(cache)minimal-elements-of-the-prime-numbers/code/famk.cc at main · xayahrainie4793/minimal-elements-of-the-prime-numbers · GitHub

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#include <list>
#include <cmath>
#include <string>
#include <random>
#include <algorithm>
#include <vector>
#include <iostream>
#include <fstream>
#include <time.h>
#include <stdlib.h>
#include <gmpxx.h>
#include <gmp.h>
#define cyclemax 24
using namespace std;

// code base mxlg
// tries to extend the current kernel for base with primes up to length mxlg, while starting with the families provided on the standard input file
// new found primes are gathered in a file newprimes{base}-suffix
// and families to be still analyzed are gathered in a file left{base}-suffix
// details of the exploration are send to the standard output

char tr[128]; int w[128];
using family=vector <string>;
using sint=long unsigned int; // std::vector<std::__cxx11::basic_string<char> >::size_type;
vector <string> found;
ifstream kern; ofstream result,reject,court;
sint b;
vector <sint> fact; string covering;
clock_t cpustarttime,cputime;
mpz_class nt,nprime,nlong,n1;
sint k,lgmax,nbsmall;
mpz_t rtt,rt1,rt2;
random_device rd;
mt19937 gen(rd()); // set random gen

string s10(mpz_class x)
{mpz_class y=x; int r; string s="";
while (y!=0){r=mpz_class{y%10}.get_si();y=y/10;s=tr[r]+s;}
return s;
}

string sb(mpz_class x)
{mpz_class y=x; int r; string s="";if(x==0)return "0";
while (y!=0){r=mpz_class{y%b}.get_si();y=y/b;s=tr[r]+s;}
return s;
}

string familystrip(family f)
{string ss; sint i;
ss="";
for(i=0;i<f.size();i=i+2)ss=ss+f[i];
return(ss);
}

string stringf(family f)
{sint i; string s;if(f.size()==1)return f[0];
if(f.size()==1){s=f[0];return s;}
for(i=0;i<f.size()-2;i=i+2)s=s+f[i]+"{"+f[i+1]+"}";
s=s+f[i];
return s;
}

long long gcd(long long i,long long j)
{long long ii,jj,kk; if(i==0)return j;if(j==0)return i;
if(j>i){ii=j;jj=i;} else {ii=i;jj=j;}
while(jj!=0){kk=ii%jj;ii=jj;jj=kk;}
return ii;}

mpz_class gcd(mpz_class i,mpz_class j)
{mpz_class ii,jj,kk; if(i==0)return j;if(j==0)return i;
if(j>i){ii=j;jj=i;} else {ii=i;jj=j;}
while(jj!=0){kk=ii%jj;ii=jj;jj=kk;}
return ii;}

int min( int i, int j)
{if(i<=j)return i;else return j;}

void buildfact()
{sint kk,n; bool ok;
fact.push_back(2);fact.push_back(3);fact.push_back(5);
for(n=7;n<b*b*b;n++)
{ok=true;for(kk=0;fact[kk]*fact[kk]<=n;kk++)
if(n%fact[kk]==0){ok=false;break;}
if(ok){fact.push_back(n);}
}
for(nbsmall=0;fact[nbsmall]<b*b;nbsmall++)continue;
}

bool cover(string el)
// checks if some member of found is a substring of el
{sint i,j,it;
for(it=0;it!=found.size();it++)
{if(el==found[it]){covering=found[it];return true;}
if(el.length()<found[it].length())continue;
i=0;j=0;
while(i<el.length())
{if(el[i]==(found[it])[j])
{i++;j++;if(j>=(found[it]).length()){covering=found[it];return true;}
if(i>=el.length())break;
}
else {i++;if(i>=el.length())break;}
}
}
return false;
}

bool newprime(string s)
{sint i; mpz_class n1=0;
for(i=0;i<s.length();i++)n1=n1*b+w[s[i]];
if(mpz_probab_prime_p(n1.get_mpz_t(),50)>0)
{nprime++;court<<s<<"\n";found.push_back(s);court.flush();return true;}
else {return false;}
}

