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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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# Versine
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> Compute the [versed sine][versed-sine].
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<section class="intro">
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The [versed sine][versed-sine] is defined as
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<!-- <equation class="equation" label="eq:versine" align="center" raw="\operatorname{versin}(\theta) = 1 - \cos \theta" alt="Versed sine."> -->
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```math
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\mathop{\mathrm{versin}}(\theta) = 1 - \cos \theta
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```
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<!-- <div class="equation" align="center" data-raw-text="\operatorname{versin}(\theta) = 1 - \cos \theta" data-equation="eq:versine">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/versin/docs/img/equation_versine.svg" alt="Versed sine.">
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<br>
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var versin = require( '@stdlib/math/base/special/versin' );
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```
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#### versin( x )
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Computes the [versed sine][versed-sine] of a `number` (in radians).
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```javascript
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var v = versin( 0.0 );
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// returns 0.0
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v = versin( 3.141592653589793/2.0 );
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// returns ~1.0
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v = versin( -3.141592653589793/6.0 );
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// returns ~0.13397
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```
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</section>
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<!-- /.usage -->
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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 uniform = require( '@stdlib/random/array/uniform' );
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var logEachMap = require( '@stdlib/console/log-each-map' );
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var TWO_PI = require( '@stdlib/constants/float64/two-pi' );
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var versin = require( '@stdlib/math/base/special/versin' );
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var opts = {
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'dtype': 'float64'
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};
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var x = uniform( 100, 0.0, TWO_PI, opts );
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logEachMap( 'versin(%0.4f) = %0.4f', x, versin );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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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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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/math/base/special/versin.h"
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```
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#### stdlib_base_versin( x )
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Computes the [versed sine][versed-sine] of a `number` (in radians).
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```c
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double out = stdlib_base_versin( 0.0 );
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// returns 0.0
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out = stdlib_base_versin( 3.141592653589793 / 2.0 );
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// returns ~1.0
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```
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The function accepts the following arguments:
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- **x**: `[in] double` input value.
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```c
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double stdlib_base_versin( const double x );
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```
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</section>
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<!-- /.usage -->
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<!-- C API 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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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/math/base/special/versin.h"
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#include <stdio.h>
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int main( void ) {
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const double x[] = { 0.0, 0.523, 0.785, 1.047, 3.14 };
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double y;
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int i;
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for ( i = 0; i < 5; i++ ) {
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y = stdlib_base_versin( x[ i ] );
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printf( "versin(%lf) = %lf\n", x[ i ], y );
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}
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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* * *
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## See Also
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- <span class="package-name">[`@stdlib/math/base/special/cos`][@stdlib/math/base/special/cos]</span><span class="delimiter">: </span><span class="description">compute the cosine of a number.</span>
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- <span class="package-name">[`@stdlib/math/base/special/sin`][@stdlib/math/base/special/sin]</span><span class="delimiter">: </span><span class="description">compute the sine of a number.</span>
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- <span class="package-name">[`@stdlib/math/base/special/vercos`][@stdlib/math/base/special/vercos]</span><span class="delimiter">: </span><span class="description">compute the versed cosine.</span>
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</section>
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<!-- /.related -->
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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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[versed-sine]: https://en.wikipedia.org/wiki/Versine
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<!-- <related-links> -->
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[@stdlib/math/base/special/cos]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cos
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[@stdlib/math/base/special/sin]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sin
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[@stdlib/math/base/special/vercos]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/vercos
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<!-- </related-links> -->
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</section>
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<!-- /.links -->
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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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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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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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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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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pkg = require( './../package.json' ).name;
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var versin = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var x;
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var y;
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var i;
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x = uniform( 100, -10.0, 10.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = versin( x[ i % x.length ] );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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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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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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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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'use strict';
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// MODULES //
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var resolve = require( 'path' ).resolve;
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var tryRequire = require( '@stdlib/utils/try-require' );
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var pkg = require( './../package.json' ).name;
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// VARIABLES //
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var versin = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( versin instanceof Error )
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};
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// MAIN //
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bench( pkg+'::native', opts, function benchmark( b ) {
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var x;
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var y;
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var i;
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x = uniform( 100, -10.0, 10.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = versin( x[ i % x.length ] );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

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