Benchmark with integer 64 bits coefficients.
#include <iostream>
using namespace F4;
using namespace std;
int F4::VERBOSE=0;
#ifdef USE_OPENMP
int F4::NB_THREAD=min(8, omp_get_num_procs());
#else
int F4::NB_THREAD=1;
#endif
int64_t modulo=4294967291LL;
int cyclic6F4(bool magma)
{
cout << "#########################################################" << endl;
cout << "# CYCLIC 6 #" << endl;
cout << "#########################################################" << endl << endl;
int nbGen;
vector<Polynomial<eltType>> polCyclic6;
polCyclic6.emplace_back("x0+x1+x2+x3+x4+x5");
polCyclic6.emplace_back("x0*x1+x1*x2+x2*x3+x3*x4+x0*x5+x4*x5");
polCyclic6.emplace_back("x0*x1*x2+x1*x2*x3+x2*x3*x4+x0*x1*x5+x0*x4*x5+x3*x4*x5");
polCyclic6.emplace_back("x0*x1*x2*x3+x1*x2*x3*x4+x0*x1*x2*x5+x0*x1*x4*x5+x0*x3*x4*x5+x2*x3*x4*x5");
polCyclic6.emplace_back("x0*x1*x2*x3*x4+x0*x1*x2*x3*x5+x0*x1*x2*x4*x5+x0*x1*x3*x4*x5+x0*x2*x3*x4*x5+x1*x2*x3*x4*x5");
polCyclic6.emplace_back("x0*x1*x2*x3*x4*x5-1");
nbGen=cyclic6.f4();
if(magma)
{
cyclic6.printReducedGroebnerBasis("cyclic6", modulo);
}
return nbGen;
}
int cyclic7F4(bool magma)
{
cout << "#########################################################" << endl;
cout << "# CYCLIC 7 #" << endl;
cout << "#########################################################" << endl << endl;
int nbGen;
vector<Polynomial<eltType>> polCyclic7;
polCyclic7.emplace_back("x0+x1+x2+x3+x4+x5+x6");
polCyclic7.emplace_back("x0*x1+x1*x2+x2*x3+x3*x4+x4*x5+x0*x6+x5*x6");
polCyclic7.emplace_back("x0*x1*x2+x1*x2*x3+x2*x3*x4+x3*x4*x5+x0*x1*x6+x0*x5*x6+x4*x5*x6");
polCyclic7.emplace_back("x0*x1*x2*x3+x1*x2*x3*x4+x2*x3*x4*x5+x0*x1*x2*x6+x0*x1*x5*x6+x0*x4*x5*x6+x3*x4*x5*x6");
polCyclic7.emplace_back("x0*x1*x2*x3*x4+x1*x2*x3*x4*x5+x0*x1*x2*x3*x6+x0*x1*x2*x5*x6+x0*x1*x4*x5*x6+x0*x3*x4*x5*x6+x2*x3*x4*x5*x6");
polCyclic7.emplace_back("x0*x1*x2*x3*x4*x5+x0*x1*x2*x3*x4*x6+x0*x1*x2*x3*x5*x6+x0*x1*x2*x4*x5*x6+x0*x1*x3*x4*x5*x6+x0*x2*x3*x4*x5*x6+x1*x2*x3*x4*x5*x6");
polCyclic7.emplace_back("x0*x1*x2*x3*x4*x5*x6-1");
nbGen=cyclic7.f4();
if(magma)
{
cyclic7.printReducedGroebnerBasis("cyclic7", modulo);
}
return nbGen;
}
int cyclic8F4(bool magma)
{
cout << "#########################################################" << endl;
cout << "# CYCLIC 8 #" << endl;
cout << "#########################################################" << endl << endl;
int nbGen;
vector<Polynomial<eltType>> polCyclic8;
polCyclic8.emplace_back("x0+x1+x2+x3+x4+x5+x6+x7");
