Question

I’m writing a compressor for a long stream of 128 bit numbers. I would like to store the numbers as differences — storing only the difference between the numbers rather than the numbers themselves because I can pack the differences in fewer bytes because they are smaller.

However, for compression then I need to subtract these 128 bit values, and for decompression I need to add these values. Maximum integer size for my compiler is 64 bits wide.

Anyone have any ideas for doing this efficiently?

Answer 1

If all you need is addition and subtraction, and you already have your 128-bit values in binary form, a library might be handy but isn’t strictly necessary. This math is trivial to do yourself.

I don’t know what your compiler uses for 64-bit types, so I’ll use INT64 and UINT64 for signed and unsigned 64-bit integer quantities.

class Int128 { public:     ...     Int128 operator+(const Int128 & rhs)     {         Int128 sum;         sum.high = high + rhs.high;         sum.low = low + rhs.low;         // check for overflow of low 64 bits, add carry to high         if (sum.low < low)             ++sum.high;         return sum;     }     Int128 operator-(const Int128 & rhs)     {         Int128 difference;         difference.high = high - rhs.high;         difference.low = low - rhs.low;         // check for underflow of low 64 bits, subtract carry to high         if (difference.low > low)             --difference.high;         return difference;     }  private:     INT64  high;     UINT64 low; };