diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/decompose/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/README.md
new file mode 100644
index 000000000000..af5c32205bfc
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/README.md
@@ -0,0 +1,142 @@
+
+
+# decompose
+
+> Factorize a sequence length into a product of integers.
+
+
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var decompose = require( '@stdlib/fft/base/fftpack/decompose' );
+```
+
+#### decompose( N, M, initial, si, oi, out, so, oo )
+
+Factorizes a sequence length into a product of integers.
+
+```javascript
+var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
+var N = 630;
+var factors = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+var numFactors = decompose( N, 4, initial, 1, 0, factors, 1, 0 );
+// returns 5
+
+console.log( factors );
+// => [ 630, 5, 2, 3, 3, 5, 7 ]
+```
+
+The function accepts the following arguments:
+
+- **N**: length of the sequence.
+- **M**: number of trial divisors.
+- **initial**: array of initial trial divisors.
+- **si**: stride length for `initial`.
+- **oi**: starting index for `initial`.
+- **out**: output array for storing factorization results.
+- **so**: stride length for `out`.
+- **oo**: starting index for `out`.
+
+The function returns the number of factors into which `N` was decomposed.
+
+
+
+
+
+
+
+
+
+## Notes
+
+- Factorization results are stored in the output array as follows:
+
+ ```text
+ [ sequence_length | number_of_factors | integer_factors | unused_storage ]
+ ```
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var decompose = require( '@stdlib/fft/base/fftpack/decompose' );
+
+var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
+var factors = [ 0, 0, 0, 0 ];
+
+var nf = decompose( 12, 4, initial, 1, 0, factors, 1, 0 );
+
+console.log( 'Sequence length: %d', 12 );
+console.log( 'Number of factors: %d', nf );
+
+console.log( 'Factors:' );
+var j;
+for ( j = 0; j < nf; j++ ) {
+ console.log( ' %d', factors[ j+2 ] );
+}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/decompose/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/benchmark/benchmark.js
new file mode 100644
index 000000000000..604afa551b4e
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/benchmark/benchmark.js
@@ -0,0 +1,107 @@
+/*
+* @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 floor = require( '@stdlib/math/base/special/floor' );
+var log2 = require( '@stdlib/math/base/special/log2' );
+var zeros = require( '@stdlib/array/zeros' );
+var pkg = require( './../package.json' ).name;
+var decompose = require( './../lib' );
+
+
+// VARIABLES //
+
+var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - sequence length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+ var factors = zeros( 2 + floor( log2( N ) ) );
+ return benchmark;
+
+ /**
+ * Benchmark function.
+ *
+ * @private
+ * @param {Benchmark} b - benchmark instance
+ */
+ function benchmark( b ) {
+ var d;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ d = decompose( N, 4, initial, 1, 0, factors, 1, 0 );
+ if ( isnan( d ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( d ) ) {
+ 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 = [
+ 12,
+ 24,
+ 36,
+ 48,
+ 60,
+ 120
+ ];
+
+ 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/decompose/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/repl.txt
new file mode 100644
index 000000000000..964ed8270c71
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/repl.txt
@@ -0,0 +1,55 @@
+
+{{alias}}( N, M, initial, si, oi, out, so, oo )
+ Factorizes a sequence length into a product of integers.
+
+ Factorization results are stored in the output array sequentially, where
+ the first element contains the sequence length N, the second element
+ contains the number of factors into which N was decomposed, and subsequent
+ elements contain the individual integer factors.
+
+ Any remaining array space remains as unused storage.
+
+ Parameters
+ ----------
+ N: integer
+ Length of the sequence.
+
+ M: integer
+ Number of trial divisors.
+
+ initial: ArrayLikeObject
+ Array of initial trial divisors.
+
+ si: integer
+ Stride length for `initial`.
+
+ oi: integer
+ Starting index for `initial`.
+
+ out: ArrayLikeObject
+ Output array for storing factorization results.
+
+ so: integer
+ Stride length for `out`.
+
+ oo: integer
+ Starting index for `out`.
+
+ Returns
+ -------
+ numFactors: integer
+ Number of factors into which N was decomposed.
+
+ Examples
+ --------
+ > var N = 630;
+ > var initial = [ 3, 4, 2, 5 ];
+ > var factors = [ 0, 0, 0, 0, 0, 0, 0 ];
+ > var numFactors = {{alias}}( N, 4, initial, 1, 0, factors, 1, 0 )
+ 5
+ > factors
+ [ 630, 5, 2, 3, 3, 5, 7 ]
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/types/index.d.ts
new file mode 100644
index 000000000000..686266a120ed
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/types/index.d.ts
@@ -0,0 +1,50 @@
+/*
+* @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';
+
+/**
+* Factorizes a sequence length into a product of integers.
