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# Fibonacci

> Compute the nth [Fibonacci number][fibonacci-number].

<section class="intro">

The [Fibonacci numbers][fibonacci-number] are the integer sequence

<!-- <equation class="equation" label="eq:fibonacci_sequence" align="center" raw="0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, \ldots" alt="Fibonacci sequence"> -->

<div class="equation" align="center" data-raw-text="0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, \ldots" data-equation="eq:fibonacci_sequence">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/fibonacci/docs/img/equation_fibonacci_sequence.svg" alt="Fibonacci sequence">
    <br>
</div> -->

<!-- </equation> -->

The sequence is defined by the recurrence relation

<!-- <equation class="equation" label="eq:fibonacci_recurrence_relation" align="center" raw="F_n = F_{n-1} + F_{n-2}" alt="Fibonacci sequence recurrence relation"> -->

<!-- <div class="equation" align="center" data-raw-text="F_n = F_{n-1} + F_{n-2}" data-equation="eq:fibonacci_recurrence_relation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/fibonacci/docs/img/equation_fibonacci_recurrence_relation.svg" alt="Fibonacci sequence recurrence relation">
    <br>
</div>

<!-- </equation> -->

with seed values `F_0 = 0` and `F_1 = 1`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var fibonacci = require( '@stdlib/math/base/special/fibonacci' );
```

#### fibonacci( n )

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

```javascript
var v = fibonacci( 0 );
// returns 0

v = fibonacci( 1 );
// returns 1

v = fibonacci( 2 );
// returns 1

v = fibonacci( 3 );
// returns 2

v = fibonacci( 78 );
// returns 8944394323791464
```

If `n > 78`, the function returns `NaN`, as larger [Fibonacci numbers][fibonacci-number] cannot be safely represented in [double-precision floating-point format][ieee754].

```javascript
var v = fibonacci( 79 );
// returns NaN
```

If not provided a nonnegative integer value, the function returns `NaN`.

```javascript
var v = fibonacci( 3.14 );
// returns NaN

v = fibonacci( -1 );
// returns NaN
```

If provided `NaN`, the function returns `NaN`.

```javascript
var v = fibonacci( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var fibonacci = require( '@stdlib/math/base/special/fibonacci' );

var v;
var i;

for ( i = 0; i < 79; i++ ) {
    v = fibonacci( i );
    console.log( v );
}
```

</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.h"
```

#### stdlib_base_fibonacci( n )

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

```c
double out = stdlib_base_fibonacci( 0.0 );
// returns 0.0

out = stdlib_base_fibonacci( 1.0 );
// returns 1.0
```

The function accepts the following arguments:

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

```c
double stdlib_base_fibonacci( const double n );
```

</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.h"
#include <stdio.h>

int main( void ) {
    double i;
    double v;

    for ( i = 0.0; i < 79.0; i++ ) {
        v = stdlib_base_fibonacci( i );
        printf( "fibonacci(%lf) = %lf\n", i, v );
    }
}
```

</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/binet`][@stdlib/math/base/special/binet]</span><span class="delimiter">: </span><span class="description">evaluate Binet's formula extended to real numbers.</span>
-   <span class="package-name">[`@stdlib/math/base/special/fibonacci-index`][@stdlib/math/base/special/fibonacci-index]</span><span class="delimiter">: </span><span class="description">compute the Fibonacci number index.</span>
-   <span class="package-name">[`@stdlib/math/base/special/lucas`][@stdlib/math/base/special/lucas]</span><span class="delimiter">: </span><span class="description">compute the nth Lucas number.</span>
-   <span class="package-name">[`@stdlib/math/base/special/negafibonacci`][@stdlib/math/base/special/negafibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth negaFibonacci 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

[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985

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

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

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

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

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

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

</section>

<!-- /.links -->
