Is mv atomic on my fs?

Interestingly enough, it seems the answer may be, "It depends".

To be clear, mv is specified to

The mv utility shall perform actions equivalent to the rename() function

The rename function specification states:

This rename() function is equivalent for regular files to that defined by the ISO C standard. Its inclusion here expands that definition to include actions on directories and specifies behavior when the new parameter names a file that already exists. That specification requires that the action of the function be atomic.

But the latest the ISO C specification for rename() states:

7.21.4.2 The rename function

Synopsis

#include <stdio.h>
int rename(const char *old, const char *new);

Description

The rename function causes the file whose name is the string pointed to by old to be henceforth known by the name given by the string pointed to by new. The file named old is no longer accessible by that name. If a file named by the string pointed to by new exists prior to the call to the rename function, the behavior is implementation-defined.

Returns

The rename function returns zero if the operation succeeds, nonzero if it fails, in which case if the file existed previously it is still known by its original name.

Surprisingly, note that there is no explicit requirement for atomicity. It may be required somewhere else in the latest publicly-available C Standard, but I haven't been able to find it. If anyone can find such a requirement, edits and comments are more than welcome.

See also Is rename() atomic?

Per the Linux man page:

If newpath already exists, it will be atomically replaced, so that there is no point at which another process attempting to access newpath will find it missing. However, there will probably be a window in which both oldpath and newpath refer to the file being renamed.

The Linux man page claims the replacement of the file will be atomic.

Testing and verifying that atomicity might be very difficult, though, if that is how far you need to go. You're not clear as to what you mean in your use of "How can I check if mv is atomic". Do you want requirements/specification/documentation that it's atomic, or do you need to actually test it?

Note also, the above assumes the two operand file names are in the same file system. I can find no standard restriction on the mv utility to enforce that.