diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md
new file mode 100644
index 000000000000..4aa185aefa1f
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md
@@ -0,0 +1,168 @@
+
+
+# rffti
+
+> Initialize a workspace array for performing a real-valued Fourier transform.
+
+
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var rffti = require( '@stdlib/fft/base/fftpack/rffti' );
+```
+
+#### rffti( N, workspace, strideW, offsetW )
+
+Initializes a workspace array for performing a real-valued Fourier transform.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var N = 8;
+var workspace = new Float64Array( ( 2*N ) + 34 );
+
+rffti( N, workspace, 1, 0 );
+
+var twiddleFactors = workspace.slice( N, 2*N );
+// returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ]
+
+var factors = workspace.slice( 2*N, ( 2*N ) + 4 );
+// returns [ 8, 2, 2, 4 ]
+```
+
+The function accepts the following arguments:
+
+- **N**: length of the sequence to transform.
+- **workspace**: workspace array.
+- **strideW**: stride length for `workspace`.
+- **offsetW**: starting index for `workspace`.
+
+
+
+
+
+
+
+
+
+## Notes
+
+- The workspace array 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, a workspace array 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 workspace, as a single data point is its own Fourier transform.
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var rffti = require( '@stdlib/fft/base/fftpack/rffti' );
+
+var workspace;
+var N;
+var nf;
+var i;
+var j;
+
+N = 8;
+workspace = new Float64Array( ( 2*N ) + 34 );
+
+rffti( N, workspace, 1, 0 );
+
+console.log( 'Sequence length: %d', N );
+console.log( 'Twiddle factors:' );
+for ( i = N; i < 2*N; i++ ) {
+ console.log( ' workspace[%d] = %d', i, workspace[ i ] );
+}
+
+console.log( 'Factorization:' );
+nf = workspace[ ( 2*N ) + 1 ];
+console.log( ' number of factors: %d', nf );
+for ( j = 0; j < nf; j++ ) {
+ console.log( ' factor[%d]: %d', j, workspace[ ( 2*N ) + 2 + j ] );
+}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/benchmark/benchmark.js
new file mode 100644
index 000000000000..07feddfa216b
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/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 format = require( '@stdlib/string/format' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var Float64Array = require( '@stdlib/array/float64' );
+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 workspace = new Float64Array( ( 2*N ) + 34 );
+ return benchmark;
+
+ /**
+ * Benchmark function.
+ *
+ * @private
+ * @param {Benchmark} b - benchmark instance
+ */
+ function benchmark( b ) {
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ rffti( N, workspace, 1, 0 );
+ if ( isnan( workspace[ N+1 ] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( workspace[ N+1 ] ) ) {
+ 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/rffti/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt
new file mode 100644
index 000000000000..aa886670dc67
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt
@@ -0,0 +1,45 @@
+
+{{alias}}( N, workspace, strideW, offsetW )
+ Initializes a workspace array for performing a real-valued Fourier
+ transform.
+
+ The workspace array is divided into three sections: scratch/workspace
+ (indices 0 to N-1), twiddle factors (indices N to 2N-1), and radix factor
+ table (indices 2N onwards).
+
+ The scratch/workspace section is used while performing transforms and is
+ not updated during initialization. The twiddle factors section stores a
+ table of reusable complex exponential constants as cosine/sine pairs. The
+ radix factor table stores the sequence length N, the number of factors into
+ which N was decomposed, and the individual integer radix factors.
+
+ Any remaining array space remains as unused storage.
+
+ Parameters
+ ----------
+ N: integer
+ Length of the sequence.
+
+ workspace: ArrayLikeObject
+ Workspace array.
+
+ strideW: integer
+ Stride length for `workspace`.
+
+ offsetW: integer
+ Starting index for `workspace`.
+
+ Examples
+ --------
+ > var {{alias:@stdlib/array/float64}} = require( '@stdlib/array/float64' );
+ > var N = 8;
+ > var workspace = new {{alias:@stdlib/array/float64}}( ( 2*N ) + 34 );
+ > {{alias}}( N, workspace, 1, 0 );
+ > var twiddleFactors = workspace.slice( N, 2*N )
+ [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ]
+ > var factors = workspace.slice( 2*N, ( 2*N ) + 4 )
+ [ 8, 2, 2, 4 ]
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts
new file mode 100644
index 000000000000..2c55a4abb09d
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts
@@ -0,0 +1,51 @@
+/*
+* @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
+
+///
+
+import { Collection } from '@stdlib/types/array';
+
+/**
+* Initializes a workspace array for performing a real-valued Fourier transform.
+*
+* @param N - length of the sequence
+* @param workspace - workspace array
+* @param strideW - stride length for `workspace`
+* @param offsetW - starting index for `workspace`
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var N = 8;
+* var workspace = new Float64Array( ( 2*N ) + 34 );
+*
+* rffti( N, workspace, 1, 0 );
+*
+* var twiddleFactors = workspace.slice( N, 2*N );
+* // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ]
+*
+* var factors = workspace.slice( 2*N, ( 2*N ) + 4 );
+* // returns [ 8, 2, 2, 4 ]
+*/
+declare function rffti( N: number, workspace: Collection, strideW: number, offsetW: number ): void;
+
+
+// EXPORTS //
+
+export = rffti;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts
new file mode 100644
index 000000000000..a01b8b17546f
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts
@@ -0,0 +1,93 @@
+/*
+* @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.
+*/
+
+import rffti = require( './index' );
+
+// TESTS //
+
+// The function returns void...
