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# cabs2

> 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="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 -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

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

[@stdlib/math/base/special/cabs]: https://github.com/stdlib-js/math/tree/main/base/special/cabs

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

<!-- <related-links> -->

[@stdlib/math/base/special/abs2]: https://github.com/stdlib-js/math/tree/main/base/special/abs2

<!-- </related-links> -->

</section>

<!-- /.links -->
