diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/README.md new file mode 100644 index 000000000000..8fce3a2870a4 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/README.md @@ -0,0 +1,167 @@ + + +# cffti + +> Initialize a workspace array for performing a complex-valued Fourier transform. + + + +
+ +
+ + + + + +
+ +## Usage + +```javascript +var cffti = require( '@stdlib/fft/base/fftpack/cffti' ); +``` + +#### cffti( N, workspace, strideW, offsetW ) + +Initializes a workspace array for performing a complex-valued Fourier transform. + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); + +var N = 8; +var workspace = new Float64Array( ( 4*N ) + 34 ); + +var out = cffti( N, workspace, 1, 0 ); +// returns + +var bool = ( out === workspace ); +// returns true + +var twiddleFactors = workspace.slice( 2*N, 4*N ); +// returns [ 1, 0, ~0.707, ~0.707, ~0, 1, ~-0.707, ~0.707, 1, 0, 1, 0, 1, 0, ~0, -1 ] + +var factors = workspace.slice( 4*N, ( 4*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 = 2N 2N 2+ceil(log2(N)/2) + ↓ ↓ ↓ + | scratch / workspace | twiddle factors | radix factor table | + ↑ ↑ ↑ + i = 0 ... 2N ... 4N ... + ``` + + - **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 `4N + 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 zeroTo = require( '@stdlib/array/zero-to' ); +var logEach = require( '@stdlib/console/log-each' ); +var cffti = require( '@stdlib/fft/base/fftpack/cffti' ); + +var N = 8; +var workspace = new Float64Array( ( 4*N ) + 34 ); + +cffti( N, workspace, 1, 0 ); +console.log( 'Sequence length: %d', N ); + +console.log( 'Twiddle factors:' ); +var idx = zeroTo( 2*N, 'generic' ); +logEach( ' workspace[ %d ] = %d', idx, workspace.slice( 2*N, 4*N ) ); + +console.log( 'Factorization:' ); +var nf = workspace[ (4*N)+1 ]; + +console.log( ' number of factors: %d', nf ); +idx = zeroTo( nf, 'generic' ); +logEach( ' factor[ %d ]: %d', idx, workspace.slice( (4*N)+2, (4*N)+2+nf ) ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +
+ + + + + +
+ +
+ + diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/benchmark/benchmark.js new file mode 100644 index 000000000000..1ee1d688b1ad --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/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 cffti = require( './../lib' ); + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} N - sequence length +* @returns {Function} benchmark function +*/ +function createBenchmark( N ) { + var workspace = new Float64Array( ( 4*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++ ) { + cffti( N, workspace, 1, 0 ); + if ( isnan( workspace[ ( 2*N ) + 1 ] ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( workspace[ ( 2*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/cffti/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/docs/repl.txt new file mode 100644 index 000000000000..846d4cb2e553 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/docs/repl.txt @@ -0,0 +1,55 @@ + +{{alias}}( N, workspace, strideW, offsetW ) + Initializes a workspace array for performing a complex-valued Fourier + transform. + + The workspace array is divided into three sections: + + 1. scratch/workspace: the section ranges from indices 0 to 2N-1 and is used + while performing transforms. This section is not updated during + initialization. + + 2. twiddle factors: the section ranges from indices 2N to 4N-1 and stores a + table of reusable complex exponential constants as cosine/sine pairs. + + 3. radix factor table: the section starts at index 4N 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: ArrayLikeObject + Workspace array. + + strideW: integer + Stride length for `workspace`. + + offsetW: integer + Starting index for `workspace`. + + Returns + ------- + out: ArrayLikeObject + Workspace array. + + Examples + -------- + > var N = 8; + > var workspace = new {{alias:@stdlib/array/float64}}( ( 4*N ) + 34 ); + > var out = {{alias}}( N, workspace, 1, 0 ) + + > var bool = ( out === workspace ) + true + > var twiddleFactors = workspace.slice( 2*N, 3*N ) + [ 1, 0, ~0.707, ~0.707, ~0, 1, ~-0.707, ~0.707 ] + > var factors = workspace.slice( 4*N, ( 4*N ) + 4 ) + [ 8, 2, 2, 4 ] + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/docs/types/index.d.ts new file mode 100644 index 000000000000..08dfaf307ff6 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/docs/types/index.d.ts @@ -0,0 +1,62 @@ +/* +* @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 complex-valued Fourier transform. +* +* ## Notes +* +* - The workspace array should have a