feat: add accessor arrays support to blas/ext/base/gcusumpw

lib/node_modules/@stdlib/blas/ext/base/gcusumpw/README.md

@@ -129,6 +129,7 @@ gcusumpw.ndarray( 4, 0.0, x, 2, 1, y, -1, y.length-1 );
 
 -   If `N <= 0`, both functions return `y` unchanged.
 -   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.
+-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor])
 -   Depending on the environment, the typed versions ([`dcusumpw`][@stdlib/blas/ext/base/dcusumpw], [`scusumpw`][@stdlib/blas/ext/base/scusumpw], etc.) are likely to be significantly more performant.
 
 </section>
@@ -197,6 +198,8 @@ console.log( y );
 
 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
 
+[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
+
 [@higham:1993a]: https://doi.org/10.1137/0914050
 
 <!-- <related-links> -->

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

@@ -20,7 +20,17 @@
 
 /// <reference types="@stdlib/types"/>
 
-import { NumericArray } from '@stdlib/types/array';
+import { NumericArray, Collection, AccessorArrayLike } from '@stdlib/types/array';
+
+/**
+* Input array.
+*/
+type InputArray = NumericArray | Collection<number> | AccessorArrayLike<number>;
+
+/**
+* Output array.
+*/
+type OutputArray = NumericArray | Collection<number> | AccessorArrayLike<number>;
 
 /**
 * Interface describing `gcusumpw`.
@@ -44,7 +54,7 @@ interface Routine {
 	* gcusumpw( x.length, 0.0, x, 1, y, 1 );
 	* // y => [ 1.0, -1.0, 1.0 ]
 	*/
-	( N: number, sum: number, x: NumericArray, strideX: number, y: NumericArray, strideY: number ): NumericArray;
+	<T extends OutputArray>( N: number, sum: number, x: InputArray, strideX: number, y: T, strideY: number ): T;
 
 	/**
 	* Computes the cumulative sum of strided array elements using pairwise summation and alternative indexing semantics.
@@ -66,7 +76,7 @@ interface Routine {
 	* gcusumpw.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 );
 	* // y => [ 1.0, -1.0, 1.0 ]
 	*/
-	ndarray( N: number, sum: number, x: NumericArray, strideX: number, offsetX: number, y: NumericArray, strideY: number, offsetY: number ): NumericArray;
+	ndarray<T extends OutputArray>( N: number, sum: number, x: InputArray, strideX: number, offsetX: number, y: T, strideY: number, offsetY: number ): T;
 }
 
 /**

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

@@ -16,6 +16,7 @@
 * limitations under the License.
 */
 
+import AccessorArray = require( '@stdlib/array/base/accessor' );
 import gcusumpw = require( './index' );
 
 
@@ -26,7 +27,8 @@ import gcusumpw = require( './index' );
 	const x = new Float64Array( 10 );
 	const y = new Float64Array( 10 );
 
-	gcusumpw( x.length, 0.0, x, 1, y, 1 ); // $ExpectType NumericArray
+	gcusumpw( x.length, 0.0, x, 1, y, 1 ); // $ExpectType Float64Array
+	gcusumpw( x.length, 0.0, new AccessorArray( x ), 1, new AccessorArray( y ), 1 ); // $ExpectType AccessorArray<number>
 }
 
 // The compiler throws an error if the function is provided a first argument which is not a number...
@@ -139,7 +141,8 @@ import gcusumpw = require( './index' );
 	const x = new Float64Array( 10 );
 	const y = new Float64Array( 10 );
 
-	gcusumpw.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 ); // $ExpectType NumericArray
+	gcusumpw.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 ); // $ExpectType Float64Array
+	gcusumpw.ndarray( x.length, 0.0, new AccessorArray( x ), 1, 0, new AccessorArray( y ), 1, 0 ); // $ExpectType AccessorArray<number>
 }
 
 // The compiler throws an error if the `ndarray` method is provided a first argument which is not a number...

