CODEWITHSUNDEEP
cbit-manipulation
user999755
user999755

Reputation: 235

understanding bit twiddling hack for bit set count by lookup table

I am reading through the stanford bit twiddling hacks here: http://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetTable

For counting bits set with lookup table, I have 2 questions: 1)

c = BitsSetTable256[v & 0xff] + 
BitsSetTable256[(v >> 8) & 0xff] + 
BitsSetTable256[(v >> 16) & 0xff] + 
BitsSetTable256[v >> 24];

How is this correct. So, the table contains bits count precomputed for 256 numbers = 2^8. Now we have a 32bit number to compute bits set. v31..v24 v23...v16 v15...v8 v7..v0

All we need to do is lookup every 8 bits in lookup table

So, it should instead be 

c = BitsSetTable256[v & 0x0F] + 
    BitsSetTable256[v>>8 & 0x0F] + 
    BitsSetTable256[v>>16 & 0x0F] +
    BitsSetTable256[v>>24]

My point is that it we should be doing & with 0x0F and not FF to get to the right number in the 256 range right?

What am I missing here? : ( : (

2) Also, what does this macro mean from the same bit twiddling hacks section for bits set

static const unsigned char BitsSetTable256[256] = 
{
 #   define B2(n) n,     n+1,     n+1,     n+2
 #   define B4(n) B2(n), B2(n+1), B2(n+1), B2(n+2)
 #   define B6(n) B4(n), B4(n+1), B4(n+1), B4(n+2)
 B6(0), B6(1), B6(1), B6(2)
};

How do you expand this?

thanks

Upvotes: 1

Views: 919

Answers (1)

Carl Norum
Carl Norum

Reputation: 225072

  1. No, that page is correct. 0x0F is binary 1111 (decimal 15) - four bits are set. 0xFF is binary 11111111 (decimal 255), 8 bits are set.