+*
+* @param N - length of the sequence
+* @param M - number of trial divisors
+* @param initial - array of initial trial divisors
+* @param si - stride length for `initial`
+* @param oi - starting index for `initial`
+* @param out - output array for storing factorization results
+* @param so - stride length for `out`
+* @param oo - starting index for `out`
+* @returns number of factors into which `N` was decomposed
+*
+* @example
+* var initial = new Float64Array( [ 3, 4, 2, 5 ] );
+* var factors = new Float64Array( 4 );
+*
+* var numFactors = decompose( 12, 4, initial, 1, 0, factors, 1, 0 );
+* // returns 2
+*/
+declare function decompose( N: number, M: number, initial: Collection, si: number, oi: number, out: Collection, so: number, oo: number ): number;
+
+
+// EXPORTS //
+
+export = decompose;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/types/test.ts
new file mode 100644
index 000000000000..011b915a8882
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/types/test.ts
@@ -0,0 +1,162 @@
+/*
+* @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 decompose = require( './index' );
+
+// TESTS //
+
+// The function returns a number...
+{
+ const initial = [ 3, 4, 2, 5 ];
+ const out = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+ decompose( 12, 4, initial, 1, 0, out, 1, 0 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a first argument which is not a number...
+{
+ const initial = [ 3, 4, 2, 5 ];
+ const out = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+ decompose( '12', 4, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( true, 4, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( false, 4, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( null, 4, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( void 0, 4, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( [], 4, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( {}, 4, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( ( x: number ): number => x, 4, initial, 1, 0, out, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a second argument which is not a number...
+{
+ const initial = [ 3, 4, 2, 5 ];
+ const out = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+ decompose( 12, '4', initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, true, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, false, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, null, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, void 0, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, [], initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, {}, initial, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, ( x: number ): number => x, initial, 1, 0, out, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a third argument which is not an array of numbers...
+{
+ const out = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+ decompose( 12, 4, '4,2,3,5', 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, 5, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, true, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, false, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, null, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, void 0, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, {}, 1, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, ( x: number ): number => x, 1, 0, out, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a fourth argument which is not a number...
+{
+ const initial = [ 3, 4, 2, 5 ];
+ const out = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+ decompose( 12, 4, initial, '1', 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, true, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, false, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, null, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, void 0, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, [], 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, {}, 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, ( x: number ): number => x, 0, out, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a fifth argument which is not a number...
+{
+ const initial = [ 3, 4, 2, 5 ];
+ const out = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+ decompose( 12, 4, initial, 1, '0', out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, true, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, false, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, null, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, void 0, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, [], out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, {}, out, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, ( x: number ): number => x, out, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a sixth argument which is not an array...
+{
+ const initial = [ 3, 4, 2, 5 ];
+
+ decompose( 12, 4, initial, 1, 0, 123, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, true, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, false, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, null, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, void 0, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, {}, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, ( x: number ): number => x, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a seventh argument which is not a number...
+{
+ const initial = [ 3, 4, 2, 5 ];
+ const out = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+ decompose( 12, 4, initial, 1, 0, out, '1', 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, true, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, false, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, null, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, void 0, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, [], 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, {}, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, ( x: number ): number => x, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an eighth argument which is not a number...
+{
+ const initial = [ 3, 4, 2, 5 ];
+ const out = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+ decompose( 12, 4, initial, 1, 0, out, 1, '0' ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, 1, true ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, 1, false ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, 1, null ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, 1, void 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, 1, [] ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, 1, {} ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, 1, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+ const initial = [ 3, 4, 2, 5 ];
+ const out = [ 0, 0, 0, 0, 0, 0, 0 ];
+
+ decompose(); // $ExpectError
+ decompose( 12 ); // $ExpectError
+ decompose( 12, 4 ); // $ExpectError
+ decompose( 12, 4, initial ); // $ExpectError
+ decompose( 12, 4, initial, 1 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, 1 ); // $ExpectError
+ decompose( 12, 4, initial, 1, 0, out, 1, 0, 123 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/decompose/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/examples/index.js
new file mode 100644
index 000000000000..11005ed1d37f
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/examples/index.js
@@ -0,0 +1,35 @@
+/**
+* @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 decompose = require( './../lib' );
+
+var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
+var factors = [ 0, 0, 0, 0 ];
+
+var nf = decompose( 12, 4, initial, 1, 0, factors, 1, 0 );
+
+console.log( 'Sequence length: %d', 12 );
+console.log( 'Number of factors: %d', nf );
+
+console.log( 'Factors:' );
+var j;
+for ( j = 0; j < nf; j++ ) {
+ console.log( ' %d', factors[ j+2 ] );
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/decompose/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/lib/index.js
new file mode 100644
index 000000000000..5e7183ef5062
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/lib/index.js
@@ -0,0 +1,54 @@
+/**
+* @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';
+
+/**
+* Factorize a sequence length into a product of integers.
