Precalculated

Precalculated refers to data or results that are computed in advance and stored for rapid retrieval during later use. In contrast to values computed on the fly, precalculated data is prepared in a preparatory step, often offline, and then accessed via direct lookup or simple interpolation. This approach trades memory and storage requirements for speed and determinism.

Common forms include lookup tables, cached results, and fixed constants embedded in software or hardware. Precalculation is widely used in algorithms, digital signal processing, computer graphics, cryptography, and numerical methods. For example, lookup tables store values of trigonometric functions or logarithms for a discrete set of inputs. In hardware, read-only memory (ROM) can contain precalculated constants or tables that drive logic without performing computations at runtime. In cryptography, precalculated tables of powers or hashes can speed up repeated operations.

Advantages include faster execution, lower latency, and predictable timing. Limitations involve increased memory usage, potential inaccuracy due to finite discretization, and the need to regenerate tables if input domains expand or precision requirements change. Precalculated data can become outdated if the underlying functions or parameters change.

Generation typically occurs in an offline stage using a script, a build process, or a dedicated preprocessing tool. Maintenance considerations include documenting the table domain, precision, and update procedures, as well as versioning the data to ensure reproducibility.