feat: add math/base/special/cinvf

lib/node_modules/@stdlib/math/base/special/cinvf/README.md

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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.
+
+-->
+
+# cinvf
+
+> Compute the inverse of a single-precision complex floating-point number.
+
+<section class="intro">
+
+The inverse (or reciprocal) of a non-zero complex number `z = a + bi` is defined as
+
+<!-- <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" > -->
+
+<div class="equation" align="center" data-raw-text="{\frac {1}{z}}=\frac{\bar{z}}{z{\bar{z}}} = \frac{a}{a^{2}+b^{2}} - \frac{b}{a^2+b^2}i." data-equation="eq:complex_inverse">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@026bc0ee34051ddb44f3222f620bc7a300b9799e/lib/node_modules/@stdlib/math/base/special/cinvf/docs/img/equation_complex_inverse.svg" alt="Complex Inverse">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var cinvf = require( '@stdlib/math/base/special/cinvf' );
+```
+
+#### cinvf( z )
+
+Computes the inverse of a single-precision complex floating-point number.
+
+```javascript
+var Complex64 = require( '@stdlib/complex/float32/ctor' );
+var real = require( '@stdlib/complex/float32/real' );
+var imag = require( '@stdlib/complex/float32/imag' );
+
+var v = cinvf( new Complex64( 2.0, 4.0 ) );
+// returns <Complex64>
+
+var re = real( v );
+// returns ~0.1
+
+var im = imag( v );
+// returns ~-0.2
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Complex64 = require( '@stdlib/complex/float32/ctor' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var cinvf = require( '@stdlib/math/base/special/cinvf' );
+
+var z1;
+var z2;
+var i;
+
+for ( i = 0; i < 100; i++ ) {
+    z1 = new Complex64( uniform( -50.0, 50.0 ), uniform( -50.0, 50.0 ) );
+    z2 = cinvf( z1 );
+    console.log( '1.0 / (%s) = %s', z1.toString(), z2.toString() );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/math/base/special/cinvf.h"
+```
+
+#### stdlib_base_cinvf( z )
+
+Computes the inverse of a single-precision complex floating-point number.
+
+```c
+#include "stdlib/complex/float32/ctor.h"
+#include "stdlib/complex/float32/real.h"
+#include "stdlib/complex/float32/imag.h"
+
+stdlib_complex64_t z = stdlib_complex64( 2.0f, 4.0f );
+
+stdlib_complex64_t out = stdlib_base_cinvf( z );
+
+float re = stdlib_complex64_real( out );
+// returns 0.1f
+
+float im = stdlib_complex64_imag( out );
+// returns -0.2f
+```
+
+The function accepts the following arguments:
+
+-   **z**: `[in] stdlib_complex64_t` input value.
+
+```c
+stdlib_complex64_t stdlib_base_cinvf( const stdlib_complex64_t z );
+```
+
+</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/cinvf.h"
+#include "stdlib/complex/float32/ctor.h"
+#include "stdlib/complex/float32/reim.h"
+#include <stdio.h>
+
+int main() {
+    const stdlib_complex64_t x[] = {
+        stdlib_complex64( 3.14f, 1.5f ),
+        stdlib_complex64( -3.14f, -1.5f ),
+        stdlib_complex64( 0.0f, 0.0f ),
+        stdlib_complex64( 0.0f / 0.0f, 0.0f / 0.0f )
+    };
+
+    stdlib_complex64_t v;
+    stdlib_complex64_t y;
+    float re1;
+    float im1;
+    float re2;
+    float im2;
+    int i;
+    for ( i = 0; i < 4; i++ ) {
+        v = x[ i ];
+        y = stdlib_base_cinvf( v );
+        stdlib_complex64_reim( v, &re1, &im1 );
+        stdlib_complex64_reim( y, &re2, &im2 );
+        printf( "cinvf(%f + %fi) = %f + %fi\n", re1, im1, re2, im2 );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+* * *
+
+<section class="references">
+
+## References
+
+-   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].
+-   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].
+-   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].
+-   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].
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[@smith:1962a]: https://doi.org/10.1145/368637.368661
+
+[@stewart:1985a]: https://doi.org/10.1145/214408.214414
+
+[@priest:2004a]: https://doi.org/10.1145/1039813.1039814
+
+[@baudin:2012a]: https://arxiv.org/abs/1210.4539
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

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

@@ -0,0 +1,58 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var Complex64 = require( '@stdlib/complex/float32/ctor' );
+var real = require( '@stdlib/complex/float32/real' );
+var imag = require( '@stdlib/complex/float32/imag' );
+var pkg = require( './../package.json' ).name;
+var cinvf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var values;
+	var y;
+	var i;
+
+	values = [
+		new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ),
+		new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) )
+	];
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = cinvf( values[ i % values.length ] );
+		if ( isnanf( real( y ) ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( imag( y ) ) ) {
+		b.fail( 'should not return not NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

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

@@ -0,0 +1,67 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var real = require( '@stdlib/complex/float32/real' );
+var imag = require( '@stdlib/complex/float32/imag' );
+var Complex64 = require( '@stdlib/complex/float32/ctor' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var cinvf = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( cinvf instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+	var values;
+	var y;
+	var i;
+
+	values = [
+		new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ),
+		new Complex64( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) )
+	];
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = cinvf( values[ i % values.length ] );
+		if ( isnanf( real( y ) ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( imag( y ) ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});