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feat: add blas/ext/base/gdiff
PR-URL: #10903 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com> Closes: stdlib-js/metr-issue-tracker#191
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‎lib/node_modules/@stdlib/blas/ext/base/gdiff/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# gdiff
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> Calculate the k-th discrete forward difference of a strided array.
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<section class="usage">
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## Usage
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```javascript
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var gdiff = require( '@stdlib/blas/ext/base/gdiff' );
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```
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<!-- lint disable maximum-heading-length -->
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#### gdiff( N, k, x, strideX, N1, prepend, strideP, N2, append, strideA, out, strideOut, workspace, strideW )
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Calculates the k-th discrete forward difference of a strided array.
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```javascript
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var x = [ 2.0, 4.0, 6.0, 8.0, 10.0 ];
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var p = [ 1.0 ];
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var a = [ 11.0 ];
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var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
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var w = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
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gdiff( x.length, 1, x, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
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console.log( out );
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// => [ 1.0, 2.0, 2.0, 2.0, 2.0, 1.0 ]
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **k**: number of times to recursively compute differences.
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- **x**: input array.
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- **strideX**: stride length for `x`.
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- **N1**: number of indexed elements to `prepend`.
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- **prepend**: array containing values to prepend prior to computing differences.
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- **strideP**: stride length for `prepend`.
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- **N2**: number of indexed elements to `append`.
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- **append**: array containing values to append prior to computing differences.
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- **strideA**: stride length for `append`.
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- **out**: output array. Must have `N + N1 + N2 - k` elements.
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- **strideOut**: stride length for `out`.
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- **workspace**: workspace array. Must have `N + N1 + N2 - 1` elements.
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- **strideW**: stride length for `workspace`.
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The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute differences of every other element:
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```javascript
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var x = [ 2.0, 4.0, 6.0, 8.0, 10.0 ];
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var p = [ 1.0 ];
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var a = [ 11.0 ];
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var out = [ 0.0, 0.0, 0.0, 0.0 ];
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var w = [ 0.0, 0.0, 0.0, 0.0 ];
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gdiff( 3, 1, x, 2, 1, p, 1, 1, a, 1, out, 1, w, 1 );
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console.log( out );
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// => [ 1.0, 4.0, 4.0, 1.0 ]
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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// Initial array...
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var x0 = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
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// Create an offset view...
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var p = [ 1.0 ];
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var a = [ 11.0 ];
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var out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
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var w = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
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gdiff( x1.length, 1, x1, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
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console.log( out );
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// => [ 3.0, 2.0, 2.0, 2.0, 1.0 ]
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```
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<!-- lint disable maximum-heading-length -->
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#### gdiff.ndarray( N, k, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, out, strideOut, offsetOut, workspace, strideW, offsetW )
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Calculates the k-th discrete forward difference of a strided array using alternative indexing semantics.
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```javascript
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var x = [ 2.0, 4.0, 6.0, 8.0, 10.0 ];
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var p = [ 1.0 ];
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var a = [ 11.0 ];
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var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
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var w = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
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gdiff.ndarray( x.length, 1, x, 1, 0, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
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console.log( out );
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// => [ 1.0, 2.0, 2.0, 2.0, 2.0, 1.0 ]
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```
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The function has the following additional parameters:
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- **offsetX**: starting index for `x`.
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- **offsetP**: starting index for `prepend`.
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- **offsetA**: starting index for `append`.
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- **offsetOut**: starting index for `out`.
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- **offsetW**: starting index for `workspace`.
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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 access only the last three elements:
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```javascript
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var x = [ 2.0, 4.0, 6.0, 8.0, 10.0 ];
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var p = [ 1.0 ];
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var a = [ 11.0 ];
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var out = [ 0.0, 0.0, 0.0, 0.0 ];
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var w = [ 0.0, 0.0, 0.0, 0.0 ];
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gdiff.ndarray( 3, 1, x, 1, x.length-3, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
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console.log( out );
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// => [ 5.0, 2.0, 2.0, 1.0 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- When `k <= 1`, the workspace array is unused and thus ignored.
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- If `N + N1 + N2 <= 1` or `k >= N + N1 + N2`, both functions return the output array unchanged.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var zeros = require( '@stdlib/array/zeros' );
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var gdiff = require( '@stdlib/blas/ext/base/gdiff' );
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var x = discreteUniform( 10, -100, 100, {
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'dtype': 'generic'
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});
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console.log( 'Input array: ', x );
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var p = discreteUniform( 2, -100, 100, {
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'dtype': 'generic'
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});
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console.log( 'Prepend array: ', p );
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var a = discreteUniform( 2, -100, 100, {
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'dtype': 'generic'
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});
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console.log( 'Append array: ', a );
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var out = zeros( 10, 'generic' );
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var w = zeros( 13, 'generic' );
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gdiff( x.length, 4, x, 1, 2, p, 1, 2, a, 1, out, 1, w, 1 );
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console.log( 'Output: ', out );
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/ext/base/gdiff/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2026 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var zeros = require( '@stdlib/array/zeros' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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var gdiff = require( './../lib/gdiff.js' );
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// VARIABLES //
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var options = {
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'dtype': 'generic'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var ol;
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var N1;
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var N2;
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var x;
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var p;
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var a;
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var w;
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var o;
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var k;
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var N;
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N = len;
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N1 = 1;
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N2 = 1;
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k = 1;
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ol = N + N1 + N2 - k;
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x = uniform( N, -100, 100, options );
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p = uniform( N1, -100, 100, options );
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a = uniform( N2, -100, 100, options );
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w = zeros( N+N1+N2-1, options.dtype );
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o = zeros( ol, options.dtype );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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gdiff( N, k, x, 1, N1, p, 1, N2, a, 1, o, 1, w, 1 );
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if ( isnan( o[ i%ol ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( o[ i%ol ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( format( '%s:len=%d', pkg, len ), f );
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}
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}
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main();

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