feat: add /blas/ext/base/dnancusumkbn2

lib/node_modules/@stdlib/blas/ext/base/dnancusumkbn2/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.
+
+-->
+
+# dnancusumkbn2
+
+> Calculate the cumulative sum of double-precision floating-point strided array elements, ignoring `NaN` values and using a second-order iterative Kahan–Babuška algorithm.
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dnancusumkbn2 = require( '@stdlib/blas/ext/base/dnancusumkbn2' );
+```
+
+#### dnancusumkbn2( N, sum, x, strideX, y, strideY )
+
+Computes the cumulative sum of double-precision floating-point strided array elements,ignoring `NaN` values and using a second-order iterative Kahan–Babuška algorithm.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, -2.0, NaN ] );
+var y = new Float64Array( x.length );
+
+dnancusumkbn2( x.length, 0.0, x, 1, y, 1 );
+// y => <Float64Array>[ 1.0, -1.0, -1.0 ]
+
+x = new Float64Array( [ 1.0, -2.0, NaN ] );
+y = new Float64Array( x.length );
+
+dnancusumkbn2( x.length, 10.0, x, 1, y, 1 );
+// y => <Float64Array>[ 11.0, 9.0, 9.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **sum**: initial sum.
+-   **x**: input [`Float64Array`][@stdlib/array/float64].
+-   **strideX**: stride length for `x`.
+-   **y**: output [`Float64Array`][@stdlib/array/float64].
+-   **strideY**: stride length for `y`.
+
+The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the cumulative sum of every other element:
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, NaN, 3.0, 4.0, 2.0 ] );
+var y = new Float64Array( x.length );
+
+var v = dnancusumkbn2( 4, 0.0, x, 2, y, 1 );
+// y => <Float64Array>[ 1.0, 3.0, 3.0, 7.0, 0.0, 0.0, 0.0, 0.0 ]
+```
+
+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' );
+
+// Initial arrays...
+var x0 = new Float64Array( [ 2.0, NaN, 2.0, NaN, -2.0, 2.0, 3.0, 4.0 ] );
+var y0 = new Float64Array( x0.length );
+
+// 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*3 ); // start at 4th element
+
+dnancusumkbn2( 4, 0.0, x1, -2, y1, 1 );
+// y0 => <Float64Array>[ 0.0, 0.0, 0.0, 4.0, 6.0, 6.0, 6.0, 0.0 ]
+```
+
+#### dnancusumkbn2.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )
+
+Computes the cumulative sum of double-precision floating-point strided array elements, ignoring `NaN` values and using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, -2.0, NaN ] );
+var y = new Float64Array( x.length );
+
+dnancusumkbn2.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 );
+// y => <Float64Array>[ 1.0, -1.0, -1.0 ]
+```
+
+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 cumulative sum of every other value in `x` starting from the second value and to store in the last `N` elements of `y` starting from the last element:
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 2.0, 1.0, 2.0, NaN, -2.0, 2.0, 3.0, NaN ] );
+var y = new Float64Array( x.length );
+
+dnancusumkbn2.ndarray( 4, 0.0, x, 2, 1, y, -1, y.length-1 );
+// y => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 1.0, 1.0 ]
+```
+
+</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 bernoulli = require( '@stdlib/random/base/bernoulli' );
+var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
+var filledarrayBy = require( '@stdlib/array/filled-by' );
+var Float64Array = require( '@stdlib/array/float64' );
+var dnancusumkbn2 = require( '@stdlib/blas/ext/base/dnancusumkbn2' );
+
+function rand() {
+    if ( bernoulli( 0.5 ) < 1 ) {
+        return discreteUniform( 0, 100 );
+    }
+    return NaN;
+}
+
+var x = filledarrayBy( 10, 'float64', rand );
+console.log( x );
+
+var y = new Float64Array( x.length );
+console.log( y );
+
+dnancusumkbn2( x.length, 0.0, x, 1, y, 1 );
+console.log( y );
+```
+
+</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/dnancusumkbn2.h"
+```
+
+#### stdlib_strided_dnancusumkbn2( N, sum, \*X, strideX, \*Y, strideY )
+
+Computes the cumulative sum of double-precision floating-point strided array elements, ingoring `NaN` values and using a second-order iterative Kahan–Babuška algorithm.
+
+```c
+const double x[] = { 1.0, 2.0, 3.0, 0.0/0.0 }
+double y[] = { 0.0, 0.0, 0.0, 0.0 }
+
+stdlib_strided_dnancusumkbn2( 4, 0.0, x, 1, y, 1 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **sum**: `[in] double` initial sum.
+-   **X**: `[in] double*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **Y**: `[out] double*` output array.
+-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
+
+```c
+void stdlib_strided_dnancusumkbn2( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, double *Y, const CBLAS_INT strideY );
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### stdlib_strided_dnancusumkbn2_ndarray( N, sum, \*X, strideX, offsetX, \*Y, strideY, offsetY )
+
+<!-- lint enable maximum-heading-length -->
+
+Computes the cumulative sum of double-precision floating-point strided array elements, ignoring `NaN` values and using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics.
+
+```c
+const double x[] = { 1.0, 2.0, 3.0, 0.0/0.0 }
+double y[] = { 0.0, 0.0, 0.0, 0.0 }
+
+stdlib_strided_dnancusumkbn2_ndarray( 4, 0.0, x, 1, 0, y, 1, 0 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **sum**: `[in] double` initial sum.
+-   **X**: `[in] double*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
+-   **Y**: `[out] double*` output array.
+-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
+-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
+
+```c
+void stdlib_strided_dnancusumkbn2_ndarray( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, 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/dnancusumkbn2.h"
+
+int main( void ) {
+    // Create strided arrays:
+    const double x[] = { 1.0, 2.0, 3.0, 0.0/0.0, 5.0, 6.0, 7.0, 0.0/0.0 };
+    double y[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+
+    // Specify the number of elements:
+    const int N = 4;
+
+    // Specify stride lengths:
+    const int strideX = 2;
+    const int strideY = -2;
+
+    // Compute the cumulative sum:
+    stdlib_strided_dnancusumkbn2( N, 0.0, x, strideX, y, strideY );
+
+    // Print the result:
+    for ( int i = 0; i < 8; i++ ) {
+        printf( "y[ %d ] = %lf\n", i, y[ i ] );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<section class="references">
+
+## References
+
+-   Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x][@klein:2005a].
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+* * *
+
+## See Also
+
+-   <span class="package-name">[`@stdlib/blas/ext/base/dcusum`][@stdlib/blas/ext/base/dcusum]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of double-precision floating-point strided array elements.</span>
+-   <span class="package-name">[`@stdlib/blas/ext/base/gcusumkbn2`][@stdlib/blas/ext/base/gcusumkbn2]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.</span>
+-   <span class="package-name">[`@stdlib/blas/ext/base/scusumkbn2`][@stdlib/blas/ext/base/scusumkbn2]</span><span class="delimiter">: </span><span class="description">calculate the cumulative sum of single-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.</span>
+
+</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">
+
+[@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
+
+[@klein:2005a]: https://doi.org/10.1007/s00607-005-0139-x
+
+<!-- <related-links> -->
+
+[@stdlib/blas/ext/base/dcusum]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/ext/base/dcusum
+
+[@stdlib/blas/ext/base/gcusumkbn2]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/ext/base/gcusumkbn2
+
+[@stdlib/blas/ext/base/scusumkbn2]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/ext/base/scusumkbn2
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->