feat: add blas/ext/base/saxpby

lib/node_modules/@stdlib/blas/ext/base/saxpby/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.
+
+-->
+
+# saxpby
+
+> Multiply a single-precision floating-point strided array `x` by a constant and add the result to a single-precision floating-point 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/saxpy`][@stdlib/blas/base/saxpy] and is a common BLAS extension in libraries such as Intel MKL, OpenBLAS, and others.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var saxpby = require( '@stdlib/blas/ext/base/saxpby' );
+```
+
+#### saxpby( N, alpha, x, strideX, beta, y, strideY )
+
+Multiplies a single-precision floating-point strided array `x` by a constant and adds the result to a single-precision floating-point strided array `y` multiplied by a constant.
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+
+var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+var y = new Float32Array( [ 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+saxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
+// y => <Float32Array>[ 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 [`Float32Array`][@stdlib/array/float32].
+-   **strideX**: stride length for `x`.
+-   **beta**: second scalar constant.
+-   **y**: output [`Float32Array`][@stdlib/array/float32].
+-   **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 of `x` by `alpha` and add to every other element of `y` multiplied by `beta`:
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+
+var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var y = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
+
+saxpby( 3, 5.0, x, 2, 2.0, y, 2 );
+// y => <Float32Array>[ 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 Float32Array = require( '@stdlib/array/float32' );
+
+// Initial arrays...
+var x0 = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var y0 = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
+
+// Create offset views...
+var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element
+
+saxpby( 3, 5.0, x1, 1, 2.0, y1, 1 );
+// y0 => <Float32Array>[ 7.0, 8.0, 28.0, 35.0, 42.0, 12.0 ]
+```
+
+#### saxpby.ndarray( N, alpha, x, strideX, offsetX, beta, y, strideY, offsetY )
+
+Multiplies a single-precision floating-point strided array `x` by a constant and adds the result to a single-precision floating-point strided array `y` multiplied by a constant using alternative indexing semantics.
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+
+var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+var y = new Float32Array( [ 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+saxpby.ndarray( x.length, 5.0, x, 1, 0, 2.0, y, 1, 0 );
+// y => <Float32Array>[ 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 Float32Array = require( '@stdlib/array/float32' );
+
+var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+var y = new Float32Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
+
+saxpby.ndarray( 3, 5.0, x, 1, x.length-3, 2.0, y, 1, y.length-3 );
+// y => <Float32Array>[ 6.0, 7.0, 31.0, 38.0, 45.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0`, both functions return `y` unchanged.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var saxpby = require( '@stdlib/blas/ext/base/saxpby' );
+
+var x = discreteUniform( 10, -100, 100, {
+    'dtype': 'float32'
+});
+console.log( x );
+
+var y = discreteUniform( 10, -100, 100, {
+    'dtype': 'float32'
+});
+console.log( y );
+
+saxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
+console.log( y );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/blas/ext/base/saxpby.h"
+```
+
+#### stdlib_strided_saxpby( N, alpha, \*X, strideX, beta, \*Y, strideY )
+
+Multiplies a single-precision floating-point strided array `x` by a constant and adds the result to a single-precision floating-point strided array `y` multiplied by a constant.
+
+```c
+const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
+float y[] = { 2.0f, 3.0f, 4.0f, 5.0f };
+
+stdlib_strided_saxpby( 4, 5.0f, x, 1, 2.0f, y, 1 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **alpha**: `[in] float` first scalar constant.
+-   **X**: `[in] float*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **beta**: `[in] float` second scalar constant.
+-   **Y**: `[inout] float*` output array.
+-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
+
+```c
+void stdlib_strided_saxpby( const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const float beta, float *Y, const CBLAS_INT strideY );
+```
+
+<!--lint disable maximum-heading-length-->
+
+#### stdlib_strided_saxpby_ndarray( N, alpha, \*X, strideX, offsetX, beta, \*Y, strideY, offsetY )
+
+<!--lint enable maximum-heading-length-->
+
+Multiplies a single-precision floating-point strided array `x` by a constant and adds the result to a single-precision floating-point strided array `y` multiplied by a constant using alternative indexing semantics.
+
+```c
+const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
+float y[] = { 2.0f, 3.0f, 4.0f, 5.0f };
+
+stdlib_strided_saxpby_ndarray( 4, 5.0f, x, 1, 0, 2.0f, y, 1, 0 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **alpha**: `[in] float` first scalar constant.
+-   **X**: `[in] float*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
+-   **beta**: `[in] float` second scalar constant.
+-   **Y**: `[inout] float*` output array.
+-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
+-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
+
+```c
+void stdlib_strided_saxpby_ndarray( const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const float beta, float *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/blas/ext/base/saxpby.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Create strided arrays:
+    const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
+    float y[] = { 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f };
+
+    // Specify the number of indexed elements:
+    const int N = 8;
+
+    // Specify strides:
+    const int strideX = 1;
+    const int strideY = 1;
+
+    // Multiply `x` by a constant and add to `y` multiplied by a constant:
+    stdlib_strided_saxpby( N, 5.0f, x, strideX, 2.0f, y, strideY );
+
+    // Print the result:
+    for ( int i = 0; i < 8; i++ ) {
+        printf( "y[ %i ] = %f\n", i, y[ i ] );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- 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-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@stdlib/array/float32]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float32
+
+[@stdlib/blas/base/saxpy]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/base/saxpy
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->