Thursday, June 11, 2009

Enumerating Bits

OK, so the enumerating the set of subsets of non-zero bits is not a common task. But what about enumerating the set of non-zero bits in an integer? That’s something that tends to happen at least one or twice in any large project. Here’s how that can be done use a related function.

Given an integer (i), the least significant non-zero bit (b) can be found using this equation:

b = (i & -i)

(This is discussed as equation (37) in Donald Knuth’s The Art of Computer Programming, Volume 4, pre-fascicle 1A, page 8.)

It is easy to turn this into a loop which enumerates the bits in an integer:
while (xInteger>0)
int xBit = (xInteger & -xInteger);
xInteger &= ~xBit;
// Do something with xBit here.

(This is probably a case where one wouldn’t want to use a generic “yield return” enumerator, since if one is working at this level of detail, efficiency is probably the main concern.)

This can also be made to work in C# with unsigned integers by using various types of casting. But if efficiency is paramount, pay attention to the generated MSIL, since casting at some points generates more efficient code than does casting at other points.

Tests in release mode show that this construct is nearly four times faster in C# (.NET 3.5 version) than is shifting! But it looks arcane at first glance, so be sure to document the code well.

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