Implementers shouldn't need to jump through these hoops. When you find yourself needing to relax or bypass spec semantics just to achieve reasonable performance, that's a sign something is wrong with the spec itself. A well-designed streaming API should be efficient by default, not require each runtime to invent its own escape hatches.
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Notice how the highlighted region shrinks at each step. The algorithm never examines points outside the narrowing window. In a balanced tree with nnn points, this takes about log4(n)\log_4(n)log4(n) steps. For a million points, that's roughly 10 steps instead of a million comparisons.