diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/README.md
new file mode 100644
index 000000000000..44ff804838e2
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/README.md
@@ -0,0 +1,175 @@
+
+
+# sinqi
+
+> Initialize a single-precision floating-point workspace array for performing a quarter-wave sine transform.
+
+
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var sinqi = require( '@stdlib/fft/base/fftpack/float32/sinqi' );
+```
+
+#### sinqi( N, workspace, strideW, offsetW )
+
+Initializes a single-precision floating-point workspace array for performing a quarter-wave sine transform.
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+
+var N = 8;
+var workspace = new Float32Array( ( 3*N ) + 34 );
+
+var out = sinqi( N, workspace, 1, 0 );
+// returns
+
+var bool = ( out === workspace );
+// returns true
+
+var cosineTable = workspace.slice( 0, N );
+// returns [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ]
+
+var twiddleFactors = workspace.slice( 2*N, 3*N );
+// returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+
+var factors = workspace.slice( 3*N, ( 3*N ) + 4 );
+// returns [ 8, 2, 2, 4 ]
+```
+
+The function accepts the following arguments:
+
+- **N**: length of the sequence to transform.
+- **workspace**: workspace [`Float32Array`][@stdlib/array/float32].
+- **strideW**: stride length for `workspace`.
+- **offsetW**: starting index for `workspace`.
+
+
+
+
+
+
+
+
+
+## Notes
+
+- The workspace array is divided into four sections:
+
+ ```text
+ size = N N N 2+ceil(log2(N)/2)
+ ↓ ↓ ↓ ↓
+ | cosine table | scratch / workspace | twiddle factors | radix factor table |
+ ↑ ↑ ↑ ↑
+ i = 0 ... N ... 2N ... 3N ...
+ ```
+
+ - **cosine table**: a table of precomputed cosine coefficients used by quarter-wave 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`, the number of factors into which `N` was decomposed, and the individual integer radix factors.
+
+- In general, a workspace array should have `3N + 34` indexed elements (as `log2(N)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing the cosine coefficients, twiddle factors, and the factorization of `N` are updated.
+
+- The radix factor table is comprised as follows:
+
+ ```text
+ | sequence_length | number_of_factors | integer_factors |
+ ```
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+var zeroTo = require( '@stdlib/array/zero-to' );
+var logEach = require( '@stdlib/console/log-each' );
+var sinqi = require( '@stdlib/fft/base/fftpack/float32/sinqi' );
+
+var N = 8;
+var workspace = new Float32Array( ( 3*N ) + 34 );
+
+sinqi( N, workspace, 1, 0 );
+console.log( 'Sequence length: %d', N );
+
+console.log( 'Cosine table:' );
+var idx = zeroTo( N, 'float32' );
+logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 0, N ) );
+
+console.log( 'Twiddle factors:' );
+idx = zeroTo( N, 'float32' );
+logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 2*N, 3*N ) );
+
+console.log( 'Factorization:' );
+var nf = workspace[ (3*N)+1 ];
+
+console.log( ' number of factors: %d', nf );
+idx = zeroTo( nf, 'float32' );
+logEach( ' factor[ %d ]: %d', idx, workspace.slice( (3*N)+2, (3*N)+2+nf ) );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[@stdlib/array/float32]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float32
+
+
+
+
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/benchmark/benchmark.js
new file mode 100644
index 000000000000..7fcc5392b977
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/benchmark/benchmark.js
@@ -0,0 +1,101 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var format = require( '@stdlib/string/format' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var Float32Array = require( '@stdlib/array/float32' );
+var pkg = require( './../package.json' ).name;
+var sinqi = require( './../lib' );
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - sequence length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+ var workspace = new Float32Array( ( 3*N ) + 34 );
+ return benchmark;
+
+ /**
+ * Benchmark function.
+ *
+ * @private
+ * @param {Benchmark} b - benchmark instance
+ */
+ function benchmark( b ) {
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ sinqi( N, workspace, 1, 0 );
+ if ( isnan( workspace[ 2*N ] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( workspace[ 2*N ] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+ }
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+ var lengths;
+ var N;
+ var f;
+ var i;
+
+ lengths = [
+ 8,
+ 16,
+ 32,
+ 64,
+ 128,
+ 256,
+ 512,
+ 1024
+ ];
+
+ for ( i = 0; i < lengths.length; i++ ) {
+ N = lengths[ i ];
+ f = createBenchmark( N );
+ bench( format( '%s:N=%d', pkg, N ), f );
+ }
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/docs/repl.txt
new file mode 100644
index 000000000000..bbb4486c91fa
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/docs/repl.txt
@@ -0,0 +1,61 @@
+
+{{alias}}( N, workspace, strideW, offsetW )
+ Initializes a single-precision floating-point workspace array for performing
+ a quarter-wave sine transform.
