eps - Floating-point relative accuracy - MATLAB (original) (raw)
Floating-point relative accuracy
Syntax
Description
[d](#mw%5F446f45e0-ecaa-4512-b766-a85d3cbfd1fd) = eps returns 2-52, which is the distance from1.0 to the next larger double-precision number.
[d](#mw%5F446f45e0-ecaa-4512-b766-a85d3cbfd1fd) = eps([x](#br8pqeh-1-x)), wherex has data type single ordouble, returns the positive distance fromabs(x) to the next larger floating-point number of the same precision as x. If x has typeduration, then eps(x) returns the next larger duration value. The command eps(1.0) is equivalent to eps.
[d](#mw%5F446f45e0-ecaa-4512-b766-a85d3cbfd1fd) = eps([datatype](#br8pqeh-1-datatype)) returns eps 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)).
[d](#mw%5F446f45e0-ecaa-4512-b766-a85d3cbfd1fd) = 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 variablep, with the same data type, sparsity, and complexity (real or complex) as p.
Examples
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.
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.
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
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
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
Output data type, specified as "double" or"single".
eps("double")is equivalent toepsandeps(1.0).eps("single")is equivalent toeps(single(1.0))andsingle(2^-23).
Data Types: char
Prototype, specified as a floating-point variable.
Data Types: double | single
Complex Number Support: Yes
Output Arguments
Output array, returned as a scalar, vector, matrix, or multidimensional array.
Extended Capabilities
This function supports tall arrays with the limitations:
- Supported syntaxes are
eps(x)andeps(like=p), where the underlying data type ofxandpmust be a floating-point type.
For more information, see Tall Arrays.
Usage notes and limitations:
- When
FlushToZeromode is enabled in Simulink, the smallest possible value returned byeps(x)in a MATLAB Function Block isrealmin(class(x)).
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 ofxandpmust be a floating-point type.
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Usage notes and limitations:
- Supported syntaxes are
eps(x)andeps(like=p), where the underlying data type ofxandpmust be a floating-point type.
For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Version History
Introduced before R2006a