From 030a34ab25db2d8d976e2a9f88780fb4da031d77 Mon Sep 17 00:00:00 2001
From: Gunj Joshi <gunjjoshi8372@gmail.com>
Date: Sat, 18 Jul 2026 07:16:08 +0530
Subject: [PATCH 1/4] feat: add initial implementation

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type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
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---
---
 .../base/fftpack/ndarray/rffti/lib/main.js    | 85 +++++++++++++++++++
 1 file changed, 85 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/main.js

diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/main.js
new file mode 100644
index 000000000000..48ccc00789fe
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/main.js
@@ -0,0 +1,85 @@
+/**
+* @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 getStride = require( '@stdlib/ndarray/base/stride' );
+var getOffset = require( '@stdlib/ndarray/base/offset' );
+var getData = require( '@stdlib/ndarray/base/data-buffer' );
+var strided = require( '@stdlib/fft/base/fftpack/rffti' );
+var ndarraylike2scalar = require( '@stdlib/ndarray/base/ndarraylike2scalar' );
+
+
+// MAIN //
+
+/**
+* Initializes a workspace array for performing a real-valued Fourier transform on a one-dimensional ndarray.
+*
+* ## Notes
+*
+* -   The function expects the following ndarrays:
+*
+*     -   a zero-dimensional ndarray containing the length of the sequence to transform.
+*     -   a one-dimensional input ndarray.
+*
+* @param {ArrayLikeObject<Object>} arrays - array-like object containing ndarrays
+* @returns {ndarrayLike} output ndarray
+*
+* @example
+* var Float64Vector = require( '@stdlib/ndarray/vector/float64' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var ndarray2array = require( '@stdlib/ndarray/to-array' );
+*
+* var N = 8;
+* var len = scalar2ndarray( N, {
+*     'dtype': 'int32'
+* });
+*
+* var workspace = new Float64Vector( ( 2*N ) + 34 );
+*
+* var out = rffti( [ len, workspace ] );
+* // returns <ndarray>
+*
+* var bool = ( out === workspace );
+* // returns true
+*
+* var workspaceArr = ndarray2array( workspace );
+* // returns <Array>
+*
+* var twiddleFactors = workspaceArr.slice( N, 2*N );
+* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+*
+* var factors = workspaceArr.slice( 2*N, ( 2*N ) + 4 );
+* // returns [ 8, 2, 2, 4 ]
+*/
+function rffti( arrays ) {
+	var workspace;
+	var N;
+
+	N = ndarraylike2scalar( arrays[ 0 ] );
+	workspace = arrays[ 1 ];
+	strided( N, getData( workspace ), getStride( workspace, 0 ), getOffset( workspace ) ); // eslint-disable-line max-len
+	return workspace;
+}
+
+
+// EXPORTS //
+
+module.exports = rffti;

From 60f690c5755a14b278818a533d680d93ce9e3251 Mon Sep 17 00:00:00 2001
From: Gunj Joshi <gunjjoshi8372@gmail.com>
Date: Sat, 18 Jul 2026 07:55:54 +0530
Subject: [PATCH 2/4] refactor: use ndarray/slice

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
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    status: passed
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    status: passed
  - task: lint_markdown_pkg_readmes
    status: na
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    status: na
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    status: na
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    status: na
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    status: na
  - task: lint_javascript_src
    status: passed
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    status: na
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    status: na
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    status: na
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    status: passed
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    status: na
  - task: lint_license_headers
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---
---
 .../fft/base/fftpack/ndarray/rffti/lib/main.js     | 14 ++++++--------
 1 file changed, 6 insertions(+), 8 deletions(-)

diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/main.js
index 48ccc00789fe..43a4aabdc8a4 100644
--- a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/main.js
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/main.js
@@ -45,7 +45,8 @@ var ndarraylike2scalar = require( '@stdlib/ndarray/base/ndarraylike2scalar' );
 * @example
 * var Float64Vector = require( '@stdlib/ndarray/vector/float64' );
 * var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
-* var ndarray2array = require( '@stdlib/ndarray/to-array' );
+* var Slice = require( '@stdlib/slice/ctor' );
+* var slice = require( '@stdlib/ndarray/slice' );
 *
 * var N = 8;
 * var len = scalar2ndarray( N, {
@@ -60,14 +61,11 @@ var ndarraylike2scalar = require( '@stdlib/ndarray/base/ndarraylike2scalar' );
 * var bool = ( out === workspace );
 * // returns true
 *
-* var workspaceArr = ndarray2array( workspace );
-* // returns <Array>
+* var twiddleFactors = slice( workspace, new Slice( N, 2*N ) );
+* // returns <ndarray>[ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
 *
-* var twiddleFactors = workspaceArr.slice( N, 2*N );
-* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
-*
-* var factors = workspaceArr.slice( 2*N, ( 2*N ) + 4 );
-* // returns [ 8, 2, 2, 4 ]
+* var factors = slice( workspace, new Slice( 2*N, ( 2*N ) + 4 ) );
+* // returns <ndarray>[ 8, 2, 2, 4 ]
 */
 function rffti( arrays ) {
 	var workspace;