+
+ The workspace array is divided into four sections:
+
+ 1. cosine table: the section ranges from indices 0 to N-1 and is used to
+ store a table of precomputed cosine coefficients used by quarter-wave sine
+ transforms.
+
+ 2. scratch/workspace: the section ranges from indices N to 2N-1 and is used
+ while performing transforms. This section is not updated during
+ initialization.
+
+ 3. twiddle factors: the section ranges from indices 2N to 3N-1 and stores a
+ table of reusable complex exponential constants as cosine/sine pairs.
+
+ 4. radix factor table: the section starts at index 3N and stores the
+ sequence length N, the number of factors into which N was decomposed, and
+ the individual integer radix factors.
+
+ Any remaining array space remains as unused storage.
+
+ Parameters
+ ----------
+ N: integer
+ Length of the sequence.
+
+ workspace: Float32Array
+ Workspace array.
+
+ strideW: integer
+ Stride length for `workspace`.
+
+ offsetW: integer
+ Starting index for `workspace`.
+
+ Returns
+ -------
+ out: Float32Array
+ Workspace array.
+
+ Examples
+ --------
+ > var N = 8;
+ > var workspace = new {{alias:@stdlib/array/float32}}( ( 3*N ) + 34 );
+ > var out = {{alias}}( N, workspace, 1, 0 )
+
+ > var bool = ( out === workspace )
+ true
+ > var cosineTable = workspace.slice( 0, N )
+ [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ]
+ > var twiddleFactors = workspace.slice( 2*N, 3*N )
+ [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+ > var factors = workspace.slice( 3*N, ( 3*N ) + 4 )
+ [ 8, 2, 2, 4 ]
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/docs/types/index.d.ts
new file mode 100644
index 000000000000..37b5ccddf1b1
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/docs/types/index.d.ts
@@ -0,0 +1,60 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Initializes a single-precision floating-point workspace array for performing a quarter-wave sine transform.
+*
+* ## Notes
+*
+* - The workspace array should have a length of at least `( 3*N ) + 34` elements.
+*
+* @param N - length of the sequence
+* @param workspace - workspace array
+* @param strideW - stride length for `workspace`
+* @param offsetW - starting index for `workspace`
+* @returns workspace array
+*
+* @example
+* var Float32Array = require( '@stdlib/array/float32' );
+*
+* var N = 8;
+* var workspace = new Float32Array( ( 3*N ) + 34 );
+*
+* var out = sinqi( N, workspace, 1, 0 );
+* // returns
+*
+* var bool = ( out === workspace );
+* // returns true
+*
+* var cosineTable = workspace.slice( 0, N );
+* // returns [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ]
+*
+* var twiddleFactors = workspace.slice( 2*N, 3*N );
+* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+*
+* var factors = workspace.slice( 3*N, ( 3*N ) + 4 );
+* // returns [ 8, 2, 2, 4 ]
+*/
+declare function sinqi( N: number, workspace: Float32Array, strideW: number, offsetW: number ): Float32Array;
+
+
+// EXPORTS //
+
+export = sinqi;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/docs/types/test.ts
new file mode 100644
index 000000000000..ec73588f1db4
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/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 sinqi = require( './index' );
+
+
+// TESTS //
+
+// The function returns a Float32Array...
+{
+ const workspace = new Float32Array( ( 3*8 ) + 34 );
+
+ sinqi( 8, workspace, 1, 0 ); // $ExpectType Float32Array
+}
+
+// The compiler throws an error if the function is provided a first argument which is not a number...
+{
+ const workspace = new Float32Array( ( 3*8 ) + 34 );
+
+ sinqi( '8', workspace, 1, 0 ); // $ExpectError
+ sinqi( true, workspace, 1, 0 ); // $ExpectError
+ sinqi( false, workspace, 1, 0 ); // $ExpectError
+ sinqi( null, workspace, 1, 0 ); // $ExpectError
+ sinqi( void 0, workspace, 1, 0 ); // $ExpectError
+ sinqi( [], workspace, 1, 0 ); // $ExpectError
+ sinqi( {}, workspace, 1, 0 ); // $ExpectError
+ sinqi( ( x: number ): number => x, workspace, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a second argument which is not a Float32Array...
+{
+ sinqi( 8, '50', 1, 0 ); // $ExpectError
+ sinqi( 8, 50, 1, 0 ); // $ExpectError
+ sinqi( 8, true, 1, 0 ); // $ExpectError
+ sinqi( 8, false, 1, 0 ); // $ExpectError
+ sinqi( 8, null, 1, 0 ); // $ExpectError
+ sinqi( 8, void 0, 1, 0 ); // $ExpectError
+ sinqi( 8, [], 1, 0 ); // $ExpectError
+ sinqi( 8, {}, 1, 0 ); // $ExpectError
+ sinqi( 8, ( x: number ): number => x, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a third argument which is not a number...
