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commit 81949d38ad849a9c2af84ecea3cb65c54b6073b0
Author: buildbot <[email protected]>
AuthorDate: Fri Mar 13 00:51:12 2020 +0000

    Automatic Site Publish by Buildbot
---
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+<!DOCTYPE html>
+<!-- Start _layouts/doc_page.html-->
+<html lang="en">
+
+<head>
+<!-- Start _include/site_head.html -->
+<meta charset="UTF-8" />
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<meta name="description" content="">
+<meta name="author" content="datasketches">
+
+<title>DataSketches | </title>
+
+<link rel="shortcut icon" href="/img/favicon.png">
+
+<link rel="stylesheet" 
href="https://maxcdn.bootstrapcdn.com/font-awesome/4.1.0/css/font-awesome.min.css";>
+<link rel="stylesheet" 
href="https://maxcdn.bootstrapcdn.com/bootstrap/3.2.0/css/bootstrap.min.css";>
+
+<link 
href='https://fonts.googleapis.com/css?family=Open+Sans+Condensed:300,700,300italic|Open+Sans:300italic,400italic,600italic,400,300,600'
+  rel='stylesheet' type='text/css'>
+
+<link rel="stylesheet" href="/css/main.css">
+<link rel="stylesheet" href="/css/header.css">
+<link rel="stylesheet" href="/css/footer.css">
+<link rel="stylesheet" href="/css/syntax.css">
+<link rel="stylesheet" href="/css/docs.css">
+
+
+<script type="text/javascript" 
src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML-full";>
+</script>
+<script src="https://code.jquery.com/jquery.min.js";></script>
+<script 
src="https://maxcdn.bootstrapcdn.com/bootstrap/3.2.0/js/bootstrap.min.js";></script>
+<!-- End _include/site_head.html -->
+</head>
+
+<body>
+<!-- Start _include/nav_bar.html -->
+<div class="navbar navbar-inverse navbar-static-top ds-nav">
+  <div class="container">
+    <div class="navbar-header">
+      <button type="button" class="navbar-toggle" data-toggle="collapse" 
data-target=".navbar-collapse">
+        <span class="sr-only">Toggle navigation</span>
+        <span class="icon-bar"></span>
+        <span class="icon-bar"></span>
+        <span class="icon-bar"></span>
+      </button>
+      <a href="/" style="padding-top: 0px; padding-bottom: 0px;">
+        <span class="ds-small-h-logo"></span></a>
+    </div>
+    <div class="navbar-collapse collapse">
+      <ul class="nav navbar-nav navbar-right">
+        <li>
+          <a href="/docs/TheChallenge.html">
+            <span class="fa fa-info-circle"></span> OVERVIEW</a>
+        </li>
+        <li>
+          <a href="/docs/Community/Downloads.html">
+            <span class="fa fa-download"></span> DOWNLOAD</a>
+        </li>
+        <li>
+          <a href="/docs/Architecture/Components.html">
+            <span class="fa fa-github"></span> GITHUB</a>
+        </li>
+        <li>
+          <a href="/docs/Community/Research.html">
+            <span class="fa fa-paper-plane"></span> RESEARCH</a>
+        </li>
+        <li>
+          <a href="/docs/Community" style="padding-top: 0; padding-bottom: 0;">
+            <img class="ds-small-man" 
src="/img/datasketches-ManWhite.svg"/>COMMUNITY</a>
+        </li>
+        <li>
+          <ul class="nav navbar-nav navbar-right ds-nav">
+            <li class="dropdown ds-nav" >
+              <a href="#" class="dropdown-toggle" data-toggle="dropdown" 
role="button" aria-haspopup="true" aria-expanded="false" style="padding-top: 0; 
padding-bottom: 0;"><img class="apache-logo" src="/img/feather.svg"/>Apache 
<span class="caret"></span></a>
+              <ul class="dropdown-menu ds-nav">
+                <li><a href="https://www.apache.org/"; 
target="_blank">Foundation</a></li>
+                <li><a href="https://www.apache.org/events/current-event"; 
target="_blank">Events</a></li>
+                <li><a href="https://www.apache.org/licenses/"; 
target="_blank">License</a></li>
+                <li><a href="https://www.apache.org/foundation/thanks.html"; 
target="_blank">Thanks</a></li>
+                <li><a href="https://www.apache.org/security/"; 