+{
+ const workspace = new Float64Array( ( 2*8 ) + 34 );
+
+ rffti( 8, workspace, 1, 0 ); // $ExpectType void
+}
+
+// The compiler throws an error if the function is provided a first argument which is not a number...
+{
+ const workspace = new Float64Array( ( 2*8 ) + 34 );
+
+ rffti( '8', workspace, 1, 0 ); // $ExpectError
+ rffti( true, workspace, 1, 0 ); // $ExpectError
+ rffti( false, workspace, 1, 0 ); // $ExpectError
+ rffti( null, workspace, 1, 0 ); // $ExpectError
+ rffti( void 0, workspace, 1, 0 ); // $ExpectError
+ rffti( [], workspace, 1, 0 ); // $ExpectError
+ rffti( {}, workspace, 1, 0 ); // $ExpectError
+ rffti( ( x: number ): number => x, workspace, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a second argument which is not an array of numbers...
+{
+ rffti( 8, '50', 1, 0 ); // $ExpectError
+ rffti( 8, 50, 1, 0 ); // $ExpectError
+ rffti( 8, true, 1, 0 ); // $ExpectError
+ rffti( 8, false, 1, 0 ); // $ExpectError
+ rffti( 8, null, 1, 0 ); // $ExpectError
+ rffti( 8, void 0, 1, 0 ); // $ExpectError
+ rffti( 8, {}, 1, 0 ); // $ExpectError
+ rffti( 8, ( x: number ): number => x, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a third argument which is not a number...
+{
+ const workspace = new Float64Array( ( 2*8 ) + 34 );
+
+ rffti( 8, workspace, '1', 0 ); // $ExpectError
+ rffti( 8, workspace, true, 0 ); // $ExpectError
+ rffti( 8, workspace, false, 0 ); // $ExpectError
+ rffti( 8, workspace, null, 0 ); // $ExpectError
+ rffti( 8, workspace, void 0, 0 ); // $ExpectError
+ rffti( 8, workspace, [], 0 ); // $ExpectError
+ rffti( 8, workspace, {}, 0 ); // $ExpectError
+ rffti( 8, workspace, ( x: number ): number => x, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a fourth argument which is not a number...
+{
+ const workspace = new Float64Array( ( 2*8 ) + 34 );
+
+ rffti( 8, workspace, 1, '0' ); // $ExpectError
+ rffti( 8, workspace, 1, true ); // $ExpectError
+ rffti( 8, workspace, 1, false ); // $ExpectError
+ rffti( 8, workspace, 1, null ); // $ExpectError
+ rffti( 8, workspace, 1, void 0 ); // $ExpectError
+ rffti( 8, workspace, 1, [] ); // $ExpectError
+ rffti( 8, workspace, 1, {} ); // $ExpectError
+ rffti( 8, workspace, 1, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+ const workspace = new Float64Array( ( 2*8 ) + 34 );
+
+ rffti(); // $ExpectError
+ rffti( 8 ); // $ExpectError
+ rffti( 8, workspace ); // $ExpectError
+ rffti( 8, workspace, 1 ); // $ExpectError
+ rffti( 8, workspace, 1, 0, 123 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js
new file mode 100644
index 000000000000..e9004065b2ee
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js
@@ -0,0 +1,46 @@
+/**
+* @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 Float64Array = require( '@stdlib/array/float64' );
+var rffti = require( './../lib' );
+
+var workspace;
+var N;
+var nf;
+var i;
+var j;
+
+N = 8;
+workspace = new Float64Array( ( 2*N ) + 34 );
+
+rffti( N, workspace, 1, 0 );
+
+console.log( 'Sequence length: %d', N );
+console.log( 'Twiddle factors:' );
+for ( i = N; i < 2*N; i++ ) {
+ console.log( ' workspace[%d] = %d', i, workspace[ i ] );
+}
+
+console.log( 'Factorization:' );
+nf = workspace[ ( 2*N ) + 1 ];
+console.log( ' number of factors: %d', nf );
+for ( j = 0; j < nf; j++ ) {
+ console.log( ' factor[%d]: %d', j, workspace[ ( 2*N ) + 2 + j ] );
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js
new file mode 100644
index 000000000000..3c440549ebce
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js
@@ -0,0 +1,49 @@
+/**
+* @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.
+*
+* @module @stdlib/fft/base/fftpack/rffti
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var rffti = require( '@stdlib/fft/base/fftpack/rffti' );
+*
+* var N = 8;
+* var workspace = new Float64Array( ( 2*N ) + 34 );
+*
+* rffti( N, workspace, 1, 0 );
+*
+* var twiddleFactors = workspace.slice( N, 2*N );
+* // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ]
+*
+* var factors = workspace.slice( 2*N, ( 2*N ) + 4 );
+* // returns [ 8, 2, 2, 4 ]
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js
new file mode 100644
index 000000000000..663a19bd35cd
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js
@@ -0,0 +1,170 @@
+/**
+* @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.
+*
+*
+* ## Notice
+*
+* The original C code and copyright notice are from the [PFFFT library]{@link https://github.com/marton78/pffft/blob/0b4ee12c4ba45a4a8e567550c16d96d1679f50ce/src/fftpack.c}. The implementation follows the original, but has been modified for JavaScript.
+*
+* ```text
+* Copyright (c) 2004 the University Corporation for Atmospheric
+* Research ("UCAR"). All rights reserved. Developed by NCAR's
+* Computational and Information Systems Laboratory, UCAR,
+* www.cisl.ucar.edu.
+*
+* Redistribution and use of the Software in source and binary forms,
+* with or without modification, is permitted provided that the
+* following conditions are met:
+*
+* - Neither the names of NCAR's Computational and Information Systems
+* Laboratory, the University Corporation for Atmospheric Research,
+* nor the names of its sponsors or contributors may be used to
+* endorse or promote products derived from this Software without
+* specific prior written permission.
