From 31957575ad5372c54e4ec65f0f242d37302a195b Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Wed, 15 Apr 2026 23:17:48 +0530 Subject: [PATCH 01/14] feat: add fft/base/fftpack/rffti --- .../@stdlib/fft/base/fftpack/rffti/README.md | 168 +++++++++++ .../base/fftpack/rffti/benchmark/benchmark.js | 101 +++++++ .../fft/base/fftpack/rffti/docs/repl.txt | 45 +++ .../base/fftpack/rffti/docs/types/index.d.ts | 51 ++++ .../fft/base/fftpack/rffti/examples/index.js | 46 +++ .../fft/base/fftpack/rffti/lib/index.js | 49 +++ .../fft/base/fftpack/rffti/lib/main.js | 170 +++++++++++ .../fft/base/fftpack/rffti/lib/rffti1.js | 185 ++++++++++++ .../fft/base/fftpack/rffti/package.json | 64 ++++ .../rffti/test/fixtures/c/fftpack/Makefile | 137 +++++++++ .../rffti/test/fixtures/c/fftpack/large.json | 1 + .../rffti/test/fixtures/c/fftpack/medium.json | 1 + .../rffti/test/fixtures/c/fftpack/runner.c | 282 ++++++++++++++++++ .../rffti/test/fixtures/c/fftpack/small.json | 1 + .../fft/base/fftpack/rffti/test/test.js | 231 ++++++++++++++ 15 files changed, 1532 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/benchmark/benchmark.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/package.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/Makefile create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md new file mode 100644 index 000000000000..4aa185aefa1f --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md @@ -0,0 +1,168 @@ + + +# rffti + +> Initialize a workspace array for performing a real-valued Fourier transform. + + + +
+ +
+ + + + + +
+ +## Usage + +```javascript +var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); +``` + +#### rffti( N, workspace, strideW, offsetW ) + +Initializes a workspace array for performing a real-valued Fourier transform. + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); + +var N = 8; +var workspace = new Float64Array( ( 2*N ) + 34 ); + +rffti( N, workspace, 1, 0 ); + +var twiddleFactors = workspace.slice( N, 2*N ); +// returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] + +var factors = workspace.slice( 2*N, ( 2*N ) + 4 ); +// returns [ 8, 2, 2, 4 ] +``` + +The function accepts the following arguments: + +- **N**: length of the sequence to transform. +- **workspace**: workspace array. +- **strideW**: stride length for `workspace`. +- **offsetW**: starting index for `workspace`. + +
+ + + + + +
+ +## Notes + +- The workspace array is divided into three sections: + + ```text + size = N N 2+ceil(log2(N)/2) + ↓ ↓ ↓ + | scratch / workspace | twiddle factors | radix factor table | + ↑ ↑ ↑ + i = 0 ... N ... 2N ... + ``` + + - **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 `2N + 34` indexed elements (as `log2(N)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing 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 | + ``` + +- If `N` equals `1`, the function returns early without modifying the workspace, as a single data point is its own Fourier transform. + +
+ + + +
+ +## Examples + + + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); + +var workspace; +var N; +var nf; +var i; +var j; + +N = 8; +workspace = new Float64Array( ( 2*N ) + 34 ); + +rffti( N, workspace, 1, 0 ); + +console.log( 'Sequence length: %d', N ); +console.log( 'Twiddle factors:' ); +for ( i = N; i < 2*N; i++ ) { + console.log( ' workspace[%d] = %d', i, workspace[ i ] ); +} + +console.log( 'Factorization:' ); +nf = workspace[ ( 2*N ) + 1 ]; +console.log( ' number of factors: %d', nf ); +for ( j = 0; j < nf; j++ ) { + console.log( ' factor[%d]: %d', j, workspace[ ( 2*N ) + 2 + j ] ); +} +``` + +
+ + + + + +
+ +
+ + + + + +
+ +
+ + + + + +
+ +
+ + diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/benchmark/benchmark.js new file mode 100644 index 000000000000..07feddfa216b --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/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 Float64Array = require( '@stdlib/array/float64' ); +var pkg = require( './../package.json' ).name; +var rffti = require( './../lib' ); + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} N - sequence length +* @returns {Function} benchmark function +*/ +function createBenchmark( N ) { + var workspace = new Float64Array( ( 2*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++ ) { + rffti( N, workspace, 1, 0 ); + if ( isnan( workspace[ N+1 ] ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( workspace[ N+1 ] ) ) { + 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/rffti/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt new file mode 100644 index 000000000000..aa886670dc67 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt @@ -0,0 +1,45 @@ + +{{alias}}( N, workspace, strideW, offsetW ) + Initializes a workspace array for performing a real-valued Fourier + transform. + + The workspace array is divided into three sections: scratch/workspace + (indices 0 to N-1), twiddle factors (indices N to 2N-1), and radix factor + table (indices 2N onwards). + + The scratch/workspace section is used while performing transforms and is + not updated during initialization. The twiddle factors section stores a + table of reusable complex exponential constants as cosine/sine pairs. The + radix factor table 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: ArrayLikeObject + Workspace array. + + strideW: integer + Stride length for `workspace`. + + offsetW: integer + Starting index for `workspace`. + + Examples + -------- + > var {{alias:@stdlib/array/float64}} = require( '@stdlib/array/float64' ); + > var N = 8; + > var workspace = new {{alias:@stdlib/array/float64}}( ( 2*N ) + 34 ); + > {{alias}}( N, workspace, 1, 0 ); + > var twiddleFactors = workspace.slice( N, 2*N ) + [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] + > var factors = workspace.slice( 2*N, ( 2*N ) + 4 ) + [ 8, 2, 2, 4 ] + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts new file mode 100644 index 000000000000..2c55a4abb09d --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts @@ -0,0 +1,51 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +// TypeScript Version: 4.1 + +/// + +import { Collection } from '@stdlib/types/array'; + +/** +* Initializes a workspace array for performing a real-valued Fourier transform. +* +* @param N - length of the sequence +* @param workspace - workspace array +* @param strideW - stride length for `workspace` +* @param offsetW - starting index for `workspace` +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var N = 8; +* var workspace = new Float64Array( ( 2*N ) + 34 ); +* +* rffti( N, workspace, 1, 0 ); +* +* var twiddleFactors = workspace.slice( N, 2*N ); +* // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] +* +* var factors = workspace.slice( 2*N, ( 2*N ) + 4 ); +* // returns [ 8, 2, 2, 4 ] +*/ +declare function rffti( N: number, workspace: Collection, strideW: number, offsetW: number ): void; + + +// EXPORTS // + +export = rffti; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js new file mode 100644 index 000000000000..e9004065b2ee --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js @@ -0,0 +1,46 @@ +/** +* @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 Float64Array = require( '@stdlib/array/float64' ); +var rffti = require( './../lib' ); + +var workspace; +var N; +var nf; +var i; +var j; + +N = 8; +workspace = new Float64Array( ( 2*N ) + 34 ); + +rffti( N, workspace, 1, 0 ); + +console.log( 'Sequence length: %d', N ); +console.log( 'Twiddle factors:' ); +for ( i = N; i < 2*N; i++ ) { + console.log( ' workspace[%d] = %d', i, workspace[ i ] ); +} + +console.log( 'Factorization:' ); +nf = workspace[ ( 2*N ) + 1 ]; +console.log( ' number of factors: %d', nf ); +for ( j = 0; j < nf; j++ ) { + console.log( ' factor[%d]: %d', j, workspace[ ( 2*N ) + 2 + j ] ); +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js new file mode 100644 index 000000000000..3c440549ebce --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js @@ -0,0 +1,49 @@ +/** +* @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 workspace array for performing a real-valued Fourier transform. +* +* @module @stdlib/fft/base/fftpack/rffti +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); +* +* var N = 8; +* var workspace = new Float64Array( ( 2*N ) + 34 ); +* +* rffti( N, workspace, 1, 0 ); +* +* var twiddleFactors = workspace.slice( N, 2*N ); +* // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] +* +* var factors = workspace.slice( 2*N, ( 2*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/rffti/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js new file mode 100644 index 000000000000..663a19bd35cd --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js @@ -0,0 +1,170 @@ +/** +* @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 rffti1 = require( './rffti1.js' ); + + +// MAIN // + +/** +* Initializes a workspace array for performing a real-valued Fourier transform. +* +* ## Notes +* +* The workspace array is divided into three sections: +* +* ```text +* size = N N 2+ceil(log2(N)/2) +* ↓ ↓ ↓ +* | scratch / workspace | twiddle factors | radix factor table | +* ↑ ↑ ↑ +* i = 0 ... N ... 2N ... +* ``` +* +* where +* +* - **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 `2N + 34` indexed elements (as `log2(N)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing twiddle factors and the factorization of `N` are updated. +* +* > Note: FFTPACK only requires `2N+15`, but we increase that number here to accommodate larger workspace arrays, where `N` may exceed `2^30` indexed elements. +* +* The first two sections each contain `N` elements, while the last section contains the sequence length, the number of integer factors, and, at most, `ceil(log2(N)/2)` integer radix factors. +* +* 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 real and backward FFT callers can reuse the same set of twiddle factors, with those performing a forward transform (e.g., `rfftf`) multiplying with `(cos,-sin)` and those performing a backward transform (e.g., `rfftb`) 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. +* +* @param {NonNegativeInteger} N - length of the sequence to transform +* @param {Float64Array} workspace - workspace array +* @param {integer} strideW - stride length for `workspace` +* @param {NonNegativeInteger} offsetW - starting index for `workspace` +* @returns {void} +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var N = 8; +* var workspace = new Float64Array( ( 2*N ) + 34 ); +* +* rffti( N, workspace, 1, 0 ); +* +* var twiddleFactors = workspace.slice( N, 2*N ); +* // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] +* +* var factors = workspace.slice( 2*N, ( 2*N ) + 4 ); +* // returns [ 8, 2, 2, 4 ] +*/ +function rffti( N, workspace, strideW, offsetW ) { + var offsetT; + var offsetF; + + // When a sub-sequence is a single data point, the FFT is the identity, so no initialization necessary... + if ( N === 1 ) { + return; + } + // Resolve the starting indices for storing twiddle factors and factorization results: + offsetT = offsetW + ( N*strideW ); // index offset for twiddle factors + offsetF = offsetT + ( N*strideW ); // index offset for factorization results + + // Initialize a provided workspace array: + rffti1( N, workspace, strideW, offsetT, workspace, strideW, offsetF ); +} + + +// EXPORTS // + +module.exports = rffti; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js new file mode 100644 index 000000000000..18a9062cce13 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js @@ -0,0 +1,185 @@ +/** +* @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 TWO_PI = require( '@stdlib/constants/float64/two-pi' ); +var floor = require( '@stdlib/math/base/special/floor' ); +var sin = require( '@stdlib/math/base/special/sin' ); +var cos = require( '@stdlib/math/base/special/cos' ); +var decompose = require( '@stdlib/fft/base/fftpack/decompose' ); + + +// VARIABLES // + +var TRIAL_FACTORS = [ 4, 2, 3, 5 ]; + + +// MAIN // + +/** +* Initializes the working arrays for applying a Fourier transform to a real-valued sequence. +* +* @private +* @param {NonNegativeInteger} n - length of the sequence +* @param {Collection} wa - array of twiddle factors +* @param {integer} strideW - stride length for `wa` +* @param {NonNegativeInteger} offsetW - starting index for `wa` +* @param {Collection} ifac - array containing a radix factorization +* @param {integer} strideF - stride length for `ifac` +* @param {NonNegativeInteger} offsetF - starting index for `ifac` +* @returns {void} +*/ +function rffti1( n, wa, strideW, offsetW, ifac, strideF, offsetF ) { + var argld; + var argh; + var nfm1; + var arg; + var ipm; + var ido; + var nf; + var fi; + var ip; + var l2; + var l1; + var ld; + var ii; + var is; + var k1; + var i; + var j; + + // Decompose the sequence length into its radix factors: + nf = decompose( n, 4, TRIAL_FACTORS, 1, 0, ifac, strideF, offsetF ); + + // Compute the master angular step (i.e., the basic angle that generates all twiddles): + argh = TWO_PI / n; + + // Initialize the index into the twiddle factor array: + is = 0; + + // Compute the number of factors minus one: + nfm1 = nf - 1; + + // Initialize a running product of factors already processed: + l1 = 1; + + // If the number of radix factors is `1`, the only twiddle factor we need is `W_N^0 = 1`, which the main transform kernels already hard-code, so nothing to pre-compute... + if ( nfm1 === 0 ) { + return; + } + // Generate twiddle factors for each radix factor... + for ( k1 = 0; k1 < nfm1; k1++ ) { + // Resolve the next radix factor (C code: ifac[k1+2] with 1-based, JS: ifac[k1+2] with 0-based): + ip = ifac[ offsetF + ((k1+2)*strideF) ]; + + // Initialize a running offset used to step the angle: + ld = 0; + + // Compute the length of the transform after including the current radix: + l2 = l1 * ip; + + // Compute the number of data points in each sub-transform: + ido = floor( n / l2 ); + + // Compute the number of iterations for the inner loop: + ipm = ip - 1; + + // Iterate over each butterfly column within the current radix... + for ( j = 0; j < ipm; j++ ) { + // Advance to the next column: + ld += l1; + + // Initialize the index into the