## fixed point

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.

See also least fixed point.

Last updated: 1995-04-13

## fixed-point

A number representation scheme where a number, F is represented by an integer I such that F=I*R^-P, where R is the (assumed) radix of the representation and P is the (fixed) number of digits after the radix point.

On computers with no floating-point unit, fixed-point calculations are significantly faster than floating-point as all the operations are basically integer operations. Fixed-point representation also has the advantage of having uniform density, i.e., the smallest resolvable difference of the representation is R^-P throughout the representable range, in contrast to floating-point representations.

For example, in PL/I, FIXED data has both a precision and a scale-factor (P above). So a number declared as 'FIXED DECIMAL(7,2)' has a precision of seven and a scale-factor of two, indicating five integer and two fractional decimal digits. The smallest difference between numbers will be 0.01.

Last updated: 2006-11-15

### Nearby terms:

fix ♦ fixed disk ♦ **fixed point** ♦ fixed-point ♦ fixed point combinator

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