Editing Division by two (section)

==Binary==
In binary arithmetic, division by two can be performed by a [[bit shift]] operation that shifts the number one place to the right.
This is a form of [[strength reduction]] optimization. For example, 1101001 in binary (the decimal number 105), shifted one place to the right, is 110100 (the decimal number 52): the lowest order bit, a 1, is removed. Similarly, division by any [[power of two]] 2<sup>''k''</sup> may be performed by right-shifting ''k'' positions. Because bit shifts are often much faster operations than division, replacing a division by a shift in this way can be a helpful step in [[program optimization]].<ref name="WC00"/> However, for the sake of [[software portability]] and readability, it is often best to write programs using the division operation and trust in the [[compiler]] to perform this replacement.<ref>{{citation|title=Write portable code: an introduction to developing software for multiple platforms|first=Brian|last=Hook|publisher=No Starch Press|year=2005|isbn=978-1-59327-056-8|page=133}}.</ref> An example from [[Common Lisp]]:

<syntaxhighlight lang="lisp">
 (setq number #b1101001)   ; #b1101001  —  105
 (ash number -1)           ; #b0110100  —  105 >> 1 ⇒ 52
 (ash number -4)           ; #b0000110  —  105 >> 4 ≡ 105 / 2⁴ ⇒ 6
</syntaxhighlight>

The above statements, however, are not always true when dealing with dividing [[Signed number representations|signed]] binary numbers. Shifting right by 1 bit will divide by two, always rounding down. However, in some languages, division of signed binary numbers round towards 0 (which, if the result is negative, means it rounds up). For example, [[Java (programming language)|Java]] is one such language: in Java, <code>-3 / 2</code> evaluates to <code>-1</code>, whereas <code>-3 >> 1</code> evaluates to <code>-2</code>. So in this case, the compiler ''cannot'' optimize division by two by replacing it by a bit shift, when the dividend could possibly be negative.