What is the purpose of libc_nonshared.a?

It was a legacy mistake in glibc's implementing extensibility for the definition of struct stat before better mechanisms (symbol redirection or versioning) were thought of. The definitions of the stat-family functions in libc_nonshared.a cause the version of the structure to bind at link-time, and the definitions there call the __xstat-family functions in the real shared libc, which take an extra argument indicating the desired structure version. This implementation is non-conforming to the standard since each shared library ends up gettings its own copy of the stat-family functions with their own addresses, breaking the requirement that pointers to the same function evaluate equal.

Here's the problem. Long ago, members of the struct stat structure had different sizes than they had today. In particular:

uid_t was 2 bytes (though I think this one was fixed in the transition from libc5 to glibc)
gid_t was 2 bytes
off_t was 4 bytes
blkcnt_t was 4 bytes
time_t was 4 bytes

also, timespec wasn't used at all and there was no room for nanosecond precision.

So all of these had to change. The only real solution was to make different versions of the stat() system call and library function and you get the version you compiled against. That is, the .a file matches the header files. These things didn't all change at once, but I think we're done changing them now.

You can't really solve this by a macro because the structure name is the same as the function name; and inline wasn't mandated to exist in the beginning so glibc couldn't demand everybody use it.

I remember there used to be this thing O_LARGEFILE for saying you could handle files bigger than 4GB; otherwise things just wouldn't work. We also used to have to define things like _LARGEFILE_SOURCE and _LARGEFILE64_SOURCE but it's all handled automatically now. Back in the day, if you weren't ready for large file support yet, you didn't define these and you didn't get the 64-bit version of the stat structure; and also worked on older kernel versions lacking the new system calls. I haven't checked; it's possible that 32-bit compilation still doesn't define these automatically, but 64-bit always does.

So you probably think; okay, fine, just don't franken-compile stuff? Just build everything that goes into the final executable with the same glibc version and largefile-choice. Ever use plugins such as browser plugins? Those are pretty much guaranteed to be compiled in different places with different compiler and glibc versions and options; and this didn't require you to upgrade your browser and replace all its plugins at the same time.