Epsilon Difference
Compute the relative difference of two real numbers in units of double-precision floating-point epsilon.
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 );
}