feat: add fft/base/fftpack/ndarray/float64/rffti

lib/node_modules/@stdlib/fft/base/fftpack/ndarray/float64/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
+
+> Initialize a workspace array for performing a real-valued Fourier transform on a one-dimensional double-precision floating-point ndarray.
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var rffti = require( '@stdlib/fft/base/fftpack/ndarray/float64/rffti' );
+```
+
+#### rffti( arrays )
+
+Initializes a workspace array for performing a real-valued Fourier transform on a one-dimensional double-precision floating-point ndarray.
+
+```javascript
+var Float64Vector = require( '@stdlib/ndarray/vector/float64' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var Slice = require( '@stdlib/slice/ctor' );
+var slice = require( '@stdlib/ndarray/slice' );
+
+var N = 8;
+var len = scalar2ndarray( N, {
+    'dtype': 'int32'
+});
+
+var w = new Float64Vector( ( 2*N ) + 34 );
+
+var out = rffti( [ w, len ] );
+// returns <ndarray>
+
+var bool = ( out === w );
+// returns true
+
+var twiddleFactors = slice( w, new Slice( N, 2*N ) );
+// returns <ndarray>[ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+
+var factors = slice( w, new Slice( 2*N, ( 2*N ) + 4 ) );
+// returns <ndarray>[ 8, 2, 2, 4 ]
+```
+
+The function has the following parameters:
+
+-   **arrays**: array-like object containing the following ndarrays:
+
+    -   a one-dimensional input ndarray.
+    -   a zero-dimensional ndarray containing the length of the sequence to transform.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Let `N` equal the number of elements in the input ndarray. The input ndarray is divided into three sections:
+
+    ```text
+              size = N                 N            2+ceil(log2(N)/2)
+                   ↓                   ↓                  ↓
+        | scratch / workspace | twiddle factors | radix factor table |
+                   ↑                   ↑                  ↑
+    i = 0         ...         N       ...       2N       ...
+    ```
+
+    -   **scratch/workspace**: used as a scratch space when performing transforms. This section is not updated during initialization.
+    -   **twiddle factors**: a table of reusable complex-exponential constants stored as cosine/sine pairs.
+    -   **radix factor table**: a table containing the sequence length `N`, the number of factors into which `N` was decomposed, and the individual integer radix factors.
+
+-   In general, an input ndarray should have `2N + 34` indexed elements (as `log2(N)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing twiddle factors and the factorization of `N` are updated.
+
+-   The radix factor table is comprised as follows:
+
+    ```text
+    | sequence_length | number_of_factors | integer_factors |
+    ```
+
+-   If `N` equals `1`, the function returns early without modifying the input ndarray, as a single data point is its own Fourier transform.
+
+-   If provided an empty one-dimensional input ndarray, the function returns the input ndarray unchanged.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Vector = require( '@stdlib/ndarray/vector/float64' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var rffti = require( '@stdlib/fft/base/fftpack/ndarray/float64/rffti' );
+
+var N = 8;
+
+var w = new Float64Vector( ( 2*N ) + 34 );
+console.log( ndarray2array( w ) );
+
+var len = scalar2ndarray( N, {
+    'dtype': 'int32'
+});
+
+var out = rffti( [ w, len ] );
+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">
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/fft/base/fftpack/ndarray/float64/rffti/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 Float64Vector = require( '@stdlib/ndarray/vector/float64' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var rffti = require( './../lib' );
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - sequence length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var len;
+	var w;
+
+	len = scalar2ndarray( N, {
+		'dtype': 'int32'
+	});
+	w = new Float64Vector( ( 2*N ) + 34 );
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var v;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			v = rffti( [ w, len ] );
+			if ( typeof v !== 'object' ) {
+				b.fail( 'should return an ndarray' );
+			}
+		}
+		b.toc();
+		if ( isnan( v.get( N ) ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var lengths;
+	var N;
+	var f;
+	var i;
+
+	lengths = [
+		8,
+		16,
+		32,
+		64,
+		128,
+		256,
+		512,
+		1024
+	];
+
+	for ( i = 0; i < lengths.length; i++ ) {
+		N = lengths[ i ];
+		f = createBenchmark( N );
+		bench( format( '%s:N=%d', pkg, N ), f );
+	}
+}
+
+main();

lib/node_modules/@stdlib/fft/base/fftpack/ndarray/float64/rffti/docs/repl.txt

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+
+{{alias}}( arrays )
+    Initializes a workspace array for performing a real-valued Fourier transform
+    on a one-dimensional double-precision floating-point ndarray.
+
+    If provided an empty input ndarray, the function returns the input ndarray
+    unchanged.
+
+    Parameters
+    ----------
+    arrays: ArrayLikeObject<ndarray>
+        Array-like object containing the following ndarrays:
+
+        - a one-dimensional input ndarray.
+        - a zero-dimensional ndarray containing the length of the sequence to
+        transform.
+
+    Returns
+    -------
+    out: ndarray
+        Input ndarray.
+
+    Examples
+    --------
+    > var N = 8;
+    > var w = new {{alias:@stdlib/ndarray/vector/float64}}( ( 2*N ) + 34 );
+    > var opts = { 'dtype': 'int32' };
+    > var len = {{alias:@stdlib/ndarray/from-scalar}}( N, opts );
+    > var out = {{alias}}( [ w, len ] )
+    <ndarray>
+    > var bool = ( out === w )
+    true
+    > var s = new {{alias:@stdlib/slice/ctor}}( N, 2*N );
+    > var twiddleFactors = {{alias:@stdlib/ndarray/slice}}( w, s )
+    <ndarray>[ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+    > s = new {{alias:@stdlib/slice/ctor}}( 2*N, ( 2*N ) + 4 );
+    > var factors = {{alias:@stdlib/ndarray/slice}}( w, s )
+    <ndarray>[ 8, 2, 2, 4 ]
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/fft/base/fftpack/ndarray/float64/rffti/docs/types/index.d.ts

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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.
+*/
+
+// TypeScript Version: 4.1
+
+/// <reference types="@stdlib/types"/>
+
+import { typedndarray, float64ndarray } from '@stdlib/types/ndarray';
+
+/**
+* Initializes a workspace array for performing a real-valued Fourier transform on a one-dimensional double-precision floating-point ndarray.
+*
+* ## Notes
+*
+* -   The function expects the following ndarrays:
+*
+*     -   a one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray containing the length of the sequence to transform.
+*
+* @param arrays - array-like object containing ndarrays
+* @returns input ndarray
+*
+* @example
+* var Float64Vector = require( '@stdlib/ndarray/vector/float64' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var Slice = require( '@stdlib/slice/ctor' );
+* var slice = require( '@stdlib/ndarray/slice' );
+*
+* var N = 8;
+* var len = scalar2ndarray( N, {
+*     'dtype': 'int32'
+* });
+*
+* var w = new Float64Vector( ( 2*N ) + 34 );
+*
+* var out = rffti( [ w, len ] );
+* // returns <ndarray>
+*
+* var bool = ( out === w );
+* // returns true
+*
+* var twiddleFactors = slice( w, new Slice( N, 2*N ) );
+* // returns <ndarray>[ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+*
+* var factors = slice( w, new Slice( 2*N, ( 2*N ) + 4 ) );
+* // returns <ndarray>[ 8, 2, 2, 4 ]
+*/
+declare function rffti( arrays: [ float64ndarray, typedndarray<number> ] ): float64ndarray;
+
+
+// EXPORTS //
+
+export = rffti;