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We explore how to speed up binary search by batching independent searches with NumPy's vectorized operations. We then reformulate the algorithm so all searches progress together with only $O(1)$ additional memory, port it to C++, and achieve up to a 25× speedup over NumPy 2.4's implementation.
Donald Knuth famously quipped that "premature optimization is the root of all evil." The reasons are straightforward: optimized code tends to be much more difficult to read and debug than simpler implementations of the same algorithm, and optimizing too early leads to greater costs down the road.
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