Tables containing common logarithms (base-10) were extensively used in computations prior to the advent of electronic calculators and computers because logarithms convert problems of multiplication and division into much easier addition and subtraction problems. Columns of differences are included to aid interpolation. In essence, one trades computing speed for the computer memory space required to store the tables.Ī page from a table of logarithms of trigonometric functions from the 2002 American Practical Navigator. For example, the use of tables of values of the cumulative distribution function of the normal distribution – so-called standard normal tables – remains commonplace today, especially in schools, although the use of scientific and graphical calculators is making such tables redundant.Ĭreating tables stored in random-access memory is a common code optimization technique in computer programming, where the use of such tables speeds up calculations in those cases where a table lookup is faster than the corresponding calculations (particularly if the computer in question doesn't have a hardware implementation of the calculations). Tables of special functions are still used. One of the last major efforts to construct such tables was the Mathematical Tables Project that was started in the United States in 1938 as a project of the Works Progress Administration (WPA), employing 450 out-of-work clerks to tabulate higher mathematical functions. From 1972 onwards, with the launch and growing use of scientific calculators, most mathematical tables went out of use. Early digital computers were developed during World War II in part to produce specialized mathematical tables for aiming artillery. This was motivated mainly by errors in logarithmic tables made by the human computers of the time.

Mechanical special-purpose computers known as difference engines were proposed in the 19th century to tabulate polynomial approximations of logarithmic functions – that is, to compute large logarithmic tables. Tables of common logarithms were used until the invention of computers and electronic calculators to do rapid multiplications, divisions, and exponentiations, including the extraction of nth roots. These mathematical tables from 1925 were distributed by the College Entrance Examination Board to students taking the mathematics portions of the tests

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