Continued fraction
The
relationship
between a pair (N,D) and a reduced pair (N’, D’)
can be rearranged according to
the structure of a continued fraction (CF) . Four situations can be
distinguished. We start again with the characteristic equation: N = K *
D + E . Case 1 : E
<
D/2
Reduction : N’ = E and D’ = D mod(
2*N’) = D - 2 * s * N’
Case 1A: D’ < N’
Case 1B: D’ > N’ Case 2 : E
>
D/2
Reduction : N’ = D - E and D’ = D mod(
2*N’) = D - 2 * s * N’
Case 2B: D’ > N’ 
