npm package: @stdlib/math-base-special-rempio2
Description: Compute `x - nπ/2 = r`.
Author: The Stdlib Authors
Latest version: 0.3.1

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# rempio2

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> Compute `x - nπ/2 = r`.

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-rempio2
```

</section>

<section class="usage">

## Usage

```javascript
var rempio2 = require( '@stdlib/math-base-special-rempio2' );
```

#### rempio2( x, y )

Computes `x - nπ/2 = r`.

```javascript
var y = [ 0.0, 0.0 ];
var n = rempio2( 128.0, y );
// returns 81

var y1 = y[ 0 ];
// returns ~0.765

var y2 = y[ 1 ];
// returns ~3.618e-17
```

When `x` is `NaN` or infinite, the function returns `0` and sets the elements of `y` to `NaN`.

```javascript
var y = [ 0.0, 0.0 ];
var n = rempio2( NaN, y );
// returns 0

var y1 = y[ 0 ];
// returns NaN

var y2 = y[ 1 ];
// returns NaN

y = [ 0.0, 0.0 ];
n = rempio2( Infinity, y );
// returns 0

y1 = y[ 0 ];
// returns NaN

y2 = y[ 1 ];
// returns NaN
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

## Notes

-   The function returns `n` and stores the remainder `r` as two numbers in `y`, such that `y[0]+y[1] = r`.
-   For input values larger than `2^20*π/2` in magnitude, the function **only** returns the last three binary digits of `n` and not the full result.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var linspace = require( '@stdlib/array-base-linspace' );
var rempio2 = require( '@stdlib/math-base-special-rempio2' );

var x = linspace( 0.0, 100.0, 100 );
var y = [ 0.0, 0.0 ];
var n;
var i;

for ( i = 0; i < x.length; i++ ) {
    n = rempio2( x[ i ], y );
    console.log( '%d - %dπ/2 = %d + %d', x[ i ], n, y[ 0 ], y[ 1 ] );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/rempio2.h"
```

#### stdlib_base_rempio2( x, &rem1, &rem2 )

Computes `x - nπ/2 = r`.

```c
#include <stdint.h>

double rem1;
double rem2;

int32_t n = stdlib_base_rempio2( 4.0, &rem1, &rem2 );
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.
-   **rem1**: `[out] double*` destination for first remainder number.
-   **rem2**: `[out] double*` destination for second remainder number.

```c
int32_t stdlib_base_rempio2( const double x, double *rem1, double *rem2 );
```

</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">

### Notes

-   The function returns `n` and stores the remainder `r` as two numbers in `rem1` and `rem2`, respectively, such that `rem1+rem2 = r`.

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/rempio2.h"
#include <stdio.h>
#include <stdint.h>
#include <inttypes.h>

int main( void ) {
    const double x[] = { 0.0, 1.0, 4.0, 128.0 };

    double rem1;
    double rem2;
    int32_t n;
    int i;
    for ( i = 0; i < 4; i++ ) {
        n = stdlib_base_rempio2( x[ i ], &rem1, &rem2 );
        printf( "%lf - %"PRId32"π/2 = %lf + %lf\n", x[ i ], n, rem1, rem2 );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="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].

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## Copyright

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

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