feat: add blas/ext/base/ndarray/gsumpw

lib/node_modules/@stdlib/blas/ext/base/ndarray/gsumpw/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# gsumpw
+
+> Compute the sum of all elements in a one-dimensional ndarray using pairwise summation.
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var gsumpw = require( '@stdlib/blas/ext/base/ndarray/gsumpw' );
+```
+
+#### gsumpw( arrays )
+
+Computes the sum of all elements in a one-dimensional ndarray using pairwise summation.
+
+```javascript
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+
+var xbuf = [ 1.0, 3.0, 4.0, 2.0 ];
+var x = new ndarray( 'generic', xbuf, [ 4 ], [ 1 ], 0, 'row-major' );
+
+var v = gsumpw( [ x ] );
+// returns 10.0
+```
+
+The function has the following parameters:
+
+-   **arrays**: array-like object containing a one-dimensional input ndarray.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If provided an empty real-valued one-dimensional ndarray, the function returns `0.0`.
+-   In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var gsumpw = require( '@stdlib/blas/ext/base/ndarray/gsumpw' );
+
+var xbuf = discreteUniform( 10, -50, 50, {
+    'dtype': 'generic'
+});
+var x = new ndarray( 'generic', xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( x ) );
+
+var v = gsumpw( [ x ] );
+console.log( v );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="references">
+
+-   Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a].
+
+</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">
+
+[@higham:1993a]: https://doi.org/10.1137/0914050
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/ext/base/ndarray/gsumpw/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var pkg = require( './../package.json' ).name;
+var gsumpw = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var xbuf;
+	var x;
+
+	xbuf = uniform( len, -10.0, 10.0, options );
+	x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
+
+	return benchmark;
+
+	function benchmark( b ) {
+		var v;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			v = gsumpw( [ x ] );
+			if ( isnan( v ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( v ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( pkg+':len='+len, f );
+	}
+}
+
+main();

lib/node_modules/@stdlib/blas/ext/base/ndarray/gsumpw/docs/repl.txt

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+
+{{alias}}( arrays )
+    Computes the sum of all elements in a one-dimensional ndarray using pairwise
+    summation.
+
+    If provided an empty ndarray, the function returns `0.0`.
+
+    Parameters
+    ----------
+    arrays: ArrayLikeObject<ndarray>
+        Array-like object containing a one-dimensional input ndarray.
+
+    Returns
+    -------
+    out: number
+        Sum.
+
+    Examples
+    --------
+    > var xbuf = [ 1.0, 2.0, 3.0 ];
+    > var dt = 'generic';
+    > var sh = [ xbuf.length ];
+    > var sx = [ 1 ];
+    > var ox = 0;
+    > var ord = 'row-major';
+    > var x = new {{alias:@stdlib/ndarray/ctor}}( dt, xbuf, sh, sx, ox, ord );
+    > {{alias}}( [ x ] )
+    6.0
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/blas/ext/base/ndarray/gsumpw/docs/types/index.d.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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
+
+/// <reference types="@stdlib/types"/>
+
+import { typedndarray } from '@stdlib/types/ndarray';
+
+/**
+* Computes the sum of all elements in a one-dimensional ndarray using pairwise summation.
+*
+* @param arrays - array-like object containing an input ndarray
+* @returns sum
+*
+* @example
+* var ndarray = require( '@stdlib/ndarray/base/ctor' );
+*
+* var xbuf = [ 1.0, 3.0, 4.0, 2.0 ];
+* var x = new ndarray( 'generic', xbuf, [ 4 ], [ 1 ], 0, 'row-major' );
+*
+* var v = gsumpw( [ x ] );
+* // returns 10.0
+*/
+declare function gsumpw<T extends typedndarray<number> = typedndarray<number>>( arrays: [ T ] ): number;
+
+
+// EXPORTS //
+
+export = gsumpw;

lib/node_modules/@stdlib/blas/ext/base/ndarray/gsumpw/docs/types/test.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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.
+*/
+
+/* eslint-disable space-in-parens */
+
+import zeros = require( '@stdlib/ndarray/zeros' );
+import gsumpw = require( './index' );
+
+
+// TESTS //
+
+// The function returns a sum...
+{
+	const x = zeros( [ 10 ], {
+		'dtype': 'float64'
+	});
+
+	gsumpw( [ x ] ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a first argument which is not an array of ndarrays...
+{
+	gsumpw( '10' ); // $ExpectError
+	gsumpw( 10 ); // $ExpectError
+	gsumpw( true ); // $ExpectError
+	gsumpw( false ); // $ExpectError
+	gsumpw( null ); // $ExpectError
+	gsumpw( undefined ); // $ExpectError
+	gsumpw( [] ); // $ExpectError
+	gsumpw( {} ); // $ExpectError
+	gsumpw( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+	const x = zeros( [ 10 ], {
+		'dtype': 'float64'
+	});
+
+	gsumpw(); // $ExpectError
+	gsumpw( [ x ], {} ); // $ExpectError
+}

lib/node_modules/@stdlib/blas/ext/base/ndarray/gsumpw/examples/index.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var gsumpw = require( './../lib' );
+
+var xbuf = discreteUniform( 10, -50, 50, {
+	'dtype': 'generic'
+});
+var x = new ndarray( 'generic', xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( x ) );
+
+var v = gsumpw( [ x ] );
+console.log( v );