diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/README.md new file mode 100644 index 000000000000..456ca6376d16 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/README.md @@ -0,0 +1,175 @@ + + +# sinti + +> Initialize a workspace array for performing a sine transform. + + + +
+ +
+ + + + + +
+ +## Usage + +```javascript +var sinti = require( '@stdlib/fft/base/fftpack/sinti' ); +``` + +#### sinti( N, workspace, strideW, offsetW ) + +Initializes a workspace array for performing a sine transform. + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var floor = require( '@stdlib/math/base/special/floor' ); + +var N = 7; +var workspace = new Float64Array( floor( 2.5*N ) + 34 ); + +var out = sinti( N, workspace, 1, 0 ); +// returns + +var bool = ( out === workspace ); +// returns true + +var sineTable = workspace.slice( 0, floor( N/2 ) ); +// returns [ ~0.765, ~1.414, ~1.848 ] + +var twiddleFactors = workspace.slice( floor( 3*N/2 ) + 1, floor( 5*N/2 ) + 2 ); +// returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] + +var factors = workspace.slice( floor( 5*N/2 ) + 2, floor(5*N/2) + 2 + 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 four sections: + + ```text + size = N/2 N+1 N+1 2+ceil(log2(N+1)/2) + ↓ ↓ ↓ ↓ + | sine table | scratch/workspace | twiddle factors | radix factor table | + ↑ ↑ ↑ ↑ + i = 0 ... N/2 ... (3N/2)+1 ... (5N/2)+2 ... + ``` + + - **sine table**: a table of precomputed sine coefficients used by sine transforms. + - **scratch/workspace**: used as a scratch space when performing transforms. This section is not updated during initialization. + - **twiddle factors**: a table of reusable complex-exponential constants stored as cosine/sine pairs. + - **radix factor table**: a table containing the sequence length `N+1`, the number of factors into which `N+1` was decomposed, and the individual integer radix factors. + +- In general, a workspace array should have `2.5N + 34` indexed elements (as `log2(N+1)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing the sine coefficients, twiddle factors, and the factorization of `N+1` are updated. + +- The radix factor table is comprised as follows: + + ```text + | sequence_length | number_of_factors | integer_factors | + ``` + +
+ + + +
+ +## Examples + + + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var zeroTo = require( '@stdlib/array/zero-to' ); +var logEach = require( '@stdlib/console/log-each' ); +var floor = require( '@stdlib/math/base/special/floor' ); +var sinti = require( '@stdlib/fft/base/fftpack/sinti' ); + +var N = 7; +var workspace = new Float64Array( floor( 2.5*N ) + 34 ); + +sinti( N, workspace, 1, 0 ); +console.log( 'Sequence length: %d', N ); + +console.log( 'Sine table:' ); +var idx = zeroTo( floor( N/2 ), 'generic' ); +logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 0, floor( N/2 ) ) ); + +console.log( 'Twiddle factors:' ); +idx = zeroTo( N+1, 'generic' ); +logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( floor( 3*N/2 ) + 1, floor( 5*N/2 ) + 2 ) ); + +console.log( 'Factorization:' ); +var nf = workspace[ floor( 5*N/2 ) + 3 ]; + +console.log( ' number of factors: %d', nf ); +idx = zeroTo( nf, 'generic' ); +logEach( ' factor[ %d ]: %d', idx, workspace.slice( floor( 5*N/2 ) + 4, floor( 5*N/2 ) + 4 + nf ) ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +
+ + + + + +
+ +
+ + diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/benchmark/benchmark.js new file mode 100644 index 000000000000..a4e586b1414e --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/benchmark/benchmark.js @@ -0,0 +1,102 @@ +/* +* @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 floor = require( '@stdlib/math/base/special/floor' ); +var Float64Array = require( '@stdlib/array/float64' ); +var pkg = require( './../package.json' ).name; +var sinti = require( './../lib' ); + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} N - sequence length +* @returns {Function} benchmark function +*/ +function createBenchmark( N ) { + var workspace = new Float64Array( floor( 2.5*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++ ) { + sinti( N, workspace, 