LongInt Algorithm::Modular_exponentiation(LongInt a,LongInt m, LongInt r)
{
//qDebug()<<"algorithm.cpp: Modular_exponentiation"<<a<<m<<r;
if(r==0)
{
//qDebug()<<"algorithm.cpp: Modular_exponentiation :( 1 )";
return LongInt(1);
}
QVector<LongInt> part;
part<<1;
LongInt a_k(1),k(1);
while(1)
{
//qDebug()<<a_k<<a<<m;
a_k=((a_k*a)%m);
part<<a_k;
if(part.last()==1)
{
part.removeLast();
//qDebug()<<"algorithm.cpp: Modular_exponentiation :"<<part.value( ((r % LongInt(part.length()))).toInt());
return part.value( ((r % LongInt(part.length()))).toInt());
}
k+=1;
if(k>r)
{
//qDebug()<<"algorithm.cpp: Modular_exponentiation :"<<part.value( ((r % LongInt(part.length()))).toInt());
return part.value( ((r % LongInt(part.length()))).toInt());
return a_k;
}
}
}
LongInt Algorithm::Random(LongInt inf,LongInt sup)// random є [inf;sup]
{
if(inf==sup)
{
return sup;
}
if(inf>sup)
{
return -LongInt(0);
}
LongInt _a;
_a=LongInt(std::rand());
_a<<=10;
//_a/=LongInt(RAND_MAX+1);
_a=( _a % (sup-inf+1))+inf;
//qDebug()<<inf<<"<="<<_a<<"<="<<sup;
return _a;
}
Number* Rational::round(){
Number* res;
Rational* one_two = new Rational(ONE,LongInt(2));
if(sgn()>=0)//正数
res = this->add(one_two)->floor();
else
res = this->sub(one_two)->ceiling();
delete one_two;
return res;
}
APPROXMVBB_EXPORT void samplePointsGrid(Matrix3Dyn & newPoints,
const MatrixBase<Derived> & points,
const unsigned int nPoints,
OOBB & oobb) {
if(nPoints >= points.cols() || nPoints < 2) {
ApproxMVBB_ERRORMSG("Wrong arguements!")
}
newPoints.resize(3,nPoints);
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_int_distribution<unsigned int> dis(0, points.cols()-1);
//total points = bottomPoints=gridSize^2 + topPoints=gridSize^2
unsigned int gridSize = std::max( static_cast<unsigned int>( std::sqrt( static_cast<double>(nPoints) / 2.0 )) , 1U );
// Set z-Axis to longest dimension
//std::cout << oobb.m_minPoint.transpose() << std::endl;
oobb.setZAxisLongest();
unsigned int halfSampleSize = gridSize*gridSize;
std::vector< std::pair<unsigned int , PREC > > topPoints(halfSampleSize, std::pair<unsigned int,PREC>{} ); // grid of indices of the top points (indexed from 1 )
std::vector< std::pair<unsigned int , PREC > > bottomPoints(halfSampleSize, std::pair<unsigned int,PREC>{} ); // grid of indices of the bottom points (indexed from 1 )
using LongInt = long long int;
MyMatrix<LongInt>::Array2 idx; // Normalized P
//std::cout << oobb.extent() << std::endl;
//std::cout << oobb.m_minPoint.transpose() << std::endl;
Array2 dxdyInv = Array2(gridSize,gridSize) / oobb.extent().head<2>(); // in K Frame;
Vector3 K_p;
Matrix33 A_KI(oobb.m_q_KI.matrix().transpose());
// Register points in grid
auto size = points.cols();
for(unsigned int i=0; i<size; ++i) {
K_p = A_KI * points.col(i);
// get x index in grid
idx = ( (K_p - oobb.m_minPoint).head<2>().array() * dxdyInv ).template cast<LongInt>();
// map to grid
idx(0) = std::max( std::min( LongInt(gridSize-1), idx(0)), 0LL );
