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<!-- | ||
@license Apache-2.0 | ||
Copyright (c) 2024 The Stdlib Authors. | ||
Licensed under the Apache License, Version 2.0 (the "License"); | ||
you may not use this file except in compliance with the License. | ||
You may obtain a copy of the License at | ||
http://www.apache.org/licenses/LICENSE-2.0 | ||
Unless required by applicable law or agreed to in writing, software | ||
distributed under the License is distributed on an "AS IS" BASIS, | ||
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
See the License for the specific language governing permissions and | ||
limitations under the License. | ||
--> | ||
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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). | ||
<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 | ||
\mathop{\mathrm{aversinf}}(\theta) = \arccos(1-\theta) | ||
``` | ||
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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 | ||
var aversinf = require( '@stdlib/math/base/special/aversinf' ); | ||
``` | ||
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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 | ||
var v = aversinf( 0.0 ); | ||
// returns 0.0 | ||
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v = aversinf( 3.141592653589793 / 2.0 ); | ||
// returns ~2.1783 | ||
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v = aversinf( 3.141592653589793 / 6.0 ); | ||
// returns ~1.0742 | ||
``` | ||
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If `x < 0`, `x > 2`, or `x` is `NaN`, the function returns `NaN`. | ||
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```javascript | ||
var v = aversinf( -1.0 ); | ||
// returns NaN | ||
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v = aversinf( 3.14 ); | ||
// returns NaN | ||
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v = aversinf( NaN ); | ||
// returns NaN | ||
``` | ||
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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 | ||
var linspace = require( '@stdlib/array/base/linspace' ); | ||
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; | ||
for ( i = 0; i < x.length; i++ ) { | ||
console.log( aversinf( x[ i ] ) ); | ||
} | ||
``` | ||
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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 | ||
#include "stdlib/math/base/special/aversinf.h" | ||
``` | ||
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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 | ||
float out = stdlib_base_aversinf( 3.141592653589793f / 2.0f ); | ||
// returns ~2.1783f | ||
``` | ||
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If `x < 0`, `x > 2`, or `x` is `NaN`, the function returns `NaN`. | ||
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```c | ||
float out = stdlib_base_aversinf( 3.141592653589793f ); | ||
// returns NaN | ||
``` | ||
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The function accepts the following arguments: | ||
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- **x**: `[in] float` input value. | ||
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```c | ||
float stdlib_base_aversinf( const float x ); | ||
``` | ||
</section> | ||
<!-- /.usage --> | ||
<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> | ||
<section class="notes"> | ||
</section> | ||
<!-- /.notes --> | ||
<!-- C API usage examples. --> | ||
<section class="examples"> | ||
### Examples | ||
```c | ||
#include "stdlib/math/base/special/aversinf.h" | ||
#include <stdio.h> | ||
int main( void ) { | ||
const float x[] = { -2.5f, -2.0f, -1.5f, -1.0f, -0.5f, 0.5f, 1.0f, 1.5f, 2.0f, 2.5f }; | ||
float v; | ||
int i; | ||
for ( i = 0; i < 10; i++ ) { | ||
v = stdlib_base_aversinf( x[ i ] ); | ||
printf( "aversinf(%f) = %f\n", x[ i ], v ); | ||
} | ||
} | ||
``` | ||
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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 --> |
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/** | ||
* @license Apache-2.0 | ||
* | ||
* Copyright (c) 2024 The Stdlib Authors. | ||
* | ||
* Licensed under the Apache License, Version 2.0 (the "License"); | ||
* you may not use this file except in compliance with the License. | ||
* You may obtain a copy of the License at | ||
* | ||
* http://www.apache.org/licenses/LICENSE-2.0 | ||
* | ||
* Unless required by applicable law or agreed to in writing, software | ||
* distributed under the License is distributed on an "AS IS" BASIS, | ||
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
* See the License for the specific language governing permissions and | ||
* limitations under the License. | ||
*/ | ||
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'use strict'; | ||
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// MODULES // | ||
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var bench = require( '@stdlib/bench' ); | ||
var randu = require( '@stdlib/random/array/uniform' ); | ||
var isnanf = require( './../../../../base/assert/is-nanf' ); | ||
var pkg = require( './../package.json' ).name; | ||
var aversinf = require( './../lib' ); | ||
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// MAIN // | ||
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bench( pkg, function benchmark( b ) { | ||
var x; | ||
var y; | ||
var i; | ||
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x = randu( 100, 0.0, 2.0 ); | ||
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b.tic(); | ||
for ( i = 0; i < b.iterations; i++ ) { | ||
y = aversinf( x[ i % x.length ] ); | ||
if ( isnanf( y ) ) { | ||
b.fail( 'should not return NaN' ); | ||
} | ||
} | ||
b.toc(); | ||
if ( isnanf( y ) ) { | ||
b.fail( 'should not return NaN' ); | ||
} | ||
b.pass( 'benchmark finished' ); | ||
b.end(); | ||
}); |
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/** | ||
* @license Apache-2.0 | ||
* | ||
* Copyright (c) 2024 The Stdlib Authors. | ||
* | ||
* Licensed under the Apache License, Version 2.0 (the "License"); | ||
* you may not use this file except in compliance with the License. | ||
* You may obtain a copy of the License at | ||
* | ||
* http://www.apache.org/licenses/LICENSE-2.0 | ||
* | ||
* Unless required by applicable law or agreed to in writing, software | ||
* distributed under the License is distributed on an "AS IS" BASIS, | ||
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
* See the License for the specific language governing permissions and | ||
* limitations under the License. | ||
*/ | ||
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'use strict'; | ||
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// MODULES // | ||
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var resolve = require( 'path' ).resolve; | ||
var bench = require( '@stdlib/bench' ); | ||
var randu = require( '@stdlib/random/array/uniform' ); | ||
var isnanf = require( './../../../../base/assert/is-nanf' ); | ||
var tryRequire = require( '@stdlib/utils/try-require' ); | ||
var pkg = require( './../package.json' ).name; | ||
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// VARIABLES // | ||
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var aversinf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); | ||
var opts = { | ||
'skip': ( aversinf instanceof Error ) | ||
}; | ||
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// MAIN // | ||
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bench( pkg+'::native', opts, function benchmark( b ) { | ||
var x; | ||
var y; | ||
var i; | ||
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x = randu( 100, 0.0, 2.0 ); | ||
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b.tic(); | ||
for ( i = 0; i < b.iterations; i++ ) { | ||
y = aversinf( x[ i % x.length ] ); | ||
if ( isnanf( y ) ) { | ||
b.fail( 'should not return NaN' ); | ||
} | ||
} | ||
b.toc(); | ||
if ( isnanf( y ) ) { | ||
b.fail( 'should not return NaN' ); | ||
} | ||
b.pass( 'benchmark finished' ); | ||
b.end(); | ||
}); |
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