From a56e1f1da7afdf83c38e63a35e49459311d6c797 Mon Sep 17 00:00:00 2001
From: Gunj Joshi <gunjjoshi8372@gmail.com>
Date: Tue, 21 Jul 2026 02:14:48 +0530
Subject: [PATCH 3/4] feat: add fft/base/fftpack/ndarray/rffti

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
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    status: passed
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    status: passed
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    status: passed
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    status: na
  - task: lint_markdown
    status: na
  - task: lint_package_json
    status: passed
  - task: lint_repl_help
    status: passed
  - task: lint_javascript_src
    status: passed
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: passed
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    status: passed
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    status: passed
  - task: lint_python
    status: na
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    status: na
  - task: lint_c_src
    status: na
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    status: na
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    status: na
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    status: passed
  - task: lint_typescript_tests
    status: passed
  - task: lint_license_headers
    status: passed
---
---
 .../fft/base/fftpack/ndarray/rffti/README.md  | 135 +++++++++
 .../ndarray/rffti/benchmark/benchmark.js      | 112 ++++++++
 .../base/fftpack/ndarray/rffti/docs/repl.txt  |  39 +++
 .../ndarray/rffti/docs/types/index.d.ts       |  68 +++++
 .../fftpack/ndarray/rffti/docs/types/test.ts  |  63 +++++
 .../fftpack/ndarray/rffti/examples/index.js   |  38 +++
 .../base/fftpack/ndarray/rffti/lib/index.js   |  60 ++++
 .../base/fftpack/ndarray/rffti/package.json   |  65 +++++
 .../base/fftpack/ndarray/rffti/test/test.js   | 256 ++++++++++++++++++
 9 files changed, 836 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/README.md
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/benchmark/benchmark.js
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/repl.txt
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/types/index.d.ts
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/types/test.ts
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/examples/index.js
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/index.js
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/package.json
 create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/test/test.js

diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/README.md
new file mode 100644
index 000000000000..7394e894e078
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/README.md
@@ -0,0 +1,135 @@
+<!--
+
+@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 ndarray.
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var rffti = require( '@stdlib/fft/base/fftpack/ndarray/rffti' );
+```
+
+#### rffti( arrays )
+
+Initializes a workspace array for performing a real-valued Fourier transform on a one-dimensional 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 workspace = new Float64Vector( ( 2*N ) + 34 );
+
+var out = rffti( [ len, workspace ] );
+// returns <ndarray>
+
+var bool = ( out === workspace );
+// returns true
+
+var twiddleFactors = slice( workspace, new Slice( N, 2*N ) );
+// returns <ndarray>[ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+
+var factors = slice( workspace, 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 zero-dimensional ndarray containing the length of the sequence to transform.
+    -   a one-dimensional input ndarray.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If provided an empty one-dimensional input ndarray, the function returns the output 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/rffti' );
+
+var opts = {
+    'dtype': 'int32'
+};
+
+var N = 8;
+
+var workspace = new Float64Vector( ( 2*N ) + 34 );
+console.log( ndarray2array( workspace ) );
+
+var len = scalar2ndarray( N, opts );
+
+var out = rffti( [ len, workspace ] );
+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 -->
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/benchmark/benchmark.js
new file mode 100644
index 000000000000..189ebcffa1e5
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/benchmark/benchmark.js
@@ -0,0 +1,112 @@
+/**
+* @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' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - sequence length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var workspace = new Float64Vector( ( 2*N ) + 34 );
+	var len = scalar2ndarray( N, options );
+
+	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( [ len, workspace ] );
+			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();
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/repl.txt
new file mode 100644
index 000000000000..dccdff0f39cd
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/repl.txt
@@ -0,0 +1,39 @@
+
+{{alias}}( arrays )
+    Initializes a workspace array for performing a real-valued Fourier
+    transform on a one-dimensional ndarray.
+
+    If provided an empty input ndarray, the function returns the output ndarray
+    unchanged.
+
+    Parameters
+    ----------
+    arrays: ArrayLikeObject<ndarray>
+        Array-like object containing the following ndarrays:
+
+        - a zero-dimensional ndarray containing the length of the sequence to
+        transform.
+        - a one-dimensional input ndarray.
+
+    Returns
+    -------
+    out: ndarray
+        Output ndarray.
+
+    Examples
+    --------
+    > var N = 8;
+    > var workspace = new {{alias:@stdlib/ndarray/vector/float64}}( ( 2*N ) + 34 );
+    > var len = {{alias:@stdlib/ndarray/from-scalar}}( N, { 'dtype': 'int32' });
+    > var out = {{alias}}( [ len, workspace ] )
+    <ndarray>
+    > var bool = ( out === workspace )
+    true
+    > var twiddleFactors = {{alias:@stdlib/ndarray/slice}}( workspace, new {{alias:@stdlib/slice/ctor}}( N, 2*N ) )
+    <ndarray>[ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+    > var factors = {{alias:@stdlib/ndarray/slice}}( workspace, new {{alias:@stdlib/slice/ctor}}( 2*N, ( 2*N ) + 4 ) )
+    <ndarray>[ 8, 2, 2, 4 ]
+
+    See Also
+    --------
+
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/types/index.d.ts
new file mode 100644
index 000000000000..6b827dfea080
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/types/index.d.ts
@@ -0,0 +1,68 @@
+/*
+* @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 { ndarray, float64ndarray } from '@stdlib/types/ndarray';
+
+/**
+* Initializes a workspace array for performing a real-valued Fourier transform on a one-dimensional ndarray.
+*
+* ## Notes
+*
+* -   The function expects the following ndarrays:
+*
+*     -   a zero-dimensional ndarray containing the length of the sequence to transform.
+*     -   a one-dimensional input ndarray.
+*
+* @param arrays - array-like object containing ndarrays
+* @returns output 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 workspace = new Float64Vector( ( 2*N ) + 34 );
+*
+* var out = rffti( [ len, workspace ] );
+* // returns <ndarray>
+*
+* var bool = ( out === workspace );
+* // returns true
+*
+* var twiddleFactors = slice( workspace, new Slice( N, 2*N ) );
+* // returns <ndarray>[ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+*
+* var factors = slice( workspace, new Slice( 2*N, ( 2*N ) + 4 ) );
+* // returns <ndarray>[ 8, 2, 2, 4 ]
+*/
+declare function rffti( arrays: [ ndarray, float64ndarray ] ): float64ndarray;
+
+
+// EXPORTS //
+
+export = rffti;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/types/test.ts
new file mode 100644
index 000000000000..cb5cba80f1b3
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/docs/types/test.ts
@@ -0,0 +1,63 @@
+/*
+* @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.
+*/
+
+/* eslint-disable space-in-parens */
+
+import zeros = require( '@stdlib/ndarray/zeros' );
+import rffti = require( './index' );
+
+
+// TESTS //
+
+// The function returns an ndarray...
+{
+	const workspace = zeros( [ 10 ], {
