My eclipse does red-underline  to uint32_t, uint16_t, etc... though I included <stdint.h> and set preprocessor path!
To know why it happens, I looked in <stdint.h>.
#ifndef _GCC_WRAP_STDINT_H
#if __STDC_HOSTED__
# if defined __cplusplus && __cplusplus >= 201103L
#  undef __STDC_LIMIT_MACROS
#  define __STDC_LIMIT_MACROS
#  undef __STDC_CONSTANT_MACROS
#  define __STDC_CONSTANT_MACROS
# endif
# include_next <stdint.h>        // here
#else
# include "stdint-gcc.h"
#endif
#define _GCC_WRAP_STDINT_H
#endif
Um, I think it seems that eclipse can't recognize #include_next. But I don't know solution.. Could you give me a advice?
 
    