feat: add math/base/special/lucasf

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 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.
+
+-->
+
+# Lucas
+
+> Computes the nth [Lucas number][lucas-number] as a single-precision floating-point number.
+
+<section class="intro">
+
+The [Lucas numbers][lucas-number] are the integer sequence
+
+<!-- <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"> -->
+
+```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:lucas_sequence">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/lucasf/docs/img/equation_lucas_sequence.svg" alt="Lucas sequence">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+The sequence is defined by the recurrence relation
+
+<!-- <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"> -->
+
+```math
+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}
+```
+
+<!-- <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">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/lucasf/docs/img/equation_lucas_recurrence_relation.svg" alt="Lucas sequence recurrence relation">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var lucasf = require( '@stdlib/math/base/special/lucasf' );
+```
+
+#### lucasf( n )
+
+Computes the nth [Lucas number][lucas-number] as a single-precision floating-point number.
+
+```javascript
+var v = lucasf( 0 );
+// returns 2
+
+v = lucasf( 1 );
+// returns 1
+
+v = lucasf( 2 );
+// returns 3
+
+v = lucasf( 3 );
+// returns 4
+
+v = lucasf( 34 );
+// returns 12752043
+```
+
+If `n > 34`, the function returns `NaN`, as larger [Lucas numbers][lucas-number] cannot be safely represented in [single-precision floating-point format][ieee754].
+
+```javascript
+var v = lucasf( 35 );
+// returns NaN
+```
+
+If not provided a nonnegative integer value, the function returns `NaN`.
+
+```javascript
+var v = lucasf( 3.14 );
+// returns NaN
+
+v = lucasf( -1 );
+// returns NaN
+```
+
+If provided `NaN`, the function returns `NaN`.
+
+```javascript
+var v = lucasf( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var lucasf = require( '@stdlib/math/base/special/lucasf' );
+
+var v;
+var i;
+
+for ( i = 0; i < 35; i++ ) {
+    v = lucasf( 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/lucasf.h"
+```
+
+#### stdlib_base_lucasf( n )
+
+Computes the nth [Lucas number][lucas-number] as a single-precision floating-point number.
+
+```c
+float out = stdlib_base_lucasf( 0 );
+// returns 2.0f
+
+out = stdlib_base_lucasf( 1 );
+// returns 1.0f
+```
+
+The function accepts the following arguments:
+
+-   **n**: `[in] int32_t` input value.
+
+```c
+float stdlib_base_lucasf( 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/lucasf.h"
+#include <stdio.h>
+#include <stdint.h>
+
+int main( void ) {
+    int32_t i;
+    float v;
+
+    for ( i = 0; i < 35; i++ ) {
+        v = stdlib_base_lucasf( i );
+        printf( "lucasf(%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 -->