length of at least `( 4*N ) + 34` elements. +* - For single-point sequences (N=1), the function returns immediately as the FFT is the identity operation. +* +* @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 Float64Array = require( '@stdlib/array/float64' ); +* +* var N = 8; +* var workspace = new Float64Array( ( 4*N ) + 34 ); +* +* var out = cffti( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true +* +* var twiddleFactors = workspace.slice( 2*N, 4*N ); +* // returns [ 1, 0, ~0.707, ~0.707, ~0, 1, ~-0.707, ~0.707, 1, 0, 1, 0, 1, 0, ~0, -1 ] +* +* var factors = workspace.slice( 4*N, ( 4*N ) + 4 ); +* // returns [ 8, 2, 2, 4 ] +*/ +declare function cffti>( N: number, workspace: T, strideW: number, offsetW: number ): T; + + +// EXPORTS // + +export = cffti; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/docs/types/test.ts new file mode 100644 index 000000000000..85634675ec83 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/docs/types/test.ts @@ -0,0 +1,94 @@ +/* +* @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 cffti = require( './index' ); + + +// TESTS // + +// The function returns a collection... +{ + const workspace = new Float64Array( ( 4*8 ) + 34 ); + + cffti( 8, workspace, 1, 0 ); // $ExpectType Float64Array +} + +// The compiler throws an error if the function is provided a first argument which is not a number... +{ + const workspace = new Float64Array( ( 4*8 ) + 34 ); + + cffti( '8', workspace, 1, 0 ); // $ExpectError + cffti( true, workspace, 1, 0 ); // $ExpectError + cffti( false, workspace, 1, 0 ); // $ExpectError + cffti( null, workspace, 1, 0 ); // $ExpectError + cffti( void 0, workspace, 1, 0 ); // $ExpectError + cffti( [], workspace, 1, 0 ); // $ExpectError + cffti( {}, workspace, 1, 0 ); // $ExpectError + cffti( ( 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 collection... +{ + cffti( 8, '50', 1, 0 ); // $ExpectError + cffti( 8, 50, 1, 0 ); // $ExpectError + cffti( 8, true, 1, 0 ); // $ExpectError + cffti( 8, false, 1, 0 ); // $ExpectError + cffti( 8, null, 1, 0 ); // $ExpectError + cffti( 8, void 0, 1, 0 ); // $ExpectError + cffti( 8, {}, 1, 0 ); // $ExpectError + cffti( 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( ( 4*8 ) + 34 ); + + cffti( 8, workspace, '1', 0 ); // $ExpectError + cffti( 8, workspace, true, 0 ); // $ExpectError + cffti( 8, workspace, false, 0 ); // $ExpectError + cffti( 8, workspace, null, 0 ); // $ExpectError + cffti( 8, workspace, void 0, 0 ); // $ExpectError + cffti( 8, workspace, [], 0 ); // $ExpectError + cffti( 8, workspace, {}, 0 ); // $ExpectError + cffti( 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( ( 4*8 ) + 34 ); + + cffti( 8, workspace, 1, '0' ); // $ExpectError + cffti( 8, workspace, 1, true ); // $ExpectError + cffti( 8, workspace, 1, false ); // $ExpectError + cffti( 8, workspace, 1, null ); // $ExpectError + cffti( 8, workspace, 1, void 0 ); // $ExpectError + cffti( 8, workspace, 1, [] ); // $ExpectError + cffti( 8, workspace, 1, {} ); // $ExpectError + cffti( 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( ( 4*8 ) + 34 ); + + cffti(); // $ExpectError + cffti( 8 ); // $ExpectError + cffti( 8, workspace ); // $ExpectError + cffti( 8, workspace, 1 ); // $ExpectError + cffti( 8, workspace, 1, 0, 123 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/examples/index.js new file mode 100644 index 000000000000..a9ad8e9b86f7 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/examples/index.js @@ -0,0 +1,41 @@ +/** +* @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 zeroTo = require( '@stdlib/array/zero-to' ); +var logEach = require( '@stdlib/console/log-each' ); +var cffti = require( './../lib' ); + +var N = 8; +var workspace = new Float64Array( ( 4*N ) + 34 ); + +cffti( N, workspace, 1, 0 ); +console.log( 'Sequence length: %d', N ); + +console.log( 'Twiddle factors:' ); +var idx = zeroTo( 2*N, 'generic' ); +logEach( ' workspace[ %d ] = %d', idx, workspace.slice( 2*N, 4*N ) ); + +console.log( 'Factorization:' ); +var nf = workspace[ (4*N)+1 ]; + +console.log( ' number of factors: %d', nf ); +idx = zeroTo( nf, 'generic' ); +logEach( ' factor[ %d ]: %d', idx, workspace.slice( (4*N)+2, (4*N)+2+nf ) ); diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/lib/cffti1.js b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/lib/cffti1.js new file mode 100644 index 000000000000..1c0ee3f46a82 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/lib/cffti1.js @@ -0,0 +1,201 @@ +/** +* @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. +* ``` +*/ + +/* eslint-disable max-len */ + +'use strict'; + +// 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 decompose = require( '@stdlib/fft/base/fftpack/decompose' ); + + +// VARIABLES // + +// Define a list of initial trial factors for FFT factorization: +var TRIAL_FACTORS = [ 3, 4, 2, 5 ]; + + +// MAIN // + +/** +* Initializes the working arrays for applying a Fourier transform to a complex-valued sequence. +* +* @private +* @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 cffti1( N, twiddles, strideT, offsetT, factors, strideF, offsetF ) { + var factor; + var argld; + var argh; + var fidx; + var Mt; + var nf; + var fi; + var l2; + var l1; + var ld; + var st; + var it; + var i1; + var M; + var m; + var k; + var j; + var i; + + // Decompose the sequence length into its radix factors: + nf = decompose( N, 4, TRIAL_FACTORS, 1, 0, factors, strideF, offsetF ); + + // Compute the master angular step (i.e., the basic angle that generates all twiddles): + argh = TWO_PI / N; + + // Define where the first computed twiddle pair should be written: + i = 0; + + // Initialize a running product of factors already processed: + l1 = 1; + + // Compute the index of the first radix factor: + fidx = offsetF + ( 2*strideF ); + + // Compute the stride length for each cosine/sine pair: + st = 2 * strideT; + + // Generate twiddle factors... + for ( k = 0; k < nf; k++ ) { + // Resolve the next radix factor: + factor = factors[ fidx ]; + + // Compute the length of the transform after including the current radix: + l2 = factor * l1; + + // 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 ); + + // Initialize a running offset used to step the angle: + ld = 0; + + // Compute the total number of twiddle factors for the current column: + Mt = ( 2 * M ) + 2; // Two twiddles per harmonic, including the trivial first harmonic + + // Iterate over each butterfly column within the current radix... + for ( j = 1; j < factor; j++ ) { + // Store the index of the first twiddle pair for this column: + i1 = i; + + // Seed the first twiddle factor for this column with trivial cosine: + twiddles[ offsetT + ( i * strideT ) ] = 1.0; + + // Seed the first twiddle factor for this column with trivial sine: + twiddles[ offsetT + ( ( ( i + 1 ) * strideT ) ) ] = 0.0; + + // Advance to the next column: + ld += l1; + + // Compute the angle step for this column: + argld = ld * argh; // 2π ⋅ j ⋅ li / N, which is the j-th column's base angle + + // Initialize a counter which counts from `1` to `M-1` (i.e., all non-trivial harmonics): + fi = 1.0; + + // Compute the index of the sine term: + it = offsetT + ( ( i + 3 ) * strideT ); + + // 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 = 3; m < Mt; 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 + + // Update for the next harmonic: + fi += 1.0; + + // Resolve the index of the next sine term: + it += st; + } + // Advance `i` by the number of twiddle factors we have just written: + i += 2 * M; + + // For radices greater than 5, copy the last-written twiddle pair back to the start of this column's block, overwriting the trivial `(1, 0)` seed so that the transform kernel can use it as a wrap-around twiddle: + if ( factor > 5 ) { + twiddles[ offsetT + ( i1 * strideT ) ] = twiddles[ offsetT + ( i * strideT ) ]; + twiddles[ offsetT + ( ( i1 + 1 ) * strideT ) ] = twiddles[ offsetT + ( ( i + 1 ) * strideT ) ]; + } + } + // Update the running product of factors already processed: + l1 = l2; + + // Resolve the index of the next radix factor: + fidx += strideF; + } +} + + +// EXPORTS // + +module.exports = cffti1; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/lib/index.js new file mode 100644 index 000000000000..a9430dc9c9a9 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/lib/index.js @@ -0,0 +1,53 @@ +/** +* @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 complex-valued Fourier transform. +* +* @module @stdlib/fft/base/fftpack/cffti +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var cffti = require( '@stdlib/fft/base/fftpack/cffti' ); +* +* var N = 8; +* var workspace = new Float64Array( ( 4*N ) + 34 ); +* +* var out = cffti( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true +* +* var twiddleFactors = workspace.slice( 2*N, 4*N ); +* // returns [ 1, 0, ~0.707, ~0.707, ~0, 1, ~-0.707, ~0.707, 1, 0, 1, 0, 1, 0, ~0, -1 ] +* +* var factors = workspace.slice( 4*N, ( 4*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/cffti/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/lib/main.js new file mode 100644 index 000000000000..2352b030ba1a --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/lib/main.js @@ -0,0 +1,176 @@ +/** +* @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 cffti1 = require( './cffti1.js' ); + + +// MAIN // + +/** +* Initializes a workspace array for performing a complex-valued Fourier transform. +* +* ## Notes +* +* The workspace array is divided into three sections: +* +* ```text +* size = 2N 2N 2+ceil(log2(N)/2) +* ↓ ↓ ↓ +* | scratch / workspace | twiddle factors | radix factor table | +* ↑ ↑ ↑ +* i = 0 ... 