142 lines
3.3 KiB
Markdown
142 lines
3.3 KiB
Markdown
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<!--
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# gcd
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> Compute the [greatest common divisor][gcd] (gcd).
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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The [greatest common divisor][gcd] (gcd) of two non-zero integers `a` and `b` is the largest positive integer which divides both `a` and `b` without a remainder. The gcd is also known as the **greatest common factor** (gcf), **highest common factor** (hcf), **highest common divisor**, and **greatest common measure** (gcm).
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var gcd = require( '@stdlib/math/base/special/gcd' );
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```
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#### gcd( a, b )
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Computes the [greatest common divisor][gcd] (gcd).
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```javascript
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var v = gcd( 48, 18 );
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// returns 6
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```
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If both `a` and `b` are `0`, the function returns `0`.
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```javascript
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var v = gcd( 0, 0 );
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// returns 0
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```
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Both `a` and `b` must have integer values; otherwise, the function returns `NaN`.
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```javascript
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var v = gcd( 3.14, 18 );
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// returns NaN
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v = gcd( 48, 3.14 );
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// returns NaN
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v = gcd( NaN, 18 );
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// returns NaN
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v = gcd( 48, NaN );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- Package usage examples. -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var round = require( '@stdlib/math/base/special/round' );
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var gcd = require( '@stdlib/math/base/special/gcd' );
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var a;
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var b;
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var v;
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var i;
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for ( i = 0; i < 100; i++ ) {
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a = round( randu()*50.0 );
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b = round( randu()*50.0 );
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v = gcd( a, b );
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console.log( 'gcd(%d,%d) = %d', a, b, v );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- 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. -->
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<section class="references">
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## References
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- Stein, Josef. 1967. "Computational problems associated with Racah algebra." _Journal of Computational Physics_ 1 (3): 397–405. doi:[10.1016/0021-9991(67)90047-2][@stein:1967].
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</section>
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<!-- /.references -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[gcd]: http://en.wikipedia.org/wiki/Greatest_common_divisor
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[@stein:1967]: https://doi.org/10.1016/0021-9991(67)90047-2
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</section>
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<!-- /.links -->
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