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Fibonacci Number Index

Compute the Fibonacci number index.

The Fibonacci number index is given by

$$n = \left \lfloor{\log_\varphi \biggl(F \cdot \sqrt{5} + \tfrac{1}{2}\biggr)}\right \rfloor$$

where φ is the golden ratio and F > 1.

Installation

npm install @stdlib/math-base-special-fibonacci-index

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the 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.

Usage

var fibonacciIndex = require( '@stdlib/math-base-special-fibonacci-index' );

fibonacciIndex( F )

Computes the Fibonacci number index for F_n > 1.

var n = fibonacciIndex( 2 );
// returns 3

n = fibonacciIndex( 3 );
// returns 4

n = fibonacciIndex( 5 );
// returns 5

If provided either a non-integer or F_n <= 1, the function returns NaN.

var n = fibonacciIndex( -1 );
// returns NaN

n = fibonacciIndex( 3.14 );
// returns NaN

If provided NaN, the function returns NaN.

var n = fibonacciIndex( NaN );
// returns NaN

Examples

var fibonacciIndex = require( '@stdlib/math-base-special-fibonacci-index' );

var F1;
var F2;
var FN;
var n;
var i;

F1 = 1;
F2 = 1;
for ( i = 3; i < 79; i++ ) {
    FN = F1 + F2;
    F1 = F2;
    F2 = FN;
    n = fibonacciIndex( FN );
    console.log( 'n(%d) = %d', FN, n );
}

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C APIs

Usage

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

stdlib_base_fibonacci_index( F )

Computes the Fibonacci number index.

double out = stdlib_base_fibonacci( 2 );
// returns 3

out = stdlib_base_fibonacci( 3 );
// returns 4

The function accepts the following arguments:

• n: [in] double input value.

double stdlib_base_fibonacci( const double F );

Examples

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

int main( void ) {
    const double x[] = { 2.0, 3.0, 5.0, 8.0 };

    double y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        y = stdlib_base_fibonacci_index( x[ i ] );
        printf( "fibonacci_index(%lf) = %lf\n", x[ i ], y );
    }
}

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See Also

• @stdlib/math-base/special/fibonacci: compute the nth Fibonacci number.

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.