bool TShapeOrientB1::evaluate_with_hess( const MsqMatrix<2,2>& T,
double& result,
MsqMatrix<2,2>& deriv_wrt_T,
MsqMatrix<2,2> second_wrt_T[3],
MsqError& err )
{
const double norm = Frobenius(T);
const double invroot = 1.0/MSQ_SQRT_TWO;
const double tau = det(T);
if (TMetric::invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
const double inv_tau = 1.0/tau;
const double invnorm = 1.0/norm;
const double f = norm - invroot * trace(T);
result = 0.5 * inv_tau * f;
const MsqMatrix<2,2> adjt = transpose_adj(T);
deriv_wrt_T = invnorm * T;
pluseq_scaled_I( deriv_wrt_T, -invroot );
deriv_wrt_T *= 0.5;
deriv_wrt_T -= result * adjt;
deriv_wrt_T *= inv_tau;
const double a = 0.5 * inv_tau * invnorm;
set_scaled_outer_product( second_wrt_T, -a*invnorm*invnorm, T );
pluseq_scaled_I( second_wrt_T, a );
pluseq_scaled_outer_product( second_wrt_T, f*inv_tau*inv_tau*inv_tau, adjt );
pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -0.5*f*inv_tau*inv_tau, T );
pluseq_scaled_sum_outer_product( second_wrt_T, -0.5*inv_tau*inv_tau*invnorm, T, adjt );
pluseq_scaled_sum_outer_product_I( second_wrt_T, 0.5*inv_tau*inv_tau*invroot, adjt );
return true;
}
bool Target3DShape::evaluate_with_hess( const MsqMatrix<3,3>& A,
const MsqMatrix<3,3>& W,
double& result,
MsqMatrix<3,3>& deriv_wrt_A,
MsqMatrix<3,3> second_wrt_A[6],
MsqError& err )
{
MsqMatrix<3,3> Winv = inverse(W);
MsqMatrix<3,3> T = A * Winv;
double f = Frobenius(T);
double d = det(T);
result = f*f*f - 3*MSQ_SQRT_THREE*d;
deriv_wrt_A = T;
deriv_wrt_A *= f;
deriv_wrt_A -= MSQ_SQRT_THREE*transpose_adj(T);
deriv_wrt_A *= 3;
deriv_wrt_A = deriv_wrt_A * transpose(Winv);
set_scaled_2nd_deriv_of_det( second_wrt_A, -3 * MSQ_SQRT_THREE, T );
pluseq_scaled_outer_product( second_wrt_A, 3.0/f, T );
pluseq_scaled_I( second_wrt_A, 3.0*f );
second_deriv_wrt_product_factor( second_wrt_A, Winv );
return true;
}
bool Target2DShapeOrientBarrier::evaluate_with_grad( const MsqMatrix<2,2>& A,
const MsqMatrix<2,2>& W,
double& result,
MsqMatrix<2,2>& deriv,
MsqError& err )
{
const MsqMatrix<2,2> Winv = inverse(W);
const MsqMatrix<2,2> T = A * Winv;
const double norm = Frobenius(T);
const double invroot = 1.0/MSQ_SQRT_TWO;
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
const double inv_tau = 1.0/tau;
const double invnorm = 1.0/norm;
result = 0.5*inv_tau*(norm - invroot * trace(T));
deriv = invnorm * T;
deriv(0,0) -= invroot;
deriv(1,1) -= invroot;
deriv *= 0.5;
deriv -= result * transpose_adj(T);
deriv *= inv_tau;
deriv = deriv * transpose(Winv);
return true;
}
template <unsigned DIM> static inline
bool hess( const MsqMatrix<DIM,DIM>& T,
double& result,
MsqMatrix<DIM,DIM>& deriv,
MsqMatrix<DIM,DIM>* second )
