-
Notifications
You must be signed in to change notification settings - Fork 0
/
nautinv.c
1752 lines (1589 loc) · 64.4 KB
/
nautinv.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/*****************************************************************************
* *
* Vertex-invariants source file for nauty 2.7. *
* *
* Copyright (1989-2013) Brendan McKay. All rights reserved. *
* Subject to waivers and disclaimers in nauty.h. *
* *
* CHANGE HISTORY *
* 13-Mar-90 : initial release for version 1.5 *
* 10-Nov-90 : changes for version 1.6 : *
* - added dummy routine nautinv_null() *
* 27-Aug-92 : renamed to version 1.7, no changes to this file *
* 5-Jun-93 : renamed to version 1.7+, no changes to this file *
* 18-Aug-93 : renamed to version 1.8, no changes to this file *
* 17-Sep-93 : changes for version 1.9 : *
* - added invariant routine adjacencies() *
* 20-Jun-96 : changes for version 2.0 : *
* - added invariants cellfano() and cellfano2() *
* 11-Jul-96 - added dynamic allocation *
* 21-Oct-98 - use shortish in place of short for BIGNAUTY *
* 9-Jan-00 - added nautinv_check() *
* 12-Feb-00 - minor code formatting *
* 16-Nov-00 - made changes listed in nauty.h *
* 22-Apr-01 : changes for version 2.1 : *
* - made all large dynamic memory external to routines *
* - added nautinv_freedyn() to free all such memory *
* - include nautinv.h rather than naututil.h *
* - removed nautinv_null() *
* - added code to facilitate compilation into Magma *
* - removed EXTDEFS *
* 12-Jul-01 - use invararg in distances() *
* - fixed comments in ind and cliq routines *
* 21-Nov-01 : use NAUTYREQUIRED in nautinv_check() *
* 10-Dec-06 : remove BIGNAUTY *
* 10-Nov-09 : remove types shortish and permutation *
* 23-Nov-09 : add refinvar() *
* 12-Jun-10 : fixed identical errors in cellcliq() and cellind() *
* 15-Jan-12 : add TLS_ATTR attributes *
* 23-Aug-12 : fix getbigcells(), thanks to Fatih Demirkale *
* 23-Jan-13 : add some parens to satisfy icc *
* *
*****************************************************************************/
#define ONE_WORD_SETS
#include "nautinv.h"
#if MAXM==1
#define M 1
#else
#define M m
#endif
#define MASH(l,i) ((((l) ^ 056345) + (i)) & 077777)
/* : expression whose long value depends only on long l and int/long i.
Anything goes, preferably non-commutative. */
#define CLEANUP(l) ((int)((l) % 077777))
/* : expression whose value depends on long l and is less than 077777
when converted to int then short. Anything goes. */
#define ACCUM(x,y) x = (((x) + (y)) & 077777)
/* : must be commutative. */
static const int fuzz1[] = {037541,061532,005257,026416};
static const int fuzz2[] = {006532,070236,035523,062437};
#define FUZZ1(x) ((x) ^ fuzz1[(x)&3])
#define FUZZ2(x) ((x) ^ fuzz2[(x)&3])
#define MAXCLIQUE 10 /* max clique size for cliques() and maxindset() */
#if MAXN
static TLS_ATTR int workshort[MAXN+2];
static TLS_ATTR int vv[MAXN],ww[MAXN];
static TLS_ATTR int workperm[MAXN];
static TLS_ATTR int bucket[MAXN+2];
static TLS_ATTR int count[MAXN];
static TLS_ATTR set workset[MAXM];
static TLS_ATTR set w01[MAXM],w02[MAXM],w03[MAXM],w12[MAXM],w13[MAXM],w23[MAXM];
static TLS_ATTR set pt0[MAXM],pt1[MAXM],pt2[MAXM];
static TLS_ATTR set wss[MAXCLIQUE-1][MAXM];
static TLS_ATTR set ws1[MAXM],ws2[MAXM];
#else
DYNALLSTAT(int,workshort,workshort_sz);
DYNALLSTAT(int,vv,vv_sz);
DYNALLSTAT(int,ww,ww_sz);
DYNALLSTAT(int,workperm,workperm_sz);