target="_blank">Security</a></li>
+                <li><a 
href="https://www.apache.org/foundation/sponsorship.html"; 
target="_blank">Sponsorship</a></li>
+              </ul>
+            </li>
+          </ul>
+        </li>
+      </ul>
+    </div>
+  </div>
+</div>
+<!-- End _include/nav_bar.html -->
+
+<!-- Start _include/javadocs.html -->
+<div class="ds-header">
+  <div class="container">
+    <h4>API Snapshots:
+      <a href="/api/java/snapshot/apidocs/index.html">Java Core</a>,
+      <a href="/api/memory/snapshot/apidocs/index.html">Memory</a>,
+      <a href="/api/pig/snapshot/apidocs/index.html">Pig</a>,
+      <a href="/api/hive/snapshot/apidocs/index.html">Hive</a>,
+    </h4>
+  </div>
+</div>
+<!-- End _include/javadocs.html -->
+
+  <div class="container">
+    <div class="row">
+      <!-- Start ToC Block -->
+      <div class="col-md-3">
+        <div class="searchbox" style="position:relative">
+          <gcse:searchbox-only></gcse:searchbox-only>
+        </div>
+<!-- Start _includes/toc.html -->
+<!-- Computer Generated File, Do Not Edit! -->
+<link rel="stylesheet" href="/css/toc.css">
+<div id="toc" class="nav toc hidden-print">
+
+  <p id="overview">
+    <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_overview">Overview</a>
+  </p>
+  <div class="collapse" id="collapse_overview">
+    <li><a href="/docs/TheChallenge.html">The Challenge</a></li>
+    <li><a href="/docs/MajorSketchFamilies.html">The Major Sketch 
Families</a></li>
+    <li><a href="/docs/SketchOrigins.html">Sketch Origins</a></li>
+    <li><a href="/docs/SketchElements.html">Sketch Elements</a></li>
+    <li><a href="/docs/LargeScale.html">Large Scale Computing</a></li>
+    <li><a 
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/DataSketches_deck.pdf";>Overview
 Slide Deck</a></li>
+    <li><a href="/docs/WhoUses.html">Who Uses</a></li>
+  </div>
+
+  <p id="architecture-and-design">
+    <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_architecture_and_design">Architecture And Design</a>
+  </p>
+  <div class="collapse" id="collapse_architecture_and_design">
+    <li><a href="/docs/Architecture/KeyFeatures.html">Key Features</a></li>
+    <li><a href="/docs/Architecture/SketchFeaturesMatrix.html">Sketch Features 
Matrix</a></li>
+    <li><a href="/docs/Architecture/Components.html">Components</a></li>
+    <li><a href="/docs/Architecture/SketchesByComponent.html">Sketches by 
Component</a></li>
+    <li><a href="/docs/Architecture/SketchCriteria.html">Sketch 
Criteria</a></li>
+
+    <p id="memory-package">
+      <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_memory_package">Memory Package</a>
+    </p>
+    <div class="collapse" id="collapse_memory_package">
+      <li><a href="/docs/Memory/MemoryPackage.html">Memory Package</a></li>
+      <li><a href="/docs/Memory/MemoryPerformance.html">Memory Package 
Performance</a></li>
+    </div>
+    <li><a href="/docs/Architecture/OrderSensitivity.html">Notes on Order 
Sensitivity</a></li>
+    <li><a href="/docs/Architecture/Concurrency.html">Notes on 
Concurrency</a></li>
+  </div>
+
+  <p id="sketch-families">
+    <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_sketch_families">Sketch Families</a>
+  </p>
+  <div class="collapse" id="collapse_sketch_families">
+
+    <p id="distinct-counting">
+      <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_distinct_counting">Distinct Counting</a>
+    </p>
+    <div class="collapse" id="collapse_distinct_counting">
+      <li><a href="/docs/DistinctCountFeaturesMatrix.html">Features 
Matrix</a></li>
+      <li><a href="/docs/DistinctCountMeritComparisons.html">Figures-of-Merit 
Comparison</a></li>
+
+      <p id="hyperloglog-sketches">
+        <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_hyperloglog_sketches">HyperLogLog Sketches</a>
+      </p>
+      <div class="collapse" id="collapse_hyperloglog_sketches">
+        <li><a href="/docs/HLL/HLL.html">HLL Sketch</a></li>
+        <li><a href="/docs/HLL/HllMap.html">HLL Map Sketch</a></li>
