Fibonacci Number Index

Compute the Fibonacci number index.

The Fibonacci number index is given by

n equals left floor log Subscript phi Baseline left-parenthesis upper F dot StartRoot 5 EndRoot plus one-half right-parenthesis right floor

where φ is the golden ratio and F > 1.

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 );
}