@stdlib/math-base-utils-float64-epsilon-difference
v0.2.2
Published
Compute the relative difference of two real numbers in units of double-precision floating-point epsilon.
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Epsilon Difference
Compute the relative difference of two real numbers in units of double-precision floating-point epsilon.
Installation
npm install @stdlib/math-base-utils-float64-epsilon-difference
Usage
var epsdiff = require( '@stdlib/math-base-utils-float64-epsilon-difference' );
epsdiff( x, y[, scale] )
Computes the relative difference of two real numbers in units of double-precision floating-point epsilon.
var d = epsdiff( 12.15, 12.149999999999999 ); // => ~0.658ε
// returns ~0.658
The following scale
functions are supported:
- max-abs: maximum absolute value of
x
andy
(default). - max: maximum value of
x
andy
. - min-abs: minimum absolute value of
x
andy
. - min: minimum value of
x
andy
. - mean-abs: arithmetic mean of the absolute values of
x
andy
. - mean: arithmetic mean of
x
andy
. - x:
x
(noncommutative). - y:
y
(noncommutative).
By default, the function scales the absolute difference by dividing the absolute difference by the maximum absolute value of x
and y
. To scale by a different function, specify a scale function name.
var d = epsdiff( 2.4341309458983933, 2.4341309458633909, 'mean-abs' ); // => ~64761.5ε => ~1.438e-11
// returns ~64761.5
To use a custom scale function, provide a function
which accepts two numeric arguments x
and y
.
function scale( x, y ) {
// Return the minimum value:
return ( x > y ) ? y : x;
}
var d = epsdiff( 1.0000000000000002, 1.0000000000000100, scale ); // => ~44ε
// returns ~44
Notes
If computing the relative difference in units of epsilon will result in overflow, the function returns the maximum double-precision floating-point number.
var d = epsdiff( 1.0e304, 1.0, 'min' ); // => ~1.798e308ε => 1.0e304/ε overflows // returns ~1.798e308
If the absolute difference of
x
andy
is0
, the relative difference is always0
.var d = epsdiff( 0.0, 0.0 ); // returns 0.0 d = epsdiff( 3.14, 3.14 ); // returns 0.0
If
x = y = +infinity
orx = y = -infinity
, the function returnsNaN
.var PINF = require( '@stdlib/constants-float64-pinf' ); var NINF = require( '@stdlib/constants-float64-ninf' ); var d = epsdiff( PINF, PINF ); // returns NaN d = epsdiff( NINF, NINF ); // returns NaN
If
x = -y = +infinity
or-x = y = +infinity
, the relative difference is+infinity
.var PINF = require( '@stdlib/constants-float64-pinf' ); var NINF = require( '@stdlib/constants-float64-ninf' ); var d = epsdiff( PINF, NINF ); // returns Infinity d = epsdiff( NINF, PINF ); // returns Infinity
If a
scale
function returns0
, the function returnsNaN
.var d = epsdiff( -1.0, 1.0, 'mean' ); // => |2/0| // returns NaN
Examples
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var epsdiff = require( '@stdlib/math-base-utils-float64-epsilon-difference' );
var sign;
var x;
var y;
var d;
var i;
for ( i = 0; i < 100; i++ ) {
x = randu();
sign = ( randu() > 0.5 ) ? 1.0 : -1.0;
y = x + ( sign*EPS*i );
d = epsdiff( x, y );
console.log( 'x = %d. y = %d. d = %dε.', x, y, d );
}
See Also
@stdlib/math-base/utils/absolute-difference
: compute the absolute difference of two real numbers.@stdlib/math-base/utils/relative-difference
: compute the relative difference of two real numbers.
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
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.