1 | /* Graph representation and manipulation functions. |
2 | Copyright (C) 2007-2023 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 (stream: f, format: "%d (%d)\t<-" , i, g->vertices[i].component); |
41 | for (e = g->vertices[i].pred; e; e = e->pred_next) |
42 | fprintf (stream: f, format: " %d" , e->src); |
43 | fprintf (stream: f, format: "\n" ); |
44 | |
45 | fprintf (stream: f, format: "\t->" ); |
46 | for (e = g->vertices[i].succ; e; e = e->succ_next) |
47 | fprintf (stream: f, format: " %d" , e->dest); |
48 | fprintf (stream: f, format: "\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 (s: g->vertices, c: 0, n: 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 | e->data = NULL; |
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]; |
95 | struct graph_edge *e, *next; |
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 |
122 | dfs_edge_src (struct graph_edge *e, bool forward) |
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 |
131 | dfs_edge_dest (struct graph_edge *e, bool forward) |
132 | { |
133 | return forward ? e->dest : e->src; |
134 | } |
135 | |
136 | /* Helper function for graphds_dfs. Returns the first edge after E (including |
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. */ |
140 | |
141 | static inline struct graph_edge * |
142 | foll_in_subgraph (struct graph_edge *e, bool forward, bitmap subgraph, |
143 | skip_edge_callback skip_edge_p) |
144 | { |
145 | int d; |
146 | |
147 | if (!e) |
148 | return e; |
149 | |
150 | if (!subgraph && (!skip_edge_p || !skip_edge_p (e))) |
151 | return e; |
152 | |
153 | while (e) |
154 | { |
155 | d = dfs_edge_dest (e, forward); |
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))) |
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 |
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. */ |
171 | |
172 | static inline struct graph_edge * |
173 | dfs_fst_edge (struct graph *g, int v, bool forward, bitmap subgraph, |
174 | skip_edge_callback skip_edge_p) |
175 | { |
176 | struct graph_edge *e; |
177 | |
178 | e = (forward ? g->vertices[v].succ : g->vertices[v].pred); |
179 | return foll_in_subgraph (e, forward, subgraph, skip_edge_p); |
180 | } |
181 | |
182 | /* Helper function for graphds_dfs. Returns the next edge after E, in the |
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. */ |
186 | |
187 | static inline struct graph_edge * |
188 | dfs_next_edge (struct graph_edge *e, bool forward, bitmap subgraph, |
189 | skip_edge_callback skip_edge_p) |
190 | { |
191 | return foll_in_subgraph (e: forward ? e->succ_next : e->pred_next, |
192 | forward, subgraph, skip_edge_p); |
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 |
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. */ |
202 | |
203 | int |
204 | graphds_dfs (struct graph *g, int *qs, int nq, vec<int> *qt, |
205 | bool forward, bitmap subgraph, |
206 | skip_edge_callback skip_edge_p) |
207 | { |
208 | int i, tick = 0, v, comp = 0, top; |
209 | struct graph_edge *e; |
210 | struct graph_edge **stack = XNEWVEC (struct graph_edge *, g->n_vertices); |
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++; |
238 | e = dfs_fst_edge (g, v, forward, subgraph, skip_edge_p); |
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; |
248 | e = dfs_next_edge (e, forward, subgraph, skip_edge_p); |
249 | } |
250 | |
251 | if (!e) |
252 | { |
253 | if (qt) |
254 | qt->safe_push (obj: v); |
255 | g->vertices[v].post = tick++; |
256 | |
257 | if (!top) |
258 | break; |
259 | |
260 | e = stack[--top]; |
261 | v = dfs_edge_src (e, forward); |
262 | e = dfs_next_edge (e, forward, subgraph, skip_edge_p); |
263 | continue; |
264 | } |
265 | |
266 | stack[top++] = e; |
267 | v = dfs_edge_dest (e, forward); |
268 | e = dfs_fst_edge (g, v, forward, subgraph, skip_edge_p); |
269 | g->vertices[v].component = comp - 1; |
270 | } |
271 | } |
272 | |
273 | free (ptr: stack); |
274 | |
275 | return comp; |
276 | } |
277 | |
278 | /* Determines the strongly connected components of G, using the algorithm of |
279 | Kosaraju -- 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 |
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. If SCC_GROUPING |
285 | is not null, the nodes will be added to it in the following order: |
286 | |
287 | - If SCC A is a direct or indirect predecessor of SCC B in the SCC dag, |
288 | A's nodes come before B's nodes. |
289 | |
290 | - All of an SCC's nodes are listed consecutively, although the order |
291 | of the nodes within an SCC is not really meaningful. |
292 | |
293 | After running this function, v->component is the number of the strongly |
294 | connected component for each vertex of G. Returns the number of the |
295 | sccs of G. */ |
296 | |
297 | int |
298 | graphds_scc (struct graph *g, bitmap subgraph, |
299 | skip_edge_callback skip_edge_p, vec<int> *scc_grouping) |
300 | { |
301 | int *queue = XNEWVEC (int, g->n_vertices); |
302 | vec<int> postorder = vNULL; |
303 | int nq, i, comp; |
