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goodsets128.c
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/* This program calculates goodsets for a tensor of structure constants.
* The tensor is input from a file. First line contains rank of tensor.
* Next rank^3 lines describe the tensor, one entry per line
*
* Maximum rank and order are compile time options for performance reason.
* Fastest options - rank limited to 64, order limited to 256.
*/
#include <stdlib.h>
#include <stdio.h>
#include <unistd.h>
#include <string.h>
#include <inttypes.h>
#include <pthread.h>
#include <limits.h>
#ifdef H128
#include "setops128.h"
#else
#include "setops.h"
#endif
#define MAXRANK 64
#ifndef ORDER16
#define ORDERTYPE uint8_t
#define MAXORDER 256
#define MASKSSIZE 256
#else
#define ORDERTYPE uint16_t
#define MAXORDER 65536
#define MASKSSIZE 16
#endif
#define ORDERMASK ((uint64_t)MAXORDER-1)
#define ORDERSPER (sizeof(long)/sizeof(ORDERTYPE))
#define ORDERBITS (sizeof(long)*sizeof(ORDERTYPE))
#define NRMASKS (1<<ORDERSPER)
#define BITSMASK (NRMASKS-1)
#define MAXTHREADS 16
pthread_t threads[MAXTHREADS];
struct threadparam {
set s_start;
set s_end;
char a_work[MAXRANK+1];
int stat;
set *output;
} params[MAXTHREADS];
pthread_mutex_t mutex;
pthread_cond_t cond;
ORDERTYPE tensor[MAXRANK][MAXRANK][MAXRANK];
ORDERTYPE dtensor_l[MAXRANK][MAXRANK][MAXRANK][MAXRANK];
static set *symsets;
static int mates[MAXRANK];
static int rank, srank, arank;
static int ur;
static set ref, sym, anti;
int verygood;
unsigned long masks[MAXORDER];
unsigned long bits[MASKSSIZE];
int readtensor(FILE *f) {
int i,j,k;
fscanf(f,"%d\n", &rank);
if(rank>MAXRANK) {
fprintf(stderr, "Error: Rank larger than %i.\n",MAXRANK);
exit(1);
}
ur=((rank-1)*sizeof(ORDERTYPE)/sizeof(long))+1;
for(i=0;i<rank;i++)for(j=0;j<rank;j++)for(k=0;k<rank;k++)
fscanf(f,"%d\n", &tensor[i][j][k]);
SET_EMPTY(ref);
for(i=0;i<rank;i++)
if(tensor[i][i][i]!=0) {
int r=1;
for(j=0;j<rank;j++) {
if ((j!=i)&&tensor[i][i][j]) {
r=0;
break;
}
}
if(r) UNITE(ref,BITN(i));
}
SET_EMPTY(sym);
for(i=0;i<rank;i++) {
if(!IS_IN(ref,i)) {
int r=0;
for(j=0;j<rank;j++) {
if(IS_IN(ref,j)&&tensor[i][i][j]) {
r=1;
break;
}
}
if(r) UNITE(sym,BITN(i));
}
}
anti=DIFFERENCE(NBITS(rank),UNION(ref,sym));
for(i=0;i<rank;i++) {
for(j=0;j<rank;j++) {
int r=0;
for(k=0;k<rank;k++) {
if(IS_IN(ref,k)&&tensor[i][j][k]) {
r=1;
break;
}
}
if(r) {
mates[i]=j;
break;
}
}
}
srank=SIZE(sym)+SIZE(anti)/2;
arank=SIZE(anti)/2;
return 0;
}
/*
* Calculates s^2, given (s-{i})^2 or (sU{i})^2.
* dtensor_l[i][j][k] is {i}{j,k}+{j,k}{i}.
* Here i,j,k represents symmetric basic sets, that is symmetric relation or
* unions of antisymmetric pairs.
