Precompute

Precomputation is the process of performing a portion of a computation ahead of time, before the results are needed at runtime. In practice, this means computing and storing intermediate results so that later operations can be answered quickly. Precomputation is often used when the same queries are repeated or latency is critical, and when the cost of computing the results online would be prohibitive.

Common techniques include caching, memory-mapped lookup tables, and materialized data such as prefix sums or hashed indices. Examples: precomputed lookup tables for trigonometric functions, prefix sums for fast range-sum queries, and precomputed lighting data such as lightmaps in computer graphics. In databases, materialized views perform precomputation to accelerate frequent queries.

Trade-offs: precomputation trades increased memory usage and longer initialization time for faster query responses. Data can become stale and require cache invalidation or refresh strategies. Systems must manage consistency, synchronization, fault tolerance, and the possibility that precomputed results are not reusable if inputs change.

Applications span algorithms, databases, graphics, and cryptography. In cryptography, precomputation can speed repeated operations in protocols or attacks, such as baby-step giant-step. In search and AI pipelines, feature preprocessing and cached embeddings can reduce online latency.

Design considerations include understanding query patterns, estimating the benefit-to-cost ratio, and choosing appropriate storage. Where appropriate, offline precomputation with scheduled refreshes or incremental updates can reduce runtime impact. Documentation should note assumptions, expiration policies, and how to invalidate stale data.