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feat: add stats/strided/meankbn
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‎lib/node_modules/@stdlib/stats/strided/meankbn/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2020 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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# meankbn
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> Calculate the [arithmetic mean][arithmetic-mean] of a strided array using an improved Kahan–Babuška algorithm.
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<section class="intro">
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The [arithmetic mean][arithmetic-mean] is defined as
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<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->
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```math
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\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
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```
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<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@a4861d8b5345a07f446bcfb2bb4bef1bc8346595/lib/node_modules/@stdlib/stats/strided/meankbn/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
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<br>
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</div> -->
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<!-- </equation> -->
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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 meankbn = require( '@stdlib/stats/strided/meankbn' );
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```
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#### meankbn( N, x, strideX )
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Computes the [arithmetic mean][arithmetic-mean] of a strided array using an improved Kahan–Babuška algorithm.
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```javascript
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var x = [ 1.0, -2.0, 2.0 ];
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var v = meankbn( x.length, x, 1 );
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// returns ~0.3333
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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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- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
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- **strideX**: stride length for `x`.
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The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [arithmetic mean][arithmetic-mean] of every other element in `x`,
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```javascript
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var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
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var v = meankbn( 4, x, 2 );
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// returns 1.25
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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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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var v = meankbn( 4, x1, 2 );
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// returns 1.25
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```
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#### meankbn.ndarray( N, x, strideX, offsetX )
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Computes the [arithmetic mean][arithmetic-mean] of a strided array using an improved Kahan–Babuška algorithm and alternative indexing semantics.
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```javascript
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var x = [ 1.0, -2.0, 2.0 ];
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var v = meankbn.ndarray( x.length, x, 1, 0 );
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// returns ~0.33333
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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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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 calculate the [arithmetic mean][arithmetic-mean] for every other element in `x` starting from the second element
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```javascript
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var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
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var v = meankbn.ndarray( 4, x, 2, 1 );
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// returns 1.25
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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 `NaN`.
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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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- Depending on the environment, the typed versions ([`dmeankbn`][@stdlib/stats/strided/dmeankbn], [`smeankbn`][@stdlib/stats/base/smeankbn], etc.) are likely to be significantly more performant.
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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 meankbn = require( '@stdlib/stats/strided/meankbn' );
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var x = discreteUniform( 10, -50, 50, {
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'dtype': 'float64'
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});
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console.log( x );
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var v = meankbn( x.length, x, 1 );
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console.log( v );
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```
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</section>
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<!-- /.examples -->
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* * *
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<section class="references">
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## References
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- Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106][@neumaier:1974a].
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</section>
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<!-- /.references -->
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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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* * *
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## See Also
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- <span class="package-name">[`@stdlib/stats/strided/dmeankbn`][@stdlib/stats/strided/dmeankbn]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a double-precision floating-point strided array using an improved Kahan–Babuška algorithm.</span>
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- <span class="package-name">[`@stdlib/stats/strided/mean`][@stdlib/stats/strided/mean]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a strided array.</span>
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- <span class="package-name">[`@stdlib/stats/base/smeankbn`][@stdlib/stats/base/smeankbn]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a single-precision floating-point strided array using an improved Kahan–Babuška algorithm.</span>
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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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[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
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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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[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106
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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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<!-- <related-links> -->
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[@stdlib/stats/strided/dmeankbn]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/strided/dmeankbn
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[@stdlib/stats/strided/mean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/strided/mean
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[@stdlib/stats/base/smeankbn]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/smeankbn
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/strided/meankbn/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) 2020 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 pkg = require( './../package.json' ).name;
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var meankbn = 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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* 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 x = uniform( len, -10, 10, options );
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return benchmark;
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function benchmark( b ) {
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var v;
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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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v = meankbn( x.length, x, 1 );
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if ( isnan( v ) ) {
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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( v ) ) {
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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( pkg+':len='+len, f );
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}
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}
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main();

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