xor: how come so slow?

[Lawrence D'Oliveiro]

In message <gdea3t$4tj$1 at lust.ihug.co.nz>, Lawrence D'Oliveiro wrote:

> In message <010a9c3f$0$20653$c3e8da3 at news.astraweb.com>, Steven D'Aprano
> wrote:
> 
>> On Sat, 18 Oct 2008 09:16:11 +1300, Lawrence D'Oliveiro wrote:
>> 
>>> Data can come in fractional bits. That's how compression works.
>> 
>> If you don't believe me, try compressing a single bit and see if you get
>> a "fractional bit".
> 
> If both states of the bit are not equally likely, then you do indeed have
> a fractional bit, since
> 
>     nrbits = (- logbase2(P[bit = 0]) - logbase2(P[bit = 1])) / 2

Oops, sorry, the formula should of course be

    nrbits = - P[bit = 0] * logbase2(P[bit = 0])
        - P[bit = 1] * logbase2(P[bit = 1])