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Stdlib Authors","url":"https://github.com/stdlib-js/stdlib/graphs/contributors"},"license":"Apache-2.0","homepage":"https://stdlib.io","keywords":["stdlib","stdmath","statistics","stats","mathematics","math","blas","extended","sum","total","pairwise","pw","summation","strided","strided array","typed","array"],"repository":{"type":"git","url":"git://github.com/stdlib-js/blas-ext-base-gapxsumpw.git"},"description":"Add a scalar constant to each strided array element and compute the sum using pairwise summation.","contributors":[{"name":"The Stdlib Authors","url":"https://github.com/stdlib-js/stdlib/graphs/contributors"}],"maintainers":[{"name":"stdlib-bot","email":"kgryte+stdlibbot@gmail.com"},{"name":"kgryte","email":"kgryte@gmail.com"},{"name":"planeshifter","email":"pgb@andrew.cmu.edu"},{"name":"rreusser","email":"rsreusser@gmail.com"}],"readme":"<!--\n\n@license Apache-2.0\n\nCopyright (c) 2020 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n-->\n\n\n<details>\n  <summary>\n    About stdlib...\n  </summary>\n  <p>We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.</p>\n  <p>The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.</p>\n  <p>When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.</p>\n  <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href=\"https://github.com/stdlib-js/stdlib\">GitHub</a>, and please consider <a href=\"https://opencollective.com/stdlib\">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>\n</details>\n\n# gapxsumpw\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->\n\n> Add a scalar constant to each strided array element and compute the sum using pairwise summation.\n\n<section class=\"intro\">\n\n</section>\n\n<!-- /.intro -->\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/blas-ext-base-gapxsumpw\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar gapxsumpw = require( '@stdlib/blas-ext-base-gapxsumpw' );\n```\n\n#### gapxsumpw( N, alpha, x, strideX )\n\nAdds a scalar constant to each strided array element and computes the sum using pairwise summation.\n\n```javascript\nvar x = [ 1.0, -2.0, 2.0 ];\n\nvar v = gapxsumpw( x.length, 5.0, x, 1 );\n// returns 16.0\n```\n\nThe function has the following parameters:\n\n-   **N**: number of indexed elements.\n-   **alpha**: scalar constant.\n-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].\n-   **strideX**: stride length.\n\nThe `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to access every other element:\n\n```javascript\nvar x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];\n\nvar v = gapxsumpw( 4, 5.0, x, 2 );\n// returns 25.0\n```\n\nNote that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.\n\n<!-- eslint-disable stdlib/capitalized-comments -->\n\n```javascript\nvar Float64Array = require( '@stdlib/array-float64' );\n\nvar x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );\nvar x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element\n\nvar v = gapxsumpw( 4, 5.0, x1, 2 );\n// returns 25.0\n```\n\n#### gapxsumpw.ndarray( N, alpha, x, strideX, offsetX )\n\nAdds a scalar constant to each strided array element and computes the sum using pairwise summation and alternative indexing semantics.\n\n```javascript\nvar x = [ 1.0, -2.0, 2.0 ];\n\nvar v = gapxsumpw.ndarray( x.length, 5.0, x, 1, 0 );\n// returns 16.0\n```\n\nThe function has the following additional parameters:\n\n-   **offsetX**: starting index.\n\nWhile [`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 every other element starting from the second element:\n\n```javascript\nvar x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];\n\nvar v = gapxsumpw.ndarray( 4, 5.0, x, 2, 1 );\n// returns 25.0\n```\n\n</section>\n\n<!-- /.usage -->\n\n<section class=\"notes\">\n\n## Notes\n\n-   If `N <= 0`, both functions return `0.0`.\n-   In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., \"simple\" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.\n-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array-base/accessor`][@stdlib/array/base/accessor]).\n-   Depending on the environment, the typed versions ([`dapxsumpw`][@stdlib/blas/ext/base/dapxsumpw], [`sapxsumpw`][@stdlib/blas/ext/base/sapxsumpw], etc.) are likely to be significantly more performant.