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@license Apache-2.0
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Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
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-->
# Fibonacci Number Index
> Compute the [Fibonacci number][fibonacci-number] index.
<section class="intro">
The [Fibonacci number][fibonacci-number] index is given by
<!-- <equation class="equation" label="eq:fibonacci_number_index" align="center" raw="n = \left \lfloor{\log_\varphi \biggl(F \cdot \sqrt{5} + \tfrac{1}{2}\biggr)}\right \rfloor" alt="Formula to compute the Fibonacci number index."> -->
<div class="equation" align="center" data-raw-text="n = \left \lfloor{\log_\varphi \biggl(F \cdot \sqrt{5} + \tfrac{1}{2}\biggr)}\right \rfloor" data-equation="eq:fibonacci_number_index">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/fibonacci-index/docs/img/equation_fibonacci_number_index.svg" alt="Formula to compute the Fibonacci number index.">
<br>
</div>
<!-- </equation> -->
where `φ` is the [golden ratio][golden-ratio] and `F > 1`.
</section>
<!-- /.intro -->
<section class="usage">
## 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
```
</section>
<!-- /.usage -->
<section class="notes">
</section>
<!-- /.notes -->
<section class="examples">
## Examples
<!-- eslint no-undef: "error" -->
```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 );
}
```
</section>
<!-- /.examples -->
<section class="links">
[fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number
[golden-ratio]: https://en.wikipedia.org/wiki/Golden_ratio
</section>
<!-- /.links -->
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