DYNALLSTAT(int,bucket,bucket_sz);
DYNALLSTAT(int,count,count_sz);
DYNALLSTAT(set,ws1,ws1_sz);
DYNALLSTAT(set,ws2,ws2_sz);
DYNALLSTAT(set,workset,workset_sz);
DYNALLSTAT(set,w01,w01_sz);
DYNALLSTAT(set,w02,w02_sz);
DYNALLSTAT(set,w03,w03_sz);
DYNALLSTAT(set,w12,w12_sz);
DYNALLSTAT(set,w13,w13_sz);
DYNALLSTAT(set,w23,w23_sz);
DYNALLSTAT(set,pt0,pt0_sz);
DYNALLSTAT(set,pt1,pt1_sz);
DYNALLSTAT(set,pt2,pt2_sz);
DYNALLSTAT(set,wss,wss_sz);
#endif
/* aproto: header new_nauty_protos.h */
/*****************************************************************************
* *
* This file contains a number of procedures which compute vertex-invariants *
* for stronger partition refinement. Since entirely different *
* vertex-invariants seem to work better for different types of graph, we *
* cannot do more than give a small collection of representative examples. *
* Any serious computations with difficult graphs may well need to use *
* specially-written vertex-invariants. The use of vertex-invariants *
* procedures is supported by nauty from version 1.5 onwards, via the *
* options userinvarproc, mininvarlevel, maxinvarlevel and invararg. *
* The meaning of these fields in detail are as follows: *
* userinvarproc is the address of the vertex-invariant procedure. If *
* no vertex-invariants is required, this field should *
* have the value NULL. *
* maxinvarlevel The absolute value of this is the maximum level in the *
* search tree at which the vertex-invariant will be *
* computed. The root of the tree is at level 1, so the *
* vertex-invariant will not be invoked at all if *
* maxinvarlevel==0. Negative values of maxinvarlevel *
* request nauty to not compute the vertex-invariant at *
* a level greater than that of the earliest node (if any) *
* on the path to the first leaf of the search tree at *
* which the vertex-invariant refines the partition. *
* mininvarlevel The absolute value of this is the minimum level in the *
* search tree at which the vertex-invariant will be *
* computed. The root of the tree is at level 1, so there *
* is no effective limit if mininvarlevel is -1, 0 or 1. *
* Negative values of mininvarlevel request nauty to not *
* compute the vertex-invariant at a level less than *
* that of the earliest node (if any) on the path to the *
* first leaf of the search tree at which the *
* vertex-invariant refines the partition. *
* invararg is passed to the vertex-invariant procedure via the *
* argument of the same name. It can be used by the *
* procedure for any purpose. *
* Note that negative values of maxinvarlevel and mininvarlevel make the *
* canonical labelling invalid, but can speed automorphism group finding. *
* Nauty already knows this and takes their absolute values. *
* *
* A vertex-invariant must be declared thus: *
* void invarproc(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) *
* All of these arguments must be treated as read-only except for invar. *
* g : the graph, exactly as passed to nauty() *
* lab,ptn : the current partition nest (see nauty.h for the format) *
* level : the level of this node in the search tree. *
* numcells : the number of cells in the partition at this node. *
* tvpos : the index in (lab,ptn) of one cell in the partition. *
* If level <= 1, the cell will be the first fragment of the *
* first active cell (as provided by the initial call to nauty), *
