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feat: add C implementation for math/base/special/cinvf
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‎lib/node_modules/@stdlib/math/base/special/cinvf/README.md‎

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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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# cinvf
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> Compute the inverse of a single-precision complex floating-point number.
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<section class="intro">
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The inverse (or reciprocal) of a non-zero complex number `z = a + bi` is defined as
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<!-- <equation class="equation" label="eq:complex_inverse" align="center" raw="{\frac {1}{z}}=\frac{\bar{z}}{z{\bar{z}}} = \frac{a}{a^{2}+b^{2}} - \frac{b}{a^2+b^2}i." alt="Complex Inverse" > -->
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```math
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{\frac {1}{z}}=\frac{\bar{z}}{z{\bar{z}}} = \frac{a}{a^{2}+b^{2}} - \frac{b}{a^2+b^2}i.
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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 cinvf = require( '@stdlib/math/base/special/cinvf' );
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```
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#### cinvf( z )
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Computes the inverse of a single-precision complex floating-point number.
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```javascript
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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var realf = require( '@stdlib/complex/float32/real' );
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var imagf = require( '@stdlib/complex/float32/imag' );
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var v = cinvf( new Complex64( 2.0, 4.0 ) );
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// returns <Complex64>
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var re = realf( v );
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// returns ~0.1
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var im = imagf( v );
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// returns ~-0.2
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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 Complex64 = require( '@stdlib/complex/float32/ctor' );
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var uniform = require( '@stdlib/random/base/uniform' );
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var cinvf = require( '@stdlib/math/base/special/cinvf' );
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var z1;
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var z2;
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var i;
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for ( i = 0; i < 100; i++ ) {
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z1 = new Complex64( uniform( -50.0, 50.0 ), uniform( -50.0, 50.0 ) );
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z2 = cinvf( z1 );
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console.log( '1.0 / (%s) = %s', z1.toString(), z2.toString() );
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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/cinvf.h"
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```
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#### stdlib_base_cinvf( z )
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Computes the inverse of a single-precision complex floating-point number.
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```c
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#include "stdlib/complex/float32/ctor.h"
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#include "stdlib/complex/float32/real.h"
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#include "stdlib/complex/float32/imag.h"
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stdlib_complex64_t z = stdlib_complex64( 2.0f, 4.0f );
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stdlib_complex64_t out = stdlib_base_cinvf( z );
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float re = stdlib_complex64_real( out );
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// returns 0.1f
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float im = stdlib_complex64_imag( out );
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// returns -0.2f
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```
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The function accepts the following arguments:
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- **z**: `[in] stdlib_complex64_t` input value.
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```c
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stdlib_complex64_t stdlib_base_cinvf( const stdlib_complex64_t z );
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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/cinvf.h"
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#include "stdlib/complex/float32/ctor.h"
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#include "stdlib/complex/float32/reim.h"
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#include <stdio.h>
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int main( void ) {
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const stdlib_complex64_t x[] = {
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stdlib_complex64( 3.14f, 1.5f ),
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stdlib_complex64( -3.14f, -1.5f ),
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stdlib_complex64( 0.0f, 0.0f ),
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stdlib_complex64( 0.0f/0.0f, 0.0f/0.0f )
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};
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stdlib_complex64_t v;
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stdlib_complex64_t y;
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float re1;
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float im1;
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float re2;
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float im2;
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int i;
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for ( i = 0; i < 4; i++ ) {
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v = x[ i ];
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y = stdlib_base_cinvf( v );
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stdlib_complex64_reim( v, &re1, &im1 );
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stdlib_complex64_reim( y, &re2, &im2 );
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printf( "cinvf(%f + %fi) = %f + %fi\n", re1, im1, re2, im2 );
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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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* * *
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<section class="references">
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## References
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- Smith, Robert L. 1962. "Algorithm 116: Complex Division." _Commun. ACM_ 5 (8). New York, NY, USA: ACM: 435. doi:[10.1145/368637.368661][@smith:1962a].
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- Stewart, G. W. 1985. "A Note on Complex Division." _ACM Trans. Math. Softw._ 11 (3). New York, NY, USA: ACM: 238–41. doi:[10.1145/214408.214414][@stewart:1985a].
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- Priest, Douglas M. 2004. "Efficient Scaling for Complex Division." _ACM Trans. Math. Softw._ 30 (4). New York, NY, USA: ACM: 389–401. doi:[10.1145/1039813.1039814][@priest:2004a].
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- Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ abs/1210.4539 \[cs.MS] (October): 1–25. [&lt;https://arxiv.org/abs/1210.4539>][@baudin:2012a].
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</section>
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<!-- /.references -->
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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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[@smith:1962a]: https://doi.org/10.1145/368637.368661
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[@stewart:1985a]: https://doi.org/10.1145/214408.214414
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[@priest:2004a]: https://doi.org/10.1145/1039813.1039814
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[@baudin:2012a]: https://arxiv.org/abs/1210.4539
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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/cinvf/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) 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/base/uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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var realf = require( '@stdlib/complex/float32/real' );
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var imagf = require( '@stdlib/complex/float32/imag' );
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var pkg = require( './../package.json' ).name;
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var cinvf = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var values;
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var y;
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var i;
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values = [
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new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ),
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new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) )
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];
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = cinvf( values[ i%values.length ] );
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if ( isnanf( realf( 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( imagf( y ) ) ) {
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b.fail( 'should not return not 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/cinvf/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) 2023 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/base/uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var realf = require( '@stdlib/complex/float32/real' );
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var imagf = require( '@stdlib/complex/float32/imag' );
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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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 cinvf = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( cinvf 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 values;
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var y;
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var i;
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values = [
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new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ),
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new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) )
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];
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = cinvf( values[ i%values.length ] );
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if ( isnanf( realf( 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( imagf( y ) ) ) {
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b.fail( 'should not return not 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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