bool difsq(string s1,int y,string s2)
{sint i; mpz_class bb,bx,xb,yb,zy,gg,xx,yy,zz,z1,z2; bool test;
xb=0;yb=0;bx=1;bb=b;zy=y;
if(!mpz_root(rtt,bb.get_mpz_t(),2))return false;
for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
for(i=0;i<s2.size();i++)bx=bx*b;
gg=gcd(zy,bb-1);
xx=(y+(b-1)*xb)/gg;
if(!mpz_root(rtt,xx.get_mpz_t(),2))return false;
yy=(bx*y-(b-1)*yb)/gg;
if(!mpz_root(rtt,yy.get_mpz_t(),2))return false;
z2=mpz_class(rtt);
zz=bx*xx;
mpz_root(rtt,zz.get_mpz_t(),2);
z1=mpz_class(rtt);
test=(z1-z2)>((b-1)/gg);
if(test)
{cout<<s1<<"{"<<tr[y]<<"}"<<s2<<" is a difference of squares "
<<b<<", "<<xx<<" and "<<yy<<"\n"; return true;}
return false;
}

bool p4p4p4b(string s1,int y,string s2)
// checks if we have a factorisation of x^4+4.y^4 for {d}
{sint i; mpz_class bb,bx,xb,yb,zy,gg,xx,yy,zz,z1,z2; bool t1,t2;
xb=0;yb=0;bx=1;bb=b;zy=y;
if(!mpz_root(rtt,bb.get_mpz_t(),4))return false;
for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
for(i=0;i<s2.size();i++)bx=bx*b;
gg=gcd(zy,bb-1);
xx=(y+(b-1)*xb)/gg;
yy=((b-1)*yb-bx*y)/gg;if(yy<=0)return false;
if(xx%4==0){z1=xx/4; t1=mpz_root(rt1,z1.get_mpz_t(),4);
t2=mpz_root(rt2,yy.get_mpz_t(),4);
if(t1&&t2)
{cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" has a Germain's factorisation ("
<<z1<<","<<yy<<")\n";return true;}
}
if(yy%4==0){z2=yy/4; t1=mpz_root(rt2,z2.get_mpz_t(),4);
t2=mpz_root(rt2,xx.get_mpz_t(),4);
if(t1&&t2)
{cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" has a Germain's factorisation ("
<<xx<<","<<z2<<")\n";return true;}
}
return false;
}

bool p4p4p4bb(string s1,string sddk,string s2)
// checks if we have a factorisation of x^4+4.y^4 for {dd} or {dddd}
{sint i,k; mpz_class bb,bx,xb,yb,y,gg,xx,yy,zz,z1,z2; bool t1,t2;

xb=0;yb=0;bx=1;y=0;k=sddk.size();for(i=0;i<k;i++)y=y*b+w[sddk[i]];
bb=b;if(k==2)if(!mpz_root(rtt,bb.get_mpz_t(),2))return false;
if(s2.size()%k!=0)
{for(i=0;i<s2.size()%k;i++){s2=sddk[0]+s2;
if(cover(s1+s2))return false;
if(newprime(s1+s2))return false;}
for(i=i;i<k;i++){s1=s1+sddk[0];
if(cover(s1+s2))return false;
if(newprime(s1+s2))return false;}
}
for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
for(i=0;i<s2.size();i++)bx=bx*b;
gg=gcd(y,bx-1);
xx=(y+(bx-1)*xb)/gg;
yy=((bx-1)*yb-bx*y)/gg;if(yy<=0)return false;
if(xx%4==0){z1=xx/4; t1=mpz_root(rt1,z1.get_mpz_t(),4);
t2=mpz_root(rt2,yy.get_mpz_t(),4);
if(t1&&t2)
{cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" has a Germain's factorisation ("
<<z1<<","<<yy<<")\n";return true;}
}
if(yy%4==0){z2=yy/4; t1=mpz_root(rt2,z2.get_mpz_t(),4);
t2=mpz_root(rt2,xx.get_mpz_t(),4);
if(t1&&t2)
{cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" has a Germain's factorisation ("
<<xx<<","<<z2<<")\n";return true;}
}
return false;
}