* or the first cell, if there were no active cells. *
* If level > 1, the cell will be the singleton cell which was *
* created to make this node of the search tree from its parent. *
* invararg : a copy of options.invararg *
* digraph : a copy of options.digraph *
* m,n : size parameters as passed to nauty() *
* invar : an array to return the answer in. The procedure must put in *
* each invar[i] (0 <= i < n) an invariant of the 6-tuple *
* (<vertex i>,g,<the partition nest to this level>,level, *
* invararg,digraph) *
* Note that invar[] is declared as an int array. Since the *
* absolute value of the invariant is irrelevant, only the *
* comparative values, any short, int or long value can be *
* assigned to the entries of invar[] without fear. However, *
* you should assign a value less than 077777 to ensure machine- *
* independence of the canonical labelling. *
* *
* The refinement procedure has already been called before the invariant *
* procedure is called. That means that the partition is equitable if *
* digraph==FALSE. *
* *
*****************************************************************************/
/*****************************************************************************
* *
* twopaths() assigns to each vertex v the sum of the weights of each vertex *
* which can be reached from v along a walk of length two (including itself *
* usually). The weight of each vertex w is defined as the ordinal number *
* of the cell containing w, starting at 1 for the first cell. *
* *
*****************************************************************************/
void
twopaths(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int i,v,w;
int wt;
set *gv,*gw;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"twopaths");
DYNALLOC1(int,workshort,workshort_sz,n+2,"twopaths");
#endif
wt = 1;
for (i = 0; i < n; ++i)
{
workshort[lab[i]] = wt;
if (ptn[i] <= level) ++wt;
}
for (v = 0, gv = (set*)g; v < n; ++v, gv += M)
{
EMPTYSET(workset,m);
w = -1;
while ((w = nextelement(gv,M,w)) >= 0)
{
gw = GRAPHROW(g,w,m);
for (i = M; --i >= 0;) UNION(workset[i],gw[i]);
}
wt = 0;
w = -1;
while ((w = nextelement(workset,M,w)) >= 0) ACCUM(wt,workshort[w]);
invar[v] = wt;
}
}
/*****************************************************************************
* *
* quadruples() assigns to each vertex v a value depending on the set of *
* weights w(v,v1,v2,v3), where w(v,v1,v2,v3) depends on the number of *
* vertices adjacent to an odd number of {v,v1,v2,v3}, and to the cells *
* that v,v1,v2,v3 belong to. {v,v1,v2,v3} are permitted to range over all *
* distinct 4-tuples which contain at least one member in the cell tvpos. *
* *
*****************************************************************************/
void
quadruples(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int i,pc;
setword sw;
set *gw;
int wt;
int v,iv,v1,v2,v3;
set *gv;
long wv,wv1,wv2,wv3;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"quadruples");
DYNALLOC1(set,ws1,ws1_sz,m,"quadruples");
DYNALLOC1(set,workset,workset_sz,m,"quadruples");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
wt = 1;
for (i = 0; i < n; ++i)
{
workshort[lab[i]] = FUZZ2(wt);
if (ptn[i] <= level) ++wt;
}
iv = tvpos - 1;
do
{
v = lab[++iv];
gv = GRAPHROW(g,v,m);
wv = workshort[v];
for (v1 = 0; v1 < n-2; ++v1)
{
wv1 = workshort[v1];
if (wv1 == wv && v1 <= v) continue;
wv1 += wv;
gw = GRAPHROW(g,v1,m);