1, 0 ); + if ( isnan( workspace[ floor( 3*N/2 ) + 1 ] ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( workspace[ floor( 3*N/2 ) + 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 = [ + 7, + 15, + 31, + 63, + 127, + 255, + 511, + 1023 + ]; + + 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/sinti/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/docs/repl.txt new file mode 100644 index 000000000000..387fdf2987d4 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/docs/repl.txt @@ -0,0 +1,64 @@ + +{{alias}}( N, workspace, strideW, offsetW ) + Initializes a workspace array for performing a sine transform. + + The workspace array is divided into four sections: + + 1. sine table: the section ranges from indices 0 to N/2 and is used to + store a table of precomputed sine coefficients used by sine transforms. + + 2. scratch/workspace: the section ranges from indices N/2 to 3N/2 and is + used while performing transforms. This section is not updated during + initialization. + + 3. twiddle factors: the section ranges from indices (3N/2)+1 to (5N/2)+1 + and stores a table of reusable complex exponential constants as cosine/sine + pairs. + + 4. radix factor table: the section starts at index (5N/2)+2 and stores the + sequence length N+1, the number of factors into which N+1 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 = 7; + > var len = {{alias:@stdlib/math/base/special/floor}}( 2.5*N ) + 34; + > var workspace = new {{alias:@stdlib/array/float64}}( len ); + > var out = {{alias}}( N, workspace, 1, 0 ) + + > var bool = ( out === workspace ) + true + > var ns2 = {{alias:@stdlib/math/base/special/floor}}( N/2 ); + > var sineTable = workspace.slice( 0, ns2 ) + [ ~0.765, ~1.414, ~1.848 ] + > var iw = ns2 + N + 1; + > var twiddleFactors = workspace.slice( iw, iw + (N+1) ) + [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] + > var fw = ns2 + 2*(N+1); + > var factors = workspace.slice( fw, fw + 4 ) + [ 8, 2, 2, 4 ] + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/docs/types/index.d.ts new file mode 100644 index 000000000000..e728169090df --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/docs/types/index.d.ts @@ -0,0 +1,65 @@ +/* +* @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 sine transform. +* +* ## Notes +* +* - The workspace array should have a length of at least `( 2.5*N ) + 34` elements. +* +* @param N - length of the sequence +* @param workspace - workspace array +* @param strideW - stride length for `workspace` +* @param offsetW - starting index for `workspace` +* @returns workspace array +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var floor = require( '@stdlib/math/base/special/floor' ); +* +* var N = 7; +* var workspace = new Float64Array( floor( 2.5*N ) + 34 ); +* +* var out = sinti( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true +* +* var sineTable = workspace.slice( 0, floor( N/2 ) ); +* // returns [ ~0.765, ~1.414, ~1.848 ] +* +* var twiddleFactors = workspace.slice( floor( 3*N/2 ) + 1, floor( 5*N/2 ) + 2 ); +* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] +* +* var factors = workspace.slice( floor( 5*N/2 ) + 2, floor(5*N/2) + 2 + 4 ); +* // returns [ 8, 2, 2, 4 ] +*/ +declare function sinti>( N: number, workspace: T, strideW: number, offsetW: number ): T; + + +// EXPORTS // + +export = sinti; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/docs/types/test.ts new file mode 100644 index 000000000000..1cf202c7bbcb --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/docs/types/test.ts @@ -0,0 +1,95 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +import floor = require( '@stdlib/math/base/special/floor' ); +import sinti = require( './index' ); + + +// TESTS // + +// The function returns a collection... +{ + const workspace = new Float64Array( floor( 2.5*7 ) + 34 ); + + sinti( 7, 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( floor( 2.5*7 ) + 34 ); + + sinti( '7', workspace, 1, 0 ); // $ExpectError + sinti( true, workspace, 1, 0 ); // $ExpectError + sinti( false, workspace, 1, 0 ); // $ExpectError + sinti( null, workspace, 1, 0 ); // $ExpectError + sinti( void 0, workspace, 1, 0 ); // $ExpectError + sinti( [], workspace, 1, 0 ); // $ExpectError + sinti( {}, workspace, 1, 0 ); // $ExpectError + sinti( ( 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... +{ + sinti( 7, '50', 1, 0 ); // $ExpectError + sinti( 7, 50, 1, 0 ); // $ExpectError + sinti( 7, true, 1, 0 ); // $ExpectError + sinti( 7, false, 1, 0 ); // $ExpectError + sinti( 7, null, 1, 0 ); // $ExpectError + sinti( 7, void 0, 1, 0 ); // $ExpectError + sinti( 7, {}, 1, 0 ); // $ExpectError + sinti( 7, ( 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( floor( 2.5*7 ) + 34 ); + + sinti( 7, workspace, '1', 0 ); // $ExpectError + sinti( 7, workspace, true, 0 ); // $ExpectError + sinti( 7, workspace, false, 0 ); // $ExpectError + sinti( 7, workspace, null, 0 ); // $ExpectError + sinti( 7, workspace, void 0, 0 ); // $ExpectError + sinti( 7, workspace, [], 0 ); // $ExpectError + sinti( 7, workspace, {}, 0 ); // $ExpectError + sinti( 7, 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( floor( 2.5*7 ) + 34 ); + + sinti( 7, workspace, 1, '0' ); // $ExpectError + sinti( 7, workspace, 1, true ); // $ExpectError + sinti( 7, workspace, 1, false ); // $ExpectError + sinti( 7, workspace, 1, null ); // $ExpectError + sinti( 7, workspace, 1, void 0 ); // $ExpectError + sinti( 7, workspace, 1, [] ); // $ExpectError + sinti( 7, workspace, 1, {} ); // $ExpectError + sinti( 7, 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( floor( 2.5*7 ) + 34 ); + + sinti(); // $ExpectError + sinti( 7 ); // $ExpectError + sinti( 7, workspace ); // $ExpectError + sinti( 7, workspace, 1 ); // $ExpectError + sinti( 7, workspace, 1, 0, 123 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/examples/index.js new file mode 100644 index 000000000000..e006767c0961 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/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 zeroTo = require( '@stdlib/array/zero-to' ); +var logEach = require( '@stdlib/console/log-each' ); +var floor = require( '@stdlib/math/base/special/floor' ); +var sinti = require( './../lib' ); + +var N = 7; +var workspace = new Float64Array( floor( 2.5*N ) + 34 ); + +sinti( N, workspace, 1, 0 ); +console.log( 'Sequence length: %d', N ); + +console.log( 'Sine table:' ); +var idx = zeroTo( floor( N/2 ), 'generic' ); +logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 0, floor( N/2 ) ) ); + +console.log( 'Twiddle factors:' ); +idx = zeroTo( N+1, 'generic' ); +logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( floor( 3*N/2 ) + 1, floor( 5*N/2 ) + 2 ) ); + +console.log( 'Factorization:' ); +var nf = workspace[ floor( 5*N/2 ) + 3 ]; + +console.log( ' number of factors: %d', nf ); +idx = zeroTo( nf, 'generic' ); +logEach( ' factor[ %d ]: %d', idx, workspace.slice( floor( 5*N/2 ) + 4, floor( 5*N/2 ) + 4 + nf ) ); diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/lib/index.js new file mode 100644 index 000000000000..a5d299466f1d --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/lib/index.js @@ -0,0 +1,57 @@ +/** +* @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 sine transform. +* +* @module @stdlib/fft/base/fftpack/sinti +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var floor = require( '@stdlib/math/base/special/floor' ); +* var sinti = require( '@stdlib/fft/base/fftpack/sinti' ); +* +* var N = 7; +* var workspace = new Float64Array( floor( 2.5*N ) + 34 ); +* +* var out = sinti( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true +* +* var sineTable = workspace.slice( 0, floor( N/2 ) ); +* // returns [ ~0.765, ~1.414, ~1.848 ] +* +* var twiddleFactors = workspace.slice( floor( 3*N/2 ) + 1, floor( 5*N/2 ) + 2 ); +* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] +* +* var factors = workspace.slice( floor( 5*N/2 ) + 2, floor(5*N/2) + 2 + 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/sinti/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/lib/main.js new file mode 100644 index 000000000000..996bea9a1f79 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/lib/main.js @@ -0,0 +1,200 @@ +/** +* @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 