Are POSIX’ read() and write() system calls atomic?

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I don’t believe the text you cites implies anything of the sort. It doesn’t even mention read() or write() or POSIX. In fact, read() and write() cannot be relied on to be atomic. The only thing POSIX says is that write() must be atomic if the size of the write is less than PIPE_BUF bytes, and even that only applies to pipes.

I didn’t read the context around the part of the paper you cited, but it sounds like the passage you cited is stating constraints which must be placed on an implementation in order for the algorithm to work correctly. In other words, it states that an implementation of this algorithm requires locking.

How you do that locking is up to you (the implementor). If we are dealing with a regular file and multiple independent processes, you might try fcntl(F_SETLKW)-style locking. If your data structure is in memory and you are dealing with multiple threads in the same process, something else might be appropriate.

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