Lookup table

In computer science, a lookup table is an array that replaces runtime computation with a simpler array indexing operation. The savings in terms of processing time can be significant, since retrieving a value from memory is often faster than undergoing an 'expensive' computation or input/output operation. The tables may be precalculated and stored in static program storage, calculated (or "pre-fetched") as part of a program's initialization phase (memoization), or even stored in hardware in application-specific platforms. Lookup tables are also used extensively to validate input values by matching against a list of valid (or invalid) items in an array and, in some programming languages, may include pointer functions (or offsets to labels) to process the matching input.

History

Before the advent of computers, lookup tables of values were used to speed up hand calculations of complex functions, such as in trigonometry, logarithms, and statistical density functions.

In ancient (499 CE) India, Aryabhata created one of the first sine tables, which he encoded in a Sanskrit-letter-based number system. In 493 A.D., Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144" Modern school children are often taught to memorize "times tables" to avoid calculations of the most commonly used numbers (up to 9 x 9 or 12 x 12).