sin = require( '@stdlib/math/base/special/sin' ); +var PI = require( '@stdlib/constants/float64/pi' ); +var floor = require( '@stdlib/math/base/special/floor' ); +var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); + + +// MAIN // + +/** +* Initializes a workspace array for performing a sine transform. +* +* ## Notes +* +* The workspace array is divided into four sections: +* +* ```text +* size = N/2 N+1 N+1 2+ceil(log2(N+1)/2) +* ↓ ↓ ↓ ↓ +* | sine table | scratch/workspace | twiddle factors | radix factor table | +* ↑ ↑ ↑ ↑ +* i = 0 ... N/2 ... (3N/2)+1 ... (5N/2)+2 ... +* ``` +* +* where +* +* - **sine table**: a table of precomputed sine coefficients used by sine transforms. +* - **scratch/workspace**: used as a scratch space when performing transforms. This section is not updated during initialization. +* - **twiddle factors**: a table of reusable complex-exponential constants stored as cosine/sine pairs. +* - **radix factor table**: a table containing the radix factorization of `N+1`. +* +* In general, a workspace array should have `2.5N + 34` indexed elements (as `log2(N+1)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing the sine coefficients, twiddle factors, and the factorization of `N+1` are updated. +* +* > Note: FFTPACK only requires `2.5N+15`, but we increase that number here to accommodate larger workspace arrays, where `N` may exceed `2^30` indexed elements. +* +* The factorization section is comprised as follows: +* +* ```text +* | sequence_length | number_of_factors | integer_factors | +* ``` +* +* The sequence length and number of factors (`nf`) comprise a single element each. Only the first `nf` elements in the integer factors section are written to, with the rest being unused. +* +* As for twiddle factors, these are small, reusable complex-exponential constants that appear inside each "butterfly" stage of a Cooley–Tukey–style FFT. Every arithmetic step in an FFT multiplies one intermediate value by some +* +* ```tex +* W_N^k +* ``` +* +* where `W_N^k` is an N-th root of unity. Formally, in a forward FFT, +* +* ```tex +* W_N^k = e^{-2\pi ik/N} +* ``` +* +* In a backward FFT, +* +* ```tex +* W_N^k = e^{+2\pi ik/N} +* ``` +* +* As may be observed, `W_N^k` for forward and backward FFTs is the same, except the sign of the exponent is flipped. As a consequence, both forward and backward FFT callers can reuse the same set of twiddle factors, with those performing a forward transform multiplying with `(cos,-sin)` and those performing a backward transform multiplying with `(cos,+sin)`. +* +* Because these constants only depend on the transform length `N` (and **not** on the input data), we can pre-compute and store them once, then "twiddle" them (i.e., reuse them with different indices) as we proceed through the factorization. +* +* > As a quick aside regarding the name "twiddle", early FFT papers (notably Gentleman & Sande, 1966) described how you "twiddle" one branch of each butterfly by a complex rotation before adding/subtracting. The coefficients themselves inherited the nickname "twiddle factors," and the term stuck. +* +* By reusing the workspace array when computing multiple transforms of the same length `N`, every subsequent `*f` (forward) or `*b` (backward) call can simply look up the pre-stored twiddle factors instead of recomputing sine and cosine on-the-fly. +* +* In short, twiddle factors are cached roots of unity that allow each stage of the algorithm to rotate data quickly and predictably. +* +* During initialization, `sinti` first writes the sine table, and then initializes the remaining three sections using `rffti`. +* +* @param {PositiveInteger} 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 floor = require( '@stdlib/math/base/special/floor' ); +* +* var N = 7; +* var workspace = new Float64Array( floor( 2.5*N ) + 34 ); +* +* var out = sinti( N, workspace, 1, 0 ); +* // returns +* +* var bool = ( out === workspace ); +* // returns true +* +* var sineTable = workspace.slice( 0, floor( N/2 ) ); +* // returns [ ~0.765, ~1.414, ~1.848 ] +* +* var twiddleFactors = workspace.slice( floor( 3*N/2 ) + 