如何使用一些常数和业者不用乘法/分支翻转的整数值的符号 [英] How to flip the sign of an integer value using some constant and operator(s) without multiplication/branching

问题描述

我要寻找一个前pression这将使我具有以下属性写：

I am looking for an expression which would enable me to write with the following properties:

f(x, SOME_CONSTANT) -> returns -x (or any negative value)
f(x, SOME_CONSTANT2) -> returns x (or any positive value)
f(0, SOME_CONSTANT) -> returns 0
f(0, SOME_CONSTANT2) -> returns 0

不用乘法/分支，尽可能有效。

without multiplication/branching, as efficient as possible.

乍一看X ^ 0x80000000的似乎是一个候选人，但是当x为0这是行不通的。

At first glance x ^ 0x80000000 seems like a candidate, but it doesn't work when x is 0.

推荐答案

好吧，我终于想通了如何做到这一点有效的：

Ok, I finally figured out how to do this efficiently:

Java的：

int f(int x, int y) {
  return (((x >> 31) | ((unsigned)-x >> 31)) ^ y) - y;
}

C / C ++：

C/C++:

int f(int x, int y) {
  return (((x > 0) - (x < 0)) ^ y) - y;
}

以上这些函数返回 -sgn（X） y为 1 和 SGN（X）其他。

或者，如果我们只需要为每一个其他值，则-2 ^ 31（最小无符号整型值）工作，以preserving绝对值的利益，这是翻转的迹象，根据功能变量y：

Or, if we just need to work for every value other then -2^31 (minimum unsigned int value), with the benefit of preserving the absolute value, this is the function which flips the sign, depending on the variable y:

int f(int x, int y) {
    return (x ^ y) - y; // returns -x for y == -1, x otherwise
}

的推导：
-x = =〜X + 1 = =（X ^ 0xFFFFFFFF的）+ 1 = =（X ^ -1）+ 1 = =（X ^ -1） - （-1）。代-1其中y，我们得到一个两可变式其具有返回如果y设置为0不变x一个有趣的性质，因为既没有（X ^ 0）也不减去0变化的结果。现在角球的情况是，如果x等于为0x8000000当这个公式不起作用。这可以通过应用的SGN（x）函数是固定的，所以我们有（SGN（x）^ Y） - Y）。最后，我们与著名的公式不使用分支代替SGN（x）的功能。

The derivation: -x == ~x + 1 == (x ^ 0xFFFFFFFF) + 1 == (x ^ -1) + 1 == (x ^ -1) - (-1). Substituting -1 with y, we obtain a two-variable formula which has an interesting property that returns unchanged x if y is set to 0, because neither (x ^ 0) nor subtracting 0 changes the result. Now the corner case is if x is equal to 0x8000000 when this formula doesn't work. This can be fixed by applying the sgn(x) function, so we have (sgn(x) ^ y) - y). Finally, we replace the sgn(x) functions with the well-known formulas which do not use branching.

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