time-to-botec

Benchmark sampling in different programming languages
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README.md (4109B)

      1 <!--
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      3 @license Apache-2.0
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      5 Copyright (c) 2018 The Stdlib Authors.
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      7 Licensed under the Apache License, Version 2.0 (the "License");
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     11    http://www.apache.org/licenses/LICENSE-2.0
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     13 Unless required by applicable law or agreed to in writing, software
     14 distributed under the License is distributed on an "AS IS" BASIS,
     15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     16 See the License for the specific language governing permissions and
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     19 -->
     20 
     21 # Non-Fibonacci
     22 
     23 > Compute the nth [non-Fibonacci number][fibonacci-number].
     24 
     25 <!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
     26 
     27 <section class="intro">
     28 
     29 The nth [non-Fibonacci number][fibonacci-number] is given by
     30 
     31 <!-- <equation class="equation" label="eq:nonfibonacci_number" align="center" raw="f(n) = \left \lfloor{ n + 1 + \log_\varphi \biggl( \sqrt{5}( n + 1 + \log_\varphi(\sqrt{5}(n+1))) - 5 + \tfrac{3}{n+1} \biggr) - 2 } \right \rfloor" alt="Formula to compute the nth non-Fibonacci number."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="f(n) = \left \lfloor{ n + 1 + \log_\varphi \biggl( \sqrt{5}( n + 1 + \log_\varphi(\sqrt{5}(n+1))) - 5 + \tfrac{3}{n+1} \biggr) - 2 } \right \rfloor" data-equation="eq:nonfibonacci_number">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/nonfibonacci/docs/img/equation_nonfibonacci_number.svg" alt="Formula to compute the nth non-Fibonacci number.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `φ` is the [golden ratio][golden-ratio].
     41 
     42 </section>
     43 
     44 <!-- /.intro -->
     45 
     46 <!-- Package usage documentation. -->
     47 
     48 <section class="usage">
     49 
     50 ## Usage
     51 
     52 ```javascript
     53 var nonfibonacci = require( '@stdlib/math/base/special/nonfibonacci' );
     54 ```
     55 
     56 #### nonfibonacci( n )
     57 
     58 Computes the nth [non-Fibonacci number][fibonacci-number].
     59 
     60 ```javascript
     61 var v = nonfibonacci( 1 );
     62 // returns 4
     63 
     64 v = nonfibonacci( 2 );
     65 // returns 6
     66 
     67 v = nonfibonacci( 3 );
     68 // returns 7
     69 ```
     70 
     71 If provided either a non-integer or `n < 1`, the function returns `NaN`. 
     72 
     73 ```javascript
     74 var v = nonfibonacci( -1 );
     75 // returns NaN
     76 
     77 v = nonfibonacci( 3.14 );
     78 // returns NaN
     79 ```
     80 
     81 If provided `NaN`, the function returns `NaN`.
     82 
     83 ```javascript
     84 var v = nonfibonacci( NaN );
     85 // returns NaN
     86 ```
     87 
     88 </section>
     89 
     90 <!-- /.usage -->
     91 
     92 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
     93 
     94 <section class="notes">
     95 
     96 </section>
     97 
     98 <!-- /.notes -->
     99 
    100 <section class="examples">
    101 
    102 ## Examples
    103 
    104 <!-- eslint no-undef: "error" -->
    105 
    106 ```javascript
    107 var nonfibonacci = require( '@stdlib/math/base/special/nonfibonacci' );
    108 
    109 var v;
    110 var i;
    111 
    112 for ( i = 1; i < 100; i++ ) {
    113     v = nonfibonacci( i );
    114     console.log( 'nonfibonacci(%d) = %d', i, v );
    115 }
    116 ```
    117 
    118 </section>
    119 
    120 <!-- /.examples -->
    121 
    122 <!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    123 
    124 * * *
    125 
    126 <section class="references">
    127 
    128 ## References
    129 
    130 -   Gould, H.W. 1965. "Non-Fibonacci Numbers." _Fibonacci Quarterly_, no. 3: 177–83. [&lt;http://www.fq.math.ca/Scanned/3-3/gould.pdf>][@gould:1965a].
    131 -   Farhi, Bakir. 2011. "An explicit formula generating the non-Fibonacci numbers." _arXiv_ abs/1105.1127 \[Math.NT] (May): 1–5. [&lt;https://arxiv.org/abs/1105.1127>][@farhi:2011a].
    132 
    133 </section>
    134 
    135 <!-- /.references -->
    136 
    137 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    138 
    139 <section class="links">
    140 
    141 [fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number
    142 
    143 [golden-ratio]: https://en.wikipedia.org/wiki/Golden_ratio
    144 
    145 [@gould:1965a]: http://www.fq.math.ca/Scanned/3-3/gould.pdf
    146 
    147 [@farhi:2011a]: https://arxiv.org/abs/1105.1127
    148 
    149 </section>
    150 
    151 <!-- /.links -->