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add euler totient function, issue #10 #93

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1 change: 1 addition & 0 deletions .gitignore
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Expand Up @@ -3,3 +3,4 @@
/.nyc_output
/npm-debug.log
dist
.lvimrc
30 changes: 29 additions & 1 deletion docs/README.md
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@@ -1,4 +1,4 @@
# [algorithms-js](https://github.com/manrajgrover/algorithms-js#readme) *0.0.8*
# [algorithms-js](https://github.com/manrajgrover/algorithms-js#readme) *0.0.13*

> Algorithms Library in JavaScript

Expand Down Expand Up @@ -138,6 +138,34 @@ https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Tangents_between



### src/algorithms/math/euler_totient.js


#### phi(n)

Euler's totient function (phi) counts the number of integers less than n
which are relatively prime to n




##### Parameters

| Name | Type | Description | |
| ---- | ---- | ----------- | -------- |
| n | `Number` | the number |   |




##### Returns


- `Number` the number of integers less than n which are relatively prime to n




### src/algorithms/math/extended_euclidean.js


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96 changes: 94 additions & 2 deletions docs/index.html
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<head>
<meta charset="utf-8">
<meta name="viewport" content="initial-scale=1">
<title>algorithms-js 0.0.8 &#8212; Algorithms Library in JavaScript</title>
<title>algorithms-js 0.0.13 &#8212; Algorithms Library in JavaScript</title>
<meta name="description" content="Algorithms Library in JavaScript">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/4.0.0-alpha.6/css/bootstrap.min.css">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/github.min.css">
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<h1>
<a href="https://github.com/manrajgrover/algorithms-js#readme">algorithms-js</a>
<small>0.0.8</small>
<small>0.0.13</small>
</h1>

<p>Algorithms Library in JavaScript</p>
Expand Down Expand Up @@ -235,6 +235,21 @@ <h1>
</li>


<li>
<a href="#src/algorithms/math/euler_totient.js" class="file"><b>src/algorithms/math/euler_totient.js</b></a>
<ul>


<li class="method-link scope-public">
<a href="#src-algorithms-math-euler_totient.js-phi" title="phi">phi</a>
</li>


</ul>

</li>


<li>
<a href="#src/algorithms/math/extended_euclidean.js" class="file"><b>src/algorithms/math/extended_euclidean.js</b></a>
<ul>
Expand Down Expand Up @@ -1628,6 +1643,83 @@ <h3>Returns</h3>



<a id="src/algorithms/math/euler_totient.js"></a>


<div class="method scope-public">

<h2 id="src-algorithms-math-euler_totient.js-phi">
<a href="#src-algorithms-math-euler_totient.js-phi" class="permalink">#</a>
<span class="method-name" title="phi(n)">phi(n)</span>
</h2>

<div class="description lead">

<p>Euler's totient function (phi) counts the number of integers less than n
which are relatively prime to n</p>


</div>


<section class="parameters">

<h3>Parameters</h3>

<div class="table-responsive">
<table class="table">

<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th>Description</th>
<th></th>
</tr>
</thead>

<tbody>
<tr>
<td>n</td>
<td>
<code>Number</code>
</td>
<td><p>the number</p>
</td>
<td>
</td>
</tr>
</tbody>

</table>
</div>

</section>




<section class="returns">

<h3>Returns</h3>



<p>
<code>Number</code>
</p>

<p>the number of integers less than n which are relatively prime to n</p>




</section>

</div>



<a id="src/algorithms/math/extended_euclidean.js"></a>


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34 changes: 34 additions & 0 deletions src/algorithms/math/euler_totient.js
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/**
* Euler's totient function (phi) counts the number of integers less than n
* which are relatively prime to n
*
* @param {Number} n the number
* @return {Number} the number of integers less than n which are relatively prime to n
*/


const phi = (n) => {
if (n < 0) return null;

let num = n;
let result = n;
let p = 2;

while (p * p <= num) {
if (num % p === 0) {
while (num % p === 0) {
num = Math.floor(num / p);
}
result -= Math.floor(result / p);
}
p += 1;
}

if (num > 1) {
result -= Math.floor(result / num);
}

return result;
};

module.exports = phi;
4 changes: 3 additions & 1 deletion src/algorithms/math/index.js
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Expand Up @@ -3,11 +3,13 @@ const gcd = require('./gcd');
const fastexp = require('./fast_exp');
const lcm = require('./lcm');
const modularInverse = require('./modular_inverse');
const eulerTotient = require('./euler_totient');

module.exports = {
extendedEuclidean,
gcd,
fastexp,
lcm,
modularInverse
modularInverse,
eulerTotient
};
28 changes: 28 additions & 0 deletions test/algorithms/math/testEulerTotient.js
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/* eslint-env mocha */
const phi = require('../../../src').algorithms.math.eulerTotient;
const assert = require('assert');

describe('Euler Totient (phi)', () => {
it('should return null for n < 0', () => {
assert.equal(phi(-1), null);
assert.equal(phi(-10), null);
assert.equal(phi(-Infinity), null);
});

it('should return 0 for n = 0', () => {
assert.equal(phi(0), 0);
});

it('should return phi(n) for n > 0', () => {
assert.equal(phi(1), 1);
assert.equal(phi(2), 1);
assert.equal(phi(3), 2);
assert.equal(phi(4), 2);
});

it('should return n-1 if n is prime', () => {
assert.equal(phi(5), 4);
assert.equal(phi(13), 12);
assert.equal(phi(29), 28);
});
});