What do you mean by Atomic instructions?

How does the following become Atomic?

TestAndSet

int TestAndSet(int *x){
   register int temp = *x;
   *x = 1;
   return temp;
}

From a software perspective, if one does not want to use non-blocking synchronization primitives, how can one ensure Atomicity of instruction? is it possible only at Hardware or some assembly level directive optimization can be used?

language-agnostic synchronization nonblocking atomic test-and-set
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