feat: add fft/rfftf

lib/node_modules/@stdlib/fft/rfftf/README.md

@@ -0,0 +1,186 @@
+<!--
+
+@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
+
+> Return a new [ndarray][@stdlib/ndarray/ctor] containing the one-dimensional discrete Fourier transform of a real-valued input [ndarray][@stdlib/ndarray/ctor].
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var rfftf = require( '@stdlib/fft/rfftf' );
+```
+
+#### rfftf( x\[, options] )
+
+Returns a new [ndarray][@stdlib/ndarray/ctor] containing the one-dimensional discrete Fourier transform of a real-valued input [ndarray][@stdlib/ndarray/ctor].
+
+```javascript
+var array = require( '@stdlib/ndarray/array' );
+
+var x = array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+var out = rfftf( x );
+// returns <ndarray>
+```
+
+The function has the following parameters:
+
+-   **x**: input [ndarray][@stdlib/ndarray/ctor]. Must have a real-valued or "generic" [data type][@stdlib/ndarray/dtypes].
+-   **options**: function options (_optional_).
+
+The function accepts the following options:
+
+-   **n**: number of points over which to compute the transform. If not provided, defaults to the length of the input [ndarray][@stdlib/ndarray/ctor]. If `n` is greater than the input length, the input is zero-padded. If `n` is less than the input length, the input is truncated.
+-   **normalize**: normalization mode. Must be one of the following: `'backward'` (default), `'ortho'`, or `'forward'`.
+
+The returned [ndarray][@stdlib/ndarray/ctor] has a complex-valued floating-point [data type][@stdlib/ndarray/dtypes] determined by the input [data type][@stdlib/ndarray/dtypes]. For example, `float64` maps to `complex128`. The returned [ndarray][@stdlib/ndarray/ctor] has a length of `floor(N/2) + 1`, where `N` is the length of the sequence to transform.
+
+By default, the number of transform points equals the length of the input [ndarray][@stdlib/ndarray/ctor]. To specify a different number of transform points, provide an `n` option.
+
+```javascript
+var array = require( '@stdlib/ndarray/array' );
+
+var x = array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+var out = rfftf( x, {
+    'n': 8
+});
+// returns <ndarray>
+```
+
+By default, no normalization is applied to the transform result. To specify a normalization mode, provide a `normalize` option.
+
+```javascript
+var array = require( '@stdlib/ndarray/array' );
+
+var x = array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+// Scale by 1/sqrt(N):
+var out = rfftf( x, {
+    'normalize': 'ortho'
+});
+// returns <ndarray>
+```
+
+The normalization modes are as follows:
+
+-   **backward**: no normalization (default).
+-   **ortho**: scale by `1/sqrt(N)`, making the transform orthonormal.
+-   **forward**: scale by `1/N`.
+
+#### rfftf.assign( x, out\[, options] )
+
+Computes the one-dimensional discrete Fourier transform of a real-valued input [ndarray][@stdlib/ndarray/ctor] and assigns the results to a provided output [ndarray][@stdlib/ndarray/ctor].
+
+```javascript
+var zeros = require( '@stdlib/ndarray/zeros' );
+var array = require( '@stdlib/ndarray/array' );
+
+var x = array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var out = zeros( [ 3 ], {
+    'dtype': 'complex128'
+});
+
+var v = rfftf.assign( x, out );
+// returns <ndarray>
+
+var bool = ( v === out );
+// returns true
+```
+
+The function has the following parameters:
+
+-   **x**: input [ndarray][@stdlib/ndarray/ctor]. Must have a real-valued or "generic" [data type][@stdlib/ndarray/dtypes].
+-   **out**: output [ndarray][@stdlib/ndarray/ctor]. Must have a complex-valued floating-point [data type][@stdlib/ndarray/dtypes].
+-   **options**: function options (_optional_).
+
+The function accepts the following options:
+
+-   **n**: number of points over which to compute the transform. If not provided, defaults to the length of the input [ndarray][@stdlib/ndarray/ctor]. If `n` is greater than the input length, the input is zero-padded. If `n` is less than the input length, the input is truncated.
+-   **normalize**: normalization mode. Must be one of the following: `'backward'` (default), `'ortho'`, or `'forward'`.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   The function does **not** mutate the input [ndarray][@stdlib/ndarray/ctor].
+-   The output [ndarray][@stdlib/ndarray/ctor] contains only the non-negative frequency terms of the full DFT, exploiting the Hermitian symmetry of real-valued input. For an input of length `N`, the output has length `floor(N/2) + 1`.
+-   The output [ndarray][@stdlib/ndarray/ctor] has a complex-valued floating-point [data type][@stdlib/ndarray/dtypes] determined by the input [data type][@stdlib/ndarray/dtypes]. For example, `float64` input maps to `complex128` output.
+-   The DC component (index `0`) and, for even-length transforms, the Nyquist component (last index) are always purely real (i.e., have zero imaginary parts).
+-   This transform is unnormalized by default. A call to this function followed by a call performing a backward transform will multiply the input by `N`. To obtain an orthonormal transform, set the `normalize` option to `'ortho'`.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var uniform = require( '@stdlib/random/uniform' );
+var rfftf = require( '@stdlib/fft/rfftf' );
+
+// Generate an ndarray of random numbers:
+var x = uniform( [ 8 ], -10.0, 10.0, {
+    'dtype': 'float64'
+});
+console.log( ndarray2array( x ) );
+
+// Perform operation:
+var out = rfftf( x );
+
+// Print the results:
+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/ndarray/ctor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/ctor
+
+[@stdlib/ndarray/dtypes]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/dtypes
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/fft/rfftf/benchmark/benchmark.assign.js

@@ -0,0 +1,118 @@
+/**
+* @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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var uniform = require( '@stdlib/random/uniform' );
+var zeros = require( '@stdlib/ndarray/zeros' );
+var getData = require( '@stdlib/ndarray/base/data-buffer' );
+var reinterpret128 = require( '@stdlib/strided/base/reinterpret-complex128' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var assign = require( './../lib/assign.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var out;
+	var M;
+	var x;
+
+	M = floor( len/2 ) + 1;
+	x = uniform( [ len ], -50.0, 50.0, options );
+	out = zeros( [ M ], {
+		'dtype': 'complex128'
+	});
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var view;
+		var o;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			o = assign( x, out );
+			if ( typeof o !== 'object' ) {
+				b.fail( 'should return an ndarray' );
+			}
+		}
+		b.toc();
+		view = reinterpret128( getData( o ), 0 );
+		if ( isnan( view[ 0 ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( format( '%s:assign:dtype=%s,len=%d', pkg, options.dtype, len ), f );
+	}
+}
+
+main();