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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 -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/fibonacci_index.h"
```

#### stdlib_base_fibonacci_index( F )

Computes the [Fibonacci number][fibonacci-number] index.

```c
double out = stdlib_base_fibonacci_index( 2 );
// returns 3

out = stdlib_base_fibonacci_index( 3 );
// returns 4
```

The function accepts the following arguments:

-   **F**: `[in] double` input value.

```c
double stdlib_base_fibonacci_index( const double F );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/fibonacci_index.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 2.0, 3.0, 5.0, 8.0 };

    double y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        y = stdlib_base_fibonacci_index( x[ i ] );
        printf( "fibonacci_index(%lf) = %lf\n", x[ i ], y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math/base/special/fibonacci`][@stdlib/math/base/special/fibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Fibonacci number.</span>

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number

[golden-ratio]: https://en.wikipedia.org/wiki/Golden_ratio

<!-- <related-links> -->

[@stdlib/math/base/special/fibonacci]: https://github.com/stdlib-js/math/tree/main/base/special/fibonacci

<!-- </related-links> -->

</section>

<!-- /.links -->