2N ... 4N ... +* ``` +* +* 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 `4N + 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 `4N+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 `2N` 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 {Collection} workspace - workspace array +* @param {integer} strideW - stride length for `workspace` +* @param {NonNegativeInteger} offsetW - starting index for `workspace` +* @returns {Collection} workspace array +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var N = 8; +* var workspace = new Float64Array( ( 4*N ) + 34 ); +* +* var out = cffti( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true +* +* var twiddleFactors = workspace.slice( 2*N, 4*N ); +* // returns [ 1, 0, ~0.707, ~0.707, ~0, 1, ~-0.707, ~0.707, 1, 0, 1, 0, 1, 0, ~0, -1 ] +* +* var factors = workspace.slice( 4*N, ( 4*N ) + 4 ); +* // returns [ 8, 2, 2, 4 ] +*/ +function cffti( 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 + ( 2*N*strideW ); // index offset for twiddle factors + offsetF = offsetT + ( 2*N*strideW ); // index offset for factorization results + + // Initialize a provided workspace array: + cffti1( N, workspace, strideW, offsetT, workspace, strideW, offsetF ); + + return workspace; +} + + +// EXPORTS // + +module.exports = cffti; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/package.json new file mode 100644 index 000000000000..74b23c91ae11 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/package.json @@ -0,0 +1,64 @@ +{ + "name": "@stdlib/fft/base/fftpack/cffti", + "version": "0.0.0", + "description": "Initialize a workspace array for performing a complex-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", + "cffti", + "fourier", + "transform", + "twiddle", + "workspace", + "initialization", + "complex" + ], + "__stdlib__": {} +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/Makefile b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/Makefile new file mode 100644 index 000000000000..7ce16281940d --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/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/cffti/test/fixtures/c/fftpack/large.json b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/large.json new file mode 100644 index 000000000000..5a7acc6fd12d --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/large.json @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/medium.json b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/medium.json new file mode 100644 index 000000000000..8864c805b858 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/medium.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/runner.c b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/runner.c new file mode 100644 index 000000000000..e8569c7ef55e --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/runner.c @@ -0,0 +1,286 @@ +/** +* @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 cffti( 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( 4*n + 15, sizeof(double) ); + if ( wsave == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + cffti( n, wsave ); + + // Copy twiddle region into flat array (2*N values starting at wsave[2*n]): + off = offsets[ i ]; + for ( j = 0; j < (unsigned int)( 2 * 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, 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 += 2 * 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/cffti/test/fixtures/c/fftpack/small.json b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/small.json new file mode 100644 index 000000000000..35ab4ed6e892 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/fixtures/c/fftpack/small.json @@ -0,0 +1 @@ +{"lengths":[15,3,10,8,5,4,13,12,7,8],"offsets":[0,30,36,56,72,82,90,116,140,154],"twiddles":[1,0,0.91354545764260087,0.40673664307580015,0.66913060635885824,0.74314482547739424,0.30901699437494745,0.95105651629515353,-0.10452846326765333,0.9945218953682734,1,0,0.66913060635885824,0.74314482547739424,-0.10452846326765333,0.9945218953682734,-0.80901699437494734,0.58778525229247325,-0.97814760073380569,-0.20791169081775907,1,0,1,0,1,0,1,0,0.30901699437494723,-0.95105651629515364,1,0,1,0,-0.50000000000000044,-0.86602540378443837,1,0,0.80901699437494745,0.58778525229247314,0.30901699437494745,0.95105651629515353,-0.30901699437494734,0.95105651629515364,-0.80901699437494734,0.58778525229247325,1,0,1,0,1,0,1,0,0.30901699437494723,-0.95105651629515364,1,0,0.70710678118654757,0.70710678118654746,6.123233995736766e-17,1,-0.70710678118654746,0.70710678118654757,1,0,1,0,1,0,-1.8369701987210297e-16,-1,1,0,1,0,1,0,1,0,0.30901699437494723,-0.95105651629515364,1,0,1,0,1,0,-1.8369701987210297e-16,-1,0.88545602565320991,0.46472317204376851,0.56806474673115581,0.82298386589365635,0.12053668025532323,0.99270887409805397,-0.35460488704253545,0.93501624268541483,-0.74851074817110086,0.66312265824079553,-0.9709418174260519,0.2393156642875581,-0.97094181742605212,-0.23931566428755743,-0.7485107481711013,-0.66312265824079497,-0.3546048870425359,-0.93501624268541472,0.12053668025532233,-0.99270887409805408,0.56806474673115559,-0.82298386589365657,0.88545602565320958,-0.46472317204376917,0.88545602565320958,-0.46472317204376917,1,0,0.86602540378443871,0.49999999999999994,0.50000000000000011,0.8660254037844386,6.123233995736766e-17,1,1,0,0.50000000000000011,0.8660254037844386,-0.49999999999999983,0.86602540378443871,-1,1.2246467991473532e-16,1,0,1,0,1,0,-1.8369701987210297e-16,-1,0.62348980185873359,0.7818314824680298,-0.22252093395631434,0.97492791218182362,-0.90096886790241903,0.43388373911755823,-0.90096886790241915,-0.43388373911755801,-0.22252093395631459,-0.97492791218182362,0.62348980185873337,-0.78183148246802991,0.62348980185873337,-0.78183148246802991,1,0,0.70710678118654757,0.70710678118654746,6.123233995736766e-17,1,-0.70710678118654746,0.70710678118654757,1,0,1,0,1,0,-1.8369701987210297e-16,-1]} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/test/test.js new file mode 100644 index 000000000000..b406ca716095 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/cffti/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 isAlmostSameValue = require( '@stdlib/number/float64/base/assert/is-almost-same-value' ); +var cffti = 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 cffti, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 4', function test( t ) { + t.strictEqual( cffti.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 Float64Array( ( 4*N ) + 34 ); + out = cffti( 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; + 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 Float64Array( ( 4*N ) + 34 ); + cffti( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ ( 2*N ) - 1 ], 0.0, 'returns expected value' ); + for ( i = 0; i < 2*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 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 Float64Array( ( 4*N ) + 34 ); + cffti( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ ( 2*N ) - 1 ], 0.0, 'returns expected value' ); + for ( i = 0; i < 2*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 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 Float64Array( ( 4*N ) + 34 ); + cffti( N, workspace, 1, 0 ); + + t.strictEqual( workspace[ ( 2*N ) - 1 ], 0.0, 'returns expected value' ); + for ( i = 0; i < 2*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 Float64Array( ( 4*N ) + 34 ); + + for ( i = 0; i < workspace.length; i++ ) { + workspace[ i ] = i + 1.0; + } + cffti( N, workspace, 1, 0 ); + for ( i = 0; i < 2*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( ( 4*N ) + 34 ); + for ( i = 0; i < workspace.length; i++ ) { + workspace[ i ] = i + 1.0; + } + expected = new Float64Array( workspace ); + + cffti( 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 + ( ( ( 4*N ) + 34 ) * stride ) ); + + cffti( N, workspace, stride, offset ); + + t.strictEqual( workspace[ offset + ( 4*N * stride ) ], N, 'returns expected value' ); + + nf = workspace[ offset + ( ( ( 4*N ) + 1 ) * stride ) ]; + t.strictEqual( nf, 2, 'returns expected value' ); + t.strictEqual( workspace[ offset + ( ( ( 4*N ) + 2 ) * stride ) ], 2, 'returns expected value' ); + t.strictEqual( workspace[ offset + ( ( ( 4*N ) + 3 ) * stride ) ], 4, 'returns expected value' ); + + expected = new Float64Array( ( 4*N ) + 34 ); + cffti( N, expected, 1, 0 ); + + for ( i = 0; i < 2*N; i++ ) { + t.strictEqual( workspace[ offset + ( ( ( 2*N ) + i ) * stride ) ], expected[ ( 2*N ) + i ], 'returns expected value' ); + } + t.end(); +});