+*
+* @module @stdlib/fft/base/fftpack/decompose
+*
+* @example
+* var decompose = require( '@stdlib/fft/base/fftpack/decompose' );
+*
+* var N = 630;
+* var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
+* var factors = [ 0, 0, 0, 0, 0, 0, 0 ];
+*
+* var numFactors = decompose( N, 4, initial, 1, 0, factors, 1, 0 );
+* // returns 5
+*
+* @example
+* var decompose = require( '@stdlib/fft/base/fftpack/decompose' );
+*
+* var N = 12;
+* var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
+* var factors = [ 0, 0, 0, 0 ];
+*
+* var numFactors = decompose( N, 4, initial, 1, 0, factors, 1, 0 );
+* // returns 2
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/decompose/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/lib/main.js
new file mode 100644
index 000000000000..921f8db5ecaa
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/lib/main.js
@@ -0,0 +1,196 @@
+/**
+* @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 floor = require( '@stdlib/math/base/special/floor' );
+
+
+// MAIN //
+
+/**
+* Factorizes a sequence length into a product of integers.
+*
+* ## Notes
+*
+* - Factorization results are stored in the output array as follows:
+*
+* ```text
+* [ sequence_length | number_of_factors | integer_factors | unused_storage ]
+* ```
+*
+* @param {NonNegativeInteger} N - length of the sequence
+* @param {NonNegativeInteger} M - number of trial divisors
+* @param {Collection} initial - strided array of initial trial divisors
+* @param {integer} si - stride length for `initial`
+* @param {NonNegativeInteger} oi - starting index for `initial`
+* @param {Collection} out - output array for storing factorization results
+* @param {integer} so - stride length for `out`
+* @param {NonNegativeInteger} oo - starting index for `out`
+* @returns {NonNegativeInteger} number of factors into which `N` was decomposed
+*
+* @example
+* var N = 630;
+* var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
+* var factors = [ 0, 0, 0, 0, 0, 0, 0 ];
+*
+* var numFactors = decompose( N, 4, initial, 1, 0, factors, 1, 0 );
+* // returns 5
+*
+* var f = factors.slice();
+* // returns [ 630, 5, 2, 3, 3, 5, 7 ]
+*
+* @example
+* var N = 8;
+* var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
+* var factors = [ 0, 0, 0, 0 ];
+*
+* var numFactors = decompose( N, 4, initial, 1, 0, factors, 1, 0 );
+* // returns 2
+*
+* var f = factors.slice();
+* // returns [ 8, 2, 2, 4 ]
+*/
+function decompose( N, M, initial, si, oi, out, so, oo ) {
+ var divisor;
+ var ntrials;
+ var nl;
+ var nf;
+ var nq;
+ var nr;
+ var ib;
+ var i;
+ var j;
+
+ if ( N === 0 ) {
+ out[ oo ] = N;
+ out[ oo+so ] = 0;
+ return 0;
+ }
+
+ // Resolve the number of trial divisors:
+ ntrials = M;
+
+ // Initialize a variable for storing a trial divisor:
+ divisor = 0;
+
+ // Initialize a variable for storing a sub-sequence length:
+ nl = N;
+
+ // Initialize a variable for keeping track of the number of factors into which `N` decomposes:
+ nf = 0;
+
+ j = 0;
+ do {
+ if ( j < ntrials ) {
+ divisor = initial[ oi + (j * si) ];
+ } else {
+ divisor += 2;
+ }
+ j += 1;
+ while ( true ) {
+ // Compute the integer quotient:
+ nq = floor( nl / divisor );
+
+ // Compute the remainder:
+ nr = nl - ( divisor * nq );
+
+ // If the divisor did not evenly divide the current sub-sequence length, try a new divisor...
+ if ( nr !== 0 ) {
+ break;
+ }
+ // We found a new factor:
+ nf += 1;
+
+ // Update the sub-sequence length:
+ nl = nq;
+
+ // Store the factor in the output array:
+ out[ oo+((nf+1)*so) ] = divisor;
+
+ // When the divisor is `2` and we've already found other factors, shift the other factors right to make room for the most recent `2` factor...
+ if ( divisor === 2 && nf !== 1 ) {
+ for ( i = 2; i <= nf; i++ ) {
+ ib = nf - i + 2;
+ out[ oo+((ib+1)*so) ] = out[ oo + (ib*so) ];
+ }
+ out[ oo+(2*so) ] = 2;
+ }
+ // If we cannot further divide the sequence length into smaller sub-sequences, we're done...