polCyclic8.emplace_back("x0*x1+x1*x2+x2*x3+x3*x4+x4*x5+x5*x6+x0*x7+x6*x7");
polCyclic8.emplace_back("x0*x1*x2+x1*x2*x3+x2*x3*x4+x3*x4*x5+x4*x5*x6+x0*x1*x7+x0*x6*x7+x5*x6*x7");
polCyclic8.emplace_back("x0*x1*x2*x3+x1*x2*x3*x4+x2*x3*x4*x5+x3*x4*x5*x6+x0*x1*x2*x7+x0*x1*x6*x7+x0*x5*x6*x7+x4*x5*x6*x7");
polCyclic8.emplace_back("x0*x1*x2*x3*x4+x1*x2*x3*x4*x5+x2*x3*x4*x5*x6+x0*x1*x2*x3*x7+x0*x1*x2*x6*x7+x0*x1*x5*x6*x7+x0*x4*x5*x6*x7+x3*x4*x5*x6*x7");
polCyclic8.emplace_back("x0*x1*x2*x3*x4*x5+x1*x2*x3*x4*x5*x6+x0*x1*x2*x3*x4*x7+x0*x1*x2*x3*x6*x7+x0*x1*x2*x5*x6*x7+x0*x1*x4*x5*x6*x7+x0*x3*x4*x5*x6*x7+x2*x3*x4*x5*x6*x7");
polCyclic8.emplace_back("x0*x1*x2*x3*x4*x5*x6+x0*x1*x2*x3*x4*x5*x7+x0*x1*x2*x3*x4*x6*x7+x0*x1*x2*x3*x5*x6*x7+x0*x1*x2*x4*x5*x6*x7+x0*x1*x3*x4*x5*x6*x7+x0*x2*x3*x4*x5*x6*x7+x1*x2*x3*x4*x5*x6*x7");
polCyclic8.emplace_back("x0*x1*x2*x3*x4*x5*x6*x7-1");
nbGen=cyclic8.f4();
if(magma)
{
cyclic8.printReducedGroebnerBasis("cyclic8", modulo);
}
return nbGen;
}
int cyclic9F4(bool magma)
{
cout << "#########################################################" << endl;
cout << "# CYCLIC 9 #" << endl;
cout << "#########################################################" << endl << endl;
int nbGen;
vector<Polynomial<eltType>> polCyclic9;
polCyclic9.emplace_back("x0+x1+x2+x3+x4+x5+x6+x7+x8");
polCyclic9.emplace_back("x0*x1+x1*x2+x2*x3+x3*x4+x4*x5+x5*x6+x6*x7+x0*x8+x7*x8");
polCyclic9.emplace_back("x0*x1*x2+x1*x2*x3+x2*x3*x4+x3*x4*x5+x4*x5*x6+x5*x6*x7+x0*x1*x8+x0*x7*x8+x6*x7*x8");
polCyclic9.emplace_back("x0*x1*x2*x3+x1*x2*x3*x4+x2*x3*x4*x5+x3*x4*x5*x6+x4*x5*x6*x7+x0*x1*x2*x8+x0*x1*x7*x8+x0*x6*x7*x8+x5*x6*x7*x8");
polCyclic9.emplace_back("x0*x1*x2*x3*x4+x1*x2*x3*x4*x5+x2*x3*x4*x5*x6+x3*x4*x5*x6*x7+x0*x1*x2*x3*x8+x0*x1*x2*x7*x8+x0*x1*x6*x7*x8+x0*x5*x6*x7*x8+x4*x5*x6*x7*x8");
polCyclic9.emplace_back("x0*x1*x2*x3*x4*x5+x1*x2*x3*x4*x5*x6+x2*x3*x4*x5*x6*x7+x0*x1*x2*x3*x4*x8+x0*x1*x2*x3*x7*x8+x0*x1*x2*x6*x7*x8+x0*x1*x5*x6*x7*x8+x0*x4*x5*x6*x7*x8+x3*x4*x5*x6*x7*x8");
polCyclic9.emplace_back("x0*x1*x2*x3*x4*x5*x6+x1*x2*x3*x4*x5*x6*x7+x0*x1*x2*x3*x4*x5*x8+x0*x1*x2*x3*x4*x7*x8+x0*x1*x2*x3*x6*x7*x8+x0*x1*x2*x5*x6*x7*x8+x0*x1*x4*x5*x6*x7*x8+x0*x3*x4*x5*x6*x7*x8+x2*x3*x4*x5*x6*x7*x8");
polCyclic9.emplace_back("x0*x1*x2*x3*x4*x5*x6*x7+x0*x1*x2*x3*x4*x5*x6*x8+x0*x1*x2*x3*x4*x5*x7*x8+x0*x1*x2*x3*x4*x6*x7*x8+x0*x1*x2*x3*x5*x6*x7*x8+x0*x1*x2*x4*x5*x6*x7*x8+x0*x1*x3*x4*x5*x6*x7*x8+x0*x2*x3*x4*x5*x6*x7*x8+x1*x2*x3*x4*x5*x6*x7*x8");
polCyclic9.emplace_back("x0*x1*x2*x3*x4*x5*x6*x7*x8-1");
nbGen=cyclic9.f4();