idx(1) = std::max( std::min( LongInt(gridSize-1), idx(1)), 0LL );
//std::cout << idx.transpose() << std::endl;
unsigned int pos = idx(0) + idx(1)*gridSize;
// Register points in grid
// if z axis of p is > topPoints[pos] -> set new top point at pos
// if z axis of p is < bottom[pos] -> set new bottom point at pos
if( topPoints[pos].first == 0) {
topPoints[pos].first = bottomPoints[pos].first = i+1;
topPoints[pos].second = bottomPoints[pos].second = K_p(2);
} else {
if( topPoints[pos].second < K_p(2) ) {
topPoints[pos].first = i+1;
topPoints[pos].second = K_p(2);
}
if( bottomPoints[pos].second > K_p(2) ) {
bottomPoints[pos].first = i+1;
bottomPoints[pos].second = K_p(2);
}
}
}
// Copy top and bottom points
unsigned int k=0;
// k does not overflow -> 2* halfSampleSize = 2*gridSize*gridSize <= nPoints;
for(unsigned int i=0; i<halfSampleSize; ++i) {
if( topPoints[i].first != 0 ) {
// comment in if you want the points top points of the grid
// Array3 a(i % gridSize,i/gridSize,oobb.m_maxPoint(2)-oobb.m_minPoint(2));
// a.head<2>()*=dxdyInv.inverse();
newPoints.col(k++) = points.col(topPoints[i].first-1); // A_KI.transpose()*(oobb.m_minPoint + a.matrix()).eval() ;
if(topPoints[i].first != bottomPoints[i].first) {
// comment in if you want the bottom points of the grid
// Array3 a(i % gridSize,i/gridSize,0);
// a.head<2>()*=dxdyInv.inverse();
newPoints.col(k++) = points.col(bottomPoints[i].first-1); // A_KI.transpose()*(oobb.m_minPoint + a.matrix()).eval() ;
}
}
}
// Add random points!
while( k < nPoints) {
newPoints.col(k++) = points.col( dis(gen) ); //= Vector3(0,0,0);//
}
}
bool operator == (const int &n) const {
return *this == LongInt(n);
}
bool Algorithm::Agrawal_Kayal_Saxena(LongInt a)
{
LongInt log_2_a=0;
LongInt _a=a;
LongInt r(2),k;
while( _a >=2)
{
_a/=2;
log_2_a += 1;
}
//+++++++++++++++1+++++++++++++++
LongInt a_=a,midle;
_a=1;
for(k=2;k <= log_2_a;k+=1)
{
_a=0;
a_=a-1;
while(1)
{
r=(a_+_a)/2;
midle=(r)^k;
if(midle==a)
{
//qDebug()<<"algorithm.cpp:"<<a<<"="<<r<<"^"<<k;
return false;
}
if(midle>a) a_=r;
if(midle<a) _a=r;
if((a_-_a)<=1) break;
}
}
//
//+++++++++++++++2+++++++++++++++
LongInt sqr_log_2=log_2_a*log_2_a;
//LongInt maxr=log_2_a^5;
bool nextR=true;
for(r=2;nextR/*&&r<maxr*/;r+=1)
{
nextR=false;
_a=1;
//qDebug()<<"\nr="<<r;
for(k=1;(!nextR)&&k<=sqr_log_2;k+=1)
{
_a=((_a*a) % r);
//qDebug()<<"algorithm.cpp:Agrawal_Kayal_Saxena"<<k<<_a;
nextR=(_a==1||_a==0);
}
}
r-=1;
//qDebug()<<"r="<<r;
//+++++++++++++++3+++++++++++++++
for(_a=r;_a>LongInt(1);_a-=1)
{
k=HCD(_a,a);
//qDebug()<<_a;
if(k==a)
{
break;
}
if(k>1)
{
return false;
}
}
//+++++++++++++++4+++++++++++++++
if(a<=r)
{
return true;
}
//
//+++++++++++++++5+++++++++++++++
k=2;
r=LongInt::Sqrt(Eulers_totient(r))*log_2_a;
//qDebug()<<"Sqrt(Eulers_totient(r))*log_2_a="<<r;
for(;k<=r;k+=1)
{
if(Modular_exponentiation(k,a,a)!=k)
{
//qDebug()<<"Modular_exponentiation("<<k<<","<<a<<","<<a<<")=\n"<<Modular_exponentiation(k,a,a);
