111 lines
2.4 KiB
Markdown
111 lines
2.4 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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# Archaversine
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> Compute the [inverse half-value versed sine][archaversine].
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<section class="intro">
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The [inverse half-value versed sine][archaversine] is defined as
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<!-- <equation class="equation" label="eq:archaversine" align="center" raw="\operatorname{ahaversin}(\theta) = 2 \cdot \arcsin(\sqrt{\theta})" alt="Inverse half-value versed sine."> -->
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<div class="equation" align="center" data-raw-text="\operatorname{ahaversin}(\theta) = 2 \cdot \arcsin(\sqrt{\theta})" data-equation="eq:archaversine">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/ahaversin/docs/img/equation_archaversine.svg" alt="Inverse half-value 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 ahaversin = require( '@stdlib/math/base/special/ahaversin' );
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```
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#### ahaversin( x )
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Computes the [inverse half-value versed sine][archaversine].
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```javascript
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var v = ahaversin( 0.0 );
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// returns 0.0
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v = ahaversin( 1.0 );
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// returns ~3.1416
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v = ahaversin( 0.5 );
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// returns ~1.5708
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```
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If `x < 0`, `x > 1`, or `x` is `NaN`, the function returns `NaN`.
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```javascript
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var v = ahaversin( 1.5 );
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// returns NaN
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v = ahaversin( -3.14 );
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// returns NaN
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v = ahaversin( 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/linspace' );
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var ahaversin = require( '@stdlib/math/base/special/ahaversin' );
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var x = linspace( 0.0, 1.0, 100 );
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var i;
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for ( i = 0; i < x.length; i++ ) {
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console.log( ahaversin( x[ i ] ) );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[archaversine]: https://en.wikipedia.org/wiki/Versine
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</section>
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<!-- /.links -->
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