# Bit Fiddling - 4

**Pre-Computing**

Pre Computing is a technique normally used to speed up algorithms and by actually computing results of a smaller problem and using interpolation or other techniques to solve a larger problem. You trade-off memory/accuracy for speed here, as you will need to load the pre-computed solutions into memory and/or use interpolation to find solutions to a desired level of accuracy.

A similar approach can be used to count number of set bits in an integer. Basically, you have a pre-computed array of the number of bits in 4,8 or 16 bit size numbers and use this to find the number of bits in an integer. You could also pre-compute for 32 bit sizes but you will need 2^{34} bytes to hold this data J

static int PreCompute8 [256] =

{

0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4,

1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,

1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,

2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,

1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,

2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,

2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,

3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,

1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,

2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,

2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,

3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,

2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,

3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,

3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,

4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8

};

int BitCountPreCompute (unsigned int u)

{

// Valid for 32 bit ints only

return PreCompute8[u&0xffu] + PreCompute8[(u>>8)&0xffu] + PreCompute8[(u>>16)&0xffu] + PreCompute8[(u>>24)&0xffu] ;

}

PreCompute8 holds the number of set bits in for all 8 bit numbers. Using this result, mask out sets of 8 bits in the given integer and index into the PreCompute8 array and compute the count.