1, floor( 5*N/2 ) + 2 ); +* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ] +* +* var factors = workspace.slice( floor( 5*N/2 ) + 2, floor(5*N/2) + 2 + 4 ); +* // returns [ 8, 2, 2, 4 ] +*/ +function sinti( N, workspace, strideW, offsetW ) { + var offsetR; + var ns2; + var dt; + var fk; + var iw; + var i; + + if ( N <= 1 ) { + return workspace; + } + + // Compute the number of sine values to store: + ns2 = floor( N / 2 ); + + // Compute the angular increment: + dt = PI / ( N + 1 ); + + // Compute and store the sine table: + fk = 0.0; + iw = offsetW; + for ( i = 0; i < ns2; i++ ) { + fk += 1.0; + workspace[ iw+(i*strideW) ] = sin( fk*dt ) * 2.0; + } + // Resolve the starting index for the `rffti` workspace: + offsetR = offsetW + (ns2*strideW); + + // Initialize the real FFT workspace for a sequence of length N+1: + rffti( N+1, workspace, strideW, offsetR ); + + return workspace; +} + + +// EXPORTS // + +module.exports = sinti; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/package.json new file mode 100644 index 000000000000..a88dc20f43a2 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/package.json @@ -0,0 +1,64 @@ +{ + "name": "@stdlib/fft/base/fftpack/sinti", + "version": "0.0.0", + "description": "Initialize a workspace array for performing a sine 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", + "sinti", + "fourier", + "transform", + "twiddle", + "workspace", + "initialization", + "sine" + ], + "__stdlib__": {} +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/Makefile b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/Makefile new file mode 100644 index 000000000000..7ce16281940d --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/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/sinti/test/fixtures/c/fftpack/large.json b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/large.json new file mode 100644 index 000000000000..867e4abd85b0 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/medium.json b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/medium.json new file mode 100644 index 000000000000..5b71d20d3c92 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/medium.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/runner.c b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/runner.c new file mode 100644 index 000000000000..1844165535d8 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/runner.c @@ -0,0 +1,304 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/** +* Generate FFTPACK test fixtures. +* +* ## Notes +* +* - Run this script from the directory in which fixtures should be written. +* +*/ + +#include +#include +#include + +/** +* Define prototypes for external functions. +*/ +extern void sinti( 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 sine and twiddle offsets +* @param sines sine values +* @param twiddles twiddle factors +* @param num number of sequence lengths +* @param total total number of sine and twiddle values +*/ +void write_data_as_json( FILE *f, const int *lengths, const int *offsets, const double *sines, 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, "sines", sines, total ); + fprintf( f, "," ); + write_named_array_f64( f, "twiddles", twiddles, total ); + fprintf( f, "}\n" ); +} + +/** +* Generates test fixtures. +* +* @param lengths sequence lengths +* @param offsets sine and twiddle offsets into flat output array +* @param num number of sequence lengths +* @param total total number of sine and twiddle values +* @param name output filename +*/ +void generate( const int *lengths, const int *offsets, const unsigned int num, const unsigned int total, const char *name ) { + unsigned int i; + unsigned int j; + double *sines; + double *twiddles; + double *wsave; + FILE *f; + int off; + int n; + + // Allocate an output array for sine values: + sines = (double*) calloc( total, sizeof(double) ); + if ( sines == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + + // Allocate an output array for twiddle factors: + twiddles = (double*) calloc( 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( (int)(2.5*n) + 15, sizeof(double) ); + if ( wsave == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + sinti( n, wsave ); + + // Copy sine region into flat array (N/2 values starting at wsave[0]): + off = offsets[ i ]; + for ( j = 0; j < (unsigned int)(n/2); j++ ) { + sines[ off + j ] = wsave[ j ]; + } + + // Copy twiddle region into flat array (N+1 values starting at wsave[(n/2)+n+1]): + off = offsets[ i ]; + for ( j = 0; j < (unsigned int)( n + 1 ); j++ ) { + twiddles[ off + j ] = wsave[ ( n/2 ) + n + 1 + 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, sines, twiddles, num, total ); + + // Close the file: + fclose( f ); + + // Free allocated memory: + free( sines ); + free( twiddles ); +} + +/** +* Computes offsets into flat sine and twiddle arrays for each sequence length. +* +* @param offsets output array of offsets +* @param lengths sequence lengths +* @param num number of sequence lengths +* @return total number of sine and twiddle values +*/ +unsigned int compute_offsets( int *offsets, const int *lengths, const unsigned int num ) { + unsigned int total; + unsigned int i; + + total = 0; + for ( i = 0; i < num; i++ ) { + offsets[ i ] = total; + total += lengths[ i ] + 1; + } + 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/sinti/test/fixtures/c/fftpack/small.json b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/small.json new file mode 100644 index 000000000000..dc1e4ec8bbb5 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/fixtures/c/fftpack/small.json @@ -0,0 +1 @@ +{"lengths":[5,3,6,7,9,7,15,9,11,9],"offsets":[0,6,10,17,25,35,43,59,69,81],"sines":[0.99999999999999989,1.7320508075688772,0,0,0,0,1.4142135623730949,0,0,0,0.86776747823511624,1.5636629649360596,1.9498558243636472,0,0,0,0,0.76536686473017956,1.4142135623730949,1.8477590650225735,0,0,0,0,0,0.61803398874989479,1.1755705045849463,1.6180339887498949,1.9021130325903071,0,0,0,0,0,0,0.76536686473017956,1.4142135623730949,1.8477590650225735,0,0,0,0,0,0.3901806440322565,0.76536686473017956,1.1111404660392044,1.4142135623730949,1.6629392246050905,1.8477590650225735,1.9615705608064609,0,0,0,0,0,0,0,0,0,0.61803398874989479,1.1755705045849463,1.6180339887498949,1.9021130325903071,0,0,0,0,0,0,0.51763809020504148,0.99999999999999989,1.4142135623730949,1.7320508075688772,1.9318516525781364,0,0,0,0,0,0,0,0.61803398874989479,1.1755705045849463,1.6180339887498949,1.9021130325903071,0,0,0,0,0,0],"twiddles":[0.50000000000000011,0.8660254037844386,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.70710678118654757,0.70710678118654746,0,0,0,0,0,0,0.80901699437494745,0.58778525229247314,0.30901699437494745,0.95105651629515353,0,0,0,0,0,0,0.70710678118654757,0.70710678118654746,0,0,0,0,0,0,0.92387953251128674,0.38268343236508978,0,0,0.70710678118654757,0.70710678118654746,0,0,0.38268343236508984,0.92387953251128674,0,0,0,0,0,0,0.80901699437494745,0.58778525229247314,0.30901699437494745,0.95105651629515353,0,0,0,0,0,0,0.86602540378443871,0.49999999999999994,0,0.50000000000000011,0.8660254037844386,0,6.123233995736766e-17,1,0,0,0,0,0.80901699437494745,0.58778525229247314,0.30901699437494745,0.95105651629515353,0,0,0,0,0,0]} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/test.js new file mode 100644 index 000000000000..a6960135d70d --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/sinti/test/test.js @@ -0,0 +1,335 @@ +/** +* @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 floor = require( '@stdlib/math/base/special/floor' ); +var sinti = 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 sinti, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 4', function test( t ) { + t.strictEqual( sinti.