for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i];
for (v2 = v1+1; v2 < n-1; ++v2)
{
wv2 = workshort[v2];
if (wv2 == wv && v2 <= v) continue;
wv2 += wv1;
gw = GRAPHROW(g,v2,m);
for (i = M; --i >= 0;) ws1[i] = workset[i] ^ gw[i];
for (v3 = v2+1; v3 < n; ++v3)
{
wv3 = workshort[v3];
if (wv3 == wv && v3 <= v) continue;
wv3 += wv2;
gw = GRAPHROW(g,v3,m);
pc = 0;
for (i = M; --i >= 0;)
if ((sw = ws1[i] ^ gw[i]) != 0) pc += POPCOUNT(sw);
wt = (FUZZ1(pc)+wv3) & 077777;
wt = FUZZ2(wt);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
ACCUM(invar[v3],wt);
}
}
}
}
while (ptn[iv] > level);
}
/*****************************************************************************
* *
* triples() assigns to each vertex v a value depending on the set of *
* weights w(v,v1,v2), where w(v,v1,v2) depends on the number of vertices *
* adjacent to an odd number of {v,v1,v2}, and to the cells that *
* v,v1,v2 belong to. {v,v1,v2} are permitted to range over all distinct *
* triples which contain at least one member in the cell tvpos. *
* *
*****************************************************************************/
void
triples(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int i,pc;
setword sw;
set *gw;
int wt;
int v,iv,v1,v2;
set *gv;
long wv,wv1,wv2;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"triples");
DYNALLOC1(int,workshort,workshort_sz,n+2,"triples");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
wt = 1;
for (i = 0; i < n; ++i)
{
workshort[lab[i]] = FUZZ1(wt);
if (ptn[i] <= level) ++wt;
}
iv = tvpos - 1;
do
{
v = lab[++iv];
gv = GRAPHROW(g,v,m);
wv = workshort[v];
for (v1 = 0; v1 < n-1; ++v1)
{
wv1 = workshort[v1];
if (wv1 == wv && v1 <= v) continue;
wv1 += wv;
gw = GRAPHROW(g,v1,m);
for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i];
for (v2 = v1+1; v2 < n; ++v2)
{
wv2 = workshort[v2];
if (wv2 == wv && v2 <= v) continue;
wv2 += wv1;
gw = GRAPHROW(g,v2,m);
pc = 0;
for (i = M; --i >= 0;)
if ((sw = workset[i] ^ gw[i]) != 0) pc += POPCOUNT(sw);
wt = (FUZZ1(pc)+wv2) & 077777;
wt = FUZZ2(wt);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
}
}
}
while (ptn[iv] > level);
}
/*****************************************************************************
* *
* adjtriang() assigns to each vertex v a value depending on the numbers *
* of common neighbours between each pair {v1,v2} of neighbours of v, and *
* which cells v1 and v2 lie in. The vertices v1 and v2 must be adjacent *
* if invararg == 0 and not adjacent if invararg == 1. *
* *
*****************************************************************************/
void
adjtriang(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int j,pc;
setword sw;
set *gi;
int wt;
int i,v1,v2;
boolean v1v2;
set *gv1,*gv2;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"adjtriang");
DYNALLOC1(int,workshort,workshort_sz,n+2,"adjtriang");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
wt = 1;
for (i = 0; i < n; ++i)
{
workshort[lab[i]] = FUZZ1(wt);
if (ptn[i] <= level) ++wt;
}
for (v1 = 0, gv1 = g; v1 < n; ++v1, gv1 += M)
{
for (v2 = (digraph ? 0 : v1+1); v2 < n; ++v2)
{
if (v2 == v1) continue;
v1v2 = (ISELEMENT(gv1,v2) != 0);
if ((invararg == 0 && !v1v2)
|| (invararg == 1 && v1v2)) continue;
wt = workshort[v1];
ACCUM(wt,workshort[v2]);
ACCUM(wt,v1v2);
gv2 = GRAPHROW(g,v2,m);
for (i = M; --i >= 0;) workset[i] = gv1[i] & gv2[i];
i = -1;