if(magma)
{
cyclic9.printReducedGroebnerBasis("cyclic9", modulo);
}
return nbGen;
}
int katsura9F4(bool magma)
{
cout << "#########################################################" << endl;
cout << "# KATSURA 9 #" << endl;
cout << "#########################################################" << endl << endl;
int nbGen;
vector<Polynomial<eltType>> polKatsura9;
polKatsura9.emplace_back("x0+2*x1+2*x2+2*x3+2*x4+2*x5+2*x6+2*x7+2*x8-1");
polKatsura9.emplace_back("x0^2+2*x1^2+2*x2^2+2*x3^2+2*x4^2+2*x5^2+2*x6^2+2*x7^2+2*x8^2-x0");
polKatsura9.emplace_back("2*x0*x1+2*x1*x2+2*x2*x3+2*x3*x4+2*x4*x5+2*x5*x6+2*x6*x7+2*x7*x8-x1");
polKatsura9.emplace_back("x1^2+2*x0*x2+2*x1*x3+2*x2*x4+2*x3*x5+2*x4*x6+2*x5*x7+2*x6*x8-x2");
polKatsura9.emplace_back("2*x1*x2+2*x0*x3+2*x1*x4+2*x2*x5+2*x3*x6+2*x4*x7+2*x5*x8-x3");
polKatsura9.emplace_back("x2^2+2*x1*x3+2*x0*x4+2*x1*x5+2*x2*x6+2*x3*x7+2*x4*x8-x4");
polKatsura9.emplace_back("2*x2*x3+2*x1*x4+2*x0*x5+2*x1*x6+2*x2*x7+2*x3*x8-x5");
polKatsura9.emplace_back("x3^2+2*x2*x4+2*x1*x5+2*x0*x6+2*x1*x7+2*x2*x8-x6");
polKatsura9.emplace_back("2*x3*x4+2*x2*x5+2*x1*x6+2*x0*x7+2*x1*x8-x7");
nbGen=katsura9.f4();
if(magma)
{
katsura9.printReducedGroebnerBasis("katsura9", modulo);
}
return nbGen;
}
int katsura10F4(bool magma)
{
cout << "#########################################################" << endl;
cout << "# KATSURA 10 #" << endl;
cout << "#########################################################" << endl << endl;
int nbGen;
vector<Polynomial<eltType>> polKatsura10;
polKatsura10.emplace_back("x0+2*x1+2*x2+2*x3+2*x4+2*x5+2*x6+2*x7+2*x8+2*x9-1");
polKatsura10.emplace_back("x0^2+2*x1^2+2*x2^2+2*x3^2+2*x4^2+2*x5^2+2*x6^2+2*x7^2+2*x8^2+2*x9^2-x0");
polKatsura10.emplace_back("2*x0*x1+2*x1*x2+2*x2*x3+2*x3*x4+2*x4*x5+2*x5*x6+2*x6*x7+2*x7*x8+2*x8*x9-x1");
polKatsura10.emplace_back("x1^2+2*x0*x2+2*x1*x3+2*x2*x4+2*x3*x5+2*x4*x6+2*x5*x7+2*x6*x8+2*x7*x9-x2");
polKatsura10.emplace_back("2*x1*x2+2*x0*x3+2*x1*x4+2*x2*x5+2*x3*x6+2*x4*x7+2*x5*x8+2*x6*x9-x3");
polKatsura10.emplace_back("x2^2+2*x1*x3+2*x0*x4+2*x1*x5+2*x2*x6+2*x3*x7+2*x4*x8+2*x5*x9-x4");
polKatsura10.emplace_back("2*x2*x3+2*x1*x4+2*x0*x5+2*x1*x6+2*x2*x7+2*x3*x8+2*x4*x9-x5");
polKatsura10.emplace_back("x3^2+2*x2*x4+2*x1*x5+2*x0*x6+2*x1*x7+2*x2*x8+2*x3*x9-x6");
polKatsura10.emplace_back("2*x3*x4+2*x2*x5+2*x1*x6+2*x0*x7+2*x1*x8+2*x2*x9-x7");
polKatsura10.emplace_back("x4^2+2*x3*x5+2*x2*x6+2*x1*x7+2*x0*x8+2*x1*x9-x8");
nbGen=katsura10.f4();
if(magma)
{