return false;
}
}
//+++++++++++++++6+++++++++++++++
return true;
}
LongInt Algorithm::Modular_Multiplicative_Inverse(LongInt a, LongInt mod, bool* is_inverse_norm)
{
//qDebug()<<"algorithm.cpp: Inverse-"<<a<<mod;
if(a==0)
{
qDebug()<<qA<<"Inverse a==0";
return a;
}
if(a<LongInt(0))
{
a+=mod;
}
if(a>=mod)
{
a=a%mod;
}
//
LongInt t;
LongInt an_2=0,an_1=1;
LongInt invert;
LongInt b=a;
a=mod;
while(b!=1&&b!=0)
{
//qDebug()<<an_2<<an_1;
//qDebug()<<"a b:"<<a<<b;
an_2=an_2-an_1*(a/b);
invert=an_1;
an_1=an_2;
an_2=invert;
//==========algorithm=HCD(a,b)============
t=b;
b=a%b;
a=t;
//========================================
}
if(b==0&&a!=mod&&a!=1)
{
qDebug()<<"algorithm.cpp:Modular_Multiplicative_Inverse: HCD(a,mod)="<<a;
qDebug()<<"Inverse number for a does not exist";
if(is_inverse_norm!=NULL)
{
(*is_inverse_norm)=false;
}
return a;
}
//
if(an_1<LongInt(0))
{
//qDebug()<<"algorithm.cpp: inverse="<<an_1+mod;
return mod+an_1;
}
if(is_inverse_norm!=NULL)
{
(*is_inverse_norm)=true;
}
//qDebug()<<"algorithm.cpp: inverse="<<an_1;
return an_1;
}
LongInt Algorithm::Toom_Cook(LongInt a, LongInt b)
{
/*/
a=LongInt("529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450");
b=LongInt("29834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450529834750827340585463450");
qDebug()<<a.length();
LongInt z=Strassen(a,b);
/*/
//===T1===========initialization=table=and=stack===
qDebug()<<"Hello Lord of Iteration";
QStack<LongInt> U,V;
QStack<LongInt> W;
QStack<int> C;
int Index,i,j;//for iteration;
//=======================Table===========
int k=1;
int Q=2,R=1;
Table table={4,2};
QVector<Table> qv_table;
qv_table<<table<<table;
QVector<Table>::iterator iter_table;//=qv_table.begin();
int last_q=4;
qDebug()<<qA<<"\"(0)\""<<Q<<R<<table.q<<table.r;
while(a.length()>(qv_table.last().q+last_q))
{
qDebug()<<"algorithm.cpp:"<<"("+QString::number(k)+")"<<Q<<R<<table.q<<table.r;
k++;
Q+=R;
table.q*=table.r;
R++;
if(R*R<=Q)//if((R+1)^2>=Q) R++;
{
table.r*=2;
}
else R--;
last_q=qv_table.last().q;
qv_table<<table;
}
qDebug()<<"algorithm.cpp:"<<"("+QString::number(k)+")"<<Q<<R<<table.q<<table.r;
iter_table=qv_table.end();
iter_table--;
LongInt numbers[10*iter_table->r+1];
//===================T2============================
C.push(-1);
C<<a.number<<-5<<b.number;
a.clear();
b.clear();
int forSwitch=1;//iter_table--;
//====================Cycle========================
//bool isEnd=0;
while(1)
{
switch(forSwitch)
{
case 1://T3
{
k--;
iter_table--;
//qDebug()<<"K="<<k;
if(!k)
{
a.clear();
b.clear();
//qDebug()<<"C="<<C;
while(!C.isEmpty())
{
Q=C.pop();
if(Q>=0)
{
b.push_front(Q);
}
else
{
break;
}
}
//qDebug()<<"C="<<C;
while(!C.isEmpty())
{
Q=C.pop();
if(Q>=0)
{
a.push_front(Q);
}
else
{
C.push(Q);
break;
}
}
//qDebug()<<"algorithm.cpp:"<<a<<"*"<<b<<"=";
forSwitch=5;
a*=b;
//qDebug()<<"algorithm.cpp:"<<a;
}
else
{
forSwitch=2;
}
break;
}
case 2://T4 T5
{