*/
void mul_sq(ORDERTYPE *mulres, set s, int difbit) {
unsigned long *m=(unsigned long *)mulres;
if(IS_IN(s,difbit)) {
int i,j,l;
l=0;
s=SYMDIF(s,BITN(difbit));
for(i=0;i<rank;i++)
if(IS_IN(s,i)) {
if(l) {
int k;
unsigned long *p = (unsigned long *)dtensor_l[difbit][j][i];
for(k=0;k<ur;k++) {
m[k]+=p[k];
}
l=0;
} else {
l=1;
j=i;
}
}
if(l) {
int k;
unsigned long *p = (unsigned long *)dtensor_l[difbit][j][j];
for(k=0;k<ur;k++) {
m[k]+=p[k];
}
}
{
int k;
unsigned long *p = (unsigned long *)dtensor_l[difbit][difbit][difbit];
for(k=0;k<ur;k++) {
m[k]+=p[k];
}
}
} else {
int i,j,l;
l=0;
for(i=0;i<rank;i++)
if(IS_IN(s,i)) {
if(l) {
int k;
unsigned long *p = (unsigned long *)dtensor_l[difbit][j][i];
for(k=0;k<ur;k++) {
m[k]-=p[k];
}
l=0;
} else {
l=1;
j=i;
}
}
if(l) {
int k;
unsigned long *p = (unsigned long *)dtensor_l[difbit][j][j];
for(k=0;k<ur;k++) {
m[k]-=p[k];
}
}
{
int k;
unsigned long *p = (unsigned long *)dtensor_l[difbit][difbit][difbit];
for(k=0;k<ur;k++) {
m[k]-=p[k];
}
}
}
}
/*
* Calculates s^2, given (s-{i})^2.
* dtensor_l[i][j][k] is {i}{j,k}+{j,k}{i}
*/
void mul_sq2(ORDERTYPE *mulres, set s, int difbit) {
unsigned long *m=(unsigned long *)mulres;
int i,j,l;
l=0;
s=DIFFERENCE(s,BITN(difbit));
for(i=0;i<rank;i++)
if(IS_IN(s,i)) {
if(l) {
int k;
unsigned long *p = (unsigned long *)dtensor_l[difbit][j][i];
for(k=0;k<ur;k++) {
m[k]+=p[k];
}
l=0;
} else {
l=1;
j=i;
}
}
if(l) {
int k;
unsigned long *p = (unsigned long *)dtensor_l[difbit][j][j];
for(k=0;k<ur;k++) {
m[k]+=p[k];
}
}
{
int k;
unsigned long *p = (unsigned long *)tensor[difbit][difbit];
for(k=0;k<ur;k++) {
m[k]+=p[k];
}
}
}
void mul(ORDERTYPE *mulres, set s, set t) {
int i,j,k;
unsigned long *m=(unsigned long *)mulres;
bzero(mulres,sizeof(ORDERTYPE)*rank);
for(i=0;i<rank;i++) for (j=0;j<rank;j++)
if(IS_IN(s,i)&&IS_IN(t,j)) {
int k;
unsigned long *p = (unsigned long *)tensor[i][j];
for(k=0;k<ur;k++) m[k]+=p[k];
}
}
/* Check whether mulres splits s */
int check_splits(ORDERTYPE *mulres, set s) {
int i,p,j;
unsigned long *m=(unsigned long *)mulres;
i=FIRST(s)-1;
p=mulres[i]&ORDERMASK;
for(j=0;j<ur;j++) {
uint64_t t;
t=m[j];
t ^= masks[p];
t &=bits[PBITS(s,j*ORDERSPER,ORDERSPER)];
if (t) {
return 1;
}
}
return 0;
}
int check_splits_partition(ORDERTYPE *mulres, set *p) {
int i;
i=1;
while(i<=SSET_SIZE(p)) {
if(check_splits(mulres,p[i])) return 1;
i++;
}
return 0;
}
int split_partition(ORDERTYPE *mulres, set *p, set *t, set nb) {
int vals[MAXRANK*MAXRANK];
set tp[MAXRANK*MAXRANK];
int i;
for(i=1;i<=SSET_SIZE(p);i++) if(check_splits(mulres, p[i])) {
int j, s, nv;
if(EQ(p[i],nb)) return 0;
nv=0;
for(j=0;j<MAXRANK;j++) if(IS_IN(p[i],j)) {
int k;
for(k=0;k<nv;k++) {
if(vals[k]==mulres[j]) {
UNITE(tp[k],BITN(j));
break;
}
}
if(k==nv) {
nv++;
tp[k]=BITN(j);
vals[k]=mulres[j];
}
}
for(j=0;j<nv;j++) SSET_ADDSET(t,tp[j]);
} else {
SSET_ADDSET(t, p[i]);
}
return 1;
}
int wl_onestep(set *p, set *t1, set nb) {
set t2[MAXRANK*MAXRANK+1];
int i,j;
ORDERTYPE mulres[MAXRANK];
SSET_SETSIZE(t2,0);
memcpy(t1, p, sizeof(set)*(SSET_SIZE(p)+1));
for(i=1;i<=SSET_SIZE(p);i++) for(j=1;j<=SSET_SIZE(p);j++) {
mul(mulres, p[i], p[j]);
SSET_SETSIZE(t2,0);
if(!split_partition(mulres, t1, t2, nb)) return 0;
if(SSET_SIZE(t2)>SSET_SIZE(t1))
memcpy(t1, t2, sizeof(set)*(SSET_SIZE(t2)+1));
}
return 1;
}
/* Stabilize p, return result in t1.