+*
+* - Redistributions of source code must retain the above copyright
+* notices, this list of conditions, and the disclaimer below.
+*
+* - Redistributions in binary form must reproduce the above copyright
+* notice, this list of conditions, and the disclaimer below in the
+* documentation and/or other materials provided with the
+* distribution.
+*
+* THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+* EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
+* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+* NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
+* HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
+* EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
+* SOFTWARE.
+* ```
+*/
+
+'use strict';
+
+// MODULES //
+
+var rffti1 = require( './rffti1.js' );
+
+
+// MAIN //
+
+/**
+* Initializes a workspace array for performing a real-valued Fourier transform.
+*
+* ## Notes
+*
+* The workspace array 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 ...
+* ```
+*
+* where
+*
+* - **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 radix factorization of `N`.
+*
+* In general, a workspace array 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.
+*
+* > Note: FFTPACK only requires `2N+15`, but we increase that number here to accommodate larger workspace arrays, where `N` may exceed `2^30` indexed elements.
+*
+* The first two sections each contain `N` elements, while the last section contains the sequence length, the number of integer factors, and, at most, `ceil(log2(N)/2)` integer radix factors.
+*
+* The factorization section is comprised as follows:
+*
+* ```text
+* | sequence_length | number_of_factors | integer_factors |
+* ```
+*
+* The sequence length and number of factors (`nf`) comprise a single element each. Only the first `nf` elements in the integer factors section are written to, with the rest being unused.
+*
+* As for twiddle factors, these are small, reusable complex-exponential constants that appear inside each "butterfly" stage of a Cooley–Tukey–style FFT. Every arithmetic step in an FFT multiplies one intermediate value by some
+*
+* ```tex
+* W_N^k
+* ```
+*
+* where `W_N^k` is an N-th root of unity. Formally, in a forward FFT,
+*
+* ```tex
+* W_N^k = e^{-2\pi ik/N}
+* ```
+*
+* In a backward FFT,
+*
+* ```tex
+* W_N^k = e^{+2\pi ik/N}
+* ```
+*
+* As may be observed, `W_N^k` for forward and backward FFTs is the same, except the sign of the exponent is flipped. As a consequence, both real and backward FFT callers can reuse the same set of twiddle factors, with those performing a forward transform (e.g., `rfftf`) multiplying with `(cos,-sin)` and those performing a backward transform (e.g., `rfftb`) multiplying with `(cos,+sin)`.
+*
+* Because these constants only depend on the transform length `N` (and **not** on the input data), we can pre-compute and store them once, then "twiddle" them (i.e., reuse them with different indices) as we proceed through the factorization.
+*
+* > As a quick aside regarding the name "twiddle", early FFT papers (notably Gentleman & Sande, 1966) described how you "twiddle" one branch of each butterfly by a complex rotation before adding/subtracting. The coefficients themselves inherited the nickname "twiddle factors," and the term stuck.
+*
+* By reusing the workspace array when computing multiple transforms of the same length `N`, every subsequent `*f` (forward) or `*b` (backward) call can simply look up the pre-stored twiddle factors instead of recomputing sine and cosine on-the-fly.
+*
+* In short, twiddle factors are cached roots of unity that allow each stage of the algorithm to rotate data quickly and predictably.
+*
+* @param {NonNegativeInteger} N - length of the sequence to transform
+* @param {Float64Array} workspace - workspace array
+* @param {integer} strideW - stride length for `workspace`
+* @param {NonNegativeInteger} offsetW - starting index for `workspace`
+* @returns {void}
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var N = 8;
+* var workspace = new Float64Array( ( 2*N ) + 34 );
+*
+* rffti( N, workspace, 1, 0 );
+*
+* var twiddleFactors = workspace.slice( N, 2*N );
+* // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ]
+*
+* var factors = workspace.slice( 2*N, ( 2*N ) + 4 );
+* // returns [ 8, 2, 2, 4 ]
+*/
+function rffti( N, workspace, strideW, offsetW ) {
+ var offsetT;
+ var offsetF;
+
+ // When a sub-sequence is a single data point, the FFT is the identity, so no initialization necessary...
+ if ( N === 1 ) {
+ return;
+ }
+ // Resolve the starting indices for storing twiddle factors and factorization results:
+ offsetT = offsetW + ( N*strideW ); // index offset for twiddle factors
+ offsetF = offsetT + ( N*strideW ); // index offset for factorization results
+
+ // Initialize a provided workspace array:
+ rffti1( N, workspace, strideW, offsetT, workspace, strideW, offsetF );
+}
+
+
+// EXPORTS //
+
+module.exports = rffti;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js
new file mode 100644
index 000000000000..18a9062cce13
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js
@@ -0,0 +1,185 @@
+/**
+* @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.
+*
+*
+* ## Notice
+*
+* The original C code and copyright notice are from the [PFFFT library]{@link https://github.com/marton78/pffft/blob/0b4ee12c4ba45a4a8e567550c16d96d1679f50ce/src/fftpack.c}. The implementation follows the original, but has been modified for JavaScript.
+*
+* ```text
+* Copyright (c) 2004 the University Corporation for Atmospheric
+* Research ("UCAR"). All rights reserved. Developed by NCAR's
+* Computational and Information Systems Laboratory, UCAR,
+* www.cisl.ucar.edu.
