1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
|
{{alias}}( x, y[, scale] )
Computes the relative difference of two real numbers in units of double-
precision floating-point epsilon.
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.
The following `scale` functions are supported:
- 'max-abs': maximum absolute value of `x` and `y` (default).
- 'max': maximum value of `x` and `y`.
- 'min-abs': minimum absolute value of `x` and `y`.
- 'min': minimum value of `x` and `y`.
- 'mean-abs': arithmetic mean of the absolute values of `x` and `y`.
- 'mean': arithmetic mean of `x` and `y`.
- 'x': `x` (*noncommutative*).
- 'y': `y` (*noncommutative*).
To use a custom scale function, provide a function which accepts two numeric
arguments `x` and `y`.
If computing the relative difference in units of epsilon will result in
overflow, the function returns the maximum double-precision floating-point
number.
If the absolute difference of `x` and `y` is `0`, the relative difference is
always `0`.
If `|x| = |y| = infinity`, the function returns `NaN`.
If `|x| = |-y| = infinity`, the relative difference is `+infinity`.
If a `scale` function returns `0`, the function returns `NaN`.
Parameters
----------
x: number
First number.
y: number
Second number.
scale: string|Function (optional)
Scale function. Default: `'max-abs'`.
Returns
-------
out: number
Relative difference in units of double-precision floating-point epsilon.
Examples
--------
> var d = {{alias}}( 12.15, 12.149999999999999 )
~0.658
> d = {{alias}}( 2.4341309458983933, 2.4341309458633909, 'mean-abs' )
~64761.512
// Custom scale function:
> function scale( x, y ) { return ( x > y ) ? y : x; };
> d = {{alias}}( 1.0000000000000002, 1.0000000000000100, scale )
~44
See Also
--------
|