* If nb is a set of some intermediate partition and is later
* split, return 0, and t1 is undefined
*/
int wl(set *p, set *t1, set nb) {
int k;
set t2[MAXRANK*MAXRANK+1];
k=SSET_SIZE(p);
if(!wl_onestep(p, t1, nb)) return 0;
while(SSET_SIZE(t1)>k) {
k=SSET_SIZE(t1);
memcpy(t2, t1, sizeof(set)*(SSET_SIZE(t1)+1));
if(!wl_onestep(t2, t1, nb)) return 0;
}
return 1;
}
set *symgoodsets_ham(set start, set end) {
set *t, *r, t1, t2, st;
int a;
char s[1000];
ORDERTYPE mulres[MAXRANK];
t=malloc(sizeof(set)*(1000000+1));
SSET_SETSIZE(t,0);
t1=start;
st=SYMDIF(t1,SET_DIV(t1,2));
st=SYMDIF(st,BITN(FIRST(t1)-1));
SET_EMPTY(t2);
for(a=0;a<srank;a++)if(IS_IN(st,a)) UNITE(t2,symsets[a+1]);
mul(mulres, t2,t2);
NEXT(end);
do {
int st2[MAXRANK];
int c,i,j,k,r;
i=FIRST(t1)-1;
st=SYMDIF(st,BITN(i));
t2=SYMDIF(t2,symsets[i+1]);
mul_sq(mulres, st, i);
if(!check_splits( mulres, t2)) {
int q;
if(verygood) {
set t3[MAXRANK*MAXRANK+1];
set p[3];
int i;
SSET_SETSIZE(p,2);
p[1]=t2;
p[2]=DIFFERENCE(NBITS(rank),t2);
q=wl(p, t3, t2);
} else q=1;
if(q) {
SSET_ADDSET(t,t2);
if((SSET_SIZE(t) % 1000000) == 0) {
t=realloc(t,(SSET_SIZE(t)+1000001)*sizeof(set));
}
}
}
NEXT(t1);
} while(!EQ(t1,end));
return t;
}
set msets[MAXRANK][2];
int msetsi[MAXRANK][2];
int anti_maxdepth;
void antigoodsets_level(set s, const ORDERTYPE *mulres, int pos, set * res, int allz) {
ORDERTYPE mulres2[MAXRANK];
if(pos<anti_maxdepth) {
set t;
antigoodsets_level(s, mulres, pos+1, res, allz);
t=UNION(s,msets[pos][0]);
memcpy(mulres2, mulres, rank*sizeof(ORDERTYPE));
mul_sq2(mulres2, t, msetsi[pos][0]);
if(!check_splits( mulres2, t)) {
int q;
if(verygood) {
set t3[MAXRANK*MAXRANK+1];
set p[3];
int i;
SSET_SETSIZE(p,2);
p[1]=t;
p[2]=DIFFERENCE(NBITS(rank),t);
q=wl(p, t3, t);
} else q=1;
if(q) {
SSET_ADDSET(res,t);
if((SSET_SIZE(res) % 1000000) == 0) {
res=realloc(res,SSET_SIZE(res)+1000000*sizeof(set));
}
}
}
antigoodsets_level(t, mulres2, pos+1, res, 0);
if(!allz) {
t=UNION(s,msets[pos][1]);
memcpy(mulres2, mulres, rank*sizeof(ORDERTYPE));
mul_sq2(mulres2, t, msetsi[pos][1]);
if(!check_splits( mulres2, t)) {
int q;
if(verygood) {
set t3[MAXRANK*MAXRANK+1];
set p[3];
int i;
SSET_SETSIZE(p,2);
p[1]=t;
p[2]=DIFFERENCE(NBITS(rank),t);
q=wl(p, t3, t);
} else q=1;
if(q) {
SSET_ADDSET(res,t);
if((SSET_SIZE(res) % 1000000) == 0) {
res=realloc(res,SSET_SIZE(res)+1000000*sizeof(set));
}
}
}
antigoodsets_level(t, mulres2, pos+1, res,0);
}
}
}
set *antigoodsets_rec(char *in) {