while ((i = nextelement(workset,M,i)) >= 0)
{
pc = 0;
gi = GRAPHROW(g,i,m);
for (j = M; --j >= 0;)
if ((sw = workset[j] & gi[j]) != 0) pc += POPCOUNT(sw);
pc = (pc + wt) & 077777;
ACCUM(invar[i],pc);
}
}
}
}
/*****************************************************************************
* *
* getbigcells(ptn,level,minsize,bigcells,cellstart,cellsize,n) is an *
* auxiliary procedure to make a list of all the large cells in the current *
* partition. On entry, ptn, level and n have their usual meanings, *
* while minsize is the smallest size of an interesting cell. On return, *
* bigcells is the number of cells of size at least minsize, cellstart[0...] *
* contains their starting positions in ptn, and cellsize[0...] contain *
* their sizes. These two arrays are in increasing order of cell size, *
* then position. *
* *
*****************************************************************************/
void
getbigcells(int *ptn, int level, int minsize, int *bigcells,
int *cellstart, int *cellsize, int n)
{
int cell1,cell2,j;
int si,st;
int bc,i,h;
bc = 0;
for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{
for (cell2 = cell1; ptn[cell2] > level; ++cell2) {}
if (cell2 >= cell1 + minsize - 1)
{
cellstart[bc] = cell1;
cellsize[bc] = cell2 - cell1 + 1;
++bc;
}
}
*bigcells = bc;
j = bc / 3;
h = 1;
do
h = 3 * h + 1;
while (h < j);
do /* shell sort */
{
for (i = h; i < bc; ++i)
{
st = cellstart[i];
si = cellsize[i];
for (j = i; cellsize[j-h] > si ||
(cellsize[j-h] == si && cellstart[j-h] > st); )
{
cellsize[j] = cellsize[j-h];
cellstart[j] = cellstart[j-h];
if ((j -= h) < h) break;
}
cellsize[j] = si;
cellstart[j] = st;
}
h /= 3;
}
while (h > 0);
}
/*****************************************************************************
* *
* celltrips() assigns to each vertex v a value depending on the set of *
* weights w(v,v1,v2), where w(v,v1,v2) depends on the number of vertices *
* adjacent to an odd number of {v,v1,v2}. {v,v1,v2} are constrained to *
* belong to the same cell. We try the cells in increasing order of size, *
* and stop as soon as any cell splits. *
* *
*****************************************************************************/
void
celltrips(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int i,pc;
setword sw;
set *gw;
int wt;
int v,iv,v1,iv1,v2,iv2;
int icell,bigcells,cell1,cell2;
int *cellstart,*cellsize;
set *gv;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"celltrips");
DYNALLOC1(int,workshort,workshort_sz,n+2,"celltrips");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/2);
getbigcells(ptn,level,3,&bigcells,cellstart,cellsize,n);
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1;
for (iv = cell1; iv <= cell2 - 2; ++iv)
{
v = lab[iv];
gv = GRAPHROW(g,v,m);
for (iv1 = iv + 1; iv1 <= cell2 - 1; ++iv1)
{
v1 = lab[iv1];
gw = GRAPHROW(g,v1,m);
for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i];
for (iv2 = iv1 + 1; iv2 <= cell2; ++iv2)
{
v2 = lab[iv2];
gw = GRAPHROW(g,v2,m);
pc = 0;
for (i = M; --i >= 0;)
if ((sw = workset[i] ^ gw[i]) != 0)
pc += POPCOUNT(sw);
wt = FUZZ1(pc);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
}
}
}
wt = invar[lab[cell1]];
for (i = cell1 + 1; i <= cell2; ++i)
if (invar[lab[i]] != wt) return;
}
}
/*****************************************************************************
* *
* cellquads() assigns to each vertex v a value depending on the set of *