//=====T4=========
Index=0;
numbers[0].clear();
//qDebug()<<"T4 C"<<C;
while(!C.isEmpty())
{
Q=C.pop();
if(Q>=0)
{
if(numbers[Index].length()>=iter_table->q)
{
//qDebug()<<"algorithm.cpp:("<<Index<<")"<<numbers[Index];
numbers[Index].normalization();
Index++;
numbers[Index].clear();
}
numbers[Index].push_front(Q);
}
else
{
break;
}
}
//qDebug()<<"algorithm.cpp:("<<Index<<")"<<numbers[Index];
R=iter_table->r+Index;
//qDebug()<<R;
//qDebug()<<Index;
for(j=0;j<=R;j++)
{
a=numbers[Index];
for(i=Index-1;i>=0;i--)
{
a*=j;
a+=numbers[i];
}
U<<a;
}
Index=0;
numbers[0].clear();
while(!C.isEmpty())
{
Q=C.pop();
if(Q>=0)
{
if(numbers[Index].length()>=iter_table->q)
{
//qDebug()<<"algorithm.cpp:("<<Index<<")"<<numbers[Index];
numbers[Index].normalization();
Index++;
numbers[Index].clear();
}
numbers[Index].push_front(Q);
}
else
{
C.push(Q);
break;
}
}
//qDebug()<<"algorithm.cpp:("<<Index<<")"<<numbers[Index];
//qDebug()<<Index;
for(j=0;j<=R;j++)
{
a=numbers[Index];
//qDebug()<<"algorithm.cpp:j="<<j;
for(i=Index-1;i>=0;i--)
{
a*=j;
a+=numbers[i];
}
//qDebug()<<"algorithm.cpp:a="<<a;
V<<a;
}
//qDebug()<<"algorithm.cpp:V="<<V;
//=====T5=========
if(!U.isEmpty()||!V.isEmpty())
{
C<<-2<<V.pop().number<<-5<<U.pop().number;
while(!U.isEmpty()||!V.isEmpty())
{
C<<-3<<V.pop().number<<-5<<U.pop().number;
}
}
else
{
//qDebug()<<"Error algorithm.cpp: U or V Empty";
}
//qDebug()<<"C="<<C;
b.clear();
b.push_front(-4);
W<<b;
forSwitch=1;
break;
}
case 3://T6
{
W<<a;
forSwitch=1;
//qDebug()<<"algorithm.cpp:a="<<a;
break;
}
case 4://T7 T8 T9
{
//qDebug()<<W<<"\n";
//W.clear();
//W<<-4<<10<<304<<1980<<7084<<18526;
Index=-1;
while (!W.isEmpty())
{
//b=W.pop();
Index++;
//qDebug()<<"W="<<W;
numbers[Index]=W.pop();
//qDebug()<<W.length();
if(numbers[Index]<0)
{
//qDebug()<<W.length();
Index--;
break;
}
}
//qDebug()<<W;
//=====T7=========
for(j=1;j<=Index;j++)
{
for(i=0;i<=Index-j;i++)
{
numbers[i]=(numbers[i]-numbers[i+1])/LongInt(j);
//qDebug()<<"numb"<<numbers[i]<<j;
}
//qDebug()<<numbers[Index-j+1]<<j;
}
//qDebug()<<numbers[Index-j+1];
/*/
for(i=0;i<=Index;i++)
{
qDebug()<<"(T7)numbers="<<numbers[i];
}
/*/
//=====T8=========
//qDebug()<<"";
for(j=Index-1;j>=1;j--)
{
for(i=Index-j;i>=1;i--)
{
//qDebug()<<j<<i;
numbers[i]-=numbers[i-1]*j;
}
}
/*/
for(i=0;i<=Index;i++)
{
qDebug()<<"(T8)numbers="<<numbers[i];
}
/*/
//=====T9=========
a=numbers[0];
//qDebug()<<iter_table->q;
for(i=1;i<=Index;i++)
{
a=(a<<iter_table->q)+numbers[i];
//qDebug()<<a<<a.length()<<iter_table->q<<numbers[i];
}
//qDebug()<<"";
forSwitch=5;
break;
}
case 5://T10
{
k++;
iter_table++;
if(!C.isEmpty())
switch(C.pop())
{
case -1:
{
/*/
qDebug()<<"a= "<<a;
qDebug()<<"z= "<<z;
if(a==z)
{
qDebug()<<"a=z";
}
/*/
return a;
break;
}
case -2:
{
W<<a;
forSwitch=4;
//qDebug()<<"-2";
break;
}
case -3:
{
forSwitch=3;
//qDebug()<<"-3";
break;
}
default:
{
//qDebug()<<"error";
break;
}
}
else
{
//qDebug()<<"Error algorithm.cpp: C Empty";
}
break;
}
}
}
}