feat: add fft/base/fftpack/ndarray/generic/rfftf

lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/rfftf/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# rfftf
+
+> Compute the forward discrete Fourier transform (DFT) of a real-valued one-dimensional ndarray.
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var rfftf = require( '@stdlib/fft/base/fftpack/ndarray/generic/rfftf' );
+```
+
+#### rfftf( arrays )
+
+Computes the forward discrete Fourier transform (DFT) of a real-valued one-dimensional ndarray.
+
+```javascript
+var Float64Vector = require( '@stdlib/ndarray/vector/float64' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var rffti = require( '@stdlib/fft/base/fftpack/ndarray/generic/rffti' );
+
+var N = 4;
+var len = scalar2ndarray( N, {
+    'dtype': 'int32'
+});
+
+var w = new Float64Vector( ( 2*N ) + 34 );
+rffti( [ w, len ] );
+
+var r = new Float64Vector( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+var out = rfftf( [ r, w ] );
+// returns <ndarray>[ 10.0, -2.0, 2.0, -2.0 ]
+
+var bool = ( out === r );
+// returns true
+```
+
+The function has the following parameters:
+
+-   **arrays**: array-like object containing the following ndarrays:
+
+    -   a one-dimensional input ndarray.
+    -   a one-dimensional workspace ndarray containing pre-computed values.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Before calling this function, initialize the workspace ndarray by calling [`rffti`][@stdlib/fft/base/fftpack/ndarray/generic/rffti] with the same sequence length and workspace layout.
+
+-   The function performs the transform in-place (i.e., the input ndarray is **mutated**).
+
+-   For `N = 4`, the output
+
+    ```text
+    [ 10.0, -2.0, 2.0, -2.0 ]
+    ```
+
+    corresponds to a zero-frequency term `10.0`, a complex coefficient `-2.0 + 2.0i` at frequency `1`, and a Nyquist term `-2.0`.
+
+-   If `N` equals `1`, the function returns early without modifying the input, as a single data point is its own Fourier transform.
+
+-   This transform is unnormalized as a call to this function followed by a call performing a [backward transform][@stdlib/fft/base/fftpack/ndarray/generic/rfftb] will multiply the input ndarray by `N`.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var zeros = require( '@stdlib/ndarray/zeros' );
+var discreteUniform = require( '@stdlib/random/discrete-uniform' );
+var rffti = require( '@stdlib/fft/base/fftpack/ndarray/generic/rffti' );
+var rfftf = require( '@stdlib/fft/base/fftpack/ndarray/generic/rfftf' );
+
+var N = 4;
+var r = discreteUniform( [ N ], -10, 10, {
+    'dtype': 'generic'
+});
+var w = zeros( [ ( 2*N ) + 34 ], {
+    'dtype': 'generic'
+});
+var len = scalar2ndarray( N, {
+    'dtype': 'int32'
+});
+
+console.log( ndarray2array( r ) );
+
+rffti( [ w, len ] );
+var out = rfftf( [ r, w ] );
+
+console.log( ndarray2array( out ) );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- 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">
+
+[@stdlib/fft/base/fftpack/ndarray/generic/rffti]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/fft/base/fftpack/ndarray/generic/rffti
+
+[@stdlib/fft/base/fftpack/ndarray/generic/rfftb]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/fft/base/fftpack/ndarray/generic/rfftb
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/rfftf/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 uniform = require( '@stdlib/random/uniform' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var copy = require( '@stdlib/ndarray/copy' );
+var zeros = require( '@stdlib/ndarray/zeros' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var format = require( '@stdlib/string/format' );
+var rffti = require( '@stdlib/fft/base/fftpack/ndarray/generic/rffti' );
+var pkg = require( './../package.json' ).name;
+var rfftf = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+var nopts = {
+	'dtype': 'int32'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} iter - number of iterations
+* @param {PositiveInteger} N - sequence length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( iter, N ) {
+	var len;
+	var x;
+	var w;
+	var i;
+
+	x = [];
+	for ( i = 0; i < iter; i++ ) {
+		x.push( uniform( [ N ], -100.0, 100.0, options ) );
+	}
+	len = scalar2ndarray( N, nopts );
+	w = zeros( [ ( 2*N ) + 34 ], options );
+	rffti( [ w, len ] );
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var xc;
+		var v;
+		var i;
+
+		xc = [];
+		for ( i = 0; i < iter; i++ ) {
+			xc.push( copy( x[ i ] ) );
+		}
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			v = rfftf( [ xc[ i ], w ] );
+			if ( typeof v !== 'object' ) {
+				b.fail( 'should return an ndarray' );
+			}
+		}
+		b.toc();
+		if ( isnan( v.get( i%N ) ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var lengths;
+	var opts;
+	var iter;
+	var N;
+	var f;
+	var i;
+
+	lengths = [
+		8,
+		16,
+		32,
+		64,
+		128,
+		256,
+		512,
+		1024
+	];
+
+	iter = 1e6;
+
+	for ( i = 0; i < lengths.length; i++ ) {
+		N = lengths[ i ];
+		f = createBenchmark( iter, N );
+		opts = {
+			'iterations': iter
+		};
+		bench( format( '%s:N=%d', pkg, N ), opts, f );
+		iter = floor( pow( iter, 3.0/4.0 ) );
+	}
+}
+
+main();

lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/rfftf/docs/repl.txt

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+
+{{alias}}( arrays )
+    Computes the forward discrete Fourier transform (DFT) of a real-valued
+    one-dimensional ndarray.
+
+    Before calling this function, one must first initialize the workspace
+    ndarray using the corresponding initialization function with the same
+    sequence length and workspace layout.
+
+    This transform is unnormalized as a call to this function followed by a
+    call performing a backward transform will multiply the input ndarray by the
+    sequence length.
+
+    Parameters
+    ----------
+    arrays: ArrayLikeObject<ndarray>
+        Array-like object containing the following ndarrays:
+
+        - a one-dimensional input ndarray.
+        - a one-dimensional workspace ndarray containing pre-computed values.
+
+    Returns
+    -------
+    out: ndarray
+        Input ndarray.
+
+    Examples
+    --------
+    > var N = 4;
+    > var opts = { 'dtype': 'int32' };
+    > var len = {{alias:@stdlib/ndarray/from-scalar}}( N, opts );
+    > var w = new {{alias:@stdlib/ndarray/vector/float64}}( ( 2*N ) + 34 );
+    > {{alias:@stdlib/fft/base/fftpack/ndarray/generic/rffti}}( [ w, len ] );
+    > var r = new {{alias:@stdlib/ndarray/vector/float64}}( [ 1.0, 2.0, 3.0, 4.0 ] );
+    > var out = {{alias}}( [ r, w ] )
+    <ndarray>[ 10.0, -2.0, 2.0, -2.0 ]
+    > var bool = ( out === r )
+    true
+
+    See Also
+    --------
+