+{
+ const workspace = new Float32Array( ( 3*8 ) + 34 );
+
+ sinqi( 8, workspace, '1', 0 ); // $ExpectError
+ sinqi( 8, workspace, true, 0 ); // $ExpectError
+ sinqi( 8, workspace, false, 0 ); // $ExpectError
+ sinqi( 8, workspace, null, 0 ); // $ExpectError
+ sinqi( 8, workspace, void 0, 0 ); // $ExpectError
+ sinqi( 8, workspace, [], 0 ); // $ExpectError
+ sinqi( 8, workspace, {}, 0 ); // $ExpectError
+ sinqi( 8, workspace, ( x: number ): number => x, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a fourth argument which is not a number...
+{
+ const workspace = new Float32Array( ( 3*8 ) + 34 );
+
+ sinqi( 8, workspace, 1, '0' ); // $ExpectError
+ sinqi( 8, workspace, 1, true ); // $ExpectError
+ sinqi( 8, workspace, 1, false ); // $ExpectError
+ sinqi( 8, workspace, 1, null ); // $ExpectError
+ sinqi( 8, workspace, 1, void 0 ); // $ExpectError
+ sinqi( 8, workspace, 1, [] ); // $ExpectError
+ sinqi( 8, workspace, 1, {} ); // $ExpectError
+ sinqi( 8, workspace, 1, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+ const workspace = new Float32Array( ( 3*8 ) + 34 );
+
+ sinqi(); // $ExpectError
+ sinqi( 8 ); // $ExpectError
+ sinqi( 8, workspace ); // $ExpectError
+ sinqi( 8, workspace, 1 ); // $ExpectError
+ sinqi( 8, workspace, 1, 0, 123 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/examples/index.js
new file mode 100644
index 000000000000..d72001c80ca7
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/examples/index.js
@@ -0,0 +1,45 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+var Float32Array = require( '@stdlib/array/float32' );
+var zeroTo = require( '@stdlib/array/zero-to' );
+var logEach = require( '@stdlib/console/log-each' );
+var sinqi = require( './../lib' );
+
+var N = 8;
+var workspace = new Float32Array( ( 3*N ) + 34 );
+
+sinqi( N, workspace, 1, 0 );
+console.log( 'Sequence length: %d', N );
+
+console.log( 'Cosine table:' );
+var idx = zeroTo( N, 'float32' );
+logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 0, N ) );
+
+console.log( 'Twiddle factors:' );
+idx = zeroTo( N, 'float32' );
+logEach( ' workspace[ %d ] = %0.4f', idx, workspace.slice( 2*N, 3*N ) );
+
+console.log( 'Factorization:' );
+var nf = workspace[ (3*N)+1 ];
+
+console.log( ' number of factors: %d', nf );
+idx = zeroTo( nf, 'float32' );
+logEach( ' factor[ %d ]: %d', idx, workspace.slice( (3*N)+2, (3*N)+2+nf ) );
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/lib/index.js
new file mode 100644
index 000000000000..88158559d510
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/lib/index.js
@@ -0,0 +1,56 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+/**
+* Initialize a single-precision floating-point workspace array for performing a quarter-wave sine transform.
+*
+* @module @stdlib/fft/base/fftpack/float32/sinqi
+*
+* @example
+* var Float32Array = require( '@stdlib/array/float32' );
+* var sinqi = require( '@stdlib/fft/base/fftpack/float32/sinqi' );
+*
+* var N = 8;
+* var workspace = new Float32Array( ( 3*N ) + 34 );
+*
+* var out = sinqi( N, workspace, 1, 0 );
+* // returns
+*
+* var bool = ( out === workspace );
+* // returns true
+*
+* var cosineTable = workspace.slice( 0, N );
+* // returns [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ]
+*
+* var twiddleFactors = workspace.slice( 2*N, 3*N );
+* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+*
+* var factors = workspace.slice( 3*N, ( 3*N ) + 4 );
+* // returns [ 8, 2, 2, 4 ]
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/lib/main.js
new file mode 100644
index 000000000000..b2108d4e530c
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/lib/main.js
@@ -0,0 +1,166 @@
+/**
+* @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 cosqi = require( '@stdlib/fft/base/fftpack/float32/cosqi' );
+
+
+// MAIN //
+
+/**
+* Initializes a single-precision floating-point workspace array for performing a quarter-wave sine transform.
