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1 | /* Graph representation and manipulation functions. | |
2 | Copyright (C) 2007-2017 Free Software Foundation, Inc. | |
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 | |
8 | Software Foundation; either version 3, or (at your option) any later | |
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 | |
17 | along with GCC; see the file COPYING3. If not see | |
18 | <http://www.gnu.org/licenses/>. */ | |
19 | ||
20 | #include "config.h" | |
21 | #include "system.h" | |
22 | #include "coretypes.h" | |
23 | #include "bitmap.h" | |
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; | |
32 | struct graph_edge *e; | |
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 | ||
59 | gcc_obstack_init (&g->ob); | |
60 | g->n_vertices = n_vertices; | |
61 | g->vertices = XOBNEWVEC (&g->ob, struct vertex, n_vertices); | |
62 | memset (g->vertices, 0, sizeof (struct vertex) * n_vertices); | |
63 | ||
64 | return g; | |
65 | } | |
66 | ||
67 | /* Adds an edge from F to T to graph G. The new edge is returned. */ | |
68 | ||
69 | struct graph_edge * | |
70 | add_edge (struct graph *g, int f, int t) | |
71 | { | |
72 | struct graph_edge *e = XOBNEW (&g->ob, struct graph_edge); | |
73 | struct vertex *vf = &g->vertices[f], *vt = &g->vertices[t]; | |
74 | ||
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 | ||
84 | return e; | |
85 | } | |
86 | ||
87 | /* Moves all the edges incident with U to V. */ | |
88 | ||
89 | void | |
90 | identify_vertices (struct graph *g, int v, int u) | |
91 | { | |
92 | struct vertex *vv = &g->vertices[v]; | |
93 | struct vertex *uu = &g->vertices[u]; | |
94 | struct graph_edge *e, *next; | |
95 | ||
96 | for (e = uu->succ; e; e = next) | |
97 | { | |
98 | next = e->succ_next; | |
99 | ||
100 | e->src = v; | |
101 | e->succ_next = vv->succ; | |
102 | vv->succ = e; | |
103 | } | |
104 | uu->succ = NULL; | |
105 | ||
106 | for (e = uu->pred; e; e = next) | |
107 | { | |
108 | next = e->pred_next; | |
109 | ||
110 | e->dest = v; | |
111 | e->pred_next = vv->pred; | |
112 | vv->pred = e; | |
113 | } | |
114 | uu->pred = NULL; | |
115 | } | |
116 | ||
117 | /* Helper function for graphds_dfs. Returns the source vertex of E, in the | |
118 | direction given by FORWARD. */ | |
119 | ||
120 | static inline int | |
121 | dfs_edge_src (struct graph_edge *e, bool forward) | |
122 | { | |
123 | return forward ? e->src : e->dest; | |
124 | } | |
125 | ||
126 | /* Helper function for graphds_dfs. Returns the destination vertex of E, in | |
127 | the direction given by FORWARD. */ | |
128 | ||
129 | static inline int | |
130 | dfs_edge_dest (struct graph_edge *e, bool forward) | |
131 | { | |
132 | return forward ? e->dest : e->src; | |
133 | } | |
134 | ||
135 | /* Helper function for graphds_dfs. Returns the first edge after E (including | |
136 | E), in the graph direction given by FORWARD, that belongs to SUBGRAPH. */ | |
137 | ||
138 | static inline struct graph_edge * | |
139 | foll_in_subgraph (struct graph_edge *e, bool forward, bitmap subgraph) | |
140 | { | |
141 | int d; | |
142 | ||
143 | if (!subgraph) | |
144 | return e; | |
145 | ||
146 | while (e) | |
147 | { | |
148 | d = dfs_edge_dest (e, forward); | |
149 | if (bitmap_bit_p (subgraph, d)) | |
150 | return e; | |
151 | ||
152 | e = forward ? e->succ_next : e->pred_next; | |
153 | } | |
154 | ||
155 | return e; | |
156 | } | |
157 | ||
158 | /* Helper function for graphds_dfs. Select the first edge from V in G, in the | |
159 | direction given by FORWARD, that belongs to SUBGRAPH. */ | |
160 | ||
161 | static inline struct graph_edge * | |
162 | dfs_fst_edge (struct graph *g, int v, bool forward, bitmap subgraph) | |
163 | { | |
164 | struct graph_edge *e; | |
165 | ||
166 | e = (forward ? g->vertices[v].succ : g->vertices[v].pred); | |
167 | return foll_in_subgraph (e, forward, subgraph); | |
168 | } | |
169 | ||
170 | /* Helper function for graphds_dfs. Returns the next edge after E, in the | |
171 | graph direction given by FORWARD, that belongs to SUBGRAPH. */ | |
172 | ||
173 | static inline struct graph_edge * | |
174 | dfs_next_edge (struct graph_edge *e, bool forward, bitmap subgraph) | |