+*
+* Redistribution and use of the Software in source and binary forms,
+* with or without modification, is permitted provided that the
+* following conditions are met:
+*
+* - Neither the names of NCAR's Computational and Information Systems
+* Laboratory, the University Corporation for Atmospheric Research,
+* nor the names of its sponsors or contributors may be used to
+* endorse or promote products derived from this Software without
+* specific prior written permission.
+*
+* - Redistributions of source code must retain the above copyright
+* notices, this list of conditions, and the disclaimer below.
+*
+* - Redistributions in binary form must reproduce the above copyright
+* notice, this list of conditions, and the disclaimer below in the
+* documentation and/or other materials provided with the
+* distribution.
+*
+* THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+* EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
+* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+* NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
+* HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
+* EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
+* SOFTWARE.
+* ```
+*/
+
+'use strict';
+
+// MODULES //
+
+var TWO_PI = require( '@stdlib/constants/float64/two-pi' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var sin = require( '@stdlib/math/base/special/sin' );
+var cos = require( '@stdlib/math/base/special/cos' );
+var decompose = require( '@stdlib/fft/base/fftpack/decompose' );
+
+
+// VARIABLES //
+
+var TRIAL_FACTORS = [ 4, 2, 3, 5 ];
+
+
+// MAIN //
+
+/**
+* Initializes the working arrays for applying a Fourier transform to a real-valued sequence.
+*
+* @private
+* @param {NonNegativeInteger} n - length of the sequence
+* @param {Collection} wa - array of twiddle factors
+* @param {integer} strideW - stride length for `wa`
+* @param {NonNegativeInteger} offsetW - starting index for `wa`
+* @param {Collection} ifac - array containing a radix factorization
+* @param {integer} strideF - stride length for `ifac`
+* @param {NonNegativeInteger} offsetF - starting index for `ifac`
+* @returns {void}
+*/
+function rffti1( n, wa, strideW, offsetW, ifac, strideF, offsetF ) {
+ var argld;
+ var argh;
+ var nfm1;
+ var arg;
+ var ipm;
+ var ido;
+ var nf;
+ var fi;
+ var ip;
+ var l2;
+ var l1;
+ var ld;
+ var ii;
+ var is;
+ var k1;
+ var i;
+ var j;
+
+ // Decompose the sequence length into its radix factors:
+ nf = decompose( n, 4, TRIAL_FACTORS, 1, 0, ifac, strideF, offsetF );
+
+ // Compute the master angular step (i.e., the basic angle that generates all twiddles):
+ argh = TWO_PI / n;
+
+ // Initialize the index into the twiddle factor array:
+ is = 0;
+
+ // Compute the number of factors minus one:
+ nfm1 = nf - 1;
+
+ // Initialize a running product of factors already processed:
+ l1 = 1;
+
+ // If the number of radix factors is `1`, the only twiddle factor we need is `W_N^0 = 1`, which the main transform kernels already hard-code, so nothing to pre-compute...
+ if ( nfm1 === 0 ) {
+ return;
+ }
+ // Generate twiddle factors for each radix factor...
+ for ( k1 = 0; k1 < nfm1; k1++ ) {
+ // Resolve the next radix factor (C code: ifac[k1+2] with 1-based, JS: ifac[k1+2] with 0-based):
+ ip = ifac[ offsetF + ((k1+2)*strideF) ];
+
+ // Initialize a running offset used to step the angle:
+ ld = 0;
+
+ // Compute the length of the transform after including the current radix:
+ l2 = l1 * ip;
+
+ // Compute the number of data points in each sub-transform:
+ ido = floor( n / l2 );
+
+ // Compute the number of iterations for the inner loop:
+ ipm = ip - 1;
+
+ // Iterate over each butterfly column within the current radix...
+ for ( j = 0; j < ipm; j++ ) {
+ // Advance to the next column:
+ ld += l1;
+
+ // Initialize the index into the twiddle factor array:
+ i = is;
+
+ // Compute the angle step for this column:
+ argld = ld * argh;
+
+ // Initialize the harmonic counter:
+ fi = 0.0;
+
+ // Iterate over each non-trivial harmonic in the column...
+ for ( ii = 2; ii < ido; ii += 2 ) {
+ // Advance the index by 2 (for cosine and sine):
+ i += 2;
+
+ // Update the harmonic counter:
+ fi += 1.0;
+
+ // Compute the angle for this harmonic:
+ arg = fi * argld;
+
+ // Store the cosine and sine values:
+ wa[ offsetW + ( ( i-1 ) * strideW ) ] = cos( arg );
+ wa[ offsetW + ( i*strideW ) ] = sin( arg );
+ }
+ // Advance the index by the number of data points in each sub-transform:
+ is += ido;
+ }
+ // Update the running product of factors already processed:
+ l1 = l2;
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = rffti1;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/package.json
new file mode 100644
index 000000000000..ea78bb766695
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/package.json
@@ -0,0 +1,64 @@
+{
+ "name": "@stdlib/fft/base/fftpack/rffti",
+ "version": "0.0.0",
+ "description": "Initialize a workspace array for performing a real-valued Fourier transform.",
+ "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"
+ ],
+ "__stdlib__": {}
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/Makefile b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/Makefile
new file mode 100644
index 000000000000..7ce16281940d
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/Makefile
@@ -0,0 +1,137 @@
+#/
+# @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.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+endif
+
+# Specify the path to FFTPACK:
+FFTPACK ?=
+
+# Specify a list of FFTPACK source files:
+FFTPACK_SRC ?=
+
+# Determine the OS:
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate [position independent code][1]:
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of C targets:
+c_targets := runner.out
+
+
+# RULES #
+
+#/
+# Compiles C source files.
