198 lines
3.9 KiB
Markdown
198 lines
3.9 KiB
Markdown
|
<!--
|
||
|
|
||
|
@license Apache-2.0
|
||
|
|
||
|
Copyright (c) 2020 The Stdlib Authors.
|
||
|
|
||
|
Licensed under the Apache License, Version 2.0 (the "License");
|
||
|
you may not use this file except in compliance with the License.
|
||
|
You may obtain a copy of the License at
|
||
|
|
||
|
http://www.apache.org/licenses/LICENSE-2.0
|
||
|
|
||
|
Unless required by applicable law or agreed to in writing, software
|
||
|
distributed under the License is distributed on an "AS IS" BASIS,
|
||
|
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
||
|
See the License for the specific language governing permissions and
|
||
|
limitations under the License.
|
||
|
|
||
|
-->
|
||
|
|
||
|
# Reciprocal Square Root
|
||
|
|
||
|
> 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="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 randu = require( '@stdlib/random/base/randu' );
|
||
|
var round = require( '@stdlib/math/base/special/round' );
|
||
|
var rsqrtf = require( '@stdlib/math/base/special/rsqrtf' );
|
||
|
|
||
|
var x;
|
||
|
var i;
|
||
|
|
||
|
for ( i = 0; i < 100; i++ ) {
|
||
|
x = round( randu() * 100.0 );
|
||
|
console.log( 'rsqrt(%d) = %d', x, rsqrtf( x ) );
|
||
|
}
|
||
|
```
|
||
|
|
||
|
</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() {
|
||
|
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 class="links">
|
||
|
|
||
|
[square-root]: https://en.wikipedia.org/wiki/Square_root
|
||
|
|
||
|
</section>
|
||
|
|
||
|
<!-- /.links -->
|