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feat: add fft/base/fftpack/decompose
PR-URL: #10354 Ref: #4121 Reviewed-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Philipp Burckhardt <pburckhardt@outlook.com> Co-authored-by: Athan Reines <kgryte@gmail.com>
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‎lib/node_modules/@stdlib/fft/base/fftpack/decompose/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# decompose
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> Factorize a sequence length into a product of integers.
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var decompose = require( '@stdlib/fft/base/fftpack/decompose' );
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```
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#### decompose( N, M, initial, si, oi, out, so, oo )
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Factorizes a sequence length into a product of integers.
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```javascript
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var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
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var N = 630;
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var factors = [ 0, 0, 0, 0, 0, 0, 0 ];
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var numFactors = decompose( N, 4, initial, 1, 0, factors, 1, 0 );
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// returns 5
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console.log( factors );
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// => [ 630, 5, 2, 3, 3, 5, 7 ]
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```
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The function accepts the following arguments:
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- **N**: length of the sequence.
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- **M**: number of trial divisors.
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- **initial**: array of initial trial divisors.
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- **si**: stride length for `initial`.
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- **oi**: starting index for `initial`.
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- **out**: output array for storing factorization results.
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- **so**: stride length for `out`.
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- **oo**: starting index for `out`.
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The function returns the number of factors into which `N` was decomposed.
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</section>
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<!-- /.usage -->
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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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## Notes
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- Factorization results are stored in the output array as follows:
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```text
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[ sequence_length | number_of_factors | integer_factors | unused_storage ]
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```
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var decompose = require( '@stdlib/fft/base/fftpack/decompose' );
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var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
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var factors = [ 0, 0, 0, 0 ];
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var nf = decompose( 12, 4, initial, 1, 0, factors, 1, 0 );
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console.log( 'Sequence length: %d', 12 );
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console.log( 'Number of factors: %d', nf );
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console.log( 'Factors:' );
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var j;
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for ( j = 0; j < nf; j++ ) {
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console.log( ' %d', factors[ j+2 ] );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- 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. -->
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<section class="references">
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</section>
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<!-- /.references -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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</section>
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<!-- /.links -->

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

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2026 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var format = require( '@stdlib/string/format' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var log2 = require( '@stdlib/math/base/special/log2' );
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var zeros = require( '@stdlib/array/zeros' );
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var pkg = require( './../package.json' ).name;
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var decompose = require( './../lib' );
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// VARIABLES //
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var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} N - sequence length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( N ) {
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var factors = zeros( 2 + floor( log2( N ) ) );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var d;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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d = decompose( N, 4, initial, 1, 0, factors, 1, 0 );
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if ( isnan( d ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( d ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var lengths;
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var N;
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var f;
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var i;
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lengths = [
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12,
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24,
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36,
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48,
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60,
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120
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];
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for ( i = 0; i < lengths.length; i++ ) {
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N = lengths[ i ];
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f = createBenchmark( N );
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bench( format( '%s:N=%d', pkg, N ), f );
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}
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}
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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 )
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Factorizes a sequence length into a product of integers.
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Factorization results are stored in the output array sequentially, where
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the first element contains the sequence length N, the second element
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contains the number of factors into which N was decomposed, and subsequent
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elements contain the individual integer factors.
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Any remaining array space remains as unused storage.
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Parameters
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----------
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N: integer
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Length of the sequence.
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M: integer
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Number of trial divisors.
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initial: ArrayLikeObject<number>
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Array of initial trial divisors.
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si: integer
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Stride length for `initial`.
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oi: integer
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Starting index for `initial`.
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out: ArrayLikeObject<number>
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Output array for storing factorization results.
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so: integer
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Stride length for `out`.
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oo: integer
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Starting index for `out`.
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Returns
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-------
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numFactors: integer
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Number of factors into which N was decomposed.
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Examples
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--------
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> var N = 630;
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> var initial = [ 3, 4, 2, 5 ];
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> var factors = [ 0, 0, 0, 0, 0, 0, 0 ];
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> var numFactors = {{alias}}( N, 4, initial, 1, 0, factors, 1, 0 )
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5
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> factors
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[ 630, 5, 2, 3, 3, 5, 7 ]
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See Also
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--------
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‎lib/node_modules/@stdlib/fft/base/fftpack/decompose/docs/types/index.d.ts‎

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2026 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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// TypeScript Version: 4.1
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/// <reference types="@stdlib/types"/>
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import { Collection } from '@stdlib/types/array';
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/**
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* Factorizes a sequence length into a product of integers.
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*
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* @param N - length of the sequence
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* @param M - number of trial divisors
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* @param initial - array of initial trial divisors
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* @param si - stride length for `initial`
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* @param oi - starting index for `initial`
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* @param out - output array for storing factorization results
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* @param so - stride length for `out`
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* @param oo - starting index for `out`
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* @returns number of factors into which `N` was decomposed
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*
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* @example
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* var initial = new Float64Array( [ 3, 4, 2, 5 ] );
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* var factors = new Float64Array( 4 );
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*
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* var numFactors = decompose( 12, 4, initial, 1, 0, factors, 1, 0 );
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* // returns 2
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*/
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declare function decompose( N: number, M: number, initial: Collection<number>, si: number, oi: number, out: Collection<number>, so: number, oo: number ): number;
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// EXPORTS //
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export = decompose;

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