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# dnannsumkbn2

> Calculate the 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 dnannsumkbn2 = require( '@stdlib/blas/ext/base/dnannsumkbn2' );
```

#### dnannsumkbn2( N, x, strideX, out, strideOut )

Computes the 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, 2.0 ] );
var out = new Float64Array( 2 );

var v = dnannsumkbn2( x.length, x, 1, out, 1 );
// returns <Float64Array>[ 1.0, 3 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Float64Array`][@stdlib/array/float64].
-   **strideX**: stride length for `x`.
-   **out**: output [`Float64Array`][@stdlib/array/float64] whose first element is the sum and whose second element is the number of non-NaN elements.
-   **strideOut**: stride length for `out`.

The `N` and stride parameters determine which elements are accessed at runtime. For example, to compute the sum of every other element:

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, 2.0, NaN, -7.0, NaN, 3.0, 4.0, 2.0 ] );
var out = new Float64Array( 2 );

var v = dnannsumkbn2( 4, x, 2, out, 1 );
// returns <Float64Array>[ 5.0, 2 ]
```

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, NaN, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var out0 = new Float64Array( 4 );
var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

var v = dnannsumkbn2( 4, x1, 2, out1, 1 );
// returns <Float64Array>[ 5.0, 4 ]
```

#### dnannsumkbn2.ndarray( N, x, strideX, offsetX, out, strideOut, offsetOut )

Computes the 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, 2.0 ] );
var out = new Float64Array( 2 );

var v = dnannsumkbn2.ndarray( x.length, x, 1, 0, out, 1, 0 );
// returns <Float64Array>[ 1.0, 3 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.
-   **offsetOut**: starting index for `out`.

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 sum of every other element starting from the second element:

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 2.0, 1.0, NaN, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var out = new Float64Array( 4 );

var v = dnannsumkbn2.ndarray( 4, x, 2, 1, out, 2, 1 );
// returns <Float64Array>[ 0.0, 5.0, 0.0, 4 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return a sum equal to `0.0`.

</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 dnannsumkbn2 = require( '@stdlib/blas/ext/base/dnannsumkbn2' );

function rand() {
    if ( bernoulli( 0.5 ) < 1 ) {
        return discreteUniform( 0, 100 );
    }
    return NaN;
}

var x = filledarrayBy( 10, 'float64', rand );
console.log( x );

var out = new Float64Array( 2 );
dnannsumkbn2( x.length, x, 1, out, 1 );
console.log( out );
```

</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/dnannsumkbn2.h"
```

#### stdlib_strided_dnannsumkbn2( N, \*X, strideX, \*n )

Computes the sum of double-precision floating-point strided array elements, ignoring `NaN` values and using a second-order iterative Kahan–Babuška algorithm.

```c
const double x[] = { 1.0, 2.0, 0.0/0.0, 4.0 };
CBLAS_INT n = 0;

double v = stdlib_strided_dnannsumkbn2( 4, x, 1, &n );
// returns 7.0
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] double*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length.
-   **n**: `[out] CBLAS_INT*` pointer for storing the number of non-NaN elements.

```c
double stdlib_strided_dnannsumkbn2( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, CBLAS_INT *n );
```

#### stdlib_strided_dnannsumkbn2_ndarray( N, \*X, strideX, offsetX, \*n )

Computes the 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, 0.0/0.0, 4.0 };
CBLAS_INT n = 0;

double v = stdlib_strided_dnannsumkbn2_ndarray( 4, x, 1, 0, &n );
// returns 7.0
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] double*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length.
-   **offsetX**: `[in] CBLAS_INT` starting index.
-   **n**: `[out] CBLAS_INT*` pointer for storing the number of non-NaN elements.

```c
double stdlib_strided_dnannsumkbn2_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, CBLAS_INT *n );
```

</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/dnannsumkbn2.h"
#include "stdlib/blas/base/shared.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 0.0/0.0, 0.0/0.0 };

    // Specify the number of elements:
    const int N = 5;

    // Specify the stride length:
    const int strideX = 2;

    // Initialize a variable for storing the number of non-NaN elements:
    CBLAS_INT n = 0;

    // Compute the sum:
    double v = stdlib_strided_dnannsumkbn2( N, x, strideX, &n );

    // Print the result:
    printf( "sum: %lf\n", v );
    printf( "n: %"CBLAS_IFMT"\n", n );
}
```

</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/dnannsum`][@stdlib/blas/ext/base/dnannsum]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements, ignoring NaN values.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/dnannsumkbn`][@stdlib/blas/ext/base/dnannsumkbn]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using an improved Kahan–Babuška algorithm.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/dnannsumors`][@stdlib/blas/ext/base/dnannsumors]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using ordinary recursive summation.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/dnannsumpw`][@stdlib/blas/ext/base/dnannsumpw]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/blas/ext/base/dsumkbn2`][@stdlib/blas/ext/base/dsumkbn2]</span><span class="delimiter">: </span><span class="description">calculate the sum of double-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://www.npmjs.com/package/@stdlib/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/dnannsum]: https://github.com/stdlib-js/blas/tree/main/ext/base/dnannsum

[@stdlib/blas/ext/base/dnannsumkbn]: https://github.com/stdlib-js/blas/tree/main/ext/base/dnannsumkbn

[@stdlib/blas/ext/base/dnannsumors]: https://github.com/stdlib-js/blas/tree/main/ext/base/dnannsumors

[@stdlib/blas/ext/base/dnannsumpw]: https://github.com/stdlib-js/blas/tree/main/ext/base/dnannsumpw

[@stdlib/blas/ext/base/dsumkbn2]: https://github.com/stdlib-js/blas/tree/main/ext/base/dsumkbn2

<!-- </related-links> -->

</section>

<!-- /.links -->
