汉明权重只用二进制操作编写吗? [英] Hamming weight written only in binary operations?

问题描述

我只需要根据二进制运算(&，^，>>)来写一个字节汉明权重的表达式；没有任何循环，只是一个公式.

I need to write an expression of one byte Hamming weight in terms of binary operations only (&, ^, >>); without any loop, just a formula.

我知道有很多算法可以计算汉明权重，但是它们都使用算术运算或循环运算.

I know that there are plenty algorithms, that allow computing Hamming weight, but all of them use arithmetical operations or looping.

如果我们采用 http://en.wikipedia.org/wiki/Hamming_weight http://en.wikipedia.org/wiki/Hamming_weight ，那么第一个和D = B + C可以写成D = B ^ C ^(B& C << 1)，但随后的两个和更复杂.

If we take an algorithm from http://en.wikipedia.org/wiki/Hamming_weight, then the first sum D=B+C can be written as D = B^C^(B&C << 1), but two following sums are more complicated.

有人暗示吗?

更新: 谢谢你们的帮助.实际上，我需要以下内容:

UPDATE: Thank you for help guys. Actually, I needed something like following:

int popcount_1(unsigned char in){

unsigned char m1  = 0x55;
unsigned char m2  = 0x33;
unsigned char m4  = 0x0f;
unsigned char B,C = 0;
unsigned char x = in;

x = (x & (x << 1) & (m1 << 1)) | (m1 & (x ^ (x >> 1)));

B = x & m2;
C = (x >>  2) & m2;
x = B ^ C ^ ((B & C) << 1);

B = (x & m4 ) ^ ((x >>  4) & m4);
C = (x & ((x >>  4) & m4)) << 1;
x = B ^ C ^ ((B & C) << 1);
return x;
}

此代码将导致汉明权重为变量 in .它不包含任何+，-或比较指令，并且可以在8位微控制器上工作. 但是，与大多数其他解决方案相比，它需要更多的操作.现在，我正在尝试简化它.

This code will result in Hamming weight of variable in. It does not contain any +, -, or comparison instructions and it can work on 8bits microcontrollers. Nevertheless, it takes more operations than most of other solutions. Now, I am trying to simplify it.

UPDATE2:@Evgeny Kluev提出了另一种基于64位寄存器的解决方案

UPDATE2: Another solution, based on 64 bits registers, is proposed by @Evgeny Kluev

推荐答案

我不确定这是否是您要搜索的内容，但这只是一个仅使用移位和按位运算的公式:

I'm not sure if this is what you search for, but here is just a formula using only shifts and bitwise and:

int weight(unsigned char x)
{
  return ((0x876543210 >>
    (((0x4332322132212110 >> ((x & 0xF) << 2)) & 0xF) << 2)) >>
    ((0x4332322132212110 >> (((x & 0xF0) >> 2)) & 0xF) << 2))
    & 0xf;
}

这里的移位操作两次被用来代替数组索引(查找4位汉明权重).还有另一种移位操作使用数组索引执行加法.

Here shift operation is twice used as a substitute for array indexing (to find 4-bit hamming weights). And one more shift operation uses array indexing to perform addition.

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