LookupTables

Lookup tables, or LUTs, are data structures that map input values to precomputed output values, allowing rapid retrieval by indexing or hashing. They replace runtime computations with a table lookup, typically achieving constant-time access and predictable performance. A LUT is usually implemented as an array of outputs, with the input value used as the index, but it can also be built on a hash-based structure for larger or sparser domains, or as a hardware ROM in digital circuits.

Common forms include direct-address LUTs implemented as contiguous arrays for small input domains; hashed LUTs where a function maps inputs to table positions; perfect hash tables that avoid collisions for a known set of keys; and hardware LUTs used in FPGAs and ASICs to implement logic.

Construction and use: A LUT can be generated by evaluating a function at all inputs in its domain or by capturing measured data. In software, LUTs can be static (compiled in) or dynamic (modifiable at runtime). The choice affects memory use, updateability, and performance. Precision and domain size influence feasibility.

Applications: Graphics and image processing use gamma correction and color mapping LUTs; audio digital signal processing employs sample-rate or nonlinear transformations; font rendering and color palettes rely on fast mappings; cryptographic S-boxes and certain compiler optimizations also rely on table-based substitutions.

Design considerations: Trade-offs between memory footprint and speed; cache locality and access patterns; domain sparsity and updateability; potential rounding errors or aliasing. Properly designed LUTs offer fast, predictable performance but require careful management of the input domain and precision. See also: hash tables, direct addressing, S-boxes, gamma correction.