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Certain patterns of access avoid any problem even if an access is interrupted. For example, a flag which is set by the handler, and tested and cleared by the main program from time to time, is always safe even if access actually requires two instructions. To show that this is so, we must consider each access that could be interrupted, and show that there is no problem if it is interrupted.
An interrupt in the middle of testing the flag is safe because either it’s recognized to be nonzero, in which case the precise value doesn’t matter, or it will be seen to be nonzero the next time it’s tested.
An interrupt in the middle of clearing the flag is no problem because either the value ends up zero, which is what happens if a signal comes in just before the flag is cleared, or the value ends up nonzero, and subsequent events occur as if the signal had come in just after the flag was cleared. As long as the code handles both of these cases properly, it can also handle a signal in the middle of clearing the flag. (This is an example of the sort of reasoning you need to do to figure out whether non-atomic usage is safe.)
Sometimes you can ensure uninterrupted access to one object by protecting its use with another object, perhaps one whose type guarantees atomicity. See Signals Close Together Merge into One, for an example.