feat: add blas/ext/base/ddiff

lib/node_modules/@stdlib/blas/ext/base/ddiff/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.
+
+-->
+
+# ddiff
+
+> Calculate the k-th discrete forward difference of a double-precision floating-point strided array.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var ddiff = require( '@stdlib/blas/ext/base/ddiff' );
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### ddiff( N, k, x, strideX, N1, prepend, strideP, N2, append, strideA, out, strideOut, workspace, strideW )
+
+Calculates the k-th discrete forward differences of a double-precision floating-point strided array.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
+var p = new Float64Array( [ 1.0 ] );
+var a = new Float64Array( [ 11.0 ] );
+var out = new Float64Array( 6 );
+var w = new Float64Array( 6 );
+
+ddiff( x.length, 1, x, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
+
+console.log( out );
+// out => <Float64Array>[ 1.0, 2.0, 2.0, 2.0, 2.0, 1.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **k**: number of times to recursively compute differences.
+-   **x**: input [`Float64Array`][@stdlib/array/float64].
+-   **strideX**: stride length for `x`.
+-   **N1**: number of elements to `prepend`.
+-   **prepend**: a [`Float64Array`][@stdlib/array/float64] containing values to prepend prior to computing differences.
+-   **strideP**: stride length for `prepend`.
+-   **N2**: number of elements to `append`.
+-   **append**: a [`Float64Array`][@stdlib/array/float64] containing values to append prior to computing differences..
+-   **strideA**: strides length for `append`.
+-   **out**: output [`Float64Array`][@stdlib/array/float64]. Must have `N + N1 + N2 - k` elements.
+-   **strideOut**: stride length for `out`.
+-   **workspace**: workspace [`Float64Array`][@stdlib/array/float64]. Must have `N + N1 + N2 - 1` elements.
+-   **strideW**: stride length for `workspace`.
+
+The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to differences of every other element:
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
+var p = new Float64Array( [ 1.0 ] );
+var a = new Float64Array( [ 11.0 ] );
+var out = new Float64Array( 4 );
+var w = new Float64Array( 4 );
+
+ddiff( 3, 1, x, 2, 1, p, 1, 1, a, 1, out, 1, w, 1 );
+
+console.log( out );
+// out => <Float64Array>[ 1.0, 4.0, 4.0, 1.0 ]
+```
+
+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 array...
+var x0 = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
+
+// Create an offset view...
+var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var p = new Float64Array( [ 1.0 ] );
+var a = new Float64Array( [ 11.0 ] );
+var out = new Float64Array( 5 );
+var w = new Float64Array( 5 );
+
+ddiff( x1.length, 1, x1, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
+
+console.log( out );
+// out => <Float64Array>[ 3.0, 2.0, 2.0, 2.0, 1.0 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### ddiff.ndarray( N, k, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, out, strideOut, offsetOut, workspace, strideW, offsetW )
+
+Calculates the k-th discrete forward differences of a double-precision floating-point strided array using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
+var p = new Float64Array( [ 1.0 ] );
+var a = new Float64Array( [ 11.0 ] );
+var out = new Float64Array( 6 );
+var w = new Float64Array( 6 );
+
+ddiff.ndarray( x.length, 1, x, 1, 0, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
+
+console.log( out );
+// out => <Float64Array>[ 1.0, 2.0, 2.0, 2.0, 2.0, 1.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index for `x`.
+-   **offsetP**: starting index for `prepend`.
+-   **offsetA**: starting index for `append`.
+-   **offsetOut**: starting index for `out`.
+-   **offsetW**: starting index of `workspace`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to access only the last three elements:
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
+var p = new Float64Array( [ 1.0 ] );
+var a = new Float64Array( [ 11.0 ] );
+var out = new Float64Array( 4 );
+var w = new Float64Array( 4 );
+
+ddiff.ndarray( 3, 1, x, 1, x.length-3, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
+
+console.log( out );
+// out => <Float64Array>[ 5.0, 2.0, 2.0, 1.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0`, both functions return `x` unchanged.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var Float64Array = require( '@stdlib/array/float64' );
+var ddiff = require( '@stdlib/blas/ext/base/ddiff' );
+
+var x = discreteUniform( 10, -100, 100, {
+    'dtype': 'float64'
+});
+console.log( 'Input array: ', x );
+
+var p = discreteUniform( 2, -100, 100, {
+    'dtype': 'float64'
+});
+console.log( 'Prepend array: ', p );
+
+var a = discreteUniform( 2, -100, 100, {
+    'dtype': 'float64'
+});
+console.log( 'Append array: ', a );
+
+var out = new Float64Array( 10 );
+
+var w = new Float64Array( 13 );
+
+ddiff( x.length, 4, x, 1, 2, p, 1, 2, a, 1, out, 1, w, 1 );
+console.log( 'Output', 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/ddiff.h"
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### stdlib_strided_ddiff( N, k, x, strideX, N1, prepend, strideP, N2, append, strideA, \*out, strideOut, workspace, strideW )
+
+Calculates the k-th discrete forward differences of a double-precision floating-point strided array.
