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So problem solved, right? 80 bits of precision means the collision didn't happen, but in 32 bits of precision it does, and that's your problem, more bits better, QED, right? Well not quite.

The guard's toe overlaps in both cases - a few millimeters is still significantly larger than ANY of the possible precisions. In both the SSE and x87 versions, the door hits the guard's toe. So far, both agree.