concurrency - What happens if two threads read & write the same piece of memory

Question

It's my understanding that if two threads are reading from the same piece of memory, and no thread is writing to that memory, then the operation is safe. However, I'm not sure what happens if one thread is reading and the other is writing. What would happen? Is the result undefined? Or would the read just be stale? If a stale read is not a concern is it ok to have unsynchronized read-write to a variable? Or is it possible the data would be corrupted, and neither the read nor the write would be correct and one should always synchronize in this case?

I want to say that I've learned it is the later case, that a race on memory access leaves the state undefined... but I don't remember where I may have learned that and I'm having a hard time finding the answer on google. My intuition is that a variable is operated on in registers, and that true (as in hardware) concurrency is impossible (or is it), so that the worst that could happen is stale data, i.e. the following:

WriteThread: copy value from memory to register
WriteThread: update value in register
ReadThread:  copy value of memory to register
WriteThread: write new value to memory

At which point the read thread has stale data.

Answer 1

The result is undefined. Corrupted data is entirely possible. For an obvious example, consider a 64-bit value being manipulated by a 32-bit processor. Let's assume the value is a simple counter, and we increment it when the lower 32-bits contain 0xffffffff. The increment produces 0x00000000. When we detect that, we increment the upper word. If, however, some other thread read the value between the time the lower word was incremented and the upper word was incremented, they get a value with an un-incremented upper word, but the lower word set to 0 -- a value completely different from what it would have been either before or after the increment is complete.