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# Reciprocal Square Root

> Compute the reciprocal of the principal [square root][square-root] of a double-precision floating-point number.

<section class="intro">

The reciprocal of the principal [square root][square-root] is defined as

<!-- <equation class="equation" label="eq:reciprocal_square_root" align="center" raw="\operatorname{rsqrt}(x)=\frac{1}{\sqrt{x}}" alt="Reciprocal square root"> -->

<div class="equation" align="center" data-raw-text="\operatorname{rsqrt}(x)=\frac{1}{\sqrt{x}}" data-equation="eq:reciprocal_square_root">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@5b8dab9d7f516fcc8e1741900ae1569e95470c73/lib/node_modules/@stdlib/math/base/special/rsqrt/docs/img/equation_reciprocal_square_root.svg" alt="Reciprocal square root">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### rsqrt( x )

Computes the reciprocal (inverse) square root of a double-precision floating-point number.

```javascript
var v = rsqrt( 1.0 );
// returns 1.0

v = rsqrt( 4.0 );
// returns 0.5

v = rsqrt( 100.0 );
// returns 0.1

v = rsqrt( 0.0 );
// returns Infinity

v = rsqrt( NaN );
// returns NaN

v = rsqrt( Infinity );
// returns 0.0
```

For negative numbers, the reciprocal square root is **not** defined.

```javascript
var v = rsqrt( -4.0 );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var rsqrt = require( '@stdlib/math/base/special/rsqrt' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 100, 0, 100, opts );

logEachMap( 'rsqrt(%d) = %0.4f', x, rsqrt );
```

</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/rsqrt.h"
```

#### stdlib_base_rsqrt( x )

Computes the reciprocal (inverse) [square root][square-root] of a double-precision floating-point number.

```c
double y = stdlib_base_rsqrt( 4.0 );
// returns 0.5
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.

```c
double stdlib_base_rsqrt( const double x );
```

</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/rsqrt.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 3.14, 9.0, 0.0, 0.0/0.0 };

    double y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        y = stdlib_base_rsqrt( x[ i ] );
        printf( "rsqrt(%lf) = %lf\n", x[ i ], 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/sqrt`][@stdlib/math/base/special/sqrt]</span><span class="delimiter">: </span><span class="description">compute the principal square root 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">

[square-root]: https://en.wikipedia.org/wiki/Square_root

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

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

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

</section>

<!-- /.links -->