lib/node_modules/@stdlib/blas/ext/base/gcusumpw/lib/accessors.js

@@ -0,0 +1,113 @@
+/**
+* @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 floor = require( '@stdlib/math/base/special/floor' );
+
+
+// VARIABLES //
+
+// Blocksize for pairwise summation:
+var BLOCKSIZE = 128;
+
+
+// MAIN //
+
+/**
+* Computes the cumulative sum of strided array elements using pairwise summation.
+*
+* ## Method
+*
+* -   This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
+*
+* ## References
+*
+* -   Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050](https://doi.org/10.1137/0914050).
+*
+* @private
+* @param {PositiveInteger} N - number of indexed elements
+* @param {number} sum - initial sum
+* @param {Object} x - input array object
+* @param {Collection} x.data - input array data
+* @param {Array<Function>} x.accessors - array element accessors
+* @param {integer} strideX - stride length for `x`
+* @param {NonNegativeInteger} offsetX - starting index for `x`
+* @param {Object} y - output array object
+* @param {Collection} y.data - output array data
+* @param {Array<Function>} y.accessors - array element accessors
+* @param {integer} strideY - stride length for `y`
+* @param {NonNegativeInteger} offsetY - starting index for `y`
+* @returns {Object} output array object
+*
+* @example
+* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
+* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
+*
+* var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
+* var y = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* gcusumpw( 4, 0.0, arraylike2object( toAccessorArray( x ) ), 2, 1, arraylike2object( toAccessorArray( y ) ), 1, 0 );
+* // y => [ 1.0, -1.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]
+*/
+function gcusumpw( N, sum, x, strideX, offsetX, y, strideY, offsetY ) {
+	var xbuf;
+	var ybuf;
+	var xget;
+	var yget;
+	var yset;
+	var ix;
+	var iy;
+	var s;
+	var n;
+	var i;
+
+	// Cache reference to array data:
+	xbuf = x.data;
+	ybuf = y.data;
+
+	// Cache reference to the element accessors:
+	xget = x.accessors[ 0 ];
+	yget = y.accessors[ 0 ];
+	yset = y.accessors[ 1 ];
+
+	ix = offsetX;
+	iy = offsetY;
+	if ( N <= BLOCKSIZE ) {
+		s = 0.0;
+		for ( i = 0; i < N; i++ ) {
+			s += xget( xbuf, ix );
+			yset( ybuf, iy, sum + s);
+			ix += strideX;
+			iy += strideY;
+		}
+		return y;
+	}
+	n = floor( N/2 );
+	gcusumpw( n, sum, x, strideX, ix, y, strideY, iy );
+	iy += (n-1) * strideY;
+	gcusumpw( N-n, yget( ybuf, iy ), x, strideX, ix+(n*strideX), y, strideY, iy+strideY ); // eslint-disable-line max-len
+	return y;
+}
+
+
+// EXPORTS //
+
+module.exports = gcusumpw;

lib/node_modules/@stdlib/blas/ext/base/gcusumpw/lib/ndarray.js

@@ -20,7 +20,9 @@
 
 // MODULES //
 
+var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
 var floor = require( '@stdlib/math/base/special/floor' );
+var accessors = require( './accessors.js' );
 
 
 // VARIABLES //
@@ -62,13 +64,21 @@ var BLOCKSIZE = 128;
 function gcusumpw( N, sum, x, strideX, offsetX, y, strideY, offsetY ) {
 	var ix;
 	var iy;
+	var ox;
+	var oy;
 	var s;
 	var n;
 	var i;
 
 	if ( N <= 0 ) {
 		return y;
 	}
+	ox = arraylike2object( x );
+	oy = arraylike2object( y );
+	if ( ox.accessorProtocol || oy.accessorProtocol ) {
+		accessors( N, sum, ox, strideX, offsetX, oy, strideY, offsetY );
+		return y;
+	}
 	ix = offsetX;
 	iy = offsetY;
 	if ( N <= BLOCKSIZE ) {