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feat: add math/base/special/negalucasf
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PR-URL: #3375
Ref: #649

---------

Signed-off-by: Philipp Burckhardt <pburckhardt@outlook.com>
Co-authored-by: stdlib-bot <82920195+stdlib-bot@users.noreply.github.com>
Co-authored-by: Philipp Burckhardt <pburckhardt@outlook.com>
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<!--
@license Apache-2.0
Copyright (c) 2024 The Stdlib Authors.
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distributed under the License is distributed on an "AS IS" BASIS,
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# negaLucas

> Compute the nth [negaLucas number][lucas-number] in single-precision floating-point format.
<section class="intro">

The [negaLucas numbers][lucas-number] are the integer sequence

<!-- <equation class="equation" label="eq:negalucasf_sequence" align="center" raw="2, -1, 3, -4, 7, -11, 18, -29, 47, -76, 123, -199, 322, \ldots" alt="NegaLucas sequence"> -->

```math
2, -1, 3, -4, 7, -11, 18, -29, 47, -76, 123, -199, 322, \ldots
```

<!-- <div class="equation" align="center" data-raw-text="2, -1, 3, -4, 7, -11, 18, -29, 47, -76, 123, -199, 322, \ldots" data-equation="eq:negalucasf_sequence">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/negalucasf/docs/img/equation_negalucas_sequence.svg" alt="NegaLucas sequence">
<br>
</div> -->

<!-- </equation> -->

The sequence is defined by the recurrence relation

<!-- <equation class="equation" label="eq:negalucasf_recurrence_relation" align="center" raw="L_{n-2} = L_{n} - L_{n-1}" alt="NegaLucas sequence recurrence relation"> -->

```math
L_{n-2} = L_{n} - L_{n-1}
```

<!-- <div class="equation" align="center" data-raw-text="L_{n-2} = L_{n} - L_{n-1}" data-equation="eq:negalucasf_recurrence_relation">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/negalucasf/docs/img/equation_negalucas_recurrence_relation.svg" alt="NegaLucas sequence recurrence relation">
<br>
</div> -->

<!-- </equation> -->

which yields

<!-- <equation class="equation" label="eq:negalucasf_lucas" align="center" raw="L_{-n} = (-1)^{n} L_n" alt="NegaLucas relationship to Lucas numbers"> -->

```math
L_{-n} = (-1)^{n} L_n
```

<!-- <div class="equation" align="center" data-raw-text="L_{-n} = (-1)^{n} L_n" data-equation="eq:negalucasf_lucas">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/negalucasf/docs/img/equation_negalucas_lucas.svg" alt="NegaLucas relationship to Lucas numbers">
<br>
</div> -->

<!-- </equation> -->

with seed values `L_0 = 2` and `L_{-1} = -1`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### negalucasf( n )

Computes the nth [negaLucas number][lucas-number] in single-precision floating-point format.

```javascript
var v = negalucasf( 0 );
// returns 2

v = negalucasf( -1 );
// returns -1

v = negalucasf( -2 );
// returns 3

v = negalucasf( -3 );
// returns -4

v = negalucasf( -34 );
// returns 12752043
```

If `n < -34`, the function returns `NaN`, as larger [negaLucas numbers][lucas-number] cannot be safely represented in [single-precision floating-point format][ieee754].

```javascript
var v = negalucasf( -35 );
// returns NaN
```

If not provided a nonpositive integer value, the function returns `NaN`.

```javascript
var v = negalucasf( -3.14 );
// returns NaN

v = negalucasf( 1 );
// returns NaN
```

If provided `NaN`, the function returns `NaN`.

```javascript
var v = negalucasf( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

var v;
var i;

for ( i = 0; i > -35; i-- ) {
v = negalucasf( i );
console.log( v );
}
```

</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/negalucasf.h"
```

#### stdlib_base_negalucasf( n )

Computes the nth [negaLucas number][lucas-number] in single-precision floating-point format.

```c
float out = stdlib_base_negalucasf( 0 );
// returns 0.0f

out = stdlib_base_negalucasf( -1 );
// returns -1.0f
```

The function accepts the following arguments:

- **n**: `[in] int32_t` input value.

```c
float stdlib_base_negalucasf( 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/negalucasf.h"
#include <stdio.h>
#include <stdint.h>
int main( void ) {
int32_t i;
float v;
for ( i = 0; i > -35; i-- ) {
v = stdlib_base_negalucasf( i );
printf( "negalucasf(%d) = %f\n", i, v );
}
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</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">

[lucas-number]: https://en.wikipedia.org/wiki/Lucas_number

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

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

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

</section>

<!-- /.links -->
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Coverage Report

Package Statements Branches Functions Lines
math/base/special/negalucasf $\color{green}225/225$
$\color{green}+100.00\%$ 		$\color{green}11/11$
$\color{green}+100.00\%$ 		$\color{green}2/2$
$\color{green}+100.00\%$ 		$\color{green}225/225$
$\color{green}+100.00\%$

The above coverage report was generated for the changes in this push.

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