* weights w(v,v1,v2,v3), where w(v,v1,v2,v3) depends on the number of *
* vertices adjacent to an odd number of {v,v1,v2,v3}. {v,v1,v2,v3} are *
* constrained to belong to the same cell. We try the cells in increasing *
* order of size, and stop as soon as any cell splits. *
* *
*****************************************************************************/
void
cellquads(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int i,pc;
setword sw;
set *gw;
int wt;
int v,iv,v1,iv1,v2,iv2,v3,iv3;
int icell,bigcells,cell1,cell2;
int *cellstart,*cellsize;
set *gv;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"cellquads");
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellquads");
DYNALLOC1(set,ws1,ws1_sz,m,"cellquads");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/2);
getbigcells(ptn,level,4,&bigcells,cellstart,cellsize,n);
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1;
for (iv = cell1; iv <= cell2 - 3; ++iv)
{
v = lab[iv];
gv = GRAPHROW(g,v,m);
for (iv1 = iv + 1; iv1 <= cell2 - 2; ++iv1)
{
v1 = lab[iv1];
gw = GRAPHROW(g,v1,m);
for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i];
for (iv2 = iv1 + 1; iv2 <= cell2 - 1; ++iv2)
{
v2 = lab[iv2];
gw = GRAPHROW(g,v2,m);
for (i = M; --i >= 0;) ws1[i] = workset[i] ^ gw[i];
for (iv3 = iv2 + 1; iv3 <= cell2; ++iv3)
{
v3 = lab[iv3];
gw = GRAPHROW(g,v3,m);
pc = 0;
for (i = M; --i >= 0;)
if ((sw = ws1[i] ^ gw[i]) != 0)
pc += POPCOUNT(sw);
wt = FUZZ1(pc);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
ACCUM(invar[v3],wt);
}
}
}
}
wt = invar[lab[cell1]];
for (i = cell1 + 1; i <= cell2; ++i)
if (invar[lab[i]] != wt) return;
}
}
/*****************************************************************************
* *
* cellquins() assigns to each vertex v a value depending on the set of *
* weights w(v,v1,v2,v3,v4), where w(v,v1,v2,v3,v4) depends on the number *
* of vertices adjacent to an odd number of {v,v1,v2,v3,v4}. *
* {v,v1,v2,v3,v4} are constrained to belong to the same cell. We try the *
* cells in increasing order of size, and stop as soon as any cell splits. *
* *
*****************************************************************************/
void
cellquins(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int i,pc;
setword sw;
set *gw;
int wt;
int v,iv,v1,iv1,v2,iv2,v3,iv3,v4,iv4;
int icell,bigcells,cell1,cell2;
int *cellstart,*cellsize;
set *gv;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"cellquins");
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellquins");
DYNALLOC1(set,ws1,ws1_sz,m,"cellquins");
DYNALLOC1(set,ws2,ws2_sz,m,"cellquins");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/2);
getbigcells(ptn,level,5,&bigcells,cellstart,cellsize,n);
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1;
for (iv = cell1; iv <= cell2 - 4; ++iv)
{
v = lab[iv];
gv = GRAPHROW(g,v,m);
for (iv1 = iv + 1; iv1 <= cell2 - 3; ++iv1)
{
v1 = lab[iv1];
gw = GRAPHROW(g,v1,m);
for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i];
for (iv2 = iv1 + 1; iv2 <= cell2 - 2; ++iv2)
{
v2 = lab[iv2];
gw = GRAPHROW(g,v2,m);
for (i = M; --i >= 0;) ws1[i] = workset[i] ^ gw[i];
for (iv3 = iv2 + 1; iv3 <= cell2 - 1; ++iv3)
{
v3 = lab[iv3];
gw = GRAPHROW(g,v3,m);
for (i = M; --i >= 0;) ws2[i] = ws1[i] ^ gw[i];
for (iv4 = iv3 + 1; iv4 <= cell2; ++iv4)
{
v4 = lab[iv4];
gw = GRAPHROW(g,v4,m);
pc = 0;
for (i = M; --i >= 0;)
if ((sw = ws2[i] ^ gw[i]) != 0)
pc += POPCOUNT(sw);