\n\n</section>\n\n<!-- /.notes -->\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\n\n```javascript\nvar discreteUniform = require( '@stdlib/random-array-discrete-uniform' );\nvar gapxsumpw = require( '@stdlib/blas-ext-base-gapxsumpw' );\n\nvar x = discreteUniform( 10, -100, 100, {\n    'dtype': 'float64'\n});\nconsole.log( x );\n\nvar v = gapxsumpw( x.length, 5.0, x, 1 );\nconsole.log( v );\n```\n\n</section>\n\n<!-- /.examples -->\n\n* * *\n\n<section class=\"references\">\n\n## References\n\n-   Higham, Nicholas J. 1993. \"The Accuracy of Floating Point Summation.\" _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a].\n\n</section>\n\n<!-- /.references -->\n\n<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->\n\n<section class=\"related\">\n\n* * *\n\n## See Also\n\n-   <span class=\"package-name\">[`@stdlib/blas-ext/base/dapxsumpw`][@stdlib/blas/ext/base/dapxsumpw]</span><span class=\"delimiter\">: </span><span class=\"description\">add a scalar constant to each double-precision floating-point strided array element and compute the sum using pairwise summation.</span>\n-   <span class=\"package-name\">[`@stdlib/blas-ext/base/gapxsum`][@stdlib/blas/ext/base/gapxsum]</span><span class=\"delimiter\">: </span><span class=\"description\">add a scalar constant to each strided array element and compute the sum.</span>\n-   <span class=\"package-name\">[`@stdlib/blas-ext/base/gsumpw`][@stdlib/blas/ext/base/gsumpw]</span><span class=\"delimiter\">: </span><span class=\"description\">calculate the sum of strided array elements using pairwise summation.</span>\n-   <span class=\"package-name\">[`@stdlib/blas-ext/base/sapxsumpw`][@stdlib/blas/ext/base/sapxsumpw]</span><span class=\"delimiter\">: </span><span class=\"description\">add a scalar constant to each single-precision floating-point strided array element and compute the sum using pairwise summation.</span>\n\n</section>\n\n<!-- /.related -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n\n<section class=\"main-repo\" >\n\n* * *\n\n## Notice\n\nThis package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.\n\nFor more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n</section>\n\n<!-- /.stdlib -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"links\">\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/blas-ext-base-gapxsumpw.svg\n[npm-url]: https://npmjs.org/package/@stdlib/blas-ext-base-gapxsumpw\n\n[test-image]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/actions/workflows/test.yml/badge.svg?branch=v0.3.1\n[test-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/actions/workflows/test.yml?query=branch:v0.3.1\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/blas-ext-base-gapxsumpw/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/blas-ext-base-gapxsumpw?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/blas-ext-base-gapxsumpw.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/blas-ext-base-gapxsumpw/main\n\n-->\n\n[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-url]: https://stdlib.zulipchat.com\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/tree/deno\n[deno-readme]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/tree/umd\n[umd-readme]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/tree/esm\n[esm-readme]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/blas-ext-base-gapxsumpw/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-ext-base-gapxsumpw/main/LICENSE\n\n[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array\n\n[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray\n\n[@stdlib/array/base/accessor]: https://www.npmjs.com/package/@stdlib/array-base-accessor\n\n[@higham:1993a]: https://doi.org/10.1137/0914050\n\n<!-- <related-links> -->\n\n[@stdlib/blas/ext/base/dapxsumpw]: https://www.npmjs.com/package/@stdlib/blas-ext-base-dapxsumpw\n\n[@stdlib/blas/ext/base/gapxsum]: https://www.npmjs.com/package/@stdlib/blas-ext-base-gapxsum\n\n[@stdlib/blas/ext/base/gsumpw]: https://www.npmjs.com/package/@stdlib/blas-ext-base-gsumpw\n\n[@stdlib/blas/ext/base/sapxsumpw]: https://www.npmjs.com/package/@stdlib/blas-ext-base-sapxsumpw\n\n<!-- </related-links> -->\n\n</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}