175 | { | |
176 | return foll_in_subgraph (forward ? e->succ_next : e->pred_next, | |
177 | forward, subgraph); | |
178 | } | |
179 | ||
180 | /* Runs dfs search over vertices of G, from NQ vertices in queue QS. | |
181 | The vertices in postorder are stored into QT. If FORWARD is false, | |
182 | backward dfs is run. If SUBGRAPH is not NULL, it specifies the | |
183 | subgraph of G to run DFS on. Returns the number of the components | |
184 | of the graph (number of the restarts of DFS). */ | |
185 | ||
186 | int | |
187 | graphds_dfs (struct graph *g, int *qs, int nq, vec<int> *qt, | |
188 | bool forward, bitmap subgraph) | |
189 | { | |
190 | int i, tick = 0, v, comp = 0, top; | |
191 | struct graph_edge *e; | |
192 | struct graph_edge **stack = XNEWVEC (struct graph_edge *, g->n_vertices); | |
193 | bitmap_iterator bi; | |
194 | unsigned av; | |
195 | ||
196 | if (subgraph) | |
197 | { | |
198 | EXECUTE_IF_SET_IN_BITMAP (subgraph, 0, av, bi) | |
199 | { | |
200 | g->vertices[av].component = -1; | |
201 | g->vertices[av].post = -1; | |
202 | } | |
203 | } | |
204 | else | |
205 | { | |
206 | for (i = 0; i < g->n_vertices; i++) | |
207 | { | |
208 | g->vertices[i].component = -1; | |
209 | g->vertices[i].post = -1; | |
210 | } | |
211 | } | |
212 | ||
213 | for (i = 0; i < nq; i++) | |
214 | { | |
215 | v = qs[i]; | |
216 | if (g->vertices[v].post != -1) | |
217 | continue; | |
218 | ||
219 | g->vertices[v].component = comp++; | |
220 | e = dfs_fst_edge (g, v, forward, subgraph); | |
221 | top = 0; | |
222 | ||
223 | while (1) | |
224 | { | |
225 | while (e) | |
226 | { | |
227 | if (g->vertices[dfs_edge_dest (e, forward)].component | |
228 | == -1) | |
229 | break; | |
230 | e = dfs_next_edge (e, forward, subgraph); | |
231 | } | |
232 | ||
233 | if (!e) | |
234 | { | |
235 | if (qt) | |
236 | qt->safe_push (v); | |
237 | g->vertices[v].post = tick++; | |
238 | ||
239 | if (!top) | |
240 | break; | |
241 | ||
242 | e = stack[--top]; | |
243 | v = dfs_edge_src (e, forward); | |
244 | e = dfs_next_edge (e, forward, subgraph); | |
245 | continue; | |
246 | } | |
247 | ||
248 | stack[top++] = e; | |
249 | v = dfs_edge_dest (e, forward); | |
250 | e = dfs_fst_edge (g, v, forward, subgraph); | |
251 | g->vertices[v].component = comp - 1; | |
252 | } | |
253 | } | |
254 | ||
255 | free (stack); | |
256 | ||
257 | return comp; | |
258 | } | |
259 | ||
260 | /* Determines the strongly connected components of G, using the algorithm of | |
261 | Tarjan -- first determine the postorder dfs numbering in reversed graph, | |
262 | then run the dfs on the original graph in the order given by decreasing | |
263 | numbers assigned by the previous pass. If SUBGRAPH is not NULL, it | |
264 | specifies the subgraph of G whose strongly connected components we want | |
265 | to determine. | |
266 | ||
267 | After running this function, v->component is the number of the strongly | |
268 | connected component for each vertex of G. Returns the number of the | |
269 | sccs of G. */ | |
270 | ||
271 | int | |
272 | graphds_scc (struct graph *g, bitmap subgraph) | |
273 | { | |
274 | int *queue = XNEWVEC (int, g->n_vertices); | |
275 | vec<int> postorder = vNULL; | |
276 | int nq, i, comp; | |
277 | unsigned v; | |
278 | bitmap_iterator bi; | |
279 | ||
280 | if (subgraph) | |
281 | { | |
282 | nq = 0; | |
283 | EXECUTE_IF_SET_IN_BITMAP (subgraph, 0, v, bi) | |
284 | { | |
285 | queue[nq++] = v; | |
286 | } | |
287 | } | |
288 | else | |
289 | { | |
290 | for (i = 0; i < g->n_vertices; i++) | |
291 | queue[i] = i; | |
292 | nq = g->n_vertices; | |
293 | } | |
294 | ||
295 | graphds_dfs (g, queue, nq, &postorder, false, subgraph); | |
296 | gcc_assert (postorder.length () == (unsigned) nq); | |
297 | ||
298 | for (i = 0; i < nq; i++) | |
299 | queue[i] = postorder[nq - i - 1]; | |
300 | comp = graphds_dfs (g, queue, nq, NULL, true, subgraph); | |
301 | ||
302 | free (queue); | |
303 | postorder.release (); | |
304 | ||
305 | return comp; | |
306 | } | |
307 | ||
308 | /* Runs CALLBACK for all edges in G. */ | |
309 | ||
310 | void | |
311 | for_each_edge (struct graph *g, graphds_edge_callback callback) | |
