time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

main.js (2256B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2018 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 */
     18 
     19 'use strict';
     20 
     21 // MODULES //
     22 
     23 var isnan = require( './../../../../base/assert/is-nan' );
     24 var isInteger = require( './../../../../base/assert/is-integer' );
     25 var ln = require( './../../../../base/special/ln' );
     26 var floor = require( './../../../../base/special/floor' );
     27 var PHI = require( '@stdlib/constants/float64/phi' );
     28 var PINF = require( '@stdlib/constants/float64/pinf' );
     29 
     30 
     31 // VARIABLES //
     32 
     33 var SQRT_5 = 2.23606797749979;
     34 var LN_PHI = ln( PHI );
     35 
     36 
     37 // MAIN //
     38 
     39 /**
     40 * Computes the nth non-Fibonacci number.
     41 *
     42 * ## References
     43 *
     44 * -   Gould, H.W. 1965. "Non-Fibonacci Numbers." _Fibonacci Quarterly_, no. 3: 177–83. <http://www.fq.math.ca/Scanned/3-3/gould.pdf>.
     45 * -   Farhi, Bakir. 2011. "An explicit formula generating the non-Fibonacci numbers." _arXiv_ abs/1105.1127 \[Math.NT\] (May): 1–5. <https://arxiv.org/abs/1105.1127>.
     46 *
     47 *
     48 * @param {NonNegativeInteger} n - the non-Fibonacci number to compute
     49 * @returns {NonNegativeInteger} non-Fibonacci number
     50 *
     51 * @example
     52 * var v = nonfibonacci( 1 );
     53 * // returns 4
     54 *
     55 * @example
     56 * var v = nonfibonacci( 2 );
     57 * // returns 6
     58 *
     59 * @example
     60 * var v = nonfibonacci( 3 );
     61 * // returns 7
     62 *
     63 * @example
     64 * var v = nonfibonacci( NaN );
     65 * // returns NaN
     66 *
     67 * @example
     68 * var v = nonfibonacci( 3.14 );
     69 * // returns NaN
     70 *
     71 * @example
     72 * var v = nonfibonacci( -1 );
     73 * // returns NaN
     74 */
     75 function nonfibonacci( n ) {
     76 	var a;
     77 	var b;
     78 	if (
     79 		isnan( n ) ||
     80 		isInteger( n ) === false ||
     81 		n < 1 ||
     82 		n === PINF
     83 	) {
     84 		return NaN;
     85 	}
     86 	n += 1;
     87 	a = ln( n * SQRT_5 ) / LN_PHI;
     88 	b = ln( (SQRT_5 * (n+a)) - 5.0 + (3.0/n) ) / LN_PHI;
     89 	return floor( n + b - 2.0 );
     90 }
     91 
     92 
     93 // EXPORTS //
     94 
     95 module.exports = nonfibonacci;