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-binet

Usage

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 ~2.12

If provided NaN, the function returns NaN.

var v = binet( NaN );
// returns NaN

Notes

• 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 );
}

C APIs

Usage

#include "stdlib/math/base/special/binet.h"

stdlib_base_binet( x )

Evaluates Binet's formula extended to real numbers.

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.

double stdlib_base_binet( const double x );

Examples

#include "stdlib/math/base/special/binet.h"
#include <stdio.h>

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: 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.