bit vector implementation of set in Programming Pearls, 2nd Edition

Question

On Page 140 of Programming Pearls, 2nd Edition, Jon proposed an implementation of sets with bit vectors.

We\'ll turn now to two final structures that exploit the fact

Answer 1

If you store your bits in an array of n words you can imagine them to be layed out as a matrix with n rows and 32 columns (BITSPERWORD):

         3                                         0
         1                                         0
      0  xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx
      1  xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx
      2  xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx     
      ....
      n  xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx

To get the k-th bit you divide k by 32. The (integer) result will give you the row (word) the bit is in, the reminder will give you which bit is within the word.

Dividing by 2^p can be done simply by shifting p postions to the right. The reminder can be obtained by getting the p rightmost bits (i.e the bitwise AND with (2^p - 1)).

In C terms:

#define div32(k) ((k) >> 5)
#define mod32(k) ((k) & 31)

#define word_the_bit_is_in(k) div32(k)
#define bit_within_word(k)    mod32(k)

Hope it helps.