twiddle factor array: + i = is; + + // Compute the angle step for this column: + argld = ld * argh; + + // Initialize the harmonic counter: + fi = 0.0; + + // Iterate over each non-trivial harmonic in the column... + for ( ii = 2; ii < ido; ii += 2 ) { + // Advance the index by 2 (for cosine and sine): + i += 2; + + // Update the harmonic counter: + fi += 1.0; + + // Compute the angle for this harmonic: + arg = fi * argld; + + // Store the cosine and sine values: + wa[ offsetW + ( ( i-1 ) * strideW ) ] = cos( arg ); + wa[ offsetW + ( i*strideW ) ] = sin( arg ); + } + // Advance the index by the number of data points in each sub-transform: + is += ido; + } + // Update the running product of factors already processed: + l1 = l2; + } +} + + +// EXPORTS // + +module.exports = rffti1; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/package.json new file mode 100644 index 000000000000..ea78bb766695 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/package.json @@ -0,0 +1,64 @@ +{ + "name": "@stdlib/fft/base/fftpack/rffti", + "version": "0.0.0", + "description": "Initialize a workspace array for performing a real-valued Fourier 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", + "rffti", + "fourier", + "transform", + "twiddle", + "workspace", + "initialization", + "real" + ], + "__stdlib__": {} +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/Makefile b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/Makefile new file mode 100644 index 000000000000..7ce16281940d --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/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) -DFFTPACK_DOUBLE_PRECISION $(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/rffti/test/fixtures/c/fftpack/large.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json new file mode 100644 index 000000000000..37ea1b0c0505 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json new file mode 100644 index 000000000000..215106655dfe --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c new file mode 100644 index 000000000000..82f5947a89b0 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c @@ -0,0 +1,282 @@ +/** +* @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 + +/** +* Define prototypes for external functions. +*/ +extern void rffti( int n, double *wsave ); + +/** +* Generates a random number on the interval [0,1]. +* +* @return random number +*/ +double rand_double( void ) { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* 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; + double delta; + + delta = (double)b - (double)a; + + for ( i = 0; i < len; i++ ) { + r = (unsigned int)( delta * rand_double() ); // truncation + out[ i ] = (int)( a + r ); + } +} + +/** +* Writes an array of doubles to a file as a series of comma-separated values. +* +* @param f file to write to +* @param x array of doubles +* @param len array length +*/ +void write_array_f64( FILE *f, const double *x, const unsigned int len ) { + unsigned int i; + + for ( i = 0; i < len; i++ ) { + fprintf( f, "%.17g", 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 doubles 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_f64( FILE *f, const char *name, const double *x, const unsigned int len ) { + fprintf( f, "\"%s\":[", name ); + write_array_f64( 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 twiddle offsets +* @param twiddles twiddle factors +* @param num number of sequence lengths +* @param total total number of twiddle values +*/ +void write_data_as_json( FILE *f, const int *lengths, const int *offsets, const double *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_f64( f, "twiddles", twiddles, total ); + fprintf( f, "}\n" ); +} + +/** +* Generates test fixtures. +* +* @param lengths sequence lengths +* @param offsets twiddle offsets into flat output array +* @param num number of sequence lengths +* @param total total number of 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; + double *twiddles; + double *wsave; + FILE *f; + int off; + int n; + + // Allocate an output array: + twiddles = (double*) malloc( total * sizeof(double) ); + if ( twiddles == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + + // Generate fixture data: + for ( i = 0; i < num; i++ ) { + n = lengths[ i ]; + wsave = (double*) calloc( 2*n + 15, sizeof(double) ); + if ( wsave == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + rffti( n, wsave ); + + // Copy twiddle region into flat array (N-1 values starting at wsave[n]): + off = offsets[ i ]; + for ( j = 0; j < (unsigned int)( n - 1 ); j++ ) { + twiddles[ off + j ] = wsave[ 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, twiddles, num, total ); + + // Close the file: + fclose( f ); + + // Free allocated memory: + free( twiddles ); +} + +/** +* Computes offsets into a flat twiddle array for each sequence length. +* +* @param offsets output array of offsets +* @param lengths sequence lengths +* @param num number of sequence lengths +* @return total number of 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 ] - 1; + } + return total; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + unsigned int total; + unsigned int num; + int *lengths; + int *offsets; + + // 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/rffti/test/fixtures/c/fftpack/small.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json new file mode 100644 index 000000000000..519a16fcee1e --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json @@ -0,0 +1 @@ +{"lengths":[2,3,12,8,9,5,2,11,11,15],"offsets":[0,1,3,14,21,29,33,34,44,54],"twiddles":[0,0,0,0.86602540378443871,0.49999999999999994,0,0.50000000000000011,0.8660254037844386,0,6.123233995736766e-17,1,0,0,0,0.70710678118654757,0.70710678118654746,0,0,0,0,0,0.76604444311897801,0.64278760968653925,0,0.17364817766693041,0.98480775301220802,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.91354545764260087,0.40673664307580015,0.66913060635885824,0.74314482547739424,0,0.66913060635885824,0.74314482547739424,-0.10452846326765333,0.9945218953682734,0,0,0,0,0]} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js new file mode 100644 index 000000000000..88262f7c17b1 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js @@ -0,0 +1,231 @@ +/** +* @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 Float64Array = require( '@stdlib/array/float64' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var rffti = 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 rffti, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 4', function test( t ) { + t.strictEqual( rffti.length, 4, 'returns expected value' ); + t.end(); +}); + +tape( 'the function correctly initializes twiddle factors (small sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var delta; + var tol; + var off; + var y; + var N; + var i; + var k; + + lengths = small.lengths; + offsets = small.offsets; + expected = small.twiddles; + + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + workspace = new Float64Array( ( 2*N ) + 34 ); + rffti( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ N ], 0.0, 