int i,n;
set s;
set *t;
ORDERTYPE mulres[MAXRANK];
if(!in) in="";
n=strlen(in);
SET_EMPTY(s);
for(i=0;i<n;i++) if(in[i]!='0') UNITE(s,msets[i][in[i]-'1']);
mul(mulres, s, s);
t=malloc(sizeof(set)*1000000);
SSET_SETSIZE(t,0);
antigoodsets_level( s, mulres, n, t, IS_EMPTY(s));
return t;
}
void *symthread(void *arg) {
struct threadparam *p=(struct threadparam *)arg;
set *t;
p->output=symgoodsets_ham(p->s_start, p->s_end);
return 0;
}
void *antithread(void *arg) {
struct threadparam *p=(struct threadparam *)arg;
set *t;
p->output=antigoodsets_rec(p->a_work);
p->stat=2;
pthread_cond_signal(&cond);
return 0;
}
int main(int argc, char *argv[]) {
FILE *f;
char s[1000];
int i;
int nthreads=1;
char *as;
set *t;
char c;
set start, end;
for(i=0;i<MAXORDER;i++) {
int j;
masks[i]=0;
for(j=0;j<ORDERSPER;j++) {
masks[i]<<=ORDERBITS;
masks[i]|=i;
}
}
for(i=0;i<NRMASKS;i++) {
int j;
bits[i]=0;
for(j=0;j<ORDERSPER;j++) {
if((i>>j)&1)
bits[i]|=((1ull<<ORDERBITS)-1)<<(j*ORDERBITS);
}
}
verygood=1;
anti_maxdepth=-1;
while ((c = getopt (argc, argv, "dm:n:")) != -1) {
switch (c) {
case 'd':
verygood=0;
break;
case 'm': /* only for single thread search */
anti_maxdepth=strtol(optarg, NULL, 0);
break;
case 'n':
nthreads=strtol(optarg, NULL, 0);
break;
}
}
if(argc>optind) {
int do_anti=1,do_sym=1;
f=fopen(argv[optind],"r");
readtensor(f);
fclose(f);
if(argc>optind+1) {
do_anti=strchr(argv[optind+1],'a')!=NULL;
do_sym=strchr(argv[optind+1],'s')!=NULL;
if(do_anti){
if(argc>optind+2) {
as=argv[optind+2];
} else {
as=NULL;
}
}
if(do_sym) {
if(argc>optind+2) {
start=INT_SET(strtoull(argv[optind+2],NULL,0));
if(argc>optind+3) {
end=INT_SET(strtoull(argv[optind+3],NULL,0));
if((!BEFORE_EQ(start,end))||(!BEFORE_EQ(end,NBITS(srank))))
end=NBITS(srank);
} else {
end=NBITS(srank);
}
} else {
start=BITN(0);
end=NBITS(srank);
}
}
} else {
start=BITN(0);
end=NBITS(srank);
as=NULL;
}
#if 0
fprintf(stderr, "rank=%i srank=%i\n", rank, srank);
gapset(ref, s);
fprintf(stderr, "%s\n",s);
gapset(sym,s);
fprintf(stderr, "%s\n",s);
gapset(anti,s);
fprintf(stderr, "%s\n",s);
for(i=0;i<rank;i++) fprintf(stderr, " %i %i\n", i+1,mates[i]+1);
#endif
if(nthreads>1) {
pthread_mutex_init(&mutex, NULL);
pthread_cond_init (&cond, NULL);
}
if(do_sym) {
int i,j,k,l;
set t1,t2;
symsets=malloc(sizeof(set)*(MAXRANK+1));
SSET_SETSIZE(symsets, 0);
for(i=0;i<rank;i++)
if(!IS_IN(ref,i) && (mates[i]>=i)) {
SSET_SETSIZE(symsets, SSET_SIZE(symsets)+1);
symsets[SSET_SIZE(symsets)]=BITN(i);
