>That section is recommended but not required for a conforming implementation:

Who cares? The C standard for math.h requires these functions to be present as specified. They are specified to round correctly, the C standard specifies them to be present as specified, therefore the C standard specifies them as present and correctly rounded. I literally quoted the relevant sections, there are no conforming C specification which give different results.

>Hyperbolic tan is in the list of recommended functions, and yet: https://github.com/numpy/numpy/issues/9187

Any evidence whatsoever that this is caused by two differing implementations of tanh, which BOTH conform to the IEEE 754 standard?

Everyone is free to write their own tanh, it is totally irrelevant what numpy gives, unless there are calls to two standard confirming tanh function which for the same datatype produce different results.

> The C standard for math.h requires these functions to be present as specified. They are specified to round correctly, the C standard specifies them to be present as specified, therefore the C standard specifies them as present and correctly rounded. I literally quoted the relevant sections, there are no conforming C specification which give different results.

Forgive me, but I cannot see that in the document sections you point out. The closest I can see is F.10-3, on page 517, but my reading of that is that it only applies to the Special cases (i.e values in Section 9.2.1), not the full domain.

In fact, my reading of F.10-10 (page 518) suggests that a conforming implementation does not even have to honor the rounding mode.