time-to-botec

Benchmark sampling in different programming languages
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README.md (3127B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      5 Copyright (c) 2018 The Stdlib Authors.
      6 
      7 Licensed under the Apache License, Version 2.0 (the "License");
      8 you may not use this file except in compliance with the License.
      9 You may obtain a copy of the License at
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     11    http://www.apache.org/licenses/LICENSE-2.0
     12 
     13 Unless required by applicable law or agreed to in writing, software
     14 distributed under the License is distributed on an "AS IS" BASIS,
     15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     16 See the License for the specific language governing permissions and
     17 limitations under the License.
     18 
     19 -->
     20 
     21 # abs2
     22 
     23 > Compute the squared [absolute value][absolute-value] of a complex number.
     24 
     25 <section class="intro">
     26 
     27 The [absolute value][absolute-value] of a complex number is defined as
     28 
     29 <!-- <equation class="equation" label="eq:absolute_value_complex" align="center" raw="|a + bi| = \sqrt{a^2 + b^2}" alt="Absolute value"> -->
     30 
     31 <div class="equation" align="center" data-raw-text="|a + bi| = \sqrt{a^2 + b^2}" data-equation="eq:absolute_value_complex">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d4edb68b52a6c646be5683023c5a24890300727f/lib/node_modules/@stdlib/math/base/special/cabs2/docs/img/equation_absolute_value_complex.svg" alt="Absolute value">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 which corresponds to the length of a vector from the origin to a complex value plotted in the complex plane.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var cabs2 = require( '@stdlib/math/base/special/cabs2' );
     50 ```
     51 
     52 #### cabs2( re, im )
     53 
     54 Computes the squared [absolute value][absolute-value] of a `complex` number comprised of a **real** component `re` and an **imaginary** component `im`.
     55 
     56 ```javascript
     57 var y = cabs2( 5.0, 3.0 );
     58 // returns 34.0
     59 ```
     60 
     61 </section>
     62 
     63 <!-- /.usage -->
     64 
     65 <section class="notes">
     66 
     67 ## Notes
     68 
     69 -   Be careful to avoid overflow and underflow.
     70 -   Depending on the environment, this function _may_ have better performance than computing the [absolute value][absolute-value] of a `complex` number and then squaring. Hence, where appropriate, consider using `cabs2()` over [`cabs()`][@stdlib/math/base/special/cabs].
     71 
     72 </section>
     73 
     74 <!-- /.notes -->
     75 
     76 <section class="examples">
     77 
     78 ## Examples
     79 
     80 <!-- eslint no-undef: "error" -->
     81 
     82 ```javascript
     83 var Complex128 = require( '@stdlib/complex/float64' );
     84 var randu = require( '@stdlib/random/base/randu' );
     85 var round = require( '@stdlib/math/base/special/round' );
     86 var real = require( '@stdlib/complex/real' );
     87 var imag = require( '@stdlib/complex/imag' );
     88 var cabs2 = require( '@stdlib/math/base/special/cabs2' );
     89 
     90 var re;
     91 var im;
     92 var z;
     93 var i;
     94 
     95 for ( i = 0; i < 100; i++ ) {
     96     re = round( randu()*100.0 ) - 50.0;
     97     im = round( randu()*100.0 ) - 50.0;
     98     z = new Complex128( re, im );
     99     console.log( 'cabs2(%s) = %d', z.toString(), cabs2( real(z), imag(z) ) );
    100 }
    101 ```
    102 
    103 </section>
    104 
    105 <!-- /.examples -->
    106 
    107 <section class="links">
    108 
    109 [absolute-value]: https://en.wikipedia.org/wiki/Absolute_value
    110 
    111 [@stdlib/math/base/special/cabs]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cabs
    112 
    113 </section>
    114 
    115 <!-- /.links -->