UNITE(symsets[SSET_SIZE(symsets)],BITN(mates[i]));
}
#if 0
for(i=1;i<=SSET_SIZE(symsets);i++) {
gapset(symsets[i],s);
fprintf(stderr, "%s ",s);
}
fprintf(stderr,"\n");
#endif
for(i=0;i<srank;i++) {
int k;
t1=symsets[i+1];
for(k=0;k<srank;k++) {
int l,j;
for(l=0;l<srank;l++) {
ORDERTYPE mulres[MAXRANK];
t2=UNION(symsets[k+1],symsets[l+1]);
mul(dtensor_l[i][k][l], t1, t2);
if((l!=k)||(l!=i)) {
mul(mulres, t2, t1);
for(j=0;j<rank;j++)dtensor_l[i][k][l][j]+=mulres[j];
}
}
}
}
if((nthreads>1)&&(srank>10)) {
set d,t;
d=SET_DIV(SET_MINUS(end,start),nthreads);
t=start;
for(i=0;i<nthreads;i++) {
params[i].s_start=t;
t=SET_PLUS(t,d);
params[i].s_end=(i==nthreads-1) ? end : SET_MINUS(t,BITN(0));
pthread_create(&threads[i], NULL, symthread, ¶ms[i]);
}
for(i=0;i<nthreads;i++) {
pthread_join(threads[i],NULL);
if( SSET_SIZE(params[i].output)>0) {
gapsets(params[i].output);
fflush(stdout);
} else printf("[],\n");
}
} else {
t=symgoodsets_ham(start,end);
if( SSET_SIZE(t)>0) {
gapsets(t);
fflush(stdout);
} else printf("[],\n");
}
}
if(do_anti) {
int t1[3],t2[3];
int i,j,k,l,n;
int wrotesomething=0;
for(i=0;i<rank;i++) {
set t1;
int k;
t1=BITN(i);
for(k=0;k<rank;k++) {
set t2;
int l,j;
for(l=0;l<rank;l++) {
ORDERTYPE mulres[MAXRANK];
t2=UNION(BITN(k),BITN(l));
mul(dtensor_l[i][k][l], t1, t2);
mul(mulres, t2, t1);
for(j=0;j<rank;j++)dtensor_l[i][k][l][j]+=mulres[j];
}
}
}
n=0;
for(i=0;i<rank;i++)
if(mates[i]>i) {
msets[n][0]=BITN(i);
msets[n][1]=BITN(mates[i]);
msetsi[n][0]=(i);
msetsi[n][1]=(mates[i]);
n++;
}
if((nthreads>1)&&(arank>8)) {
int i, nz, p, n, done;
char *nsf3[27]={
"100", "101", "102", "110", "111", "112", "120", "121", "122",
"200", "201", "202", "210", "211", "212", "220", "221", "222",
"001", "010", "011", "012", "002", "020", "021", "022", "000" };
char *ns3[14]={ "001", "010", "011", "012",
"100", "101", "102", "110", "111", "112", "120", "121", "122",
"000" };
char *ns4[41]={
"0102", "0110", "0111", "0112", "0120", "0121", "0122",
"1000", "1001", "1002", "1010", "1011", "1012", "1020",
"1021", "1022", "1100", "1101", "1102", "1110", "1111",
"1112", "1120", "1121", "1122", "1200", "1201", "1202",
"1210", "1211", "1212", "1220", "1221", "1222",
"0100", "0101", "0010", "0011", "0012", "0001", "0000"
};
char **st;
if(as) {
int allz=1;
char *t=as;
while(*t) {
if (*t!='0')allz=0;
t++;
}
anti_maxdepth=3+strlen(as);
if(allz) {
st=ns3;
p=14;
} else {
st=nsf3;
p=27;
}
// as itself is missed.