'returns expected value' ); + for ( i = 0; i < N-1; i++ ) { + y = workspace[ N+i+1 ]; + if ( y === expected[ off+i ] ) { + t.strictEqual( y, expected[ off+i ], 'returns expected value' ); + } else { + delta = abs( y - expected[ off+i ] ); + tol = EPS * abs( expected[ off+i ] ); + t.ok( delta <= tol, 'within tolerance. N: '+N+'. workspace['+(N+i+1)+']. Value: '+y+'. Expected: '+expected[off+i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + } + t.end(); +}); + +tape( 'the function correctly initializes twiddle factors (medium sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var delta; + var tol; + var off; + var y; + var N; + var i; + var k; + + lengths = medium.lengths; + offsets = medium.offsets; + expected = medium.twiddles; + + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + workspace = new Float64Array( ( 2*N ) + 34 ); + rffti( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ N ], 0.0, 'returns expected value' ); + for ( i = 0; i < N-1; i++ ) { + y = workspace[ N+i+1 ]; + if ( y === expected[ off+i ] ) { + t.strictEqual( y, expected[ off+i ], 'returns expected value' ); + } else { + delta = abs( y - expected[ off+i ] ); + tol = EPS * abs( expected[ off+i ] ); + t.ok( delta <= tol, 'within tolerance. N: '+N+'. workspace['+(N+i+1)+']. Value: '+y+'. Expected: '+expected[off+i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + } + t.end(); +}); + +tape( 'the function correctly initializes twiddle factors (large sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var delta; + var tol; + var off; + var y; + var N; + var i; + var k; + + lengths = large.lengths; + offsets = large.offsets; + expected = large.twiddles; + + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + workspace = new Float64Array( ( 2*N ) + 34 ); + rffti( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ N ], 0.0, 'returns expected value' ); + for ( i = 0; i < N-1; i++ ) { + y = workspace[ N+i+1 ]; + if ( y === expected[ off+i ] ) { + t.strictEqual( y, expected[ off+i ], 'returns expected value' ); + } else { + delta = abs( y - expected[ off+i ] ); + tol = EPS * abs( expected[ off+i ] ); + t.ok( delta <= tol, 'within tolerance. N: '+N+'. workspace['+(N+i+1)+']. Value: '+y+'. Expected: '+expected[off+i]+'. tol: '+tol+'. delta: '+delta+'.' ); + } + } + } + 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 Float64Array( ( 2*N ) + 34 ); + + for ( i = 0; i < workspace.length; i++ ) { + workspace[ i ] = i + 1.0; + } + rffti( N, workspace, 1, 0 ); + for ( i = 0; i < N; i++ ) { + t.strictEqual( workspace[ i ], i + 1.0, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function does not modify the workspace when N is 1', function test( t ) { + var workspace; + var expected; + var N; + var i; + + N = 1; + workspace = new Float64Array( ( 2*N ) + 34 ); + for ( i = 0; i < workspace.length; i++ ) { + workspace[ i ] = i + 1.0; + } + expected = new Float64Array( workspace ); + + rffti( N, workspace, 1, 0 ); + + t.deepEqual( workspace, expected, '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 Float64Array( offset + ( ( ( 2*N ) + 34 ) * stride ) ); + + rffti( N, workspace, stride, offset ); + + t.strictEqual( workspace[ offset + ( 2*N * stride ) ], N, 'returns expected value' ); + + nf = workspace[ offset + ( ( ( 2*N ) + 1 ) * stride ) ]; + t.strictEqual( nf, 2, 'returns expected value' ); + t.strictEqual( workspace[ offset + ( ( ( 2*N ) + 2 ) * stride ) ], 2, 'returns expected value' ); + t.strictEqual( workspace[ offset + ( ( ( 2*N ) + 3 ) * stride ) ], 4, 'returns expected value' ); + + expected = new Float64Array( ( 2*N ) + 34 ); + rffti( N, expected, 1, 0 ); + + for ( i = 0; i < N-1; i++ ) { + t.strictEqual( workspace[ offset + ( ( N+i+1 ) * stride ) ], expected[ N+i+1 ], 'returns expected value' ); + } + t.end(); +}); From 64909dfa9a3573d27ea4bebacf702f7aece3a435 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Wed, 15 Apr 2026 23:22:04 +0530 Subject: [PATCH 02/14] docs: add test.ts --- .../fft/base/fftpack/rffti/docs/types/test.ts | 93 +++++++++++++++++++ 1 file changed, 93 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts new file mode 100644 index 000000000000..a01b8b17546f --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts @@ -0,0 +1,93 @@ +/* +* @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 rffti = require( './index' ); + +// TESTS // + +// The function returns void... +{ + const workspace = new Float64Array( ( 2*8 ) + 34 ); + + rffti( 8, workspace, 1, 0 ); // $ExpectType void +} + +// The compiler throws an error if the function is provided a first argument which is not a number... +{ + const workspace = new Float64Array( ( 2*8 ) + 34 ); + + rffti( '8', workspace, 1, 0 ); // $ExpectError + rffti( true, workspace, 1, 0 ); // $ExpectError + rffti( false, workspace, 1, 0 ); // $ExpectError + rffti( null, workspace, 1, 0 ); // $ExpectError + rffti( void 0, workspace, 1, 0 ); // $ExpectError + rffti( [], workspace, 1, 0 ); // $ExpectError + rffti( {}, workspace, 1, 0 ); // $ExpectError + rffti( ( x: number ): number => x, workspace, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a second argument which is not an array of numbers... +{ + rffti( 8, '50', 1, 0 ); // $ExpectError + rffti( 8, 50, 1, 0 ); // $ExpectError + rffti( 8, true, 1, 0 ); // $ExpectError + rffti( 8, false, 1, 0 ); // $ExpectError + rffti( 8, null, 1, 0 ); // $ExpectError + rffti( 8, void 0, 1, 0 ); // $ExpectError + rffti( 8, {}, 1, 0 ); // $ExpectError + rffti( 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 Float64Array( ( 2*8 ) + 34 ); + + rffti( 8, workspace, '1', 0 ); // $ExpectError + rffti( 8, workspace, true, 0 ); // $ExpectError + rffti( 8, workspace, false, 0 ); // $ExpectError + rffti( 8, workspace, null, 0 ); // $ExpectError + rffti( 8, workspace, void 0, 0 ); // $ExpectError + rffti( 8, workspace, [], 0 ); // $ExpectError + rffti( 8, workspace, {}, 0 ); // $ExpectError + rffti( 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 Float64Array( ( 2*8 ) + 34 ); + + rffti( 8, workspace, 1, '0' ); // $ExpectError + rffti( 8, workspace, 1, true ); // $ExpectError + rffti( 8, workspace, 1, false ); // $ExpectError + rffti( 8, workspace, 1, null ); // $ExpectError + rffti( 8, workspace, 1, void 0 ); // $ExpectError + rffti( 8, workspace, 1, [] ); // $ExpectError + rffti( 8, workspace, 1, {} ); // $ExpectError + rffti( 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 Float64Array( ( 2*8 ) + 34 ); + + rffti(); // $ExpectError + rffti( 8 ); // $ExpectError + rffti( 8, workspace ); // $ExpectError + rffti( 8, workspace, 1 ); // $ExpectError + rffti( 8, workspace, 1, 0, 123 ); // $ExpectError +} From 274ca8ed1d63d93d466461d0d2e070111b4a961d Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Fri, 17 Apr 2026 22:14:39 +0530 Subject: [PATCH 03/14] test: use is-almost-same-value --- 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 status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - 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: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rffti/test/test.js | 45 +++++++------------ 