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feat: add fft/base/fftpack/cosqi
PR-URL: #12881 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com> Signed-off-by: Athan Reines <kgryte@gmail.com> Closes: stdlib-js/metr-issue-tracker#811 Ref: #4121
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‎lib/node_modules/@stdlib/fft/base/fftpack/cosqi/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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# cosqi
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> Initialize a workspace array for performing a quarter-wave cosine transform.
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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 cosqi = require( '@stdlib/fft/base/fftpack/cosqi' );
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```
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#### cosqi( N, workspace, strideW, offsetW )
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Initializes a workspace array for performing a quarter-wave cosine transform.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var N = 8;
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var workspace = new Float64Array( ( 3*N ) + 34 );
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var out = cosqi( N, workspace, 1, 0 );
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// returns <Float64Array>
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var bool = ( out === workspace );
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// returns true
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var cosineTable = workspace.slice( 0, N );
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// returns <Float64Array>[ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ]
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var twiddleFactors = workspace.slice( 2*N, 3*N );
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// returns <Float64Array>[ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ]
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var factors = workspace.slice( 3*N, ( 3*N ) + 4 );
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// returns <Float64Array>[ 8, 2, 2, 4 ]
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```
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The function accepts the following arguments:
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- **N**: length of the sequence to transform.
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- **workspace**: workspace array.
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- **strideW**: stride length for `workspace`.
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- **offsetW**: starting index for `workspace`.
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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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- The workspace array is divided into four sections:
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```text
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size = N N N 2+ceil(log2(N)/2)
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↓ ↓ ↓ ↓
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| cosine table | scratch / workspace | twiddle factors | radix factor table |
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↑ ↑ ↑ ↑
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i = 0 ... N ... 2N ... 3N ...
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```
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- **cosine table**: a table of precomputed cosine coefficients used by quarter-wave cosine transforms.
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- **scratch/workspace**: used as a scratch space when performing transforms. This section is not updated during initialization.
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- **twiddle factors**: a table of reusable complex-exponential constants stored as cosine/sine pairs.
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- **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.
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- In general, a workspace array should have `3N + 34` indexed elements (as `log2(N)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing the cosine coefficients, twiddle factors, and the factorization of `N` are updated.
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- The radix factor table is comprised as follows:
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```text
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| sequence_length | number_of_factors | integer_factors |
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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 Float64Array = require( '@stdlib/array/float64' );
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var zeroTo = require( '@stdlib/array/zero-to' );
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var logEach = require( '@stdlib/console/log-each' );
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var cosqi = require( '@stdlib/fft/base/fftpack/cosqi' );
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var N = 8;
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var workspace = new Float64Array( ( 3*N ) + 34 );
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cosqi( N, workspace, 1, 0 );
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console.log( 'Sequence length: %d', N );
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console.log( 'Cosine table:' );
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var idx = zeroTo( N, 'generic' );
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logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 0, N ) );
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console.log( 'Twiddle factors:' );
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idx = zeroTo( N, 'generic' );
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logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 2*N, 3*N ) );
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console.log( 'Factorization:' );
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var nf = workspace[ (3*N)+1 ];
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console.log( ' number of factors: %d', nf );
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idx = zeroTo( nf, 'generic' );
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logEach( ' factor[ %d ]: %d', idx, workspace.slice( (3*N)+2, (3*N)+2+nf ) );
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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/cosqi/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 Float64Array = require( '@stdlib/array/float64' );
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var pkg = require( './../package.json' ).name;
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var cosqi = require( './../lib' );
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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 workspace = new Float64Array( ( 3*N ) + 34 );
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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 i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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cosqi( N, workspace, 1, 0 );
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if ( isnan( workspace[ ( 2*N ) + 1 ] ) ) {
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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( workspace[ ( 2*N ) + 1 ] ) ) {
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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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8,
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16,
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32,
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64,
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128,
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256,
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512,
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1024
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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/cosqi/docs/repl.txt‎

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{{alias}}( N, workspace, strideW, offsetW )
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Initializes a workspace array for performing a quarter-wave cosine
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transform.
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The workspace array is divided into four sections:
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1. cosine table: the section ranges from indices 0 to N-1 and is used to
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store a table of precomputed cosine coefficients used by quarter-wave
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cosine transforms.
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2. scratch/workspace: the section ranges from indices N to 2N-1 and is used
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while performing transforms. This section is not updated during
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initialization.
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3. twiddle factors: the section ranges from indices 2N to 3N-1 and stores a
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table of reusable complex exponential constants as cosine/sine pairs.
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4. radix factor table: the section starts at index 3N and stores the
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sequence length N, the number of factors into which N was decomposed, and
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the individual integer radix 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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workspace: ArrayLikeObject<number>
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Workspace array.
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strideW: integer
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Stride length for `workspace`.
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offsetW: integer
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Starting index for `workspace`.
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Returns
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-------
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out: ArrayLikeObject<number>
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Workspace array.
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Examples
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--------
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> var N = 8;
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> var workspace = new {{alias:@stdlib/array/float64}}( ( 3*N ) + 34 );
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> var out = {{alias}}( N, workspace, 1, 0 )
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<Float64Array>
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> var bool = ( out === workspace )
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true
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> var cosineTable = workspace.slice( 0, N )
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<Float64Array>[ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ]
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> var twiddleFactors = workspace.slice( 2*N, 3*N )
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<Float64Array>[ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ]
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> var factors = workspace.slice( 3*N, ( 3*N ) + 4 )
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<Float64Array>[ 8, 2, 2, 4 ]
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See Also
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--------
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