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Compute the relative difference of two real numbers in units of double-precision floating-point epsilon.
import epsdiff from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-utils-float64-epsilon-difference@deno/mod.js';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 ~0.658The following scale functions are supported:
- max-abs: maximum absolute value of
xandy(default). - max: maximum value of
xandy. - min-abs: minimum absolute value of
xandy. - min: minimum value of
xandy. - mean-abs: arithmetic mean of the absolute values of
xandy. - mean: arithmetic mean of
xandy. - 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 ~64761.5To 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-
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
xandyis0, 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 = +infinityorx = y = -infinity, the function returnsNaN.import PINF from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-pinf@deno/mod.js'; import NINF from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-ninf@deno/mod.js'; var d = epsdiff( PINF, PINF ); // returns NaN d = epsdiff( NINF, NINF ); // returns NaN
-
If
x = -y = +infinityor-x = y = +infinity, the relative difference is+infinity.import PINF from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-pinf@deno/mod.js'; import NINF from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-ninf@deno/mod.js'; var d = epsdiff( PINF, NINF ); // returns Infinity d = epsdiff( NINF, PINF ); // returns Infinity
-
If a
scalefunction returns0, the function returnsNaN.var d = epsdiff( -1.0, 1.0, 'mean' ); // => |2/0| // returns NaN
import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import EPS from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-eps@deno/mod.js';
import epsdiff from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-utils-float64-epsilon-difference@deno/mod.js';
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 );
}@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.
This package is part of stdlib, a standard library 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.
See LICENSE.
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