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# cfloorn

> Round each component of a double-precision complex floating-point number to the nearest multiple of `10^n` toward negative infinity.

<section class="usage">

## Usage

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

#### cfloorn( z, n )

Rounds each component of a double-precision complex floating-point number to the nearest multiple of `10^n` toward negative infinity.

```javascript
var Complex128 = require( '@stdlib/complex/float64' );
var real = require( '@stdlib/complex/real' );
var imag = require( '@stdlib/complex/imag' );

// Round components to 2 decimal places:
var v = cfloorn( new Complex128( -3.141592653589793, 3.141592653589793 ), -2 );
// returns <Complex128>

var re = real( v );
// returns -3.15

var im = imag( v );
// returns 3.14

// If n = 0, `cfloorn` behaves like `cfloor`:
v = cfloorn( new Complex128( -3.141592653589793, 3.141592653589793 ), 0 );
// returns <Complex128>

re = real( v );
// returns -4.0

im = imag( v );
// returns 3.0

// Round components to the nearest thousand:
v = cfloorn( new Complex128( -12368.0, 12368.0 ), 3 );
// returns <Complex128>

re = real( v );
// returns -13000.0

im = imag( v );
// returns 12000.0

v = cfloorn( new Complex128( NaN, NaN ), 0 );
// returns <Complex128>

re = real( v );
// returns NaN

im = imag( v );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   When operating on [floating-point numbers][ieee754] in bases other than `2`, rounding to specified digits can be **inexact**. For example,

    ```javascript
    var Complex128 = require( '@stdlib/complex/float64' );
    var real = require( '@stdlib/complex/real' );
    var imag = require( '@stdlib/complex/imag' );

    var x = -0.2 - 0.1;
    // returns -0.30000000000000004

    // Should round components to 0.3:
    var v = cfloorn( new Complex128( x, x ), -16 );
    // returns <Complex128>

    var re = real( v );
    // returns -0.3000000000000001

    var im = imag( v );
    // returns -0.3000000000000001
    ```

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var Complex128 = require( '@stdlib/complex/float64' );
var randu = require( '@stdlib/random/base/randu' );
var uniform = require( '@stdlib/random/base/uniform' );
var floor = require( '@stdlib/math/base/special/floor' );
var cfloorn = require( '@stdlib/math/base/special/cfloorn' );
var randint = require( '@stdlib/random/base/discrete-uniform' );

var z;
var w;
var n;
var i;

for ( i = 0; i < 100; i++ ) {
    z = new Complex128( uniform( -50.0, 50.0 ), uniform( -50.0, 50.0 ) );

    n = randint( -5.0, 0.0 );
    w = cfloorn( z, n );

    console.log( 'floorn(%s,%s) = %s', z.toString(), n.toString(), w.toString() );
}
```

</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/cfloorn.h"
```

#### stdlib_base_cfloorn( z, n )

Rounds each component of a double-precision complex floating-point number to the nearest multiple of `10^n` toward negative infinity.

```c
#include "stdlib/complex/float64.h"
#include "stdlib/complex/real.h"
#include "stdlib/complex/imag.h"

stdlib_complex128_t z = stdlib_complex128( -3.141592653589793, 3.141592653589793 );
stdlib_complex128_t out = stdlib_base_cfloorn( z, -2 );

double re = stdlib_real( out );
// returns -3.15

double im = stdlib_imag( out );
// returns 3.14
```

The function accepts the following arguments:

-   **z**: `[in] stdlib_complex128_t` input value.
-   **n**: `[in] int32_t` integer power of 10.

```c
stdlib_complex128_t stdlib_base_cfloorn( const stdlib_complex128_t z, const int32_t n );
```

</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/cfloorn.h"
#include "stdlib/complex/float64.h"
#include "stdlib/complex/reim.h"
#include <stdio.h>

int main() {
    const stdlib_complex128_t x[] = {
        stdlib_complex128( 3.14, 1.5 ),
        stdlib_complex128( -3.14, -1.5 ),
        stdlib_complex128( 0.0, 0.0 ),
        stdlib_complex128( 0.0/0.0, 0.0/0.0 )
    };

    stdlib_complex128_t v;
    stdlib_complex128_t y;
    double re1;
    double im1;
    double re2;
    double im2;
    int i;
    for ( i = 0; i < 4; i++ ) {
        v = x[ i ];
        y = stdlib_base_cfloorn( v, -2 );
        stdlib_reim( v, &re1, &im1 );
        stdlib_reim( y, &re2, &im2 );
        printf( "cfloorn(%lf + %lfi, -2) = %lf + %lfi\n", re1, im1, re2, im2 );
    }
}
```

</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/cceiln`][@stdlib/math/base/special/cceiln]</span><span class="delimiter">: </span><span class="description">round each component of a double-precision complex floating-point number to the nearest multiple of 10^n toward positive infinity.</span>
-   <span class="package-name">[`@stdlib/math/base/special/cfloor`][@stdlib/math/base/special/cfloor]</span><span class="delimiter">: </span><span class="description">round a double-precision complex floating-point number toward negative infinity.</span>
-   <span class="package-name">[`@stdlib/math/base/special/croundn`][@stdlib/math/base/special/croundn]</span><span class="delimiter">: </span><span class="description">round each component of a double-precision complex floating-point number to the nearest multiple of 10^n.</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">

[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985

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

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

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

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

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

</section>

<!-- /.links -->