+*
+* ## Notes
+*
+* The workspace array is divided into four sections:
+*
+* ```text
+* size = N N N 2+ceil(log2(N)/2)
+* ↓ ↓ ↓ ↓
+* | cosine table | scratch/workspace | twiddle factors | radix factor table |
+* ↑ ↑ ↑ ↑
+* i = 0 ... N ... 2N ... 3N ...
+* ```
+*
+* where
+*
+* - **cosine table**: a table of precomputed cosine coefficients used by quarter-wave 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`.
+*
+* In general, a workspace array should have `3N + 34` indexed elements (as `log2(N)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing the cosine coefficients, twiddle factors, and the factorization of `N` are updated.
+*
+* > Note: FFTPACK only requires `3N+15`, but we increase that number here to accommodate larger workspace arrays, where `N` may exceed `2^30` indexed elements.
+*
+* The factorization section is comprised as follows:
+*
+* ```text
+* | sequence_length | number_of_factors | integer_factors |
+* ```
+*
+* The sequence length and number of factors (`nf`) comprise a single element each. Only the first `nf` elements in the integer factors section are written to, with the rest being unused.
+*
+* As for twiddle factors, these are small, reusable complex-exponential constants that appear inside each "butterfly" stage of a Cooley–Tukey–style FFT. Every arithmetic step in an FFT multiplies one intermediate value by some
+*
+* ```tex
+* W_N^k
+* ```
+*
+* where `W_N^k` is an N-th root of unity. Formally, in a forward FFT,
+*
+* ```tex
+* W_N^k = e^{-2\pi ik/N}
+* ```
+*
+* In a backward FFT,
+*
+* ```tex
+* W_N^k = e^{+2\pi ik/N}
+* ```
+*
+* As may be observed, `W_N^k` for forward and backward FFTs is the same, except the sign of the exponent is flipped. As a consequence, both forward and backward FFT callers can reuse the same set of twiddle factors, with those performing a forward transform (e.g., `sinqf`) multiplying with `(cos,-sin)` and those performing a backward transform (e.g., `sinqb`) 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, `sinqi` first writes the cosine table, and then initializes the remaining three sections using `rffti`.
+*
+* @param {PositiveInteger} N - length of the sequence to transform
+* @param {Float32Array} workspace - workspace array
+* @param {integer} strideW - stride length for `workspace`
+* @param {NonNegativeInteger} offsetW - starting index for `workspace`
+* @returns {Float32Array} workspace array
+*
+* @example
+* var Float32Array = require( '@stdlib/array/float32' );
+*
+* var N = 8;
+* var workspace = new Float32Array( ( 3*N ) + 34 );
+*
+* var out = sinqi( N, workspace, 1, 0 );
+* // returns
+*
+* var bool = ( out === workspace );
+* // returns true
+*
+* var cosineTable = workspace.slice( 0, N );
+* // returns [ ~0.98, ~0.92, ~0.83, ~0.7, ~0.56, ~0.38, ~0.2, ~0.0 ]
+*
+* var twiddleFactors = workspace.slice( 2*N, 3*N );
+* // returns [ ~0.707, ~0.707, 0, 0, 0, 0, 0, 0 ]
+*
+* var factors = workspace.slice( 3*N, ( 3*N ) + 4 );
+* // returns [ 8, 2, 2, 4 ]
+*/
+function sinqi( N, workspace, strideW, offsetW ) {
+ return cosqi( N, workspace, strideW, offsetW );
+}
+
+
+// EXPORTS //
+
+module.exports = sinqi;
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/package.json
new file mode 100644
index 000000000000..bcfe24daab9d
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/package.json
@@ -0,0 +1,66 @@
+{
+ "name": "@stdlib/fft/base/fftpack/float32/sinqi",
+ "version": "0.0.0",
+ "description": "Initialize a single-precision floating-point workspace array for performing a quarter-wave 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",
+ "sinqi",
+ "fourier",
+ "transform",
+ "twiddle",
+ "workspace",
+ "initialization",
+ "sine",
+ "single",
+ "float32"
+ ],
+ "__stdlib__": {}
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/Makefile b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/Makefile
new file mode 100644
index 000000000000..77b6a5f13549
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/Makefile
@@ -0,0 +1,137 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2026 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+endif
+
+# Specify the path to FFTPACK:
+FFTPACK ?=
+
+# Specify a list of FFTPACK source files:
+FFTPACK_SRC ?=
+
+# Determine the OS:
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate [position independent code][1]:
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of C targets:
+c_targets := runner.out
+
+
+# RULES #
+
+#/
+# Compiles C source files.
+#
+# @param {string} [C_COMPILER] - C compiler
+# @param {string} [CFLAGS] - C compiler flags
+# @param {(string|void)} [fPIC] - flag indicating whether to generate position independent code
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler
+# @param {string} CFLAGS - C compiler flags
+# @param {(string|void)} fPIC - flag indicating whether to generate position independent code
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) $(fPIC) -o $@ $(FFTPACK_SRC) $< -lm
+
+#/
+# Generates test fixtures.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
+
+#/
+# Removes generated test fixtures.