312 | { | |
313 | struct graph_edge *e; | |
314 | int i; | |
315 | ||
316 | for (i = 0; i < g->n_vertices; i++) | |
317 | for (e = g->vertices[i].succ; e; e = e->succ_next) | |
318 | callback (g, e); | |
319 | } | |
320 | ||
321 | /* Releases the memory occupied by G. */ | |
322 | ||
323 | void | |
324 | free_graph (struct graph *g) | |
325 | { | |
326 | obstack_free (&g->ob, NULL); | |
327 | free (g); | |
328 | } | |
329 | ||
330 | /* Returns the nearest common ancestor of X and Y in tree whose parent | |
331 | links are given by PARENT. MARKS is the array used to mark the | |
332 | vertices of the tree, and MARK is the number currently used as a mark. */ | |
333 | ||
334 | static int | |
335 | tree_nca (int x, int y, int *parent, int *marks, int mark) | |
336 | { | |
337 | if (x == -1 || x == y) | |
338 | return y; | |
339 | ||
340 | /* We climb with X and Y up the tree, marking the visited nodes. When | |
341 | we first arrive to a marked node, it is the common ancestor. */ | |
342 | marks[x] = mark; | |
343 | marks[y] = mark; | |
344 | ||
345 | while (1) | |
346 | { | |
347 | x = parent[x]; | |
348 | if (x == -1) | |
349 | break; | |
350 | if (marks[x] == mark) | |
351 | return x; | |
352 | marks[x] = mark; | |
353 | ||
354 | y = parent[y]; | |
355 | if (y == -1) | |
356 | break; | |
357 | if (marks[y] == mark) | |
358 | return y; | |
359 | marks[y] = mark; | |
360 | } | |
361 | ||
362 | /* If we reached the root with one of the vertices, continue | |
363 | with the other one till we reach the marked part of the | |
364 | tree. */ | |
365 | if (x == -1) | |
366 | { | |
367 | for (y = parent[y]; marks[y] != mark; y = parent[y]) | |
368 | continue; | |
369 | ||
370 | return y; | |
371 | } | |
372 | else | |
373 | { | |
374 | for (x = parent[x]; marks[x] != mark; x = parent[x]) | |
375 | continue; | |
376 | ||
377 | return x; | |
378 | } | |
379 | } | |
380 | ||
381 | /* Determines the dominance tree of G (stored in the PARENT, SON and BROTHER | |
382 | arrays), where the entry node is ENTRY. */ | |
383 | ||
384 | void | |
385 | graphds_domtree (struct graph *g, int entry, | |
386 | int *parent, int *son, int *brother) | |
387 | { | |
388 | vec<int> postorder = vNULL; | |
389 | int *marks = XCNEWVEC (int, g->n_vertices); | |
390 | int mark = 1, i, v, idom; | |
391 | bool changed = true; | |
392 | struct graph_edge *e; | |
393 | ||
394 | /* We use a slight modification of the standard iterative algorithm, as | |
395 | described in | |
396 | ||
397 | K. D. Cooper, T. J. Harvey and K. Kennedy: A Simple, Fast Dominance | |
398 | Algorithm | |
399 | ||
400 | sort vertices in reverse postorder | |
401 | foreach v | |
402 | dom(v) = everything | |
403 | dom(entry) = entry; | |
404 | ||
405 | while (anything changes) | |
406 | foreach v | |
407 | dom(v) = {v} union (intersection of dom(p) over all predecessors of v) | |
408 | ||
409 | The sets dom(v) are represented by the parent links in the current version | |
410 | of the dominance tree. */ | |
411 | ||
412 | for (i = 0; i < g->n_vertices; i++) | |
413 | { | |
414 | parent[i] = -1; | |
415 | son[i] = -1; | |
416 | brother[i] = -1; | |
417 | } | |
418 | graphds_dfs (g, &entry, 1, &postorder, true, NULL); | |
419 | gcc_assert (postorder.length () == (unsigned) g->n_vertices); | |
420 | gcc_assert (postorder[g->n_vertices - 1] == entry); | |
421 | ||
422 | while (changed) | |
423 | { | |
424 | changed = false; | |
425 | ||
426 | for (i = g->n_vertices - 2; i >= 0; i--) | |
427 | { | |
428 | v = postorder[i]; | |
429 | idom = -1; | |
430 | for (e = g->vertices[v].pred; e; e = e->pred_next) | |
431 | { | |
432 | if (e->src != entry | |
433 | && parent[e->src] == -1) | |
434 | continue; | |
435 | ||
436 | idom = tree_nca (idom, e->src, parent, marks, mark++); | |
437 | } | |
438 | ||
439 | if (idom != parent[v]) | |
440 | { | |
441 | parent[v] = idom; | |
442 | changed = true; | |
443 | } | |
444 | } | |
445 | } | |
446 | ||
447 | free (marks); | |
448 | postorder.release (); | |
449 | ||
450 | for (i = 0; i < g->n_vertices; i++) | |
451 | if (parent[i] != -1) | |
452 | { | |
453 | brother[i] = son[parent[i]]; | |
454 | son[parent[i]] = i; | |
455 | } | |
456 | } |