+
+        <p id="hll-examples">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_hll_examples">HLL Examples</a>
+        </p>
+        <div class="collapse" id="collapse_hll_examples">
+          <li><a href="/docs/HLL/HllJavaExample.html">HLL Sketch Java 
Example</a></li>
+          <li><a href="/docs/HLL/HllPigUDFs.html">HLL Sketch Pig UDFs</a></li>
+          <li><a href="/docs/HLL/HllHiveUDFs.html">HLL Sketch Hive 
UDFs</a></li>
+          <li><a href="/docs/DruidIntegration.html">Using Sketches in 
Druid</a></li>
+        </div>
+
+        <p id="hll-studies">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_hll_studies">HLL Studies</a>
+        </p>
+        <div class="collapse" id="collapse_hll_studies">
+          <li><a href="/docs/HLL/Hll_vs_CS_Hllpp.html">HLL vs Clearspring 
HLL++</a></li>
+          <li><a 
href="/docs/HLL/HllSketchVsDruidHyperLogLogCollector.html">HLL Sketch vs Druid 
HyperLogLogCollector</a></li>
+        </div>
+      </div>
+
+      <p id="theta-sketches">
+        <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_theta_sketches">Theta Sketches</a>
+      </p>
+      <div class="collapse" id="collapse_theta_sketches">
+        <li><a href="/docs/Theta/ThetaSketchFramework.html">Theta Sketch 
Framework</a></li>
+
+        <p id="theta-examples">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_theta_examples">Theta Examples</a>
+        </p>
+        <div class="collapse" id="collapse_theta_examples">
+          <li><a href="/docs/Theta/ConcurrentThetaSketch.html">Concurrent 
Theta Sketch</a></li>
+          <li><a href="/docs/Theta/ThetaJavaExample.html">Theta Sketch Java 
Example</a></li>
+          <li><a href="/docs/Theta/ThetaSparkExample.html">Theta Sketch Spark 
Example</a></li>
+          <li><a href="/docs/Theta/ThetaPigUDFs.html">Theta Sketch Pig 
UDFs</a></li>
+          <li><a href="/docs/Theta/ThetaHiveUDFs.html">Theta Sketch Hive 
UDFs</a></li>
+          <li><a href="/docs/DruidIntegration.html">Using Sketches in 
Druid</a></li>
+        </div>
+
+        <p id="kmv-tutorial">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_kmv_tutorial">KMV Tutorial</a>
+        </p>
+        <div class="collapse" id="collapse_kmv_tutorial">
+          <li><a href="/docs/Theta/InverseEstimate.html">The Inverse 
Estimate</a></li>
+          <li><a href="/docs/Theta/KMVempty.html">Empty Sketch</a></li>
+          <li><a href="/docs/Theta/KMVfirstEst.html">First Estimator</a></li>
+          <li><a href="/docs/Theta/KMVbetterEst.html">Better Estimator</a></li>
+          <li><a href="/docs/Theta/KMVrejection.html">Rejection Rules</a></li>
+          <li><a href="/docs/Theta/KMVupdateVkth.html">Update V(kth) 
Rule</a></li>
+        </div>
+
+        <p id="set-operations-and-p-sampling">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_set_operations_and_p-sampling">Set Operations and P-sampling</a>
+        </p>
+        <div class="collapse" id="collapse_set_operations_and_p-sampling">
+          <li><a href="/docs/Theta/ThetaSketchSetOps.html">Set 
Operations</a></li>
+          <li><a 
href="/docs/Theta/ThetaPSampling.html"><i>p</i>-Sampling</a></li>
+        </div>
+
+        <p id="accuracy">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_accuracy">Accuracy</a>
+        </p>
+        <div class="collapse" id="collapse_accuracy">
+          <li><a href="/docs/Theta/ThetaAccuracy.html">Basic Accuracy</a></li>
+          <li><a href="/docs/Theta/ThetaAccuracyPlots.html">Accuracy 
Plots</a></li>
+          <li><a href="/docs/Theta/ThetaErrorTable.html">Relative Error 
Table</a></li>
+          <li><a href="/docs/Theta/ThetaSketchSetOpsAccuracy.html">SetOp 
Accuracy</a></li>
+          <li><a href="/docs/Theta/AccuracyOfDifferentKUnions.html">Unions 
With Different k</a></li>
+        </div>
+
+        <p id="size">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_size">Size</a>
+        </p>
+        <div class="collapse" id="collapse_size">