{
const double norm = Frobenius(T);
const double invroot = 1.0/DimConst<DIM>::sqrt();
const double tau = det(T);
if (TMetric::invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
const double inv_tau = 1.0/tau;
const double invnorm = 1.0/norm;
const double f = norm - invroot * trace(T);
result = 0.5 * inv_tau * f;
const MsqMatrix<DIM,DIM> adjt = transpose_adj(T);
deriv = invnorm * T;
pluseq_scaled_I( deriv, -invroot );
deriv *= 0.5;
deriv -= result * adjt;
deriv *= inv_tau;
const double a = 0.5 * inv_tau * invnorm;
set_scaled_outer_product( second, -a*invnorm*invnorm, T );
pluseq_scaled_I( second, a );
pluseq_scaled_outer_product( second, f*inv_tau*inv_tau*inv_tau, adjt );
pluseq_scaled_2nd_deriv_of_det( second, -0.5*f*inv_tau*inv_tau, T );
pluseq_scaled_sum_outer_product( second, -0.5*inv_tau*inv_tau*invnorm, T, adjt );
pluseq_scaled_sum_outer_product_I( second, 0.5*inv_tau*inv_tau*invroot, adjt );
return true;
}
bool TShapeB1::evaluate_with_hess( const MsqMatrix<3,3>& T,
double& result,
MsqMatrix<3,3>& deriv_wrt_T,
MsqMatrix<3,3> second_wrt_T[6],
MsqError& err )
{
double d = det(T);
if (invalid_determinant(d)) {
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
double id = 1.0/d;
double norm = Frobenius(T);
double den = 1.0/(3 * MSQ_SQRT_THREE * d);
double norm_cube = norm*norm*norm;
result = norm_cube * den - 1.0;
MsqMatrix<3,3> adjt = transpose_adj(T);
deriv_wrt_T = T;
deriv_wrt_T *= 3 * norm * den;
deriv_wrt_T -= norm_cube * den * id * transpose_adj(T);
set_scaled_outer_product( second_wrt_T, 3 * den / norm, T );
pluseq_scaled_I( second_wrt_T, 3 * norm * den );
pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -den * norm_cube * id, T );
pluseq_scaled_outer_product( second_wrt_T, 2 * den * norm_cube * id * id , adjt );
pluseq_scaled_sum_outer_product( second_wrt_T, -3 * norm * den * id, T, adjt );
return true;
}
virtual double metric(stk_classic::mesh::Entity& element, bool& valid)
{
valid = true;
JacobianUtil jacA, jacSA, jacW;
jacSA.m_scale_to_unit = true;
double SA_ = 0.0, A_ = 0.0, W_ = 0.0; // current and reference detJ
jacA(A_, *m_eMesh, element, m_coord_field_current, m_topology_data);
jacSA(SA_, *m_eMesh, element, m_coord_field_current, m_topology_data);
jacW(W_, *m_eMesh, element, m_coord_field_original, m_topology_data);
double val=0.0, val_shape=0.0;
val_shape = 0.0;
//val_shape = std::numeric_limits<double>::max();
for (int i=0; i < jacA.m_num_nodes; i++)
{
double detAi = jacA.m_detJ[i];
double detSAi = jacSA.m_detJ[i];
//double detWi = jacW.m_detJ[i];
double FAi = Frobenius(jacA.m_detJ[i]);
double FWi = Frobenius(jacW.m_detJ[i]);
if (detAi < 0)
{
valid = false;
}
double shape_metric = 0.0;
