按位与到位模运算符 [英] Bitwise and in place of modulus operator
问题描述
我们知道，两个功率的例子模可以pssed这样EX $ P $：
We know that for example modulo of power of two can be expressed like this:
x % 2 inpower n == x & (2 inpower n - 1).
例如：
x % 2 == x & 1
x % 4 == x & 3
x % 8 == x & 7
那么两个数字的一般非电力？
What about general nonpower of two numbers?
让我们说：
X％7 ==？
推荐答案
首先，它实际上是不准确的说，
First of all, it's actually not accurate to say that
x % 2 == x & 1
简单的反例： X = -1 。在许多语言，包括Java， 1％2 == -1 。也就是说，％不一定模的传统的数学定义。 Java调用它的余运算符为例。
Simple counterexample: x = -1. In many languages, including Java, -1 % 2 == -1. That is, % is not necessarily the traditional mathematical definition of modulo. Java calls it the "remainder operator", for example.
至于按位优化，只能模两可轻松在按位算术做的权力。一般来说，基础的的B仅模权力的可以轻松地与基地的乙做的数字再presentation。
With regards to bitwise optimization, only modulo powers of two can "easily" be done in bitwise arithmetics. Generally speaking, only modulo powers of base b can "easily" be done with base b representation of numbers.
在基地10，例如，对于非负 N ， N模10 ^氏/ code>只是走最低显著 K 的数字。
In base 10, for example, for non-negative N, N mod 10^k is just taking the least significant k digits.
- JLS 15.17.3 Remainder Operator %
- Wikipedia/Modulo Operation
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