eps

Floating-point relative accuracy

Syntax

d = eps

d = eps(x)

d = eps(datatype)

Description

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

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.

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

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 = single
    1.1921e-07

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

Compute log2(eps('single')).

d = log2(eps('single'))

d = single
    -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 = single
    9.5367e-07

Input Arguments

x — Input array

scalar | 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

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).