How to convert a hex float to a float in C/C++ using _mm_extract_ps SSE GCC instrinc function

You should be able to use _MM_EXTRACT_FLOAT.

Incidentally it looks to me as if _mm_extract_ps and _MM_EXTRACT_FLOAT should be the other way around, i.e. _mm_extract_ps should return a float and _MM_EXTRACT_FLOAT should return the int representation, but what do I know.

_mm_cvtss_f32(_mm_shuffle_ps(__X, __X, __N)) will do the job.