Re: [hash2] Comments

From: Peter Dimov (pdimov_at_[hidden])
Date: 2024-12-07 01:06:51

> Andrey Semashev wrote:
> > 2. Somewhat related, on the use case of extending the size of the hash
> > value by repeatedly calling result(). Is this something that should be
> > encouraged? I'm not a specialist, but my understanding is that
> > extending the hash value this way does not improve its quality, as you
> > get a series of bits in the value that are predetermined based on the
> > lower bits. Isn't that effectively equivalent to just e.g. zero-extending the
> hash value?
> 
> No, it isn't. Hashes often have more internal state than they output as the final
> result, so extension can actually produce non-redundant bits. This is true, for
> example, for xxhash and siphash, and there's an example in the docs of
> extending xxhash.
> 
> Even if the effective number of bits doesn't change, it's still not the same as
> zero-extending, because a zero-extended hash is of very poor quality.
> (The constant zero bits, being constant and zero, are completely unaffected by
> the input.)
> 
> Somewhat related, if you ask get_integral_result for more bits than there are
> in the input value, it takes care to not just give you something zero- extended,
> for the same reason.
> 
> Ideally, each bit in the hash value should have about 50% probability of being
> 1. This is called "avalanche property".

So, for example, if you have a 32 bit hash function and you need 64 bits, this
is how you would do it, ordered from best to worst:

// as good as possible
uint64_t f1( Hash& hash )
{
    uint32_t r1 = hash.result();
    uint32_t r2 = hash.result();
    return (uint64_t(r1) << 32) | r2;
}

// not that bad, but worse than the above
uint64_t f2( Hash& hash )
{
    return get_integral_result<uint64_t>( hash.result() );
}

// pretty bad, but at least better than the next one
uint64_t f3( Hash& hash )
{
    uint32_t r = hash.result();
    return (uint64_t(r) << 32) | r;
}

// worst possible
uint64_t f4( Hash& hash )
{
    return hash.result();
}