+#
+# @example
+# make clean-fixtures
+#/
+clean-fixtures:
+ $(QUIET) -rm -f *.json
+
+.PHONY: clean-fixtures
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/large.json b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/large.json
new file mode 100644
index 000000000000..41474425ee1b
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/large.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/medium.json b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/medium.json
new file mode 100644
index 000000000000..4c8e307035fd
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/medium.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/runner.c b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/runner.c
new file mode 100644
index 000000000000..e49de595b505
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/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 sinqi( int n, float *wsave );
+
+/**
+* Generates a random number on the interval [0,1].
+*
+* @return random number
+*/
+float rand_float( void ) {
+ int r = rand();
+ return (float)r / ( (float)RAND_MAX + 1.0f );
+}
+
+/**
+* Generates an array of pseudorandom integers drawn from a uniform distribution.
+*
+* ## Notes
+*
+* - WARNING: the method used here is not particularly robust, as some integer values may be sampled more frequently than others.
+*
+*
+* @param out output array
+* @param len array length
+* @param a lower bound (inclusive)
+* @param b upper bound (exclusive)
+*/
+void rand_array_i32( int *out, const unsigned int len, const int a, const int b ) {
+ unsigned int i;
+ unsigned int r;
+ float delta;
+
+ delta = (float)b - (float)a;
+
+ for ( i = 0; i < len; i++ ) {
+ r = (unsigned int)( delta * rand_float() ); // truncation
+ out[ i ] = (int)( a + r );
+ }
+}
+
+/**
+* Writes an array of floats to a file as a series of comma-separated values.
+*
+* @param f file to write to
+* @param x array of floats
+* @param len array length
+*/
+void write_array_f32( FILE *f, const float *x, const unsigned int len ) {
+ unsigned int i;
+
+ for ( i = 0; i < len; i++ ) {
+ fprintf( f, "%.9g", x[ i ] );
+ if ( i < len-1 ) {
+ fprintf( f, "," );
+ }
+ }
+}
+
+/**
+* Writes an array of integers to a file as a series of comma-separated values.
+*
+* @param f file to write to
+* @param x array of integers
+* @param len array length
+*/
+void write_array_i32( FILE *f, const int *x, const unsigned int len ) {
+ unsigned int i;
+
+ for ( i = 0; i < len; i++ ) {
+ fprintf( f, "%d", x[ i ] );
+ if ( i < len-1 ) {
+ fprintf( f, "," );
+ }
+ }
+}
+
+/**
+* Writes a named array of floats to a file as JSON.
+*
+* @param f file to write to
+* @param name array name
+* @param x data
+* @param len array length
+*/
+void write_named_array_f32( FILE *f, const char *name, const float *x, const unsigned int len ) {
+ fprintf( f, "\"%s\":[", name );
+ write_array_f32( f, x, len );
+ fprintf( f, "]" );
+}
+
+/**
+* Writes a named array of integers to a file as JSON.
+*
+* @param f file to write to
+* @param name array name
+* @param x data
+* @param len array length
+*/
+void write_named_array_i32( FILE *f, const char *name, const int *x, const unsigned int len ) {
+ fprintf( f, "\"%s\":[", name );
+ write_array_i32( f, x, len );
+ fprintf( f, "]" );
+}
+
+/**
+* Writes data to a file as JSON.
+*
+* ## Notes
+*
+* - This function SHOULD be tailored to the input data (e.g., input types, output types, number of arguments, etc) and may vary from use case to use case.
+*
+*
+* @param f file to write to
+* @param lengths sequence lengths
+* @param offsets cosine and twiddle offsets
+* @param cosines cosine values
+* @param twiddles twiddle factors
+* @param num number of sequence lengths
+* @param total total number of cosine and twiddle values
+*/
+void write_data_as_json( FILE *f, const int *lengths, const int *offsets, const float *cosines, const float *twiddles, const unsigned int num, const unsigned int total ) {
+ fprintf( f, "{" );
+ write_named_array_i32( f, "lengths", lengths, num );
+ fprintf( f, "," );
+ write_named_array_i32( f, "offsets", offsets, num );
+ fprintf( f, "," );
+ write_named_array_f32( f, "cosines", cosines, total );
+ fprintf( f, "," );
+ write_named_array_f32( f, "twiddles", twiddles, total );
+ fprintf( f, "}\n" );
+}
+
+/**
+* Generates test fixtures.
