这是一个分而治之的策略，用于计数位的一部分，所谓的人口的功能。学术处理这个策​​略可以在莱因戈尔德和Nievergelt，1977年被发现。

This is part of a divide-and-conquer strategy for counting bits, called a "population" function. The scholarly treatment of this strategy can be found in Reingold and Nievergelt, 1977.

我们的想法是第一总和位配对，然后4明智的，那么8明智等等。例如，如果你有位 1011 ，然后第一对 10 变成 01 ，因为有一个位和第二变，因为 10 = 2 在$ C $ 10二进制和有在两位 11 。这里的基本事实是：

The idea is to first sum the bits pairwise, then 4-wise, then 8-wise and so on. For example, if you have the bits 1011, then the first pair 10 becomes 01 because there is one bit and the second becomes 10 because 10 = 2 in binary and there are two bits in 11. The essential fact here is that:

population(x) = x - (x/2) - (x/4) - (x/8) - (x/16) - ... etc.

确切的算法，你是所谓的HAKMEM算法的变体（见比勒，高斯帕和Schroppel，1972年）。该算法计数 1 的在并行4位字段，那么这些款项被转换为8位的总和。最后一步是一个操作由 0x01010101 相乘来添加这些4个字节。该 0x0F0F0F0F 面膜通过屏蔽掉非金额信息获取4明智的字节总和。例如，假设8明智的字段是 10110110 ，然后有5位等于 0101 ，因此，我们将有 10110101 。只有最后4位显著，所以我们屏蔽掉第4位，即：

The exact algorithm you have is a variant of what is known as the "HAKMEM" algorithm (see Beeler, Gosper and Schroppel, 1972). This algorithm counts 1's in 4-bit fields in parallel, then these sums are converted into 8-bit sums. The last step is an operation to add these 4 bytes by multiplying by 0x01010101. The 0x0F0F0F0F mask gets the 4-wise bytes sums by masking out non-sum information. For example, lets say the 8-wise field is 10110110, then there are 5 bits which is equal to 0101, thus we will have 10110101. Only the last four bits are significant, so we mask out the first four, ie:

10110101 & 0x0F = 00000101

您可以找到的书黑客的喜悦，由亨利·沃伦计数位的细枝末节整整一章。

You can find an entire chapter on the minutiae of counting bits in the book "Hacker's Delight" by Henry Warren.