304 | unsigned v; |
305 | bitmap_iterator bi; |
306 | |
307 | if (subgraph) |
308 | { |
309 | nq = 0; |
310 | EXECUTE_IF_SET_IN_BITMAP (subgraph, 0, v, bi) |
311 | { |
312 | queue[nq++] = v; |
313 | } |
314 | } |
315 | else |
316 | { |
317 | for (i = 0; i < g->n_vertices; i++) |
318 | queue[i] = i; |
319 | nq = g->n_vertices; |
320 | } |
321 | |
322 | graphds_dfs (g, qs: queue, nq, qt: &postorder, forward: false, subgraph, skip_edge_p); |
323 | gcc_assert (postorder.length () == (unsigned) nq); |
324 | |
325 | for (i = 0; i < nq; i++) |
326 | queue[i] = postorder[nq - i - 1]; |
327 | comp = graphds_dfs (g, qs: queue, nq, qt: scc_grouping, forward: true, subgraph, skip_edge_p); |
328 | |
329 | free (ptr: queue); |
330 | postorder.release (); |
331 | |
332 | return comp; |
333 | } |
334 | |
335 | /* Runs CALLBACK for all edges in G. DATA is private data for CALLBACK. */ |
336 | |
337 | void |
338 | for_each_edge (struct graph *g, graphds_edge_callback callback, void *data) |
339 | { |
340 | struct graph_edge *e; |
341 | int i; |
342 | |
343 | for (i = 0; i < g->n_vertices; i++) |
344 | for (e = g->vertices[i].succ; e; e = e->succ_next) |
345 | callback (g, e, data); |
346 | } |
347 | |
348 | /* Releases the memory occupied by G. */ |
349 | |
350 | void |
351 | free_graph (struct graph *g) |
352 | { |
353 | obstack_free (&g->ob, NULL); |
354 | free (ptr: g); |
355 | } |
356 | |
357 | /* Returns the nearest common ancestor of X and Y in tree whose parent |
358 | links are given by PARENT. MARKS is the array used to mark the |
359 | vertices of the tree, and MARK is the number currently used as a mark. */ |
360 | |
361 | static int |
362 | tree_nca (int x, int y, int *parent, int *marks, int mark) |
363 | { |
364 | if (x == -1 || x == y) |
365 | return y; |
366 | |
367 | /* We climb with X and Y up the tree, marking the visited nodes. When |
368 | we first arrive to a marked node, it is the common ancestor. */ |
369 | marks[x] = mark; |
370 | marks[y] = mark; |
371 | |
372 | while (1) |
373 | { |
374 | x = parent[x]; |
375 | if (x == -1) |
376 | break; |
377 | if (marks[x] == mark) |
378 | return x; |
379 | marks[x] = mark; |
380 | |
381 | y = parent[y]; |
382 | if (y == -1) |
383 | break; |
384 | if (marks[y] == mark) |
385 | return y; |
386 | marks[y] = mark; |
387 | } |
388 | |
389 | /* If we reached the root with one of the vertices, continue |
390 | with the other one till we reach the marked part of the |
391 | tree. */ |
392 | if (x == -1) |
393 | { |
394 | for (y = parent[y]; marks[y] != mark; y = parent[y]) |
395 | continue; |
396 | |
397 | return y; |
398 | } |
399 | else |
400 | { |
401 | for (x = parent[x]; marks[x] != mark; x = parent[x]) |
402 | continue; |
403 | |
404 | return x; |
405 | } |
406 | } |
407 | |
408 | /* Determines the dominance tree of G (stored in the PARENT, SON and BROTHER |
409 | arrays), where the entry node is ENTRY. */ |
410 | |
411 | void |
412 | graphds_domtree (struct graph *g, int entry, |
413 | int *parent, int *son, int *brother) |
414 | { |
415 | vec<int> postorder = vNULL; |
416 | int *marks = XCNEWVEC (int, g->n_vertices); |
417 | int mark = 1, i, v, idom; |
418 | bool changed = true; |
419 | struct graph_edge *e; |
420 | |
421 | /* We use a slight modification of the standard iterative algorithm, as |
422 | described in |
423 | |
424 | K. D. Cooper, T. J. Harvey and K. Kennedy: A Simple, Fast Dominance |
425 | Algorithm |
426 | |
427 | sort vertices in reverse postorder |
428 | foreach v |
429 | dom(v) = everything |
430 | dom(entry) = entry; |
431 | |
432 | while (anything changes) |
433 | foreach v |
434 | dom(v) = {v} union (intersection of dom(p) over all predecessors of v) |
435 | |
436 | The sets dom(v) are represented by the parent links in the current version |
437 | of the dominance tree. */ |
438 | |
439 | for (i = 0; i < g->n_vertices; i++) |
440 | { |
441 | parent[i] = -1; |
442 | son[i] = -1; |
443 | brother[i] = -1; |
444 | } |
445 | graphds_dfs (g, qs: &entry, nq: 1, qt: &postorder, forward: true, NULL); |
446 | gcc_assert (postorder.length () == (unsigned) g->n_vertices); |
447 | gcc_assert (postorder[g->n_vertices - 1] == entry); |
448 | |
449 | while (changed) |
450 | { |
451 | changed = false; |
452 | |
453 | for (i = g->n_vertices - 2; i >= 0; i--) |
454 | { |
455 | v = postorder[i]; |
456 | idom = -1; |
457 | for (e = g->vertices[v].pred; e; e = e->pred_next) |
458 | { |
459 | if (e->src != entry |
460 | && parent[e->src] == -1) |
461 | continue; |
462 | |
463 | idom = tree_nca (x: idom, y: e->src, parent, marks, mark: mark++); |
464 | } |
465 | |
466 | if (idom != parent[v]) |
467 | { |
468 | parent[v] = idom; |
469 | changed = true; |
470 | } |
471 | } |
472 | } |
473 | |
474 | free (ptr: marks); |
475 | postorder.release (); |
476 | |
477 | for (i = 0; i < g->n_vertices; i++) |
478 | if (parent[i] != -1) |
479 | { |
480 | brother[i] = son[parent[i]]; |
481 | son[parent[i]] = i; |
482 | } |
483 | } |
484 | |