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# Epsilon

> Difference between one and the smallest value greater than one that can be represented as a [double-precision floating-point number][ieee754].

<section class="intro">

[Epsilon][machine-epsilon] is defined as

<!-- <equation class="equation" label="eq:epsilon_float64" align="center" raw="\epsilon = b^{-(p-1)}" alt="Epsilon for a double-precision floating-point number."> -->

<div class="equation" align="center" data-raw-text="\epsilon = b^{-(p-1)}" data-equation="eq:epsilon_float64">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@5d87cc7cb2c58aeb732872f89562d2c89571cc8a/lib/node_modules/@stdlib/constants/float64/eps/docs/img/equation_epsilon_float64.svg" alt="Epsilon for a double-precision floating-point number.">
    <br>
</div>

<!-- </equation> -->

where `b` is the radix (base) and `p` is the precision (number of radix bits in the significand). For [double-precision floating-point numbers][ieee754], `b` is `2` and `p` is `53`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var FLOAT64_EPSILON = require( '@stdlib/constants/float64/eps' );
```

#### FLOAT64_EPSILON

Difference between one and the smallest value greater than one that can be represented as a [double-precision floating-point number][ieee754].

```javascript
var bool = ( FLOAT64_EPSILON === 2.220446049250313e-16 );
// returns true
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var abs = require( '@stdlib/math/base/special/abs' );
var max = require( '@stdlib/math/base/special/max' );
var randu = require( '@stdlib/random/base/randu' );
var FLOAT64_EPSILON = 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 = FLOAT64_EPSILON * 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 ) );
}
```

</section>

<!-- /.examples -->

<section class="links">

[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985

[machine-epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon

</section>

<!-- /.links -->