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EPS

Difference between one and the smallest value greater than one that can be represented as a double-precision floating-point number.

Epsilon is defined as

$$\epsilon = b^{-(p-1)}$$

where b is the radix (base) and p is the precision (number of radix bits in the significand). For double-precision floating-point numbers, b is 2 and p is 53.

Installation

npm install @stdlib/constants-float64-eps

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var EPS = require( '@stdlib/constants-float64-eps' );

EPS

Difference between one and the smallest value greater than one that can be represented as a double-precision floating-point number.

var bool = ( EPS === 2.220446049250313e-16 );
// returns true

Examples

var abs = require( '@stdlib/math-base-special-abs' );
var max = require( '@stdlib/math-base-special-max' );
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );

var bool;
var a;
var b;
var i;

function isApprox( a, b ) {
    var delta;
    var tol;

    delta = abs( a - b );
    tol = EPS * max( abs( a ), abs( b ) );

    return ( delta <= tol );
}

for ( i = 0; i < 100; i++ ) {
    a = randu() * 10.0;
    b = a + (randu()*5.0e-15) - 2.5e-15;
    bool = isApprox( a, b );
    console.log( '%d %s approximately equal to %d. Delta: %d.', a, ( bool ) ? 'is' : 'is not', b, abs( a - b ) );
}

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C APIs

Usage

#include "stdlib/constants/float64/eps.h"

STDLIB_CONSTANT_FLOAT64_EPS

Macro for the difference between one and the smallest value greater than one that can be represented as a double-precision floating-point number.

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See Also

• @stdlib/constants-float32/eps: difference between one and the smallest value greater than one that can be represented as a single-precision floating-point number.

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.