  2. You can just run your preprocessor on it to see (some edits on my part to make it readable):

    static const unsigned char BitsSetTable256[256] =
{
    0, 0 +1, 0 +1, 0 +2, 0 +1, 0 +1 +1, 0 +1 +1, 0 +1 +2, 0 +1,
    0 +1 +1, 0 +1 +1, 0 +1 +2, 0 +2, 0 +2 +1, 0 +2 +1, 0 +2 +2,
    0 +1, 0 +1 +1, 0 +1 +1, 0 +1 +2, 0 +1 +1, 0 +1 +1 +1, 0 +1 +1 +1,
    0 +1 +1 +2, 0 +1 +1, 0 +1 +1 +1, 0 +1 +1 +1, 0 +1 +1 +2, 0 +1 +2,
    0 +1 +2 +1, 0 +1 +2 +1, 0 +1 +2 +2, 0 +1, 0 +1 +1, 0 +1 +1, 0 +1 +2,
    0 +1 +1, 0 +1 +1 +1, 0 +1 +1 +1, 0 +1 +1 +2, 0 +1 +1, 0 +1 +1 +1,
    0 +1 +1 +1, 0 +1 +1 +2, 0 +1 +2, 0 +1 +2 +1, 0 +1 +2 +1, 0 +1 +2 +2,
    0 +2, 0 +2 +1, 0 +2 +1, 0 +2 +2, 0 +2 +1, 0 +2 +1 +1, 0 +2 +1 +1,
    0 +2 +1 +2, 0 +2 +1, 0 +2 +1 +1, 0 +2 +1 +1, 0 +2 +1 +2, 0 +2 +2,
    0 +2 +2 +1, 0 +2 +2 +1, 0 +2 +2 +2, 1, 1 +1, 1 +1, 1 +2, 1 +1, 1 +1 +1,
    1 +1 +1, 1 +1 +2, 1 +1, 1 +1 +1, 1 +1 +1, 1 +1 +2, 1 +2, 1 +2 +1, 1 +2 +1,
    1 +2 +2, 1 +1, 1 +1 +1, 1 +1 +1, 1 +1 +2, 1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +1,
    1 +1 +1 +2, 1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +2, 1 +1 +2,
    1 +1 +2 +1, 1 +1 +2 +1, 1 +1 +2 +2, 1 +1, 1 +1 +1, 1 +1 +1, 1 +1 +2,
    1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +2, 1 +1 +1, 1 +1 +1 +1,
    1 +1 +1 +1, 1 +1 +1 +2, 1 +1 +2, 1 +1 +2 +1, 1 +1 +2 +1, 1 +1 +2 +2,
    1 +2, 1 +2 +1, 1 +2 +1, 1 +2 +2, 1 +2 +1, 1 +2 +1 +1, 1 +2 +1 +1,
    1 +2 +1 +2, 1 +2 +1, 1 +2 +1 +1, 1 +2 +1 +1, 1 +2 +1 +2, 1 +2 +2,
    1 +2 +2 +1, 1 +2 +2 +1, 1 +2 +2 +2, 1, 1 +1, 1 +1, 1 +2, 1 +1, 1 +1 +1,
    1 +1 +1, 1 +1 +2, 1 +1, 1 +1 +1, 1 +1 +1, 1 +1 +2, 1 +2, 1 +2 +1,
    1 +2 +1, 1 +2 +2, 1 +1, 1 +1 +1, 1 +1 +1, 1 +1 +2, 1 +1 +1, 1 +1 +1 +1,
    1 +1 +1 +1, 1 +1 +1 +2, 1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +2, 
    1 +1 +2, 1 +1 +2 +1, 1 +1 +2 +1, 1 +1 +2 +2, 1 +1, 1 +1 +1, 1 +1 +1, 
    1 +1 +2, 1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +2, 1 +1 +1,
    1 +1 +1 +1, 1 +1 +1 +1, 1 +1 +1 +2, 1 +1 +2, 1 +1 +2 +1, 1 +1 +2 +1,
    1 +1 +2 +2, 1 +2, 1 +2 +1, 1 +2 +1, 1 +2 +2, 1 +2 +1, 1 +2 +1 +1,
    1 +2 +1 +1, 1 +2 +1 +2, 1 +2 +1, 1 +2 +1 +1, 1 +2 +1 +1, 1 +2 +1 +2,
    1 +2 +2, 1 +2 +2 +1, 1 +2 +2 +1, 1 +2 +2 +2, 2, 2 +1, 2 +1, 2 +2, 2 +1,
    2 +1 +1, 2 +1 +1, 2 +1 +2, 2 +1, 2 +1 +1, 2 +1 +1, 2 +1 +2, 2 +2,
    2 +2 +1, 2 +2 +1, 2 +2 +2, 2 +1, 2 +1 +1, 2 +1 +1, 2 +1 +2, 2 +1 +1,
    2 +1 +1 +1, 2 +1 +1 +1, 2 +1 +1 +2, 2 +1 +1, 2 +1 +1 +1, 2 +1 +1 +1,
    2 +1 +1 +2, 2 +1 +2, 2 +1 +2 +1, 2 +1 +2 +1, 2 +1 +2 +2, 2 +1
    2 +1 +1, 2 +1 +1, 2 +1 +2, 2 +1 +1, 2 +1 +1 +1, 2 +1 +1 +1, 2 +1 +1 +2,
    2 +1 +1, 2 +1 +1 +1, 2 +1 +1 +1, 2 +1 +1 +2, 2 +1 +2, 2 +1 +2 +1,
    2 +1 +2 +1, 2 +1 +2 +2, 2 +2, 2 +2 +1, 2 +2 +1, 2 +2 +2, 2 +2 +1,
    2 +2 +1 +1, 2 +2 +1 +1, 2 +2 +1 +2, 2 +2 +1, 2 +2 +1 +1, 2 +2 +1 +1,
    2 +2 +1 +2, 2 +2 +2, 2 +2 +2 +1, 2 +2 +2 +1, 2 +2 +2 +2
};

Upvotes: 5

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