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https://github.com/stdlib-js/math-base-special-binet
Evaluate Binet's formula extended to real numbers.
https://github.com/stdlib-js/math-base-special-binet
binet fib fibonacci function javascript math mathematics node node-js nodejs number reals special special-functions stdlib
Last synced: 3 months ago
JSON representation
Evaluate Binet's formula extended to real numbers.
- Host: GitHub
- URL: https://github.com/stdlib-js/math-base-special-binet
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:19:43.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-10-01T12:55:53.000Z (4 months ago)
- Last Synced: 2024-10-22T02:29:11.167Z (4 months ago)
- Topics: binet, fib, fibonacci, function, javascript, math, mathematics, node, node-js, nodejs, number, reals, special, special-functions, stdlib
- Language: Python
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 1.28 MB
- Stars: 3
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
Awesome Lists containing this project
README
About stdlib...
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The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.
When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.
To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
# Binet's Formula
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> 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
```math
F_n = \frac{\varphi^n - \psi^n}{\sqrt{5}}
```
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
```math
F_x = \frac{\varphi^x - \varphi^{-x} \cdot \cos(\pi x)}{\sqrt{5}}
```
## Installation
```bash
npm install @stdlib/math-base-special-binet
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## 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 );
}
```
* * *
## C APIs
### Usage
```c
#include "stdlib/math/base/special/binet.h"
```
#### stdlib_base_binet( x )
Evaluates [Binet's formula][fibonacci-number] extended to real numbers.
```c
double out = stdlib_base_binet( 0.0 );
// returns 0.0
out = stdlib_base_binet( 1.0 );
// returns 1.0
```
The function accepts the following arguments:
- **x**: `[in] double` input value.
```c
double stdlib_base_binet( const double x );
```
### Examples
```c
#include "stdlib/math/base/special/binet.h"
#include
int main( void ) {
const double x[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
double y;
int i;
for ( i = 0; i < 5; i++ ) {
y = stdlib_base_binet( x[ i ] );
printf( "binet(%lf) = %lf\n", x[ i ], y );
}
}
```
* * *
## See Also
- [`@stdlib/math-base/special/fibonacci`][@stdlib/math/base/special/fibonacci]: compute the nth Fibonacci number.
- [`@stdlib/math-base/special/negafibonacci`][@stdlib/math/base/special/negafibonacci]: compute the nth negaFibonacci number.
* * *
## Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
## License
See [LICENSE][stdlib-license].
## Copyright
Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-binet.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-binet
[test-image]: https://github.com/stdlib-js/math-base-special-binet/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/math-base-special-binet/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-binet/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-binet?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-special-binet/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-binet/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-binet/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-binet/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-binet/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-binet/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-binet/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-binet/main/LICENSE
[fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number
[golden-ratio]: https://en.wikipedia.org/wiki/Golden_ratio
[@stdlib/math/base/special/fibonacci]: https://github.com/stdlib-js/math-base-special-fibonacci
[@stdlib/math/base/special/negafibonacci]: https://github.com/stdlib-js/math-base-special-negafibonacci