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feat: add math/base/special/negafibonaccif
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‎lib/node_modules/@stdlib/math/base/special/negafibonaccif/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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# negaFibonaccif
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> Compute the nth [negaFibonacci number][fibonacci-number] as a single-precision floating-point number.
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<section class="intro">
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The [negaFibonacci numbers][fibonacci-number] are the integer sequence
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<!-- <equation class="equation" label="eq:negafibonacci_sequence" align="center" raw="0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, \ldots" alt="NegaFibonacci sequence"> -->
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```math
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0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, \ldots
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```
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<!-- <div class="equation" align="center" data-raw-text="0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, \ldots" data-equation="eq:negafibonacci_sequence">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/negafibonacci/docs/img/equation_negafibonacci_sequence.svg" alt="NegaFibonacci 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:negafibonacci_recurrence_relation" align="center" raw="F_{n-2} = F_{n} - F_{n-1}" alt="NegaFibonacci sequence recurrence relation"> -->
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```math
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F_{n-2} = F_{n} - F_{n-1}
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```
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<!-- <div class="equation" align="center" data-raw-text="F_{n-2} = F_{n} - F_{n-1}" data-equation="eq:negafibonacci_recurrence_relation">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/negafibonacci/docs/img/equation_negafibonacci_recurrence_relation.svg" alt="NegaFibonacci sequence recurrence relation">
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<br>
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</div> -->
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<!-- </equation> -->
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which yields
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<!-- <equation class="equation" label="eq:negafibonacci_fibonacci" align="center" raw="F_{-n} = (-1)^{n+1} F_n" alt="NegaFibonacci relationship to Fibonacci numbers"> -->
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```math
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F_{-n} = (-1)^{n+1} F_n
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```
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<!-- <div class="equation" align="center" data-raw-text="F_{-n} = (-1)^{n+1} F_n" data-equation="eq:negafibonacci_fibonacci">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/negafibonacci/docs/img/equation_negafibonacci_fibonacci.svg" alt="NegaFibonacci relationship to Fibonacci numbers">
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<br>
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</div> -->
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<!-- </equation> -->
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with seed values `F_0 = 0` and `F_{-1} = 1`.
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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 negafibonaccif = require( '@stdlib/math/base/special/negafibonaccif' );
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```
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#### negafibonaccif( n )
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Computes the nth [negaFibonacci number][fibonacci-number] as a single-precision floating-point number.
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```javascript
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var v = negafibonaccif( 0 );
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// returns 0
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v = negafibonaccif( -1 );
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// returns 1
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v = negafibonaccif( -2 );
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// returns -1
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v = negafibonaccif( -3 );
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// returns 2
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v = negafibonaccif( -36 );
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// returns -14930352
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```
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If `n < -36`, the function returns `NaN`, as larger [negaFibonacci numbers][fibonacci-number] cannot be safely represented in [single-precision floating-point format][ieee754].
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```javascript
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var v = negafibonaccif( -37 );
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// returns NaN
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```
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If not provided a nonpositive integer value, the function returns `NaN`.
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```javascript
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var v = negafibonaccif( -3.14 );
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// returns NaN
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v = negafibonaccif( 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 = negafibonaccif( 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 negafibonaccif = require( '@stdlib/math/base/special/negafibonaccif' );
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var v;
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var i;
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for ( i = 0; i > -37; i-- ) {
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v = negafibonaccif( 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/negafibonaccif.h"
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```
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#### stdlib_base_negafibonaccif( n )
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Computes the nth [negaFibonacci number][fibonacci-number] as a single-precision floating-point number.
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```c
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float out = stdlib_base_negafibonaccif( 0 );
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// returns 0.0f
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out = stdlib_base_fibonaccif( -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_negafibonaccif( 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/negafibonaccif.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 > -37; i-- ) {
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v = stdlib_base_negafibonaccif( i );
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printf( "negafibonaccif(%d) = %f\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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</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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[fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number
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[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

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