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feat: add complex/float64/base/div
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‎lib/node_modules/@stdlib/complex/float64/base/div/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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# cdiv
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> Divide two double-precision complex floating-point numbers.
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<section class="intro">
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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 cdiv = require( '@stdlib/complex/float64/base/div' );
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```
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#### cdiv( z1, z2 )
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Divides two double-precision complex floating-point numbers.
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```javascript
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var real = require( '@stdlib/complex/float64/real' );
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var imag = require( '@stdlib/complex/float64/imag' );
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var z1 = new Complex128( -13.0, -1.0 );
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var z2 = new Complex128( -2.0, 1.0 );
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var v = cdiv( z1, z2 );
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// returns <Complex128>
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var re = real( v );
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// returns 5.0
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var im = imag( v );
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// returns 3.0
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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 Complex128 = require( '@stdlib/complex/float64/ctor' );
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var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
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var real = require( '@stdlib/complex/float64/real' );
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var imag = require( '@stdlib/complex/float64/imag' );
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var cdiv = require( '@stdlib/complex/float64/base/div' );
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function randomComplex() {
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var re = discreteUniform( -50, 50 );
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var im = discreteUniform( -50, 50 );
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return new Complex128( re, im );
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}
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var z1;
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var z2;
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var z3;
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var i;
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for ( i = 0; i < 100; i++ ) {
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z1 = randomComplex();
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z2 = randomComplex();
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z3 = cdiv( z1, z2 );
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console.log( '(%s) / (%s) = %s', z1.toString(), z2.toString(), z3.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/complex/float64/base/div.h"
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```
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#### stdlib_base_complex128_div( z1, z2 )
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Divides two double-precision complex floating-point numbers.
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```c
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#include "stdlib/complex/float64/ctor.h"
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#include "stdlib/complex/float64/real.h"
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#include "stdlib/complex/float64/imag.h"
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stdlib_complex128_t z1 = stdlib_complex128( -13.0, -1.0 );
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stdlib_complex128_t z2 = stdlib_complex128( -2.0, 1.0 );
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stdlib_complex128_t out = stdlib_base_complex128_div( z1, z2 );
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double re = stdlib_complex128_real( out );
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// returns 5.0
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double im = stdlib_complex128_imag( out );
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// returns 3.0
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```
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The function accepts the following arguments:
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- **z1**: `[in] stdlib_complex128_t` input value.
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- **z2**: `[in] stdlib_complex128_t` input value.
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```c
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stdlib_complex128_t stdlib_base_complex128_div( const stdlib_complex128_t z1, const stdlib_complex128_t z2 );
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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/complex/float64/base/div.h"
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#include "stdlib/complex/float64/ctor.h"
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#include "stdlib/complex/float64/reim.h"
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#include <stdio.h>
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int main( void ) {
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const stdlib_complex128_t x[] = {
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stdlib_complex128( 3.14, 1.5 ),
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stdlib_complex128( -3.14, 1.5 ),
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stdlib_complex128( 0.0, -0.0 ),
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stdlib_complex128( 0.0/0.0, 0.0/0.0 )
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};
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stdlib_complex128_t v;
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stdlib_complex128_t y;
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double re;
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double im;
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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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stdlib_complex128_reim( v, &re, &im );
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printf( "z = %lf + %lfi\n", re, im );
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y = stdlib_base_complex128_div( v, v );
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stdlib_complex128_reim( y, &re, &im );
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printf( "cdiv(z, z) = %lf + %lfi\n", re, im );
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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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* * *
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## See Also
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- <span class="package-name">[`@stdlib/complex/float64/base/add`][@stdlib/complex/float64/base/add]</span><span class="delimiter">: </span><span class="description">add two double-precision complex floating-point numbers.</span>
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- <span class="package-name">[`@stdlib/complex/float64/base/mul`][@stdlib/complex/float64/base/mul]</span><span class="delimiter">: </span><span class="description">multiply two double-precision complex floating-point numbers.</span>
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- <span class="package-name">[`@stdlib/math/base/ops/csub`][@stdlib/math/base/ops/csub]</span><span class="delimiter">: </span><span class="description">subtract two double-precision complex floating-point numbers.</span>
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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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[@stdlib/complex/float64/base/add]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/complex/float64/base/add
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[@stdlib/complex/float64/base/mul]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/complex/float64/base/mul
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[@stdlib/math/base/ops/csub]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/ops/csub
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/complex/float64/base/div/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 Complex128 = require( '@stdlib/complex/float64/ctor' );
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var isComplex128 = require( '@stdlib/assert/is-complex128' );
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var uniform = require( '@stdlib/random/base/uniform' );
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var real = require( '@stdlib/complex/float64/real' );
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var imag = require( '@stdlib/complex/float64/imag' );
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var abs = require( '@stdlib/math/base/special/abs' );
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var pkg = require( './../package.json' ).name;
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var cdiv = 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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var z;
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values = [
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new Complex128( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ),
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new Complex128( 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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z = values[ i % values.length ];
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y = cdiv( z, z );
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if ( typeof y !== 'object' ) {
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b.fail( 'should return an object' );
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}
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}
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b.toc();
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if ( !isComplex128( y ) ) {
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b.fail( 'should return a Complex128' );
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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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bench( pkg+'::smiths_algorithm', 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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var z;
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values = [
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new Complex128( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ),
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new Complex128( 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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z = values[ i % values.length ];
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y = cdiv( z, z );
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if ( typeof y !== 'object' ) {
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b.fail( 'should return an object' );
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}
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}
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b.toc();
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if ( !isComplex128( y ) ) {
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b.fail( 'should return a Complex128' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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function cdiv( z1, z2 ) {
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var re1;
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var re2;
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var im1;
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var im2;
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var a;
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var b;
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re1 = real( z1 );
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re2 = real( z2 );
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im1 = imag( z1 );
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im2 = imag( z2 );
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if ( abs( re2 ) >= abs( im2 ) ) {
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a = im2 / re2;
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b = re2 + ( im2 * a );
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return new Complex128( ( re1 + (im1 * a) )/b, (im1 - (re1*a) )/b );
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}
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a = re2 / im2;
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b = ( re2 * a ) + im2;
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return new Complex128( ( (re1*a) + im1 )/b, ( (im1*a) - re1 )/b );
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}
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});

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