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feat: add math/base/special/lucasf
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‎lib/node_modules/@stdlib/math/base/special/lucasf/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Lucasf
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> Compute the nth [Lucas number][lucas-number] in single-precision floating-point format.
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<section class="intro">
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The [Lucas numbers][lucas-number] are the integer sequence
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<!-- <equation class="equation" label="eq:lucas_sequence" align="center" raw="2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, \ldots" alt="Lucas sequence"> -->
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```math
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2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, \ldots
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```
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<!-- <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:lucas_sequence">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/lucas/docs/img/equation_lucas_sequence.svg" alt="Lucas sequence">
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<br>
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</div> -->
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<!-- </equation> -->
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The sequence is defined by the recurrence relation
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<!-- <equation class="equation" label="eq:lucas_recurrence_relation" align="center" raw="L_n = \begin{cases}2 & \textrm{if}\ n = 0\\1 & \textrm{if}\ n = 1\\L_{n-1} + L_{n-2} & \textrm{if}\ n > 1\end{cases}" alt="Lucas sequence recurrence relation"> -->
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```math
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L_n = \begin{cases}2 & \textrm{if}\ n = 0\\1 & \textrm{if}\ n = 1\\L_{n-1} + L_{n-2} & \textrm{if}\ n > 1\end{cases}
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```
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<!-- <div class="equation" align="center" data-raw-text="L_n = \begin{cases}2 &amp; \textrm{if}\ n = 0\\1 &amp; \textrm{if}\ n = 1\\L_{n-1} + L_{n-2} &amp; \textrm{if}\ n &gt; 1\end{cases}" data-equation="eq:lucas_recurrence_relation">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/lucas/docs/img/equation_lucas_recurrence_relation.svg" alt="Lucas sequence recurrence relation">
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<br>
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var lucasf = require( '@stdlib/math/base/special/lucasf' );
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```
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#### lucasf( n )
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Computes the nth [Lucas number][lucas-number] in single-precision floating-point format.
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```javascript
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var v = lucasf( 0 );
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// returns 2
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v = lucasf( 1 );
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// returns 1
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v = lucasf( 2 );
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// returns 3
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v = lucasf( 3 );
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// returns 4
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v = lucasf( 34 );
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// returns 12752043
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```
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If `n > 34`, the function returns `NaN`, as larger [Lucas numbers][lucas-number] cannot be safely represented in [single-precision floating-point format][ieee754].
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```javascript
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var v = lucasf( 35 );
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// returns NaN
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```
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If not provided a nonnegative integer value, the function returns `NaN`.
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```javascript
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var v = lucasf( 3.14 );
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// returns NaN
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v = lucasf( -1 );
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// returns NaN
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```
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If provided `NaN`, the function returns `NaN`.
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```javascript
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var v = lucasf( NaN );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var lucasf = require( '@stdlib/math/base/special/lucasf' );
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var v;
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var i;
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for ( i = 0; i < 35; i++ ) {
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v = lucasf( i );
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console.log( v );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/math/base/special/lucasf.h"
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```
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#### stdlib_base_lucasf( n )
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Computes the nth [Lucas number][lucas-number] in single-precision floating-point format.
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```c
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double out = stdlib_base_lucasf( 0 );
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// returns 2.0f
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out = stdlib_base_lucasf( 1 );
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// returns 1.0f
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```
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The function accepts the following arguments:
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- **n**: `[in] int32_t` input value.
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```c
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float stdlib_base_lucas( const int32_t n );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/math/base/special/lucasf.h"
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#include <stdio.h>
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#include <stdint.h>
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int main( void ) {
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int32_t i;
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float v;
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for ( i = 0; i < 35; i++ ) {
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v = stdlib_base_lucasf( i );
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printf( "lucasf(%d) = %lf\n", i, v );
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}
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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* * *
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## See Also
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- <span class="package-name">[`@stdlib/math/base/special/fibonacci`][@stdlib/math/base/special/fibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Fibonacci number.</span>
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- <span class="package-name">[`@stdlib/math/base/special/negalucas`][@stdlib/math/base/special/negalucas]</span><span class="delimiter">: </span><span class="description">compute the nth negaLucas number.</span>
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[lucas-number]: https://en.wikipedia.org/wiki/Lucas_number
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[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
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<!-- <related-links> -->
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[@stdlib/math/base/special/fibonacci]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/fibonacci
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[@stdlib/math/base/special/negalucas]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/negalucas
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

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