# 2020q3 Homework5 (quiz5)
contributed by < `erickuo5124` >
###### tags: `2020進階電腦系統理論與實作`

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## Q1

#include <stdio.h>
#include <stdlib.h>

double divop(double orig, int slots) {
    if (slots == 1 || orig == 0)
        return orig;
    int od = slots & 1;
    double result = divop(orig / 2, od ? (slots + 1) >> 1 : slots >> 1);
    if (od)
        result += divop(result, slots);
    return result;
}

原理：
$$
\begin{split}
\frac{orig}{slots} &= \frac{orig/2}{slots/2} \\
&=\frac{orig}{slots} \times \frac{slots+1}{slots+1} \\
&=\frac{orig/2}{(slots+1)/2} \times \frac{slots+1}{slots} = \frac{orig/2}{(slots+1)/2} \times (1+\frac{1}{slots})
\end{split}
$$
將除術與被除數同除以 2　來作除法運算。若被除數為奇數，上下同乘被除數+1

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## Q2