+          <li><a href="/docs/Theta/ThetaSize.html">Theta Sketch Size</a></li>
+        </div>
+
+        <p id="speed">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_speed">Speed</a>
+        </p>
+        <div class="collapse" id="collapse_speed">
+          <li><a href="/docs/Theta/ThetaUpdateSpeed.html">Update Speed</a></li>
+          <li><a href="/docs/Theta/ThetaMergeSpeed.html">Merge Speed</a></li>
+        </div>
+
+        <p id="theta-sketch-theory">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_theta_sketch_theory">Theta Sketch Theory</a>
+        </p>
+        <div class="collapse" id="collapse_theta_sketch_theory">
+          <li><a 
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/ThetaSketchFramework.pdf";>Theta
 Sketch Framework (PDF)</a></li>
+          <li><a 
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/SketchEquations.pdf";>Sketch
 Equations (PDF)</a></li>
+          <li><a 
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/DataSketches.pdf";>DataSketches
 (PDF)</a></li>
+          <li><a href="/docs/Theta/ThetaConfidenceIntervals.html">Confidence 
Intervals Notes</a></li>
+          <li><a href="/docs/Theta/ThetaMergingAlgorithm.html">Merging 
Algorithm Notes</a></li>
+          <li><a href="/docs/Theta/ThetaReferences.html">Theta 
References</a></li>
+        </div>
+      </div>
+
+      <p id="tuple-sketches">
+        <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_tuple_sketches">Tuple Sketches</a>
+      </p>
+      <div class="collapse" id="collapse_tuple_sketches">
+        <li><a href="/docs/Tuple/TupleOverview.html">Tuple Overview</a></li>
+
+        <p id="tuple-examples">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_tuple_examples">Tuple Examples</a>
+        </p>
+        <div class="collapse" id="collapse_tuple_examples">
+          <li><a href="/docs/Tuple/TupleJavaExample.html">Tuple Java 
Example</a></li>
+          <li><a href="/docs/Tuple/TupleEngagementExample.html">Tuple 
Engagement Example</a></li>
+          <li><a 
href="/docs/Frequency/FrequentDistinctTuplesSketch.html">Frequent Distinct 
Tuples Sketch</a></li>
+          <li><a href="/docs/Tuple/TuplePigUDFs.html">Tuple Pig UDFs</a></li>
+          <li><a href="/docs/Tuple/TupleHiveUDFs.html">Tuple Hive UDFs</a></li>
+          <li><a href="/docs/DruidIntegration.html">Using Sketches in 
Druid</a></li>
+        </div>
+      </div>
+    </div>
+
+    <p id="most-frequent">
+      <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_most_frequent">Most Frequent</a>
+    </p>
+    <div class="collapse" id="collapse_most_frequent">
+      <li><a href="/docs/Frequency/FrequencySketchesOverview.html">Frequency 
Sketches Overview</a></li>
+
+      <p id="frequent-item-sketches">
+        <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_frequent_item_sketches">Frequent Item Sketches</a>
+      </p>
+      <div class="collapse" id="collapse_frequent_item_sketches">
+        <li><a href="/docs/Frequency/FrequentItemsOverview.html">Frequent 
Items Overview</a></li>
+        <li><a href="/docs/Frequency/FrequentItemsErrorTable.html">Frequent 
Items Error Table</a></li>
+        <li><a href="/docs/Frequency/FrequentItemsReferences.html">Frequent 
Items References</a></li>
+
+        <p id="most-frequent-examples">
+          <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_most_frequent_examples">Most Frequent Examples</a>
+        </p>
+        <div class="collapse" id="collapse_most_frequent_examples">
+          <li><a href="/docs/Frequency/FrequentItemsJavaExample.html">Frequent 
Items Java Example</a></li>
+          <li><a href="/docs/Frequency/FrequentItemsPigUDFs.html">Frequent 
Items Pig UDFs</a></li>
+          <li><a href="/docs/Frequency/FrequentItemsHiveUDFs.html">Frequent 
Items Hive UDFs</a></li>
+          <li><a href="/docs/DruidIntegration.html">Using Sketches in 
Druid</a></li>
+        </div>
+      </div>
+
+      <p id="frequent-distinct-sketches">