+#
+# @param {string} [C_COMPILER] - C compiler
+# @param {string} [CFLAGS] - C compiler flags
+# @param {(string|void)} [fPIC] - flag indicating whether to generate position independent code
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler
+# @param {string} CFLAGS - C compiler flags
+# @param {(string|void)} fPIC - flag indicating whether to generate position independent code
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) -DFFTPACK_DOUBLE_PRECISION $(fPIC) -o $@ $(FFTPACK_SRC) $< -lm
+
+#/
+# Generates test fixtures.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
+
+#/
+# Removes generated test fixtures.
+#
+# @example
+# make clean-fixtures
+#/
+clean-fixtures:
+ $(QUIET) -rm -f *.json
+
+.PHONY: clean-fixtures
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json
new file mode 100644
index 000000000000..37ea1b0c0505
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json
new file mode 100644
index 000000000000..215106655dfe
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json
@@ -0,0 +1 @@
+{"lengths":[58,74,109,19,21,75,91,16,58,23],"offsets":[0,57,130,238,256,276,350,440,455,512],"twiddles":[0.9941379571543596,0.10811901842394177,0.97662055571008666,0.21497044021102407,0.94765317118280246,0.31930153013598001,0.90757541967095701,0.4198891015602646,0.85685717616758927,0.51555385717702173,0.79609306570564375,0.60517421519376513,0.72599549192313084,0.68769945885342332,0.64738628478182758,0.76216205512763646,0.56118706536238228,0.82768899815689057,0.46840844069979015,0.88351204444602294,0.37013815533991434,0.92897671981679142,0.26752833852922075,0.96354999251922302,0.16178199655276462,0.98682652254152614,0.05413890858541761,0.99853341385112382,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.99639748854252652,0.084805924475509192,0.98561591034770846,0.16900082032184907,0.96773294693349887,0.25197806138512518,0.94287744546108421,0.33313979474205757,0.91122849038813569,0.4119012482439926,0.87301411316118815,0.48769494381363454,0.82850964924384218,0.55997478613759533,0.77803575431843952,0.62821999729564226,0.72195609395452454,0.69193886897754608,0.66067472339008149,0.75067230525272433,0.59463317630428669,0.80399713036694054,0.52430728355723166,0.85152913773331129,0.45020374481767328,0.89292585814956849,0.37285647778030861,0.92788902729650935,0.29282277127655043,0.95616673473925096,0.21067926999572642,0.97755523894768614,0.12701781974687887,0.99190043525887683,0.042441203196148462,0.99909896620468142,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.95557280578614068,0.29475517441090421,0.82623877431599491,0.56332005806362206,0.62348980185873359,0.7818314824680298,0,0.82623877431599491,0.56332005806362206,0.36534102436639498,0.93087374864420425,-0.22252093395631434,0.97492791218182362,0,0,0,0,0,0,0,0.99649285924950437,0.083677843332315482,0.98599603707050498,0.16676874671610226,0.96858316112863119,0.24868988716485474,0.94437637023748111,0.32886664673858318,0.91354545764260087,0.40673664307580015,0.87630668004386358,0.48175367410171521,0.83292124071009954,0.55339154924334399,0.78369345732583984,0.6211477802783103,0.72896862742141155,0.68454710592868862,0.66913060635885824,0.74314482547739424,0.60459911486237494,0.79652991802419626,0.53582679497899677,0.84432792550201496,0,0.98599603707050498,0.16676874671610226,0.94437637023748111,0.32886664673858318,0.87630668004386358,0.48175367410171521,0.78369345732583984,0.6211477802783103,0.66913060635885824,0.74314482547739424,0.53582679497899677,0.84432792550201496,0.3875155864521031,0.92186315158850052,0.22835087011065588,0.97357890287316018,0.062790519529313527,0.99802672842827156,-0.10452846326765333,0.9945218953682734,-0.26891982061526559,0.96316256679765822,-0.42577929156507233,0.90482705246601969,0,0.96858316112863119,0.24868988716485474,0.87630668004386358,0.48175367410171521,0,0.87630668004386358,0.48175367410171521,0.53582679497899677,0.84432792550201496,0,0.72896862742141155,0.68454710592868862,0.062790519529313527,0.99802672842827156,0,0.53582679497899677,0.84432792550201496,-0.42577929156507233,0.90482705246601969,0,0,0,0,0,0.99761727230124764,0.068991144404324925,0.99048044398756319,0.13765351458716821,0.97862352529595531,0.20565990308593657,0.96210301984360058,0.27268622848949375,0.94099765536237645,0.33841307983367042,0.91540800852536641,0.40252723873996749,0,0.99048044398756319,0.13765351458716821,0.96210301984360058,0.27268622848949375,0.91540800852536641,0.40252723873996749,0.85128444158435124,0.52470448779900802,0.7709531747949796,0.63689182933488919,0.67594364414475439,0.73695331598433667,0,0.97862352529595531,0.20565990308593657,0.91540800852536641,0.40252723873996749,0.81305609947853252,0.58218534772077069,0.67594364414475439,0.73695331598433667,0.50993260439013599,0.86021435641350064,0.32212044179849075,0.94669869598280587,0,0.96210301984360058,0.27268622848949375,0.85128444158435124,0.52470448779900802,0.67594364414475439,0.73695331598433667,0.44937040096716135,0.89334553378556314,0.18873759545291671,0.98202755565343036,-0.086200379880619196,0.99627781994202647,0,0.94099765536237645,0.33841307983367042,0.7709531747949796,0.63689182933488919,0.50993260439013577,0.86021435641350075,0.18873759545291671,0.98202755565343036,-0.15472933479028111,0.98795689832874645,-0.47993747795978653,0.87730269419944185,0,0.91540800852536641,0.40252723873996749,0.67594364414475439,0.73695331598433667,0.32212044179849075,0.94669869598280587,-0.086200379880619196,0.99627781994202647,-0.47993747795978614,0.87730269419944207,-0.79247684195109025,0.60990200440007303,0,0,0,0,0,0,0,0,0,0,0,0,0,0.92387953251128674,0.38268343236508978,0,0,0.70710678118654757,0.70710678118654746,0,0,0.38268343236508984,0.92387953251128674,0,0,0,0,0,0.9941379571543596,0.10811901842394177,0.97662055571008666,0.21497044021102407,0.94765317118280246,0.31930153013598001,0.90757541967095701,0.4198891015602646,0.85685717616758927,0.51555385717702173,0.79609306570564375,0.60517421519376513,0.72599549192313084,0.68769945885342332,0.64738628478182758,0.76216205512763646,0.56118706536238228,0.82768899815689057,0.46840844069979015,0.88351204444602294,0.37013815533991434,0.92897671981679142,0.26752833852922075,0.96354999251922302,0.16178199655276462,0.98682652254152614,0.05413890858541761,0.99853341385112382,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c
new file mode 100644
index 000000000000..82f5947a89b0
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c
@@ -0,0 +1,282 @@
+/**
+* @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.
