feat: add fft/base/fftpack/float32/hc2c

lib/node_modules/@stdlib/fft/base/fftpack/float32/hc2c/README.md

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+<!--
+
+@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.
+
+-->
+
+# hc2c
+
+> Convert a real-valued single-precision floating-point array in [FFTPACK][fftpack] half-complex format to a single-precision complex floating-point array.
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var hc2c = require( '@stdlib/fft/base/fftpack/float32/hc2c' );
+```
+
+#### hc2c( N, hc, strideHc, offsetHc, out, strideOut, offsetOut )
+
+Converts a real-valued single-precision floating-point array in [FFTPACK][fftpack] half-complex format to a single-precision complex floating-point array.
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+var Complex64Array = require( '@stdlib/array/complex64' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var rffti = require( '@stdlib/fft/base/fftpack/float32/rffti' );
+var rfftf = require( '@stdlib/fft/base/fftpack/float32/rfftf' );
+
+var N = 4;
+var w = new Float32Array( ( 2*N ) + 34 );
+
+rffti( N, w, 1, 0 );
+
+var r = new Float32Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+rfftf( N, r, 1, 0, w, 1, 0 );
+// r => <Float32Array>[ 10.0, -2.0, 2.0, -2.0 ]
+
+var out = new Complex64Array( floor( N/2 ) + 1 );
+
+hc2c( N, r, 1, 0, out, 1, 0 );
+// out => <Complex64Array>[ 10.0, 0.0, -2.0, 2.0, -2.0, 0.0 ]
+```
+
+The function accepts the following arguments:
+
+-   **N**: length of the original real sequence.
+-   **hc**: input array in [FFTPACK][fftpack] half-complex format.
+-   **strideHc**: stride length for `hc`.
+-   **offsetHc**: starting index for `hc`.
+-   **out**: output complex array.
+-   **strideOut**: stride length for `out`.
+-   **offsetOut**: starting index for `out`.
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+## Notes
+
+-   [FFTPACK][fftpack]'s [`rfftf`][@stdlib/fft/base/fftpack/float32/rfftf] stores the forward DFT of a length `N` real sequence in `N` real values using the following layout:
+
+    ```text
+    Even N: [ DC, Re(1), Im(1), Re(2), Im(2), ..., Re(N/2-1), Im(N/2-1), Nyquist ]
+    Odd N:  [ DC, Re(1), Im(1), Re(2), Im(2), ..., Re((N-1)/2), Im((N-1)/2) ]
+    ```
+
+    where `DC` is the zero-frequency component and `Nyquist` is the component at frequency `N/2` (even `N` only). Both are always purely real.
+
+-   The output is a complex-valued array of length `floor(N/2) + 1`. The `DC` and `Nyquist` components are stored with an explicit zero imaginary part.
+
+-   This half-complex format differs from other conventions (e.g., [FFTW][fftw-halfcomplex]). In FFTW's half-complex format, all real components are stored first, followed by imaginary components in reverse order.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+var Complex64Array = require( '@stdlib/array/complex64' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var rffti = require( '@stdlib/fft/base/fftpack/float32/rffti' );
+var rfftf = require( '@stdlib/fft/base/fftpack/float32/rfftf' );
+var hc2c = require( '@stdlib/fft/base/fftpack/float32/hc2c' );
+
+var N = 8;
+var opts = {
+    'dtype': 'float32'
+};
+var r = discreteUniform( N, -10, 10, opts );
+var w = new Float32Array( ( 2*N ) + 34 );
+
+console.log( r );
+
+rffti( N, w, 1, 0 );
+rfftf( N, r, 1, 0, w, 1, 0 );
+
+console.log( r );
+
+var out = new Complex64Array( floor( N/2 ) + 1 );
+
+hc2c( N, r, 1, 0, out, 1, 0 );
+
+console.log( out );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[fftpack]: https://www.netlib.org/fftpack/
+
+[fftw-halfcomplex]: https://www.fftw.org/fftw3_doc/The-Halfcomplex_002dformat-DFT.html
+
+[@stdlib/fft/base/fftpack/float32/rfftf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/fft/base/fftpack/float32/rfftf
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/fft/base/fftpack/float32/hc2c/benchmark/benchmark.js