//MsqMatrix<3,3>& A = jacA.m_J[i];
double scale_factor = (FAi < FWi ? FAi/FWi : (FAi > 1.e-6? FWi / FAi : 1.0));
scale_factor = FAi/FWi;
//scale_factor = 1.0;
//double sign_SA = (detSAi > 0.0 ? 1.0 : -1.0);
//double fac = 0.2;
//shape_metric = scale_factor* (detSAi > fac ? fac : detSAi);
shape_metric = scale_factor*detSAi;
val_shape += shape_metric;
//val_shape = std::min(val_shape, shape_metric);
//std::cout << "tmp srk i= " << i << " detAi = " << detAi << " detSAi= " << detSAi << " shape_metric= " << shape_metric << " val_shape= " << val_shape << " scale_factor= " << scale_factor << " FAi= " << FAi << " FWi= " << FWi << std::endl;
}
val = -val_shape;
//std::cout << "tmp srk val = " << val << std::endl;
return val;
}
bool Target3DShape::evaluate( const MsqMatrix<3,3>& A,
const MsqMatrix<3,3>& W,
double& result,
MsqError& )
{
MsqMatrix<3,3> T = A * inverse(W);
double f = Frobenius(T);
double d = det(T);
result = f*f*f - 3*MSQ_SQRT_THREE*d;
return true;
}
template <unsigned DIM> static inline
bool eval( const MsqMatrix<DIM,DIM>& T, double& result )
{
const double tau = det(T);
if (TMetric::invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
result = 0.5/tau * (Frobenius( T ) - trace(T)/DimConst<DIM>::sqrt());
return true;
}
bool TShapeOrientB1::evaluate( const MsqMatrix<2,2>& T,
double& result,
MsqError& err )
{
const double tau = det(T);
if (TMetric::invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
result = 0.5/tau * (Frobenius( T ) - trace(T)/MSQ_SQRT_TWO);
return true;
}
bool Target2DShapeOrientBarrier::evaluate( const MsqMatrix<2,2>& A,
const MsqMatrix<2,2>& W,
double& result,
MsqError& )
{
MsqMatrix<2,2> T = A * inverse(W);
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
result = 0.5/tau * (Frobenius( T ) - trace(T)/MSQ_SQRT_TWO);
return true;
}
bool TShapeSizeB3::evaluate( const MsqMatrix<3,3>& T,
double& result,
MsqError& err )
{
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
double n = Frobenius(T);
result = n*n*n - 3*MSQ_SQRT_THREE*( log(tau) + 1 );
return true;
}
bool TShapeB1::evaluate( const MsqMatrix<3,3>& T,
double& result,
MsqError& err)
{
double f = Frobenius(T);
double d = det(T);
double den = 3 * MSQ_SQRT_THREE * d;
if (invalid_determinant(d)) {
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
result = (f*f*f)/den - 1.0;
return true;
}
bool TShapeSize3DB4::evaluate( const MsqMatrix<3,3>& T,
double& result,
MsqError& err )
{
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
const double norm = Frobenius(T);
result = norm*norm*norm / (3*MSQ_SQRT_THREE*tau) - 1
+ mGamma * (tau + 1/tau - 2);
return true;
}
bool Target3DShape::evaluate_with_grad( const MsqMatrix<3,3>& A,
