feat: add math/base/special/tribonaccif

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# Tribonaccif
+
+> Compute the nth [Tribonacci number][tribonacci-number] for [single-precision floating-point number][ieee754].
+
+<section class="intro">
+
+The [Tribonacci numbers][tribonacci-number] are the integer sequence
+
+<!-- <equation class="equation" label="eq:tribonacci_sequence" align="center" raw="0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, \ldots" alt="Tribonacci sequence"> -->
+
+```math
+0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, \ldots
+```
+
+<!-- <div class="equation" align="center" data-raw-text="0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, \ldots" data-equation="eq:tribonacci_sequence">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@3249a68fb57cd71148f87ef3b2774be70a04d80a/lib/node_modules/@stdlib/math/base/special/tribonacci/docs/img/equation_tribonacci_sequence.svg" alt="Tribonacci sequence">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+The sequence is defined by the recurrence relation
+
+<!-- <equation class="equation" label="eq:tribonacci_recurrence_relation" align="center" raw="F_n = F_{n-1} + F_{n-2} + F_{n-3}" alt="Tribonacci sequence recurrence relation"> -->
+
+```math
+F_n = F_{n-1} + F_{n-2} + F_{n-3}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="F_n = F_{n-1} + F_{n-2} + F_{n-3}" data-equation="eq:tribonacci_recurrence_relation">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@3249a68fb57cd71148f87ef3b2774be70a04d80a/lib/node_modules/@stdlib/math/base/special/tribonacci/docs/img/equation_tribonacci_recurrence_relation.svg" alt="Tribonacci sequence recurrence relation">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+with seed values `F_0 = 0`, `F_1 = 0`, and `F_2 = 1`.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var tribonaccif = require( '@stdlib/math/base/special/tribonaccif' );
+```
+
+#### tribonaccif( n )
+
+Computes the nth [Tribonacci number][tribonacci-number] for [single-precision floating-point number][ieee754].
+
+```javascript
+var v = tribonaccif( 0 );
+// returns 0
+
+v = tribonaccif( 1 );
+// returns 0
+
+v = tribonaccif( 2 );
+// returns 1
+
+v = tribonaccif( 3 );
+// returns 1
+
+v = tribonaccif( 30 );
+// returns 15902591
+```
+
+If `n > 30`, the function returns `NaN`, as larger [Tribonacci numbers][tribonacci-number] cannot be safely represented in [single-precision floating-point format][ieee754].
+
+```javascript
+var v = tribonaccif( 32 );
+// returns NaN
+```
+
+If not provided a nonnegative integer value, the function returns `NaN`.
+
+```javascript
+var v = tribonaccif( 3.14 );
+// returns NaN
+
+v = tribonaccif( -1 );
+// returns NaN
+```
+
+If provided `NaN`, the function returns `NaN`.
+
+```javascript
+var v = tribonaccif( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var tribonaccif = require( '@stdlib/math/base/special/tribonaccif' );
+
+var v;
+var i;
+
+for ( i = 0; i < 31; i++ ) {
+    v = tribonaccif( 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/tribonaccif.h"
+```
+
+#### stdlib_base_tribonaccif( n )
+
+Computes the nth [Tribonacci number][tribonacci-number] [single-precision floating-point number][ieee754].
+
+```c
+float out = stdlib_base_tribonaccif( 0f );
+// returns 0f
+
+out = stdlib_base_tribonaccif( 1f );
+// returns 0f
+```
+
+The function accepts the following arguments:
+
+-   **n**: `[in] int32_t` input value.
+
+```c
+float stdlib_base_tribonaccif( 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/tribonaccif.h"
+#include <stdio.h>
+#include <stdint.h>
+
+int main( void ) {
+    int32_t i;
+    float v;
+
+    for ( i = 0; i < 31; i++ ) {
+        v = stdlib_base_tribonaccif( i );
+        printf( "tribonaccif(%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">
+
+[tribonacci-number]: https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers
+
+[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
+
+</section>
+
+<!-- /.links -->