bool difpowb(string s1,int y,string s2,int k)
{sint i; mpz_class bb,bx,xb,yb,zy,gg,xx,yy,zz,rt,rtk,z1,z2; bool test;
xb=0;yb=0;bx=1;bb=b;zy=y;
if(!mpz_root(rtt,bb.get_mpz_t(),k))return false;
for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
for(i=0;i<s2.size();i++)bx=bx*b;
gg=gcd(zy,bb-1);
xx=(y+(b-1)*xb)/gg;
if(!mpz_root(rtt,xx.get_mpz_t(),k))return false;
yy=(bx*y-(b-1)*yb)/gg;
if(yy<0&&k%2==0)return false;
if(!mpz_root(rtt,yy.get_mpz_t(),k))return false;
zz=bx*xx;
mpz_root(rt1,zz.get_mpz_t(),k);z1=mpz_class(rt1);
mpz_root(rt2,yy.get_mpz_t(),k);z2=mpz_class(rt2);
test=(z1-z2)>((b-1)/gg);
if(test)
{cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" is a difference of "
<<k<<"th powers: "<<b<<"^*."<<xx<<" and "<<yy<<"\n";
return true;}
return false;
}

bool difpowbb(string s1,string sddk,string s2)
{sint i,k; mpz_class bb,bx,xb,yb,y,gg,xx,yy,zz,rt,rtk,z1,z2; bool test;
xb=0;yb=0;bx=1;y=0;k=sddk.size();for(i=0;i<k;i++)y=y*b+w[sddk[i]];
bb=1;for(i=0;i<k;i++){bb=bb*b;}
if(s2.size()%k!=0)
{for(i=0;i<s2.size()%k;i++){s2=sddk[0]+s2;
if(cover(s1+s2))return false;
if(newprime(s1+s2))return false;}
for(i=i;i<k;i++){s1=s1+sddk[0];
if(cover(s1+s2))return false;
if(newprime(s1+s2))return false;}
}
for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
for(i=0;i<s2.size();i++)bx=bx*b;
gg=gcd(y,bb-1);
xx=(y+(bb-1)*xb)/gg;
if(!mpz_root(rtt,xx.get_mpz_t(),k)){return false;}
yy=(bx*y-(bb-1)*yb)/gg;
if(yy<0&&k%2==0)return false;
if(!mpz_root(rtt,yy.get_mpz_t(),k))return false;
zz=bx*xx;
mpz_root(rt1,zz.get_mpz_t(),k);z1=mpz_class(rt1);
mpz_root(rt2,yy.get_mpz_t(),k);z2=mpz_class(rt2);
test=(z1-z2)>((bb-1)/gg);
if(test)
{cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" is a difference of "
<<k<<"th powers: "<<bb<<", "<<xx<<" and "<<yy<<"\n";
return true;}
return false;
}