+*
+* @param lengths sequence lengths
+* @param offsets cosine and twiddle offsets into flat output array
+* @param num number of sequence lengths
+* @param total total number of cosine and twiddle values
+* @param name output filename
+*/
+void generate( const int *lengths, const int *offsets, const unsigned int num, const unsigned int total, const char *name ) {
+ unsigned int i;
+ unsigned int j;
+ float *cosines;
+ float *twiddles;
+ float *wsave;
+ FILE *f;
+ int off;
+ int n;
+
+ // Allocate an output array for cosine values:
+ cosines = (float*) malloc( total * sizeof(float) );
+ if ( cosines == NULL ) {
+ printf( "Error allocating memory.\n" );
+ exit( 1 );
+ }
+
+ // Allocate an output array for twiddle factors:
+ twiddles = (float*) malloc( total * sizeof(float) );
+ if ( twiddles == NULL ) {
+ printf( "Error allocating memory.\n" );
+ exit( 1 );
+ }
+
+ // Generate fixture data:
+ for ( i = 0; i < num; i++ ) {
+ n = lengths[ i ];
+ wsave = (float*) calloc( 3*n + 15, sizeof(float) );
+ if ( wsave == NULL ) {
+ printf( "Error allocating memory.\n" );
+ exit( 1 );
+ }
+ sinqi( n, wsave );
+
+ // Copy cosine region into flat array (N values starting at wsave[0]):
+ off = offsets[ i ];
+ for ( j = 0; j < (unsigned int)n; j++ ) {
+ cosines[ off + j ] = wsave[ j ];
+ }
+
+ // Copy twiddle region into flat array (N values starting at wsave[2*n]):
+ off = offsets[ i ];
+ for ( j = 0; j < (unsigned int)n; j++ ) {
+ twiddles[ off + j ] = wsave[ ( 2*n ) + j ];
+ }
+ free( wsave );
+ }
+ // Open a new file:
+ f = fopen( name, "w" );
+ if ( f == NULL ) {
+ printf( "Error opening file.\n" );
+ exit( 1 );
+ }
+
+ // Write data as JSON:
+ write_data_as_json( f, lengths, offsets, cosines, twiddles, num, total );
+
+ // Close the file:
+ fclose( f );
+
+ // Free allocated memory:
+ free( cosines );
+ free( twiddles );
+}
+
+/**
+* Computes offsets into flat cosine and twiddle arrays for each sequence length.
+*
+* @param offsets output array of offsets
+* @param lengths sequence lengths
+* @param num number of sequence lengths
+* @return total number of cosine and twiddle values
+*/
+unsigned int compute_offsets( int *offsets, const int *lengths, const unsigned int num ) {
+ unsigned int total;
+ unsigned int i;
+
+ total = 0;
+ for ( i = 0; i < num; i++ ) {
+ offsets[ i ] = total;
+ total += lengths[ i ];
+ }
+ return total;
+}
+
+/**
+* Main execution sequence.
+*/
+int main( void ) {
+ unsigned int total;
+ unsigned int num;
+ int *lengths;
+ int *offsets;
+
+ // Use the current time to seed the random number generator:
+ srand( time( NULL ) );
+
+ // Define the number of sequence lengths per range:
+ num = 10;
+
+ // Allocate arrays:
+ lengths = (int*) malloc( num * sizeof(int) );
+ if ( lengths == NULL ) {
+ printf( "Error allocating memory.\n" );
+ exit( 1 );
+ }
+ offsets = (int*) malloc( num * sizeof(int) );
+ if ( offsets == NULL ) {
+ printf( "Error allocating memory.\n" );
+ exit( 1 );
+ }
+
+ // Generate fixture data:
+ rand_array_i32( lengths, num, 2, 16 );
+ total = compute_offsets( offsets, lengths, num );
+ generate( lengths, offsets, num, total, "small.json" );
+
+ rand_array_i32( lengths, num, 16, 128 );
+ total = compute_offsets( offsets, lengths, num );
+ generate( lengths, offsets, num, total, "medium.json" );
+
+ rand_array_i32( lengths, num, 128, 1024 );
+ total = compute_offsets( offsets, lengths, num );
+ generate( lengths, offsets, num, total, "large.json" );
+
+ // Free allocated memory:
+ free( lengths );
+ free( offsets );
+
+ return 0;
+}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/small.json b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/small.json
new file mode 100644
index 000000000000..b8b62e4c21b4
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/fixtures/c/fftpack/small.json
@@ -0,0 +1 @@