const MsqMatrix<3,3>& W,
double& result,
MsqMatrix<3,3>& deriv_wrt_A,
MsqError& err )
{
MsqMatrix<3,3> Winv = inverse(W);
MsqMatrix<3,3> T = A * Winv;
double f = Frobenius(T);
double d = det(T);
result = f*f*f - 3*MSQ_SQRT_THREE*d;
deriv_wrt_A = T;
deriv_wrt_A *= f;
deriv_wrt_A -= MSQ_SQRT_THREE*transpose_adj(T);
deriv_wrt_A *= 3;
deriv_wrt_A = deriv_wrt_A * transpose(Winv);
return true;
}
bool TShapeB1::evaluate_with_grad( const MsqMatrix<3,3>& T,
double& result,
MsqMatrix<3,3>& wrt_T,
MsqError& err )
{
double d = det(T);
if (invalid_determinant(d)) {
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
double norm = Frobenius(T);
double den = 1.0/(3 * MSQ_SQRT_THREE * d);
double norm_cube = norm*norm*norm;
result = norm_cube * den - 1.0;
wrt_T = T;
wrt_T *= 3 * norm * den;
wrt_T -= norm_cube * den/d * transpose_adj(T);
return true;
}
bool TShapeSize3DB4::evaluate_with_hess( const MsqMatrix<3,3>& T,
double& result,
MsqMatrix<3,3>& deriv,
MsqMatrix<3,3> second[6],
MsqError& err )
{
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
const double norm = Frobenius(T);
const double f = norm*norm/3.0;
const double h = 1/(MSQ_SQRT_THREE * tau);
const double g = norm * h;
const double inv_tau = 1.0/tau;
result = f * g - 1 + mGamma * (tau + inv_tau - 2);
const double g1 = mGamma * (1 - inv_tau*inv_tau);
const MsqMatrix<3,3> adjt = transpose_adj(T);
deriv = g*T;
deriv += (g1 - f*g*inv_tau) * adjt;
if (norm > 1e-50)
{
const double inv_norm = 1/norm;
set_scaled_outer_product( second, h*inv_norm, T );
pluseq_scaled_I( second, norm * h );
pluseq_scaled_2nd_deriv_of_det( second, g1 - f*g*inv_tau, T );
pluseq_scaled_outer_product( second, (f*g + mGamma*inv_tau)*2*inv_tau*inv_tau, adjt );
pluseq_scaled_sum_outer_product( second, -g*inv_tau, T, adjt );
}
else
{
std::cout << "Warning: Division by zero avoided in TShapeSize3DB4::evaluate_with_hess()" << std::endl;
}
return true;
}
bool Target2DShapeOrientBarrier::evaluate_with_hess( const MsqMatrix<2,2>& A,
const MsqMatrix<2,2>& W,
double& result,
MsqMatrix<2,2>& deriv,
MsqMatrix<2,2> second[3],
MsqError& err )
{
const MsqMatrix<2,2> Winv = inverse(W);
const MsqMatrix<2,2> T = A * Winv;
const double norm = Frobenius(T);
const double invroot = 1.0/MSQ_SQRT_TWO;
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
const double inv_tau = 1.0/tau;
const double invnorm = 1.0/norm;
const double f = norm - invroot * trace(T);
result = 0.5 * inv_tau * f;
const MsqMatrix<2,2> adjt = transpose_adj(T);
deriv = invnorm * T;
deriv(0,0) -= invroot;
deriv(1,1) -= invroot;
deriv *= 0.5;
deriv -= result * adjt;
deriv *= inv_tau;
deriv = deriv * transpose(Winv);
const double a = 0.5 * inv_tau * invnorm;
