340 | ||
341 | /* Releases the memory occupied by G. */ | |
342 | ||
343 | void | |
344 | free_graph (struct graph *g) | |
345 | { | |
2c41c19d | 346 | obstack_free (&g->ob, NULL); |
66f97d31 ZD |
347 | free (g); |
348 | } | |
349 | ||
350 | /* Returns the nearest common ancestor of X and Y in tree whose parent | |
351 | links are given by PARENT. MARKS is the array used to mark the | |
352 | vertices of the tree, and MARK is the number currently used as a mark. */ | |
353 | ||
354 | static int | |
355 | tree_nca (int x, int y, int *parent, int *marks, int mark) | |
356 | { | |
357 | if (x == -1 || x == y) | |
358 | return y; | |
359 | ||
360 | /* We climb with X and Y up the tree, marking the visited nodes. When | |
361 | we first arrive to a marked node, it is the common ancestor. */ | |
362 | marks[x] = mark; | |
363 | marks[y] = mark; | |
364 | ||
365 | while (1) | |
366 | { | |
367 | x = parent[x]; | |
368 | if (x == -1) | |
369 | break; | |
370 | if (marks[x] == mark) | |
371 | return x; | |
372 | marks[x] = mark; | |
373 | ||
374 | y = parent[y]; | |
375 | if (y == -1) | |
376 | break; | |
377 | if (marks[y] == mark) | |
378 | return y; | |
379 | marks[y] = mark; | |
380 | } | |
381 | ||
382 | /* If we reached the root with one of the vertices, continue | |
383 | with the other one till we reach the marked part of the | |
384 | tree. */ | |
385 | if (x == -1) | |
386 | { | |
387 | for (y = parent[y]; marks[y] != mark; y = parent[y]) | |
388 | continue; | |
389 | ||
390 | return y; | |
391 | } | |
392 | else | |
393 | { | |
394 | for (x = parent[x]; marks[x] != mark; x = parent[x]) | |
395 | continue; | |
396 | ||
397 | return x; | |
398 | } | |
399 | } | |
400 | ||
401 | /* Determines the dominance tree of G (stored in the PARENT, SON and BROTHER | |
402 | arrays), where the entry node is ENTRY. */ | |
403 | ||
404 | void | |
405 | graphds_domtree (struct graph *g, int entry, | |
406 | int *parent, int *son, int *brother) | |
407 | { | |
6e1aa848 | 408 | vec<int> postorder = vNULL; |
66f97d31 ZD |
409 | int *marks = XCNEWVEC (int, g->n_vertices); |
410 | int mark = 1, i, v, idom; | |
411 | bool changed = true; | |
ae50c0cb | 412 | struct graph_edge *e; |
66f97d31 ZD |
413 | |
414 | /* We use a slight modification of the standard iterative algorithm, as | |
415 | described in | |
b8698a0f | 416 | |
66f97d31 ZD |
417 | K. D. Cooper, T. J. Harvey and K. Kennedy: A Simple, Fast Dominance |
418 | Algorithm | |
419 | ||
420 | sort vertices in reverse postorder | |
421 | foreach v | |
422 | dom(v) = everything | |
423 | dom(entry) = entry; | |
424 | ||
425 | while (anything changes) | |
426 | foreach v | |
427 | dom(v) = {v} union (intersection of dom(p) over all predecessors of v) | |
428 | ||
429 | The sets dom(v) are represented by the parent links in the current version | |
430 | of the dominance tree. */ | |
431 | ||
432 | for (i = 0; i < g->n_vertices; i++) | |
433 | { | |
434 | parent[i] = -1; | |
435 | son[i] = -1; | |
436 | brother[i] = -1; | |
437 | } | |
438 | graphds_dfs (g, &entry, 1, &postorder, true, NULL); | |
9771b263 DN |
439 | gcc_assert (postorder.length () == (unsigned) g->n_vertices); |
440 | gcc_assert (postorder[g->n_vertices - 1] == entry); | |
66f97d31 ZD |
441 | |
442 | while (changed) | |
443 | { | |
444 | changed = false; | |
445 | ||
446 | for (i = g->n_vertices - 2; i >= 0; i--) | |
447 | { | |
9771b263 | 448 | v = postorder[i]; |
66f97d31 ZD |
449 | idom = -1; |
450 | for (e = g->vertices[v].pred; e; e = e->pred_next) | |
451 | { | |
452 | if (e->src != entry | |
453 | && parent[e->src] == -1) | |
454 | continue; | |
455 | ||
456 | idom = tree_nca (idom, e->src, parent, marks, mark++); | |
457 | } | |
458 | ||
459 | if (idom != parent[v]) | |
460 | { | |
461 | parent[v] = idom; | |
462 | changed = true; | |
463 | } | |
464 | } | |
465 | } | |
466 | ||
467 | free (marks); | |
9771b263 | 468 | postorder.release (); |
66f97d31 ZD |
469 | |
470 | for (i = 0; i < g->n_vertices; i++) | |
471 | if (parent[i] != -1) | |
472 | { | |
473 | brother[i] = son[parent[i]]; | |
474 | son[parent[i]] = i; | |
475 | } | |
476 | } |