bool smallfactor(family f)
{sint i,ii,i1,i2;mpz_class n1;
for(ii=0;ii<nbsmall;ii++)
{i=fact[ii];n1=0;
for(i1=0;i1<f.size();i1++)
{if(i1%2==0)
{for(i2=0;i2<f[i1].size();i2++)n1=(n1*b+w[f[i1][i2]])%i;
}
else
{for(i2=0;i2<f[i1].size();i2++){if(n1!=((n1*b+w[f[i1][i2]])%i))break;}
if(i2!=f[i1].size())break;
}
}
if(i1!=f.size())continue;
if(n1==0){cout<<"small factor "<<i<<" for "<<stringf(f)<<"\n";return true;}
}
if(f.size()==3)if(f[1].size()==1)
{for(i=2;i<cyclemax;i++)if(difpowb(f[0],w[f[1][0]],f[2],i))return true;
if(p4p4p4b(f[0],w[f[1][0]],f[2]))return true;
}
return false;
ff=f;ff[ic2].erase(jc2,1);ff[ic1].erase(jc1,1);
cout<<"split2 "<<stringf(f)<<" without ("<<ic1<<","<<f[ic1][jc1]<<") and ("<<ic2<<","<<f[ic2][jc2]<<")-ext="<<lc2<<"\n";
handelf(ff);fff=ff;
ff.insert(ff.begin()+ic1+1,p1);ff.insert(ff.begin()+ic1+2,ff[ic1]+f[ic1][jc1]);
cout<<"extend21 "<<stringf(f)<<" with ("<<ic1<<","<<f[ic1][jc1]<<
") and without ("<<ic2<<","<<f[ic2][jc2]<<")\n";
handelf(ff);ff=fff;
ff.insert(ff.begin()+ic2+1,p2);ff.insert(ff.begin()+ic2+2,ff[ic2]+f[ic2][jc2]);
cout<<"extend22 "<<stringf(f)<<" with ("<<ic2<<","<<f[ic2][jc2]<<
") and without ("<<ic1<<","<<f[ic1][jc1]<<")\n";
handelf(ff);ff=fff;
if(ic1!=ic2)
{ff.insert(ff.begin()+ic1+1,p1);ff.insert(ff.begin()+ic1+2,f[ic1]);
ff.insert(ff.begin()+ic2+3,p2);ff.insert(ff.begin()+ic2+4,f[ic2]);
cout<<"extend212 "<<stringf(f)<<" with ("<<ic1<<","<<f[ic1][jc1]<<
") and ("<<ic2<<","<<f[ic2][jc2]<<")\n";
handelf(ff);
} else
{ff[ic1]=ff[ic1]+p2;ff.insert(ff.begin()+ic1+1,p1);ff.insert(ff.begin()+ic1+2,fff[ic1]+p1);
ff.insert(ff.begin()+ic2+3,p2);ff.insert(ff.begin()+ic2+4,f[ic2]);
cout<<"extend212 "<<stringf(f)<<" with ("<<ic1<<","<<f[ic1][jc1]<<
") and ("<<ic2<<","<<f[ic2][jc2]<<")\n";
handelf(ff);ff=fff;
ff[ic1]=ff[ic1]+p1;ff.insert(ff.begin()+ic1+1,p2);ff.insert(ff.begin()+ic1+2,fff[ic2]+p2);
ff.insert(ff.begin()+ic2+3,p1);ff.insert(ff.begin()+ic2+4,f[ic1]);
cout<<"extend221 "<<stringf(f)<<" with ("<<ic1<<","<<f[ic1][jc2]<<
") and ("<<ic2<<","<<f[ic2][jc1]<<")\n";
handelf(ff);
}
}

} // fin du traitement de la base

int main(int argc, char *argv[])
{string ms,pref,prefms,p,ss,chunkl,chunkr; family f;
sint i,ilb,ilh,irb,irh,il,ir,j;
mpz_init(rtt); mpz_init(rt1); mpz_init(rt2);
ms=argv[1];b=atoi(argv[1]); lgmax=atoi(argv[2]);
pref="kernel"; prefms=pref+ms;
kern.open(prefms.c_str());
pref="result"; prefms=pref+ms;
result.open(prefms.c_str(),ios::out);
pref="newprimes"; prefms=pref+ms;
court.open(prefms.c_str(),ios::out);
pref="left"; prefms=pref+ms;
reject.open(prefms.c_str(),ios::out);
for(char c='0';c<='9';c++){w[c]=0+c-'0';tr[0+c-'0']=c;}
for(char c='A';c<='Z';c++){w[c]=10+c-'A';tr[10+c-'A']=c;}
for(char c='a';c<='z';c++){w[c]=36+c-'a';tr[36+c-'a']=c;}
buildfact();
cout<<"lgmax="<<lgmax<<"\n";cout.flush();
found.clear();nt=0;nprime=0;nlong=0;
while(kern>>p)
{found.push_back(p);
}
// initialisation
cpustarttime=clock();
while(cin>>p)
{f.clear();ss="";
for(i=0;i<p.length();i++)
{if(p[i]=='{'||p[i]=='}'){f.push_back(ss);ss="";} else ss=ss+p[i];}
f.push_back(ss);
//construction of the familles to be explored
handelf(f);
}

cputime = clock()-cpustarttime; cputime=cputime/1000000;
result<<"\nFinally, in "<<cputime<<" time units, we explored "
<<nt<<" families of numbers for base "<<b;
if(chunkl!="")result<<" and the initial digit "<<chunkl;
if(chunkr!="")result<<" and the terminal digit "<<chunkr;
result<<"\nthere remains "<<nprime<<" primes to incorporate in the kernel, and "
<<nlong<<" families to analyse\n";
} // end main