I'm really bad at math and I want to do a binary operation

Question

I have the following piece of code:

    public void AddHash( int val )
    {
        m_Hash ^= (val & 0x3FFFFFF);
        m_Hash ^= (val >> 26) & 0x3F;
    }

I would like very much to know what the heck it does, but I would be satisfied to know how to build a bool HasHash( int val ) that tells me whether m_Hash has that number or not...

something like this?

    public bool HasHash( int val )
    {
        return (m_Hash & val) == 0;
    }

Answer 1

EDIT to fix the bug that @schnaader found: What it does? This code probably wants to rotate val leftwards (clockwise) by 6 bits and form the ones-complement sum (edit: not the product, as I'd said before) -- the xor -- of that rotated value and the current value of m_Hash to yield a new m_Hash. That new m_Hash will be used the next time AddHash( ) is called.

However, the code as written has a bug: it rotates only the high-order 6 bits of val leftwards, leaving in place the low-order 26 bits of val. The code then xors together three values:

1. the new low-order (old high-order) 6 bits of val;
2. the original, unshifted low-order 26 bits of val; and
3. the current value of m_Hash

leaving the result in m_Hash.

How does it do it? You can just map it out and emulate it:

1. val & 0x3FFFFFF means extract the low-order 26 bits of val.

2. xor those 26 bits with the current value of m_Hash

3. now shift val rightwards such that the low-order 26 bits drop off the low-order end, leaving what used to be the high-order 6 bits of val in the low-order 6 bits of val.

4. Mask with 0x3f to extract only those low-order 6 bits (in case some extraneous bits got shifted into the high order part of val).
5. xor those low-order 6 bits with the current value of m_Hash to give the new m_Hash.

You know that rotating and exclusive-oring are common operations in calculating a hash.

EDIT: @schnaader pointed out the bug in the original code: that code forgot to do the other leg of the rotate: shifting the low-order 26 bits left by 6. To fix that, the code should read something like:

public void AddHash( int val )
{
  m_Hash ^= ((val & 0x3FFFFFF) << 6);
  m_Hash ^= (val >> 26) & 0x3F;
}

As to your HasHash( ) function: you should know that saying

return (m_Hash & val) == 0;

will return TRUE under many conditions, including some you might not want. For example, the function will return TRUE if m_Hash == 0xC0 and val == 0x03.