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Sorted lists of integers are commonly used in inverted indexes and database systems. They are often compressed in memory. We can use the single‐instruction, multiple data (SIMD) instructions available in common processors to boost the speed of integer compression schemes. Our S4‐BP128‐D4 scheme uses as little as 0.7 CPU cycles per decoded 32‐bit integer while still providing state‐of‐the‐art compression...