+*/
+
+/**
+* Generate FFTPACK test fixtures.
+*
+* ## Notes
+*
+* - Run this script from the directory in which fixtures should be written.
+*
+*/
+
+#include
+#include
+
+/**
+* Define prototypes for external functions.
+*/
+extern void rffti( int n, double *wsave );
+
+/**
+* Generates a random number on the interval [0,1].
+*
+* @return random number
+*/
+double rand_double( void ) {
+ int r = rand();
+ return (double)r / ( (double)RAND_MAX + 1.0 );
+}
+
+/**
+* Generates an array of pseudorandom integers drawn from a uniform distribution.
+*
+* ## Notes
+*
+* - WARNING: the method used here is not particularly robust, as some integer values may be sampled more frequently than others.
+*
+*
+* @param out output array
+* @param len array length
+* @param a lower bound (inclusive)
+* @param b upper bound (exclusive)
+*/
+void rand_array_i32( int *out, const unsigned int len, const int a, const int b ) {
+ unsigned int i;
+ unsigned int r;
+ double delta;
+
+ delta = (double)b - (double)a;
+
+ for ( i = 0; i < len; i++ ) {
+ r = (unsigned int)( delta * rand_double() ); // truncation
+ out[ i ] = (int)( a + r );
+ }
+}
+
+/**
+* Writes an array of doubles to a file as a series of comma-separated values.
+*
+* @param f file to write to
+* @param x array of doubles
+* @param len array length
+*/
+void write_array_f64( FILE *f, const double *x, const unsigned int len ) {
+ unsigned int i;
+
+ for ( i = 0; i < len; i++ ) {
+ fprintf( f, "%.17g", x[ i ] );
+ if ( i < len-1 ) {
+ fprintf( f, "," );
+ }
+ }
+}
+
+/**
+* Writes an array of integers to a file as a series of comma-separated values.
+*
+* @param f file to write to
+* @param x array of integers
+* @param len array length
+*/
+void write_array_i32( FILE *f, const int *x, const unsigned int len ) {
+ unsigned int i;
+
+ for ( i = 0; i < len; i++ ) {
+ fprintf( f, "%d", x[ i ] );
+ if ( i < len-1 ) {
+ fprintf( f, "," );
+ }
+ }
+}
+
+/**
+* Writes a named array of doubles to a file as JSON.
+*
+* @param f file to write to
+* @param name array name
+* @param x data
+* @param len array length
+*/
+void write_named_array_f64( FILE *f, const char *name, const double *x, const unsigned int len ) {
+ fprintf( f, "\"%s\":[", name );
+ write_array_f64( f, x, len );
+ fprintf( f, "]" );
+}
+
+/**
+* Writes a named array of integers to a file as JSON.
+*
+* @param f file to write to
+* @param name array name
+* @param x data
+* @param len array length
+*/
+void write_named_array_i32( FILE *f, const char *name, const int *x, const unsigned int len ) {
+ fprintf( f, "\"%s\":[", name );
+ write_array_i32( f, x, len );
+ fprintf( f, "]" );
+}
+
+/**
+* Writes data to a file as JSON.
+*
+* ## Notes
+*
+* - This function SHOULD be tailored to the input data (e.g., input types, output types, number of arguments, etc) and may vary from use case to use case.
+*
+*
+* @param f file to write to
+* @param lengths sequence lengths
+* @param offsets twiddle offsets
+* @param twiddles twiddle factors
+* @param num number of sequence lengths
+* @param total total number of twiddle values
+*/
+void write_data_as_json( FILE *f, const int *lengths, const int *offsets, const double *twiddles, const unsigned int num, const unsigned int total ) {
+ fprintf( f, "{" );
+ write_named_array_i32( f, "lengths", lengths, num );
+ fprintf( f, "," );
+ write_named_array_i32( f, "offsets", offsets, num );
+ fprintf( f, "," );
+ write_named_array_f64( f, "twiddles", twiddles, total );
+ fprintf( f, "}\n" );
+}
+
+/**
+* Generates test fixtures.