katsura10.printReducedGroebnerBasis("katsura10", modulo);
}
return nbGen;
}
int katsura11F4(bool magma)
{
cout << "#########################################################" << endl;
cout << "# KATSURA 11 #" << endl;
cout << "#########################################################" << endl << endl;
int nbGen;
vector<Polynomial<eltType>> polKatsura11;
polKatsura11.emplace_back("x0+2*x1+2*x2+2*x3+2*x4+2*x5+2*x6+2*x7+2*x8+2*x9+2*x10-1");
polKatsura11.emplace_back("x0^2+2*x1^2+2*x2^2+2*x3^2+2*x4^2+2*x5^2+2*x6^2+2*x7^2+2*x8^2+2*x9^2+2*x10^2-x0");
polKatsura11.emplace_back("2*x0*x1+2*x1*x2+2*x2*x3+2*x3*x4+2*x4*x5+2*x5*x6+2*x6*x7+2*x7*x8+2*x8*x9+2*x9*x10-x1");
polKatsura11.emplace_back("x1^2+2*x0*x2+2*x1*x3+2*x2*x4+2*x3*x5+2*x4*x6+2*x5*x7+2*x6*x8+2*x7*x9+2*x8*x10-x2");
polKatsura11.emplace_back("2*x1*x2+2*x0*x3+2*x1*x4+2*x2*x5+2*x3*x6+2*x4*x7+2*x5*x8+2*x6*x9+2*x7*x10-x3");
polKatsura11.emplace_back("x2^2+2*x1*x3+2*x0*x4+2*x1*x5+2*x2*x6+2*x3*x7+2*x4*x8+2*x5*x9+2*x6*x10-x4");
polKatsura11.emplace_back("2*x2*x3+2*x1*x4+2*x0*x5+2*x1*x6+2*x2*x7+2*x3*x8+2*x4*x9+2*x5*x10-x5");
polKatsura11.emplace_back("x3^2+2*x2*x4+2*x1*x5+2*x0*x6+2*x1*x7+2*x2*x8+2*x3*x9+2*x4*x10-x6");
polKatsura11.emplace_back("2*x3*x4+2*x2*x5+2*x1*x6+2*x0*x7+2*x1*x8+2*x2*x9+2*x3*x10-x7");
polKatsura11.emplace_back("x4^2+2*x3*x5+2*x2*x6+2*x1*x7+2*x0*x8+2*x1*x9+2*x2*x10-x8");
polKatsura11.emplace_back("2*x4*x5+2*x3*x6+2*x2*x7+2*x1*x8+2*x0*x9+2*x1*x10-x9");
nbGen=katsura11.f4();
if(magma)
{
katsura11.printReducedGroebnerBasis("katsura11", modulo);
}
return nbGen;
}
int katsura12F4(bool magma)
{
cout << "#########################################################" << endl;
cout << "# KATSURA 12 #" << endl;
cout << "#########################################################" << endl << endl;
int nbGen;
vector<Polynomial<eltType>> polKatsura12;
polKatsura12.emplace_back("x0+2*x1+2*x2+2*x3+2*x4+2*x5+2*x6+2*x7+2*x8+2*x9+2*x10+2*x11-1");
polKatsura12.emplace_back("x0^2+2*x1^2+2*x2^2+2*x3^2+2*x4^2+2*x5^2+2*x6^2+2*x7^2+2*x8^2+2*x9^2+2*x10^2+2*x11^2-x0");
polKatsura12.emplace_back("2*x0*x1+2*x1*x2+2*x2*x3+2*x3*x4+2*x4*x5+2*x5*x6+2*x6*x7+2*x7*x8+2*x8*x9+2*x9*x10+2*x10*x11-x1");
polKatsura12.emplace_back("x1^2+2*x0*x2+2*x1*x3+2*x2*x4+2*x3*x5+2*x4*x6+2*x5*x7+2*x6*x8+2*x7*x9+2*x8*x10+2*x9*x11-x2");
polKatsura12.emplace_back("2*x1*x2+2*x0*x3+2*x1*x4+2*x2*x5+2*x3*x6+2*x4*x7+2*x5*x8+2*x6*x9+2*x7*x10+2*x8*x11-x3");
polKatsura12.emplace_back("x2^2+2*x1*x3+2*x0*x4+2*x1*x5+2*x2*x6+2*x3*x7+2*x4*x8+2*x5*x9+2*x6*x10+2*x7*x11-x4");
