How can I find the implementations of Linux kernel system calls?
System calls aren't handled like regular function calls. It takes special code to make the transition from user space to kernel space, basically a bit of inline assembly code injected into your program at the call site. The kernel side code that "catches" the system call is also low-level stuff you probably don't need to understand deeply, at least at first.
In include/linux/syscalls.h under your kernel source directory, you find this:
asmlinkage long sys_mkdir(const char __user *pathname, int mode);
Then in /usr/include/asm*/unistd.h, you find this:
#define __NR_mkdir 83
__SYSCALL(__NR_mkdir, sys_mkdir)
This code is saying mkdir(2) is system call #83. That is to say, system calls are called by number, not by address as with a normal function call within your own program or to a function in a library linked to your program. The inline assembly glue code I mentioned above uses this to make the transition from user to kernel space, taking your parameters along with it.
Another bit of evidence that things are a little weird here is that there isn't always a strict parameter list for system calls: open(2), for instance, can take either 2 or 3 parameters. That means open(2) is overloaded, a feature of C++, not C, yet the syscall interface is C-compatible. (This is not the same thing as C's varargs feature, which allows a single function to take a variable number of arguments.)
To answer your first question, there is no single file where mkdir() exists. Linux supports many different file systems and each one has its own implementation of the "mkdir" operation. The abstraction layer that lets the kernel hide all that behind a single system call is called the VFS. So, you probably want to start digging in fs/namei.c, with vfs_mkdir(). The actual implementations of the low-level file system modifying code are elsewhere. For instance, the ext4 implementation is called ext4_mkdir(), defined in fs/ext4/namei.c.
As for your second question, yes there are patterns to all this, but not a single rule. What you actually need is a fairly broad understanding of how the kernel works in order to figure out where you should look for any particular system call. Not all system calls involve the VFS, so their kernel-side call chains don't all start in fs/namei.c. mmap(2), for instance, starts in mm/mmap.c, because it's part of the memory management ("mm") subsystem of the kernel.
I recommend you get a copy of "Understanding the Linux Kernel" by Bovet and Cesati.
This probably doesn't answer your question directly, but I've found strace to be really cool when trying to understand the underlying system calls, in action, that are made for even the simplest shell commands. e.g.
strace -o trace.txt mkdir mynewdir
The system calls for the command mkdir mynewdir will be dumped to trace.txt for your viewing pleasure.
A good place to read the Linux kernel source is the Linux cross-reference (LXR)¹. Searches return typed matches (functions prototypes, variable declarations, etc.) in addition to free text search results, so it's handier than a mere grep (and faster too).
LXR doesn't expand preprocessor definitions. System calls have their name mangled by the preprocessor all over the place. However, most (all?) system calls are defined with one of the SYSCALL_DEFINEx families of macros. Since mkdir takes two arguments, a search for SYSCALL_DEFINE2(mkdir leads to the declaration of the mkdir syscall:
SYSCALL_DEFINE2(mkdir, const char __user *, pathname, int, mode)
{
return sys_mkdirat(AT_FDCWD, pathname, mode);
}
ok, sys_mkdirat means it's the mkdirat syscall, so clicking on it only leads you to the declaration in include/linux/syscalls.h, but the definition is just above.
The main job of mkdirat is to call vfs_mkdir (VFS is the generic filesystem layer). Cliking on that shows two search results: the declaration in include/linux/fs.h, and the definition a few lines above. The main job of vfs_mkdir is to call the filesystem-specific implementation: dir->i_op->mkdir. To find how this is implemented, you need to turn to the implementation of the individual filesystem, and there's no hard-and-fast rule — it could even be a module outside the kernel tree.
¹ LXR is an indexing program. There are several websites that provide an interface to LXR, with slightly different sets of known versions and slightly different web interfaces. They tend to come and go, so if the one you're used to isn't available, do a web search for “linux cross-reference” to find another.