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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: 3, Interesting) by Rich on Thursday June 20 2019, @09:19PM

    by Rich (945) on Thursday June 20 2019, @09:19PM (#858223) Journal

    The most amazing bit juggling I've seen on the 6502 is the loader code on the Apple Disk II controller. It somehow manages to generate the mapping table from 8-bit disk nibbles to 6-bit data (according to tricky rules about consecutive zeroes and ones) and decode a sector with it in 256 bytes of slot ROM code. 256 bytes which it has also has to share with code to slot-independently start the drive, smoothly drive the head stepper to track 0, identify when sector 0 passes under the head, read its nibbles, and jump to the loaded code. That, and the PROM logic of the Woz-Machine, is, for its time, like alien knowledge sent down to make a disk drive work with the absolutely most low-end hardware around it. That advantage was as good as being able to print money, and it paid for the Mac development.

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