set_scaled_outer_product( second, -a*invnorm*invnorm, T );
pluseq_scaled_I( second, a );
pluseq_scaled_outer_product( second, f*inv_tau*inv_tau*inv_tau, adjt );
pluseq_scaled_2nd_deriv_of_det( second, -0.5*f*inv_tau*inv_tau );
pluseq_scaled_sum_outer_product( second, -0.5*inv_tau*inv_tau*invnorm, T, adjt );
pluseq_scaled_sum_outer_product_I( second, 0.5*inv_tau*inv_tau*invroot, adjt );
second_deriv_wrt_product_factor( second, Winv );
return true;
}
bool TShapeSizeB3::evaluate_with_grad( const MsqMatrix<3,3>& T,
double& result,
MsqMatrix<3,3>& deriv_wrt_T,
MsqError& err )
{
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
double n = Frobenius(T);
result = n*n*n - 3*MSQ_SQRT_THREE*( log(tau) + 1 );
const MsqMatrix<3,3> adjt = transpose_adj(T);
deriv_wrt_T = T;
deriv_wrt_T *= 3*n;
deriv_wrt_T -= 3*MSQ_SQRT_THREE/tau * adjt;
return true;
}
bool TShapeSize3DB4::evaluate_with_grad( const MsqMatrix<3,3>& T,
double& result,
MsqMatrix<3,3>& deriv,
MsqError& err )
{
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
const double norm = Frobenius(T);
const double f = norm*norm/3.0;
const double g = norm / (MSQ_SQRT_THREE * tau);
const double inv_tau = 1.0/tau;
result = f * g - 1 + mGamma * (tau + inv_tau - 2);
deriv = g*T;
deriv += (mGamma * (1 - inv_tau*inv_tau) - f*g*inv_tau) * transpose_adj(T);
return true;
}
bool TShapeOrientB1::evaluate_with_grad( const MsqMatrix<2,2>& T,
double& result,
MsqMatrix<2,2>& deriv_wrt_T,
MsqError& err )
{
const double norm = Frobenius(T);
const double invroot = 1.0/MSQ_SQRT_TWO;
const double tau = det(T);
if (TMetric::invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
const double inv_tau = 1.0/tau;
const double invnorm = 1.0/norm;
result = 0.5*inv_tau*(norm - invroot * trace(T));
deriv_wrt_T = invnorm * T;
pluseq_scaled_I( deriv_wrt_T, -invroot );
deriv_wrt_T *= 0.5;
deriv_wrt_T -= result * transpose_adj(T);
deriv_wrt_T *= inv_tau;
return true;
}
template <unsigned DIM> static inline
bool grad( const MsqMatrix<DIM,DIM>& T,
double& result,
MsqMatrix<DIM,DIM>& deriv )
{
const double norm = Frobenius(T);
const double invroot = 1.0/DimConst<DIM>::sqrt();
const double tau = det(T);
if (TMetric::invalid_determinant(tau)) { // barrier
result = 0.0;
return false;
}
const double inv_tau = 1.0/tau;
const double invnorm = 1.0/norm;
result = 0.5*inv_tau*(norm - invroot * trace(T));
deriv = invnorm * T;
pluseq_scaled_I( deriv, -invroot );
deriv *= 0.5;
deriv -= result * transpose_adj(T);
deriv *= inv_tau;
return true;
}
bool TShapeSizeB3::evaluate_with_hess( const MsqMatrix<3,3>& T,
double& result,
MsqMatrix<3,3>& deriv_wrt_T,
MsqMatrix<3,3> second_wrt_T[6],
MsqError& err )
{
const double tau = det(T);
