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feat: add math/base/special/aversinf
PR-URL: #2852 Ref: #649 Reviewed-by: Philipp Burckhardt <[email protected]>
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‎lib/node_modules/@stdlib/math/base/special/aversinf/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2024 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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# Arcversinef
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> Compute the [inverse versed sine][inverse-versed-sine] of a single-precision floating-point number (in radians).
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<section class="intro">
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The [inverse versed sine][inverse-versed-sine] is defined as
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<!-- <equation class="equation" label="eq:arcversine" align="center" raw="\operatorname{aversinf}(\theta) = \arccos(1-\theta)" alt="Inverse versed sine."> -->
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```math
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\mathop{\mathrm{aversinf}}(\theta) = \arccos(1-\theta)
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```
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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 aversinf = require( '@stdlib/math/base/special/aversinf' );
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```
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#### aversinf( x )
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Computes the [inverse versed sine][inverse-versed-sine] of a single-precision floating-point number (in radians).
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```javascript
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var v = aversinf( 0.0 );
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// returns 0.0
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v = aversinf( 3.141592653589793 / 2.0 );
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// returns ~2.1783
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v = aversinf( 3.141592653589793 / 6.0 );
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// returns ~1.0742
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```
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If `x < 0`, `x > 2`, or `x` is `NaN`, the function returns `NaN`.
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```javascript
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var v = aversinf( -1.0 );
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// returns NaN
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v = aversinf( 3.14 );
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// returns NaN
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v = aversinf( 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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<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 linspace = require( '@stdlib/array/base/linspace' );
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var aversinf = require( '@stdlib/math/base/special/aversinf' );
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var x = linspace( 0.0, 2.0, 100 );
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var i;
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for ( i = 0; i < x.length; i++ ) {
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console.log( aversinf( x[ i ] ) );
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}
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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/aversinf.h"
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```
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#### stdlib_base_aversinf( x )
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Compute the [inverse versed sine][inverse-versed-sine] of a single-precision floating-point number (in radians).
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```c
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float out = stdlib_base_aversinf( 3.141592653589793f / 2.0f );
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// returns ~2.1783f
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```
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If `x < 0`, `x > 2`, or `x` is `NaN`, the function returns `NaN`.
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```c
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float out = stdlib_base_aversinf( 3.141592653589793f );
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// returns NaN
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```
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The function accepts the following arguments:
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- **x**: `[in] float` input value.
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```c
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float stdlib_base_aversinf( const float 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/aversinf.h"
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#include <stdio.h>
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int main( void ) {
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const float x[] = { -2.5f, -2.0f, -1.5f, -1.0f, -0.5f, 0.5f, 1.0f, 1.5f, 2.0f, 2.5f };
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float v;
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int i;
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for ( i = 0; i < 10; i++ ) {
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v = stdlib_base_aversinf( x[ i ] );
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printf( "aversinf(%f) = %f\n", x[ i ], v );
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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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</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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[inverse-versed-sine]: https://en.wikipedia.org/wiki/Versine
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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/math/base/special/aversinf/benchmark/benchmark.js

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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 bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/array/uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var pkg = require( './../package.json' ).name;
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var aversinf = 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 = randu( 100, 0.0, 2.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = aversinf( x[ i % x.length ] );
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if ( isnanf( 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 ( isnanf( 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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});

‎lib/node_modules/@stdlib/math/base/special/aversinf/benchmark/benchmark.native.js

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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 randu = require( '@stdlib/random/array/uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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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 aversinf = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( aversinf 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 = randu( 100, 0.0, 2.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = aversinf( x[ i % x.length ] );
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if ( isnanf( 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 ( isnanf( 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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