It currently doesn't build in C mode, because NLerp uses HMM_Normalize() instead of HMM_NormalizeQuaternion().

I also doubt that a compiler enforcing real C99 mode would be very happy about your usage of inline in the implementation.
Having function declarations like extern float HMM_CosF(float Angle); and then the implementation as inline float HMM_CosF(float Angle) looks very wrong.
And C99 and newer has that weird thing where functions declared inline in the header must be implemented twice: inline in the header and not-inline in the implementation - which is pretty much the opposite of what you're doing there (to get classic/C++ inline behavior one would just supply a static inline implementation in the header).