+*
+* @param lengths sequence lengths
+* @param offsets twiddle offsets into flat output array
+* @param num number of sequence lengths
+* @param total total number of twiddle values
+* @param name output filename
+*/
+void generate( const int *lengths, const int *offsets, const unsigned int num, const unsigned int total, const char *name ) {
+ unsigned int i;
+ unsigned int j;
+ double *twiddles;
+ double *wsave;
+ FILE *f;
+ int off;
+ int n;
+
+ // Allocate an output array:
+ twiddles = (double*) malloc( total * sizeof(double) );
+ if ( twiddles == NULL ) {
+ printf( "Error allocating memory.\n" );
+ exit( 1 );
+ }
+
+ // Generate fixture data:
+ for ( i = 0; i < num; i++ ) {
+ n = lengths[ i ];
+ wsave = (double*) calloc( 2*n + 15, sizeof(double) );
+ if ( wsave == NULL ) {
+ printf( "Error allocating memory.\n" );
+ exit( 1 );
+ }
+ rffti( n, wsave );
+
+ // Copy twiddle region into flat array (N-1 values starting at wsave[n]):
+ off = offsets[ i ];
+ for ( j = 0; j < (unsigned int)( n - 1 ); j++ ) {
+ twiddles[ off + j ] = wsave[ n + j ];
+ }
+ free( wsave );
+ }
+ // Open a new file:
+ f = fopen( name, "w" );
+ if ( f == NULL ) {
+ printf( "Error opening file.\n" );
+ exit( 1 );
+ }
+
+ // Write data as JSON:
+ write_data_as_json( f, lengths, offsets, twiddles, num, total );
+
+ // Close the file:
+ fclose( f );
+
+ // Free allocated memory:
+ free( twiddles );
+}
+
+/**
+* Computes offsets into a flat twiddle array for each sequence length.
+*
+* @param offsets output array of offsets
+* @param lengths sequence lengths
+* @param num number of sequence lengths
+* @return total number of twiddle values
+*/
+unsigned int compute_offsets( int *offsets, const int *lengths, const unsigned int num ) {
+ unsigned int total;
+ unsigned int i;
+
+ total = 0;
+ for ( i = 0; i < num; i++ ) {
+ offsets[ i ] = total;
+ total += lengths[ i ] - 1;
+ }
+ return total;
+}
+
+/**
+* Main execution sequence.
+*/
+int main( void ) {
+ unsigned int total;
+ unsigned int num;
+ int *lengths;
+ int *offsets;
+
+ // Define the number of sequence lengths per range:
+ num = 10;
+
+ // Allocate arrays:
+ lengths = (int*) malloc( num * sizeof(int) );
+ if ( lengths == NULL ) {
+ printf( "Error allocating memory.\n" );
+ exit( 1 );
+ }
+ offsets = (int*) malloc( num * sizeof(int) );
+ if ( offsets == NULL ) {
+ printf( "Error allocating memory.\n" );
+ exit( 1 );
+ }
+
+ // Generate fixture data:
+ rand_array_i32( lengths, num, 2, 16 );
+ total = compute_offsets( offsets, lengths, num );
+ generate( lengths, offsets, num, total, "small.json" );
+
+ rand_array_i32( lengths, num, 16, 128 );
+ total = compute_offsets( offsets, lengths, num );
+ generate( lengths, offsets, num, total, "medium.json" );
+
+ rand_array_i32( lengths, num, 128, 1024 );
+ total = compute_offsets( offsets, lengths, num );
+ generate( lengths, offsets, num, total, "large.json" );
+
+ // Free allocated memory:
+ free( lengths );
+ free( offsets );
+
+ return 0;
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json
new file mode 100644
index 000000000000..519a16fcee1e
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json
@@ -0,0 +1 @@
+{"lengths":[2,3,12,8,9,5,2,11,11,15],"offsets":[0,1,3,14,21,29,33,34,44,54],"twiddles":[0,0,0,0.86602540378443871,0.49999999999999994,0,0.50000000000000011,0.8660254037844386,0,6.123233995736766e-17,1,0,0,0,0.70710678118654757,0.70710678118654746,0,0,0,0,0,0.76604444311897801,0.64278760968653925,0,0.17364817766693041,0.98480775301220802,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.91354545764260087,0.40673664307580015,0.66913060635885824,0.74314482547739424,0,0.66913060635885824,0.74314482547739424,-0.10452846326765333,0.9945218953682734,0,0,0,0,0]}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js
new file mode 100644
index 000000000000..88262f7c17b1
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js
@@ -0,0 +1,231 @@
+/**
+* @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 tape = require( 'tape' );
+var Float64Array = require( '@stdlib/array/float64' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var rffti = require( './../lib' );
+
+
+// FIXTURES //
+
+var small = require( './fixtures/c/fftpack/small.json' );
+var medium = require( './fixtures/c/fftpack/medium.json' );
+var large = require( './fixtures/c/fftpack/large.json' );
+
+
+// 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 4', function test( t ) {
+ t.strictEqual( rffti.length, 4, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function correctly initializes twiddle factors (small sequence lengths)', function test( t ) {
+ var workspace;
+ var expected;
+ var lengths;
+ var offsets;