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( floor( 2.5*N ) + 34 ); + out = sinti( N, workspace, 1, 0 ); + + t.strictEqual( out, workspace, 'same reference' ); + t.end(); +}); + +tape( 'the function correctly initializes sine values (small sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var ns2; + var off; + var y; + var e; + var N; + var i; + var k; + + lengths = small.lengths; + offsets = small.offsets; + expected = small.sines; + + ulps = 1; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + ns2 = floor( N / 2 ); + workspace = new Float64Array( floor( 2.5*N ) + 34 ); + sinti( N, workspace, 1, 0 ); + + for ( i = 0; i < ns2; i++ ) { + y = workspace[ i ]; + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); + } + } + t.end(); +}); + +tape( 'the function correctly initializes twiddle factors (small sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var ns2; + var off; + var iw; + 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 ]; + ns2 = floor( N / 2 ); + iw = ns2 + N + 1; + workspace = new Float64Array( floor( 2.5*N ) + 34 ); + sinti( N, workspace, 1, 0 ); + + for ( i = 0; i < N+1; i++ ) { + y = workspace[ iw + 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 sine values (medium sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var ns2; + var off; + var y; + var e; + var N; + var i; + var k; + + lengths = medium.lengths; + offsets = medium.offsets; + expected = medium.sines; + + ulps = 1; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + ns2 = floor( N / 2 ); + workspace = new Float64Array( floor( 2.5*N ) + 34 ); + sinti( N, workspace, 1, 0 ); + + for ( i = 0; i < ns2; i++ ) { + y = workspace[ i ]; + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); + } + } + t.end(); +}); + +tape( 'the function correctly initializes twiddle factors (medium sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var ns2; + var off; + var iw; + 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 ]; + ns2 = floor( N / 2 ); + iw = ns2 + N + 1; + workspace = new Float64Array( floor( 2.5*N ) + 34 ); + sinti( N, workspace, 1, 0 ); + + for ( i = 0; i < N+1; i++ ) { + y = workspace[ iw + 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 sine values (large sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var ns2; + var off; + var y; + var e; + var N; + var i; + var k; + + lengths = large.lengths; + offsets = large.offsets; + expected = large.sines; + + ulps = 1; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + ns2 = floor( N / 2 ); + workspace = new Float64Array( floor( 2.5*N ) + 34 ); + sinti( N, workspace, 1, 0 ); + + for ( i = 0; i < ns2; i++ ) { + y = workspace[ i ]; + e = expected[ off+i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e ); + } + } + t.end(); +}); + +tape( 'the function correctly initializes twiddle factors (large sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var ulps; + var ns2; + var off; + var iw; + 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 ]; + ns2 = floor( N / 2 ); + iw = ns2 + N + 1; + workspace = new Float64Array( floor( 2.5*N ) + 34 ); + sinti( N, workspace, 1, 0 ); + + for ( i = 0; i < N+1; i++ ) { + y = workspace[ iw + 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 ns2; + var N; + var i; + + N = 8; + ns2 = floor( N / 2 ); + workspace = new Float64Array( floor( 2.5*N ) + 34 ); + + for ( i = 0; i < workspace.length; i++ ) { + workspace[ i ] = i + 1.0; + } + sinti( N, workspace, 1, 0 ); + for ( i = ns2; i < ns2 + N + 1; i++ ) { + t.strictEqual( workspace[ i ], i + 1.0, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function correctly handles stride and offset parameters', function test( t ) { + var workspace; + var expected; + var stride; + var offset; + var ns2; + var nf; + var iw; + var fw; + var N; + var i; + + N = 9; + ns2 = floor( N / 2 ); + stride = 2; + offset = 3; + workspace = new Float64Array( offset + ( ( floor( 2.5*N ) + 34 ) * stride ) ); + + sinti( N, workspace, stride, offset ); + + fw = ns2 + ( 2 * ( N+1 ) ); + t.strictEqual( workspace[ offset + ( fw * stride ) ], N+1, 'returns expected value' ); + + nf = workspace[ offset + ( ( fw+1 ) * stride ) ]; + t.strictEqual( nf, 2, 'returns expected value' ); + t.strictEqual( workspace[ offset + ( ( fw+2 ) * stride ) ], 2, 'returns expected value' ); + t.strictEqual( workspace[ offset + ( ( fw+3 ) * stride ) ], 5, 'returns expected value' ); + + expected = new Float64Array( floor( 2.5*N ) + 34 ); + sinti( N, expected, 1, 0 ); + + iw = ns2 + N + 1; + for ( i = 0; i < N+1; i++ ) { + t.strictEqual( workspace[ offset + ( ( iw+i ) * stride ) ], expected[ iw+i ], 'returns expected value' ); + } + t.end(); +});