+
+```c
+double x[] = { 2.0, 4.0, 6.0, 8.0, 10.0 };
+double p[] = { 1.0 };
+double a[] = { 11.0 };
+double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+double w[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+
+stdlib_strided_ddiff( 5, 1, x, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **k**: `[in] CBLAS_INT` number of times to recursively compute differences.
+-   **x**: `[in] double` input [`Float64Array`][@stdlib/array/float64].
+-   **strideX**: `[in] CBLAS_INT` stride length for `x`.
+-   **N1**: `[in] CBLAS_INT` number of elements in `prepend`.
+-   **prepend**: `[in] double` a [`Float64Array`][@stdlib/array/float64] containing values to prepend prior to computing differences.
+-   **strideP**: `[in] CBLAS_INT` stride length for `prepend`.
+-   **N2**: `[in] CBLAS_INT` number of elements in `append`.
+-   **append**: `[in] double` a [`Float64Array`][@stdlib/array/float64] containing values to append prior to computing differences..
+-   **strideA**: `[in] CBLAS_INT` strides length for `append`.
+-   **out**: `[in] double` output [`Float64Array`][@stdlib/array/float64]. Must have `N + N1 + N2 - k` elements.
+-   **strideOut**: `[in] CBLAS_INT` stride length for `out`.
+-   **workspace**: `[in] double` workspace [`Float64Array`][@stdlib/array/float64]. Must have `N + N1 + N2 - 1` elements.
+-   **strideW**: `[in] CBLAS_INT` stride length for `workspace`.
+
+```c
+void stdlib_strided_ddiff( const CBLAS_INT N, const CBLAS_INT k, const double *X, const CBLAS_INT strideX, const CBLAS_INT N1, const double *prepend,  const CBLAS_INT strideP,  const CBLAS_INT N2, const double *append, const CBLAS_INT strideA, double *out,  const CBLAS_INT strideOut, double *workspace,  const CBLAS_INT strideW );
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### stdlib_strided_ddiff_ndarray( N, k, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, \*out, strideOut, offsetOut, w, strideW, offsetW )
+
+Calculates the k-th discrete forward differences of a double-precision floating-point strided array using alternative indexing semantics.
+
+```c
+double x[] = { 2.0, 4.0, 6.0, 8.0, 10.0 };
+double p[] = { 1.0 };
+double a[] = { 11.0 };
+double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+double w[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+
+stdlib_strided_ddiff_ndarray( 5, 1, x, 1, 0, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **k**: `[in] CBLAS_INT` number of times to recursively compute differences.
+-   **x**: `[in] double` input [`Float64Array`][@stdlib/array/float64].
+-   **strideX**: `[in] CBLAS_INT` stride length for `x`.
+-   **offsetX**: `[in] CBLAS_INT` starting index for `x`.
+-   **N1**: `[in] CBLAS_INT` number of elements in `prepend`.
+-   **prepend**: `[in] double` a [`Float64Array`][@stdlib/array/float64] containing values to prepend prior to computing differences.
+-   **strideP**: `[in] CBLAS_INT` stride length for `prepend`.
+-   **offsetP**: `[in] CBLAS_INT` starting index for `prepend`.
+-   **N2**: `[in] CBLAS_INT` number of elements in `append`.
+-   **append**: `[in] double` a [`Float64Array`][@stdlib/array/float64] containing values to append prior to computing differences..
+-   **strideA**: `[in] CBLAS_INT` strides length for `append`.
+-   **offsetA**: `[in] CBLAS_INT` starting index for `append`.
+-   **out**: `[in] double` output [`Float64Array`][@stdlib/array/float64]. Must have `N + N1 + N2 - k` elements.
+-   **strideOut**: `[in] CBLAS_INT` stride length for `out`.
+-   **offsetOut**: `[in] CBLAS_INT` starting index for `out`.
+-   **workspace**: `[in] double` workspace [`Float64Array`][@stdlib/array/float64]. Must have `N + N1 + N2 - 1` elements.
+-   **strideW**: `[in] CBLAS_INT` stride length for `workspace`.
+-   **offsetW**: `[in] CBLAS_INT` starting index for `workspace`.
+
+```c
+void stdlib_strided_ddiff_ndarray( const CBLAS_INT N, const CBLAS_INT k, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const CBLAS_INT N1, const double *prepend,  const CBLAS_INT strideP, const CBLAS_INT offsetP,  const CBLAS_INT N2, const double *append, const CBLAS_INT strideA, const CBLAS_INT offsetA, double *out,  const CBLAS_INT strideOut, const CBLAS_INT offsetOut, double *workspace,  const CBLAS_INT strideW, const CBLAS_INT offsetW );
+```
+
+</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/ddiff.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 };
+
+    // Define prepend values:
+    const double p[] = { -1.0 };
+
+    // Define append values:
+    const double a[] = { 10.0 };
+
+    // Define output array:
+    double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+
+    // Define workspace:
+    double w[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+
+    // Compute forward differences:
+    stdlib_strided_ddiff( 8, 3, x, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
+
+    // Print the result:
+    for ( int i = 0; i < 7; i++ ) {
+        printf( "out[ %i ] = %lf\n", i, out[ 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">
+
+[@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
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->