feat: add blas/ext/base/gaxpby

lib/node_modules/@stdlib/blas/ext/base/gaxpby/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.
+
+-->
+
+# gaxpby
+
+> Multiply a strided array `x` by a constant and add the result to a strided array `y` multiplied by a constant.
+
+<section class="intro">
+
+This BLAS extension implements the operation
+
+<!-- <equation class="equation" label="eq:axpby" align="center" raw="\mathbf{y} = \alpha \mathbf{x} + \beta \mathbf{y}" alt="Equation for axpby operation."> -->
+
+```math
+\mathbf{y} = \alpha \mathbf{x} + \beta \mathbf{y}
+```
+
+<!-- </equation> -->
+
+This API is complementary to the package [`@stdlib/blas/base/gaxpy`][@stdlib/blas/base/gaxpy] and is a common BLAS extension in libraries such as Intel MKL, OpenBLAS, and others.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var gaxpby = require( '@stdlib/blas/ext/base/gaxpby' );
+```
+
+#### gaxpby( N, alpha, x, strideX, beta, y, strideY )
+
+Multiplies a strided array `x` by a constant and adds the result to a strided array `y` multiplied by a constant.
+
+```javascript
+var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
+var y = [ 2.0, 3.0, 4.0, 5.0, 6.0 ];
+
+gaxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
+// y => [ 9.0, 16.0, 23.0, 30.0, 37.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **alpha**: first scalar constant.
+-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
+-   **strideX**: stride length for `x`.
+-   **beta**: second scalar constant.
+-   **y**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
+-   **strideY**: stride length for `y`.
+
+The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to multiply every other element in `x` by `alpha` and add to every other element in `y` multiplied by `beta`:
+
+```javascript
+var x = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
+var y = [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ];
+
+gaxpby( 3, 5.0, x, 2, 2.0, y, 2 );
+// y => [ 19.0, 8.0, 33.0, 10.0, 47.0, 12.0 ]
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
+
+// Create offset views...
+var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element
+
+gaxpby( 3, 5.0, x1, 1, 2.0, y1, 1 );
+// y0 => <Float64Array>[ 7.0, 8.0, 28.0, 35.0, 42.0, 12.0 ]
+```
+
+#### gaxpby.ndarray( N, alpha, x, strideX, offsetX, beta, y, strideY, offsetY )
+
+Multiplies a strided array `x` by a constant and adds the result to a strided array `y` multiplied by a constant using alternative indexing semantics.
+
+```javascript
+var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
+var y = [ 2.0, 3.0, 4.0, 5.0, 6.0 ];
+
+gaxpby.ndarray( x.length, 5.0, x, 1, 0, 2.0, y, 1, 0 );
+// y => [ 9.0, 16.0, 23.0, 30.0, 37.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index for `x`.
+-   **offsetY**: starting index for `y`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to multiply the last three elements of `x` by `alpha` and add to the last three elements of `y` multiplied by `beta`:
+
+```javascript
+var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
+var y = [ 6.0, 7.0, 8.0, 9.0, 10.0 ];
+
+gaxpby.ndarray( 3, 5.0, x, 1, x.length-3, 2.0, y, 1, y.length-3 );
+// y => [ 6.0, 7.0, 31.0, 38.0, 45.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0`, both functions return `y` unchanged.
+-   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]).
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var gaxpby = require( '@stdlib/blas/ext/base/gaxpby' );
+
+var x = discreteUniform( 10, -100, 100, {
+    'dtype': 'float64'
+});
+console.log( x );
+
+var y = discreteUniform( 10, -100, 100, {
+    'dtype': 'float64'
+});
+console.log( y );
+
+gaxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
+console.log( y );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- 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">
+
+[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
+
+[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
+
+[@stdlib/blas/base/gaxpy]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/base/gaxpy
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/ext/base/gaxpby/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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var gaxpby = require( './../lib/main.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Create a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var x = uniform( len, -100, 100, options );
+	var y = uniform( len, -100, 100, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var z;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			z = gaxpby( x.length, 5.0, x, 1, 3.0, y, 1 );
+			if ( isnan( z[ i%x.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( z[ i%x.length ] ) ) {
+			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( format( '%s:len=%d', pkg, len ), f );
+	}
+}
+
+main();