[wfleming]

We’re in very nitpicky terminology weeds here (and I’m not the person you’re replying to), but my understanding is “commutative” is specifically about reordering operands of one binary op (4+3 == 3+4), while “associative” is about reordering a longer chain of the same operation (1+2+3 == 1+3+2).

Edit: Wikipedia actually says associativity is definitionally about changing parens[0]. Mostly amounts to the same thing for standard arithmetic operators, but it’s an interesting distinction.

[0]: https://en.wikipedia.org/wiki/Associative_property

[nyrikki]

It is not a nit it is fundamental, a•b•c is associativity, specifically operator associativity.

Rounding and eventual underflow in IEEE means an expression X•Y for any algebraic operation • produces, if finite, a result (X•Y)·( 1 + ß ) + µ where |µ| cannot exceed half the smallest gap between numbers in the destination’s format, and |ß| < 2^-N , and ß·µ = 0 . ( µ ≠ 0 only when Underflow occurs.)

And yes that is a binary relation only

a•b•c is really (a•b)•c assuming left operator associativity, one of the properties that IEEE doesn't have.