# fixed point

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## fixed point

[¦fikst ′pȯint]
(engineering)
A reproducible value, as for temperature, used to standardize measurements; derived from intrinsic properties of pure substances.
(mathematics)
For a function ƒ mapping a set S to itself, any element of S which ƒ sends to itself.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Fixed Point

a form of representation of numbers in a digital computer with constant position of the point that sepa-rates the whole part of the number from the fraction. The fixed point corresponds to the natural form of representation of numbers. The point may be fixed at any position of the number—for example, in a digital computer five-place numbers with a fixed point after the second place are represented as +74.531, +07.453, +00.745, and so on. To prevent the numbers formed in the process of calculations from going beyond the range of representable numbers, scale factors are incorporated into the input data and intermediate and final results when drawing up programs for computers with a fixed point. However, the fixing of the point before the high-order digit of the modulus of the number (a number less than 1) is more expedient; in such a case the word format of the digital computer is not overloaded during multiplication of numbers. The range of representable numbers is narrower in a digital computer with a fixed point than in a digital computer with a floating point. The complication of programming when a fixed point is used is compensated in some cases by the simplicity of the devices of the digital computer and the ease in carrying out arithmetic operations, and also by the possibility of achieving greater speed in addition and subtraction. A fixed point was used in the Soviet Minsk-1, Setun’, and Ural-1 digital computers and in most digital control computers.

A. V. GUSEV

## fixed point

(mathematics)
The fixed point of a function, f is any value, x for which f x = x. A function may have any number of fixed points from none (e.g. f x = x+1) to infinitely many (e.g. f x = x). The fixed point combinator, written as either "fix" or "Y" will return the fixed point of a function.