Doesn't it mean that, when you compute - say - sin(123.45) then the resulting computed value is - of all the finite numbers of possible floating point values th

Doesn't it mean that, when you compute - say - sin(123.45) then the resulting computed value is - of all the finite numbers of possible floating point values that the underlying MPFR representation can encode - the one that is closest to the true value of sin(123.45)? That may not be what it does, but that's certainly what I'd expect "correct rounding" to do.