1 file changed, 16 insertions(+), 29 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js index 88262f7c17b1..4f158aa9df20 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js @@ -22,8 +22,7 @@ var tape = require( 'tape' ); var Float64Array = require( '@stdlib/array/float64' ); -var abs = require( '@stdlib/math/base/special/abs' ); -var EPS = require( '@stdlib/constants/float64/eps' ); +var isAlmostSameValue = require( '@stdlib/number/float64/base/assert/is-almost-same-value' ); var rffti = require( './../lib' ); @@ -52,10 +51,10 @@ tape( 'the function correctly initializes twiddle factors (small sequence length var expected; var lengths; var offsets; - var delta; - var tol; + var ulps; var off; var y; + var e; var N; var i; var k; @@ -64,6 +63,7 @@ tape( 'the function correctly initializes twiddle factors (small sequence length offsets = small.offsets; expected = small.twiddles; + ulps = 1; for ( k = 0; k < lengths.length; k++ ) { N = lengths[ k ]; off = offsets[ k ]; @@ -73,13 +73,8 @@ tape( 'the function correctly initializes twiddle factors (small sequence length t.strictEqual( workspace[ N ], 0.0, 'returns expected value' ); for ( i = 0; i < N-1; i++ ) { y = workspace[ N+i+1 ]; - if ( y === expected[ off+i ] ) { - t.strictEqual( y, expected[ off+i ], 'returns expected value' ); - } else { - delta = abs( y - expected[ off+i ] ); - tol = EPS * abs( expected[ off+i ] ); - t.ok( delta <= tol, 'within tolerance. N: '+N+'. workspace['+(N+i+1)+']. Value: '+y+'. Expected: '+expected[off+i]+'. tol: '+tol+'. delta: '+delta+'.' ); - } + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); } } t.end(); @@ -90,10 +85,10 @@ tape( 'the function correctly initializes twiddle factors (medium sequence lengt var expected; var lengths; var offsets; - var delta; - var tol; + var ulps; var off; var y; + var e; var N; var i; var k; @@ -102,6 +97,7 @@ tape( 'the function correctly initializes twiddle factors (medium sequence lengt offsets = medium.offsets; expected = medium.twiddles; + ulps = 1; for ( k = 0; k < lengths.length; k++ ) { N = lengths[ k ]; off = offsets[ k ]; @@ -111,13 +107,8 @@ tape( 'the function correctly initializes twiddle factors (medium sequence lengt t.strictEqual( workspace[ N ], 0.0, 'returns expected value' ); for ( i = 0; i < N-1; i++ ) { y = workspace[ N+i+1 ]; - if ( y === expected[ off+i ] ) { - t.strictEqual( y, expected[ off+i ], 'returns expected value' ); - } else { - delta = abs( y - expected[ off+i ] ); - tol = EPS * abs( expected[ off+i ] ); - t.ok( delta <= tol, 'within tolerance. N: '+N+'. workspace['+(N+i+1)+']. Value: '+y+'. Expected: '+expected[off+i]+'. tol: '+tol+'. delta: '+delta+'.' ); - } + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); } } t.end(); @@ -128,10 +119,10 @@ tape( 'the function correctly initializes twiddle factors (large sequence length var expected; var lengths; var offsets; - var delta; - var tol; + var ulps; var off; var y; + var e; var N; var i; var k; @@ -140,6 +131,7 @@ tape( 'the function correctly initializes twiddle factors (large sequence length offsets = large.offsets; expected = large.twiddles; + ulps = 1; for ( k = 0; k < lengths.length; k++ ) { N = lengths[ k ]; off = offsets[ k ]; @@ -149,13 +141,8 @@ tape( 'the function correctly initializes twiddle factors (large sequence length t.strictEqual( workspace[ N ], 0.0, 'returns expected value' ); for ( i = 0; i < N-1; i++ ) { y = workspace[ N+i+1 ]; - if ( y === expected[ off+i ] ) { - t.strictEqual( y, expected[ off+i ], 'returns expected value' ); - } else { - delta = abs( y - expected[ off+i ] ); - tol = EPS * abs( expected[ off+i ] ); - t.ok( delta <= tol, 'within tolerance. N: '+N+'. workspace['+(N+i+1)+']. Value: '+y+'. Expected: '+expected[off+i]+'. tol: '+tol+'. delta: '+delta+'.' ); - } + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); } } t.end(); From e7f37ce235f7f5c280067988337e63438aefa25a Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Fri, 17 Apr 2026 22:18:08 +0530 Subject: [PATCH 04/14] Update README examples Co-authored-by: Athan Signed-off-by: Gunj Joshi --- .../@stdlib/fft/base/fftpack/rffti/README.md | 17 ++++++----------- 1 file changed, 6 insertions(+), 11 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md index 4aa185aefa1f..bd22a2a55aff 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md @@ -114,28 +114,23 @@ The function accepts the following arguments: var Float64Array = require( '@stdlib/array/float64' ); var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); -var workspace; -var N; -var nf; -var i; -var j; - -N = 8; -workspace = new Float64Array( ( 2*N ) + 34 ); +var N = 8; +var workspace = new Float64Array( ( 2*N ) + 34 ); rffti( N, workspace, 1, 0 ); console.log( 'Sequence length: %d', N ); console.log( 'Twiddle factors:' ); +var i; for ( i = N; i < 2*N; i++ ) { console.log( ' workspace[%d] = %d', i, workspace[ i ] ); } console.log( 'Factorization:' ); -nf = workspace[ ( 2*N ) + 1 ]; +var nf = workspace[ ( 2*N ) + 1 ]; console.log( ' number of factors: %d', nf ); -for ( j = 0; j < nf; j++ ) { - console.log( ' factor[%d]: %d', j, workspace[ ( 2*N ) + 2 + j ] ); +for ( i = 0; i < nf; i++ ) { + console.log( ' factor[%d]: %d', i, workspace[ ( 2*N ) + 2 + i ] ); } ``` From 9ca9dbf2b1dc9c6d69ace948dea08c993e301144 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Fri, 17 Apr 2026 22:20:15 +0530 Subject: [PATCH 05/14] docs: update examples --- 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 status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: passed - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - 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: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rffti/examples/index.js | 17 ++++++----------- 1 file changed, 6 insertions(+), 11 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js index e9004065b2ee..bf8d4caa83ab 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js @@ -21,26 +21,21 @@ var Float64Array = require( '@stdlib/array/float64' ); var rffti = require( './../lib' ); -var workspace; -var N; -var nf; -var i; -var j; - -N = 8; -workspace = new Float64Array( ( 2*N ) + 34 ); +var N = 8; +var workspace = new Float64Array( ( 2*N ) + 34 ); rffti( N, workspace, 1, 0 ); console.log( 'Sequence length: %d', N ); console.log( 'Twiddle factors:' ); +var i; for ( i = N; i < 2*N; i++ ) { console.log( ' workspace[%d] = %d', i, workspace[ i ] ); } console.log( 'Factorization:' ); -nf = workspace[ ( 2*N ) + 1 ]; +var nf = workspace[ ( 2*N ) + 1 ]; console.log( ' number of factors: %d', nf ); -for ( j = 0; j < nf; j++ ) { - console.log( ' factor[%d]: %d', j, workspace[ ( 2*N ) + 2 + j ] ); +for ( i = 0; i < nf; i++ ) { + console.log( ' factor[%d]: %d', i, workspace[ ( 2*N ) + 2 + i ] ); } From cba0e7f1b0ff57b4e0bb7f607152ddbb84cd220b Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Fri, 17 Apr 2026 22:40:29 +0530 Subject: [PATCH 06/14] docs: update repl text --- 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 status: na - task: lint_package_json status: na - task: lint_repl_help status: passed - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - 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: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rffti/docs/repl.txt | 21 +++++++++++-------- 1 file changed, 12 insertions(+), 9 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt index aa886670dc67..d8aa85b19e9f 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt @@ -3,15 +3,18 @@ Initializes a workspace array for performing a real-valued Fourier transform. - The workspace array is divided into three sections: scratch/workspace - (indices 0 to N-1), twiddle factors (indices N to 2N-1), and radix factor - table (indices 2N onwards). - - The scratch/workspace section is used while performing transforms and is - not updated during initialization. The twiddle factors section stores a - table of reusable complex exponential constants as cosine/sine pairs. The - radix factor table stores the sequence length N, the number of factors into - which N was decomposed, and the individual integer radix factors. + The workspace array is divided into three sections: + + 1. scratch/workspace: the section ranges from indices 0 to N-1 and is used + while performing transforms. This section is not updated during + initialization. + + 2. twiddle factors: the section ranges from indices N to 2N-1 and stores a + table of reusable complex exponential constants as cosine/sine pairs. + + 3. radix factor table: the section starts at index 2N 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. From c27a17540c50c003f558a70565326f37828d3be1 Mon Sep 17 00:00:00 2001 From: Athan Date: Sun, 19 Apr 2026 03:10:00 -0700 Subject: [PATCH 07/14] style: add empty line Signed-off-by: Athan --- .../@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts | 1 + 1 file changed, 1 insertion(+) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts index 2c55a4abb09d..c8ab146082dd 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts @@ -32,6 +32,7 @@ import { Collection } from '@stdlib/types/array'; * * @example * var Float64Array = require( '@stdlib/array/float64' ); +* * var N = 8; * var workspace = new Float64Array( ( 2*N ) + 34 ); * From 500b84b9a7efe2a06414679ca3820342ef6b20b7 Mon Sep 17 00:00:00 2001 From: Athan Date: Sun, 19 Apr 2026 03:12:29 -0700 Subject: [PATCH 08/14] style: add empty line Signed-off-by: Athan --- .../@stdlib/fft/base/fftpack/rffti/docs/types/test.ts | 1 + 1 file changed, 1 insertion(+) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts index a01b8b17546f..e2bf310b07b7 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts @@ -18,6 +18,7 @@ import rffti = require( './index' ); + // TESTS // // The function returns void... From daef1f3d7cd9da9a052a4502883040bf2f74f4cb Mon Sep 17 00:00:00 2001 From: Athan Date: Sun, 19 Apr 2026 03:29:05 -0700 Subject: [PATCH 09/14] Apply suggestions from code review Co-authored-by: Athan Signed-off-by: Athan --- lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md | 1 + .../@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts | 3 ++- .../@stdlib/fft/base/fftpack/rffti/docs/types/test.ts | 4 ++-- .../@stdlib/fft/base/fftpack/rffti/examples/index.js | 1 + lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js | 6 ++++-- 5 files changed, 10 insertions(+), 5 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md index bd22a2a55aff..9cb66af3c708 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md @@ -128,6 +128,7 @@ for ( i = N; i < 2*N; i++ ) { console.log( 'Factorization:' ); var nf = workspace[ ( 2*N ) + 1 ]; + console.log( ' number of factors: %d', nf ); for ( i = 0; i < nf; i++ ) { console.log( ' factor[%d]: %d', i, workspace[ ( 2*N ) + 2 + i ] ); diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts index c8ab146082dd..7bd195ea2ca8 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts @@ -29,6 +29,7 @@ import { Collection } from '@stdlib/types/array'; * @param workspace - workspace array * @param strideW - stride length for `workspace` * @param offsetW - starting index for `workspace` +* @returns workspace array * * @example * var Float64Array = require( '@stdlib/array/float64' ); @@ -44,7 +45,7 @@ import { Collection } from '@stdlib/types/array'; * var factors = workspace.slice( 2*N, ( 2*N ) + 4 ); * // returns [ 8, 2, 2, 4 ] */ -declare function rffti( N: number, workspace: Collection, strideW: number, offsetW: number ): void; +declare function rffti>( N: number, workspace: T, strideW: number, offsetW: number ): T; // EXPORTS // diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts index e2bf310b07b7..6d1f815d9301 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/test.ts @@ -21,11 +21,11 @@ import rffti = require( './index' ); // TESTS // -// The function returns void... +// The function returns a collection... { const workspace = new Float64Array( ( 2*8 ) + 34 ); - rffti( 8, workspace, 1, 0 ); // $ExpectType void + rffti( 8, workspace, 1, 0 ); // $ExpectType Float64Array } // The compiler throws an error if the function is provided a first argument which is not a number... diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js index bf8d4caa83ab..92a7803afedf 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/examples/index.js @@ -35,6 +35,7 @@ for ( i = N; i < 2*N; i++ ) { console.log( 'Factorization:' ); var nf = workspace[ ( 2*N ) + 1 ]; + console.log( ' number of factors: %d', nf ); for ( i = 0; i < nf; i++ ) { console.log( ' factor[%d]: %d', i, workspace[ ( 2*N ) + 2 + i ] ); diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js index 663a19bd35cd..e7a656fddbc4 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js @@ -129,10 +129,10 @@ var rffti1 = require( './rffti1.js' ); * In short, twiddle factors are cached roots of unity that allow each stage of the algorithm to rotate data quickly and predictably. * * @param {NonNegativeInteger} N - length of the sequence to transform -* @param {Float64Array} workspace - workspace array +* @param {Collection} workspace - workspace array * @param {integer} strideW - stride length for `workspace` * @param {NonNegativeInteger} offsetW - starting index for `workspace` -* @returns {void} +* @returns {Collection} workspace array * * @example * var Float64Array = require( '@stdlib/array/float64' ); @@ -162,6 +162,8 @@ function rffti( N, workspace, strideW, offsetW ) { // Initialize a provided workspace array: rffti1( N, workspace, strideW, offsetT, workspace, strideW, offsetF ); + + return workspace; } From 5c8446bed0ae7a600777e05f608e321e724dbf56 Mon Sep 17 00:00:00 2001 From: Athan Date: Sun, 19 Apr 2026 03:31:32 -0700 Subject: [PATCH 10/14] Apply suggestions from code review Co-authored-by: Athan Signed-off-by: Athan --- .../@stdlib/fft/base/fftpack/rffti/docs/repl.txt | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt index d8aa85b19e9f..fe99f4ad3524 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt @@ -32,6 +32,11 @@ offsetW: integer Starting index for `workspace`. + Returns + ------- + out: ArrayLikeObject + Workspace array. + Examples -------- > var {{alias:@stdlib/array/float64}} = require( '@stdlib/array/float64' ); From 