Fibonacci Number Index
Compute the Fibonacci number index.
The Fibonacci number index is given by
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 );
}
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] doubleinput 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 );
}
}