feat: add math/base/special/nonfibonaccif

PR-URL: #3391
Ref: #649
Co-authored-by: Athan Reines <[email protected]>
Co-authored-by: Gunj Joshi <[email protected]>
Reviewed-by: Athan Reines <[email protected]> 
Reviewed-by: Gunj Joshi <[email protected]>
Co-authored-by: stdlib-bot <[email protected]>

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

@@ -0,0 +1,249 @@
+<!--
+
+@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.
+
+-->
+
+# Non-Fibonacci
+
+> Compute the nth [non-Fibonacci][fibonacci-number] single-precision floating-point number.
+
+<!-- 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">
+
+The nth [non-Fibonacci number][fibonacci-number] is given by
+
+<!-- <equation class="equation" label="eq:nonfibonaccif_number" align="center" raw="f(n) = \left \lfloor{ n + 1 + \log_\varphi \biggl( \sqrt{5}( n + 1 + \log_\varphi(\sqrt{5}(n+1))) - 5 + \tfrac{3}{n+1} \biggr) - 2 } \right \rfloor" alt="Formula to compute the nth non-Fibonacci number."> -->
+
+```math
+f(n) = \left \lfloor{ n + 1 + \log_\varphi \biggl( \sqrt{5}( n + 1 + \log_\varphi(\sqrt{5}(n+1))) - 5 + \tfrac{3}{n+1} \biggr) - 2 } \right \rfloor
+```
+
+<!-- <div class="equation" align="center" data-raw-text="f(n) = \left \lfloor{ n + 1 + \log_\varphi \biggl( \sqrt{5}( n + 1 + \log_\varphi(\sqrt{5}(n+1))) - 5 + \tfrac{3}{n+1} \biggr) - 2 } \right \rfloor" data-equation="eq:nonfibonaccif_number">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/nonfibonaccif/docs/img/equation_nonfibonacci_number.svg" alt="Formula to compute the nth non-Fibonacci number.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `φ` is the [golden ratio][golden-ratio].
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var nonfibonaccif = require( '@stdlib/math/base/special/nonfibonaccif' );
+```
+
+#### nonfibonaccif( n )
+
+Computes the nth [non-Fibonacci][fibonacci-number] single-precision floating-point number.
+
+```javascript
+var v = nonfibonaccif( 1 );
+// returns 4
+
+v = nonfibonaccif( 2 );
+// returns 6
+
+v = nonfibonaccif( 3 );
+// returns 7
+```
+
+If provided either a non-integer or `n < 1`, the function returns `NaN`. 
+
+```javascript
+var v = nonfibonaccif( -1 );
+// returns NaN
+
+v = nonfibonaccif( 3.14 );
+// returns NaN
+```
+
+If provided `NaN`, the function returns `NaN`.
+
+```javascript
+var v = nonfibonaccif( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var nonfibonaccif = require( '@stdlib/math/base/special/nonfibonaccif' );
+
+var i;
+for ( i = 1; i < 100; i++ ) {
+    console.log( 'nonfibonaccif(%d) = %d', i, nonfibonaccif( i ) );
+}
+```
+
+</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/nonfibonaccif.h"
+```
+
+#### stdlib_base_nonfibonaccif( x )
+
+Computes the nth non-Fibonacci single-precision floating-point number.
+
+```c
+float out = stdlib_base_nonfibonaccif( 1 );
+// returns 4.0f
+
+out = stdlib_base_nonfibonaccif( 2 );
+// returns 6.0f
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] int32_t` input value.
+
+```c
+float stdlib_base_nonfibonaccif( const int32_t x );
+```
+
+</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/nonfibonaccif.h"
+#include <stdio.h>
+
+int main( void ) {
+    int i;
+    
+    for ( i = 1; i < 12; i++ ) {
+        printf( "x: %i => result: %f", i , stdlib_base_nonfibonaccif( i ) );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+* * *
+
+<section class="references">
+
+## References
+
+-   Gould, H.W. 1965. "Non-Fibonacci Numbers." _Fibonacci Quarterly_, no. 3: 177–83. [&lt;http://www.fq.math.ca/Scanned/3-3/gould.pdf>][@gould:1965a].
+-   Farhi, Bakir. 2011. "An explicit formula generating the non-Fibonacci numbers." _arXiv_ abs/1105.1127 \[Math.NT] (May): 1–5. [&lt;https://arxiv.org/abs/1105.1127>][@farhi:2011a].
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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
+
+[golden-ratio]: https://en.wikipedia.org/wiki/Golden_ratio
+
+[@gould:1965a]: http://www.fq.math.ca/Scanned/3-3/gould.pdf
+
+[@farhi:2011a]: https://arxiv.org/abs/1105.1127
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/base/special/nonfibonaccif/benchmark/benchmark.js

@@ -0,0 +1,52 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/array/discrete-uniform' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var pkg = require( './../package.json' ).name;
+var nonfibonaccif = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	x = randu( 100, 1, 100 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = nonfibonaccif( x[ i % 100 ] );
+		if ( isnanf( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/math/base/special/nonfibonaccif/benchmark/benchmark.native.js

@@ -0,0 +1,61 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var randu = require( '@stdlib/random/array/discrete-uniform' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var bench = require( '@stdlib/bench' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var nonfibonaccif = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( nonfibonaccif instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	x = randu( 100, 1, 100 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = nonfibonaccif( x[ i % 100 ] );
+		if ( isnanf( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});