cc @mdickinson

A safe way to do what you want is:

(1) Take the integral part of the double v that you want to check, for example using modf, still represented as a double. (Note that the integral part of an IEEE 754 floating-point number is always exactly representable in the same format.)
(2) Check that (double)TYPE_MIN <= int_part_of_v < (double)(TYPE_MAX + 1) (using a mixture of C casts and Python chained comparisons here, but you know what I mean)

Computing TYPE_MAX + 1 while avoiding overflow may take some type-specific effort.

The reason that step (2) is safe is that, making the fairly safe assumption of 2s complement (no trap representation, etc., etc.) for signed integers, TYPE_MIN and TYPE_MAX + 1 will always be exactly representable as a double (well, assuming that we're not dealing with 1024-bit integers, that is). But TYPE_MAX can't be assumed to be exactly representable as a double - whether it is or not will depend on the width of the type being tested.

When you're done making the requested changes, leave the comment: I have made the requested changes; please review again.

And if you don't make the requested changes, you will be put in the comfy chair!

@vstinner any update on this?

I failed finding time to finish the PR. I prefer to abandon it.