Often (parts of) the C standard library (those needed for a freestanding environment) are actually "baked in" to the compiler, and not actually separate header

Often (parts of) the C standard library (those needed for a freestanding environment) are actually "baked in" to the compiler, and not actually separate header files at all (though equivalent headers may be provided as well). In C89, those are float.h, limits.h, iso646.h, stdarg.h, and stddef.h. C99 added stdbool.h, and stdint.h. C11 added stdalign.h, and stdnoreturn.h. So those headers are part of the standard library, but they're also usually part of the compiler. The line gets very blurry.