It might be notable that on very small lists (up to around 50, maybe 100 depending on cpu/cache) insertion sort is fastest of all, even on difficult input distributions. Its so simple that cpu can skip through it rapidly. I noticed this myself and have also read other developers mention it in sort design discussions. A popular general purpose sort called 'Timsort' defaults to it for small sequences. Its possible to tweak the insert algorithm to sum distance of elements moved so far and escape to a more substantial algorithm when it gets excessive. If little rearrangement is required insertion sort is about as fast as scanning through memory can be.

I think in practice the answer to the question "which should I use" (rather than "which should ideally be used") is the best developed hybrid sort library for the platform. Beyond the suitable case for insertion sort, its a really substantial job for an individual to develop, test and optimize a high performance sort library that can handle a range of distribution types.

LSB radix sort can be slow, but MSB radix sort is the fastest sorting algorithm for an array of machine words.

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