if (invalid_determinant(tau)) { // barrier
MSQ_SETERR(err)( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
double n = Frobenius(T);
result = n*n*n - 3*MSQ_SQRT_THREE*( log(tau) + 1 );
const MsqMatrix<3,3> adjt = transpose_adj(T);
const double it = 1/tau;
deriv_wrt_T = T;
deriv_wrt_T *= 3*n;
deriv_wrt_T -= 3*MSQ_SQRT_THREE*it * adjt;
if (n > 1e-50)
{
set_scaled_outer_product( second_wrt_T, 3/n, T );
pluseq_scaled_I( second_wrt_T, 3*n );
pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -3*MSQ_SQRT_THREE*it, T );
pluseq_scaled_outer_product( second_wrt_T, 3*MSQ_SQRT_THREE*it*it, adjt );
}
else
{
std::cout << "Warning: Division by zero avoided in TShapeSizeB3::evaluate_with_hess()" << std::endl;
}
return true;
}
GT PFC::multi_miller(int n,G2** QQ,G1** PP)
{
GT z;
ZZn *Px,*Py;
int i,j,*k,nb;
ECn3 *Q,*A,*A2;
ECn P;
ZZn18 res,rd;
Big m;
Big X=*x;
Px=new ZZn[n];
Py=new ZZn[n];
Q=new ECn3[n];
A=new ECn3[n];
A2=new ECn3[n];
k=new int[n];
m=X/7;
nb=bits(m);
res=1;
for (j=0;j<n;j++)
{
k[j]=0;
P=PP[j]->g; normalise(P); Q[j]=QQ[j]->g;
extract(P,Px[j],Py[j]);
}
for (j=0;j<n;j++) A[j]=Q[j];
for (i=nb-2;i>=0;i--)
{
res*=res;
for (j=0;j<n;j++)
{
if (QQ[j]->ptable==NULL)
res*=g(A[j],A[j],Px[j],Py[j]);
else
res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
}
if (bit(m,i)==1)
for (j=0;j<n;j++)
{
if (QQ[j]->ptable==NULL)
res*=g(A[j],Q[j],Px[j],Py[j]);
else
res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
}
if (res.iszero()) return 0;
}
rd=res;
res*=res;
for (j=0;j<n;j++)
{
if (QQ[j]->ptable==NULL)
{
Q[j]=A[j];
res*=g(A[j],A[j],Px[j],Py[j]);
}
else res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
}
rd*=res;
for (j=0;j<n;j++)
{
if (QQ[j]->ptable==NULL)
{
A2[j]=A[j];
rd*=g(A[j],Q[j],Px[j],Py[j]);
}
else rd*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
}
res*=Frobenius(rd,*frob,6);
for (j=0;j<n;j++)
{
if (QQ[j]->ptable==NULL)
{
A[j]=psi(A[j],*frob,6);
res*=g(A[j],A2[j],Px[j],Py[j]);
}
else
res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
}
delete [] k;
delete [] A2;
delete [] A;
delete [] Q;
delete [] Py;
delete [] Px;
z.g=res;
return z;
}
GT PFC::miller_loop(const G2& QQ,const G1& PP)
{
GT z;
Big n;
int i,j,nb,nbw,nzs;
ECn3 A,m2A,Q;
ECn P;
ZZn Px,Py;
BOOL precomp;
ZZn18 r,rd;
Big X=*x;
Q=QQ.g; P=PP.g;
precomp=FALSE;
if (QQ.ptable!=NULL) precomp=TRUE;
normalise(P);
extract(P,Px,Py);
A=Q;
n=(X/7);
nb=bits(n);
r=1; j=0;
r.mark_as_miller();
for (i=nb-2;i>=0;i--)
{
r*=r;
if (precomp) r*=gp(QQ.ptable,j,Px,Py);
else r*=g(A,A,Px,Py);
if (bit(n,i))
{
if (precomp) r*=gp(QQ.ptable,j,Px,Py);
else r*=g(A,Q,Px,Py);
}
}
rd=r;
r*=r;
Q=A;
if (precomp) r*=gp(QQ.ptable,j,Px,Py);
else r*=g(A,A,Px,Py);
rd*=r;
m2A=A;
