# Function compareNatural #

Compare two values of any type in a deterministic, natural way.

For numeric values, the function works the same as `math.compare`. For types of values that can’t be compared mathematically, the function compares in a natural way.

For numeric values, x and y are considered equal when the relative difference between x and y is smaller than the configured epsilon. The function cannot be used to compare values smaller than approximately 2.22e-16.

For Complex numbers, first the real parts are compared. If equal, the imaginary parts are compared.

Strings are compared with a natural sorting algorithm, which orders strings in a “logic” way following some heuristics. This differs from the function `compare`, which converts the string into a numeric value and compares that. The function `compareText` on the other hand compares text lexically.

Arrays and Matrices are compared value by value until there is an unequal pair of values encountered. Objects are compared by sorted keys until the keys or their values are unequal.

## Syntax #

``````math.compareNatural(x, y)
``````

### Parameters #

Parameter Type Description
`x` * First value to compare
`y` * Second value to compare

### Returns #

Type Description
number Returns the result of the comparison: 1 when x > y, -1 when x < y, and 0 when x == y.

## Examples #

``````math.compareNatural(6, 1)              // returns 1
math.compareNatural(2, 3)              // returns -1
math.compareNatural(7, 7)              // returns 0

math.compareNatural('10', '2')         // returns 1
math.compareText('10', '2')            // returns -1
math.compare('10', '2')                // returns 1

// Error: Cannot convert "Answer: 10" to a number

const a = math.unit('5 cm')
const b = math.unit('40 mm')
math.compareNatural(a, b)              // returns 1

const c = math.complex('2 + 3i')
const d = math.complex('2 + 4i')
math.compareNatural(c, d)              // returns -1

math.compareNatural([1, 2, 4], [1, 2, 3]) // returns 1
math.compareNatural([1, 2, 3], [1, 2])    // returns 1
math.compareNatural([1, 5], [1, 2, 3])    // returns 1
math.compareNatural([1, 2], [1, 2])       // returns 0

math.compareNatural({a: 2}, {a: 4})       // returns -1
``````