+ var delta;
+ var tol;
+ var off;
+ var y;
+ var N;
+ var i;
+ var k;
+
+ lengths = small.lengths;
+ offsets = small.offsets;
+ expected = small.twiddles;
+
+ for ( k = 0; k < lengths.length; k++ ) {
+ N = lengths[ k ];
+ off = offsets[ k ];
+ workspace = new Float64Array( ( 2*N ) + 34 );
+ rffti( N, workspace, 1, 0 );
+
+ t.strictEqual( workspace[ N ], 0.0, 'returns expected value' );
+ for ( i = 0; i < N-1; i++ ) {
+ y = workspace[ N+i+1 ];
+ if ( y === expected[ off+i ] ) {
+ t.strictEqual( y, expected[ off+i ], 'returns expected value' );
+ } else {
+ delta = abs( y - expected[ off+i ] );
+ tol = EPS * abs( expected[ off+i ] );
+ t.ok( delta <= tol, 'within tolerance. N: '+N+'. workspace['+(N+i+1)+']. Value: '+y+'. Expected: '+expected[off+i]+'. tol: '+tol+'. delta: '+delta+'.' );
+ }
+ }
+ }
+ t.end();
+});
+
+tape( 'the function correctly initializes twiddle factors (medium sequence lengths)', function test( t ) {
+ var workspace;
+ var expected;
+ var lengths;
+ var offsets;
+ var delta;
+ var tol;
+ var off;
+ var y;
+ var N;
+ var i;
+ var k;
+
+ lengths = medium.lengths;
+ offsets = medium.offsets;
+ expected = medium.twiddles;
+
+ for ( k = 0; k < lengths.length; k++ ) {
+ N = lengths[ k ];
+ off = offsets[ k ];
+ workspace = new Float64Array( ( 2*N ) + 34 );
+ rffti( N, workspace, 1, 0 );
+
+ t.strictEqual( workspace[ N ], 0.0, 'returns expected value' );
+ for ( i = 0; i < N-1; i++ ) {
+ y = workspace[ N+i+1 ];
+ if ( y === expected[ off+i ] ) {
+ t.strictEqual( y, expected[ off+i ], 'returns expected value' );
+ } else {
+ delta = abs( y - expected[ off+i ] );
+ tol = EPS * abs( expected[ off+i ] );
+ t.ok( delta <= tol, 'within tolerance. N: '+N+'. workspace['+(N+i+1)+']. Value: '+y+'. Expected: '+expected[off+i]+'. tol: '+tol+'. delta: '+delta+'.' );
+ }
+ }
+ }
+ t.end();
+});
+
+tape( 'the function correctly initializes twiddle factors (large sequence lengths)', function test( t ) {
+ var workspace;
+ var expected;
+ var lengths;
+ var offsets;
+ var delta;
+ var tol;
+ var off;
+ var y;
+ var N;
+ var i;
+ var k;
+
+ lengths = large.lengths;
+ offsets = large.offsets;
+ expected = large.twiddles;
+
+ for ( k = 0; k < lengths.length; k++ ) {
+ N = lengths[ k ];
+ off = offsets[ k ];
+ workspace = new Float64Array( ( 2*N ) + 34 );
+ rffti( N, workspace, 1, 0 );
+
+ t.strictEqual( workspace[ N ], 0.0, 'returns expected value' );
+ for ( i = 0; i < N-1; i++ ) {
+ y = workspace[ N+i+1 ];
+ if ( y === expected[ off+i ] ) {
+ t.strictEqual( y, expected[ off+i ], 'returns expected value' );
+ } else {
+ delta = abs( y - expected[ off+i ] );
+ tol = EPS * abs( expected[ off+i ] );
+ t.ok( delta <= tol, 'within tolerance. N: '+N+'. workspace['+(N+i+1)+']. Value: '+y+'. Expected: '+expected[off+i]+'. tol: '+tol+'. delta: '+delta+'.' );
+ }
+ }
+ }
+ t.end();
+});
+
+tape( 'the function does not modify the scratch region of the workspace', function test( t ) {
+ var workspace;
+ var N;
+ var i;
+
+ N = 8;
+ workspace = new Float64Array( ( 2*N ) + 34 );
+
+ for ( i = 0; i < workspace.length; i++ ) {
+ workspace[ i ] = i + 1.0;
+ }
+ rffti( N, workspace, 1, 0 );
+ for ( i = 0; i < N; i++ ) {
+ t.strictEqual( workspace[ i ], i + 1.0, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function does not modify the workspace when N is 1', function test( t ) {
+ var workspace;
+ var expected;
+ var N;
+ var i;
+
+ N = 1;
+ workspace = new Float64Array( ( 2*N ) + 34 );
+ for ( i = 0; i < workspace.length; i++ ) {
+ workspace[ i ] = i + 1.0;
+ }
+ expected = new Float64Array( workspace );
+
+ rffti( N, workspace, 1, 0 );
+
+ t.deepEqual( workspace, expected, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function correctly handles stride and offset parameters', function test( t ) {
+ var workspace;
+ var expected;
+ var stride;
+ var offset;
+ var nf;
+ var N;
+ var i;
+
+ N = 8;
+ stride = 2;
+ offset = 3;
+ workspace = new Float64Array( offset + ( ( ( 2*N ) + 34 ) * stride ) );
+
+ rffti( N, workspace, stride, offset );
+
+ t.strictEqual( workspace[ offset + ( 2*N * stride ) ], N, 'returns expected value' );
+
+ nf = workspace[ offset + ( ( ( 2*N ) + 1 ) * stride ) ];
+ t.strictEqual( nf, 2, 'returns expected value' );
+ t.strictEqual( workspace[ offset + ( ( ( 2*N ) + 2 ) * stride ) ], 2, 'returns expected value' );
+ t.strictEqual( workspace[ offset + ( ( ( 2*N ) + 3 ) * stride ) ], 4, 'returns expected value' );
+
+ expected = new Float64Array( ( 2*N ) + 34 );
+ rffti( N, expected, 1, 0 );
+
+ for ( i = 0; i < N-1; i++ ) {
+ t.strictEqual( workspace[ offset + ( ( N+i+1 ) * stride ) ], expected[ N+i+1 ], 'returns expected value' );
+ }
+ t.end();
+});