I\'ve heard that i++ isn\'t a thread-safe statement since in assembly it reduces down to storing the original value as a temp somewhere, incrementing it, and then replacing
The 1998 C++ standard has nothing to say about threads, although the next standard (due this year or the next) does. Therefore, you can't say anything intelligent about thread-safety of operations without referring to the implementation. It's not just the processor being used, but the combination of the compiler, the OS, and the thread model.
In the absence of documentation to the contrary, I wouldn't assume that any action is thread-safe, particularly with multi-core processors (or multi-processor systems). Nor would I trust tests, as thread synchronization problems are likely to come up only by accident.
Nothing is thread-safe unless you have documentation that says it is for the particular system you're using.