polKatsura12.emplace_back("2*x2*x3+2*x1*x4+2*x0*x5+2*x1*x6+2*x2*x7+2*x3*x8+2*x4*x9+2*x5*x10+2*x6*x11-x5");
polKatsura12.emplace_back("x3^2+2*x2*x4+2*x1*x5+2*x0*x6+2*x1*x7+2*x2*x8+2*x3*x9+2*x4*x10+2*x5*x11-x6");
polKatsura12.emplace_back("2*x3*x4+2*x2*x5+2*x1*x6+2*x0*x7+2*x1*x8+2*x2*x9+2*x3*x10+2*x4*x11-x7");
polKatsura12.emplace_back("x4^2+2*x3*x5+2*x2*x6+2*x1*x7+2*x0*x8+2*x1*x9+2*x2*x10+2*x3*x11-x8");
polKatsura12.emplace_back("2*x4*x5+2*x3*x6+2*x2*x7+2*x1*x8+2*x0*x9+2*x1*x10+2*x2*x11-x9");
polKatsura12.emplace_back("x5^2+2*x4*x6+2*x3*x7+2*x2*x8+2*x1*x9+2*x0*x10+2*x1*x11-x10");
nbGen=katsura12.f4();
if(magma)
{
katsura12.printReducedGroebnerBasis("katsura12", modulo);
}
return nbGen;
}
int randomIdealF4(bool magma)
{
cout << "#########################################################" << endl;
cout << "# RANDOM 10 #" << endl;
cout << "#########################################################" << endl << endl;
int nbGen;
vector<Polynomial<eltType>> polRandomIdeal;
polRandomIdeal.emplace_back("3321501046*x1^5 + 4216465410*x1*x2^2*x3*x4 + 2865932757*x0^2*x3*x4*x5 + 3788788464*x0*x2*x4^2*x5 + 1581014319*x1*x2*x4*x5^2 + 3084424461*x3^2*x4^2 + 3351310712*x0^2*x4*x5 + 2966593550*x0^2*x4 + 3511552994*x3*x4^2 + 723879516*x5");
polRandomIdeal.emplace_back("2990172668*x1^4*x2 + 155715702*x0*x2^3*x3 + 1144902916*x0^4*x4 + 4219786921*x1*x2^2*x3*x4 + 3945895781*x0*x1*x2*x5^2 + 179502760*x0*x2*x4*x5 + 3436179860*x2*x4^2*x5 + 3175135897*x1^2*x2 + 3694637170*x0*x3*x4 + 315970291*x3^2*x5");
polRandomIdeal.emplace_back("2801464433*x0^3*x1*x2 + 2259511787*x0^2*x3^3 + 3274964350*x0^2*x1*x3*x4 + 3346018573*x2*x3*x4^3 + 4062905208*x2^2*x3^2*x5 + 3037120434*x1^2*x4^2*x5 + 1543552908*x1^2*x4*x5^2 + 2152568847*x1*x4*x5^3 + 2527771819*x0^2*x2*x5 + 1827741362*x2*x3*x5^2");
polRandomIdeal.emplace_back("2372585190*x1^3*x2^2 + 843546292*x1*x2^3*x4 + 1830835342*x1*x4^4 + 3647353261*x0*x2^3*x5 + 1441593613*x2^2*x4^2*x5 + 2161696749*x1^3*x5^2 + 721144626*x0*x3^2*x5^2 + 2827514473*x2*x4^2*x5^2 + 1505861843*x1^2*x3^2 + 2627219029*x3^2*x5^2");
polRandomIdeal.emplace_back("1977110653*x0^4*x1 + 2132293093*x3^5 + 3411929992*x0^3*x3*x4 + 666107476*x1*x3^3*x5 + 855576284*x0^2*x1*x4*x5 + 1369827629*x1^3*x5^2 + 3804083343*x3^2*x4*x5^2 + 3657029571*x0*x3*x5^3 + 4095698964*x0^2*x2*x4 + 2073811847*x2^2*x4");
polRandomIdeal.emplace_back("1691167827*x2^2*x3^2*x4 + 494059007*x2*x3^2*x4*x5 + 235691670*x1*x4^3*x5 + 2284461611*x1^2*x2*x5^2 + 3334537854*x1*x2*x3*x5^2 + 2027318262*x3^2*x5^3 + 865640818*x1*x3*x4^2 + 1973672771*x0*x1^2 + 1291108331*x2*x3^2 + 968241936*x3^2*x5");
