From 92011115dff76440c80a295dfdcaca2e1a10e44a Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Sat, 29 Aug 2026 22:33:49 +0530 Subject: [PATCH] feat: add fft/base/fftpack/float32/cosqi --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: passed - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: passed - task: lint_repl_help status: passed - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: passed - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: passed - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: passed - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: passed - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/float32/cosqi/README.md | 175 ++++++++++ .../float32/cosqi/benchmark/benchmark.js | 101 ++++++ .../base/fftpack/float32/cosqi/docs/repl.txt | 61 ++++ .../float32/cosqi/docs/types/index.d.ts | 60 ++++ .../fftpack/float32/cosqi/docs/types/test.ts | 95 ++++++ .../fftpack/float32/cosqi/examples/index.js | 45 +++ .../base/fftpack/float32/cosqi/lib/index.js | 56 ++++ .../base/fftpack/float32/cosqi/lib/main.js | 192 +++++++++++ .../base/fftpack/float32/cosqi/package.json | 66 ++++ .../cosqi/test/fixtures/c/fftpack/Makefile | 137 ++++++++ .../cosqi/test/fixtures/c/fftpack/large.json | 1 + .../cosqi/test/fixtures/c/fftpack/medium.json | 1 + .../cosqi/test/fixtures/c/fftpack/runner.c | 304 +++++++++++++++++ .../cosqi/test/fixtures/c/fftpack/small.json | 1 + .../base/fftpack/float32/cosqi/test/test.js | 314 ++++++++++++++++++ 15 files changed, 1609 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/README.md create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/benchmark/benchmark.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/repl.txt create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/types/index.d.ts create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/types/test.ts create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/examples/index.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/lib/index.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/lib/main.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/package.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/Makefile create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/large.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/medium.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/runner.c create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/small.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/test.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/README.md new file mode 100644 index 000000000000..c7c2b3af91fb --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/README.md @@ -0,0 +1,175 @@ + + +# cosqi + +> Initialize a single-precision floating-point workspace array for performing a quarter-wave cosine transform. + + + +
+ +
+ + + + + +
+ +## Usage + +```javascript +var cosqi = require( '@stdlib/fft/base/fftpack/float32/cosqi' ); +``` + +#### cosqi( N, workspace, strideW, offsetW ) + +Initializes a single-precision floating-point workspace array for performing a quarter-wave cosine transform. + +```javascript +var Float32Array = require( '@stdlib/array/float32' ); + +var N = 8; +var workspace = new Float32Array( ( 3*N ) + 34 ); + +var out = cosqi( N, workspace, 1, 0 ); +// returns + +var bool = ( out === workspace ); +// returns true + +var cosineTable = workspace.slice( 0, N ); +// returns [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ] + +var twiddleFactors = workspace.slice( 2*N, 3*N ); +// returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] + +var factors = workspace.slice( 3*N, ( 3*N ) + 4 ); +// returns [ 8, 2, 2, 4 ] +``` + +The function accepts the following arguments: + +- **N**: length of the sequence to transform. +- **workspace**: workspace [`Float32Array`][@stdlib/array/float32]. +- **strideW**: stride length for `workspace`. +- **offsetW**: starting index for `workspace`. + +
+ + + + + +
+ +## Notes + +- The workspace array is divided into four sections: + + ```text + size = N N N 2+ceil(log2(N)/2) + ↓ ↓ ↓ ↓ + | cosine table | scratch / workspace | twiddle factors | radix factor table | + ↑ ↑ ↑ ↑ + i = 0 ... N ... 2N ... 3N ... + ``` + + - **cosine table**: a table of precomputed cosine coefficients used by quarter-wave cosine transforms. + - **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 `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. + +- The radix factor table is comprised as follows: + + ```text + | sequence_length | number_of_factors | integer_factors | + ``` + +
