The Big-O for sorting algorithms is typically on the number of comparisons. The problem with that is that a comparison takes 1 cycle and you can do 4 per cycle in scalar code or much more in SIMD. Obviously comparisons of doubles are going to be a bit more expensive. Memory reads, on the other hand, take 4 cycles from L1, 10 from L2, and it goes up from there. If you have a predictable memory access pattern, the CPU can preload everything into cache for you, and if you have a deep enough pipeline you can cover up memory reads. Memory access is often completely ignored when analyzing sorting algorithms.
Heapsort has the minimum number of comparisons. Search up "An optimal algorithm for deleting the root of a heap" by Svante Carlsson. Notice how Heapsort is commonly used only as a fallback sort? That's because minimizing comparisons isn't the most important.
Heapsort has the minimum number of comparisons. Search up "An optimal algorithm for deleting the root of a heap" by Svante Carlsson. Notice how Heapsort is commonly used only as a fallback sort? That's because minimizing comparisons isn't the most important.