# Binet's Formula
> Evaluate [Binet's formula][fibonacci-number] extended to real numbers.
[Binet's formula][fibonacci-number] refers to the closed-form solution for computing the nth [Fibonacci number][fibonacci-number] and may be expressed
where `φ` is the [golden ratio][golden-ratio] and `ψ` is `1 - φ`. To extend [Fibonacci numbers][fibonacci-number] to real numbers, we may express [Binet's formula][fibonacci-number] as
## Usage
```javascript
var binet = require( '@stdlib/math/base/special/binet' );
```
#### binet( x )
Evaluates [Binet's formula][fibonacci-number] extended to real numbers.
```javascript
var v = binet( 0.0 );
// returns 0.0
v = binet( 1.0 );
// returns 1.0
v = binet( 2.0 );
// returns 1.0
v = binet( 3.0 );
// returns 2.0
v = binet( -1.0 );
// returns 1.0
v = binet( 3.14 );
// returns ~2.12
```
If provided `NaN`, the function returns `NaN`.
```javascript
var v = binet( NaN );
// returns NaN
```
## Notes
- The function returns only **approximate** [Fibonacci numbers][fibonacci-number] for nonnegative integers.
- The function does **not** return complex numbers, guaranteeing real-valued return values.
## Examples
```javascript
var binet = require( '@stdlib/math/base/special/binet' );
var v;
var i;
for ( i = 0; i < 79; i++ ) {
v = binet( i );
console.log( v );
}
```
[fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number
[golden-ratio]: https://en.wikipedia.org/wiki/Golden_ratio
