15.5: Fun with Inexact Representations

To add a nail to the coffin, let’s play a bit more with inexact representations. Let us try to see the difference between different numbers:

{
((2.8 asTrueFraction roundTo: 0.01 asTrueFraction) - (2.8 predecessor)) abs -> -1.
((2.8 asTrueFraction roundTo: 0.01 asTrueFraction) - (2.8)) abs -> 0.
((2.8 asTrueFraction roundTo: 0.01 asTrueFraction) - (2.8 successor)) abs -> 1.
} detectMin: [:e | e key ]

    → 0.0->1

The following expression returns 0.0->1, which means that: (2.8 asTrueFraction roundTo: 0.01 asTrueFraction) asFloat = (2.8 successor)

But remember that

(2.8 asTrueFraction roundTo: 0.01 asTrueFraction) ∼= (2.8 successor)

It must be interpreted as the nearest Float to (2.8 asTrueFraction roundTo: 0.01 asTrueFraction) is (2.8 successor).

If you want to know how far it is, then get an idea with:

((2.8 asTrueFraction roundTo: 0.01 asTrueFraction) - (2.8 successor asTrueFraction)) asFloat
    → -2.0816681711721685e-16

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