if(!allz){
int i,n;
set s;
set *t;
ORDERTYPE mulres[MAXRANK];
n=strlen(as);
SET_EMPTY(s);
for(i=0;i<n;i++) if(as[i]!='0') UNITE(s,msets[i][as[i]-'1']);
mul(mulres, s, s);
if(!check_splits( mulres, s)) {
int q;
if(verygood) {
set t3[MAXRANK*MAXRANK+1];
set p[3];
int i;
SSET_SETSIZE(p,2);
p[1]=s;
p[2]=DIFFERENCE(NBITS(rank),s);
q=wl(p, t3, s);
} else q=1;
if(q) {
set t[3];
SSET_SETSIZE(t,2);
t[1]=s;
SET_EMPTY(t[2]);
for(j=1;j<MAXRANK;j++) if (IS_IN(t[1],j)) UNITE(t[2],BITN(mates[j]));
gapsets(t);
wrotesomething=1;
}
}
}
} else {
anti_maxdepth=4;
st=ns4;
p=41;
}
t=antigoodsets_rec(as);
gapsets(t);
for(i=1;i<=SSET_SIZE(t);i++) {
set t1;
int j;
t1=EMPTYSET;
for(j=1;j<MAXRANK;j++) if (IS_IN(t[i],j)) UNITE(t1,BITN(mates[j]));
t[i]=t1;
}
if( SSET_SIZE(t)>0) {
gapsets(t);
wrotesomething=1;
}
fflush(stdout);
anti_maxdepth=arank;
for(i=0;i<nthreads;i++) params[i].stat=0;
n=0;
done=0;
pthread_mutex_lock(&mutex);
while(done<p) {
struct timespec tw;
for(i=0;i<nthreads;i++) if(n<p &&(params[i].stat==0)) {
params[i].stat=1;
if(as) {
strcpy(params[i].a_work,as);
strcat(params[i].a_work,st[n]);
} else {
strcpy(params[i].a_work,st[n]);
}
pthread_create(&threads[i], NULL, antithread, ¶ms[i]);
n++;
}
clock_gettime(CLOCK_REALTIME_COARSE, &tw);
tw.tv_sec+=10;
pthread_cond_timedwait(&cond, &mutex, &tw);
do {
nz=0;
for(i=0;i<nthreads;i++) if(params[i].stat==2) {
set t1;
int j,k;
nz=1;
pthread_join(threads[i],NULL);
gapsets(params[i].output);
for(k=1;k<=SSET_SIZE(params[i].output);k++) {
t1=EMPTYSET;
for(j=1;j<MAXRANK;j++) if (IS_IN(params[i].output[k],j)) UNITE(t1,BITN(mates[j]));
params[i].output[k]=t1;
}
if( SSET_SIZE(params[i].output)>0) {
gapsets(params[i].output);
wrotesomething=1;
fflush(stdout);
}
params[i].stat=0;
done++;
}
} while(nz);
}
} else { /* single thread */
set t1;
int j;
if(anti_maxdepth<1 || anti_maxdepth>arank)anti_maxdepth=arank;
t=antigoodsets_rec(as);
gapsets(t);
for(i=1;i<=SSET_SIZE(t);i++) {
t1=EMPTYSET;
for(j=1;j<MAXRANK;j++) if (IS_IN(t[i],j)) UNITE(t1,BITN(mates[j]));
t[i]=t1;
}
if( SSET_SIZE(t)>0) {
gapsets(t);
wrotesomething=1;
}
// as itself is missed.
if(as){
int i,n;
set s;
set *t;
ORDERTYPE mulres[MAXRANK];
n=strlen(as);
SET_EMPTY(s);
for(i=0;i<n;i++) if(as[i]!='0') UNITE(s,msets[i][as[i]-'1']);
if(!IS_EMPTY(s)) {
mul(mulres, s, s);
if(!check_splits( mulres, s)) {
int q;
if(verygood) {
set t3[MAXRANK*MAXRANK+1];
set p[3];
int i;
SSET_SETSIZE(p,2);
p[1]=s;
p[2]=DIFFERENCE(NBITS(rank),s);
q=wl(p, t3, s);
} else q=1;
if(q) {
set t[3];
SSET_SETSIZE(t,2);
t[1]=s;
SET_EMPTY(t[2]);
for(j=1;j<MAXRANK;j++) if (IS_IN(t[1],j)) UNITE(t[2],BITN(mates[j]));
gapsets(t);
wrotesomething=1;
}
}
}
}
}
if(!wrotesomething)printf(" [],\n");
}
}
return 0;
}