feat: add fft/fftpack/rffti

lib/node_modules/@stdlib/fft/fftpack/rffti/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.
+
+-->
+
+# rffti
+
+> Return an initialized one-dimensional workspace [ndarray][@stdlib/ndarray/ctor] for computing a real-valued discrete Fourier transform.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var rffti = require( '@stdlib/fft/fftpack/rffti' );
+```
+
+#### rffti( n\[, options] )
+
+Returns an initialized one-dimensional workspace [ndarray][@stdlib/ndarray/ctor] for computing a real-valued discrete Fourier transform.
+
+```javascript
+var getDType = require( '@stdlib/ndarray/dtype' );
+var getShape = require( '@stdlib/ndarray/shape' );
+
+var ws = rffti( 4 );
+// returns <ndarray>
+
+var dt = String( getDType( ws ) );
+// returns 'float64'
+
+var sh = getShape( ws );
+// returns [ 42 ]
+```
+
+The function has the following parameters:
+
+-   **n**: sequence length.
+-   **options**: function options (_optional_).
+
+The function accepts the following options:
+
+-   **dtype**: workspace [data type][@stdlib/ndarray/dtypes]. Must be a real-valued floating-point [data type][@stdlib/ndarray/dtypes]. Default: `'float64'`.
+
+To specify the workspace [data type][@stdlib/ndarray/dtypes], provide a `dtype` option.
+
+```javascript
+var getDType = require( '@stdlib/ndarray/dtype' );
+
+var ws = rffti( 4, {
+    'dtype': 'float32'
+});
+// returns <ndarray>
+
+var dt = String( getDType( ws ) );
+// returns 'float32'
+```
+
+#### rffti.assign( workspace, n )
+
+Initializes a provided one-dimensional workspace [ndarray][@stdlib/ndarray/ctor] for computing a real-valued discrete Fourier transform.
+
+```javascript
+var zeros = require( '@stdlib/ndarray/zeros' );
+
+var ws = zeros( [ 42 ], {
+    'dtype': 'float64'
+});
+// returns <ndarray>
+
+var out = rffti.assign( ws, 4 );
+// returns <ndarray>
+
+var bool = ( ws === out );
+// returns true
+```
+
+The function has the following parameters:
+
+-   **workspace**: workspace [ndarray][@stdlib/ndarray/ctor]. Must have a real-valued floating-point [data type][@stdlib/ndarray/dtypes].
+-   **n**: sequence length.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   The returned workspace [ndarray][@stdlib/ndarray/ctor] has a length of `(2*n) + 34`.
+-   The workspace contains precomputed twiddle factors and factorization data used by the FFTPACK forward and backward real-valued FFT routines.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var getDType = require( '@stdlib/ndarray/dtype' );
+var getShape = require( '@stdlib/ndarray/shape' );
+var rffti = require( '@stdlib/fft/fftpack/rffti' );
+
+// Initialize a workspace for a sequence of length 8:
+var ws = rffti( 8 );
+console.log( 'dtype: %s', getDType( ws ) );
+console.log( 'shape: [%s]', getShape( ws ).join( ', ' ) );
+
+// Initialize a single-precision workspace:
+var ws32 = rffti( 8, {
+    'dtype': 'float32'
+});
+console.log( 'dtype: %s', getDType( ws32 ) );
+console.log( 'shape: [%s]', getShape( ws32 ).join( ', ' ) );
+```
+
+</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/fftpack/rffti/benchmark/benchmark.assign.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 isndarrayLike = require( '@stdlib/assert/is-ndarray-like' );
+var zeros = require( '@stdlib/ndarray/zeros' );
+var pow = require( '@stdlib/math/base/special/pow' );
+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 - sequence length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var ws = zeros( [ ( 2*len ) + 34 ], options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var out;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			out = assign( ws, len );
+			if ( typeof out !== 'object' ) {
+				b.fail( 'should return an ndarray' );
+			}
+		}
+		b.toc();
+		if ( !isndarrayLike( out ) ) {
+			b.fail( 'should return an ndarray' );
+		}
+		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();

lib/node_modules/@stdlib/fft/fftpack/rffti/benchmark/benchmark.js

@@ -0,0 +1,101 @@
+/**
+* @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 isndarrayLike = require( '@stdlib/assert/is-ndarray-like' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var rffti = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - sequence length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var ws;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			ws = rffti( len, options );
+			if ( typeof ws !== 'object' ) {
+				b.fail( 'should return an ndarray' );
+			}
+		}
+		b.toc();
+		if ( !isndarrayLike( ws ) ) {
+			b.fail( 'should return an ndarray' );
+		}
+		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:dtype=%s,len=%d', pkg, options.dtype, len ), f );
+	}
+}
+
+main();