polRandomIdeal.emplace_back("3982484885*x1^2*x2*x4^2 + 930970978*x1*x2^2*x4^2 + 3002178393*x2^2*x4^2*x5 + 803098703*x2*x4^3*x5 + 3315200638*x0^2*x2*x5 + 2783456165*x1^2*x2*x5 + 626963622*x2^2*x3*x5 + 1411188710*x0*x3^2*x5 + 14110205*x2*x3*x5^2 + 3927669247*x4^2");
polRandomIdeal.emplace_back("918584053*x0^3*x1*x2 + 1073858013*x0*x3^3*x4 + 872803870*x0*x1*x2*x3*x5 + 4092631501*x1^3*x4*x5 + 2210825489*x1*x2^2*x4*x5 + 1869783427*x3*x4*x5^3 + 3445272271*x2*x4^3 + 2082153076*x4^4 + 1969494894*x1^3*x5 + 2022009333*x5^3");
polRandomIdeal.emplace_back("2758266573*x0*x3^4 + 371075551*x1^2*x2*x3*x4 + 3544184607*x2^4*x5 + 1974875405*x0^2*x1^2 + 18571056*x0*x2^2*x4 + 1259555927*x2*x3^2*x5 + 740166081*x2^2*x5^2 + 3059201349*x1*x3*x5^2 + 3508031906*x2*x4*x5 + 1400156252*x2*x5^2");
polRandomIdeal.emplace_back("3236514088*x1^2*x2^3 + 1114154358*x1*x2^3*x3 + 752687686*x3^4*x4 + 1276406837*x0*x1*x4^3 + 3548353877*x0^3*x4*x5 + 3375755375*x3*x5^4 + 200174983*x2*x3*x5^2 + 634766406*x2^3 + 3370377929*x0*x2*x3 + 938930957*x1*x3");
nbGen=randomIdeal.f4();
if(magma)
{
randomIdeal.printReducedGroebnerBasis("randomIdeal", modulo);
}
return nbGen;
}
int main (int argc, char **argv)
{
cout << "#########################################################" << endl;
cout << "# BENCHMARK LONG #" << endl;
cout << "#########################################################" << endl << endl;
chrono::steady_clock::time_point start;
typedef chrono::duration<int,milli> millisecs_t;
cout << NB_THREAD << " threads used " << endl << endl;
bool magma = false;
int nbGen;
ofstream file("benchmark-long.txt");
if (file)
{
file << "Benchmark for ideal with integer long type coefficient." << endl << endl << endl;
}
start=chrono::steady_clock::now();
nbGen=randomIdealF4(magma);
if (file)
{
file << "Random 10 : " << chrono::duration_cast<millisecs_t>(chrono::steady_clock::now()-start).count() << " ms (" << nbGen << " generators)" << endl << endl;
}
start=chrono::steady_clock::now();
nbGen=cyclic8F4(magma);
if (file)
{
file << "Cyclic 8 : " << chrono::duration_cast<millisecs_t>(chrono::steady_clock::now()-start).count() << " ms (" << nbGen << " generators)" << endl << endl;
}
start=chrono::steady_clock::now();
nbGen=katsura12F4(magma);
if (file)
{
file << "Katsura 12 : " << chrono::duration_cast<millisecs_t>(chrono::steady_clock::now()-start).count() << " ms (" << nbGen << " generators)" << endl << endl;
}
return 0;
}