+{"lengths":[4,6,3,12,5,11,5,2,15,5],"offsets":[0,4,10,13,25,30,41,46,48,63],"cosines":[0.923879504,0.707106769,0.382683426,-4.37113883e-08,0.965925813,0.866025388,0.707106769,0.49999997,0.258819073,-4.37113883e-08,0.866025388,0.49999997,-4.37113883e-08,0.991444886,0.965925813,0.923879504,0.866025388,0.793353319,0.707106769,0.60876137,0.49999997,0.382683426,0.258819073,0.130526125,-4.37113883e-08,0.95105654,0.809017003,0.587785244,0.309016973,-4.37113883e-08,0.989821434,0.959492981,0.909631968,0.841253519,0.755749524,0.654860675,0.540640771,0.415414959,0.281732529,0.142314747,-1.62920685e-07,0.95105654,0.809017003,0.587785244,0.309016973,-4.37113883e-08,0.707106769,-4.37113883e-08,0.994521916,0.978147626,0.95105654,0.91354543,0.866025388,0.809017003,0.74314481,0.669130564,0.587785244,0.49999997,0.406736612,0.309016973,0.207911655,0.10452842,-4.37113883e-08,0.95105654,0.809017003,0.587785244,0.309016973,-4.37113883e-08],"twiddles":[0,0,0,0,0.49999997,0.866025448,0,0,0,0,0,0,0,0.866025388,0.5,0,0.49999997,0.866025448,0,-4.37113883e-08,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.91354543,0.406736642,0.669130564,0.74314487,0,0.669130564,0.74314487,-0.104528509,0.994521916,0,0,0,0,0,0,0,0,0,0,0]}
diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/test.js
new file mode 100644
index 000000000000..7824a1b057ef
--- /dev/null
+++ b/lib/node_modules/@stdlib/fft/base/fftpack/float32/sinqi/test/test.js
@@ -0,0 +1,314 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var Float32Array = require( '@stdlib/array/float32' );
+var isAlmostSameValue = require( '@stdlib/number/float32/base/assert/is-almost-same-value' );
+var sinqi = 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 sinqi, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function has an arity of 4', function test( t ) {
+ t.strictEqual( sinqi.length, 4, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function returns a reference to the workspace array', function test( t ) {
+ var workspace;
+ var out;
+ var N;
+
+ N = 8;
+ workspace = new Float32Array( ( 3*N ) + 34 );
+ out = sinqi( N, workspace, 1, 0 );
+
+ t.strictEqual( out, workspace, 'same reference' );
+ t.end();
+});
+
+tape( 'the function correctly initializes cosine values (small sequence lengths)', function test( t ) {
+ var workspace;
+ var expected;
+ var lengths;
+ var offsets;
+ var ulps;
+ var off;
+ var y;
+ var e;
+ var N;
+ var i;
+ var k;
+
+ lengths = small.lengths;
+ offsets = small.offsets;
+ expected = small.cosines;
+
+ ulps = 1;
+ for ( k = 0; k < lengths.length; k++ ) {
+ N = lengths[ k ];
+ off = offsets[ k ];
+ workspace = new Float32Array( ( 3*N ) + 34 );
+ sinqi( N, workspace, 1, 0 );
+
+ t.strictEqual( workspace[ N ], 0.0, 'returns expected value' );
+ for ( i = 0; i < N; i++ ) {
+ y = workspace[ i ];
+ e = expected[ off+i ];
+ t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function correctly initializes twiddle factors (small sequence lengths)', function test( t ) {
+ var workspace;
+ var expected;
+ var lengths;
+ var offsets;
+ var ulps;
+ var off;
+ var y;
+ var e;
+ var N;
+ var i;
+ var k;
+
+ lengths = small.lengths;
+ offsets = small.offsets;
+ expected = small.twiddles;
+
+ ulps = 1;
+ for ( k = 0; k < lengths.length; k++ ) {
+ N = lengths[ k ];
+ off = offsets[ k ];
+ workspace = new Float32Array( ( 3*N ) + 34 );
+ sinqi( N, workspace, 1, 0 );
+
+ t.strictEqual( workspace[ (2*N) - 1 ], 0.0, 'returns expected value' );
+ for ( i = 0; i < N; i++ ) {
+ y = workspace[ (2*N) + i ];
+ e = expected[ off+i ];
+ t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function correctly initializes cosine values (medium sequence lengths)', function test( t ) {
+ var workspace;
+ var expected;
+ var lengths;
+ var offsets;
+ var ulps;
+ var off;
+ var y;
+ var e;
+ var N;
+ var i;
+ var k;
+
+ lengths = medium.lengths;
+ offsets = medium.offsets;
+ expected = medium.cosines;
+
+ ulps = 1;
+ for ( k = 0; k < lengths.length; k++ ) {
+ N = lengths[ k ];
