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bitvector: polynomial ring over GF(2) operations

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This commit is contained in:
Jiri Pittner
2023-12-28 17:06:07 +01:00
parent c428d4650c
commit 1a38fe48ba
4 changed files with 229 additions and 18 deletions
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74
t.cc
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@@ -2852,7 +2852,7 @@ cout <<endl<<"Inverse via svd\n"<<ainv2<<endl;
cout <<"Difference of inverses = "<<(ainv-ainv2).norm()<<endl;
}
if(1)
if(0)
{
int seed;
int f=open("/dev/random",O_RDONLY);
@@ -2864,17 +2864,79 @@ int n;
cin >>n;
bitvector v(n);
v.randomize();
//do{
// cout <<v <<endl;
// v>>=1;
//}while(!v.iszero());
do{
cout <<v << " NLZ "<<v.nlz()<<" DEG "<<v.degree()<<" NTZ "<<v.ntz()<<endl;
v>>=1;
}while(!v.iszero());
cout <<v << " NLZ "<<v.nlz()<< " DEG "<<v.degree()<<" NTZ "<<v.ntz()<<endl;
v.randomize();
for(int i=0; i<n; ++i)
{
cout <<v <<endl;
cout <<v << " size "<<v.size()<<" NLZ "<<v.nlz()<< " DEG "<<v.degree()<<" NTZ "<<v.ntz()<<endl;
v<<=1;
}
cout <<v << " size "<<v.size()<<" NLZ "<<v.nlz()<< " DEG "<<v.degree()<<" NTZ "<<v.ntz()<<endl;
v.randomize();
for(int i=0; i<v.size(); ++i) cout <<(v<<i)<<endl;
}
if(1)
{
int seed;
int f=open("/dev/random",O_RDONLY);
if(sizeof(int)!=read(f,&seed,sizeof(int))) laerror("cannot read /dev/random");
close(f);
srand(seed);
int n;
cin >>n;
bitvector v(n),u(n);
u.randomize();
v.randomize();
bitvector w=u*v;
bitvector z=v*u;
cout <<u<<endl;
cout <<v<<endl;
cout <<w<<endl;
if(w!=z) laerror("error in bitvector multiplication");
if(w.degree()!=v.degree()+u.degree()) laerror("error in degree or multiplication");
cout <<w/u-v<<endl;
cout <<w%u<<endl;
cout <<w/v-u<<endl;
cout <<w%v<<endl;
if(!(w/u-v).is_zero()) laerror("error in division");
if(!(w/v-u).is_zero()) laerror("error in division");
if(!(w%u).is_zero()) laerror("error in division");
if(!(w%v).is_zero()) laerror("error in division");
cout <<w.gcd(u)-u<<endl;
cout <<w.gcd(v)-v<<endl;
if(!(w.gcd(u)-u).is_zero()) laerror("error in gcd");
if(!(w.gcd(v)-v).is_zero()) laerror("error in gcd");
u.randomize();
v.randomize();
bitvector g=u.gcd(v);
bitvector l=u.lcm(v);
cout <<u<<endl;
cout <<v<<endl;
cout <<g<<endl;
cout <<l<<endl;
cout <<l/u - v/g<<endl;
cout <<l/v - u/g<<endl;
cout <<l%u<<endl;
cout <<l%v<<endl;
cout <<u%g<<endl;
cout <<v%g<<endl;
if(!(l/u - v/g).is_zero()) laerror("error in gcd");
if(!(l/v - u/g).is_zero()) laerror("error in gcd");
if(!(l%u).is_zero()) laerror("error in gcd");
if(!(l%v).is_zero()) laerror("error in gcd");
if(!(u%g).is_zero()) laerror("error in gcd");
if(!(v%g).is_zero()) laerror("error in gcd");
}
}