Continued fraction/Arithmetic/G(matrix ng, continued fraction n1, continued fraction n2)

This task performs the basic mathematical functions on 2 continued fractions. This requires the full version of matrix NG:

${\begin{bmatrix}a_{1}2&a_{1}&a_{2}&a\\b_{1}2&b_{1}&b_{2}&b\end{bmatrix}}$

I may perform perform the following operations:

Input the next term of continued fraction N₁

Input the next term of continued fraction N₂

Output a term of the continued fraction resulting from the operation.

I output a term if the integer parts of ${\frac {a}{b}}$ and ${\frac {a_{1}}{b_{1}}}$ and ${\frac {a_{2}}{b_{2}}}$ and ${\frac {a_{12}}{b_{12}}}$ are equal. Otherwise I input a term from continued fraction N₁ or continued fraction N₂. If I need a term from N but N has no more terms I inject $\infty$.

When I input a term t from continued fraction N₁ I change my internal state:

${\begin{bmatrix}a_{12}&a_{1}&a_{2}&a\\b_{12}&b_{1}&b_{2}&b\end{bmatrix}}$ is transposed thus ${\begin{bmatrix}a_{2}+a_{12}*t&a+a_{1}*t&a_{1}2&a_{1}\\b_{2}+b_{12}*t&b+b_{1}*t&b_{1}2&b_{1}\end{bmatrix}}$

   if(cfn==0){t=a; a=a1; a1=t+a1*n; t=a2; a2=a12; a12=t+a12*n; t=b; b=b1; b1=t+b1*n; t=b2; b2=b12; b12=t+b12*n;}
   else{t=a; a=a2; a2=t+a2*n; t=a1; a1=a12; a12=t+a12*n; t=b; b=b2; b2=t+b2*n; t=b1; b1=b12; b12=t+b12*n;}