if (precomp) rd*=gp(QQ.ptable,j,Px,Py);
else rd*=g(A,Q,Px,Py);
r*=Frobenius(rd,*frob,6);
if (precomp) r*=gp(QQ.ptable,j,Px,Py);
else
{
A=psi(A,*frob,6);
r*=g(A,m2A,Px,Py);
}
z.g=r;
return z;
}
ZZn18 HardExpo(ZZn18 &f3x0, ZZn &X, Big &x){
//vector=[ 3, 5, 7, 14, 15, 21, 25, 35, 49, 54, 62, 70, 87, 98, 112, 245, 273, 319, 343, 434, 450, 581, 609, 784, 931, 1407, 1911, 4802, 6517 ]
ZZn18 xA;
ZZn18 xB;
ZZn18 t0;
ZZn18 t1;
ZZn18 t2;
ZZn18 t3;
ZZn18 t4;
ZZn18 t5;
ZZn18 t6;
ZZn18 t7;
ZZn18 f3x1;
ZZn18 f3x2;
ZZn18 f3x3;
ZZn18 f3x4;
ZZn18 f3x5;
ZZn18 f3x6;
ZZn18 f3x7;
f3x1=pow(f3x0,x);
f3x2=pow(f3x1,x);
f3x3=pow(f3x2,x);
f3x4=pow(f3x3,x);
f3x5=pow(f3x4,x);
f3x6=pow(f3x5,x);
f3x7=pow(f3x6,x);
xA=Frobenius(inverse(f3x1),X,2);
xB=Frobenius(inverse(f3x0),X,2);
t0=xA*xB;
xB=Frobenius(inverse(f3x2),X,2);
t1=t0*xB;
t0=t0*t0;
xB=Frobenius(inverse(f3x0),X,2);
t0=t0*xB;
xB=Frobenius(f3x1,X,1);
t0=t0*xB;
xA=Frobenius(inverse(f3x5),X,2)*Frobenius(f3x4,X,4)*Frobenius(f3x2,X,5);
//xB=Frobenius(f3x1,X,1);
t5=xA*xB;
t0=t0*t0;
t3=t0*t1;
xA=Frobenius(inverse(f3x4),X,2)*Frobenius(f3x1,X,5);
xB=Frobenius(f3x2,X,1);
t1=xA*xB;
xA=xB;//Frobenius(f3x2,X,1);
xB=xA; //xB=Frobenius(f3x2,X,1);
t0=xA*xB;
xB=Frobenius(f3x2,X,4);
t0=t0*xB;
xB=Frobenius(f3x1,X,4);
t2=t3*xB;
xB=Frobenius(inverse(f3x1),X,2);
t4=t3*xB;
t2=t2*t2;
xB=Frobenius(inverse(f3x2),X,3);
t3=t0*xB;
xB=inverse(f3x2);
t0=t3*xB;
t4=t3*t4;
xB=Frobenius(inverse(f3x3),X,3);
t0=t0*xB;
t3=t0*t2;
xB=Frobenius(inverse(f3x3),X,2)*Frobenius(f3x0,X,5);
t2=t3*xB;
t3=t3*t5;
t5=t3*t2;
xB=inverse(f3x3);
t2=t2*xB;
xA=Frobenius(inverse(f3x6),X,3);
//xB=inverse(f3x3);
t3=xA*xB;
t2=t2*t2;
t4=t2*t4;
xB=Frobenius(f3x3,X,1);
t2=t1*xB;
xA=xB; //xA=Frobenius(f3x3,X,1);
xB=Frobenius(inverse(f3x2),X,3);
t1=xA*xB;
t6=t2*t4;
xB=Frobenius(f3x4,X,1);
t4=t2*xB;
xB=Frobenius(f3x3,X,4);
t2=t6*xB;
xB=Frobenius(inverse(f3x5),X,3)*Frobenius(f3x5,X,4);
t7=t6*xB;
t4=t2*t4;
xB=Frobenius(f3x6,X,1);
t2=t2*xB;
t4=t4*t4;
t4=t4*t5;
xA=inverse(f3x4);
xB=Frobenius(inverse(f3x4),X,3);
t5=xA*xB;
// xB=Frobenius(inverse(f3x4),X,3);
t3=t3*xB;
xA=Frobenius(f3x5,X,1);
xB=xA; //xB=Frobenius(f3x5,X,1);
t6=xA*xB;
t7=t6*t7;
xB=Frobenius(f3x0,X,3);
t6=t5*xB;
t4=t6*t4;
xB=Frobenius(inverse(f3x7),X,3);
t6=t6*xB;
t0=t4*t0;
xB=Frobenius(f3x6,X,4);
t4=t4*xB;
t0=t0*t0;
xB=inverse(f3x5);
t0=t0*xB;
t1=t7*t1;
t4=t4*t7;
t1=t1*t1;
t2=t1*t2;
t1=t0*t3;
xB=Frobenius(inverse(f3x3),X,3);
t0=t1*xB;
t1=t1*t6;
t0=t0*t0;
t0=t0*t5;
xB=inverse(f3x6);
t2=t2*xB;
t2=t2*t2;
t2=t2*t4;
t0=t0*t0;
t0=t0*t3;
t1=t2*t1;
t0=t1*t0;
// xB=inverse(f3x6);
t1=t1*xB;
t0=t0*t0;
t0=t0*t2;
xB=f3x0*inverse(f3x7);
t0=t0*xB;
// xB=f3x0*inverse(f3x7);
t1=t1*xB;
t0=t0*t0;
t0=t0*t1;
return t0;
}