Mask

A Mask provides a dense bitset implementation. This replaces uses of BitSet. The major difference is that we don't box the Ints.

An explanation of some of the arithmetic you'll see here:

We store the bits in array of words. Each word contains 64 bits and the words are in order. So, the word containing bit n is n >>> 6 - we simply drop the lower 6 bits (divide by 64). If n is set, then the bit n & 0x3FL (the last 6 bits - ie n % 64 if n was an unsigned int), in word bits(n >>> 6) will be true. We can check this by masking the word with 1L << (n & 0x3FL) and checking if the result is non-zero.

Note that we use shift-without-carry (> > >) and intersection (&) to divide and mod by 64 instead of using / and % because they do not behave correctly with negative numbers; they carry the sign through in the result, and we want the absolute value.

An invariant of the underlying bits array is that the highest order word (ie. bits(bits.length - 1)) is always non-zero (except if bits has 0 length). This sometimes means we must *trim* the array for some operations that could possibly zero out the highest order word (eg. intersection and subtraction.