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+/**
+* @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 uniform = require( '@stdlib/random/array/uniform' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var Complex64Array = require( '@stdlib/array/complex64' );
+var Float32Array = require( '@stdlib/array/float32' );
+var reinterpret = require( '@stdlib/strided/base/reinterpret-complex64' );
+var rffti = require( '@stdlib/fft/base/fftpack/float32/rffti' );
+var rfftf = require( '@stdlib/fft/base/fftpack/float32/rfftf' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var hc2c = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float32'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - sequence length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var out;
+	var w;
+	var r;
+	var M;
+
+	M = floor( N/2 ) + 1;
+	r = uniform( N, -100.0, 100.0, options );
+	w = new Float32Array( ( 2*N ) + 34 );
+	rffti( N, w, 1, 0 );
+	rfftf( N, r, 1, 0, w, 1, 0 );
+	out = new Complex64Array( M );
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var view;
+		var v;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			v = hc2c( N, r, 1, 0, out, 1, 0 );
+			if ( typeof v !== 'object' ) {
+				b.fail( 'should return an object' );
+			}
+		}
+		b.toc();
+		view = reinterpret( v, 0 );
+		if ( isnanf( view[ 0 ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var lengths;
+	var opts;
+	var iter;
+	var N;
+	var f;
+	var i;
+
+	lengths = [
+		8,
+		16,
+		32,
+		64,
+		128,
+		256,
+		512,
+		1024
+	];
+
+	iter = 1e6;
+
+	for ( i = 0; i < lengths.length; i++ ) {
+		N = lengths[ i ];
+		f = createBenchmark( N );
+		opts = {
+			'iterations': iter
+		};
+		bench( format( '%s:N=%d', pkg, N ), opts, f );
+		iter = floor( pow( iter, 3.0/4.0 ) );
+	}
+}
+
+main();

lib/node_modules/@stdlib/fft/base/fftpack/float32/hc2c/docs/repl.txt

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+
+{{alias}}( N, hc, strideHc, offsetHc, out, strideOut, offsetOut )
+    Converts a real-valued single-precision floating-point array in FFTPACK
+    half-complex format to a single-precision complex floating-point array.
+
+    The output complex array must have a length of at least `floor(N/2) + 1`.
+
+    Parameters
+    ----------
+    N: integer
+        Length of the original real sequence.
+
+    hc: Float32Array
+        Input array in FFTPACK half-complex format.
+
+    strideHc: integer
+        Stride length for `hc`.
+
+    offsetHc: integer
+        Starting index for `hc`.
+
+    out: Complex64Array
+        Output complex array.
+
+    strideOut: integer
+        Stride length for `out`.
+
+    offsetOut: integer
+        Starting index for `out`.
+
+    Returns
+    -------
+    out: Complex64Array
+        Output complex array.
+
+    Examples
+    --------
+    > var N = 4;
+    > var w = new {{alias:@stdlib/array/float32}}( ( 2*N ) + 34 );
+    > {{alias:@stdlib/fft/base/fftpack/float32/rffti}}( N, w, 1, 0 )
+    <Float32Array>
+    > var r = new {{alias:@stdlib/array/float32}}( [ 1.0, 2.0, 3.0, 4.0 ] );
+    > {{alias:@stdlib/fft/base/fftpack/float32/rfftf}}( N, r, 1, 0, w, 1, 0 )
+    <Float32Array>[ 10.0, -2.0, 2.0, -2.0 ]
+    > var out = new {{alias:@stdlib/array/complex64}}( ( N/2 ) + 1 );
+    > {{alias}}( N, r, 1, 0, out, 1, 0 )
+    <Complex64Array>[ 10.0, 0.0, -2.0, 2.0, -2.0, 0.0 ]
+
+    See Also
+    --------