feat: add fft/base/fftpack/rfftf

lib/node_modules/@stdlib/fft/base/fftpack/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 real-valued fast Fourier transform (FFT).
+
+<!-- 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 -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var rfftf = require( '@stdlib/fft/base/fftpack/rfftf' );
+```
+
+#### rfftf( N, r, strideR, offsetR, workspace, strideW, offsetW )
+
+Computes the forward real-valued fast Fourier transform (FFT).
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var rffti = require( '@stdlib/fft/base/fftpack/rffti' );
+
+var N = 4;
+var workspace = new Float64Array( ( 2*N ) + 34 );
+
+rffti( N, workspace, 1, 0 );
+
+var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+rfftf( N, r, 1, 0, workspace, 1, 0 );
+
+// r => <Float64Array>[ 10.0, -2.0, 2.0, -2.0 ]
+```
+
+The function accepts the following arguments:
+
+-   **N**: length of the sequence to transform.
+-   **r**: input array.
+-   **strideR**: stride length for `r`.
+-   **offsetR**: starting index for `r`.
+-   **workspace**: workspace array containing pre-computed values.
+-   **strideW**: stride length for `workspace`.
+-   **offsetW**: starting index for `workspace`.
+
+</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">
+
+## Notes
+
+-   Before calling this function, initialize the workspace by calling [`rffti`][@stdlib/fft/base/fftpack/rffti] with the same sequence length and workspace layout.
+
+-   The function performs the transform in-place and returns the same input array reference.
+
+-   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. In that case, the function still returns the same input array reference.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var zeros = require( '@stdlib/array/zeros' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var rffti = require( '@stdlib/fft/base/fftpack/rffti' );
+var rfftf = require( '@stdlib/fft/base/fftpack/rfftf' );
+
+var N = 4;
+var opts = {
+    'dtype': 'float64'
+};
+var r = discreteUniform( N, -10, 10, opts );
+var workspace = zeros( ( 2*N ) + 34 );
+
+console.log( r );
+
+rffti( N, workspace, 1, 0 );
+rfftf( N, r, 1, 0, workspace, 1, 0 );
+
+console.log( r );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- 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">
+
+</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">
+
+[@stdlib/fft/base/fftpack/rffti]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/fft/base/fftpack/rffti
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/fft/base/fftpack/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 slice = require( '@stdlib/array/slice' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var format = require( '@stdlib/string/format' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var Float64Array = require( '@stdlib/array/float64' );
+var dcopy = require( '@stdlib/blas/base/dcopy' );
+var rffti = require( '@stdlib/fft/base/fftpack/rffti' );
+var pkg = require( './../package.json' ).name;
+var rfftf = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// 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 workspace = new Float64Array( ( 2*N ) + 34 );
+	var x;
+	var i;
+
+	x = [];
+	for ( i = 0; i < iter; i++ ) {
+		x.push( uniform( N, -100.0, 100.0, options ) );
+	}
+
+	rffti( N, workspace, 1, 0 );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var xc;
+		var y;
+		var i;
+
+		xc = slice( x );
+		for ( i = 0; i < iter; i++ ) {
+			xc[ i ] = dcopy( N, x[ i ], 1, new Float64Array( N ), 1 );
+		}
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			y = rfftf( N, xc[ i ], 1, 0, workspace, 1, 0 );
+			if ( isnan( y[ i%N ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( y[ 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/rfftf/docs/repl.txt

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+
+{{alias}}( N, r, strideR, offsetR, workspace, strideW, offsetW )
+    Computes the forward real-valued fast Fourier transform (FFT).
+
+    Before calling this function, initialize the workspace by calling
+    `@stdlib/fft/base/fftpack/rffti` with the same sequence length and workspace
+    layout.
+
+    Parameters
+    ----------
+    N: integer
+        Length of the sequence to transform.
+
+    r: ArrayLikeObject<number>
+        Input array.
+
+    strideR: integer
+        Stride length for `r`.
+
+    offsetR: integer
+        Starting index for `r`.
+
+    workspace: ArrayLikeObject<number>
+        Workspace array containing pre-computed values.
+
+    strideW: integer
+        Stride length for `workspace`.
+
+    offsetW: integer
+        Starting index for `workspace`.
+
+    Returns
+    -------
+    r: ArrayLikeObject<number>
+        Input array.
+
+    Examples
+    --------
+    > var rffti = require( '@stdlib/fft/base/fftpack/rffti' );
+    > var N = 4;
+    > var r = new {{alias:@stdlib/array/float64}}( [ 1.0, 2.0, 3.0, 4.0 ] );
+    > var workspace = new {{alias:@stdlib/array/float64}}( ( 2*N ) + 34 );
+    > rffti( N, workspace, 1, 0 )
+    <Float64Array>
+    > var out = {{alias}}( N, r, 1, 0, workspace, 1, 0 )
+    <Float64Array>
+    > var bool = ( out === r )
+    true
+    > r
+    <Float64Array>[ 10.0, -2.0, 2.0, -2.0 ]
+
+    See Also
+    --------
+