npm package: @stdlib/math-base-special-cabs2
Description: Compute the squared absolute value of a double-precision complex floating-point number.
Author: The Stdlib Authors
Latest version: 0.2.3

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# cabs2

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the squared [absolute value][absolute-value] of a double-precision [complex][@stdlib/complex/float64/ctor] floating-point number.

<section class="intro">

The [absolute value][absolute-value] of a [complex][@stdlib/complex/float64/ctor] number is defined as

<!-- <equation class="equation" label="eq:absolute_value_complex" align="center" raw="|a + bi| = \sqrt{a^2 + b^2}" alt="Absolute value"> -->

<div class="equation" align="center" data-raw-text="|a + bi| = \sqrt{a^2 + b^2}" data-equation="eq:absolute_value_complex">
    <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">
    <br>
</div>

<!-- </equation> -->

which corresponds to the length of a vector from the origin to a complex value plotted in the complex plane.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-cabs2
```

</section>

<section class="usage">

## Usage

```javascript
var cabs2 = require( '@stdlib/math-base-special-cabs2' );
```

#### cabs2( z )

Computes the squared [absolute value][absolute-value] of a double-precision [complex][@stdlib/complex/float64/ctor] floating-point number.

```javascript
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var y = cabs2( new Complex128( 5.0, 3.0 ) );
// returns 34.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Be careful to avoid overflow and underflow.
-   Depending on the environment, this function _may_ have better performance than computing the [absolute value][absolute-value] of a [complex][@stdlib/complex/float64/ctor] number and then squaring. Hence, where appropriate, consider using `cabs2()` over [`cabs()`][@stdlib/math/base/special/cabs].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint-disable max-len -->

<!-- eslint no-undef: "error" -->

```javascript
var Complex128 = require( '@stdlib/complex-float64-ctor' );
var discreteUniform = require( '@stdlib/random-base-discrete-uniform' ).factory;
var cabs2 = require( '@stdlib/math-base-special-cabs2' );

// Create a PRNG to generate uniformly distributed pseudorandom integers:
var rand = discreteUniform( -50, 50 );

// Compute the squared absolute value for a set of random numbers...
var z;
var i;
for ( i = 0; i < 100; i++ ) {
    z = new Complex128( rand(), rand() );
    console.log( 'cabs2(%s) = %d', z.toString(), cabs2( z ) );
}
```

</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/cabs2.h"
```

#### stdlib_base_cabs2( z )

Computes the squared [absolute value][absolute-value] of a double-precision complex floating-point number.

```c
#include "stdlib/complex/float64/ctor.h"

stdlib_complex128_t z = stdlib_complex128( 5.0, 3.0 );

double y = stdlib_base_cabs2( z );
// returns 34.0
```

The function accepts the following arguments:

-   **z**: `[in] stdlib_complex128_t` input value.

```c
double stdlib_base_cabs2( const stdlib_complex128_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/cabs2.h"
#include "stdlib/complex/float64/ctor.h"
#include "stdlib/complex/float64/reim.h"
#include <stdio.h>

int main( void ) {
    const stdlib_complex128_t x[] = {
        stdlib_complex128( 3.14, 1.0 ),
        stdlib_complex128( -3.14, -1.0 ),
        stdlib_complex128( 0.0, 0.0 ),
        stdlib_complex128( 0.0/0.0, 0.0/0.0 )
    };

    stdlib_complex128_t v;
    double re;
    double im;
    double y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        v = x[ i ];
        y = stdlib_base_cabs2( v );
        stdlib_complex128_reim( v, &re, &im );
        printf( "f(%lf + %lf) = %lf\n", re, im, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/cabs`][@stdlib/math/base/special/cabs]</span><span class="delimiter">: </span><span class="description">compute the absolute value of a double-precision complex floating-point number.</span>
-   <span class="package-name">[`@stdlib/math-base/special/abs2`][@stdlib/math/base/special/abs2]</span><span class="delimiter">: </span><span class="description">compute the squared absolute value of a double-precision floating-point number.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[absolute-value]: https://en.wikipedia.org/wiki/Absolute_value

[@stdlib/math/base/special/cabs]: https://www.npmjs.com/package/@stdlib/math-base-special-cabs

[@stdlib/complex/float64/ctor]: https://www.npmjs.com/package/@stdlib/complex-float64-ctor

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[@stdlib/math/base/special/abs2]: https://www.npmjs.com/package/@stdlib/math-base-special-abs2

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