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

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

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.

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 );
}

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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.
• @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.