wt = FUZZ1(pc);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
ACCUM(invar[v3],wt);
ACCUM(invar[v4],wt);
}
}
}
}
}
wt = invar[lab[cell1]];
for (i = cell1 + 1; i <= cell2; ++i)
if (invar[lab[i]] != wt) return;
}
}
/*****************************************************************************
* *
* uniqinter(s1,s2,m) returns the number in both sets if it is unique, *
* or -1 if there is none or it is not unique. *
*****************************************************************************/
static int
uniqinter(set *s1, set *s2, int m)
{
int i,j;
setword w;
for (i = 0; i < M; ++i)
{
if ((w = s1[i] & s2[i]) != 0)
{
j = FIRSTBITNZ(w);
if (w != BITT[j]) return -1;
j += TIMESWORDSIZE(i);
for (++i; i < M; ++i)
if (s1[i] & s2[i]) return -1;
return j;
}
}
return -1;
}
/*****************************************************************************
* *
* cellfano2() assigns to each vertex v a value depending on the set of *
* weights w(v,v1,v2,v3), where w(v,v1,v2,v3) depends on the number of *
* fano-plane analogues containing {v,v1,v2,v3}. {v,v1,v2,v3} are *
* constrained to belong to the same cell and being independent and *
* non-collinear. We try the cells in increasing order of size, and stop *
* as soon as any cell splits. *
* *
*****************************************************************************/
void
cellfano2(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int i,pc;
setword sw;
int wt;
int v0,v1,v2,v3,iv0,iv1,iv2,iv3;
int icell,bigcells,cell1,cell2;
int *cellstart,*cellsize;
int nw,x01,x02,x03,x12,x13,x23;
int pnt0,pnt1,pnt2;
set *gv0,*gv1,*gv2,*gv3;
set *gp0,*gp1,*gp2;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellfano2");
DYNALLOC1(int,vv,vv_sz,n,"cellfano2");
DYNALLOC1(int,ww,ww_sz,n,"cellfano2");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/2);
getbigcells(ptn,level,4,&bigcells,cellstart,cellsize,n);
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1;
for (iv0 = cell1; iv0 <= cell2 - 3; ++iv0)
{
v0 = lab[iv0];
gv0 = GRAPHROW(g,v0,m);
nw = 0;
for (iv1 = iv0 + 1; iv1 <= cell2; ++iv1)
{
v1 = lab[iv1];
if (ISELEMENT(gv0,v1)) continue;
if ((x01 = uniqinter(gv0,GRAPHROW(g,v1,m),m)) < 0) continue;
vv[nw] = v1;
ww[nw] = x01;
++nw;
}
for (iv1 = 0; iv1 < nw-2; ++iv1)
{
v1 = vv[iv1];
gv1 = GRAPHROW(g,v1,m);
x01 = ww[iv1];
for (iv2 = iv1 + 1; iv2 < nw-1; ++iv2)
{
x02 = ww[iv2];
if (x02 == x01) continue;
v2 = vv[iv2];
if (ISELEMENT(gv1,v2)) continue;
gv2 = GRAPHROW(g,v2,m);
if ((x12 = uniqinter(gv1,gv2,m)) < 0) continue;
for (iv3 = iv2 + 1; iv3 < nw; ++iv3)
{
x03 = ww[iv3];
if (x03 == x01 || x03 == x02) continue;
v3 = vv[iv3];
if (ISELEMENT(gv1,v3) || ISELEMENT(gv2,v3))
continue;
gv3 = GRAPHROW(g,v3,m);
if ((x13 = uniqinter(gv1,gv3,m)) < 0) continue;
if ((x23 = uniqinter(gv2,gv3,m)) < 0
|| x23 == x13) continue;
if ((pnt0 = uniqinter(GRAPHROW(g,x01,m),
GRAPHROW(g,x23,m),m)) < 0)
continue;
if ((pnt1 = uniqinter(GRAPHROW(g,x02,m),
GRAPHROW(g,x13,m),m)) < 0)
continue;
if ((pnt2 = uniqinter(GRAPHROW(g,x03,m),
GRAPHROW(g,x12,m),m)) < 0)
continue;
gp0 = GRAPHROW(g,pnt0,m);
gp1 = GRAPHROW(g,pnt1,m);
gp2 = GRAPHROW(g,pnt2,m);
pc = 0;
for (i = M; --i >= 0;)
{
sw = gp0[i] & gp1[i] & gp2[i];
if (sw) pc += POPCOUNT(sw);
}
wt = FUZZ1(pc);
ACCUM(invar[v0],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
ACCUM(invar[v3],wt);
}
}
}
}
wt = invar[lab[cell1]];
for (i = cell1 + 1; i <= cell2; ++i)
