Your cplusplus changes look good.

Based on this definition:
The <time.h> header declares the structure timespec, which has at least the following members:

time_t tv_sec seconds
long tv_nsec nanoseconds

Please try the following cast on your side for consistency with the definition (e.g. use time_t and long):
struct timespec sleep_time = {
.tv_sec = (time_t)(ms / MS_PER_SECOND),
.tv_nsec = (long)((ms % MS_PER_SECOND) * NS_PER_MS)
};

This compiles ok on my side w/o warnings.