+ off = offsets[ k ];
+ workspace = new Float32Array( ( 3*N ) + 34 );
+ sinqi( N, workspace, 1, 0 );
+
+ t.strictEqual( workspace[ N ], 0.0, 'returns expected value' );
+ for ( i = 0; i < N; i++ ) {
+ y = workspace[ i ];
+ e = expected[ off+i ];
+ t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function correctly initializes twiddle factors (medium sequence lengths)', function test( t ) {
+ var workspace;
+ var expected;
+ var lengths;
+ var offsets;
+ var ulps;
+ var off;
+ var y;
+ var e;
+ var N;
+ var i;
+ var k;
+
+ lengths = medium.lengths;
+ offsets = medium.offsets;
+ expected = medium.twiddles;
+
+ ulps = 1;
+ for ( k = 0; k < lengths.length; k++ ) {
+ N = lengths[ k ];
+ off = offsets[ k ];
+ workspace = new Float32Array( ( 3*N ) + 34 );
+ sinqi( N, workspace, 1, 0 );
+
+ t.strictEqual( workspace[ (2*N) - 1 ], 0.0, 'returns expected value' );
+ for ( i = 0; i < N; i++ ) {
+ y = workspace[ (2*N) + i ];
+ e = expected[ off+i ];
+ t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function correctly initializes cosine values (large sequence lengths)', function test( t ) {
+ var workspace;
+ var expected;
+ var lengths;
+ var offsets;
+ var ulps;
+ var off;
+ var y;
+ var e;
+ var N;
+ var i;
+ var k;
+
+ lengths = large.lengths;
+ offsets = large.offsets;
+ expected = large.cosines;
+
+ ulps = 1;
+ for ( k = 0; k < lengths.length; k++ ) {
+ N = lengths[ k ];
+ off = offsets[ k ];
+ workspace = new Float32Array( ( 3*N ) + 34 );
+ sinqi( N, workspace, 1, 0 );
+
+ t.strictEqual( workspace[ N ], 0.0, 'returns expected value' );
+ for ( i = 0; i < N; i++ ) {
+ y = workspace[ i ];
+ e = expected[ off+i ];
+ t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function correctly initializes twiddle factors (large sequence lengths)', function test( t ) {
+ var workspace;
+ var expected;
+ var lengths;
+ var offsets;
+ var ulps;
+ var off;
+ var y;
+ var e;
+ var N;
+ var i;
+ var k;
+
+ lengths = large.lengths;
+ offsets = large.offsets;
+ expected = large.twiddles;
+
+ ulps = 1;
+ for ( k = 0; k < lengths.length; k++ ) {
+ N = lengths[ k ];
+ off = offsets[ k ];
+ workspace = new Float32Array( ( 3*N ) + 34 );
+ sinqi( N, workspace, 1, 0 );
+
+ t.strictEqual( workspace[ (2*N) - 1 ], 0.0, 'returns expected value' );
+ for ( i = 0; i < N; i++ ) {
+ y = workspace[ (2*N) + i ];
+ e = expected[ off+i ];
+ t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within '+ulps+' ULPs. N: '+N+'. y: '+y+'. E: '+e );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function does not modify the scratch region of the workspace', function test( t ) {
+ var workspace;
+ var N;
+ var i;
+
+ N = 8;
+ workspace = new Float32Array( ( 3*N ) + 34 );
+
+ for ( i = 0; i < workspace.length; i++ ) {
+ workspace[ i ] = i + 1.0;
+ }
+ sinqi( N, workspace, 1, 0 );
+ for ( i = N; i < 2*N; i++ ) {
+ t.strictEqual( workspace[ i ], i + 1.0, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'the function correctly handles stride and offset parameters', function test( t ) {
+ var workspace;
+ var expected;
+ var stride;
+ var offset;
+ var nf;
+ var N;
+ var i;
+
+ N = 8;
+ stride = 2;
+ offset = 3;
+ workspace = new Float32Array( offset + ( ( ( 3*N ) + 34 ) * stride ) );
+
+ sinqi( N, workspace, stride, offset );
+
+ t.strictEqual( workspace[ offset + ( 3*N * stride ) ], N, 'returns expected value' );
+
+ nf = workspace[ offset + ( ( ( 3*N ) + 1 ) * stride ) ];
+ t.strictEqual( nf, 2, 'returns expected value' );
+ t.strictEqual( workspace[ offset + ( ( ( 3*N ) + 2 ) * stride ) ], 2, 'returns expected value' );
+ t.strictEqual( workspace[ offset + ( ( ( 3*N ) + 3 ) * stride ) ], 4, 'returns expected value' );
+
+ expected = new Float32Array( ( 3*N ) + 34 );
+ sinqi( N, expected, 1, 0 );
+
+ for ( i = 0; i < N; i++ ) {
+ t.strictEqual( workspace[ offset + ( ( (2*N)+i ) * stride ) ], expected[ (2*N)+i ], 'returns expected value' );
+ }
+ t.end();
+});