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feat: add math/base/special/negafibonaccif
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273 changes: 273 additions & 0 deletions lib/node_modules/@stdlib/math/base/special/negafibonaccif/README.md
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<!--
@license Apache-2.0
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# negaFibonaccif

> Compute the nth [negaFibonacci number][fibonacci-number] as a single-precision floating-point number.
<section class="intro">

The [negaFibonacci numbers][fibonacci-number] are the integer sequence

<!-- <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"> -->

```math
0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, \ldots
```

<!-- <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">
<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">
<br>
</div> -->

<!-- </equation> -->

The sequence is defined by the recurrence relation

<!-- <equation class="equation" label="eq:negafibonacci_recurrence_relation" align="center" raw="F_{n-2} = F_{n} - F_{n-1}" alt="NegaFibonacci sequence recurrence relation"> -->

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

<!-- <div class="equation" align="center" data-raw-text="F_{n-2} = F_{n} - F_{n-1}" data-equation="eq:negafibonacci_recurrence_relation">
<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">
<br>
</div> -->

<!-- </equation> -->

which yields

<!-- <equation class="equation" label="eq:negafibonacci_fibonacci" align="center" raw="F_{-n} = (-1)^{n+1} F_n" alt="NegaFibonacci relationship to Fibonacci numbers"> -->

```math
F_{-n} = (-1)^{n+1} F_n
```

<!-- <div class="equation" align="center" data-raw-text="F_{-n} = (-1)^{n+1} F_n" data-equation="eq:negafibonacci_fibonacci">
<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">
<br>
</div> -->

<!-- </equation> -->

with seed values `F_0 = 0` and `F_{-1} = 1`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### negafibonaccif( n )

Computes the nth [negaFibonacci number][fibonacci-number] as a single-precision floating-point number.

```javascript
var v = negafibonaccif( 0 );
// returns 0

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

v = negafibonaccif( -2 );
// returns -1

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

v = negafibonaccif( -36 );
// returns -14930352
```

If `n < -36`, the function returns `NaN`, as larger [negaFibonacci numbers][fibonacci-number] cannot be safely represented in [single-precision floating-point format][ieee754].

```javascript
var v = negafibonaccif( -37 );
// returns NaN
```

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

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

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

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

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

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

var v;
var i;

for ( i = 0; i > -37; i-- ) {
v = negafibonaccif( 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/negafibonaccif.h"
```

#### stdlib_base_negafibonaccif( n )

Computes the nth [negaFibonacci number][fibonacci-number] as a single-precision floating-point number.

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

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

The function accepts the following arguments:

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

```c
float stdlib_base_negafibonaccif( 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/negafibonaccif.h"
#include <stdio.h>
#include <stdint.h>
int main( void ) {
int32_t i;
float v;
for ( i = 0; i > -37; i-- ) {
v = stdlib_base_negafibonaccif( i );
printf( "negafibonaccif(%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">

[fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number

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

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

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

</section>

<!-- /.links -->
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