feat: add blas/ext/base/drsskbn

lib/node_modules/@stdlib/blas/ext/base/drsskbn/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.
+
+-->
+
+# drsskbn
+
+> Calculate the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays using an improved Kahan–Babuška algorithm.
+
+<section class="intro">
+
+The [residual sum of squares][wikipedia-residual-sum-of-squares] (also referred to as the **sum of squared residuals** (SSR) and the **sum of squared errors** (SSE)) is defined as
+
+<!-- <equation class="equation" label="eq:residual_sum_of_squares" align="center" raw="d = \sum_{i=0}^{N-1} (y_i - x_i)^2" alt="Equation for residual sum of squares."> -->
+
+```math
+\mathop{\mathrm{RSS}} = \sum_{i=0}^{N-1} (y_i - x_i)^2
+```
+
+<!-- <div class="equation" align="center" data-raw-text="d = \sum_{i=0}^{N-1} (y_i - x_i)^2" data-equation="eq:residual_sum_of_squares">
+    <img src="" alt="residual sum of squares.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var drsskbn = require( '@stdlib/blas/ext/base/drsskbn' );
+```
+
+#### drsskbn( N, x, strideX, y, strideY )
+
+Computes the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays using an improved Kahan–Babuška algorithm.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+var y = new Float64Array( [ 1.0, 1.0, -4.0 ] );
+
+var z = drsskbn( x.length, x, 1, y, 1 );
+// returns 45.0
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **x**: first input [`Float64Array`][@stdlib/array/float64].
+-   **strideX**: stride length for `x`.
+-   **y**: second input [`Float64Array`][@stdlib/array/float64].
+-   **strideY**: stride length for `y`.
+
+The `N` and stride parameters determine which elements in strided arrays are accessed at runtime. For example, to compute the [residual sum of squares][wikipedia-residual-sum-of-squares] of every other element in `x` and `y`
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
+var y = new Float64Array( [ 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
+
+var z = drsskbn( x.length, x, 1, y, 1 );
+// returns 72.0
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
+var y0 = new Float64Array( [ 8.0, -2.0, 3.0, -2.0, 7.0, -2.0, 0.0, -1.0 ] );
+
+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*1 ); // start at 2nd element
+
+var z = drsskbn( 4, x1, 2, y1, 2 );
+// returns 50.0
+```
+
+If `N` is less than or equal to `0`, the function returns `0`.
+
+#### drsskbn.ndarray( N, x, strideX, offsetX,  y, strideY, offsetY )
+
+Computes the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays using an improved Kahan–Babuška algorithm and alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+var y = new Float64Array( [ 1.0, 1.0, -4.0 ] );
+
+var z = drsskbn.ndarray( x.length, x, 1, 0, y, 1, 0 );
+// returns 45.0
+```
+
+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 calculate the [residual sum of squares][wikipedia-residual-sum-of-squares] for every other element in `x` and `y` starting from the second element
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, 6.0 ] );
+var y = new Float64Array( [ 8.0, -2.0, 3.0, -2.0, 7.0, -2.0, 0.0, -1.0, 4.0 ] );
+
+var z = drsskbn.ndarray( 4, x, 2, 1, y, 2, 1 );
+// returns 50.0
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0`, both functions return `0.0`.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var drsskbn = require( '@stdlib/blas/ext/base/drsskbn' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var x = discreteUniform( 10, -50, 50, opts );
+console.log( x );
+
+var y = discreteUniform( 10, -50, 50, opts );
+console.log( y );
+
+var d = drsskbn( x.length, x, 1, y, 1 );
+console.log( d );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- 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 -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/blas/ext/base/drsskbn.h"
+```
+
+#### stdlib_strided_drsskbn( N, \*X, strideX, \*Y, strideY )
+
+Computes the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays using an improved Kahan–Babuška algorithm.
+
+```c
+const double x[] = { 1.0, -2.0, 2.0 };
+const double y[] = { 1.0, 1.0, -4.0 };
+
+double z = stdlib_strided_drsskbn( 3, x, 1, y, 1 );
+// returns 45.0
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **X**: `[in] double*` first input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **Y**: `[in] double*` second input array.
+-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
+
+```c
+double stdlib_strided_drsskbn( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY );
+```
+
+<!--lint ignore maximum-heading-length-->
+
+#### stdlib_strided_drsskbn_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY )
+
+<!--lint enable maximum-heading-length-->
+
+Computes the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays using an improved Kahan–Babuška algorithm and alternative indexing semantics.
+
+```c
+const double x[] = { 1.0, -2.0, 2.0 };
+const double y[] = { 1.0, 1.0, -4.0 };
+
+double v = stdlib_strided_drsskbn_ndarray( 3, x, 1, 0, y, 1, 0 );
+// returns 45.0
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **X**: `[in] double*` first input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
+-   **Y**: `[in] double*` second input array.
+-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
+-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
+
+```c
+double stdlib_strided_drsskbn_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/blas/ext/base/drsskbn.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Create two strided arrays:
+    const double x[] = { 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 };
+    const double y[] = { 5.0, 12.0, -8.0, 15.0, 9.0, 0.0 };
+
+    // Specify the number of elements:
+    const int N = 5;
+
+    // Specify the stride lengths:
+    const int strideX = 1;
+    const int strideY = 1;
+
+    // Compute the residual sum of squares of `x` and `y`:
+    double d = stdlib_strided_drsskbn( N, x, strideX, y, strideY );
+
+    // Print the result:
+    printf( "drsskbn: %lf\n", d );
+
+    // Specify index offsets:
+    const int offsetX = 1;
+    const int offsetY = 1;
+
+    // Compute the residual sum of squares of `x` and `y` with offsets:
+    d = stdlib_strided_drsskbn_ndarray( N, x, strideX, offsetX, y, strideY, offsetY );
+
+    // Print the result:
+    printf( "drsskbn: %lf\n", d );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+* * *
+
+<section class="references">
+
+## References
+
+-   Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106][@neumaier:1974a].
+
+</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">
+
+[wikipedia-residual-sum-of-squares]: https://en.wikipedia.org/wiki/Residual_sum_of_squares
+
+[@stdlib/array/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float64
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106
+
+</section>
+
+<!-- /.links -->