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posted by Fnord666 on Thursday June 20 2019, @09:43AM   Printer-friendly
from the abusing-bits-for-fun-and...profit? dept.

Submitted via IRC for Bytram

Abusing A CPU's Adders To Optimize Bit Counting

If you like nitpicking around C code and generated assembly language — and we’ll admit that we do — you shouldn’t miss [Scaramanga’s] analysis of what’s known as Kernighan’s trick. If you haven’t heard of the trick, it’s a pretty efficient way of counting bits.

Like the Wheatstone bridge and a lot of other things, the Kernighan trick is misnamed. Brian Kernighan made it famous, but it was actually first published in 1960 and again in 1964 before he wrote about it in 1988. The naive way to count bits would be to scan through each bit position noting how many one bits you encounter, but the problem is, that takes a loop for each bit. A 64-bit word, then, takes 64 loops no matter what it contains. You can do slightly better by removing each bit you find and stopping when the word goes to zero, but that still could take 64 cycles if the last bit you test is set.

Using the trick, you make the observation that X & (X-1) will always clear the least significant bit of a word. Try a few examples:

   X      X-1   X&(X-1)
000100000000
001000010000
001100100010
101010011000
110010111000
111111101110

You can probably see where this is going. By computing X&(X-1) you clear a bit on each loop iteration and you only have to go through the number of bits that are actually set.

[...] If you like this sort of thing, be sure to check out [Sean Anderson’s] extensive list of bit hacks. It shows several different ways to count bits and do other common and uncommon tasks with different tradeoffs. For example, you could dedicate a 256-entry lookup table and do the whole thing with one loop per byte with great speed but bad memory utilization. Always a trade-off.


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  • (Score: 0) by Anonymous Coward on Thursday June 20 2019, @12:52PM (1 child)

    by Anonymous Coward on Thursday June 20 2019, @12:52PM (#857880)

    xcuse me, but how is & 0xff different from & 255 and why are you bringing up 256 aka 0x100 ????

  • (Score: 1, Informative) by Anonymous Coward on Thursday June 20 2019, @01:15PM

    by Anonymous Coward on Thursday June 20 2019, @01:15PM (#857889)

    Because AND is not the same operation as DIV.

    When you want the remainder of a power of two, you AND it against the value - 1. So N % 256 becomes N & (256 - 1).