npm package: @stdlib/math-base-special-rsqrtf
Description: Compute the reciprocal square root of a single-precision floating-point number.
Author: The Stdlib Authors
Latest version: 0.2.4

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# Reciprocal Square Root

[![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 reciprocal of the principal [square root][square-root] of a single-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{rsqrtf}(x)=\frac{1}{\sqrt{x}}" alt="Reciprocal square root"> -->

<div class="equation" align="center" data-raw-text="\operatorname{rsqrtf}(x)=\frac{1}{\sqrt{x}}" data-equation="eq:reciprocal_square_root">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@0fa0140fef638265646fb520a52170d5e0495023/lib/node_modules/@stdlib/math/base/special/rsqrtf/docs/img/equation_reciprocal_square_root.svg" alt="Reciprocal square root">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### rsqrtf( x )

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

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

v = rsqrtf( 4.0 );
// returns 0.5

v = rsqrtf( 0.0 );
// returns Infinity

v = rsqrtf( NaN );
// returns NaN

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

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

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

var opts = {
    'dtype': 'float32'
};
var x = discreteUniform( 100, 0, 100, opts );

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

</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/rsqrtf.h"
```

#### stdlib_base_rsqrtf( x )

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

```c
float y = stdlib_base_rsqrtf( 4.0 );
// returns 0.5
```

The function accepts the following arguments:

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

```c
float stdlib_base_rsqrtf( const float 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/rsqrtf.h"
#include <stdio.h>

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

    float y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        y = stdlib_base_rsqrtf( x[ i ] );
        printf( "rsqrt(%f) = %f\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/rsqrt`][@stdlib/math/base/special/rsqrt]</span><span class="delimiter">: </span><span class="description">compute the reciprocal square root of a double-precision floating-point number.</span>
-   <span class="package-name">[`@stdlib/math-base/special/sqrtf`][@stdlib/math/base/special/sqrtf]</span><span class="delimiter">: </span><span class="description">compute the principal square root of a single-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="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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-rsqrtf/main/LICENSE

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

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

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

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

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</section>

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