# Fibonacci Number Index
> Compute the [Fibonacci number][fibonacci-number] index.
The [Fibonacci number][fibonacci-number] index is given by
where `φ` is the [golden ratio][golden-ratio] and `F > 1`.
## Usage
```javascript
var fibonacciIndex = require( '@stdlib/math/base/special/fibonacci-index' );
```
#### fibonacciIndex( F )
Computes the [Fibonacci number][fibonacci-number] index for `F_n > 1`.
```javascript
var n = fibonacciIndex( 2 );
// returns 3
n = fibonacciIndex( 3 );
// returns 4
n = fibonacciIndex( 5 );
// returns 5
```
If provided either a non-integer or `F_n <= 1`, the function returns `NaN`.
```javascript
var n = fibonacciIndex( -1 );
// returns NaN
n = fibonacciIndex( 3.14 );
// returns NaN
```
If provided `NaN`, the function returns `NaN`.
```javascript
var n = fibonacciIndex( NaN );
// returns NaN
```
## Examples
```javascript
var fibonacciIndex = require( '@stdlib/math/base/special/fibonacci-index' );
var F1;
var F2;
var FN;
var n;
var i;
F1 = 1;
F2 = 1;
for ( i = 3; i < 79; i++ ) {
FN = F1 + F2;
F1 = F2;
F2 = FN;
n = fibonacciIndex( FN );
console.log( 'n(%d) = %d', FN, n );
}
```
[fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number
[golden-ratio]: https://en.wikipedia.org/wiki/Golden_ratio
