1 \magnification=\magstep3
6 \font\eins=cmb10 scaled \magstep 3
9 \def\frac#1#2{{{#1} \over {#2}}}
13 \centerline{\eins Binary Splitting}
17 \centerline{$\displaystyle S_{[n_1,n_2)} = {\sum\limits_{n=n_1}^{n_2-1} \frac{a(n)}{b(n)} \, \frac{p(n_1) \cdots p(n)}{q(n_1) \cdots q(n)}}$}
19 Compute $P = {p(n_1) \cdots p(n_2-1)}$, $Q = {q(n_1) \cdots q(n_2-1)}$,
21 $B = {b(n_1) \cdots b(n_2-1)}$ and $T$ with
23 \centerline{$\displaystyle S_{[n_1,n_2)} = \frac{T}{B \cdot Q}$}
25 \quad $n_2 - n_1 < 4$ \quad $\rightarrow$ directly
27 \quad $n_2 - n_1 \geq 4$ \quad $\rightarrow$ split
29 \centerline{$P = P_L \cdot P_R$}
30 \centerline{$Q = Q_L \cdot Q_R$}
31 \centerline{$B = B_L \cdot B_R$}
32 \centerline{$T = B_R \cdot Q_R \cdot T_L + B_L \cdot P_L \cdot T_R$}