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eps

Floating-point relative accuracy

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Syntax

d = eps
d = eps(x)
d = eps(datatype)
d = eps("like",p)

Description

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

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)).

example

d = eps("like",p) 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) as p.

example

Examples

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Open Live Script

Return the distance from 1.0 to the next larger 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.

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

d = eps(10.0)
d = 
1.7764e-15
Open Live Script

Return the distance from 1.0 to the next larger 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.

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

d = eps(single(10.0))
d = single

9.5367e-07
Open Live Script

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 = eps("like",p)
d = single

1.1921e-07 +0.0000e+00i
Open Live Script

Create a 10-by-10 sparse matrix.

p = sparse(10,10,pi);

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 = eps("like",p)
d = sparse double
   (1,1)      2.2204e-16

Input Arguments

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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: double | single | duration
Complex Number Support: Yes

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

Prototype, specified as a floating-point variable.

Data Types: double | single
Complex Number Support: Yes

Extended Capabilities

Version History

Introduced before R2006a

See Also

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