eps - Floating-point relative accuracy - MATLAB (original) (raw)

Floating-point relative accuracy

Syntax

Description

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

example

d = eps([x](#br8pqeh-1-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](#br8pqeh-1-datatype)) returnseps according to the data type specified bydatatype, which can be either "double" or"single". The syntax eps("double") (default) is equivalent to eps, andeps("single") is equivalent toeps(single(1.0)).

example

d = eps("like",[p](#mw%5F86fcb61c-1557-4b41-9962-92a6041aeb2f)) returns the positive distance from 1.0 to the next larger floating-point number of the same precision as the floating-point variable p, with the same data type, sparsity, and complexity (real or complex) asp.

example

Examples

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Accuracy in Double Precision

Return the distance from 1.0 to the next larger double-precision number.

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

Compute log2(eps).

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

Return the distance from 10.0 to the next larger double-precision number.

Accuracy in Single Precision

Return the distance from 1.0 to the next larger single-precision number.

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

Compute log2(eps("single")).

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

Return the distance from the single-precision representation of 10.0 to the next larger single-precision number.

Specify Data Type and Complexity from Existing Array

Return the distance from 1.0 to the next larger floating-point number with the same data type and complexity as an existing array.

First, create a complex vector of single data type.

p = single([0.12+2i -0.5i 3]);

Return the distance from 1.0 to the next larger floating-point number as a scalar that is complex like p.

d = single

1.1921e-07 +0.0000e+00i

Specify Sparsity from Existing Array

Create a 10-by-10 sparse matrix.

Return the distance from 1.0 to the next larger floating-point number with the same data type and sparsity as p. The output is a 1-by-1 sparse matrix.

d = sparse double (1,1) 2.2204e-16

Input Arguments

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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, theneps(x) returns NaN.

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

datatype — Output data type

"double" (default) | "single"

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

• eps("double") is equivalent toeps andeps(1.0).
• eps("single") is equivalent toeps(single(1.0)) andsingle(2^-23).

Data Types: char

p — Prototype

floating-point variable

Prototype, specified as a floating-point variable.

Data Types: double | single
Complex Number Support: Yes

Extended Capabilities

Tall Arrays

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

This function supports tall arrays with the limitations:

• Supported syntaxes are eps(x) andeps("like",p), where the underlying data type ofx and p must be a floating-point type.

For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• When FlushToZero mode is enabled in Simulink, the smallest possible value returned by eps(x) in a MATLAB Function Block is realmin(class(x)).

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

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

The eps function supports GPU array input with these usage notes and limitations:

• Supported syntaxes are eps(x) andeps("like",p), where the underlying data type ofx and p must be a floating-point type.

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™.

Usage notes and limitations:

• Supported syntaxes are eps(x) andeps("like",p), where the underlying data type ofx and p must be a floating-point type.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a