stdint header for functions exported from dll

Question

I have a header for exporting some methods from a DLL which can be used both from C and C++ code:

#ifdef __cplusplus
extern "C"
 {
#endif

    API_EXPORT uint32_t __cdecl GetSomeValue();

#ifdef __cplusplus
 }
#endif

and for uint32_t, I need to include a header, but which one is correct?

Option 1: <stdint.h>

#ifdef __cplusplus
extern "C"
{
#endif

#include <stdint.h>

Option 2:

#ifdef __cplusplus
extern "C"
{
#endif

#include <cstdint>

Option 3: both.

#ifdef __cplusplus
extern "C"
{
#include <cstdint>
#else
#include <stdint.h>
#endif

Answer 1

You... just include the header.

#include <stdint.h>

#ifdef __cplusplus
extern "C"
 {
#endif

    API_EXPORT uint32_t __cdecl GetSomeValue();

#ifdef __cplusplus
 }
#endif

You don't need to use extern "C" {} around built-in headers. (Sometimes you might find libraries that do need it)

Answer 2

Your option 2 generally will not work in conjunction with C compilers, so that's out. Your option 1, or the variation presented in @user253751's answer, should be fine, but if you are concerned with protecting against buggy C, C++, or standard library implementations then I would go with this variation on your option 3:

#ifdef __cplusplus
#include <cstdint>
extern "C"
{
#else
#include <stdint.h>
#endif