if (invar[lab[i]] != wt) return;
}
}
/*****************************************************************************
* *
* setnbhd(g,m,n,w,wn) is an auxiliary routine that sets wn to the union *
* of the neighbours of the vertices in w. *
* *
*****************************************************************************/
void
setnbhd(graph *g, int m, int n, set *w, set *wn)
{
int i,j;
set *gi;
i = nextelement(w,M,-1);
if (i < 0)
{
EMPTYSET(wn,M);
return;
}
gi = GRAPHROW(g,i,M);
for (j = M; --j >= 0;) wn[j] = gi[j];
while ((i = nextelement(w,M,i)) >= 0)
{
gi = GRAPHROW(g,i,M);
for (j = M; --j >= 0;) wn[j] |= gi[j];
}
}
/*****************************************************************************
* *
* cellfano() assigns to each vertex v a value depending on the set of *
* weights w(v,v1,v2,v3), where w(v,v1,v2,v3) depends on the number of *
* fano-plane analogues containing {v,v1,v2,v3}. {v,v1,v2,v3} are *
* constrained to belong to the same cell and being independent. We try *
* the cells in increasing order of size, and stop as soon as any cell *
* splits. *
* *
*****************************************************************************/
void
cellfano(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int i,pc;
setword sw;
int wt;
int v0,v1,v2,v3,iv0,iv1,iv2,iv3;
int icell,bigcells,cell1,cell2;
int *cellstart,*cellsize;
set *gv0,*gv1,*gv2,*gv3;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellfano");
DYNALLOC1(set,w01,w01_sz,m,"cellfano");
DYNALLOC1(set,w02,w02_sz,m,"cellfano");
DYNALLOC1(set,w03,w03_sz,m,"cellfano");
DYNALLOC1(set,w12,w12_sz,m,"cellfano");
DYNALLOC1(set,w13,w13_sz,m,"cellfano");
DYNALLOC1(set,w23,w23_sz,m,"cellfano");
DYNALLOC1(set,pt0,pt0_sz,m,"cellfano");
DYNALLOC1(set,pt1,pt1_sz,m,"cellfano");
DYNALLOC1(set,pt2,pt2_sz,m,"cellfano");
DYNALLOC1(set,workset,workset_sz,m,"cellfano");
#else
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/2);
getbigcells(ptn,level,4,&bigcells,cellstart,cellsize,n);
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1;
for (iv0 = cell1; iv0 <= cell2 - 3; ++iv0)
{
v0 = lab[iv0];
gv0 = GRAPHROW(g,v0,m);
for (iv1 = iv0 + 1; iv1 <= cell2 - 2; ++iv1)
{
v1 = lab[iv1];
if (ISELEMENT(gv0,v1)) continue;
gv1 = GRAPHROW(g,v1,m);
for (i = M; --i >= 0;) workset[i] = gv0[i] & gv1[i];
setnbhd(g,m,n,workset,w01);
for (iv2 = iv1 + 1; iv2 <= cell2 - 1; ++iv2)
{
v2 = lab[iv2];
if (ISELEMENT(gv0,v2) || ISELEMENT(gv1,v2))
continue;
gv2 = GRAPHROW(g,v2,m);
for (i = M; --i >= 0;) workset[i] = gv0[i] & gv2[i];
setnbhd(g,m,n,workset,w02);
for (i = M; --i >= 0;) workset[i] = gv1[i] & gv2[i];
setnbhd(g,m,n,workset,w12);
for (iv3 = iv2 + 1; iv3 <= cell2; ++iv3)
{
v3 = lab[iv3];
if (ISELEMENT(gv0,v3) || ISELEMENT(gv1,v3) ||
ISELEMENT(gv2,v3))
continue;
gv3 = GRAPHROW(g,v3,m);
for (i = M; --i >= 0;) workset[i] = gv0[i] & gv3[i];
setnbhd(g,m,n,workset,w03);
for (i = M; --i >= 0;) workset[i] = gv1[i] & gv3[i];
setnbhd(g,m,n,workset,w13);
for (i = M; --i >= 0;) workset[i] = gv2[i] & gv3[i];
setnbhd(g,m,n,workset,w23);
for (i = M; --i >= 0;) workset[i] = w01[i] & w23[i];
setnbhd(g,m,n,workset,pt0);
for (i = M; --i >= 0;) workset[i] = w03[i] & w12[i];
setnbhd(g,m,n,workset,pt1);
for (i = M; --i >= 0;) workset[i] = w02[i] & w13[i];
setnbhd(g,m,n,workset,pt2);
pc = 0;
for (i = M; --i >= 0;)
{
sw = pt0[i] & pt1[i] & pt2[i];
if (sw) pc += POPCOUNT(sw);
}
wt = FUZZ1(pc);
ACCUM(invar[v0],wt);
ACCUM(invar[v1],wt);