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There's no syscall on every allocation. With many allocators, the common case is popping a node off a linked list.

That's why I put the word "potential" in there. Every allocation potentially needs to go to the OS for more pages.

And every memory access potentially enters the kernel via a page fault.

Any given CPU instruction potentially isn't in cache.

And yet, they can't all not be in cache. As soon as the cache is accessed for one instruction, a bunch more are pulled in too.

Any given vector.push call could reallocate the vector, but it's amortized O(1).