2eb785a61a269785cdc6046511eae4a386e95182 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sat, 25 Apr 2026 13:56:23 +0530 Subject: [PATCH 11/14] refactor: revert to old implementation --- 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 status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - 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: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rffti/lib/rffti1.js | 120 +++++++++--------- 1 file changed, 59 insertions(+), 61 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js index 18a9062cce13..60c1bfee8e0d 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/rffti1.js @@ -60,15 +60,15 @@ // MODULES // +var sincos = require( '@stdlib/math/base/special/sincos' ).assign; var TWO_PI = require( '@stdlib/constants/float64/two-pi' ); var floor = require( '@stdlib/math/base/special/floor' ); -var sin = require( '@stdlib/math/base/special/sin' ); -var cos = require( '@stdlib/math/base/special/cos' ); var decompose = require( '@stdlib/fft/base/fftpack/decompose' ); // VARIABLES // +// Define a list of initial trial factors for FFT factorization: var TRIAL_FACTORS = [ 4, 2, 3, 5 ]; @@ -78,104 +78,102 @@ var TRIAL_FACTORS = [ 4, 2, 3, 5 ]; * Initializes the working arrays for applying a Fourier transform to a real-valued sequence. * * @private -* @param {NonNegativeInteger} n - length of the sequence -* @param {Collection} wa - array of twiddle factors -* @param {integer} strideW - stride length for `wa` -* @param {NonNegativeInteger} offsetW - starting index for `wa` -* @param {Collection} ifac - array containing a radix factorization -* @param {integer} strideF - stride length for `ifac` -* @param {NonNegativeInteger} offsetF - starting index for `ifac` +* @param {NonNegativeInteger} N - length of the sequence +* @param {Collection} twiddles - array of twiddle factors +* @param {integer} strideT - stride length for `twiddles` +* @param {NonNegativeInteger} offsetT - starting index for `twiddles` +* @param {Collection} factors - array containing a radix factorization +* @param {integer} strideF - stride length for `factors` +* @param {NonNegativeInteger} offsetF - starting index for `factors` * @returns {void} */ -function rffti1( n, wa, strideW, offsetW, ifac, strideF, offsetF ) { +function rffti1( N, twiddles, strideT, offsetT, factors, strideF, offsetF ) { + var factor; var argld; var argh; - var nfm1; - var arg; - var ipm; - var ido; + var fidx; var nf; var fi; - var ip; var l2; var l1; var ld; - var ii; - var is; - var k1; - var i; + var st; + var it; + var im; + var M; + var m; + var k; var j; // Decompose the sequence length into its radix factors: - nf = decompose( n, 4, TRIAL_FACTORS, 1, 0, ifac, strideF, offsetF ); + nf = decompose( N, 4, TRIAL_FACTORS, 1, 0, factors, strideF, offsetF ); + // If the number of radix factors is `1`, the only twiddle factor we need is `W_N^0 = 1`, which the main transform kernels already hard-code, so nothing to pre-compute... + if ( nf-1 === 0 ) { + return; + } // Compute the master angular step (i.e., the basic angle that generates all twiddles): - argh = TWO_PI / n; - - // Initialize the index into the twiddle factor array: - is = 0; + argh = TWO_PI / N; - // Compute the number of factors minus one: - nfm1 = nf - 1; + // Define the location of the first sine term we want to compute: + im = 1; // Initialize a running product of factors already processed: l1 = 1; - // If the number of radix factors is `1`, the only twiddle factor we need is `W_N^0 = 1`, which the main transform kernels already hard-code, so nothing to pre-compute... - if ( nfm1 === 0 ) { - return; - } - // Generate twiddle factors for each radix factor... - for ( k1 = 0; k1 < nfm1; k1++ ) { - // Resolve the next radix factor (C code: ifac[k1+2] with 1-based, JS: ifac[k1+2] with 0-based): - ip = ifac[ offsetF + ((k1+2)*strideF) ]; + // Compute the index of the first radix factor: + fidx = offsetF + ( 2*strideF ); - // Initialize a running offset used to step the angle: - ld = 0; + // Compute the stride length for each cosine/sine pair: + st = 2 * strideT; + + // Generate twiddle factors... + for ( k = 0; k < nf-1; k++ ) { + // Resolve the next radix factor: + factor = factors[ fidx ]; // Compute the length of the transform after including the current radix: - l2 = l1 * ip; + l2 = factor * l1; - // Compute the number of data points in each sub-transform: - ido = floor( n / l2 ); + // Compute the number of the "butterfly wings" (at this stage, the data is viewed as a `factor`-point transform of sub-vectors of length `l1`; `M` describes how many such vectors fit in the full array of length `N`): + M = floor( N / l2 ); - // Compute the number of iterations for the inner loop: - ipm = ip - 1; + // Initialize a running offset used to step the angle: + ld = 0; // Iterate over each butterfly column within the current radix... - for ( j = 0; j < ipm; j++ ) { + for ( j = 1; j < factor; j++ ) { // Advance to the next column: ld += l1; - // Initialize the index into the twiddle factor array: - i = is; - // Compute the angle step for this column: - argld = ld * argh; + argld = ld * argh; // 2π ⋅ j ⋅ li / N, which is the j-th column's base angle - // Initialize the harmonic counter: - fi = 0.0; + // Initialize a counter which counts from `1` to `(M/2)-1` (i.e., all non-trivial harmonics): + fi = 1.0; - // Iterate over each non-trivial harmonic in the column... - for ( ii = 2; ii < ido; ii += 2 ) { - // Advance the index by 2 (for cosine and sine): - i += 2; + // Compute the index of the sine term: + it = offsetT + ( (im+1)*strideT ); - // Update the harmonic counter: - fi += 1.0; + // Iterate over each non-trivial harmonic in the column (note: we skip the `m=0` and `m=1` (i.e., the first cosine/sine pair, the first harmonic `W_N^0 = cos(0) + j sin(0) = 1 + j⋅0` is trivial and hard-coded by transform kernels)... + for ( m = 2; m < M; m += 2 ) { + // Compute `(cos(fi*argld), sin(fi*argld))`: + sincos( fi*argld, twiddles, -strideT, it ); // note: `sincos` returns the sine and cosine, in that order, so we need to use a negative stride when assigning the values to `twiddles` to ensure that cosine comes before sine in the twiddles table - // Compute the angle for this harmonic: - arg = fi * argld; + // Update for the next harmonic: + fi += 1.0; - // Store the cosine and sine values: - wa[ offsetW + ( ( i-1 ) * strideW ) ] = cos( arg ); - wa[ offsetW + ( i*strideW ) ] = sin( arg ); + // Resolve the index of the next sine term: + it += st; } - // Advance the index by the number of data points in each sub-transform: - is += ido; + // Advance `im` by the size of the current block, skipping the cosine/sine pairs we have just written: + im += M; } // Update the running product of factors already processed: l1 = l2; + + // Resolve the index of the next radix factor: + fidx += strideF; } } From 40a06063cd90c47d30c57e494b7caecbdecaf682 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sat, 25 Apr 2026 14:35:32 +0530 Subject: [PATCH 12/14] test: add test confirming the workspace