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Try this:

| a b c |
a := 16rFFFFFFFFFFFFF710 / 16r1000000000000.
b := 16rFFFFFFFFFFFFF701 / 16r1000000000000.
c := a asFloat.
Array
    with: ((Set new) add: a; add: b; add: c; size)
    with: ((Set new) add: c; add: a; add: b; size).

you will get one set of size 2, and one set of size 1.

I argue that i should have one set of size 3, because c machine representation is (16rFFFFFFFFFFFFF700 / 16r1000000000000), neither equal to a nor b.

So where is the mistake ?
I think it is in coercing Fraction to Float or Double.
Float and Double are subsets of Fraction, they are less general (and they are certainly not covering Real numbers, no machine can do that, it is proven that some real numbers do not even have an algorithm that can compute them).

The price for making more efficient arithmetic, but less rigourous is the above bug among others.
Can we tolerate such behavior ?

Nicolas

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