[adrian_b]

They are indeed a useful error signal, like also infinities or NaNs.

Moreover, they are much more benign than infinities or NaNs, which signal bugs that you most likely have to fix.

Denormals cause only very small errors, which may be acceptable in most applications. Therefore you may choose to ignore such bugs and not fix them, because a modified algorithm that avoids underflows may be significantly more complex than the original algorithm.

Configuring the non-standard option to flush denormals to zero is bad for two reasons. Not only it removes evidence that something bad has happened, but unlike with denormals, this can cause huge errors, even infinite errors.

When the operations are done according to the IEEE standard, every operation has a limit for the relative error and it is possible to do a numeric analysis of some computational algorithm and estimate the maximum errors that can affect its results.

When underflows generate neither exceptions nor denormals, all guarantees are removed and you can no longer predict anything about the final errors of an algorithm.