array is returned --- 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 status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - 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: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../@stdlib/fft/base/fftpack/rffti/test/test.js | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js index 4f158aa9df20..8173a6ee269a 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/test.js @@ -46,6 +46,19 @@ tape( 'the function has an arity of 4', function test( t ) { 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 Float64Array( ( 2*N ) + 34 ); + out = rffti( N, workspace, 1, 0 ); + + t.strictEqual( out, workspace, 'same reference' ); + t.end(); +}); + tape( 'the function correctly initializes twiddle factors (small sequence lengths)', function test( t ) { var workspace; var expected; From 7b69d8448ff375261a0c7f1d41979e29aae7dd4f Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Sat, 25 Apr 2026 15:10:28 +0530 Subject: [PATCH 13/14] docs: update examples to reflect the returned workspace array --- 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 status: passed - task: lint_package_json status: na - task: lint_repl_help status: passed - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - 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: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: skipped - task: lint_license_headers status: passed --- --- lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md | 6 +++++- .../@stdlib/fft/base/fftpack/rffti/docs/repl.txt | 5 ++++- .../@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts | 6 +++++- .../@stdlib/fft/base/fftpack/rffti/lib/index.js | 6 +++++- lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js | 6 +++++- 5 files changed, 24 insertions(+), 5 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md index 9cb66af3c708..c2de5f7a15f6 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/README.md @@ -50,7 +50,11 @@ var Float64Array = require( '@stdlib/array/float64' ); var N = 8; var workspace = new Float64Array( ( 2*N ) + 34 ); -rffti( N, workspace, 1, 0 ); +var out = rffti( N, workspace, 1, 0 ); +// returns + +var bool = ( out === workspace ); +// returns true var twiddleFactors = workspace.slice( N, 2*N ); // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt index fe99f4ad3524..92ba0e409b67 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/repl.txt @@ -42,7 +42,10 @@ > var {{alias:@stdlib/array/float64}} = require( '@stdlib/array/float64' ); > var N = 8; > var workspace = new {{alias:@stdlib/array/float64}}( ( 2*N ) + 34 ); - > {{alias}}( N, workspace, 1, 0 ); + > var out = {{alias}}( N, workspace, 1, 0 ) + + > var bool = ( out === workspace ) + true > var twiddleFactors = workspace.slice( N, 2*N ) [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] > var factors = workspace.slice( 2*N, ( 2*N ) + 4 ) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts index 7bd195ea2ca8..648888833e33 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/docs/types/index.d.ts @@ -37,7 +37,11 @@ import { Collection } from '@stdlib/types/array'; * var N = 8; * var workspace = new Float64Array( ( 2*N ) + 34 ); * -* rffti( N, workspace, 1, 0 ); +* var out = rffti( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true * * var twiddleFactors = workspace.slice( N, 2*N ); * // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js index 3c440549ebce..51c16c7bcb35 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/index.js @@ -30,7 +30,11 @@ * var N = 8; * var workspace = new Float64Array( ( 2*N ) + 34 ); * -* rffti( N, workspace, 1, 0 ); +* var out = rffti( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true * * var twiddleFactors = workspace.slice( N, 2*N ); * // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js index e7a656fddbc4..08aafc0ffdb1 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/lib/main.js @@ -140,7 +140,11 @@ var rffti1 = require( './rffti1.js' ); * var N = 8; * var workspace = new Float64Array( ( 2*N ) + 34 ); * -* rffti( N, workspace, 1, 0 ); +* var out = rffti( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true * * var twiddleFactors = workspace.slice( N, 2*N ); * // returns [ 0, ~0.707, ~0.707, 0, 0, 0, 0, 0 ] From d51d175f424230d2f3200afc914ee93a983dbfd0 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Fri, 22 May 2026 22:51:01 +0530 Subject: [PATCH 14/14] test: seed the fixture generator --- 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 status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - 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: missing_dependencies - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json | 2 +- .../base/fftpack/rffti/test/fixtures/c/fftpack/medium.json | 2 +- .../fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c | 4 ++++ .../fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json | 2 +- 4 files changed, 7 insertions(+), 3 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json index 37ea1b0c0505..01ea1093cdc9 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/large.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json index 215106655dfe..9426aa08c1c5 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/medium.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c index 82f5947a89b0..6f783f0bf820 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/runner.c @@ -27,6 +27,7 @@ #include #include +#include /** * Define prototypes for external functions. @@ -246,6 +247,9 @@ int main( void ) { 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; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json index 519a16fcee1e..fbf7013f13bc 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rffti/test/fixtures/c/fftpack/small.json @@ -1 +1 @@ -{"lengths":[2,3,12,8,9,5,2,11,11,15],"offsets":[0,1,3,14,21,29,33,34,44,54],"twiddles":[0,0,0,0.86602540378443871,0.49999999999999994,0,0.50000000000000011,0.8660254037844386,0,6.123233995736766e-17,1,0,0,0,0.70710678118654757,0.70710678118654746,0,0,0,0,0,0.76604444311897801,0.64278760968653925,0,0.17364817766693041,0.98480775301220802,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.91354545764260087,0.40673664307580015,0.66913060635885824,0.74314482547739424,0,0.66913060635885824,0.74314482547739424,-0.10452846326765333,0.9945218953682734,0,0,0,0,0]} +{"lengths":[13,13,12,9,14,4,5,5,15,11],"offsets":[0,12,24,35,43,56,59,63,67,81],"twiddles":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.86602540378443871,0.49999999999999994,0,0.50000000000000011,0.8660254037844386,0,6.123233995736766e-17,1,0,0,0,0.76604444311897801,0.64278760968653925,0,0.17364817766693041,0.98480775301220802,0,0,0,0.90096886790241915,0.43388373911755812,0.62348980185873359,0.7818314824680298,0.22252093395631445,0.97492791218182362,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.91354545764260087,0.40673664307580015,0.66913060635885824,0.74314482547739424,0,0.66913060635885824,0.74314482547739424,-0.10452846326765333,0.9945218953682734,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}