Evaluate Binet's formula extended to real numbers.
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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
F_n = \frac{\varphi^n - \psi^n}{\sqrt{5}}
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
F_x = \frac{\varphi^x - \varphi^{-x} \cdot \cos(\pi x)}{\sqrt{5}}
npm install @stdlib/math-base-special-binet
Alternatively,
script
tag without installation and bundlers, use the ES Module available on the esm
branch (see README).deno
branch (see README for usage intructions).umd
branch (see README).The branches.md 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.
var binet = require( '@stdlib/math-base-special-binet' );
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
var binet = require( '@stdlib/math-base-special-binet' );
var v;
var i;
for ( i = 0; i < 79; i++ ) {
v = binet( i );
console.log( v );
}
#include "stdlib/math/base/special/binet.h"
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:
[in] double
input value.double stdlib_base_binet( const double x );
#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 );
}
}
@stdlib/math-base/special/fibonacci
: compute the nth Fibonacci number.
@stdlib/math-base/special/negafibonacci
: compute the nth negaFibonacci number.
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.
See LICENSE.
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