+ + + +
+ +## Examples + + + +```javascript +var Float32Array = require( '@stdlib/array/float32' ); +var zeroTo = require( '@stdlib/array/zero-to' ); +var logEach = require( '@stdlib/console/log-each' ); +var cosqi = require( '@stdlib/fft/base/fftpack/float32/cosqi' ); + +var N = 8; +var workspace = new Float32Array( ( 3*N ) + 34 ); + +cosqi( N, workspace, 1, 0 ); +console.log( 'Sequence length: %d', N ); + +console.log( 'Cosine table:' ); +var idx = zeroTo( N, 'float32' ); +logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 0, N ) ); + +console.log( 'Twiddle factors:' ); +idx = zeroTo( N, 'float32' ); +logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 2*N, 3*N ) ); + +console.log( 'Factorization:' ); +var nf = workspace[ (3*N)+1 ]; + +console.log( ' number of factors: %d', nf ); +idx = zeroTo( nf, 'float32' ); +logEach( ' factor[ %d ]: %d', idx, workspace.slice( (3*N)+2, (3*N)+2+nf ) ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +
+ + + + + +
+ +[@stdlib/array/float32]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float32 + +
+ + diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/benchmark/benchmark.js new file mode 100644 index 000000000000..68638c7cb6ca --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/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 Float32Array = require( '@stdlib/array/float32' ); +var pkg = require( './../package.json' ).name; +var cosqi = require( './../lib' ); + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} N - sequence length +* @returns {Function} benchmark function +*/ +function createBenchmark( N ) { + var workspace = new Float32Array( ( 3*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++ ) { + cosqi( N, workspace, 1, 0 ); + if ( isnan( workspace[ 2*N ] ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( workspace[ 2*N ] ) ) { + 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/float32/cosqi/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/repl.txt new file mode 100644 index 000000000000..fa0fb3cacf31 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/repl.txt @@ -0,0 +1,61 @@ + +{{alias}}( N, workspace, strideW, offsetW ) + Initializes a single-precision floating-point workspace array for performing + a quarter-wave cosine transform. + + The workspace array is divided into four sections: + + 1. cosine table: the section ranges from indices 0 to N-1 and is used to + store a table of precomputed cosine coefficients used by quarter-wave + cosine transforms. + + 2. scratch/workspace: the section ranges from indices N to 2N-1 and is used + while performing transforms. This section is not updated during + initialization. + + 3. twiddle factors: the section ranges from indices 2N to 3N-1 and stores a + table of reusable complex exponential constants as cosine/sine pairs. + + 4. radix factor table: the section starts at index 3N and 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: Float32Array + Workspace array. + + strideW: integer + Stride length for `workspace`. + + offsetW: integer + Starting index for `workspace`. + + Returns + ------- + out: Float32Array + Workspace array. + + Examples + -------- + > var N = 8; + > var workspace = new {{alias:@stdlib/array/float32}}( ( 3*N ) + 34 ); + > var out = {{alias}}( N, workspace, 1, 0 ) + + > var bool = ( out === workspace ) + true + > var cosineTable = workspace.slice( 0, N ) + [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ] + > var twiddleFactors = workspace.slice( 2*N, 3*N ) + [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] + > var factors = workspace.slice( 3*N, ( 3*N ) + 4 ) + [ 8, 2, 2, 4 ] + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/types/index.d.ts new file mode 100644 index 000000000000..96c8db03acaf --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/types/index.d.ts @@ -0,0 +1,60 @@ +/* +* @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 + +/** +* Initializes a single-precision floating-point workspace array for performing a quarter-wave cosine transform. +* +* ## Notes +* +* - The workspace array should have a length