void rotnumber(long double xi1, long double yi1, int time) {
__float128 x = xi1;
__float128 y = yi1;
__float128 xn;
__float128 yn;
__float128 xav=0.Q;
__float128 yav=0.Q;
__float128 cosval=0.Q;
__float128 dot, mo, mn, theta;
__float128 rho=0.Q;
__float128 wsum=0.Q;
for(int t=0; t< time; t++) {
wsum+=weight((__float128)t/(__float128)time);
}
for(int t=0; t < time; t++) {
xav+=x*weight((__float128)t/(__float128)time);
yav+=y*weight((__float128)t/(__float128)time);
xn = smod(x+y,2.Q*M_PIq);
yn = smod(y+1.4Q*sinq(x+y),2.Q*M_PIq);
x=xn;
y=yn;
}
xav/=wsum;
yav/=wsum;
mn = sqrtq((x-xav)*(x-xav) + (y-yav)*(y-yav));
for(int t=0; t< time; t++) {
xn = smod(x+y,2.Q*M_PIq);
yn = smod(y+1.4Q*sinq(x+y),2.Q*M_PIq);
dot = (xn-xav)*(x-xav) + (yn-yav)*(y-yav);
mo = mn;
mn = sqrtq((xn-xav)*(xn-xav) + (yn-yav)*(yn-yav));
cosval = dot/(mo*mn);
theta = acosq(cosval);
rho += theta*weight((__float128)t/(__float128)time);
x=xn;
y=yn;
}
rho/=wsum*2.Q*M_PIq;
printf("The rotation number at (xi=%Lf, yi=%Lf) is %.20Lf\n",xi1,yi1,(long double)rho);
}
inline void eval_acos(float128_backend& result, const float128_backend& arg)
{
result.value() = acosq(arg.value());
}
inline Quad Acos( const Quad& alpha ) { return acosq(alpha); }
