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feat: add blas/ext/base/gaxpby
PR-URL: #12380 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com> Signed-off-by: Athan Reines <kgryte@gmail.com> Closes: stdlib-js/metr-issue-tracker#613
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‎lib/node_modules/@stdlib/blas/ext/base/gaxpby/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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# gaxpby
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> Multiply a strided array `x` by a constant and add the result to a strided array `y` multiplied by a constant.
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<section class="intro">
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This BLAS extension implements the operation
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<!-- <equation class="equation" label="eq:axpby" align="center" raw="\mathbf{y} = \alpha \mathbf{x} + \beta \mathbf{y}" alt="Equation for axpby operation."> -->
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```math
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\mathbf{y} = \alpha \mathbf{x} + \beta \mathbf{y}
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```
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<!-- </equation> -->
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This API is complementary to the package [`@stdlib/blas/base/gaxpy`][@stdlib/blas/base/gaxpy] and is a common BLAS extension in libraries such as Intel MKL, OpenBLAS, and others.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var gaxpby = require( '@stdlib/blas/ext/base/gaxpby' );
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```
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#### gaxpby( N, alpha, x, strideX, beta, y, strideY )
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Multiplies a strided array `x` by a constant and adds the result to a strided array `y` multiplied by a constant.
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```javascript
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var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
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var y = [ 2.0, 3.0, 4.0, 5.0, 6.0 ];
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gaxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
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// y => [ 9.0, 16.0, 23.0, 30.0, 37.0 ]
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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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- **alpha**: first scalar constant.
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- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
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- **strideX**: stride length for `x`.
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- **beta**: second scalar constant.
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- **y**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
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- **strideY**: stride length for `y`.
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The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to multiply every other element in `x` by `alpha` and add to every other element in `y` multiplied by `beta`:
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```javascript
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var x = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
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var y = [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ];
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gaxpby( 3, 5.0, x, 2, 2.0, y, 2 );
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// y => [ 19.0, 8.0, 33.0, 10.0, 47.0, 12.0 ]
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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 arrays...
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var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
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// Create offset views...
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element
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gaxpby( 3, 5.0, x1, 1, 2.0, y1, 1 );
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// y0 => <Float64Array>[ 7.0, 8.0, 28.0, 35.0, 42.0, 12.0 ]
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```
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#### gaxpby.ndarray( N, alpha, x, strideX, offsetX, beta, y, strideY, offsetY )
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Multiplies a strided array `x` by a constant and adds the result to a strided array `y` multiplied by a constant using alternative indexing semantics.
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```javascript
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var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
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var y = [ 2.0, 3.0, 4.0, 5.0, 6.0 ];
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gaxpby.ndarray( x.length, 5.0, x, 1, 0, 2.0, y, 1, 0 );
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// y => [ 9.0, 16.0, 23.0, 30.0, 37.0 ]
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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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- **offsetY**: starting index for `y`.
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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 multiply the last three elements of `x` by `alpha` and add to the last three elements of `y` multiplied by `beta`:
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```javascript
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var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
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var y = [ 6.0, 7.0, 8.0, 9.0, 10.0 ];
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gaxpby.ndarray( 3, 5.0, x, 1, x.length-3, 2.0, y, 1, y.length-3 );
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// y => [ 6.0, 7.0, 31.0, 38.0, 45.0 ]
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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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- If `N <= 0`, both functions return `y` unchanged.
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- 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]).
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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 gaxpby = require( '@stdlib/blas/ext/base/gaxpby' );
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var x = discreteUniform( 10, -100, 100, {
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'dtype': 'float64'
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});
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console.log( x );
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var y = discreteUniform( 10, -100, 100, {
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'dtype': 'float64'
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});
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console.log( y );
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gaxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
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console.log( y );
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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-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
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[@stdlib/blas/base/gaxpy]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/base/gaxpy
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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/gaxpby/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 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 gaxpby = require( './../lib/main.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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* Create 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 x = uniform( len, -100, 100, options );
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var y = uniform( len, -100, 100, options );
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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 z;
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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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z = gaxpby( x.length, 5.0, x, 1, 3.0, y, 1 );
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if ( isnan( z[ i%x.length ] ) ) {
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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( z[ i%x.length ] ) ) {
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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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