feat: add fft/base/fftpack/decompose

lib/node_modules/@stdlib/fft/base/fftpack/decompose/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# decompose
+
+> Factorize a sequence length into a product of integers.
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## 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.
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+## Notes
+
+-   Factorization results are stored in the output array as follows:
+
+    ```text
+    [ sequence_length | number_of_factors | integer_factors | unused_storage ]
+    ```
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```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 ] );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/fft/base/fftpack/decompose/benchmark/benchmark.js

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var 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();

lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/repl.txt

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+
+{{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<number>
+        Array of initial trial divisors.
+
+    si: integer
+        Stride length for `initial`.
+
+    oi: integer
+        Starting index for `initial`.
+
+    out: ArrayLikeObject<number>
+        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
+    --------
+

lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/types/index.d.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+// TypeScript Version: 4.1
+
+/// <reference types="@stdlib/types"/>
+
+import { 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<number>, si: number, oi: number, out: Collection<number>, so: number, oo: number ): number;
+
+
+// EXPORTS //
+
+export = decompose;