Epsilon

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

Epsilon is defined as

where b is the radix (base) and p is the precision (number of radix bits in the significand). For half-precision floating-point numbers, b is 2 and p is 11.

Installation

npm install @stdlib/constants-float16-eps

Usage

var FLOAT16_EPSILON = require( '@stdlib/constants-float16-eps' );

FLOAT16_EPSILON

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

var bool = ( FLOAT16_EPSILON === 0.0009765625 );
// returns true

Examples

var abs = require( '@stdlib/math-base-special-abs' );
var maxabs = require( '@stdlib/math-base-special-maxabs' );
var randu = require( '@stdlib/random-base-randu' );
var FLOAT16_EPSILON = require( '@stdlib/constants-float16-eps' );

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

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

    delta = abs( a - b );
    tol = FLOAT16_EPSILON * maxabs( a, b );

    return ( delta <= tol );
}

for ( i = 0; i < 100; i++ ) {
    a = randu() * 10.0;
    b = a + (randu()*2.0e-3) - 1.0e-3;
    bool = isApprox( a, b );
    console.log( '%d %s approximately equal to %d', a, ( bool ) ? 'is' : 'is not', b );
}

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.
• @stdlib/constants-float64/eps: difference between one and the smallest value greater than one that can be represented as a double-precision floating-point number.

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.

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License

See LICENSE.

Copyright

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