+        <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_frequent_distinct_sketches">Frequent Distinct Sketches</a>
+      </p>
+      <div class="collapse" id="collapse_frequent_distinct_sketches">
+        <li><a 
href="/docs/Frequency/FrequentDistinctTuplesSketch.html">Frequent Distinct 
Tuples Sketch</a></li>
+      </div>
+    </div>
+
+    <p id="quantiles-and-histograms">
+      <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
+    </p>
+    <div class="collapse" id="collapse_quantiles_and_histograms">
+      <li><a href="/docs/Quantiles/QuantilesOverview.html">Quantiles 
Overview</a></li>
+      <li><a href="/docs/Quantiles/QuantilesAccuracy.html">Quantiles Accuracy 
and Size</a></li>
+
+      <p id="quantiles-examples">
+        <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_quantiles_examples">Quantiles Examples</a>
+      </p>
+      <div class="collapse" id="collapse_quantiles_examples">
+        <li><a href="/docs/Quantiles/QuantilesJavaExample.html">Quantiles 
Sketch Java Example</a></li>
+        <li><a href="/docs/Quantiles/QuantilesPigUDFs.html">Quantiles Sketch 
Pig UDFs</a></li>
+        <li><a href="/docs/Quantiles/QuantilesHiveUDFs.html">Quantiles Sketch 
Hive UDFs</a></li>
+        <li><a href="/docs/DruidIntegration.html">Using Sketches in 
Druid</a></li>
+      </div>
+
+      <p id="quantiles-studies">
+        <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_quantiles_studies">Quantiles Studies</a>
+      </p>
+      <div class="collapse" id="collapse_quantiles_studies">
+        <li><a href="/docs/Quantiles/KLLSketch.html">New KLL sketch and 
comparison with DoublesSketch</a></li>
+        <li><a href="/docs/Quantiles/KllSketchVsTDigest.html">KLL sketch vs 
t-digest</a></li>
+        <li><a href="/docs/Quantiles/DruidApproxHistogramStudy.html">Druid 
Approximate Histogram</a></li>
+        <li><a href="/docs/Quantiles/MomentsSketchStudy.html">Moments Sketch 
Study</a></li>
+        <li><a href="/docs/Quantiles/QuantilesStreamAStudy.html">Quantiles 
StreamA Study</a></li>
+      </div>
+
+      <p id="quantiles-sketch-theory">
+        <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_quantiles_sketch_theory">Quantiles Sketch Theory</a>
+      </p>
+      <div class="collapse" id="collapse_quantiles_sketch_theory">
+        <li><a 
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/Quantiles_KLL.pdf";>Optimal
 Quantile Approximation in Streams</a></li>
+        <li><a href="/docs/Quantiles/QuantilesReferences.html">Quantiles 
References</a></li>
+      </div>
+    </div>
+
+    <p id="sampling">
+      <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_sampling">Sampling</a>
+    </p>
+    <div class="collapse" id="collapse_sampling">
+      <li><a href="/docs/Sampling/ReservoirSampling.html">Reservoir 
Sampling</a></li>
+      <li><a href="/docs/Sampling/ReservoirSamplingPerformance.html">Reservoir 
Sampling Performance</a></li>
+      <li><a href="/docs/Sampling/VarOptSampling.html">VarOpt Sampling</a></li>
+
+      <p id="sampling-examples">
+        <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_sampling_examples">Sampling Examples</a>
+      </p>
+      <div class="collapse" id="collapse_sampling_examples">
+        <li><a href="/docs/Sampling/ReservoirSamplingJava.html">Reservoir 
Sampling Java Example</a></li>
+        <li><a href="/docs/Sampling/ReservoirSamplingPigUDFs.html">Reservoir 
Sampling Pig UDFs</a></li>
+        <li><a href="/docs/Sampling/VarOptSamplingJava.html">VarOpt Sampling 
Java Example</a></li>
+        <li><a href="/docs/Sampling/VarOptPigUDFs.html">VarOpt Sampling Pig 
UDFs</a></li>
+      </div>
+    </div>
+  </div>
+
+  <p id="community">
+    <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_community">Community</a>
+  </p>
+  <div class="collapse" id="collapse_community">
+    <li><a href="/docs/Community/index.html">Community</a></li>
+  </div>
+
+  <p id="research">
+    <a data-toggle="collapse" class="menu collapsed" 
