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Re: stretch/squash LUT computing

 - stretch() is computed from squash() in paq and derivatives.
But how should it normally work?
Let's compute stretch() first, with enough precision.
But then we want a very limited number of values on squash output,
and we know the specific values for corresponding squash inputs (-n..n),
so we can list the values in the precise stretch table, matching these inputs,
Now a question: what value should we use for squash(x), when we known that
a probability range p1..p2 matches x?
The error cost when it should be p, but squash(x) gives q is
(-p*log2(q)-(1-p)*log2(1-q)) - (-p*log2(p)-(1-p)*log2(1-p))
And we have such an error for all probabilities in range p1..p2,
so it has to be summed and minimized by q.

D[ Sum[ p*Log[2,q/p] + (1-p)*Log[2,(1-q)/(1-p)], {p, p1, p2}] ,q]
Solve[((p1-p2-1)*(p1+p2-2*q))/(2*q*(q-1)*Log[2])==0,q] -> q=(p1+p2)/2

Well, this is rather nice and simple, but isn't it different from how
paq stretch/squash init works?