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Binet's Formula
Evaluate Binet's formula extended to real numbers.
Binet's formula refers to the closed-form solution for computing the nth Fibonacci number and may be expressed
where φ is the golden ratio and ψ is 1 - φ. To extend Fibonacci numbers to real numbers, we may express Binet's formula as
Installation
npm install @stdlib/math-base-special-binetUsage
var binet = require( '@stdlib/math-base-special-binet' );binet( x )
Evaluates Binet's formula extended to real numbers.
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 ~2.12If provided NaN, the function returns NaN.
var v = binet( NaN );
// returns NaNNotes
- The function returns only approximate Fibonacci numbers for nonnegative integers.
- The function does not return complex numbers, guaranteeing real-valued return values.
Examples
var binet = require( '@stdlib/math-base-special-binet' );
var v;
var i;
for ( i = 0; i < 79; i++ ) {
v = binet( i );
console.log( v );
}See Also
-
@stdlib/math-base/special/fibonacci: compute the nth Fibonacci number. -
@stdlib/math-base/special/negafibonacci: compute the nth negaFibonacci number.
Notice
This package is part of 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, see the main project repository.
Community
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.