[hansvm]

That's not totally true. It's sufficient to be exactly representable, but you only need the reciprocal rounding error to be small enough to guarantee the multiplication rounding step fixes it across the entire range of numerators. For IEEE754 f16 values, there are 28 such extra values, the positive and negative sides of 1705/x where x is a power of 2 at least as great as 2048.

[mgaunard]

Interesting, but pretty limited corner case. Would compilers even identify those 28 values and do the transformation?

[hansvm]

Maybe for f16. The compiler's implementation could just be checking all numerators to see if the transformation is safe. The corner cases are messy and not quickly brute-forceable for f32 or brute-forceable at all for f64 though, so I doubt they'd bother, especially when I bet those constants have showed up literally zero times across all programs.