+		'dtype': 'float64'
+	});
+	const N = zeros( [], {
+		'dtype': 'int32'
+	});
+
+	rffti( [ N, workspace ] ); // $ExpectType float64ndarray
+}
+
+// The compiler throws an error if the function is provided a first argument which is not an array of ndarrays...
+{
+	rffti( '10' ); // $ExpectError
+	rffti( 10 ); // $ExpectError
+	rffti( true ); // $ExpectError
+	rffti( false ); // $ExpectError
+	rffti( null ); // $ExpectError
+	rffti( undefined ); // $ExpectError
+	rffti( [] ); // $ExpectError
+	rffti( {} ); // $ExpectError
+	rffti( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+	const workspace = zeros( [ 10 ], {
+		'dtype': 'float64'
+	});
+	const N = zeros( [], {
+		'dtype': 'int32'
+	});
+
+	rffti(); // $ExpectError
+	rffti( [ N, workspace ], {} ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/examples/index.js
new file mode 100644
index 000000000000..04270542fb5f
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/examples/index.js
@@ -0,0 +1,38 @@
+/**
+* @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';
+
+var Float64Vector = require( '@stdlib/ndarray/vector/float64' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var rffti = require( './../lib' );
+
+var opts = {
+	'dtype': 'int32'
+};
+
+var N = 8;
+
+var workspace = new Float64Vector( ( 2*N ) + 34 );
+console.log( ndarray2array( workspace ) );
+
+var len = scalar2ndarray( N, opts );
+
+var out = rffti( [ len, workspace ] );
+console.log( ndarray2array( out ) );
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/index.js
new file mode 100644
index 000000000000..a211755d6c5c
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/lib/index.js
@@ -0,0 +1,60 @@
+/**
+* @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';
+
+/**
+* Initialize a workspace array for performing a real-valued Fourier transform on a one-dimensional ndarray.
+*
+* @module @stdlib/fft/base/fftpack/ndarray/rffti
+*
+* @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 rffti = require( '@stdlib/fft/base/fftpack/ndarray/rffti' );
+*
+* var N = 8;
+* var len = scalar2ndarray( N, {
+*     'dtype': 'int32'
+* });
+*
+* var workspace = new Float64Vector( ( 2*N ) + 34 );
+*
+* var out = rffti( [ len, workspace ] );
+* // returns <ndarray>
+*
+* var bool = ( out === workspace );
+* // returns true
+*
+* var twiddleFactors = slice( workspace, new Slice( N, 2*N ) );
+* // returns <ndarray>[ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+*
+* var factors = slice( workspace, new Slice( 2*N, ( 2*N ) + 4 ) );
+* // returns <ndarray>[ 8, 2, 2, 4 ]
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/package.json
new file mode 100644
index 000000000000..4a473186e063
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/package.json
@@ -0,0 +1,65 @@
+{
+  "name": "@stdlib/fft/base/fftpack/ndarray/rffti",
+  "version": "0.0.0",
+  "description": "Initialize a workspace array for performing a real-valued Fourier transform on a one-dimensional ndarray.",
+  "license": "Apache-2.0",
+  "author": {
+    "name": "The Stdlib Authors",
+    "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+  },
+  "contributors": [
+    {
+      "name": "The Stdlib Authors",
+      "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+    }
+  ],
+  "main": "./lib",
+  "directories": {
+    "benchmark": "./benchmark",
+    "doc": "./docs",
+    "example": "./examples",
+    "lib": "./lib",
+    "test": "./test"
+  },
+  "types": "./docs/types",
+  "scripts": {},
+  "homepage": "https://github.com/stdlib-js/stdlib",
+  "repository": {
+    "type": "git",
+    "url": "git://github.com/stdlib-js/stdlib.git"
+  },
+  "bugs": {
+    "url": "https://github.com/stdlib-js/stdlib/issues"
+  },
+  "dependencies": {},
+  "devDependencies": {},
+  "engines": {
+    "node": ">=0.10.0",
+    "npm": ">2.7.0"
+  },
+  "os": [
+    "aix",
+    "darwin",
+    "freebsd",
+    "linux",
+    "macos",
+    "openbsd",
+    "sunos",
+    "win32",
+    "windows"
+  ],
+  "keywords": [
+    "stdlib",
+    "fft",
+    "fftpack",
+    "rffti",
+    "fourier",
+    "transform",
+    "twiddle",
+    "workspace",
+    "initialization",
+    "real",
+    "ndarray"
+  ],
+  "__stdlib__": {}
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/test/test.js
new file mode 100644
index 000000000000..0a743d847968
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/test/test.js
@@ -0,0 +1,256 @@
+/**
+* @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.
+*/
+
+/* eslint-disable max-len */
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var isSameFloat64Array = require( '@stdlib/assert/is-same-float64array' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
+var Float64Array = require( '@stdlib/array/float64' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var getData = require( '@stdlib/ndarray/data-buffer' );
+var rffti = require( './../lib' );
+
+
+// FUNCTIONS //
+
+/**
+* Returns a one-dimensional ndarray.
+*
+* @private
+* @param {Collection} buffer - underlying data buffer
+* @param {NonNegativeInteger} length - number of indexed elements
+* @param {integer} stride - stride length
+* @param {NonNegativeInteger} offset - index offset
+* @returns {ndarray} one-dimensional ndarray
+*/
+function vector( buffer, length, stride, offset ) {
+	return new ndarray( 'float64', buffer, [ length ], [ stride ], offset, 'row-major' );
+}
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof rffti, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'the function has an arity of 1', function test( t ) {
+	t.strictEqual( rffti.length, 1, 'has expected arity' );
