FPoly operator*(const FPoly& a,const FPoly& b)
{
FPoly prod;
fterm *iptr,*pos;
fterm *ptr=b.start;
if (&a==&b)
{ // squaring
pos=NULL;
while (ptr!=NULL)
{ // diagonal terms
pos=prod.addterm(ptr->an*ptr->an,ptr->n+ptr->n,pos);
ptr=ptr->next;
}
ptr=b.start;
while (ptr!=NULL)
{ // above the diagonal
iptr=ptr->next;
pos=NULL;
while (iptr!=NULL)
{
pos=prod.addterm(2*ptr->an*iptr->an,ptr->n+iptr->n,pos);
iptr=iptr->next;
}
ptr=ptr->next;
}
}
else while (ptr!=NULL)
{
FPoly t=a;
t.multerm(ptr->an,ptr->n);
ptr=ptr->next;
prod+=t;
}
return prod;
}
void class_poly(Complex& lam,Float *Fi2,Big A,Big B,Big C,Big D,BOOL conj,BOOL P1363)
{
Big ac,l,t;
int i,j,k,g,e,m,n,dm8;
Complex cinv;
if (P1363)
{
g=1;
if (D%3==0) g=3;
ac=A*C;
if (ac%2==1)
{
j=0;
l=A-C+A*A*C;
}
if (C%2==0) j=1;
if (A%2==0) j=2;
if (A%2==0)
{
t=(C*C-1)/8;
if (t%2==0) m=1;
else m=-1;
}
else
{
t=(A*A-1)/8;
if (t%2==0) m=1;
else m=-1;
}
dm8=D%8;
i=geti(D);
k=getk(D);
switch (dm8)
{
case 1:
case 2: n=m;
if (C%2==0) l=A+2*C-A*C*C;
if (A%2==0) l=A-C-A*C*C;
break;
case 3: if (ac%2==1) n=1;
else n=-m;
if (C%2==0) l=A+2*C-A*C*C;
if (A%2==0) l=A-C+5*A*C*C;
break;
case 5: n=1;
if (C%2==0) l=A-C+A*A*C;
if (A%2==0) l=A-C-A*C*C;
break;
case 6: n=m;
if (C%2==0) l=A+2*C-A*C*C;
if (A%2==0) l=A-C-A*C*C;
break;
case 7: if (ac%2==0) n=1;
else n=m;
if (C%2==0) l=A+2*C-A*C*C;
if (A%2==0) l=A-C-A*C*C;
break;
default: break;
}
e=(k*B*l)%48;
if (e<0) e+=48;
cinv=pow(lam,e);
cinv*=(n*Fi2[i]);
cinv=pow(cinv*pow(F(j,A,B,C,D,0),k),g);
}
else
{
int N=getN(D);
// adjust A and B
if (N==2)
{
j=3;
if (A%3!=0)
{
if (B%3!=0)
{
if ((B+A+A)%3!=0) B+=(4*A);
else B+=(A+A);
}
}
else
{
if (B%3!=0)
{
if (C%3!=0)
{
if ((C+B)%3!=0) B+=(4*A);
else B+=(A+A);
}
}
}
A*=3;
}
else
{
j=4;
if ((A%N)==0)
{
A=C;
B=-B;
}
while (B%N!=0) B+=(A+A);
A*=N;
}
cinv=F(j,A,B,C,D,N);
}
// multiply polynomial by new term(s)
FPoly F;
if (conj)
{ // conjugate pair
// t^2-2a+(a^2+b^2) , where cinv=a+ib
F.addterm((Float)1,2);
F.addterm(-2*real(cinv),1);
F.addterm(real(cinv)*real(cinv)+imaginary(cinv)*imaginary(cinv),0);
}
else
{ // t-cinv
F.addterm((Float)1,1);
F.addterm(-real(cinv),0);
// store as a linear polynomial, or combine 2 to make a quadratic
if (T[0].iszero())
{
T[0]=F;
return;
}
else
{
F=T[0]*F; // got a quadratic
T[0].clear();
}
}
// accumulate Polynomial as 2^m degree components
// This allows the use of karatsuba via the "special" function
// This is the time critical bit....
for (i=1;;i++)
{
if (T[i].iszero())
{
T[i]=F; // store this 2^i degree polynomial
break;
}
else
{
F=special(T[i],F); // e.g. if i=1 two quadratics make a quartic..
T[i].clear();
}
}
}