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eps

Floating-point relative accuracy

Syntax

Description

example

d = eps returns the distance from 1.0 to the next larger double-precision number, that is, eps = 2^-52.

example

d = eps(x), where x has data type single or double, returns the positive distance from abs(x) to the next larger floating-point number of the same precision as x. If x has type duration, then eps(x) returns the next larger duration value. The command eps(1.0) is equivalent to eps.

example

d = eps(datatype) returns eps according to the data type specified by datatype, which can be either 'double' or 'single'. The syntax eps('double') (default) is equivalent to eps, and eps('single') is equivalent to eps(single(1.0)).

Examples

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Accuracy in Double Precision

Display the distance from 1.0 to the next largest double-precision number.

d = eps
d =

   2.2204e-16

eps is equivalent to eps(1.0) and eps('double').

Compute log2(eps).

d = log2(eps)
d =

   -52

In base 2, eps is equal to 2^-52.

Find the distance from 10.0 to the next largest double-precision number.

d = eps(10.0)
d =

   1.7764e-15

Accuracy in Single Precision

Display the distance from 1.0 to the next largest single-precision number.

d = eps('single')
d =

  1.1921e-07

eps('single') is equivalent to eps(single(1.0)).

Compute log2(eps('single')).

d = log2(eps('single'))
d =

   -23

In base 2, single-precision eps is equal to 2^-23.

Find the distance from the single-precision representation of 10.0 to the next largest single-precision number.

d = eps(single(10.0))
d =

  9.5367e-07

Input Arguments

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x — Input arrayscalar | vector | matrix | multidimensional array

Input array, specified as a scalar, vector, matrix, or multidimensional array. d is the same size as x. For all x, eps(x) = eps(-x) = eps(abs(x)). If x is complex, d is the distance to the next larger floating-point number in magnitude. If x is Inf or NaN, then eps(x) returns NaN.

Data Types: single | double | duration
Complex Number Support: Yes

datatype — Output data type'double' (default) | 'single'

Output data type, specified as 'double' or 'single'.

  • eps('double') is equivalent to eps and eps(1.0).

  • eps('single') is equivalent to eps(single(1.0)) and single(2^-23).

Data Types: char

Introduced before R2006a

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