+	t.end();
+});
+
+tape( 'the function correctly initializes twiddle and integer factors in a one-dimensional ndarray `workspace`', function test( t ) {
+	var expectedTwiddles;
+	var expectedFactors;
+	var workspaceBuf;
+	var workspace;
+	var ulps;
+	var len;
+	var N;
+	var v;
+	var i;
+	var y;
+	var e;
+
+	N = 8;
+	len = scalar2ndarray( N, {
+		'dtype': 'int32'
+	});
+	workspaceBuf = new Float64Array( ( 2 * N ) + 34 );
+	workspace = vector( workspaceBuf, ( 2 * N ) + 34, 1, 0 );
+	v = rffti( [ len, workspace ] );
+	t.strictEqual( v, workspace, 'returns expected workspace reference' );
+
+	expectedTwiddles = new Float64Array( [ 0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+	expectedFactors = new Float64Array( [ 8, 2, 2, 4 ] );
+
+	ulps = 1;
+	for ( i = 0; i < expectedTwiddles.length; i++ ) {
+		y = workspaceBuf[ N + i ];
+		e = expectedTwiddles[ i ];
+		t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within ' + ulps + ' ULPs. N: ' + N + '. y: ' + y + '. E: ' + e );
+	}
+
+	for ( i = 0; i < expectedFactors.length; i++ ) {
+		y = workspaceBuf[ ( 2 * N ) + i ];
+		e = expectedFactors[ i ];
+		t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within ' + ulps + ' ULPs. N: ' + N + '. y: ' + y + '. E: ' + e );
+	}
+
+	t.end();
+});
+
+tape( 'if provided an empty ndarray, the function returns the output ndarray unchanged', function test( t ) {
+	var workspaceBuf;
+	var workspace;
+	var expected;
+	var len;
+	var N;
+	var v;
+
+	N = 4;
+	workspaceBuf = new Float64Array( [] );
+	workspace = vector( workspaceBuf, 0, 1, 0 );
+	len = scalar2ndarray( N, {
+		'dtype': 'int32'
+	});
+
+	v = rffti( [ len, workspace ] );
+
+	expected = new Float64Array( [] );
+	t.strictEqual( v, workspace, 'returns expected value' );
+	t.strictEqual( isSameFloat64Array( getData( v ), expected ), true, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function supports a one-dimensional ndarray having a non-unit stride', function test( t ) {
+	var expectedTwiddles;
+	var expectedFactors;
+	var workspaceBuf;
+	var workspace;
+	var ulps;
+	var len;
+	var y;
+	var e;
+	var i;
+	var N;
+	var v;
+
+	N = 8;
+	workspaceBuf = new Float64Array( ( 4 * N ) + 68 );
+	workspace = vector( workspaceBuf, ( 2 * N ) + 34, 2, 0 );
+	len = scalar2ndarray( N, {
+		'dtype': 'int32'
+	});
+
+	v = rffti( [ len, workspace ] );
+
+	expectedTwiddles = new Float64Array( [ 0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+	expectedFactors = new Float64Array( [ 8, 2, 2, 4 ] );
+
+	t.strictEqual( v, workspace, 'returns expected value' );
+
+	ulps = 1;
+	for ( i = 0; i < expectedTwiddles.length; i++ ) {
+		y = workspaceBuf[ ( 2 * N ) + ( 2 * i ) ];
+		e = expectedTwiddles[ i ];
+		t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within ' + ulps + ' ULPs. N: ' + N + '. y: ' + y + '. E: ' + e );
+	}
+
+	for ( i = 0; i < expectedFactors.length; i++ ) {
+		y = workspaceBuf[ ( 4 * N ) + ( 2 * i ) ];
+		e = expectedFactors[ i ];
+		t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within ' + ulps + ' ULPs. N: ' + N + '. y: ' + y + '. E: ' + e );
+	}
+
+	t.end();
+});
+
+tape( 'the function supports a one-dimensional ndarray having a negative stride', function test( t ) {
+	var expectedTwiddles;
+	var expectedFactors;
+	var workspaceBuf;
+	var workspace;
+	var ulps;
+	var len;
+	var v;
+	var y;
+	var e;
+	var i;
+	var N;
+
+	N = 8;
+	workspaceBuf = new Float64Array( ( 2 * N ) + 34 );
+	workspace = vector( workspaceBuf, ( 2 * N ) + 34, -1, ( 2 * N ) + 33 );
+	len = scalar2ndarray( N, {
+		'dtype': 'int32'
+	});
+
+	v = rffti( [ len, workspace ] );
+	t.strictEqual( v, workspace, 'returns expected value' );
+
+	expectedTwiddles = new Float64Array( [ 0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+	expectedFactors = new Float64Array( [ 8.0, 2.0, 2.0, 4.0 ] );
+
+	ulps = 1;
+	for ( i = 0; i < expectedTwiddles.length; i++ ) {
+		y = workspaceBuf[ N + 33 - i ];
+		e = expectedTwiddles[ i ];
+		t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within ' + ulps + ' ULPs. N: ' + N + '. y: ' + y + '. E: ' + e );
+	}
+
+	for ( i = 0; i < expectedFactors.length; i++ ) {
+		y = workspaceBuf[ 33 - i ];
+		e = expectedFactors[ i ];
+		t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within ' + ulps + ' ULPs. N: ' + N + '. y: ' + y + '. E: ' + e );
+	}
+
+	t.end();
+});
+
+tape( 'the function supports a one-dimensional ndarray having a non-zero offset', function test( t ) {
+	var expectedTwiddles;
+	var expectedFactors;
+	var workspaceBuf;
+	var workspace;
+	var ulps;
+	var len;
+	var v;
+	var y;
+	var e;
+	var i;
+	var N;
+
+	N = 8;
+	workspaceBuf = new Float64Array( ( 2 * N ) + 34 + 2 );
+	workspace = vector( workspaceBuf, ( 2 * N ) + 34, 1, 2 );
+	len = scalar2ndarray( N, {
+		'dtype': 'int32'
+	});
+
+	v = rffti( [ len, workspace ] );
+
+	t.strictEqual( v, workspace, 'returns expected value' );
+
+	expectedTwiddles = new Float64Array( [ 0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+	expectedFactors = new Float64Array( [ 8.0, 2.0, 2.0, 4.0 ] );
+
+	ulps = 1;
+	for ( i = 0; i < expectedTwiddles.length; i++ ) {
+		y = workspaceBuf[ N + i + 2 ];
+		e = expectedTwiddles[ i ];
+		t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within ' + ulps + ' ULPs. N: ' + N + '. y: ' + y + '. E: ' + e );
+	}
+
+	for ( i = 0; i < expectedFactors.length; i++ ) {
+		y = workspaceBuf[ ( 2 * N ) + i + 2 ];
+		e = expectedFactors[ i ];
+		t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within ' + ulps + ' ULPs. N: ' + N + '. y: ' + y + '. E: ' + e );
+	}
+
+	t.end();
+});