href="#collapse_research">Research</a>
+  </p>
+  <div class="collapse" id="collapse_research">
+    <li><a href="/docs/Community/Research.html">Research</a></li>
+  </div>
+</div>
+<!-- End _includes/toc.html -->
+<!-- Start _includes/tocScript.html -->
+<script>
+  (function () {
+
+    var findLineItem = function (path) {
+      return document.querySelector(`[href="${path}"]`);
+    };
+
+    var highlighLineItem = function (element) {
+      element.classList.add('highlight');
+    };
+
+    var checkHasClass = function (element, className) {
+      return element.className.split(' ').find(function (item) { return item 
=== className || '' })
+    }
+
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+      var collapseMenus = [];
+      var elementPointer = element;
+      while (elementPointer !== document.body) {
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+<h1 id="hyper-log-log-sketch-c-example">Hyper Log Log Sketch C++ Example</h1>
+
+<div class="highlighter-rouge"><div class="highlight"><pre 
class="highlight"><code>#include &lt;iostream&gt;
+#include &lt;fstream&gt;
+
+#include &lt;hll.hpp&gt;
+
+//simplified file operations and no error handling for clarity
+int main(int argc, char **argv) {
+  const int lg_k = 11;
+  const auto type = datasketches::HLL_4; // this is the default, but explicit 
here for illustration
+
+  // this section generates two sketches with some overlap and serializes them 
into files
+  {
+    // 100000 distinct keys
+    datasketches::hll_sketch sketch1(lg_k, type); // type is optional, 
defaults to HLL_4
+    for (int key = 0; key &lt; 100000; key++) sketch1.update(key);
+    std::ofstream os1("hll_sketch1.bin");
+    sketch1.serialize_compact(os1);
+
+    // 100000 distinct keys
+    datasketches::hll_sketch sketch2(lg_k, type); // type is optional, 
defaults to HLL_4
+    for (int key = 50000; key &lt; 150000; key++) sketch2.update(key);
+    std::ofstream os2("hll_sketch2.bin");
+    sketch2.serialize_compact(os2);
+  }
+
+  // this section deserializes the sketches, produces union and prints the 
result
+  {
+    std::ifstream is1("hll_sketch1.bin");
+    datasketches::hll_sketch sketch1 = 
datasketches::hll_sketch::deserialize(is1);
+
+    std::ifstream is2("hll_sketch2.bin");
+    datasketches::hll_sketch sketch2 = 
datasketches::hll_sketch::deserialize(is2);
+
+    datasketches::hll_union u(lg_k);
+    u.update(sketch1);
+    u.update(sketch2);
+    datasketches::hll_sketch sketch = u.get_result(type); // type is optional, 
defaults to HLL_4
+
+    // debug summary of the union result sketch
+    sketch.to_string(std::cout);
+
+    std::cout &lt;&lt; "Distinct count estimate: " &lt;&lt; 
sketch.get_estimate() &lt;&lt; std::endl;
+    std::cout &lt;&lt; "Distinct count lower bound 95% confidence: " &lt;&lt; 
sketch.get_lower_bound(2) &lt;&lt; std::endl;
+    std::cout &lt;&lt; "Distinct count upper bound 95% confidence: " &lt;&lt; 
sketch.get_upper_bound(2) &lt;&lt; std::endl;
+  }
+
+  return 0;
+}
+
+### HLL SKETCH SUMMARY: 
+  Log Config K   : 11
+  Hll Target     : HLL_4
+  Current Mode   : HLL
+  LB             : 148634
+  Estimate       : 152041
+  UB             : 155614
+  OutOfOrder flag: true
+  CurMin         : 4
+  NumAtCurMin    : 21
+  HipAccum       : 147291
+  KxQ0           : 19.889
+  KxQ1           : 0
+Distinct count estimate: 152041
+Distinct count lower bound 95% confidence: 145234
+Distinct count upper bound 95% confidence: 159184
+</code></pre></div></div>
+
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+        <div>Copyright © 2019 <a href="https://www.apache.org";>Apache Software 
Foundation</a>, 
+          Licensed under the Apache License, Version 2.0. All Rights 
Reserved.<br/>
+          Apache DataSketches, Apache, the Apache feather logo, and the Apache 
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+          All other marks mentioned may be trademarks or registered trademarks 
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