of at least `( 3*N ) + 34` elements. +* +* @param N - length of the sequence +* @param workspace - workspace array +* @param strideW - stride length for `workspace` +* @param offsetW - starting index for `workspace` +* @returns workspace array +* +* @example +* var Float32Array = require( '@stdlib/array/float32' ); +* +* var N = 8; +* var workspace = new Float32Array( ( 3*N ) + 34 ); +* +* var out = cosqi( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true +* +* var cosineTable = workspace.slice( 0, N ); +* // returns [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ] +* +* var twiddleFactors = workspace.slice( 2*N, 3*N ); +* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] +* +* var factors = workspace.slice( 3*N, ( 3*N ) + 4 ); +* // returns [ 8, 2, 2, 4 ] +*/ +declare function cosqi( N: number, workspace: Float32Array, strideW: number, offsetW: number ): Float32Array; + + +// EXPORTS // + +export = cosqi; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/types/test.ts new file mode 100644 index 000000000000..b6a865c9e117 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/docs/types/test.ts @@ -0,0 +1,95 @@ +/* +* @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 cosqi = require( './index' ); + + +// TESTS // + +// The function returns a Float32Array... +{ + const workspace = new Float32Array( ( 3*8 ) + 34 ); + + cosqi( 8, workspace, 1, 0 ); // $ExpectType Float32Array +} + +// The compiler throws an error if the function is provided a first argument which is not a number... +{ + const workspace = new Float32Array( ( 3*8 ) + 34 ); + + cosqi( '8', workspace, 1, 0 ); // $ExpectError + cosqi( true, workspace, 1, 0 ); // $ExpectError + cosqi( false, workspace, 1, 0 ); // $ExpectError + cosqi( null, workspace, 1, 0 ); // $ExpectError + cosqi( void 0, workspace, 1, 0 ); // $ExpectError + cosqi( [], workspace, 1, 0 ); // $ExpectError + cosqi( {}, workspace, 1, 0 ); // $ExpectError + cosqi( ( x: number ): number => x, workspace, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a second argument which is not a Float32Array... +{ + cosqi( 8, '50', 1, 0 ); // $ExpectError + cosqi( 8, 50, 1, 0 ); // $ExpectError + cosqi( 8, true, 1, 0 ); // $ExpectError + cosqi( 8, false, 1, 0 ); // $ExpectError + cosqi( 8, null, 1, 0 ); // $ExpectError + cosqi( 8, void 0, 1, 0 ); // $ExpectError + cosqi( 8, [], 1, 0 ); // $ExpectError + cosqi( 8, {}, 1, 0 ); // $ExpectError + cosqi( 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 Float32Array( ( 3*8 ) + 34 ); + + cosqi( 8, workspace, '1', 0 ); // $ExpectError + cosqi( 8, workspace, true, 0 ); // $ExpectError + cosqi( 8, workspace, false, 0 ); // $ExpectError + cosqi( 8, workspace, null, 0 ); // $ExpectError + cosqi( 8, workspace, void 0, 0 ); // $ExpectError + cosqi( 8, workspace, [], 0 ); // $ExpectError + cosqi( 8, workspace, {}, 0 ); // $ExpectError + cosqi( 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 Float32Array( ( 3*8 ) + 34 ); + + cosqi( 8, workspace, 1, '0' ); // $ExpectError + cosqi( 8, workspace, 1, true ); // $ExpectError + cosqi( 8, workspace, 1, false ); // $ExpectError + cosqi( 8, workspace, 1, null ); // $ExpectError + cosqi( 8, workspace, 1, void 0 ); // $ExpectError + cosqi( 8, workspace, 1, [] ); // $ExpectError + cosqi( 8, workspace, 1, {} ); // $ExpectError + cosqi( 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 Float32Array( ( 3*8 ) + 34 ); + + cosqi(); // $ExpectError + cosqi( 8 ); // $ExpectError + cosqi( 8, workspace ); // $ExpectError + cosqi( 8, workspace, 1 ); // $ExpectError + cosqi( 8, workspace, 1, 0, 123 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/examples/index.js new file mode 100644 index 000000000000..76b99bdada35 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/examples/index.js @@ -0,0 +1,45 @@ +/** +* @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 Float32Array = require( '@stdlib/array/float32' ); +var zeroTo = require( '@stdlib/array/zero-to' ); +var logEach = require( '@stdlib/console/log-each' ); +var cosqi = require( './../lib' ); + +var N = 8; +var workspace = new Float32Array( ( 3*N ) + 34 ); + +cosqi( N, workspace, 1, 0 ); +console.log( 'Sequence length: %d', N ); + +console.log( 'Cosine table:' ); +var idx = zeroTo( N, 'float32' ); +logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 0, N ) ); + +console.log( 'Twiddle factors:' ); +idx = zeroTo( N, 'float32' ); +logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 2*N, 3*N ) ); + +console.log( 'Factorization:' ); +var nf = workspace[ (3*N)+1 ]; + +console.log( ' number of factors: %d', nf ); +idx = zeroTo( nf, 'float32' ); +logEach( ' factor[ %d ]: %d', idx, workspace.slice( (3*N)+2, (3*N)+2+nf ) ); diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/lib/index.js new file mode 100644 index 000000000000..525c61a19005 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/lib/index.js @@ -0,0 +1,56 @@ +/** +* @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 single-precision floating-point workspace array for performing a quarter-wave cosine transform. +* +* @module @stdlib/fft/base/fftpack/float32/cosqi +* +* @example +* var Float32Array = require( '@stdlib/array/float32' ); +* var cosqi = require( '@stdlib/fft/base/fftpack/float32/cosqi' ); +* +* var N = 8; +* var workspace = new Float32Array( ( 3*N ) + 34 ); +* +* var out = cosqi( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true +* +* var cosineTable = workspace.slice( 0, N ); +* // returns [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ] +* +* var twiddleFactors = workspace.slice( 2*N, 3*N ); +* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] +* +* var factors = workspace.slice( 3*N, ( 3*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/float32/cosqi/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/lib/main.js new file mode 100644 index 000000000000..c854199e964a --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/lib/main.js @@ -0,0 +1,192 @@ +/** +* @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 cosf = require( '@stdlib/math/base/special/cosf' ); +var HALF_PI = require( '@stdlib/constants/float32/half-pi' ); +var f32 = require( '@stdlib/number/float64/base/to-float32' ); +var rffti = require( '@stdlib/fft/base/fftpack/float32/rffti' ); + + +// MAIN // + +/** +* Initializes a single-precision floating-point workspace array for performing a quarter-wave cosine transform. +* +* ## Notes +* +* The workspace array is divided into four sections: +* +* ```text +* size = N N N 2+ceil(log2(N)/2) +* ↓ ↓ ↓ ↓ +* | cosine table | scratch/workspace | twiddle factors | radix factor table | +* ↑ ↑ ↑ ↑ +* i = 0 ... N ... 2N ... 3N ... +* ``` +* +* where +* +* - **cosine table**: a table of precomputed cosine coefficients used by quarter-wave cosine transforms. +* - **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 `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. +* +* > Note: FFTPACK only requires `3N+15`, but we increase that number here to accommodate larger workspace arrays, where `N` may exceed `2^30` indexed elements. +* +* 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 forward and backward FFT callers can reuse the same set of twiddle factors, with those performing a forward transform (e.g., `cosqf`) multiplying with `(cos,-sin)` and those performing a backward transform (e.g., `cosqb`) 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. +* +* During initialization, `cosqi` first writes the cosine table, and then initializes the remaining three sections using `rffti`. +* +* @param {PositiveInteger} N - length of the sequence to transform +* @param {Float32Array} workspace - workspace array +* @param {integer} strideW - stride length for `workspace` +* @param {NonNegativeInteger} offsetW - starting index for `workspace` +* @returns {Float32Array} workspace array +* +* @example +* var Float32Array = require( '@stdlib/array/float32' ); +* +* var N = 8; +* var workspace = new Float32Array( ( 3*N ) + 34 ); +* +* var out = cosqi( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true +* +* var cosineTable = workspace.slice( 0, N ); +* // returns [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ] +* +* var twiddleFactors = workspace.slice( 2*N, 3*N ); +* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] +* +* var factors = workspace.slice( 3*N, ( 3*N ) + 4 ); +* // returns [ 8, 2, 2, 4 ] +*/ +function cosqi( N, workspace, strideW, offsetW ) { + var offsetR; + var dt; + var iw; + var fk; + var i; + + // Compute the angular increment: + dt = f32( HALF_PI/N ); + + // Compute and store the cosine table: + fk = 0.0; + iw = offsetW; + for ( i = 0; i < N; i++ ) { + fk = f32( fk+1.0 ); + workspace[ iw ] = cosf( f32( fk*dt ) ); + iw += strideW; + } + // Resolve the starting index for the `rffti` workspace: + offsetR = offsetW + ( N*strideW ); + + // Initialize the real FFT workspace: + rffti( N, workspace, strideW, offsetR ); + + return workspace; +} + + +// EXPORTS // + +module.exports = cosqi; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/package.json new file mode 100644 index 000000000000..51feef72bbec --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/package.json @@ -0,0 +1,66 @@ +{ + "name": "@stdlib/fft/base/fftpack/float32/cosqi", + "version": "0.0.0", + "description": "Initialize a single-precision floating-point workspace array for performing a quarter-wave cosine 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", + "cosqi", + "fourier", + "transform", + "twiddle", + "workspace", + "initialization", + "cosine", + "single", + "float32" + ], + "__stdlib__": {} +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/Makefile b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/Makefile new file mode 100644 index 000000000000..77b6a5f13549 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/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) $(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/float32/cosqi/test/fixtures/c/fftpack/large.json b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/large.json new file mode 100644 index 000000000000..97444854b123 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/medium.json b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/medium.json new file mode 100644 index 000000000000..800241e153d1 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/medium.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/runner.c b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/runner.c new file mode 100644 index 000000000000..925618e4452b --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/runner.c @@ -0,0 +1,304 @@ +/** +* @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 +#include + +/** +* Define prototypes for external functions. +*/ +extern void cosqi( int n, float *wsave ); + +/** +* Generates a random number on the interval [0,1]. +* +* @return random number +*/ +float rand_float( void ) { + int r = rand(); + return (float)r / ( (float)RAND_MAX + 1.0f ); +} + +/** +* 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; + float delta; + + delta = (float)b - (float)a; + + for ( i = 0; i < len; i++ ) { + r = (unsigned int)( delta * rand_float() ); // truncation + out[ i ] = (int)( a + r ); + } +} + +/** +* Writes an array of floats to a file as a series of comma-separated values. +* +* @param f file to write to +* @param x array of floats +* @param len array length +*/ +void write_array_f32( FILE *f, const float *x, const unsigned int len ) { + unsigned int i; + + for ( i = 0; i < len; i++ ) { + fprintf( f, "%.9g", 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 floats 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_f32( FILE *f, const char *name, const float *x, const unsigned int len ) { + fprintf( f, "\"%s\":[", name ); + write_array_f32( 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 cosine and twiddle offsets +* @param cosines cosine values +* @param twiddles twiddle factors +* @param num number of sequence lengths +* @param total total number of cosine and twiddle values +*/ +void write_data_as_json( FILE *f, const int *lengths, const int *offsets, const float *cosines, const float *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_f32( f, "cosines", cosines, total ); + fprintf( f, "," ); + write_named_array_f32( f, "twiddles", twiddles, total ); + fprintf( f, "}\n" ); +} + +/** +* Generates test fixtures. +* +* @param lengths sequence lengths +* @param offsets cosine and twiddle offsets into flat output array +* @param num number of sequence lengths +* @param total total number of cosine and 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; + float *cosines; + float *twiddles; + float *wsave; + FILE *f; + int off; + int n; + + // Allocate an output array for cosine values: + cosines = (float*) malloc( total * sizeof(float) ); + if ( cosines == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + + // Allocate an output array for twiddle factors: + twiddles = (float*) malloc( total * sizeof(float) ); + if ( twiddles == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + + // Generate fixture data: + for ( i = 0; i < num; i++ ) { + n = lengths[ i ]; + wsave = (float*) calloc( 3*n + 15, sizeof(float) ); + if ( wsave == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + cosqi( n, wsave ); + + // Copy cosine region into flat array (N values starting at wsave[0]): + off = offsets[ i ]; + for ( j = 0; j < (unsigned int)n; j++ ) { + cosines[ off + j ] = wsave[ j ]; + } + + // Copy twiddle region into flat array (N values starting at wsave[2*n]): + off = offsets[ i ]; + for ( j = 0; j < (unsigned int)n; j++ ) { + twiddles[ off + j ] = wsave[ ( 2*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, cosines, twiddles, num, total ); + + // Close the file: + fclose( f ); + + // Free allocated memory: + free( cosines ); + free( twiddles ); +} + +/** +* Computes offsets into flat cosine and twiddle arrays for each sequence length. +* +* @param offsets output array of offsets +* @param lengths sequence lengths +* @param num number of sequence lengths +* @return total number of cosine and 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 ]; + } + return total; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + unsigned int total; + unsigned int num; + int *lengths; + int *offsets; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + // 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/float32/cosqi/test/fixtures/c/fftpack/small.json b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/small.json new file mode 100644 index 000000000000..1fc288ad1dff --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/fixtures/c/fftpack/small.json @@ -0,0 +1 @@ +{"lengths":[12,5,4,6,4,5,4,14,5,10],"offsets":[0,12,17,21,27,31,36,40,54,59],"cosines":[0.991444886,0.965925813,0.923879504,0.866025388,0.793353319,0.707106769,0.60876137,0.49999997,0.382683426,0.258819073,0.130526125,-4.37113883e-08,0.95105654,0.809017003,0.587785244,0.309016973,-4.37113883e-08,0.923879504,0.707106769,0.382683426,-4.37113883e-08,0.965925813,0.866025388,0.707106769,0.49999997,0.258819073,-4.37113883e-08,0.923879504,0.707106769,0.382683426,-4.37113883e-08,0.95105654,0.809017003,0.587785244,0.309016973,-4.37113883e-08,0.923879504,0.707106769,0.382683426,-4.37113883e-08,0.993712187,0.974927902,0.9438833,0.90096885,0.846724212,0.781831443,0.707106769,0.623489797,0.532032013,0.433883756,0.330279052,0.222520858,0.111964479,-4.37113883e-08,0.95105654,0.809017003,0.587785244,0.309016973,-4.37113883e-08,0.987688363,0.95105654,0.891006529,0.809017003,0.707106769,0.587785244,0.453990519,0.309016973,0.156434372,-4.37113883e-08],"twiddles":[0.866025388,0.5,0,0.49999997,0.866025448,0,-4.37113883e-08,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0.49999997,0.866025448,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.90096885,0.433883756,0.623489797,0.781831503,0.222520858,0.974927902,0,0,0,0,0,0,0,0,0,0,0,0,0,0.809017003,0.587785244,0.309016973,0.95105654,0,0,0,0,0,0]} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/test.js new file mode 100644 index 000000000000..3a69f920ea14 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/cosqi/test/test.js @@ -0,0 +1,314 @@ +/** +* @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 Float32Array = require( '@stdlib/array/float32' ); +var isAlmostSameValue = require( '@stdlib/number/float32/base/assert/is-almost-same-value' ); +var cosqi = 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 cosqi, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 4', function test( t ) { + t.strictEqual( cosqi.length, 4, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns a reference to the workspace array', function test( t ) { + var workspace; + var out; + var N; + + N = 8; + workspace = new Float32Array( ( 3*N ) + 34 ); + out = cosqi( N, workspace, 1, 0 ); + + t.strictEqual( out, workspace, 'same reference' ); + t.end(); +}); + +tape( 'the function correctly initializes cosine values (small sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var off; + var y; + var e; + var N; + var i; + var k; + + lengths = small.lengths; + offsets = small.offsets; + expected = small.cosines; + + ulps = 1; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + workspace = new Float32Array( ( 3*N ) + 34 ); + cosqi( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ N ], 0.0, 'returns expected value' ); + for ( i = 0; i < N; i++ ) { + y = workspace[ i ]; + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); + } + } + t.end(); +}); + +tape( 'the function correctly initializes twiddle factors (small sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var off; + var y; + var e; + var N; + var i; + var k; + + lengths = small.lengths; + offsets = small.offsets; + expected = small.twiddles; + + ulps = 1; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + workspace = new Float32Array( ( 3*N ) + 34 ); + cosqi( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ (2*N) - 1 ], 0.0, 'returns expected value' ); + for ( i = 0; i < N; i++ ) { + y = workspace[ (2*N) + i ]; + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); + } + } + t.end(); +}); + +tape( 'the function correctly initializes cosine values (medium sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var off; + var y; + var e; + var N; + var i; + var k; + + lengths = medium.lengths; + offsets = medium.offsets; + expected = medium.cosines; + + ulps = 1; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + workspace = new Float32Array( ( 3*N ) + 34 ); + cosqi( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ N ], 0.0, 'returns expected value' ); + for ( i = 0; i < N; i++ ) { + y = workspace[ i ]; + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); + } + } + t.end(); +}); + +tape( 'the function correctly initializes twiddle factors (medium sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var off; + var y; + var e; + var N; + var i; + var k; + + lengths = medium.lengths; + offsets = medium.offsets; + expected = medium.twiddles; + + ulps = 1; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + workspace = new Float32Array( ( 3*N ) + 34 ); + cosqi( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ (2*N) - 1 ], 0.0, 'returns expected value' ); + for ( i = 0; i < N; i++ ) { + y = workspace[ (2*N) + i ]; + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); + } + } + t.end(); +}); + +tape( 'the function correctly initializes cosine values (large sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var off; + var y; + var e; + var N; + var i; + var k; + + lengths = large.lengths; + offsets = large.offsets; + expected = large.cosines; + + ulps = 1; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + workspace = new Float32Array( ( 3*N ) + 34 ); + cosqi( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ N ], 0.0, 'returns expected value' ); + for ( i = 0; i < N; i++ ) { + y = workspace[ i ]; + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); + } + } + t.end(); +}); + +tape( 'the function correctly initializes twiddle factors (large sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var off; + var y; + var e; + var N; + var i; + var k; + + lengths = large.lengths; + offsets = large.offsets; + expected = large.twiddles; + + ulps = 1; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + workspace = new Float32Array( ( 3*N ) + 34 ); + cosqi( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ (2*N) - 1 ], 0.0, 'returns expected value' ); + for ( i = 0; i < N; i++ ) { + y = workspace[ (2*N) + i ]; + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); + } + } + 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 Float32Array( ( 3*N ) + 34 ); + + for ( i = 0; i < workspace.length; i++ ) { + workspace[ i ] = i + 1.0; + } + cosqi( N, workspace, 1, 0 ); + for ( i = N; i < 2*N; i++ ) { + t.strictEqual( workspace[ i ], i + 1.0, '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 Float32Array( offset + ( ( ( 3*N ) + 34 ) * stride ) ); + + cosqi( N, workspace, stride, offset ); + + t.strictEqual( workspace[ offset + ( 3*N * stride ) ], N, 'returns expected value' ); + + nf = workspace[ offset + ( ( ( 3*N ) + 1 ) * stride ) ]; + t.strictEqual( nf, 2, 'returns expected value' ); + t.strictEqual( workspace[ offset + ( ( ( 3*N ) + 2 ) * stride ) ], 2, 'returns expected value' ); + t.strictEqual( workspace[ offset + ( ( ( 3*N ) + 3 ) * stride ) ], 4, 'returns expected value' ); + + expected = new Float32Array( ( 3*N ) + 34 ); + cosqi( N, expected, 1, 0 ); + + for ( i = 0; i < N; i++ ) { + t.strictEqual( workspace[ offset + ( ( (2*N)+i ) * stride ) ], expected[ (2*N)+i ], 'returns expected value' ); + } + t.end(); +});