From 77183d917a7fc3a01da2b76a4a5dc4cede73019e Mon Sep 17 00:00:00 2001
From: Gunj Joshi <gunjjoshi8372@gmail.com>
Date: Tue, 21 Jul 2026 02:39:18 +0530
Subject: [PATCH 4/4] bench: use int32

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
  - task: lint_filenames
    status: passed
  - task: lint_editorconfig
    status: passed
  - task: lint_markdown_pkg_readmes
    status: na
  - task: lint_markdown_docs
    status: na
  - task: lint_markdown
    status: na
  - task: lint_package_json
    status: na
  - task: lint_repl_help
    status: na
  - task: lint_javascript_src
    status: na
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: na
  - task: lint_javascript_benchmarks
    status: passed
  - task: lint_python
    status: na
  - task: lint_r
    status: na
  - task: lint_c_src
    status: na
  - task: lint_c_examples
    status: na
  - task: lint_c_benchmarks
    status: na
  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: passed
  - task: lint_typescript_tests
    status: na
  - task: lint_license_headers
    status: passed
---
---
 .../fft/base/fftpack/ndarray/rffti/benchmark/benchmark.js       | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/benchmark/benchmark.js
index 189ebcffa1e5..de088b0d6d40 100644
--- a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/benchmark/benchmark.js
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/rffti/benchmark/benchmark.js
@@ -32,7 +32,7 @@ var rffti = require( './../lib' );
 // VARIABLES //
 
 var options = {
-	'dtype': 'float64'
+	'dtype': 'int32'
 };