+ if ( nl === 1 ) {
+ break;
+ }
+ }
+ } while ( nl !== 1 );
+
+ // Store the sequence length:
+ out[ oo ] = N;
+
+ // Store the number of factors:
+ out[ oo+so ] = nf;
+
+ // Return the number of factors:
+ return nf;
+}
+
+
+// EXPORTS //
+
+module.exports = decompose;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/decompose/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/package.json
new file mode 100644
index 000000000000..b56ddcebca1c
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/package.json
@@ -0,0 +1,64 @@
+{
+ "name": "@stdlib/fft/base/fftpack/decompose",
+ "version": "0.0.0",
+ "description": "Factorize a sequence length into a product of integers.",
+ "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",
+ "decompose",
+ "factorization",
+ "factorize",
+ "factor",
+ "prime",
+ "sequence",
+ "product"
+ ],
+ "__stdlib__": {}
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/decompose/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/test/test.js
new file mode 100644
index 000000000000..d5088dbe227b
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/decompose/test/test.js
@@ -0,0 +1,128 @@
+/**
+* @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 decompose = require( './../lib' );
+
+
+// VARIABLES //
+
+var INITIAL = [ 3, 4, 2, 5 ]; // as found in FFTPACK
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof decompose, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function has an arity of 8', function test( t ) {
+ t.strictEqual( decompose.length, 8, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function correctly factorizes a sequence length into a product of integers', function test( t ) {
+ var factors;
+ var nf;
+
+ factors = [ 0, 0, 0, 0, 0, 0, 0 ];
+ nf = decompose( 630, 4, INITIAL, 1, 0, factors, 1, 0 );
+
+ t.strictEqual( nf, 5, 'returns expected value' );
+ t.strictEqual( factors[ 0 ], 630, 'returns expected value' );
+ t.strictEqual( factors[ 1 ], 5, 'returns expected value' );
+ t.strictEqual( factors[ 2 ], 2, 'returns expected value' );
+ t.strictEqual( factors[ 3 ], 3, 'returns expected value' );
+ t.strictEqual( factors[ 4 ], 3, 'returns expected value' );
+ t.strictEqual( factors[ 5 ], 5, 'returns expected value' );
+ t.strictEqual( factors[ 6 ], 7, 'returns expected value' );
+
+ factors = [ 0, 0, 0, 0 ];
+ nf = decompose( 8, 4, INITIAL, 1, 0, factors, 1, 0 );
+
+ t.strictEqual( nf, 2, 'returns expected value' );
+ t.strictEqual( factors[ 0 ], 8, 'returns expected value' );
+ t.strictEqual( factors[ 1 ], 2, 'returns expected value' );
+ t.strictEqual( factors[ 2 ], 2, 'returns expected value' );
+ t.strictEqual( factors[ 3 ], 4, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function correctly factorizes prime numbers', function test( t ) {
+ var primesList;
+ var factors;
+ var nf;
+ var i;
+
+ // First 10 prime numbers:
+ primesList = [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ];
+
+ for ( i = 0; i < primesList.length; i++ ) {
+ factors = [ 0, 0, 0 ];
+ nf = decompose( primesList[ i ], 4, INITIAL, 1, 0, factors, 1, 0 );
+
+ t.strictEqual( nf, 1, 'returns expected value for ' + primesList[ i ] );
+ t.strictEqual( factors[ 0 ], primesList[ i ], 'returns expected value' );
+ t.strictEqual( factors[ 1 ], 1, 'returns expected value' );
+ t.strictEqual( factors[ 2 ], primesList[ i ], 'returns expected value' );
+ }
+
+ t.end();
+});
+
+tape( 'the function returns expected results when provided a sequence length of 0', function test( t ) {
+ var factors;
+ var nf;
+
+ factors = [ 0, 0 ];
+ nf = decompose( 0, 4, INITIAL, 1, 0, factors, 1, 0 );
+
+ t.strictEqual( nf, 0, 'returns expected value' );
+ t.strictEqual( factors[ 0 ], 0, 'returns expected value' );
+ t.strictEqual( factors[ 1 ], 0, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function correctly handles stride and offset parameters', function test( t ) {
+ var expected;
+ var factors;
+ var so;
+ var oo;
+ var nf;
+
+ factors = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ];
+
+ so = 2;
+ oo = 1;
+ nf = decompose( 12, 4, INITIAL, 1, 0, factors, so, oo );
+
+ expected = [ 0, 12, 0, 2, 0, 3, 0, 4, 0, 0, 0 ];
+
+ t.strictEqual( nf, 2, 'returns expected value' );
+ t.deepEqual( factors, expected, 'returns expected value' );
+
+ t.end();
+});